1,1,149,0,0.227688," ","integrate(x^m*(B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{B c m^{2} x^{4} x^{m} + B b m^{2} x^{3} x^{m} + A c m^{2} x^{3} x^{m} + 5 \, B c m x^{4} x^{m} + A b m^{2} x^{2} x^{m} + 6 \, B b m x^{3} x^{m} + 6 \, A c m x^{3} x^{m} + 6 \, B c x^{4} x^{m} + 7 \, A b m x^{2} x^{m} + 8 \, B b x^{3} x^{m} + 8 \, A c x^{3} x^{m} + 12 \, A b x^{2} x^{m}}{m^{3} + 9 \, m^{2} + 26 \, m + 24}"," ",0,"(B*c*m^2*x^4*x^m + B*b*m^2*x^3*x^m + A*c*m^2*x^3*x^m + 5*B*c*m*x^4*x^m + A*b*m^2*x^2*x^m + 6*B*b*m*x^3*x^m + 6*A*c*m*x^3*x^m + 6*B*c*x^4*x^m + 7*A*b*m*x^2*x^m + 8*B*b*x^3*x^m + 8*A*c*x^3*x^m + 12*A*b*x^2*x^m)/(m^3 + 9*m^2 + 26*m + 24)","B",0
2,1,29,0,0.146311," ","integrate(x^3*(B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{7} \, B c x^{7} + \frac{1}{6} \, B b x^{6} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, A b x^{5}"," ",0,"1/7*B*c*x^7 + 1/6*B*b*x^6 + 1/6*A*c*x^6 + 1/5*A*b*x^5","A",0
3,1,29,0,0.146635," ","integrate(x^2*(B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{6} \, B c x^{6} + \frac{1}{5} \, B b x^{5} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, A b x^{4}"," ",0,"1/6*B*c*x^6 + 1/5*B*b*x^5 + 1/5*A*c*x^5 + 1/4*A*b*x^4","A",0
4,1,29,0,0.145789," ","integrate(x*(B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{5} \, B c x^{5} + \frac{1}{4} \, B b x^{4} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, A b x^{3}"," ",0,"1/5*B*c*x^5 + 1/4*B*b*x^4 + 1/4*A*c*x^4 + 1/3*A*b*x^3","A",0
5,1,29,0,0.144877," ","integrate((B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{4} \, B c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, A b x^{2}"," ",0,"1/4*B*c*x^4 + 1/3*B*b*x^3 + 1/3*A*c*x^3 + 1/2*A*b*x^2","A",0
6,1,26,0,0.146859," ","integrate((B*x+A)*(c*x^2+b*x)/x,x, algorithm=""giac"")","\frac{1}{3} \, B c x^{3} + \frac{1}{2} \, B b x^{2} + \frac{1}{2} \, A c x^{2} + A b x"," ",0,"1/3*B*c*x^3 + 1/2*B*b*x^2 + 1/2*A*c*x^2 + A*b*x","A",0
7,1,22,0,0.144845," ","integrate((B*x+A)*(c*x^2+b*x)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, B c x^{2} + B b x + A c x + A b \log\left({\left| x \right|}\right)"," ",0,"1/2*B*c*x^2 + B*b*x + A*c*x + A*b*log(abs(x))","A",0
8,1,23,0,0.147601," ","integrate((B*x+A)*(c*x^2+b*x)/x^3,x, algorithm=""giac"")","B c x + {\left(B b + A c\right)} \log\left({\left| x \right|}\right) - \frac{A b}{x}"," ",0,"B*c*x + (B*b + A*c)*log(abs(x)) - A*b/x","A",0
9,1,26,0,0.149792," ","integrate((B*x+A)*(c*x^2+b*x)/x^4,x, algorithm=""giac"")","B c \log\left({\left| x \right|}\right) - \frac{A b + 2 \, {\left(B b + A c\right)} x}{2 \, x^{2}}"," ",0,"B*c*log(abs(x)) - 1/2*(A*b + 2*(B*b + A*c)*x)/x^2","A",0
10,1,27,0,0.147885," ","integrate((B*x+A)*(c*x^2+b*x)/x^5,x, algorithm=""giac"")","-\frac{6 \, B c x^{2} + 3 \, B b x + 3 \, A c x + 2 \, A b}{6 \, x^{3}}"," ",0,"-1/6*(6*B*c*x^2 + 3*B*b*x + 3*A*c*x + 2*A*b)/x^3","A",0
11,1,27,0,0.151807," ","integrate((B*x+A)*(c*x^2+b*x)/x^6,x, algorithm=""giac"")","-\frac{6 \, B c x^{2} + 4 \, B b x + 4 \, A c x + 3 \, A b}{12 \, x^{4}}"," ",0,"-1/12*(6*B*c*x^2 + 4*B*b*x + 4*A*c*x + 3*A*b)/x^4","A",0
12,1,27,0,0.149119," ","integrate((B*x+A)*(c*x^2+b*x)/x^7,x, algorithm=""giac"")","-\frac{20 \, B c x^{2} + 15 \, B b x + 15 \, A c x + 12 \, A b}{60 \, x^{5}}"," ",0,"-1/60*(20*B*c*x^2 + 15*B*b*x + 15*A*c*x + 12*A*b)/x^5","A",0
13,1,27,0,0.145984," ","integrate((B*x+A)*(c*x^2+b*x)/x^8,x, algorithm=""giac"")","-\frac{15 \, B c x^{2} + 12 \, B b x + 12 \, A c x + 10 \, A b}{60 \, x^{6}}"," ",0,"-1/60*(15*B*c*x^2 + 12*B*b*x + 12*A*c*x + 10*A*b)/x^6","A",0
14,1,340,0,0.173297," ","integrate(x^m*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{B c^{2} m^{3} x^{6} x^{m} + 2 \, B b c m^{3} x^{5} x^{m} + A c^{2} m^{3} x^{5} x^{m} + 12 \, B c^{2} m^{2} x^{6} x^{m} + B b^{2} m^{3} x^{4} x^{m} + 2 \, A b c m^{3} x^{4} x^{m} + 26 \, B b c m^{2} x^{5} x^{m} + 13 \, A c^{2} m^{2} x^{5} x^{m} + 47 \, B c^{2} m x^{6} x^{m} + A b^{2} m^{3} x^{3} x^{m} + 14 \, B b^{2} m^{2} x^{4} x^{m} + 28 \, A b c m^{2} x^{4} x^{m} + 108 \, B b c m x^{5} x^{m} + 54 \, A c^{2} m x^{5} x^{m} + 60 \, B c^{2} x^{6} x^{m} + 15 \, A b^{2} m^{2} x^{3} x^{m} + 63 \, B b^{2} m x^{4} x^{m} + 126 \, A b c m x^{4} x^{m} + 144 \, B b c x^{5} x^{m} + 72 \, A c^{2} x^{5} x^{m} + 74 \, A b^{2} m x^{3} x^{m} + 90 \, B b^{2} x^{4} x^{m} + 180 \, A b c x^{4} x^{m} + 120 \, A b^{2} x^{3} x^{m}}{m^{4} + 18 \, m^{3} + 119 \, m^{2} + 342 \, m + 360}"," ",0,"(B*c^2*m^3*x^6*x^m + 2*B*b*c*m^3*x^5*x^m + A*c^2*m^3*x^5*x^m + 12*B*c^2*m^2*x^6*x^m + B*b^2*m^3*x^4*x^m + 2*A*b*c*m^3*x^4*x^m + 26*B*b*c*m^2*x^5*x^m + 13*A*c^2*m^2*x^5*x^m + 47*B*c^2*m*x^6*x^m + A*b^2*m^3*x^3*x^m + 14*B*b^2*m^2*x^4*x^m + 28*A*b*c*m^2*x^4*x^m + 108*B*b*c*m*x^5*x^m + 54*A*c^2*m*x^5*x^m + 60*B*c^2*x^6*x^m + 15*A*b^2*m^2*x^3*x^m + 63*B*b^2*m*x^4*x^m + 126*A*b*c*m*x^4*x^m + 144*B*b*c*x^5*x^m + 72*A*c^2*x^5*x^m + 74*A*b^2*m*x^3*x^m + 90*B*b^2*x^4*x^m + 180*A*b*c*x^4*x^m + 120*A*b^2*x^3*x^m)/(m^4 + 18*m^3 + 119*m^2 + 342*m + 360)","B",0
15,1,53,0,0.169614," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{9} \, B c^{2} x^{9} + \frac{1}{4} \, B b c x^{8} + \frac{1}{8} \, A c^{2} x^{8} + \frac{1}{7} \, B b^{2} x^{7} + \frac{2}{7} \, A b c x^{7} + \frac{1}{6} \, A b^{2} x^{6}"," ",0,"1/9*B*c^2*x^9 + 1/4*B*b*c*x^8 + 1/8*A*c^2*x^8 + 1/7*B*b^2*x^7 + 2/7*A*b*c*x^7 + 1/6*A*b^2*x^6","A",0
16,1,53,0,0.170319," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{8} \, B c^{2} x^{8} + \frac{2}{7} \, B b c x^{7} + \frac{1}{7} \, A c^{2} x^{7} + \frac{1}{6} \, B b^{2} x^{6} + \frac{1}{3} \, A b c x^{6} + \frac{1}{5} \, A b^{2} x^{5}"," ",0,"1/8*B*c^2*x^8 + 2/7*B*b*c*x^7 + 1/7*A*c^2*x^7 + 1/6*B*b^2*x^6 + 1/3*A*b*c*x^6 + 1/5*A*b^2*x^5","A",0
17,1,53,0,0.160625," ","integrate(x*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{7} \, B c^{2} x^{7} + \frac{1}{3} \, B b c x^{6} + \frac{1}{6} \, A c^{2} x^{6} + \frac{1}{5} \, B b^{2} x^{5} + \frac{2}{5} \, A b c x^{5} + \frac{1}{4} \, A b^{2} x^{4}"," ",0,"1/7*B*c^2*x^7 + 1/3*B*b*c*x^6 + 1/6*A*c^2*x^6 + 1/5*B*b^2*x^5 + 2/5*A*b*c*x^5 + 1/4*A*b^2*x^4","A",0
18,1,53,0,0.147231," ","integrate((B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{2} x^{6} + \frac{2}{5} \, B b c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{4} \, B b^{2} x^{4} + \frac{1}{2} \, A b c x^{4} + \frac{1}{3} \, A b^{2} x^{3}"," ",0,"1/6*B*c^2*x^6 + 2/5*B*b*c*x^5 + 1/5*A*c^2*x^5 + 1/4*B*b^2*x^4 + 1/2*A*b*c*x^4 + 1/3*A*b^2*x^3","A",0
19,1,53,0,0.178211," ","integrate((B*x+A)*(c*x^2+b*x)^2/x,x, algorithm=""giac"")","\frac{1}{5} \, B c^{2} x^{5} + \frac{1}{2} \, B b c x^{4} + \frac{1}{4} \, A c^{2} x^{4} + \frac{1}{3} \, B b^{2} x^{3} + \frac{2}{3} \, A b c x^{3} + \frac{1}{2} \, A b^{2} x^{2}"," ",0,"1/5*B*c^2*x^5 + 1/2*B*b*c*x^4 + 1/4*A*c^2*x^4 + 1/3*B*b^2*x^3 + 2/3*A*b*c*x^3 + 1/2*A*b^2*x^2","A",0
20,1,49,0,0.149774," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^2,x, algorithm=""giac"")","\frac{1}{4} \, B c^{2} x^{4} + \frac{2}{3} \, B b c x^{3} + \frac{1}{3} \, A c^{2} x^{3} + \frac{1}{2} \, B b^{2} x^{2} + A b c x^{2} + A b^{2} x"," ",0,"1/4*B*c^2*x^4 + 2/3*B*b*c*x^3 + 1/3*A*c^2*x^3 + 1/2*B*b^2*x^2 + A*b*c*x^2 + A*b^2*x","A",0
21,1,46,0,0.149861," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^3,x, algorithm=""giac"")","\frac{1}{3} \, B c^{2} x^{3} + B b c x^{2} + \frac{1}{2} \, A c^{2} x^{2} + B b^{2} x + 2 \, A b c x + A b^{2} \log\left({\left| x \right|}\right)"," ",0,"1/3*B*c^2*x^3 + B*b*c*x^2 + 1/2*A*c^2*x^2 + B*b^2*x + 2*A*b*c*x + A*b^2*log(abs(x))","A",0
22,1,46,0,0.161012," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^4,x, algorithm=""giac"")","\frac{1}{2} \, B c^{2} x^{2} + 2 \, B b c x + A c^{2} x - \frac{A b^{2}}{x} + {\left(B b^{2} + 2 \, A b c\right)} \log\left({\left| x \right|}\right)"," ",0,"1/2*B*c^2*x^2 + 2*B*b*c*x + A*c^2*x - A*b^2/x + (B*b^2 + 2*A*b*c)*log(abs(x))","A",0
23,1,47,0,0.159239," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^5,x, algorithm=""giac"")","B c^{2} x + {\left(2 \, B b c + A c^{2}\right)} \log\left({\left| x \right|}\right) - \frac{A b^{2} + 2 \, {\left(B b^{2} + 2 \, A b c\right)} x}{2 \, x^{2}}"," ",0,"B*c^2*x + (2*B*b*c + A*c^2)*log(abs(x)) - 1/2*(A*b^2 + 2*(B*b^2 + 2*A*b*c)*x)/x^2","A",0
24,1,51,0,0.165183," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^6,x, algorithm=""giac"")","B c^{2} \log\left({\left| x \right|}\right) - \frac{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,"B*c^2*log(abs(x)) - 1/6*(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
25,1,51,0,0.149181," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^7,x, algorithm=""giac"")","-\frac{12 \, B c^{2} x^{3} + 12 \, B b c x^{2} + 6 \, A c^{2} x^{2} + 4 \, B b^{2} x + 8 \, A b c x + 3 \, A b^{2}}{12 \, x^{4}}"," ",0,"-1/12*(12*B*c^2*x^3 + 12*B*b*c*x^2 + 6*A*c^2*x^2 + 4*B*b^2*x + 8*A*b*c*x + 3*A*b^2)/x^4","A",0
26,1,51,0,0.164101," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^8,x, algorithm=""giac"")","-\frac{30 \, B c^{2} x^{3} + 40 \, B b c x^{2} + 20 \, A c^{2} x^{2} + 15 \, B b^{2} x + 30 \, A b c x + 12 \, A b^{2}}{60 \, x^{5}}"," ",0,"-1/60*(30*B*c^2*x^3 + 40*B*b*c*x^2 + 20*A*c^2*x^2 + 15*B*b^2*x + 30*A*b*c*x + 12*A*b^2)/x^5","A",0
27,1,603,0,0.254552," ","integrate(x^m*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{B c^{3} m^{4} x^{8} x^{m} + 3 \, B b c^{2} m^{4} x^{7} x^{m} + A c^{3} m^{4} x^{7} x^{m} + 22 \, B c^{3} m^{3} x^{8} x^{m} + 3 \, B b^{2} c m^{4} x^{6} x^{m} + 3 \, A b c^{2} m^{4} x^{6} x^{m} + 69 \, B b c^{2} m^{3} x^{7} x^{m} + 23 \, A c^{3} m^{3} x^{7} x^{m} + 179 \, B c^{3} m^{2} x^{8} x^{m} + B b^{3} m^{4} x^{5} x^{m} + 3 \, A b^{2} c m^{4} x^{5} x^{m} + 72 \, B b^{2} c m^{3} x^{6} x^{m} + 72 \, A b c^{2} m^{3} x^{6} x^{m} + 582 \, B b c^{2} m^{2} x^{7} x^{m} + 194 \, A c^{3} m^{2} x^{7} x^{m} + 638 \, B c^{3} m x^{8} x^{m} + A b^{3} m^{4} x^{4} x^{m} + 25 \, B b^{3} m^{3} x^{5} x^{m} + 75 \, A b^{2} c m^{3} x^{5} x^{m} + 633 \, B b^{2} c m^{2} x^{6} x^{m} + 633 \, A b c^{2} m^{2} x^{6} x^{m} + 2136 \, B b c^{2} m x^{7} x^{m} + 712 \, A c^{3} m x^{7} x^{m} + 840 \, B c^{3} x^{8} x^{m} + 26 \, A b^{3} m^{3} x^{4} x^{m} + 230 \, B b^{3} m^{2} x^{5} x^{m} + 690 \, A b^{2} c m^{2} x^{5} x^{m} + 2412 \, B b^{2} c m x^{6} x^{m} + 2412 \, A b c^{2} m x^{6} x^{m} + 2880 \, B b c^{2} x^{7} x^{m} + 960 \, A c^{3} x^{7} x^{m} + 251 \, A b^{3} m^{2} x^{4} x^{m} + 920 \, B b^{3} m x^{5} x^{m} + 2760 \, A b^{2} c m x^{5} x^{m} + 3360 \, B b^{2} c x^{6} x^{m} + 3360 \, A b c^{2} x^{6} x^{m} + 1066 \, A b^{3} m x^{4} x^{m} + 1344 \, B b^{3} x^{5} x^{m} + 4032 \, A b^{2} c x^{5} x^{m} + 1680 \, A b^{3} x^{4} x^{m}}{m^{5} + 30 \, m^{4} + 355 \, m^{3} + 2070 \, m^{2} + 5944 \, m + 6720}"," ",0,"(B*c^3*m^4*x^8*x^m + 3*B*b*c^2*m^4*x^7*x^m + A*c^3*m^4*x^7*x^m + 22*B*c^3*m^3*x^8*x^m + 3*B*b^2*c*m^4*x^6*x^m + 3*A*b*c^2*m^4*x^6*x^m + 69*B*b*c^2*m^3*x^7*x^m + 23*A*c^3*m^3*x^7*x^m + 179*B*c^3*m^2*x^8*x^m + B*b^3*m^4*x^5*x^m + 3*A*b^2*c*m^4*x^5*x^m + 72*B*b^2*c*m^3*x^6*x^m + 72*A*b*c^2*m^3*x^6*x^m + 582*B*b*c^2*m^2*x^7*x^m + 194*A*c^3*m^2*x^7*x^m + 638*B*c^3*m*x^8*x^m + A*b^3*m^4*x^4*x^m + 25*B*b^3*m^3*x^5*x^m + 75*A*b^2*c*m^3*x^5*x^m + 633*B*b^2*c*m^2*x^6*x^m + 633*A*b*c^2*m^2*x^6*x^m + 2136*B*b*c^2*m*x^7*x^m + 712*A*c^3*m*x^7*x^m + 840*B*c^3*x^8*x^m + 26*A*b^3*m^3*x^4*x^m + 230*B*b^3*m^2*x^5*x^m + 690*A*b^2*c*m^2*x^5*x^m + 2412*B*b^2*c*m*x^6*x^m + 2412*A*b*c^2*m*x^6*x^m + 2880*B*b*c^2*x^7*x^m + 960*A*c^3*x^7*x^m + 251*A*b^3*m^2*x^4*x^m + 920*B*b^3*m*x^5*x^m + 2760*A*b^2*c*m*x^5*x^m + 3360*B*b^2*c*x^6*x^m + 3360*A*b*c^2*x^6*x^m + 1066*A*b^3*m*x^4*x^m + 1344*B*b^3*x^5*x^m + 4032*A*b^2*c*x^5*x^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
28,1,77,0,0.154944," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{11} \, B c^{3} x^{11} + \frac{3}{10} \, B b c^{2} x^{10} + \frac{1}{10} \, A c^{3} x^{10} + \frac{1}{3} \, B b^{2} c x^{9} + \frac{1}{3} \, A b c^{2} x^{9} + \frac{1}{8} \, B b^{3} x^{8} + \frac{3}{8} \, A b^{2} c x^{8} + \frac{1}{7} \, A b^{3} x^{7}"," ",0,"1/11*B*c^3*x^11 + 3/10*B*b*c^2*x^10 + 1/10*A*c^3*x^10 + 1/3*B*b^2*c*x^9 + 1/3*A*b*c^2*x^9 + 1/8*B*b^3*x^8 + 3/8*A*b^2*c*x^8 + 1/7*A*b^3*x^7","A",0
29,1,77,0,0.179217," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{10} \, B c^{3} x^{10} + \frac{1}{3} \, B b c^{2} x^{9} + \frac{1}{9} \, A c^{3} x^{9} + \frac{3}{8} \, B b^{2} c x^{8} + \frac{3}{8} \, A b c^{2} x^{8} + \frac{1}{7} \, B b^{3} x^{7} + \frac{3}{7} \, A b^{2} c x^{7} + \frac{1}{6} \, A b^{3} x^{6}"," ",0,"1/10*B*c^3*x^10 + 1/3*B*b*c^2*x^9 + 1/9*A*c^3*x^9 + 3/8*B*b^2*c*x^8 + 3/8*A*b*c^2*x^8 + 1/7*B*b^3*x^7 + 3/7*A*b^2*c*x^7 + 1/6*A*b^3*x^6","A",0
30,1,77,0,0.156051," ","integrate(x*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{9} \, B c^{3} x^{9} + \frac{3}{8} \, B b c^{2} x^{8} + \frac{1}{8} \, A c^{3} x^{8} + \frac{3}{7} \, B b^{2} c x^{7} + \frac{3}{7} \, A b c^{2} x^{7} + \frac{1}{6} \, B b^{3} x^{6} + \frac{1}{2} \, A b^{2} c x^{6} + \frac{1}{5} \, A b^{3} x^{5}"," ",0,"1/9*B*c^3*x^9 + 3/8*B*b*c^2*x^8 + 1/8*A*c^3*x^8 + 3/7*B*b^2*c*x^7 + 3/7*A*b*c^2*x^7 + 1/6*B*b^3*x^6 + 1/2*A*b^2*c*x^6 + 1/5*A*b^3*x^5","A",0
31,1,77,0,0.150418," ","integrate((B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{8} \, B c^{3} x^{8} + \frac{3}{7} \, B b c^{2} x^{7} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{2} \, B b^{2} c x^{6} + \frac{1}{2} \, A b c^{2} x^{6} + \frac{1}{5} \, B b^{3} x^{5} + \frac{3}{5} \, A b^{2} c x^{5} + \frac{1}{4} \, A b^{3} x^{4}"," ",0,"1/8*B*c^3*x^8 + 3/7*B*b*c^2*x^7 + 1/7*A*c^3*x^7 + 1/2*B*b^2*c*x^6 + 1/2*A*b*c^2*x^6 + 1/5*B*b^3*x^5 + 3/5*A*b^2*c*x^5 + 1/4*A*b^3*x^4","A",0
32,1,77,0,0.149905," ","integrate((B*x+A)*(c*x^2+b*x)^3/x,x, algorithm=""giac"")","\frac{1}{7} \, B c^{3} x^{7} + \frac{1}{2} \, B b c^{2} x^{6} + \frac{1}{6} \, A c^{3} x^{6} + \frac{3}{5} \, B b^{2} c x^{5} + \frac{3}{5} \, A b c^{2} x^{5} + \frac{1}{4} \, B b^{3} x^{4} + \frac{3}{4} \, A b^{2} c x^{4} + \frac{1}{3} \, A b^{3} x^{3}"," ",0,"1/7*B*c^3*x^7 + 1/2*B*b*c^2*x^6 + 1/6*A*c^3*x^6 + 3/5*B*b^2*c*x^5 + 3/5*A*b*c^2*x^5 + 1/4*B*b^3*x^4 + 3/4*A*b^2*c*x^4 + 1/3*A*b^3*x^3","A",0
33,1,76,0,0.146624," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{3} x^{6} + \frac{3}{5} \, B b c^{2} x^{5} + \frac{1}{5} \, A c^{3} x^{5} + \frac{3}{4} \, B b^{2} c x^{4} + \frac{3}{4} \, A b c^{2} x^{4} + \frac{1}{3} \, B b^{3} x^{3} + A b^{2} c x^{3} + \frac{1}{2} \, A b^{3} x^{2}"," ",0,"1/6*B*c^3*x^6 + 3/5*B*b*c^2*x^5 + 1/5*A*c^3*x^5 + 3/4*B*b^2*c*x^4 + 3/4*A*b*c^2*x^4 + 1/3*B*b^3*x^3 + A*b^2*c*x^3 + 1/2*A*b^3*x^2","A",0
34,1,72,0,0.156300," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^3,x, algorithm=""giac"")","\frac{1}{5} \, B c^{3} x^{5} + \frac{3}{4} \, B b c^{2} x^{4} + \frac{1}{4} \, A c^{3} x^{4} + B b^{2} c x^{3} + A b c^{2} x^{3} + \frac{1}{2} \, B b^{3} x^{2} + \frac{3}{2} \, A b^{2} c x^{2} + A b^{3} x"," ",0,"1/5*B*c^3*x^5 + 3/4*B*b*c^2*x^4 + 1/4*A*c^3*x^4 + B*b^2*c*x^3 + A*b*c^2*x^3 + 1/2*B*b^3*x^2 + 3/2*A*b^2*c*x^2 + A*b^3*x","B",0
35,1,70,0,0.148570," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^4,x, algorithm=""giac"")","\frac{1}{4} \, B c^{3} x^{4} + B b c^{2} x^{3} + \frac{1}{3} \, A c^{3} x^{3} + \frac{3}{2} \, B b^{2} c x^{2} + \frac{3}{2} \, A b c^{2} x^{2} + B b^{3} x + 3 \, A b^{2} c x + A b^{3} \log\left({\left| x \right|}\right)"," ",0,"1/4*B*c^3*x^4 + B*b*c^2*x^3 + 1/3*A*c^3*x^3 + 3/2*B*b^2*c*x^2 + 3/2*A*b*c^2*x^2 + B*b^3*x + 3*A*b^2*c*x + A*b^3*log(abs(x))","A",0
36,1,71,0,0.181194," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^5,x, algorithm=""giac"")","\frac{1}{3} \, B c^{3} x^{3} + \frac{3}{2} \, B b c^{2} x^{2} + \frac{1}{2} \, A c^{3} x^{2} + 3 \, B b^{2} c x + 3 \, A b c^{2} x - \frac{A b^{3}}{x} + {\left(B b^{3} + 3 \, A b^{2} c\right)} \log\left({\left| x \right|}\right)"," ",0,"1/3*B*c^3*x^3 + 3/2*B*b*c^2*x^2 + 1/2*A*c^3*x^2 + 3*B*b^2*c*x + 3*A*b*c^2*x - A*b^3/x + (B*b^3 + 3*A*b^2*c)*log(abs(x))","A",0
37,1,69,0,0.150854," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^6,x, algorithm=""giac"")","\frac{1}{2} \, B c^{3} x^{2} + 3 \, B b c^{2} x + A c^{3} x + 3 \, {\left(B b^{2} c + A b c^{2}\right)} \log\left({\left| x \right|}\right) - \frac{A b^{3} + 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x}{2 \, x^{2}}"," ",0,"1/2*B*c^3*x^2 + 3*B*b*c^2*x + A*c^3*x + 3*(B*b^2*c + A*b*c^2)*log(abs(x)) - 1/2*(A*b^3 + 2*(B*b^3 + 3*A*b^2*c)*x)/x^2","A",0
38,1,70,0,0.150533," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^7,x, algorithm=""giac"")","B c^{3} x + {\left(3 \, B b c^{2} + A c^{3}\right)} \log\left({\left| x \right|}\right) - \frac{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,"B*c^3*x + (3*B*b*c^2 + A*c^3)*log(abs(x)) - 1/6*(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
39,1,73,0,0.180513," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^8,x, algorithm=""giac"")","B c^{3} \log\left({\left| x \right|}\right) - \frac{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,"B*c^3*log(abs(x)) - 1/12*(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
40,1,75,0,0.150311," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^9,x, algorithm=""giac"")","-\frac{20 \, B c^{3} x^{4} + 30 \, B b c^{2} x^{3} + 10 \, A c^{3} x^{3} + 20 \, B b^{2} c x^{2} + 20 \, A b c^{2} x^{2} + 5 \, B b^{3} x + 15 \, A b^{2} c x + 4 \, A b^{3}}{20 \, x^{5}}"," ",0,"-1/20*(20*B*c^3*x^4 + 30*B*b*c^2*x^3 + 10*A*c^3*x^3 + 20*B*b^2*c*x^2 + 20*A*b*c^2*x^2 + 5*B*b^3*x + 15*A*b^2*c*x + 4*A*b^3)/x^5","A",0
41,1,75,0,0.175124," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^10,x, algorithm=""giac"")","-\frac{30 \, B c^{3} x^{4} + 60 \, B b c^{2} x^{3} + 20 \, A c^{3} x^{3} + 45 \, B b^{2} c x^{2} + 45 \, A b c^{2} x^{2} + 12 \, B b^{3} x + 36 \, A b^{2} c x + 10 \, A b^{3}}{60 \, x^{6}}"," ",0,"-1/60*(30*B*c^3*x^4 + 60*B*b*c^2*x^3 + 20*A*c^3*x^3 + 45*B*b^2*c*x^2 + 45*A*b*c^2*x^2 + 12*B*b^3*x + 36*A*b^2*c*x + 10*A*b^3)/x^6","A",0
42,1,75,0,0.164644," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^11,x, algorithm=""giac"")","-\frac{140 \, B c^{3} x^{4} + 315 \, B b c^{2} x^{3} + 105 \, A c^{3} x^{3} + 252 \, B b^{2} c x^{2} + 252 \, A b c^{2} x^{2} + 70 \, B b^{3} x + 210 \, A b^{2} c x + 60 \, A b^{3}}{420 \, x^{7}}"," ",0,"-1/420*(140*B*c^3*x^4 + 315*B*b*c^2*x^3 + 105*A*c^3*x^3 + 252*B*b^2*c*x^2 + 252*A*b*c^2*x^2 + 70*B*b^3*x + 210*A*b^2*c*x + 60*A*b^3)/x^7","A",0
43,1,100,0,0.156784," ","integrate(x^4*(e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{3 \, c^{3} x^{4} e + 4 \, c^{3} d x^{3} - 4 \, b c^{2} x^{3} e - 6 \, b c^{2} d x^{2} + 6 \, b^{2} c x^{2} e + 12 \, b^{2} c d x - 12 \, b^{3} x e}{12 \, c^{4}} - \frac{{\left(b^{3} c d - b^{4} e\right)} \log\left({\left| c x + b \right|}\right)}{c^{5}}"," ",0,"1/12*(3*c^3*x^4*e + 4*c^3*d*x^3 - 4*b*c^2*x^3*e - 6*b*c^2*d*x^2 + 6*b^2*c*x^2*e + 12*b^2*c*d*x - 12*b^3*x*e)/c^4 - (b^3*c*d - b^4*e)*log(abs(c*x + b))/c^5","A",0
44,1,74,0,0.163380," ","integrate(x^3*(e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, c^{2} x^{3} e + 3 \, c^{2} d x^{2} - 3 \, b c x^{2} e - 6 \, b c d x + 6 \, b^{2} x e}{6 \, c^{3}} + \frac{{\left(b^{2} c d - b^{3} e\right)} \log\left({\left| c x + b \right|}\right)}{c^{4}}"," ",0,"1/6*(2*c^2*x^3*e + 3*c^2*d*x^2 - 3*b*c*x^2*e - 6*b*c*d*x + 6*b^2*x*e)/c^3 + (b^2*c*d - b^3*e)*log(abs(c*x + b))/c^4","A",0
45,1,49,0,0.149083," ","integrate(x^2*(e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{c x^{2} e + 2 \, c d x - 2 \, b x e}{2 \, c^{2}} - \frac{{\left(b c d - b^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{c^{3}}"," ",0,"1/2*(c*x^2*e + 2*c*d*x - 2*b*x*e)/c^2 - (b*c*d - b^2*e)*log(abs(c*x + b))/c^3","A",0
46,1,28,0,0.137692," ","integrate(x*(e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{x e}{c} + \frac{{\left(c d - b e\right)} \log\left({\left| c x + b \right|}\right)}{c^{2}}"," ",0,"x*e/c + (c*d - b*e)*log(abs(c*x + b))/c^2","A",0
47,1,33,0,0.147710," ","integrate((e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{d \log\left({\left| x \right|}\right)}{b} - \frac{{\left(c d - b e\right)} \log\left({\left| c x + b \right|}\right)}{b c}"," ",0,"d*log(abs(x))/b - (c*d - b*e)*log(abs(c*x + b))/(b*c)","A",0
48,1,53,0,0.242210," ","integrate((e*x+d)/x/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{{\left(c d - b e\right)} \log\left({\left| x \right|}\right)}{b^{2}} - \frac{d}{b x} + \frac{{\left(c^{2} d - b c e\right)} \log\left({\left| c x + b \right|}\right)}{b^{2} c}"," ",0,"-(c*d - b*e)*log(abs(x))/b^2 - d/(b*x) + (c^2*d - b*c*e)*log(abs(c*x + b))/(b^2*c)","A",0
49,1,78,0,0.184193," ","integrate((e*x+d)/x^2/(c*x^2+b*x),x, algorithm=""giac"")","\frac{{\left(c^{2} d - b c e\right)} \log\left({\left| x \right|}\right)}{b^{3}} - \frac{{\left(c^{3} d - b c^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c} - \frac{b^{2} d - 2 \, {\left(b c d - b^{2} e\right)} x}{2 \, b^{3} x^{2}}"," ",0,"(c^2*d - b*c*e)*log(abs(x))/b^3 - (c^3*d - b*c^2*e)*log(abs(c*x + b))/(b^3*c) - 1/2*(b^2*d - 2*(b*c*d - b^2*e)*x)/(b^3*x^2)","A",0
50,1,103,0,0.159749," ","integrate((e*x+d)/x^3/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{{\left(c^{3} d - b c^{2} e\right)} \log\left({\left| x \right|}\right)}{b^{4}} + \frac{{\left(c^{4} d - b c^{3} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{4} c} - \frac{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,"-(c^3*d - b*c^2*e)*log(abs(x))/b^4 + (c^4*d - b*c^3*e)*log(abs(c*x + b))/(b^4*c) - 1/6*(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
51,1,107,0,0.159818," ","integrate(x^5*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} c d - 4 \, b^{3} e\right)} \log\left({\left| c x + b \right|}\right)}{c^{5}} + \frac{2 \, c^{4} x^{3} e + 3 \, c^{4} d x^{2} - 6 \, b c^{3} x^{2} e - 12 \, b c^{3} d x + 18 \, b^{2} c^{2} x e}{6 \, c^{6}} + \frac{b^{3} c d - b^{4} e}{{\left(c x + b\right)} c^{5}}"," ",0,"(3*b^2*c*d - 4*b^3*e)*log(abs(c*x + b))/c^5 + 1/6*(2*c^4*x^3*e + 3*c^4*d*x^2 - 6*b*c^3*x^2*e - 12*b*c^3*d*x + 18*b^2*c^2*x*e)/c^6 + (b^3*c*d - b^4*e)/((c*x + b)*c^5)","A",0
52,1,81,0,0.154044," ","integrate(x^4*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, b c d - 3 \, b^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{c^{4}} + \frac{c^{2} x^{2} e + 2 \, c^{2} d x - 4 \, b c x e}{2 \, c^{4}} - \frac{b^{2} c d - b^{3} e}{{\left(c x + b\right)} c^{4}}"," ",0,"-(2*b*c*d - 3*b^2*e)*log(abs(c*x + b))/c^4 + 1/2*(c^2*x^2*e + 2*c^2*d*x - 4*b*c*x*e)/c^4 - (b^2*c*d - b^3*e)/((c*x + b)*c^4)","A",0
53,1,51,0,0.173262," ","integrate(x^3*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{x e}{c^{2}} + \frac{{\left(c d - 2 \, b e\right)} \log\left({\left| c x + b \right|}\right)}{c^{3}} + \frac{b c d - b^{2} e}{{\left(c x + b\right)} c^{3}}"," ",0,"x*e/c^2 + (c*d - 2*b*e)*log(abs(c*x + b))/c^3 + (b*c*d - b^2*e)/((c*x + b)*c^3)","A",0
54,1,35,0,0.153727," ","integrate(x^2*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{e \log\left({\left| c x + b \right|}\right)}{c^{2}} - \frac{c d - b e}{{\left(c x + b\right)} c^{2}}"," ",0,"e*log(abs(c*x + b))/c^2 - (c*d - b*e)/((c*x + b)*c^2)","A",0
55,1,48,0,0.149253," ","integrate(x*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{d \log\left({\left| c x + b \right|}\right)}{b^{2}} + \frac{d \log\left({\left| x \right|}\right)}{b^{2}} + \frac{b c d - b^{2} e}{{\left(c x + b\right)} b^{2} c}"," ",0,"-d*log(abs(c*x + b))/b^2 + d*log(abs(x))/b^2 + (b*c*d - b^2*e)/((c*x + b)*b^2*c)","A",0
56,1,77,0,0.174007," ","integrate((e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, c d - b e\right)} \log\left({\left| x \right|}\right)}{b^{3}} - \frac{2 \, c d x - b x e + b d}{{\left(c x^{2} + b x\right)} b^{2}} + \frac{{\left(2 \, c^{2} d - b c e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c}"," ",0,"-(2*c*d - b*e)*log(abs(x))/b^3 - (2*c*d*x - b*x*e + b*d)/((c*x^2 + b*x)*b^2) + (2*c^2*d - b*c*e)*log(abs(c*x + b))/(b^3*c)","A",0
57,1,111,0,0.159432," ","integrate((e*x+d)/x/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(3 \, c^{2} d - 2 \, b c e\right)} \log\left({\left| x \right|}\right)}{b^{4}} - \frac{{\left(3 \, c^{3} d - 2 \, b c^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{4} c} - \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(c x + b\right)} b^{4} x^{2}}"," ",0,"(3*c^2*d - 2*b*c*e)*log(abs(x))/b^4 - (3*c^3*d - 2*b*c^2*e)*log(abs(c*x + b))/(b^4*c) - 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)/((c*x + b)*b^4*x^2)","A",0
58,1,139,0,0.154129," ","integrate((e*x+d)/x^2/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, c^{3} d - 3 \, b c^{2} e\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{{\left(4 \, c^{4} d - 3 \, b c^{3} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} - \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(c x + b\right)} b^{5} x^{3}}"," ",0,"-(4*c^3*d - 3*b*c^2*e)*log(abs(x))/b^5 + (4*c^4*d - 3*b*c^3*e)*log(abs(c*x + b))/(b^5*c) - 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)/((c*x + b)*b^5*x^3)","A",0
59,1,104,0,0.150533," ","integrate(x^6*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(b c d - 2 \, b^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{c^{5}} + \frac{c^{3} x^{2} e + 2 \, c^{3} d x - 6 \, b c^{2} x e}{2 \, c^{6}} - \frac{5 \, b^{3} c d - 7 \, b^{4} e + 2 \, {\left(3 \, b^{2} c^{2} d - 4 \, b^{3} c e\right)} x}{2 \, {\left(c x + b\right)}^{2} c^{5}}"," ",0,"-3*(b*c*d - 2*b^2*e)*log(abs(c*x + b))/c^5 + 1/2*(c^3*x^2*e + 2*c^3*d*x - 6*b*c^2*x*e)/c^6 - 1/2*(5*b^3*c*d - 7*b^4*e + 2*(3*b^2*c^2*d - 4*b^3*c*e)*x)/((c*x + b)^2*c^5)","A",0
60,1,74,0,0.189006," ","integrate(x^5*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{x e}{c^{3}} + \frac{{\left(c d - 3 \, b e\right)} \log\left({\left| c x + b \right|}\right)}{c^{4}} + \frac{3 \, b^{2} c d - 5 \, b^{3} e + 2 \, {\left(2 \, b c^{2} d - 3 \, b^{2} c e\right)} x}{2 \, {\left(c x + b\right)}^{2} c^{4}}"," ",0,"x*e/c^3 + (c*d - 3*b*e)*log(abs(c*x + b))/c^4 + 1/2*(3*b^2*c*d - 5*b^3*e + 2*(2*b*c^2*d - 3*b^2*c*e)*x)/((c*x + b)^2*c^4)","A",0
61,1,55,0,0.153378," ","integrate(x^4*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{e \log\left({\left| c x + b \right|}\right)}{c^{3}} - \frac{2 \, {\left(c d - 2 \, b e\right)} x + \frac{b c d - 3 \, b^{2} e}{c}}{2 \, {\left(c x + b\right)}^{2} c^{2}}"," ",0,"e*log(abs(c*x + b))/c^3 - 1/2*(2*(c*d - 2*b*e)*x + (b*c*d - 3*b^2*e)/c)/((c*x + b)^2*c^2)","A",0
62,1,26,0,0.180406," ","integrate(x^3*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{2 \, c x e + c d + b e}{2 \, {\left(c x + b\right)}^{2} c^{2}}"," ",0,"-1/2*(2*c*x*e + c*d + b*e)/((c*x + b)^2*c^2)","A",0
63,1,60,0,0.166764," ","integrate(x^2*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{d \log\left({\left| c x + b \right|}\right)}{b^{3}} + \frac{d \log\left({\left| x \right|}\right)}{b^{3}} + \frac{2 \, b c^{2} d x + 3 \, b^{2} c d - b^{3} e}{2 \, {\left(c x + b\right)}^{2} b^{3} c}"," ",0,"-d*log(abs(c*x + b))/b^3 + d*log(abs(x))/b^3 + 1/2*(2*b*c^2*d*x + 3*b^2*c*d - b^3*e)/((c*x + b)^2*b^3*c)","A",0
64,1,107,0,0.160353," ","integrate(x*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, c d - b e\right)} \log\left({\left| x \right|}\right)}{b^{4}} + \frac{{\left(3 \, c^{2} d - b c e\right)} \log\left({\left| c x + b \right|}\right)}{b^{4} c} - \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(c x + b\right)}^{2} b^{4} x}"," ",0,"-(3*c*d - b*e)*log(abs(x))/b^4 + (3*c^2*d - b*c*e)*log(abs(c*x + b))/(b^4*c) - 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)/((c*x + b)^2*b^4*x)","A",0
65,1,132,0,0.204846," ","integrate((e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, c^{2} d - b c e\right)} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{3 \, {\left(2 \, c^{3} d - b c^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} + \frac{12 \, c^{3} d x^{3} - 6 \, b c^{2} x^{3} e + 18 \, b c^{2} d x^{2} - 9 \, b^{2} c x^{2} e + 4 \, b^{2} c d x - 2 \, b^{3} x e - b^{3} d}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4}}"," ",0,"3*(2*c^2*d - b*c*e)*log(abs(x))/b^5 - 3*(2*c^3*d - b*c^2*e)*log(abs(c*x + b))/(b^5*c) + 1/2*(12*c^3*d*x^3 - 6*b*c^2*x^3*e + 18*b*c^2*d*x^2 - 9*b^2*c*x^2*e + 4*b^2*c*d*x - 2*b^3*x*e - b^3*d)/((c*x^2 + b*x)^2*b^4)","A",0
66,1,165,0,0.171606," ","integrate((e*x+d)/x/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, c^{3} d - 3 \, b c^{2} e\right)} \log\left({\left| x \right|}\right)}{b^{6}} + \frac{2 \, {\left(5 \, c^{4} d - 3 \, b c^{3} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{6} c} - \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}{6 \, {\left(c x + b\right)}^{2} b^{6} x^{3}}"," ",0,"-2*(5*c^3*d - 3*b*c^2*e)*log(abs(x))/b^6 + 2*(5*c^4*d - 3*b*c^3*e)*log(abs(c*x + b))/(b^6*c) - 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)/((c*x + b)^2*b^6*x^3)","A",0
67,1,188,0,0.217897," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B x + \frac{B b c^{4} + 12 \, A c^{5}}{c^{5}}\right)} x - \frac{3 \, {\left(3 \, B b^{2} c^{3} - 4 \, A b c^{4}\right)}}{c^{5}}\right)} x + \frac{7 \, {\left(3 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)}}{c^{5}}\right)} x - \frac{35 \, {\left(3 \, B b^{4} c - 4 \, A b^{3} c^{2}\right)}}{c^{5}}\right)} x + \frac{105 \, {\left(3 \, B b^{5} - 4 \, A b^{4} c\right)}}{c^{5}}\right)} + \frac{7 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{11}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*B*x + (B*b*c^4 + 12*A*c^5)/c^5)*x - 3*(3*B*b^2*c^3 - 4*A*b*c^4)/c^5)*x + 7*(3*B*b^3*c^2 - 4*A*b^2*c^3)/c^5)*x - 35*(3*B*b^4*c - 4*A*b^3*c^2)/c^5)*x + 105*(3*B*b^5 - 4*A*b^4*c)/c^5) + 7/1024*(3*B*b^6 - 4*A*b^5*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
68,1,160,0,0.241097," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, B x + \frac{B b c^{3} + 10 \, A c^{4}}{c^{4}}\right)} x - \frac{7 \, B b^{2} c^{2} - 10 \, A b c^{3}}{c^{4}}\right)} x + \frac{5 \, {\left(7 \, B b^{3} c - 10 \, A b^{2} c^{2}\right)}}{c^{4}}\right)} x - \frac{15 \, {\left(7 \, B b^{4} - 10 \, A b^{3} c\right)}}{c^{4}}\right)} - \frac{{\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x)*(2*(4*(6*(8*B*x + (B*b*c^3 + 10*A*c^4)/c^4)*x - (7*B*b^2*c^2 - 10*A*b*c^3)/c^4)*x + 5*(7*B*b^3*c - 10*A*b^2*c^2)/c^4)*x - 15*(7*B*b^4 - 10*A*b^3*c)/c^4) - 1/256*(7*B*b^5 - 10*A*b^4*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
69,1,132,0,0.431295," ","integrate(x*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, B x + \frac{B b c^{2} + 8 \, A c^{3}}{c^{3}}\right)} x - \frac{5 \, B b^{2} c - 8 \, A b c^{2}}{c^{3}}\right)} x + \frac{3 \, {\left(5 \, B b^{3} - 8 \, A b^{2} c\right)}}{c^{3}}\right)} + \frac{{\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*B*x + (B*b*c^2 + 8*A*c^3)/c^3)*x - (5*B*b^2*c - 8*A*b*c^2)/c^3)*x + 3*(5*B*b^3 - 8*A*b^2*c)/c^3) + 1/128*(5*B*b^4 - 8*A*b^3*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
70,1,102,0,0.197509," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, B x + \frac{B b c + 6 \, A c^{2}}{c^{2}}\right)} x - \frac{3 \, {\left(B b^{2} - 2 \, A b c\right)}}{c^{2}}\right)} - \frac{{\left(B b^{3} - 2 \, A b^{2} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*(4*B*x + (B*b*c + 6*A*c^2)/c^2)*x - 3*(B*b^2 - 2*A*b*c)/c^2) - 1/16*(B*b^3 - 2*A*b^2*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
71,1,77,0,0.233169," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(2 \, B x + \frac{B b + 4 \, A c}{c}\right)} + \frac{{\left(B b^{2} - 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*B*x + (B*b + 4*A*c)/c) + 1/8*(B*b^2 - 4*A*b*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
72,1,82,0,0.214515," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^2,x, algorithm=""giac"")","\sqrt{c x^{2} + b x} B - \frac{{\left(B b + 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}} + \frac{2 \, A b}{\sqrt{c} x - \sqrt{c x^{2} + b x}}"," ",0,"sqrt(c*x^2 + b*x)*B - 1/2*(B*b + 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + 2*A*b/(sqrt(c)*x - sqrt(c*x^2 + b*x))","A",0
73,1,151,0,0.255056," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^3,x, algorithm=""giac"")","-B \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right) + \frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b \sqrt{c} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A c^{\frac{3}{2}} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b c + A b^{2} \sqrt{c}\right)}}{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} \sqrt{c}}"," ",0,"-B*sqrt(c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b)) + 2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*sqrt(c) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*c^(3/2) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b*c + A*b^2*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x))^3*sqrt(c))","B",0
74,1,191,0,0.249766," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B c + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b \sqrt{c} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{\frac{3}{2}} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} + 25 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} \sqrt{c} + 3 \, A b^{3}\right)}}{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5}}"," ",0,"2/15*(15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*c + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*sqrt(c) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^(3/2) + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2 + 25*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*sqrt(c) + 3*A*b^3)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^5","B",0
75,1,251,0,0.228049," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B c^{\frac{3}{2}} + 175 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c + 140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A c^{2} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} \sqrt{c} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{\frac{3}{2}} + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} + 273 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} \sqrt{c} + 15 \, A b^{4}\right)}}{105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7}}"," ",0,"2/105*(105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*c^(3/2) + 175*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c + 140*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*c^2 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*sqrt(c) + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^(3/2) + 21*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3 + 273*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*sqrt(c) + 15*A*b^4)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^7","B",0
76,1,311,0,0.197647," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B c^{2} + 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{\frac{3}{2}} + 630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{\frac{5}{2}} + 819 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c + 1764 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{2} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} \sqrt{c} + 1995 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{\frac{3}{2}} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} + 1125 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} \sqrt{c} + 35 \, A b^{5}\right)}}{315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(420*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*c^2 + 945*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^(3/2) + 630*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^(5/2) + 819*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c + 1764*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^2 + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*sqrt(c) + 1995*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^(3/2) + 45*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4 + 1125*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*sqrt(c) + 35*A*b^5)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^9","B",0
77,1,371,0,0.195694," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^7,x, algorithm=""giac"")","\frac{2 \, {\left(6930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B c^{\frac{5}{2}} + 19404 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b c^{2} + 11088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A c^{3} + 21945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{\frac{3}{2}} + 36960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{\frac{5}{2}} + 12375 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c + 51480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{2} + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} \sqrt{c} + 38115 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{\frac{3}{2}} + 385 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{5} + 15785 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} \sqrt{c} + 315 \, A b^{6}\right)}}{3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11}}"," ",0,"2/3465*(6930*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*c^(5/2) + 19404*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b*c^2 + 11088*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*c^3 + 21945*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^(3/2) + 36960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^(5/2) + 12375*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c + 51480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^2 + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*sqrt(c) + 38115*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^(3/2) + 385*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^5 + 15785*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*sqrt(c) + 315*A*b^6)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^11","B",0
78,1,431,0,0.200794," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^8,x, algorithm=""giac"")","\frac{2 \, {\left(144144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B c^{3} + 480480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b c^{\frac{5}{2}} + 240240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A c^{\frac{7}{2}} + 669240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{2} c^{2} + 926640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b c^{3} + 495495 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} c^{\frac{3}{2}} + 1531530 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{\frac{5}{2}} + 205205 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{4} c + 1401400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c^{2} + 45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{5} \sqrt{c} + 765765 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} c^{\frac{3}{2}} + 4095 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{6} + 249795 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{5} c + 45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{6} \sqrt{c} + 3465 \, A b^{7}\right)}}{45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13}}"," ",0,"2/45045*(144144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*c^3 + 480480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b*c^(5/2) + 240240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*c^(7/2) + 669240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^2*c^2 + 926640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b*c^3 + 495495*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*c^(3/2) + 1531530*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^(5/2) + 205205*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^4*c + 1401400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c^2 + 45045*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^5*sqrt(c) + 765765*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*c^(3/2) + 4095*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^6 + 249795*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^5*c + 45045*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^6*sqrt(c) + 3465*A*b^7)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^13","B",0
79,1,249,0,0.224652," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{573440} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, B c x + \frac{17 \, B b c^{7} + 16 \, A c^{8}}{c^{7}}\right)} x + \frac{B b^{2} c^{6} + 80 \, A b c^{7}}{c^{7}}\right)} x - \frac{11 \, B b^{3} c^{5} - 16 \, A b^{2} c^{6}}{c^{7}}\right)} x + \frac{9 \, {\left(11 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right)}}{c^{7}}\right)} x - \frac{21 \, {\left(11 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right)}}{c^{7}}\right)} x + \frac{105 \, {\left(11 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right)}}{c^{7}}\right)} x - \frac{315 \, {\left(11 \, B b^{7} c - 16 \, A b^{6} c^{2}\right)}}{c^{7}}\right)} - \frac{9 \, {\left(11 \, B b^{8} - 16 \, A b^{7} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{13}{2}}}"," ",0,"1/573440*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*(4*(14*B*c*x + (17*B*b*c^7 + 16*A*c^8)/c^7)*x + (B*b^2*c^6 + 80*A*b*c^7)/c^7)*x - (11*B*b^3*c^5 - 16*A*b^2*c^6)/c^7)*x + 9*(11*B*b^4*c^4 - 16*A*b^3*c^5)/c^7)*x - 21*(11*B*b^5*c^3 - 16*A*b^4*c^4)/c^7)*x + 105*(11*B*b^6*c^2 - 16*A*b^5*c^3)/c^7)*x - 315*(11*B*b^7*c - 16*A*b^6*c^2)/c^7) - 9/32768*(11*B*b^8 - 16*A*b^7*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(13/2)","A",0
80,1,222,0,0.237200," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{107520} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, B c x + \frac{15 \, B b c^{6} + 14 \, A c^{7}}{c^{6}}\right)} x + \frac{3 \, B b^{2} c^{5} + 182 \, A b c^{6}}{c^{6}}\right)} x - \frac{3 \, {\left(9 \, B b^{3} c^{4} - 14 \, A b^{2} c^{5}\right)}}{c^{6}}\right)} x + \frac{7 \, {\left(9 \, B b^{4} c^{3} - 14 \, A b^{3} c^{4}\right)}}{c^{6}}\right)} x - \frac{35 \, {\left(9 \, B b^{5} c^{2} - 14 \, A b^{4} c^{3}\right)}}{c^{6}}\right)} x + \frac{105 \, {\left(9 \, B b^{6} c - 14 \, A b^{5} c^{2}\right)}}{c^{6}}\right)} + \frac{{\left(9 \, B b^{7} - 14 \, A b^{6} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{11}{2}}}"," ",0,"1/107520*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*(12*B*c*x + (15*B*b*c^6 + 14*A*c^7)/c^6)*x + (3*B*b^2*c^5 + 182*A*b*c^6)/c^6)*x - 3*(9*B*b^3*c^4 - 14*A*b^2*c^5)/c^6)*x + 7*(9*B*b^4*c^3 - 14*A*b^3*c^4)/c^6)*x - 35*(9*B*b^5*c^2 - 14*A*b^4*c^3)/c^6)*x + 105*(9*B*b^6*c - 14*A*b^5*c^2)/c^6) + 1/2048*(9*B*b^7 - 14*A*b^6*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
81,1,194,0,0.216590," ","integrate(x*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B c x + \frac{13 \, B b c^{5} + 12 \, A c^{6}}{c^{5}}\right)} x + \frac{3 \, {\left(B b^{2} c^{4} + 44 \, A b c^{5}\right)}}{c^{5}}\right)} x - \frac{7 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}}{c^{5}}\right)} x + \frac{5 \, {\left(7 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)}}{c^{5}}\right)} x - \frac{15 \, {\left(7 \, B b^{5} c - 12 \, A b^{4} c^{2}\right)}}{c^{5}}\right)} - \frac{{\left(7 \, B b^{6} - 12 \, A b^{5} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*B*c*x + (13*B*b*c^5 + 12*A*c^6)/c^5)*x + 3*(B*b^2*c^4 + 44*A*b*c^5)/c^5)*x - (7*B*b^3*c^3 - 12*A*b^2*c^4)/c^5)*x + 5*(7*B*b^4*c^2 - 12*A*b^3*c^3)/c^5)*x - 15*(7*B*b^5*c - 12*A*b^4*c^2)/c^5) - 1/1024*(7*B*b^6 - 12*A*b^5*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
82,1,162,0,0.218851," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{640} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, B c x + \frac{11 \, B b c^{4} + 10 \, A c^{5}}{c^{4}}\right)} x + \frac{B b^{2} c^{3} + 30 \, A b c^{4}}{c^{4}}\right)} x - \frac{5 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)}}{c^{4}}\right)} x + \frac{15 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)}}{c^{4}}\right)} + \frac{3 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/640*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*B*c*x + (11*B*b*c^4 + 10*A*c^5)/c^4)*x + (B*b^2*c^3 + 30*A*b*c^4)/c^4)*x - 5*(B*b^3*c^2 - 2*A*b^2*c^3)/c^4)*x + 15*(B*b^4*c - 2*A*b^3*c^2)/c^4) + 3/256*(B*b^5 - 2*A*b^4*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
83,1,138,0,0.208909," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, B c x + \frac{9 \, B b c^{3} + 8 \, A c^{4}}{c^{3}}\right)} x + \frac{3 \, B b^{2} c^{2} + 56 \, A b c^{3}}{c^{3}}\right)} x - \frac{3 \, {\left(3 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)}}{c^{3}}\right)} - \frac{{\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{5}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*B*c*x + (9*B*b*c^3 + 8*A*c^4)/c^3)*x + (3*B*b^2*c^2 + 56*A*b*c^3)/c^3)*x - 3*(3*B*b^3*c - 8*A*b^2*c^2)/c^3) - 1/128*(3*B*b^4 - 8*A*b^3*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
84,1,109,0,0.238081," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, B c x + \frac{7 \, B b c^{2} + 6 \, A c^{3}}{c^{2}}\right)} x + \frac{3 \, {\left(B b^{2} c + 10 \, A b c^{2}\right)}}{c^{2}}\right)} + \frac{{\left(B b^{3} - 6 \, A b^{2} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*(4*B*c*x + (7*B*b*c^2 + 6*A*c^3)/c^2)*x + 3*(B*b^2*c + 10*A*b*c^2)/c^2) + 1/16*(B*b^3 - 6*A*b^2*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
85,1,109,0,0.259399," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^3,x, algorithm=""giac"")","\frac{2 \, A b^{2}}{\sqrt{c} x - \sqrt{c x^{2} + b x}} + \frac{1}{4} \, {\left(2 \, B c x + \frac{5 \, B b c + 4 \, A c^{2}}{c}\right)} \sqrt{c x^{2} + b x} - \frac{3 \, {\left(B b^{2} + 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, \sqrt{c}}"," ",0,"2*A*b^2/(sqrt(c)*x - sqrt(c*x^2 + b*x)) + 1/4*(2*B*c*x + (5*B*b*c + 4*A*c^2)/c)*sqrt(c*x^2 + b*x) - 3/8*(B*b^2 + 4*A*b*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c)","A",0
86,1,181,0,0.268561," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^4,x, algorithm=""giac"")","\sqrt{c x^{2} + b x} B c - \frac{{\left(3 \, B b c + 2 \, A c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}} + \frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} \sqrt{c} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{\frac{3}{2}} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c + A b^{3} \sqrt{c}\right)}}{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} \sqrt{c}}"," ",0,"sqrt(c*x^2 + b*x)*B*c - 1/2*(3*B*b*c + 2*A*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + 2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*sqrt(c) + 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^(3/2) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c + A*b^3*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x))^3*sqrt(c))","A",0
87,1,270,0,0.247022," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^5,x, algorithm=""giac"")","-B c^{\frac{3}{2}} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right) + \frac{2 \, {\left(30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c^{\frac{3}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A c^{\frac{5}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{2} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} \sqrt{c} + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{\frac{3}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c + 3 \, A b^{4} \sqrt{c}\right)}}{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} \sqrt{c}}"," ",0,"-B*c^(3/2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b)) + 2/15*(30*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c^(3/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*c^(5/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c + 30*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^2 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*sqrt(c) + 30*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^(3/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c + 3*A*b^4*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x))^5*sqrt(c))","B",0
88,1,311,0,0.229440," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B c^{2} + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{\frac{3}{2}} + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{\frac{5}{2}} + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{2} + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} \sqrt{c} + 140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{\frac{3}{2}} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} + 98 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} \sqrt{c} + 5 \, A b^{5}\right)}}{35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7}}"," ",0,"2/35*(35*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*c^2 + 70*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^(3/2) + 35*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^(5/2) + 70*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^2 + 35*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*sqrt(c) + 140*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^(3/2) + 7*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4 + 98*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c + 35*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*sqrt(c) + 5*A*b^5)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^7","B",0
89,1,371,0,0.225311," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^7,x, algorithm=""giac"")","\frac{2 \, {\left(315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B c^{\frac{5}{2}} + 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b c^{2} + 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A c^{3} + 1260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{\frac{3}{2}} + 1575 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{\frac{5}{2}} + 882 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c + 2583 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{2} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} \sqrt{c} + 2310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{\frac{3}{2}} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{5} + 1170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} \sqrt{c} + 35 \, A b^{6}\right)}}{315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*c^(5/2) + 945*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b*c^2 + 420*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*c^3 + 1260*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^(3/2) + 1575*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^(5/2) + 882*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c + 2583*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^2 + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*sqrt(c) + 2310*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^(3/2) + 45*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^5 + 1170*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*sqrt(c) + 35*A*b^6)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^9","B",0
90,1,431,0,0.397732," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^8,x, algorithm=""giac"")","\frac{2 \, {\left(4620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B c^{3} + 17325 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b c^{\frac{5}{2}} + 6930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A c^{\frac{7}{2}} + 28413 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{2} c^{2} + 30492 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b c^{3} + 25410 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} c^{\frac{3}{2}} + 58905 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{\frac{5}{2}} + 12870 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{4} c + 63855 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c^{2} + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{5} \sqrt{c} + 41580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} c^{\frac{3}{2}} + 385 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{6} + 16170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{5} c + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{6} \sqrt{c} + 315 \, A b^{7}\right)}}{3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11}}"," ",0,"2/3465*(4620*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*c^3 + 17325*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b*c^(5/2) + 6930*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*c^(7/2) + 28413*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^2*c^2 + 30492*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b*c^3 + 25410*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*c^(3/2) + 58905*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^(5/2) + 12870*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^4*c + 63855*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c^2 + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^5*sqrt(c) + 41580*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*c^(3/2) + 385*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^6 + 16170*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^5*c + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^6*sqrt(c) + 315*A*b^7)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^11","B",0
91,1,491,0,0.214676," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^9,x, algorithm=""giac"")","\frac{2 \, {\left(30030 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B c^{\frac{7}{2}} + 132132 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b c^{3} + 48048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A c^{4} + 255255 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{2} c^{\frac{5}{2}} + 240240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b c^{\frac{7}{2}} + 276705 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{3} c^{2} + 531960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{2} c^{3} + 180180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{4} c^{\frac{3}{2}} + 675675 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} c^{\frac{5}{2}} + 70070 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{5} c + 535535 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{4} c^{2} + 15015 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{6} \sqrt{c} + 270270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{5} c^{\frac{3}{2}} + 1365 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{7} + 84630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{6} c + 15015 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{7} \sqrt{c} + 1155 \, A b^{8}\right)}}{15015 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13}}"," ",0,"2/15015*(30030*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*c^(7/2) + 132132*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b*c^3 + 48048*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*c^4 + 255255*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^2*c^(5/2) + 240240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b*c^(7/2) + 276705*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^3*c^2 + 531960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^2*c^3 + 180180*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^4*c^(3/2) + 675675*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*c^(5/2) + 70070*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^5*c + 535535*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^4*c^2 + 15015*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^6*sqrt(c) + 270270*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^5*c^(3/2) + 1365*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^7 + 84630*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^6*c + 15015*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^7*sqrt(c) + 1155*A*b^8)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^13","B",0
92,1,551,0,0.334500," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^10,x, algorithm=""giac"")","\frac{2 \, {\left(144144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B c^{4} + 720720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b c^{\frac{7}{2}} + 240240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A c^{\frac{9}{2}} + 1595880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{2} c^{3} + 1338480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b c^{4} + 2027025 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{3} c^{\frac{5}{2}} + 3333330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{2} c^{\frac{7}{2}} + 1606605 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{4} c^{2} + 4844840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{3} c^{3} + 810810 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{5} c^{\frac{3}{2}} + 4513509 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{4} c^{\frac{5}{2}} + 253890 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{6} c + 2788695 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{5} c^{2} + 45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{7} \sqrt{c} + 1141140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{6} c^{\frac{3}{2}} + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{8} + 297990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{7} c + 45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{8} \sqrt{c} + 3003 \, A b^{9}\right)}}{45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{15}}"," ",0,"2/45045*(144144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*c^4 + 720720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b*c^(7/2) + 240240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*c^(9/2) + 1595880*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^2*c^3 + 1338480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b*c^4 + 2027025*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^3*c^(5/2) + 3333330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^2*c^(7/2) + 1606605*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^4*c^2 + 4844840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^3*c^3 + 810810*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^5*c^(3/2) + 4513509*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^4*c^(5/2) + 253890*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^6*c + 2788695*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^5*c^2 + 45045*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^7*sqrt(c) + 1141140*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^6*c^(3/2) + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^8 + 297990*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^7*c + 45045*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^8*sqrt(c) + 3003*A*b^9)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^15","B",0
93,1,309,0,0.259191," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{41287680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, {\left(18 \, B c^{2} x + \frac{41 \, B b c^{10} + 20 \, A c^{11}}{c^{9}}\right)} x + \frac{383 \, B b^{2} c^{9} + 740 \, A b c^{10}}{c^{9}}\right)} x + \frac{15 \, {\left(B b^{3} c^{8} + 412 \, A b^{2} c^{9}\right)}}{c^{9}}\right)} x - \frac{5 \, {\left(13 \, B b^{4} c^{7} - 20 \, A b^{3} c^{8}\right)}}{c^{9}}\right)} x + \frac{11 \, {\left(13 \, B b^{5} c^{6} - 20 \, A b^{4} c^{7}\right)}}{c^{9}}\right)} x - \frac{99 \, {\left(13 \, B b^{6} c^{5} - 20 \, A b^{5} c^{6}\right)}}{c^{9}}\right)} x + \frac{231 \, {\left(13 \, B b^{7} c^{4} - 20 \, A b^{6} c^{5}\right)}}{c^{9}}\right)} x - \frac{1155 \, {\left(13 \, B b^{8} c^{3} - 20 \, A b^{7} c^{4}\right)}}{c^{9}}\right)} x + \frac{3465 \, {\left(13 \, B b^{9} c^{2} - 20 \, A b^{8} c^{3}\right)}}{c^{9}}\right)} + \frac{11 \, {\left(13 \, B b^{10} - 20 \, A b^{9} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{262144 \, c^{\frac{15}{2}}}"," ",0,"1/41287680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(4*(14*(16*(18*B*c^2*x + (41*B*b*c^10 + 20*A*c^11)/c^9)*x + (383*B*b^2*c^9 + 740*A*b*c^10)/c^9)*x + 15*(B*b^3*c^8 + 412*A*b^2*c^9)/c^9)*x - 5*(13*B*b^4*c^7 - 20*A*b^3*c^8)/c^9)*x + 11*(13*B*b^5*c^6 - 20*A*b^4*c^7)/c^9)*x - 99*(13*B*b^6*c^5 - 20*A*b^5*c^6)/c^9)*x + 231*(13*B*b^7*c^4 - 20*A*b^6*c^5)/c^9)*x - 1155*(13*B*b^8*c^3 - 20*A*b^7*c^4)/c^9)*x + 3465*(13*B*b^9*c^2 - 20*A*b^8*c^3)/c^9) + 11/262144*(13*B*b^10 - 20*A*b^9*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(15/2)","A",0
94,1,282,0,0.461740," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{2064384} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, B c^{2} x + \frac{37 \, B b c^{9} + 18 \, A c^{10}}{c^{8}}\right)} x + \frac{3 \, {\left(103 \, B b^{2} c^{8} + 198 \, A b c^{9}\right)}}{c^{8}}\right)} x + \frac{5 \, B b^{3} c^{7} + 1458 \, A b^{2} c^{8}}{c^{8}}\right)} x - \frac{11 \, B b^{4} c^{6} - 18 \, A b^{3} c^{7}}{c^{8}}\right)} x + \frac{9 \, {\left(11 \, B b^{5} c^{5} - 18 \, A b^{4} c^{6}\right)}}{c^{8}}\right)} x - \frac{21 \, {\left(11 \, B b^{6} c^{4} - 18 \, A b^{5} c^{5}\right)}}{c^{8}}\right)} x + \frac{105 \, {\left(11 \, B b^{7} c^{3} - 18 \, A b^{6} c^{4}\right)}}{c^{8}}\right)} x - \frac{315 \, {\left(11 \, B b^{8} c^{2} - 18 \, A b^{7} c^{3}\right)}}{c^{8}}\right)} - \frac{5 \, {\left(11 \, B b^{9} - 18 \, A b^{8} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{65536 \, c^{\frac{13}{2}}}"," ",0,"1/2064384*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(4*(14*(16*B*c^2*x + (37*B*b*c^9 + 18*A*c^10)/c^8)*x + 3*(103*B*b^2*c^8 + 198*A*b*c^9)/c^8)*x + (5*B*b^3*c^7 + 1458*A*b^2*c^8)/c^8)*x - (11*B*b^4*c^6 - 18*A*b^3*c^7)/c^8)*x + 9*(11*B*b^5*c^5 - 18*A*b^4*c^6)/c^8)*x - 21*(11*B*b^6*c^4 - 18*A*b^5*c^5)/c^8)*x + 105*(11*B*b^7*c^3 - 18*A*b^6*c^4)/c^8)*x - 315*(11*B*b^8*c^2 - 18*A*b^7*c^3)/c^8) - 5/65536*(11*B*b^9 - 18*A*b^8*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(13/2)","A",0
95,1,253,0,0.256104," ","integrate(x*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{344064} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, B c^{2} x + \frac{33 \, B b c^{8} + 16 \, A c^{9}}{c^{7}}\right)} x + \frac{243 \, B b^{2} c^{7} + 464 \, A b c^{8}}{c^{7}}\right)} x + \frac{3 \, B b^{3} c^{6} + 592 \, A b^{2} c^{7}}{c^{7}}\right)} x - \frac{3 \, {\left(9 \, B b^{4} c^{5} - 16 \, A b^{3} c^{6}\right)}}{c^{7}}\right)} x + \frac{7 \, {\left(9 \, B b^{5} c^{4} - 16 \, A b^{4} c^{5}\right)}}{c^{7}}\right)} x - \frac{35 \, {\left(9 \, B b^{6} c^{3} - 16 \, A b^{5} c^{4}\right)}}{c^{7}}\right)} x + \frac{105 \, {\left(9 \, B b^{7} c^{2} - 16 \, A b^{6} c^{3}\right)}}{c^{7}}\right)} + \frac{5 \, {\left(9 \, B b^{8} - 16 \, A b^{7} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{11}{2}}}"," ",0,"1/344064*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(12*(14*B*c^2*x + (33*B*b*c^8 + 16*A*c^9)/c^7)*x + (243*B*b^2*c^7 + 464*A*b*c^8)/c^7)*x + (3*B*b^3*c^6 + 592*A*b^2*c^7)/c^7)*x - 3*(9*B*b^4*c^5 - 16*A*b^3*c^6)/c^7)*x + 7*(9*B*b^5*c^4 - 16*A*b^4*c^5)/c^7)*x - 35*(9*B*b^6*c^3 - 16*A*b^5*c^4)/c^7)*x + 105*(9*B*b^7*c^2 - 16*A*b^6*c^3)/c^7) + 5/32768*(9*B*b^8 - 16*A*b^7*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
96,1,221,0,0.222784," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{21504} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, B c^{2} x + \frac{29 \, B b c^{7} + 14 \, A c^{8}}{c^{6}}\right)} x + \frac{37 \, B b^{2} c^{6} + 70 \, A b c^{7}}{c^{6}}\right)} x + \frac{3 \, {\left(B b^{3} c^{5} + 126 \, A b^{2} c^{6}\right)}}{c^{6}}\right)} x - \frac{7 \, {\left(B b^{4} c^{4} - 2 \, A b^{3} c^{5}\right)}}{c^{6}}\right)} x + \frac{35 \, {\left(B b^{5} c^{3} - 2 \, A b^{4} c^{4}\right)}}{c^{6}}\right)} x - \frac{105 \, {\left(B b^{6} c^{2} - 2 \, A b^{5} c^{3}\right)}}{c^{6}}\right)} - \frac{5 \, {\left(B b^{7} - 2 \, A b^{6} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{9}{2}}}"," ",0,"1/21504*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(12*B*c^2*x + (29*B*b*c^7 + 14*A*c^8)/c^6)*x + (37*B*b^2*c^6 + 70*A*b*c^7)/c^6)*x + 3*(B*b^3*c^5 + 126*A*b^2*c^6)/c^6)*x - 7*(B*b^4*c^4 - 2*A*b^3*c^5)/c^6)*x + 35*(B*b^5*c^3 - 2*A*b^4*c^4)/c^6)*x - 105*(B*b^6*c^2 - 2*A*b^5*c^3)/c^6) - 5/2048*(B*b^7 - 2*A*b^6*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
97,1,198,0,0.233636," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x,x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B c^{2} x + \frac{25 \, B b c^{6} + 12 \, A c^{7}}{c^{5}}\right)} x + \frac{9 \, {\left(15 \, B b^{2} c^{5} + 28 \, A b c^{6}\right)}}{c^{5}}\right)} x + \frac{5 \, B b^{3} c^{4} + 372 \, A b^{2} c^{5}}{c^{5}}\right)} x - \frac{5 \, {\left(5 \, B b^{4} c^{3} - 12 \, A b^{3} c^{4}\right)}}{c^{5}}\right)} x + \frac{15 \, {\left(5 \, B b^{5} c^{2} - 12 \, A b^{4} c^{3}\right)}}{c^{5}}\right)} + \frac{{\left(5 \, B b^{6} - 12 \, A b^{5} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{7}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*B*c^2*x + (25*B*b*c^6 + 12*A*c^7)/c^5)*x + 9*(15*B*b^2*c^5 + 28*A*b*c^6)/c^5)*x + (5*B*b^3*c^4 + 372*A*b^2*c^5)/c^5)*x - 5*(5*B*b^4*c^3 - 12*A*b^3*c^4)/c^5)*x + 15*(5*B*b^5*c^2 - 12*A*b^4*c^3)/c^5) + 1/1024*(5*B*b^6 - 12*A*b^5*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
98,1,170,0,0.239658," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^2,x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, B c^{2} x + \frac{21 \, B b c^{5} + 10 \, A c^{6}}{c^{4}}\right)} x + \frac{93 \, B b^{2} c^{4} + 170 \, A b c^{5}}{c^{4}}\right)} x + \frac{5 \, {\left(3 \, B b^{3} c^{3} + 118 \, A b^{2} c^{4}\right)}}{c^{4}}\right)} x - \frac{15 \, {\left(3 \, B b^{4} c^{2} - 10 \, A b^{3} c^{3}\right)}}{c^{4}}\right)} - \frac{{\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{5}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x)*(2*(4*(6*(8*B*c^2*x + (21*B*b*c^5 + 10*A*c^6)/c^4)*x + (93*B*b^2*c^4 + 170*A*b*c^5)/c^4)*x + 5*(3*B*b^3*c^3 + 118*A*b^2*c^4)/c^4)*x - 15*(3*B*b^4*c^2 - 10*A*b^3*c^3)/c^4) - 1/256*(3*B*b^5 - 10*A*b^4*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
99,1,141,0,0.224111," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^3,x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, B c^{2} x + \frac{17 \, B b c^{4} + 8 \, A c^{5}}{c^{3}}\right)} x + \frac{59 \, B b^{2} c^{3} + 104 \, A b c^{4}}{c^{3}}\right)} x + \frac{3 \, {\left(5 \, B b^{3} c^{2} + 88 \, A b^{2} c^{3}\right)}}{c^{3}}\right)} + \frac{5 \, {\left(B b^{4} - 8 \, A b^{3} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{3}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*B*c^2*x + (17*B*b*c^4 + 8*A*c^5)/c^3)*x + (59*B*b^2*c^3 + 104*A*b*c^4)/c^3)*x + 3*(5*B*b^3*c^2 + 88*A*b^2*c^3)/c^3) + 5/128*(B*b^4 - 8*A*b^3*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
100,1,141,0,0.242738," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^4,x, algorithm=""giac"")","\frac{2 \, A b^{3}}{\sqrt{c} x - \sqrt{c x^{2} + b x}} + \frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, B c^{2} x + \frac{13 \, B b c^{3} + 6 \, A c^{4}}{c^{2}}\right)} x + \frac{3 \, {\left(11 \, B b^{2} c^{2} + 18 \, A b c^{3}\right)}}{c^{2}}\right)} - \frac{5 \, {\left(B b^{3} + 6 \, A b^{2} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, \sqrt{c}}"," ",0,"2*A*b^3/(sqrt(c)*x - sqrt(c*x^2 + b*x)) + 1/24*sqrt(c*x^2 + b*x)*(2*(4*B*c^2*x + (13*B*b*c^3 + 6*A*c^4)/c^2)*x + 3*(11*B*b^2*c^2 + 18*A*b*c^3)/c^2) - 5/16*(B*b^3 + 6*A*b^2*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c)","A",0
101,1,211,0,0.281925," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^5,x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, B c^{2} x + \frac{9 \, B b c^{2} + 4 \, A c^{3}}{c}\right)} \sqrt{c x^{2} + b x} - \frac{5 \, {\left(3 \, B b^{2} c + 4 \, A b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, \sqrt{c}} + \frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} \sqrt{c} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{\frac{3}{2}} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c + A b^{4} \sqrt{c}\right)}}{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} \sqrt{c}}"," ",0,"1/4*(2*B*c^2*x + (9*B*b*c^2 + 4*A*c^3)/c)*sqrt(c*x^2 + b*x) - 5/8*(3*B*b^2*c + 4*A*b*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + 2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*sqrt(c) + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^(3/2) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c + A*b^4*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x))^3*sqrt(c))","A",0
102,1,304,0,0.268257," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^6,x, algorithm=""giac"")","\sqrt{c x^{2} + b x} B c^{2} - \frac{{\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}} + \frac{2 \, {\left(45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c^{\frac{3}{2}} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{\frac{5}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{2} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} \sqrt{c} + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c^{\frac{3}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} c + 3 \, A b^{5} \sqrt{c}\right)}}{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} \sqrt{c}}"," ",0,"sqrt(c*x^2 + b*x)*B*c^2 - 1/2*(5*B*b*c^2 + 2*A*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + 2/15*(45*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c^(3/2) + 45*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^(5/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c + 45*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^2 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*sqrt(c) + 35*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c^(3/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*c + 3*A*b^5*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x))^5*sqrt(c))","B",0
103,1,390,0,0.274948," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^7,x, algorithm=""giac"")","-B c^{\frac{5}{2}} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right) + \frac{2 \, {\left(315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b c^{\frac{5}{2}} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A c^{\frac{7}{2}} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{2} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{3} + 245 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c^{\frac{3}{2}} + 525 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{\frac{5}{2}} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} c + 525 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{2} + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{5} \sqrt{c} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c^{\frac{3}{2}} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} c + 15 \, A b^{6} \sqrt{c}\right)}}{105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} \sqrt{c}}"," ",0,"-B*c^(5/2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b)) + 2/105*(315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b*c^(5/2) + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*c^(7/2) + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^2 + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^3 + 245*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c^(3/2) + 525*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^(5/2) + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*c + 525*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^2 + 21*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^5*sqrt(c) + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c^(3/2) + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*c + 15*A*b^6*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x))^7*sqrt(c))","B",0
104,1,431,0,0.225835," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^8,x, algorithm=""giac"")","\frac{2 \, {\left(63 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B c^{3} + 189 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b c^{\frac{5}{2}} + 63 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A c^{\frac{7}{2}} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{2} c^{2} + 273 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b c^{3} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} c^{\frac{3}{2}} + 567 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{\frac{5}{2}} + 189 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{4} c + 693 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c^{2} + 63 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{5} \sqrt{c} + 525 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} c^{\frac{3}{2}} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{6} + 243 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{5} c + 63 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{6} \sqrt{c} + 7 \, A b^{7}\right)}}{63 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9}}"," ",0,"2/63*(63*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*c^3 + 189*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b*c^(5/2) + 63*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*c^(7/2) + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^2*c^2 + 273*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b*c^3 + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*c^(3/2) + 567*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^(5/2) + 189*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^4*c + 693*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c^2 + 63*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^5*sqrt(c) + 525*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*c^(3/2) + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^6 + 243*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^5*c + 63*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^6*sqrt(c) + 7*A*b^7)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^9","B",0
105,1,491,0,0.223801," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^9,x, algorithm=""giac"")","\frac{2 \, {\left(693 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B c^{\frac{7}{2}} + 3003 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b c^{3} + 924 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A c^{4} + 6237 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{2} c^{\frac{5}{2}} + 4851 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b c^{\frac{7}{2}} + 7623 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{3} c^{2} + 11781 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{2} c^{3} + 5775 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{4} c^{\frac{3}{2}} + 16863 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} c^{\frac{5}{2}} + 2673 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{5} c + 15345 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{4} c^{2} + 693 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{6} \sqrt{c} + 9009 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{5} c^{\frac{3}{2}} + 77 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{7} + 3311 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{6} c + 693 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{7} \sqrt{c} + 63 \, A b^{8}\right)}}{693 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11}}"," ",0,"2/693*(693*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*c^(7/2) + 3003*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b*c^3 + 924*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*c^4 + 6237*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^2*c^(5/2) + 4851*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b*c^(7/2) + 7623*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^3*c^2 + 11781*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^2*c^3 + 5775*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^4*c^(3/2) + 16863*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*c^(5/2) + 2673*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^5*c + 15345*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^4*c^2 + 693*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^6*sqrt(c) + 9009*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^5*c^(3/2) + 77*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^7 + 3311*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^6*c + 693*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^7*sqrt(c) + 63*A*b^8)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^11","B",0
106,1,551,0,0.236660," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^10,x, algorithm=""giac"")","\frac{2 \, {\left(12012 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B c^{4} + 63063 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b c^{\frac{7}{2}} + 18018 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A c^{\frac{9}{2}} + 153153 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{2} c^{3} + 108108 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b c^{4} + 219219 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{3} c^{\frac{5}{2}} + 297297 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{2} c^{\frac{7}{2}} + 199485 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{4} c^{2} + 485199 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{3} c^{3} + 117117 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{5} c^{\frac{3}{2}} + 513513 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{4} c^{\frac{5}{2}} + 43043 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{6} c + 363363 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{5} c^{2} + 9009 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{7} \sqrt{c} + 171171 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{6} c^{\frac{3}{2}} + 819 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{8} + 51597 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{7} c + 9009 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{8} \sqrt{c} + 693 \, A b^{9}\right)}}{9009 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13}}"," ",0,"2/9009*(12012*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*c^4 + 63063*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b*c^(7/2) + 18018*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*c^(9/2) + 153153*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^2*c^3 + 108108*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b*c^4 + 219219*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^3*c^(5/2) + 297297*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^2*c^(7/2) + 199485*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^4*c^2 + 485199*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^3*c^3 + 117117*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^5*c^(3/2) + 513513*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^4*c^(5/2) + 43043*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^6*c + 363363*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^5*c^2 + 9009*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^7*sqrt(c) + 171171*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^6*c^(3/2) + 819*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^8 + 51597*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^7*c + 9009*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^8*sqrt(c) + 693*A*b^9)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^13","B",0
107,1,611,0,0.236361," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^11,x, algorithm=""giac"")","\frac{2 \, {\left(90090 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B c^{\frac{9}{2}} + 540540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b c^{4} + 144144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A c^{5} + 1486485 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{2} c^{\frac{7}{2}} + 960960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b c^{\frac{9}{2}} + 2425995 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{3} c^{3} + 2934360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{2} c^{4} + 2567565 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{4} c^{\frac{5}{2}} + 5360355 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{3} c^{\frac{7}{2}} + 1816815 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{5} c^{2} + 6451445 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{4} c^{3} + 855855 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{6} c^{\frac{3}{2}} + 5324319 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{5} c^{\frac{5}{2}} + 257985 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{7} c + 3042585 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{6} c^{2} + 45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{8} \sqrt{c} + 1186185 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{7} c^{\frac{3}{2}} + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{9} + 301455 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{8} c + 45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{9} \sqrt{c} + 3003 \, A b^{10}\right)}}{45045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{15}}"," ",0,"2/45045*(90090*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*c^(9/2) + 540540*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b*c^4 + 144144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*c^5 + 1486485*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^2*c^(7/2) + 960960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b*c^(9/2) + 2425995*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^3*c^3 + 2934360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^2*c^4 + 2567565*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^4*c^(5/2) + 5360355*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^3*c^(7/2) + 1816815*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^5*c^2 + 6451445*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^4*c^3 + 855855*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^6*c^(3/2) + 5324319*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^5*c^(5/2) + 257985*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^7*c + 3042585*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^6*c^2 + 45045*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^8*sqrt(c) + 1186185*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^7*c^(3/2) + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^9 + 301455*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^8*c + 45045*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^9*sqrt(c) + 3003*A*b^10)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^15","B",0
108,1,671,0,0.242422," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^12,x, algorithm=""giac"")","\frac{2 \, {\left(2450448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} B c^{5} + 16336320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b c^{\frac{9}{2}} + 4084080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A c^{\frac{11}{2}} + 49884120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{2} c^{4} + 29755440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b c^{5} + 91126035 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{3} c^{\frac{7}{2}} + 99549450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{2} c^{\frac{9}{2}} + 109674565 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{4} c^{3} + 200800600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{3} c^{4} + 90513423 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{5} c^{\frac{5}{2}} + 270315045 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{4} c^{\frac{7}{2}} + 51723945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{6} c^{2} + 254303595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{5} c^{3} + 20165145 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{7} c^{\frac{3}{2}} + 170255085 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{6} c^{\frac{5}{2}} + 5124735 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{8} c + 80994375 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{7} c^{2} + 765765 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{9} \sqrt{c} + 26801775 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{8} c^{\frac{3}{2}} + 51051 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{10} + 5870865 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{9} c + 765765 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{10} \sqrt{c} + 45045 \, A b^{11}\right)}}{765765 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{17}}"," ",0,"2/765765*(2450448*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*B*c^5 + 16336320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b*c^(9/2) + 4084080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*c^(11/2) + 49884120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^2*c^4 + 29755440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b*c^5 + 91126035*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^3*c^(7/2) + 99549450*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^2*c^(9/2) + 109674565*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^4*c^3 + 200800600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^3*c^4 + 90513423*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^5*c^(5/2) + 270315045*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^4*c^(7/2) + 51723945*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^6*c^2 + 254303595*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^5*c^3 + 20165145*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^7*c^(3/2) + 170255085*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^6*c^(5/2) + 5124735*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^8*c + 80994375*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^7*c^2 + 765765*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^9*sqrt(c) + 26801775*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^8*c^(3/2) + 51051*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^10 + 5870865*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^9*c + 765765*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^10*sqrt(c) + 45045*A*b^11)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^17","B",0
109,1,165,0,0.231207," ","integrate(x^4*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, {\left(\frac{8 \, B x}{c} - \frac{9 \, B b c^{3} - 10 \, A c^{4}}{c^{5}}\right)} x + \frac{7 \, {\left(9 \, B b^{2} c^{2} - 10 \, A b c^{3}\right)}}{c^{5}}\right)} x - \frac{35 \, {\left(9 \, B b^{3} c - 10 \, A b^{2} c^{2}\right)}}{c^{5}}\right)} x + \frac{105 \, {\left(9 \, B b^{4} - 10 \, A b^{3} c\right)}}{c^{5}}\right)} + \frac{7 \, {\left(9 \, B b^{5} - 10 \, A b^{4} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{11}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x)*(2*(4*(6*(8*B*x/c - (9*B*b*c^3 - 10*A*c^4)/c^5)*x + 7*(9*B*b^2*c^2 - 10*A*b*c^3)/c^5)*x - 35*(9*B*b^3*c - 10*A*b^2*c^2)/c^5)*x + 105*(9*B*b^4 - 10*A*b^3*c)/c^5) + 7/256*(9*B*b^5 - 10*A*b^4*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
110,1,137,0,0.265167," ","integrate(x^3*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(\frac{6 \, B x}{c} - \frac{7 \, B b c^{2} - 8 \, A c^{3}}{c^{4}}\right)} x + \frac{5 \, {\left(7 \, B b^{2} c - 8 \, A b c^{2}\right)}}{c^{4}}\right)} x - \frac{15 \, {\left(7 \, B b^{3} - 8 \, A b^{2} c\right)}}{c^{4}}\right)} - \frac{5 \, {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*B*x/c - (7*B*b*c^2 - 8*A*c^3)/c^4)*x + 5*(7*B*b^2*c - 8*A*b*c^2)/c^4)*x - 15*(7*B*b^3 - 8*A*b^2*c)/c^4) - 5/128*(7*B*b^4 - 8*A*b^3*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
111,1,109,0,0.231484," ","integrate(x^2*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(\frac{4 \, B x}{c} - \frac{5 \, B b c - 6 \, A c^{2}}{c^{3}}\right)} x + \frac{3 \, {\left(5 \, B b^{2} - 6 \, A b c\right)}}{c^{3}}\right)} + \frac{{\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*(4*B*x/c - (5*B*b*c - 6*A*c^2)/c^3)*x + 3*(5*B*b^2 - 6*A*b*c)/c^3) + 1/16*(5*B*b^3 - 6*A*b^2*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
112,1,83,0,0.235134," ","integrate(x*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(\frac{2 \, B x}{c} - \frac{3 \, B b - 4 \, A c}{c^{2}}\right)} - \frac{{\left(3 \, B b^{2} - 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*B*x/c - (3*B*b - 4*A*c)/c^2) - 1/8*(3*B*b^2 - 4*A*b*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
113,1,60,0,0.223772," ","integrate((B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x} B}{c} + \frac{{\left(B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"sqrt(c*x^2 + b*x)*B/c + 1/2*(B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
114,1,59,0,0.321055," ","integrate((B*x+A)/x/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{B \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b \right|}\right)}{\sqrt{c}} + \frac{2 \, A}{\sqrt{c} x - \sqrt{c x^{2} + b x}}"," ",0,"-B*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b))/sqrt(c) + 2*A/(sqrt(c)*x - sqrt(c*x^2 + b*x))","A",0
115,1,76,0,0.223873," ","integrate((B*x+A)/x^2/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A \sqrt{c} + A b\right)}}{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3}}"," ",0,"2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*sqrt(c) + A*b)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^3","A",0
116,1,133,0,0.224728," ","integrate((B*x+A)/x^3/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B \sqrt{c} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A c + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b \sqrt{c} + 3 \, A b^{2}\right)}}{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5}}"," ",0,"2/15*(15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*sqrt(c) + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*c + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b*sqrt(c) + 3*A*b^2)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^5","A",0
117,1,191,0,0.218626," ","integrate((B*x+A)/x^4/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B c + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b \sqrt{c} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{\frac{3}{2}} + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} + 252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} \sqrt{c} + 15 \, A b^{3}\right)}}{105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7}}"," ",0,"2/105*(140*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*c + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*sqrt(c) + 210*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^(3/2) + 21*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2 + 252*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*sqrt(c) + 15*A*b^3)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^7","A",0
118,1,251,0,0.219669," ","integrate((B*x+A)/x^5/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B c^{\frac{3}{2}} + 756 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c + 1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A c^{2} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} \sqrt{c} + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{\frac{3}{2}} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} + 1080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} \sqrt{c} + 35 \, A b^{4}\right)}}{315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(630*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*c^(3/2) + 756*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c + 1008*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*c^2 + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*sqrt(c) + 1680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^(3/2) + 45*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3 + 1080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*sqrt(c) + 35*A*b^4)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^9","A",0
119,1,311,0,0.222552," ","integrate((B*x+A)/x^6/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(11088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B c^{2} + 18480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{\frac{3}{2}} + 18480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{\frac{5}{2}} + 11880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c + 39600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{2} + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} \sqrt{c} + 34650 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{\frac{3}{2}} + 385 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} + 15400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} \sqrt{c} + 315 \, A b^{5}\right)}}{3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11}}"," ",0,"2/3465*(11088*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*c^2 + 18480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^(3/2) + 18480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^(5/2) + 11880*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c + 39600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^2 + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*sqrt(c) + 34650*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^(3/2) + 385*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4 + 15400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*sqrt(c) + 315*A*b^5)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^11","A",0
120,1,163,0,0.261671," ","integrate(x^4*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, x {\left(\frac{4 \, B x}{c^{2}} - \frac{11 \, B b c^{10} - 6 \, A c^{11}}{c^{13}}\right)} + \frac{3 \, {\left(19 \, B b^{2} c^{9} - 14 \, A b c^{10}\right)}}{c^{13}}\right)} + \frac{5 \, {\left(7 \, B b^{3} - 6 \, A b^{2} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{9}{2}}} + \frac{2 \, {\left(B b^{4} - A b^{3} c\right)}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} c + b \sqrt{c}\right)} c^{4}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*x*(4*B*x/c^2 - (11*B*b*c^10 - 6*A*c^11)/c^13) + 3*(19*B*b^2*c^9 - 14*A*b*c^10)/c^13) + 5/16*(7*B*b^3 - 6*A*b^2*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2) + 2*(B*b^4 - A*b^3*c)/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*c + b*sqrt(c))*c^4)","A",0
121,1,135,0,0.305194," ","integrate(x^3*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(\frac{2 \, B x}{c^{2}} - \frac{7 \, B b c^{5} - 4 \, A c^{6}}{c^{8}}\right)} - \frac{3 \, {\left(5 \, B b^{2} - 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{7}{2}}} - \frac{2 \, {\left(B b^{3} - A b^{2} c\right)}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} c + b \sqrt{c}\right)} c^{3}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*B*x/c^2 - (7*B*b*c^5 - 4*A*c^6)/c^8) - 3/8*(5*B*b^2 - 4*A*b*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2) - 2*(B*b^3 - A*b^2*c)/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*c + b*sqrt(c))*c^3)","A",0
122,1,106,0,0.278162," ","integrate(x^2*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x} B}{c^{2}} + \frac{{\left(3 \, B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}} + \frac{2 \, {\left(B b^{2} - A b c\right)}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} c + b \sqrt{c}\right)} c^{2}}"," ",0,"sqrt(c*x^2 + b*x)*B/c^2 + 1/2*(3*B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2) + 2*(B*b^2 - A*b*c)/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*c + b*sqrt(c))*c^2)","A",0
123,-2,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{1,[1]%%%},[2,2]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3]%%%}+%%%{1,[0,4]%%%} / %%%{%%%{1,[2]%%%},[2,0]%%%}+%%%{%%{[%%%{-2,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1]%%%},[0,2]%%%} Error: Bad Argument Value","F(-2)",0
124,1,33,0,0.218747," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{A}{b} - \frac{{\left(B b - 2 \, A c\right)} x}{b^{2}}\right)}}{\sqrt{c x^{2} + b x}}"," ",0,"-2*(A/b - (B*b - 2*A*c)*x/b^2)/sqrt(c*x^2 + b*x)","A",0
125,0,0,0,0.000000," ","integrate((B*x+A)/x/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(3/2)*x), x)","F",0
126,0,0,0,0.000000," ","integrate((B*x+A)/x^2/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(3/2)*x^2), x)","F",0
127,0,0,0,0.000000," ","integrate((B*x+A)/x^3/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(3/2)*x^3), x)","F",0
128,0,0,0,0.000000," ","integrate((B*x+A)/x^4/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(3/2)*x^4), x)","F",0
129,1,253,0,0.493492," ","integrate(x^5*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(\frac{2 \, B x}{c^{3}} - \frac{11 \, B b c^{7} - 4 \, A c^{8}}{c^{11}}\right)} - \frac{5 \, {\left(7 \, B b^{2} - 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{9}{2}}} - \frac{2 \, {\left(12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c^{\frac{3}{2}} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{\frac{5}{2}} + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} c - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c^{2} + 10 \, B b^{5} \sqrt{c} - 7 \, A b^{4} c^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b\right)}^{3} c^{5}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*B*x/c^3 - (11*B*b*c^7 - 4*A*c^8)/c^11) - 5/8*(7*B*b^2 - 4*A*b*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2) - 2/3*(12*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c^(3/2) - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^(5/2) + 21*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*c - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c^2 + 10*B*b^5*sqrt(c) - 7*A*b^4*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b)^3*c^5)","A",0
130,1,224,0,0.287836," ","integrate(x^4*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x} B}{c^{3}} + \frac{{\left(5 \, B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{7}{2}}} + \frac{2 \, {\left(9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c^{\frac{3}{2}} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{\frac{5}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} c - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{2} + 7 \, B b^{4} \sqrt{c} - 4 \, A b^{3} c^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b\right)}^{3} c^{4}}"," ",0,"sqrt(c*x^2 + b*x)*B/c^3 + 1/2*(5*B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2) + 2/3*(9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c^(3/2) - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^(5/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*c - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^2 + 7*B*b^4*sqrt(c) - 4*A*b^3*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b)^3*c^4)","A",0
131,-2,0,0,0.000000," ","integrate(x^3*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{1,[2]%%%},[4,4]%%%}+%%%{%%{[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,5]%%%}+%%%{%%%{6,[1]%%%},[2,6]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7]%%%}+%%%{1,[0,8]%%%} / %%%{%%%{1,[4]%%%},[4,0]%%%}+%%%{%%{[%%%{-4,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1]%%%}+%%%{%%%{6,[3]%%%},[2,2]%%%}+%%%{%%{[%%%{-4,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3]%%%}+%%%{%%%{1,[2]%%%},[0,4]%%%} Error: Bad Argument Value","F(-2)",0
132,1,119,0,0.231001," ","integrate(x^2*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B c + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b \sqrt{c} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A c^{\frac{3}{2}} + B b^{2} + 2 \, A b c\right)}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b\right)}^{3} c^{\frac{3}{2}}}"," ",0,"2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*c + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b*sqrt(c) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*c^(3/2) + B*b^2 + 2*A*b*c)/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b)^3*c^(3/2))","B",0
133,0,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} x}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*x/(c*x^2 + b*x)^(5/2), x)","F",0
134,1,82,0,0.243187," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(4 \, x {\left(\frac{2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x}{b^{4}} + \frac{3 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)}}{b^{4}}\right)} + \frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)}}{b^{4}}\right)} x + \frac{A}{b}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((4*x*(2*(B*b*c^2 - 2*A*c^3)*x/b^4 + 3*(B*b^2*c - 2*A*b*c^2)/b^4) + 3*(B*b^3 - 2*A*b^2*c)/b^4)*x + A/b)/(c*x^2 + b*x)^(3/2)","A",0
135,0,0,0,0.000000," ","integrate((B*x+A)/x/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(5/2)*x), x)","F",0
136,0,0,0,0.000000," ","integrate((B*x+A)/x^2/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(5/2)*x^2), x)","F",0
137,0,0,0,0.000000," ","integrate((B*x+A)/x^3/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(5/2)*x^3), x)","F",0
138,1,147,0,0.233425," ","integrate((e*x+d)/(c*x^2+b*x)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(8 \, {\left(2 \, {\left(4 \, x {\left(\frac{2 \, {\left(2 \, c^{5} d - b c^{4} e\right)} x}{b^{6}} + \frac{5 \, {\left(2 \, b c^{4} d - b^{2} c^{3} e\right)}}{b^{6}}\right)} + \frac{15 \, {\left(2 \, b^{2} c^{3} d - b^{3} c^{2} e\right)}}{b^{6}}\right)} x + \frac{5 \, {\left(2 \, b^{3} c^{2} d - b^{4} c e\right)}}{b^{6}}\right)} x - \frac{5 \, {\left(2 \, b^{4} c d - b^{5} e\right)}}{b^{6}}\right)} x + \frac{3 \, d}{b}\right)}}{15 \, {\left(c x^{2} + b x\right)}^{\frac{5}{2}}}"," ",0,"-2/15*((8*(2*(4*x*(2*(2*c^5*d - b*c^4*e)*x/b^6 + 5*(2*b*c^4*d - b^2*c^3*e)/b^6) + 15*(2*b^2*c^3*d - b^3*c^2*e)/b^6)*x + 5*(2*b^3*c^2*d - b^4*c*e)/b^6)*x - 5*(2*b^4*c*d - b^5*e)/b^6)*x + 3*d/b)/(c*x^2 + b*x)^(5/2)","A",0
139,1,205,0,0.332370," ","integrate((e*x+d)/(c*x^2+b*x)^(9/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, x {\left(\frac{2 \, {\left(2 \, c^{7} d - b c^{6} e\right)} x}{b^{8}} + \frac{7 \, {\left(2 \, b c^{6} d - b^{2} c^{5} e\right)}}{b^{8}}\right)} + \frac{35 \, {\left(2 \, b^{2} c^{5} d - b^{3} c^{4} e\right)}}{b^{8}}\right)} x + \frac{35 \, {\left(2 \, b^{3} c^{4} d - b^{4} c^{3} e\right)}}{b^{8}}\right)} x + \frac{35 \, {\left(2 \, b^{4} c^{3} d - b^{5} c^{2} e\right)}}{b^{8}}\right)} x - \frac{7 \, {\left(2 \, b^{5} c^{2} d - b^{6} c e\right)}}{b^{8}}\right)} x + \frac{7 \, {\left(2 \, b^{6} c d - b^{7} e\right)}}{b^{8}}\right)} x - \frac{5 \, d}{b}\right)}}{35 \, {\left(c x^{2} + b x\right)}^{\frac{7}{2}}}"," ",0,"2/35*((4*(2*(8*(2*(4*x*(2*(2*c^7*d - b*c^6*e)*x/b^8 + 7*(2*b*c^6*d - b^2*c^5*e)/b^8) + 35*(2*b^2*c^5*d - b^3*c^4*e)/b^8)*x + 35*(2*b^3*c^4*d - b^4*c^3*e)/b^8)*x + 35*(2*b^4*c^3*d - b^5*c^2*e)/b^8)*x - 7*(2*b^5*c^2*d - b^6*c*e)/b^8)*x + 7*(2*b^6*c*d - b^7*e)/b^8)*x - 5*d/b)/(c*x^2 + b*x)^(7/2)","A",0
140,1,29,0,0.219727," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{15} \, B c x^{\frac{15}{2}} + \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{13} \, A c x^{\frac{13}{2}} + \frac{2}{11} \, A b x^{\frac{11}{2}}"," ",0,"2/15*B*c*x^(15/2) + 2/13*B*b*x^(13/2) + 2/13*A*c*x^(13/2) + 2/11*A*b*x^(11/2)","A",0
141,1,29,0,0.194763," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{13} \, B c x^{\frac{13}{2}} + \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{11} \, A c x^{\frac{11}{2}} + \frac{2}{9} \, A b x^{\frac{9}{2}}"," ",0,"2/13*B*c*x^(13/2) + 2/11*B*b*x^(11/2) + 2/11*A*c*x^(11/2) + 2/9*A*b*x^(9/2)","A",0
142,1,29,0,0.153726," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{11} \, B c x^{\frac{11}{2}} + \frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{9} \, A c x^{\frac{9}{2}} + \frac{2}{7} \, A b x^{\frac{7}{2}}"," ",0,"2/11*B*c*x^(11/2) + 2/9*B*b*x^(9/2) + 2/9*A*c*x^(9/2) + 2/7*A*b*x^(7/2)","A",0
143,1,29,0,0.146562," ","integrate((B*x+A)*(c*x^2+b*x)*x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{7} \, A c x^{\frac{7}{2}} + \frac{2}{5} \, A b x^{\frac{5}{2}}"," ",0,"2/9*B*c*x^(9/2) + 2/7*B*b*x^(7/2) + 2/7*A*c*x^(7/2) + 2/5*A*b*x^(5/2)","A",0
144,1,29,0,0.148814," ","integrate((B*x+A)*(c*x^2+b*x)/x^(1/2),x, algorithm=""giac"")","\frac{2}{7} \, B c x^{\frac{7}{2}} + \frac{2}{5} \, B b x^{\frac{5}{2}} + \frac{2}{5} \, A c x^{\frac{5}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}}"," ",0,"2/7*B*c*x^(7/2) + 2/5*B*b*x^(5/2) + 2/5*A*c*x^(5/2) + 2/3*A*b*x^(3/2)","A",0
145,1,29,0,0.173667," ","integrate((B*x+A)*(c*x^2+b*x)/x^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, B c x^{\frac{5}{2}} + \frac{2}{3} \, B b x^{\frac{3}{2}} + \frac{2}{3} \, A c x^{\frac{3}{2}} + 2 \, A b \sqrt{x}"," ",0,"2/5*B*c*x^(5/2) + 2/3*B*b*x^(3/2) + 2/3*A*c*x^(3/2) + 2*A*b*sqrt(x)","A",0
146,1,29,0,0.148239," ","integrate((B*x+A)*(c*x^2+b*x)/x^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, B c x^{\frac{3}{2}} + 2 \, B b \sqrt{x} + 2 \, A c \sqrt{x} - \frac{2 \, A b}{\sqrt{x}}"," ",0,"2/3*B*c*x^(3/2) + 2*B*b*sqrt(x) + 2*A*c*sqrt(x) - 2*A*b/sqrt(x)","A",0
147,1,27,0,0.150619," ","integrate((B*x+A)*(c*x^2+b*x)/x^(7/2),x, algorithm=""giac"")","2 \, B c \sqrt{x} - \frac{2 \, {\left(3 \, B b x + 3 \, A c x + A b\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2*B*c*sqrt(x) - 2/3*(3*B*b*x + 3*A*c*x + A*b)/x^(3/2)","A",0
148,1,27,0,0.148103," ","integrate((B*x+A)*(c*x^2+b*x)/x^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, B c x^{2} + 5 \, B b x + 5 \, A c x + 3 \, A b\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*B*c*x^2 + 5*B*b*x + 5*A*c*x + 3*A*b)/x^(5/2)","A",0
149,1,53,0,0.151579," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{19} \, B c^{2} x^{\frac{19}{2}} + \frac{4}{17} \, B b c x^{\frac{17}{2}} + \frac{2}{17} \, A c^{2} x^{\frac{17}{2}} + \frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{4}{15} \, A b c x^{\frac{15}{2}} + \frac{2}{13} \, A b^{2} x^{\frac{13}{2}}"," ",0,"2/19*B*c^2*x^(19/2) + 4/17*B*b*c*x^(17/2) + 2/17*A*c^2*x^(17/2) + 2/15*B*b^2*x^(15/2) + 4/15*A*b*c*x^(15/2) + 2/13*A*b^2*x^(13/2)","A",0
150,1,53,0,0.159626," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{17} \, B c^{2} x^{\frac{17}{2}} + \frac{4}{15} \, B b c x^{\frac{15}{2}} + \frac{2}{15} \, A c^{2} x^{\frac{15}{2}} + \frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{4}{13} \, A b c x^{\frac{13}{2}} + \frac{2}{11} \, A b^{2} x^{\frac{11}{2}}"," ",0,"2/17*B*c^2*x^(17/2) + 4/15*B*b*c*x^(15/2) + 2/15*A*c^2*x^(15/2) + 2/13*B*b^2*x^(13/2) + 4/13*A*b*c*x^(13/2) + 2/11*A*b^2*x^(11/2)","A",0
151,1,53,0,0.150668," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{15} \, B c^{2} x^{\frac{15}{2}} + \frac{4}{13} \, B b c x^{\frac{13}{2}} + \frac{2}{13} \, A c^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B b^{2} x^{\frac{11}{2}} + \frac{4}{11} \, A b c x^{\frac{11}{2}} + \frac{2}{9} \, A b^{2} x^{\frac{9}{2}}"," ",0,"2/15*B*c^2*x^(15/2) + 4/13*B*b*c*x^(13/2) + 2/13*A*c^2*x^(13/2) + 2/11*B*b^2*x^(11/2) + 4/11*A*b*c*x^(11/2) + 2/9*A*b^2*x^(9/2)","A",0
152,1,53,0,0.153515," ","integrate((B*x+A)*(c*x^2+b*x)^2*x^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, B c^{2} x^{\frac{13}{2}} + \frac{4}{11} \, B b c x^{\frac{11}{2}} + \frac{2}{11} \, A c^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B b^{2} x^{\frac{9}{2}} + \frac{4}{9} \, A b c x^{\frac{9}{2}} + \frac{2}{7} \, A b^{2} x^{\frac{7}{2}}"," ",0,"2/13*B*c^2*x^(13/2) + 4/11*B*b*c*x^(11/2) + 2/11*A*c^2*x^(11/2) + 2/9*B*b^2*x^(9/2) + 4/9*A*b*c*x^(9/2) + 2/7*A*b^2*x^(7/2)","A",0
153,1,53,0,0.155070," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, B c^{2} x^{\frac{11}{2}} + \frac{4}{9} \, B b c x^{\frac{9}{2}} + \frac{2}{9} \, A c^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B b^{2} x^{\frac{7}{2}} + \frac{4}{7} \, A b c x^{\frac{7}{2}} + \frac{2}{5} \, A b^{2} x^{\frac{5}{2}}"," ",0,"2/11*B*c^2*x^(11/2) + 4/9*B*b*c*x^(9/2) + 2/9*A*c^2*x^(9/2) + 2/7*B*b^2*x^(7/2) + 4/7*A*b*c*x^(7/2) + 2/5*A*b^2*x^(5/2)","A",0
154,1,53,0,0.191716," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{9} \, B c^{2} x^{\frac{9}{2}} + \frac{4}{7} \, B b c x^{\frac{7}{2}} + \frac{2}{7} \, A c^{2} x^{\frac{7}{2}} + \frac{2}{5} \, B b^{2} x^{\frac{5}{2}} + \frac{4}{5} \, A b c x^{\frac{5}{2}} + \frac{2}{3} \, A b^{2} x^{\frac{3}{2}}"," ",0,"2/9*B*c^2*x^(9/2) + 4/7*B*b*c*x^(7/2) + 2/7*A*c^2*x^(7/2) + 2/5*B*b^2*x^(5/2) + 4/5*A*b*c*x^(5/2) + 2/3*A*b^2*x^(3/2)","A",0
155,1,53,0,0.151449," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, B c^{2} x^{\frac{7}{2}} + \frac{4}{5} \, B b c x^{\frac{5}{2}} + \frac{2}{5} \, A c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B b^{2} x^{\frac{3}{2}} + \frac{4}{3} \, A b c x^{\frac{3}{2}} + 2 \, A b^{2} \sqrt{x}"," ",0,"2/7*B*c^2*x^(7/2) + 4/5*B*b*c*x^(5/2) + 2/5*A*c^2*x^(5/2) + 2/3*B*b^2*x^(3/2) + 4/3*A*b*c*x^(3/2) + 2*A*b^2*sqrt(x)","A",0
156,1,53,0,0.164462," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{5} \, B c^{2} x^{\frac{5}{2}} + \frac{4}{3} \, B b c x^{\frac{3}{2}} + \frac{2}{3} \, A c^{2} x^{\frac{3}{2}} + 2 \, B b^{2} \sqrt{x} + 4 \, A b c \sqrt{x} - \frac{2 \, A b^{2}}{\sqrt{x}}"," ",0,"2/5*B*c^2*x^(5/2) + 4/3*B*b*c*x^(3/2) + 2/3*A*c^2*x^(3/2) + 2*B*b^2*sqrt(x) + 4*A*b*c*sqrt(x) - 2*A*b^2/sqrt(x)","A",0
157,1,51,0,0.196492," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(9/2),x, algorithm=""giac"")","\frac{2}{3} \, B c^{2} x^{\frac{3}{2}} + 4 \, B b c \sqrt{x} + 2 \, A c^{2} \sqrt{x} - \frac{2 \, {\left(3 \, B b^{2} x + 6 \, A b c x + A b^{2}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*B*c^2*x^(3/2) + 4*B*b*c*sqrt(x) + 2*A*c^2*sqrt(x) - 2/3*(3*B*b^2*x + 6*A*b*c*x + A*b^2)/x^(3/2)","A",0
158,1,77,0,0.155171," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2}{23} \, B c^{3} x^{\frac{23}{2}} + \frac{2}{7} \, B b c^{2} x^{\frac{21}{2}} + \frac{2}{21} \, A c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B b^{2} c x^{\frac{19}{2}} + \frac{6}{19} \, A b c^{2} x^{\frac{19}{2}} + \frac{2}{17} \, B b^{3} x^{\frac{17}{2}} + \frac{6}{17} \, A b^{2} c x^{\frac{17}{2}} + \frac{2}{15} \, A b^{3} x^{\frac{15}{2}}"," ",0,"2/23*B*c^3*x^(23/2) + 2/7*B*b*c^2*x^(21/2) + 2/21*A*c^3*x^(21/2) + 6/19*B*b^2*c*x^(19/2) + 6/19*A*b*c^2*x^(19/2) + 2/17*B*b^3*x^(17/2) + 6/17*A*b^2*c*x^(17/2) + 2/15*A*b^3*x^(15/2)","A",0
159,1,77,0,0.151773," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2}{21} \, B c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B b c^{2} x^{\frac{19}{2}} + \frac{2}{19} \, A c^{3} x^{\frac{19}{2}} + \frac{6}{17} \, B b^{2} c x^{\frac{17}{2}} + \frac{6}{17} \, A b c^{2} x^{\frac{17}{2}} + \frac{2}{15} \, B b^{3} x^{\frac{15}{2}} + \frac{2}{5} \, A b^{2} c x^{\frac{15}{2}} + \frac{2}{13} \, A b^{3} x^{\frac{13}{2}}"," ",0,"2/21*B*c^3*x^(21/2) + 6/19*B*b*c^2*x^(19/2) + 2/19*A*c^3*x^(19/2) + 6/17*B*b^2*c*x^(17/2) + 6/17*A*b*c^2*x^(17/2) + 2/15*B*b^3*x^(15/2) + 2/5*A*b^2*c*x^(15/2) + 2/13*A*b^3*x^(13/2)","A",0
160,1,77,0,0.155429," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2}{19} \, B c^{3} x^{\frac{19}{2}} + \frac{6}{17} \, B b c^{2} x^{\frac{17}{2}} + \frac{2}{17} \, A c^{3} x^{\frac{17}{2}} + \frac{2}{5} \, B b^{2} c x^{\frac{15}{2}} + \frac{2}{5} \, A b c^{2} x^{\frac{15}{2}} + \frac{2}{13} \, B b^{3} x^{\frac{13}{2}} + \frac{6}{13} \, A b^{2} c x^{\frac{13}{2}} + \frac{2}{11} \, A b^{3} x^{\frac{11}{2}}"," ",0,"2/19*B*c^3*x^(19/2) + 6/17*B*b*c^2*x^(17/2) + 2/17*A*c^3*x^(17/2) + 2/5*B*b^2*c*x^(15/2) + 2/5*A*b*c^2*x^(15/2) + 2/13*B*b^3*x^(13/2) + 6/13*A*b^2*c*x^(13/2) + 2/11*A*b^3*x^(11/2)","A",0
161,1,77,0,0.164421," ","integrate((B*x+A)*(c*x^2+b*x)^3*x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, B c^{3} x^{\frac{17}{2}} + \frac{2}{5} \, B b c^{2} x^{\frac{15}{2}} + \frac{2}{15} \, A c^{3} x^{\frac{15}{2}} + \frac{6}{13} \, B b^{2} c x^{\frac{13}{2}} + \frac{6}{13} \, A b c^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B b^{3} x^{\frac{11}{2}} + \frac{6}{11} \, A b^{2} c x^{\frac{11}{2}} + \frac{2}{9} \, A b^{3} x^{\frac{9}{2}}"," ",0,"2/17*B*c^3*x^(17/2) + 2/5*B*b*c^2*x^(15/2) + 2/15*A*c^3*x^(15/2) + 6/13*B*b^2*c*x^(13/2) + 6/13*A*b*c^2*x^(13/2) + 2/11*B*b^3*x^(11/2) + 6/11*A*b^2*c*x^(11/2) + 2/9*A*b^3*x^(9/2)","A",0
162,1,77,0,0.173481," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, B c^{3} x^{\frac{15}{2}} + \frac{6}{13} \, B b c^{2} x^{\frac{13}{2}} + \frac{2}{13} \, A c^{3} x^{\frac{13}{2}} + \frac{6}{11} \, B b^{2} c x^{\frac{11}{2}} + \frac{6}{11} \, A b c^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B b^{3} x^{\frac{9}{2}} + \frac{2}{3} \, A b^{2} c x^{\frac{9}{2}} + \frac{2}{7} \, A b^{3} x^{\frac{7}{2}}"," ",0,"2/15*B*c^3*x^(15/2) + 6/13*B*b*c^2*x^(13/2) + 2/13*A*c^3*x^(13/2) + 6/11*B*b^2*c*x^(11/2) + 6/11*A*b*c^2*x^(11/2) + 2/9*B*b^3*x^(9/2) + 2/3*A*b^2*c*x^(9/2) + 2/7*A*b^3*x^(7/2)","A",0
163,1,77,0,0.153794," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{13} \, B c^{3} x^{\frac{13}{2}} + \frac{6}{11} \, B b c^{2} x^{\frac{11}{2}} + \frac{2}{11} \, A c^{3} x^{\frac{11}{2}} + \frac{2}{3} \, B b^{2} c x^{\frac{9}{2}} + \frac{2}{3} \, A b c^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B b^{3} x^{\frac{7}{2}} + \frac{6}{7} \, A b^{2} c x^{\frac{7}{2}} + \frac{2}{5} \, A b^{3} x^{\frac{5}{2}}"," ",0,"2/13*B*c^3*x^(13/2) + 6/11*B*b*c^2*x^(11/2) + 2/11*A*c^3*x^(11/2) + 2/3*B*b^2*c*x^(9/2) + 2/3*A*b*c^2*x^(9/2) + 2/7*B*b^3*x^(7/2) + 6/7*A*b^2*c*x^(7/2) + 2/5*A*b^3*x^(5/2)","A",0
164,1,77,0,0.151943," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{11} \, B c^{3} x^{\frac{11}{2}} + \frac{2}{3} \, B b c^{2} x^{\frac{9}{2}} + \frac{2}{9} \, A c^{3} x^{\frac{9}{2}} + \frac{6}{7} \, B b^{2} c x^{\frac{7}{2}} + \frac{6}{7} \, A b c^{2} x^{\frac{7}{2}} + \frac{2}{5} \, B b^{3} x^{\frac{5}{2}} + \frac{6}{5} \, A b^{2} c x^{\frac{5}{2}} + \frac{2}{3} \, A b^{3} x^{\frac{3}{2}}"," ",0,"2/11*B*c^3*x^(11/2) + 2/3*B*b*c^2*x^(9/2) + 2/9*A*c^3*x^(9/2) + 6/7*B*b^2*c*x^(7/2) + 6/7*A*b*c^2*x^(7/2) + 2/5*B*b^3*x^(5/2) + 6/5*A*b^2*c*x^(5/2) + 2/3*A*b^3*x^(3/2)","A",0
165,1,77,0,0.156040," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{9} \, B c^{3} x^{\frac{9}{2}} + \frac{6}{7} \, B b c^{2} x^{\frac{7}{2}} + \frac{2}{7} \, A c^{3} x^{\frac{7}{2}} + \frac{6}{5} \, B b^{2} c x^{\frac{5}{2}} + \frac{6}{5} \, A b c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B b^{3} x^{\frac{3}{2}} + 2 \, A b^{2} c x^{\frac{3}{2}} + 2 \, A b^{3} \sqrt{x}"," ",0,"2/9*B*c^3*x^(9/2) + 6/7*B*b*c^2*x^(7/2) + 2/7*A*c^3*x^(7/2) + 6/5*B*b^2*c*x^(5/2) + 6/5*A*b*c^2*x^(5/2) + 2/3*B*b^3*x^(3/2) + 2*A*b^2*c*x^(3/2) + 2*A*b^3*sqrt(x)","A",0
166,1,77,0,0.154472," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(9/2),x, algorithm=""giac"")","\frac{2}{7} \, B c^{3} x^{\frac{7}{2}} + \frac{6}{5} \, B b c^{2} x^{\frac{5}{2}} + \frac{2}{5} \, A c^{3} x^{\frac{5}{2}} + 2 \, B b^{2} c x^{\frac{3}{2}} + 2 \, A b c^{2} x^{\frac{3}{2}} + 2 \, B b^{3} \sqrt{x} + 6 \, A b^{2} c \sqrt{x} - \frac{2 \, A b^{3}}{\sqrt{x}}"," ",0,"2/7*B*c^3*x^(7/2) + 6/5*B*b*c^2*x^(5/2) + 2/5*A*c^3*x^(5/2) + 2*B*b^2*c*x^(3/2) + 2*A*b*c^2*x^(3/2) + 2*B*b^3*sqrt(x) + 6*A*b^2*c*sqrt(x) - 2*A*b^3/sqrt(x)","A",0
167,1,75,0,0.155955," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(11/2),x, algorithm=""giac"")","\frac{2}{5} \, B c^{3} x^{\frac{5}{2}} + 2 \, B b c^{2} x^{\frac{3}{2}} + \frac{2}{3} \, A c^{3} x^{\frac{3}{2}} + 6 \, B b^{2} c \sqrt{x} + 6 \, A b c^{2} \sqrt{x} - \frac{2 \, {\left(3 \, B b^{3} x + 9 \, A b^{2} c x + A b^{3}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/5*B*c^3*x^(5/2) + 2*B*b*c^2*x^(3/2) + 2/3*A*c^3*x^(3/2) + 6*B*b^2*c*sqrt(x) + 6*A*b*c^2*sqrt(x) - 2/3*(3*B*b^3*x + 9*A*b^2*c*x + A*b^3)/x^(3/2)","A",0
168,1,115,0,0.192922," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b^{4} - A b^{3} c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} c^{4}} + \frac{2 \, {\left(15 \, B c^{6} x^{\frac{7}{2}} - 21 \, B b c^{5} x^{\frac{5}{2}} + 21 \, A c^{6} x^{\frac{5}{2}} + 35 \, B b^{2} c^{4} x^{\frac{3}{2}} - 35 \, A b c^{5} x^{\frac{3}{2}} - 105 \, B b^{3} c^{3} \sqrt{x} + 105 \, A b^{2} c^{4} \sqrt{x}\right)}}{105 \, c^{7}}"," ",0,"2*(B*b^4 - A*b^3*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^4) + 2/105*(15*B*c^6*x^(7/2) - 21*B*b*c^5*x^(5/2) + 21*A*c^6*x^(5/2) + 35*B*b^2*c^4*x^(3/2) - 35*A*b*c^5*x^(3/2) - 105*B*b^3*c^3*sqrt(x) + 105*A*b^2*c^4*sqrt(x))/c^7","A",0
169,1,91,0,0.168425," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, {\left(B b^{3} - A b^{2} c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} c^{3}} + \frac{2 \, {\left(3 \, B c^{4} x^{\frac{5}{2}} - 5 \, B b c^{3} x^{\frac{3}{2}} + 5 \, A c^{4} x^{\frac{3}{2}} + 15 \, B b^{2} c^{2} \sqrt{x} - 15 \, A b c^{3} \sqrt{x}\right)}}{15 \, c^{5}}"," ",0,"-2*(B*b^3 - A*b^2*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^3) + 2/15*(3*B*c^4*x^(5/2) - 5*B*b*c^3*x^(3/2) + 5*A*c^4*x^(3/2) + 15*B*b^2*c^2*sqrt(x) - 15*A*b*c^3*sqrt(x))/c^5","A",0
170,1,64,0,0.157176," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b^{2} - A b c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} c^{2}} + \frac{2 \, {\left(B c^{2} x^{\frac{3}{2}} - 3 \, B b c \sqrt{x} + 3 \, A c^{2} \sqrt{x}\right)}}{3 \, c^{3}}"," ",0,"2*(B*b^2 - A*b*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^2) + 2/3*(B*c^2*x^(3/2) - 3*B*b*c*sqrt(x) + 3*A*c^2*sqrt(x))/c^3","A",0
171,1,39,0,0.178047," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{c} - \frac{2 \, {\left(B b - A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} c}"," ",0,"2*B*sqrt(x)/c - 2*(B*b - A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c)","A",0
172,1,39,0,0.151232," ","integrate((B*x+A)/(c*x^2+b*x)/x^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(B b - A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b} - \frac{2 \, A}{b \sqrt{x}}"," ",0,"2*(B*b - A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b) - 2*A/(b*sqrt(x))","A",0
173,1,55,0,0.163479," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, {\left(B b c - A c^{2}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{2}} - \frac{2 \, {\left(3 \, B b x - 3 \, A c x + A b\right)}}{3 \, b^{2} x^{\frac{3}{2}}}"," ",0,"-2*(B*b*c - A*c^2)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^2) - 2/3*(3*B*b*x - 3*A*c*x + A*b)/(b^2*x^(3/2))","A",0
174,1,80,0,0.155989," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b c^{2} - A c^{3}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{3}} + \frac{2 \, {\left(15 \, B b c x^{2} - 15 \, A c^{2} x^{2} - 5 \, B b^{2} x + 5 \, A b c x - 3 \, A b^{2}\right)}}{15 \, b^{3} x^{\frac{5}{2}}}"," ",0,"2*(B*b*c^2 - A*c^3)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^3) + 2/15*(15*B*b*c*x^2 - 15*A*c^2*x^2 - 5*B*b^2*x + 5*A*b*c*x - 3*A*b^2)/(b^3*x^(5/2))","A",0
175,1,104,0,0.160218," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, {\left(B b c^{3} - A c^{4}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{4}} - \frac{2 \, {\left(105 \, B b c^{2} x^{3} - 105 \, A c^{3} x^{3} - 35 \, B b^{2} c x^{2} + 35 \, A b c^{2} x^{2} + 21 \, B b^{3} x - 21 \, A b^{2} c x + 15 \, A b^{3}\right)}}{105 \, b^{4} x^{\frac{7}{2}}}"," ",0,"-2*(B*b*c^3 - A*c^4)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^4) - 2/105*(105*B*b*c^2*x^3 - 105*A*c^3*x^3 - 35*B*b^2*c*x^2 + 35*A*b*c^2*x^2 + 21*B*b^3*x - 21*A*b^2*c*x + 15*A*b^3)/(b^4*x^(7/2))","A",0
176,1,128,0,0.161927," ","integrate((B*x+A)/x^(9/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b c^{4} - A c^{5}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{5}} + \frac{2 \, {\left(315 \, B b c^{3} x^{4} - 315 \, A c^{4} x^{4} - 105 \, B b^{2} c^{2} x^{3} + 105 \, A b c^{3} x^{3} + 63 \, B b^{3} c x^{2} - 63 \, A b^{2} c^{2} x^{2} - 45 \, B b^{4} x + 45 \, A b^{3} c x - 35 \, A b^{4}\right)}}{315 \, b^{5} x^{\frac{9}{2}}}"," ",0,"2*(B*b*c^4 - A*c^5)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^5) + 2/315*(315*B*b*c^3*x^4 - 315*A*c^4*x^4 - 105*B*b^2*c^2*x^3 + 105*A*b*c^3*x^3 + 63*B*b^3*c*x^2 - 63*A*b^2*c^2*x^2 - 45*B*b^4*x + 45*A*b^3*c*x - 35*A*b^4)/(b^5*x^(9/2))","A",0
177,1,122,0,0.164662," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, B b^{3} - 5 \, A b^{2} c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} c^{4}} + \frac{B b^{3} \sqrt{x} - A b^{2} c \sqrt{x}}{{\left(c x + b\right)} c^{4}} + \frac{2 \, {\left(3 \, B c^{8} x^{\frac{5}{2}} - 10 \, B b c^{7} x^{\frac{3}{2}} + 5 \, A c^{8} x^{\frac{3}{2}} + 45 \, B b^{2} c^{6} \sqrt{x} - 30 \, A b c^{7} \sqrt{x}\right)}}{15 \, c^{10}}"," ",0,"-(7*B*b^3 - 5*A*b^2*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^4) + (B*b^3*sqrt(x) - A*b^2*c*sqrt(x))/((c*x + b)*c^4) + 2/15*(3*B*c^8*x^(5/2) - 10*B*b*c^7*x^(3/2) + 5*A*c^8*x^(3/2) + 45*B*b^2*c^6*sqrt(x) - 30*A*b*c^7*sqrt(x))/c^10","A",0
178,1,95,0,0.159821," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(5 \, B b^{2} - 3 \, A b c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} c^{3}} - \frac{B b^{2} \sqrt{x} - A b c \sqrt{x}}{{\left(c x + b\right)} c^{3}} + \frac{2 \, {\left(B c^{4} x^{\frac{3}{2}} - 6 \, B b c^{3} \sqrt{x} + 3 \, A c^{4} \sqrt{x}\right)}}{3 \, c^{6}}"," ",0,"(5*B*b^2 - 3*A*b*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^3) - (B*b^2*sqrt(x) - A*b*c*sqrt(x))/((c*x + b)*c^3) + 2/3*(B*c^4*x^(3/2) - 6*B*b*c^3*sqrt(x) + 3*A*c^4*sqrt(x))/c^6","A",0
179,1,65,0,0.155221," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{c^{2}} - \frac{{\left(3 \, B b - A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} c^{2}} + \frac{B b \sqrt{x} - A c \sqrt{x}}{{\left(c x + b\right)} c^{2}}"," ",0,"2*B*sqrt(x)/c^2 - (3*B*b - A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^2) + (B*b*sqrt(x) - A*c*sqrt(x))/((c*x + b)*c^2)","A",0
180,1,60,0,0.161793," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(B b + A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b c} - \frac{B b \sqrt{x} - A c \sqrt{x}}{{\left(c x + b\right)} b c}"," ",0,"(B*b + A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b*c) - (B*b*sqrt(x) - A*c*sqrt(x))/((c*x + b)*b*c)","A",0
181,1,60,0,0.167309," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(B b - 3 \, A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{2}} + \frac{B b x - 3 \, A c x - 2 \, A b}{{\left(c x^{\frac{3}{2}} + b \sqrt{x}\right)} b^{2}}"," ",0,"(B*b - 3*A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^2) + (B*b*x - 3*A*c*x - 2*A*b)/((c*x^(3/2) + b*sqrt(x))*b^2)","A",0
182,1,85,0,0.259929," ","integrate((B*x+A)/(c*x^2+b*x)^2/x^(1/2),x, algorithm=""giac"")","-\frac{{\left(3 \, B b c - 5 \, A c^{2}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{3}} - \frac{B b c \sqrt{x} - A c^{2} \sqrt{x}}{{\left(c x + b\right)} b^{3}} - \frac{2 \, {\left(3 \, B b x - 6 \, A c x + A b\right)}}{3 \, b^{3} x^{\frac{3}{2}}}"," ",0,"-(3*B*b*c - 5*A*c^2)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^3) - (B*b*c*sqrt(x) - A*c^2*sqrt(x))/((c*x + b)*b^3) - 2/3*(3*B*b*x - 6*A*c*x + A*b)/(b^3*x^(3/2))","A",0
183,1,110,0,0.164547," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{4}} + \frac{B b c^{2} \sqrt{x} - A c^{3} \sqrt{x}}{{\left(c x + b\right)} b^{4}} + \frac{2 \, {\left(30 \, B b c x^{2} - 45 \, A c^{2} x^{2} - 5 \, B b^{2} x + 10 \, A b c x - 3 \, A b^{2}\right)}}{15 \, b^{4} x^{\frac{5}{2}}}"," ",0,"(5*B*b*c^2 - 7*A*c^3)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^4) + (B*b*c^2*sqrt(x) - A*c^3*sqrt(x))/((c*x + b)*b^4) + 2/15*(30*B*b*c*x^2 - 45*A*c^2*x^2 - 5*B*b^2*x + 10*A*b*c*x - 3*A*b^2)/(b^4*x^(5/2))","A",0
184,1,136,0,0.164493," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, B b c^{3} - 9 \, A c^{4}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{\sqrt{b c} b^{5}} - \frac{B b c^{3} \sqrt{x} - A c^{4} \sqrt{x}}{{\left(c x + b\right)} b^{5}} - \frac{2 \, {\left(315 \, B b c^{2} x^{3} - 420 \, A c^{3} x^{3} - 70 \, B b^{2} c x^{2} + 105 \, A b c^{2} x^{2} + 21 \, B b^{3} x - 42 \, A b^{2} c x + 15 \, A b^{3}\right)}}{105 \, b^{5} x^{\frac{7}{2}}}"," ",0,"-(7*B*b*c^3 - 9*A*c^4)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^5) - (B*b*c^3*sqrt(x) - A*c^4*sqrt(x))/((c*x + b)*b^5) - 2/105*(315*B*b*c^2*x^3 - 420*A*c^3*x^3 - 70*B*b^2*c*x^2 + 105*A*b*c^2*x^2 + 21*B*b^3*x - 42*A*b^2*c*x + 15*A*b^3)/(b^5*x^(7/2))","A",0
185,1,146,0,0.214688," ","integrate(x^(13/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{7 \, {\left(9 \, B b^{3} - 5 \, A b^{2} c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} c^{5}} + \frac{17 \, B b^{3} c x^{\frac{3}{2}} - 13 \, A b^{2} c^{2} x^{\frac{3}{2}} + 15 \, B b^{4} \sqrt{x} - 11 \, A b^{3} c \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} c^{5}} + \frac{2 \, {\left(3 \, B c^{12} x^{\frac{5}{2}} - 15 \, B b c^{11} x^{\frac{3}{2}} + 5 \, A c^{12} x^{\frac{3}{2}} + 90 \, B b^{2} c^{10} \sqrt{x} - 45 \, A b c^{11} \sqrt{x}\right)}}{15 \, c^{15}}"," ",0,"-7/4*(9*B*b^3 - 5*A*b^2*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^5) + 1/4*(17*B*b^3*c*x^(3/2) - 13*A*b^2*c^2*x^(3/2) + 15*B*b^4*sqrt(x) - 11*A*b^3*c*sqrt(x))/((c*x + b)^2*c^5) + 2/15*(3*B*c^12*x^(5/2) - 15*B*b*c^11*x^(3/2) + 5*A*c^12*x^(3/2) + 90*B*b^2*c^10*sqrt(x) - 45*A*b*c^11*sqrt(x))/c^15","A",0
186,1,119,0,0.183650," ","integrate(x^(11/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{5 \, {\left(7 \, B b^{2} - 3 \, A b c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} c^{4}} - \frac{13 \, B b^{2} c x^{\frac{3}{2}} - 9 \, A b c^{2} x^{\frac{3}{2}} + 11 \, B b^{3} \sqrt{x} - 7 \, A b^{2} c \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} c^{4}} + \frac{2 \, {\left(B c^{6} x^{\frac{3}{2}} - 9 \, B b c^{5} \sqrt{x} + 3 \, A c^{6} \sqrt{x}\right)}}{3 \, c^{9}}"," ",0,"5/4*(7*B*b^2 - 3*A*b*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^4) - 1/4*(13*B*b^2*c*x^(3/2) - 9*A*b*c^2*x^(3/2) + 11*B*b^3*sqrt(x) - 7*A*b^2*c*sqrt(x))/((c*x + b)^2*c^4) + 2/3*(B*c^6*x^(3/2) - 9*B*b*c^5*sqrt(x) + 3*A*c^6*sqrt(x))/c^9","A",0
187,1,87,0,0.160080," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{c^{3}} - \frac{3 \, {\left(5 \, B b - A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} c^{3}} + \frac{9 \, B b c x^{\frac{3}{2}} - 5 \, A c^{2} x^{\frac{3}{2}} + 7 \, B b^{2} \sqrt{x} - 3 \, A b c \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} c^{3}}"," ",0,"2*B*sqrt(x)/c^3 - 3/4*(5*B*b - A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*c^3) + 1/4*(9*B*b*c*x^(3/2) - 5*A*c^2*x^(3/2) + 7*B*b^2*sqrt(x) - 3*A*b*c*sqrt(x))/((c*x + b)^2*c^3)","A",0
188,1,82,0,0.158982," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(3 \, B b + A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} b c^{2}} - \frac{5 \, B b c x^{\frac{3}{2}} - A c^{2} x^{\frac{3}{2}} + 3 \, B b^{2} \sqrt{x} + A b c \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} b c^{2}}"," ",0,"1/4*(3*B*b + A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b*c^2) - 1/4*(5*B*b*c*x^(3/2) - A*c^2*x^(3/2) + 3*B*b^2*sqrt(x) + A*b*c*sqrt(x))/((c*x + b)^2*b*c^2)","A",0
189,1,82,0,0.159091," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(B b + 3 \, A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} b^{2} c} + \frac{B b c x^{\frac{3}{2}} + 3 \, A c^{2} x^{\frac{3}{2}} - B b^{2} \sqrt{x} + 5 \, A b c \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} b^{2} c}"," ",0,"1/4*(B*b + 3*A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^2*c) + 1/4*(B*b*c*x^(3/2) + 3*A*c^2*x^(3/2) - B*b^2*sqrt(x) + 5*A*b*c*sqrt(x))/((c*x + b)^2*b^2*c)","A",0
190,1,86,0,0.204512," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(B b - 5 \, A c\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} b^{3}} - \frac{2 \, A}{b^{3} \sqrt{x}} + \frac{3 \, B b c x^{\frac{3}{2}} - 7 \, A c^{2} x^{\frac{3}{2}} + 5 \, B b^{2} \sqrt{x} - 9 \, A b c \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} b^{3}}"," ",0,"3/4*(B*b - 5*A*c)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^3) - 2*A/(b^3*sqrt(x)) + 1/4*(3*B*b*c*x^(3/2) - 7*A*c^2*x^(3/2) + 5*B*b^2*sqrt(x) - 9*A*b*c*sqrt(x))/((c*x + b)^2*b^3)","A",0
191,1,108,0,0.164818," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(3 \, B b c - 7 \, A c^{2}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} b^{4}} - \frac{2 \, {\left(3 \, B b x - 9 \, A c x + A b\right)}}{3 \, b^{4} x^{\frac{3}{2}}} - \frac{7 \, B b c^{2} x^{\frac{3}{2}} - 11 \, A c^{3} x^{\frac{3}{2}} + 9 \, B b^{2} c \sqrt{x} - 13 \, A b c^{2} \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} b^{4}}"," ",0,"-5/4*(3*B*b*c - 7*A*c^2)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^4) - 2/3*(3*B*b*x - 9*A*c*x + A*b)/(b^4*x^(3/2)) - 1/4*(7*B*b*c^2*x^(3/2) - 11*A*c^3*x^(3/2) + 9*B*b^2*c*sqrt(x) - 13*A*b*c^2*sqrt(x))/((c*x + b)^2*b^4)","A",0
192,1,135,0,0.174742," ","integrate((B*x+A)/(c*x^2+b*x)^3/x^(1/2),x, algorithm=""giac"")","\frac{7 \, {\left(5 \, B b c^{2} - 9 \, A c^{3}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} b^{5}} + \frac{11 \, B b c^{3} x^{\frac{3}{2}} - 15 \, A c^{4} x^{\frac{3}{2}} + 13 \, B b^{2} c^{2} \sqrt{x} - 17 \, A b c^{3} \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} b^{5}} + \frac{2 \, {\left(45 \, B b c x^{2} - 90 \, A c^{2} x^{2} - 5 \, B b^{2} x + 15 \, A b c x - 3 \, A b^{2}\right)}}{15 \, b^{5} x^{\frac{5}{2}}}"," ",0,"7/4*(5*B*b*c^2 - 9*A*c^3)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^5) + 1/4*(11*B*b*c^3*x^(3/2) - 15*A*c^4*x^(3/2) + 13*B*b^2*c^2*sqrt(x) - 17*A*b*c^3*sqrt(x))/((c*x + b)^2*b^5) + 2/15*(45*B*b*c*x^2 - 90*A*c^2*x^2 - 5*B*b^2*x + 15*A*b*c*x - 3*A*b^2)/(b^5*x^(5/2))","A",0
193,1,159,0,0.173701," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{9 \, {\left(7 \, B b c^{3} - 11 \, A c^{4}\right)} \arctan\left(\frac{c \sqrt{x}}{\sqrt{b c}}\right)}{4 \, \sqrt{b c} b^{6}} - \frac{15 \, B b c^{4} x^{\frac{3}{2}} - 19 \, A c^{5} x^{\frac{3}{2}} + 17 \, B b^{2} c^{3} \sqrt{x} - 21 \, A b c^{4} \sqrt{x}}{4 \, {\left(c x + b\right)}^{2} b^{6}} - \frac{2 \, {\left(210 \, B b c^{2} x^{3} - 350 \, A c^{3} x^{3} - 35 \, B b^{2} c x^{2} + 70 \, A b c^{2} x^{2} + 7 \, B b^{3} x - 21 \, A b^{2} c x + 5 \, A b^{3}\right)}}{35 \, b^{6} x^{\frac{7}{2}}}"," ",0,"-9/4*(7*B*b*c^3 - 11*A*c^4)*arctan(c*sqrt(x)/sqrt(b*c))/(sqrt(b*c)*b^6) - 1/4*(15*B*b*c^4*x^(3/2) - 19*A*c^5*x^(3/2) + 17*B*b^2*c^3*sqrt(x) - 21*A*b*c^4*sqrt(x))/((c*x + b)^2*b^6) - 2/35*(210*B*b*c^2*x^3 - 350*A*c^3*x^3 - 35*B*b^2*c*x^2 + 70*A*b*c^2*x^2 + 7*B*b^3*x - 21*A*b^2*c*x + 5*A*b^3)/(b^6*x^(7/2))","A",0
194,1,158,0,0.215336," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2}{9009} \, B {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} - \frac{2}{3465} \, A {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)}"," ",0,"2/9009*B*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) - 2/3465*A*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5)","A",0
195,1,134,0,0.187065," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{2}{3465} \, B {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} + \frac{2}{315} \, A {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)}"," ",0,"-2/3465*B*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) + 2/315*A*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4)","A",0
196,1,110,0,0.192691," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, B {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} - \frac{2}{105} \, A {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)}"," ",0,"2/315*B*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) - 2/105*A*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3)","A",0
197,1,86,0,0.240369," ","integrate((B*x+A)*x^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{2}{105} \, B {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} + \frac{2}{15} \, A {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)}"," ",0,"-2/105*B*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) + 2/15*A*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2)","A",0
198,1,60,0,0.167064," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, B {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)} + \frac{2}{3} \, A {\left(\frac{{\left(c x + b\right)}^{\frac{3}{2}}}{c} - \frac{b^{\frac{3}{2}}}{c}\right)}"," ",0,"2/15*B*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2) + 2/3*A*((c*x + b)^(3/2)/c - b^(3/2)/c)","A",0
199,1,103,0,0.184757," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(3/2),x, algorithm=""giac"")","\frac{2 \, A b \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{2 \, {\left(3 \, A b c \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + B \sqrt{-b} b^{\frac{3}{2}} + 3 \, A \sqrt{-b} \sqrt{b} c\right)}}{3 \, \sqrt{-b} c} + \frac{2 \, {\left({\left(c x + b\right)}^{\frac{3}{2}} B c^{2} + 3 \, \sqrt{c x + b} A c^{3}\right)}}{3 \, c^{3}}"," ",0,"2*A*b*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - 2/3*(3*A*b*c*arctan(sqrt(b)/sqrt(-b)) + B*sqrt(-b)*b^(3/2) + 3*A*sqrt(-b)*sqrt(b)*c)/(sqrt(-b)*c) + 2/3*((c*x + b)^(3/2)*B*c^2 + 3*sqrt(c*x + b)*A*c^3)/c^3","A",0
200,1,61,0,0.277750," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{c x + b} B c - \frac{\sqrt{c x + b} A c}{x} + \frac{{\left(2 \, B b c + A c^{2}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}}}{c}"," ",0,"(2*sqrt(c*x + b)*B*c - sqrt(c*x + b)*A*c/x + (2*B*b*c + A*c^2)*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b))/c","A",0
201,1,110,0,0.274883," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(7/2),x, algorithm=""giac"")","\frac{\frac{{\left(4 \, B b c^{2} - A c^{3}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} - \frac{4 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c^{2} - 4 \, \sqrt{c x + b} B b^{2} c^{2} + {\left(c x + b\right)}^{\frac{3}{2}} A c^{3} + \sqrt{c x + b} A b c^{3}}{b c^{2} x^{2}}}{4 \, c}"," ",0,"1/4*((4*B*b*c^2 - A*c^3)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) - (4*(c*x + b)^(3/2)*B*b*c^2 - 4*sqrt(c*x + b)*B*b^2*c^2 + (c*x + b)^(3/2)*A*c^3 + sqrt(c*x + b)*A*b*c^3)/(b*c^2*x^2))/c","A",0
202,1,128,0,0.273126," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(9/2),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, B b c^{3} - A c^{4}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{6 \, {\left(c x + b\right)}^{\frac{5}{2}} B b c^{3} - 6 \, \sqrt{c x + b} B b^{3} c^{3} - 3 \, {\left(c x + b\right)}^{\frac{5}{2}} A c^{4} + 8 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{4} + 3 \, \sqrt{c x + b} A b^{2} c^{4}}{b^{2} c^{3} x^{3}}}{24 \, c}"," ",0,"-1/24*(3*(2*B*b*c^3 - A*c^4)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (6*(c*x + b)^(5/2)*B*b*c^3 - 6*sqrt(c*x + b)*B*b^3*c^3 - 3*(c*x + b)^(5/2)*A*c^4 + 8*(c*x + b)^(3/2)*A*b*c^4 + 3*sqrt(c*x + b)*A*b^2*c^4)/(b^2*c^3*x^3))/c","A",0
203,1,343,0,0.246204," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2}{45045} \, B c {\left(\frac{1024 \, b^{\frac{15}{2}}}{c^{7}} - \frac{3003 \, {\left(c x + b\right)}^{\frac{15}{2}} - 20790 \, {\left(c x + b\right)}^{\frac{13}{2}} b + 61425 \, {\left(c x + b\right)}^{\frac{11}{2}} b^{2} - 100100 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{3} + 96525 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{4} - 54054 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{5} + 15015 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{6}}{c^{7}}\right)} + \frac{2}{9009} \, B b {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} + \frac{2}{9009} \, A c {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} - \frac{2}{3465} \, A b {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)}"," ",0,"-2/45045*B*c*(1024*b^(15/2)/c^7 - (3003*(c*x + b)^(15/2) - 20790*(c*x + b)^(13/2)*b + 61425*(c*x + b)^(11/2)*b^2 - 100100*(c*x + b)^(9/2)*b^3 + 96525*(c*x + b)^(7/2)*b^4 - 54054*(c*x + b)^(5/2)*b^5 + 15015*(c*x + b)^(3/2)*b^6)/c^7) + 2/9009*B*b*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) + 2/9009*A*c*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) - 2/3465*A*b*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5)","B",0
204,1,295,0,0.287816," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2}{9009} \, B c {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} - \frac{2}{3465} \, B b {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} - \frac{2}{3465} \, A c {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} + \frac{2}{315} \, A b {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)}"," ",0,"2/9009*B*c*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) - 2/3465*B*b*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) - 2/3465*A*c*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) + 2/315*A*b*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4)","B",0
205,1,247,0,0.219988," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)*x^(1/2),x, algorithm=""giac"")","-\frac{2}{3465} \, B c {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} + \frac{2}{315} \, B b {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} + \frac{2}{315} \, A c {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} - \frac{2}{105} \, A b {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)}"," ",0,"-2/3465*B*c*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) + 2/315*B*b*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) + 2/315*A*c*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) - 2/105*A*b*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3)","B",0
206,1,199,0,0.205579," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, B c {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} - \frac{2}{105} \, B b {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} - \frac{2}{105} \, A c {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} + \frac{2}{15} \, A b {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)}"," ",0,"2/315*B*c*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) - 2/105*B*b*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) - 2/105*A*c*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) + 2/15*A*b*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2)","B",0
207,1,149,0,0.189257," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(3/2),x, algorithm=""giac"")","-\frac{2}{105} \, B c {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} + \frac{2}{15} \, B b {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)} + \frac{2}{15} \, A c {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)} + \frac{2}{3} \, A b {\left(\frac{{\left(c x + b\right)}^{\frac{3}{2}}}{c} - \frac{b^{\frac{3}{2}}}{c}\right)}"," ",0,"-2/105*B*c*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) + 2/15*B*b*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2) + 2/15*A*c*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2) + 2/3*A*b*((c*x + b)^(3/2)/c - b^(3/2)/c)","B",0
208,1,123,0,0.199394," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(5/2),x, algorithm=""giac"")","\frac{2 \, A b^{2} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{2 \, {\left(15 \, A b^{2} c \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + 3 \, B \sqrt{-b} b^{\frac{5}{2}} + 20 \, A \sqrt{-b} b^{\frac{3}{2}} c\right)}}{15 \, \sqrt{-b} c} + \frac{2 \, {\left(3 \, {\left(c x + b\right)}^{\frac{5}{2}} B c^{4} + 5 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{5} + 15 \, \sqrt{c x + b} A b c^{5}\right)}}{15 \, c^{5}}"," ",0,"2*A*b^2*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - 2/15*(15*A*b^2*c*arctan(sqrt(b)/sqrt(-b)) + 3*B*sqrt(-b)*b^(5/2) + 20*A*sqrt(-b)*b^(3/2)*c)/(sqrt(-b)*c) + 2/15*(3*(c*x + b)^(5/2)*B*c^4 + 5*(c*x + b)^(3/2)*A*c^5 + 15*sqrt(c*x + b)*A*b*c^5)/c^5","A",0
209,1,93,0,0.268174," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left(c x + b\right)}^{\frac{3}{2}} B c + 6 \, \sqrt{c x + b} B b c + 6 \, \sqrt{c x + b} A c^{2} - \frac{3 \, \sqrt{c x + b} A b c}{x} + \frac{3 \, {\left(2 \, B b^{2} c + 3 \, A b c^{2}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}}}{3 \, c}"," ",0,"1/3*(2*(c*x + b)^(3/2)*B*c + 6*sqrt(c*x + b)*B*b*c + 6*sqrt(c*x + b)*A*c^2 - 3*sqrt(c*x + b)*A*b*c/x + 3*(2*B*b^2*c + 3*A*b*c^2)*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b))/c","A",0
210,1,119,0,0.419410," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(9/2),x, algorithm=""giac"")","\frac{8 \, \sqrt{c x + b} B c^{2} + \frac{3 \, {\left(4 \, B b c^{2} + A c^{3}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{4 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c^{2} - 4 \, \sqrt{c x + b} B b^{2} c^{2} + 5 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{3} - 3 \, \sqrt{c x + b} A b c^{3}}{c^{2} x^{2}}}{4 \, c}"," ",0,"1/4*(8*sqrt(c*x + b)*B*c^2 + 3*(4*B*b*c^2 + A*c^3)*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - (4*(c*x + b)^(3/2)*B*b*c^2 - 4*sqrt(c*x + b)*B*b^2*c^2 + 5*(c*x + b)^(3/2)*A*c^3 - 3*sqrt(c*x + b)*A*b*c^3)/(c^2*x^2))/c","A",0
211,1,145,0,0.321721," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(11/2),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(6 \, B b c^{3} - A c^{4}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} - \frac{30 \, {\left(c x + b\right)}^{\frac{5}{2}} B b c^{3} - 48 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{2} c^{3} + 18 \, \sqrt{c x + b} B b^{3} c^{3} + 3 \, {\left(c x + b\right)}^{\frac{5}{2}} A c^{4} + 8 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{4} - 3 \, \sqrt{c x + b} A b^{2} c^{4}}{b c^{3} x^{3}}}{24 \, c}"," ",0,"1/24*(3*(6*B*b*c^3 - A*c^4)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) - (30*(c*x + b)^(5/2)*B*b*c^3 - 48*(c*x + b)^(3/2)*B*b^2*c^3 + 18*sqrt(c*x + b)*B*b^3*c^3 + 3*(c*x + b)^(5/2)*A*c^4 + 8*(c*x + b)^(3/2)*A*b*c^4 - 3*sqrt(c*x + b)*A*b^2*c^4)/(b*c^3*x^3))/c","A",0
212,1,176,0,0.319687," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(13/2),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, B b c^{4} - 3 \, A c^{5}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{24 \, {\left(c x + b\right)}^{\frac{7}{2}} B b c^{4} + 40 \, {\left(c x + b\right)}^{\frac{5}{2}} B b^{2} c^{4} - 88 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{3} c^{4} + 24 \, \sqrt{c x + b} B b^{4} c^{4} - 9 \, {\left(c x + b\right)}^{\frac{7}{2}} A c^{5} + 33 \, {\left(c x + b\right)}^{\frac{5}{2}} A b c^{5} + 33 \, {\left(c x + b\right)}^{\frac{3}{2}} A b^{2} c^{5} - 9 \, \sqrt{c x + b} A b^{3} c^{5}}{b^{2} c^{4} x^{4}}}{192 \, c}"," ",0,"-1/192*(3*(8*B*b*c^4 - 3*A*c^5)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (24*(c*x + b)^(7/2)*B*b*c^4 + 40*(c*x + b)^(5/2)*B*b^2*c^4 - 88*(c*x + b)^(3/2)*B*b^3*c^4 + 24*sqrt(c*x + b)*B*b^4*c^4 - 9*(c*x + b)^(7/2)*A*c^5 + 33*(c*x + b)^(5/2)*A*b*c^5 + 33*(c*x + b)^(3/2)*A*b^2*c^5 - 9*sqrt(c*x + b)*A*b^3*c^5)/(b^2*c^4*x^4))/c","A",0
213,1,192,0,0.351269," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(15/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(2 \, B b c^{5} - A c^{6}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} + \frac{30 \, {\left(c x + b\right)}^{\frac{9}{2}} B b c^{5} - 140 \, {\left(c x + b\right)}^{\frac{7}{2}} B b^{2} c^{5} + 140 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{4} c^{5} - 30 \, \sqrt{c x + b} B b^{5} c^{5} - 15 \, {\left(c x + b\right)}^{\frac{9}{2}} A c^{6} + 70 \, {\left(c x + b\right)}^{\frac{7}{2}} A b c^{6} - 128 \, {\left(c x + b\right)}^{\frac{5}{2}} A b^{2} c^{6} - 70 \, {\left(c x + b\right)}^{\frac{3}{2}} A b^{3} c^{6} + 15 \, \sqrt{c x + b} A b^{4} c^{6}}{b^{3} c^{5} x^{5}}}{640 \, c}"," ",0,"1/640*(15*(2*B*b*c^5 - A*c^6)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + (30*(c*x + b)^(9/2)*B*b*c^5 - 140*(c*x + b)^(7/2)*B*b^2*c^5 + 140*(c*x + b)^(3/2)*B*b^4*c^5 - 30*sqrt(c*x + b)*B*b^5*c^5 - 15*(c*x + b)^(9/2)*A*c^6 + 70*(c*x + b)^(7/2)*A*b*c^6 - 128*(c*x + b)^(5/2)*A*b^2*c^6 - 70*(c*x + b)^(3/2)*A*b^3*c^6 + 15*sqrt(c*x + b)*A*b^4*c^6)/(b^3*c^5*x^5))/c","A",0
214,1,560,0,0.309156," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2}{109395} \, B c^{2} {\left(\frac{2048 \, b^{\frac{17}{2}}}{c^{8}} + \frac{6435 \, {\left(c x + b\right)}^{\frac{17}{2}} - 51051 \, {\left(c x + b\right)}^{\frac{15}{2}} b + 176715 \, {\left(c x + b\right)}^{\frac{13}{2}} b^{2} - 348075 \, {\left(c x + b\right)}^{\frac{11}{2}} b^{3} + 425425 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{4} - 328185 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{5} + 153153 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{6} - 36465 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{7}}{c^{8}}\right)} - \frac{4}{45045} \, B b c {\left(\frac{1024 \, b^{\frac{15}{2}}}{c^{7}} - \frac{3003 \, {\left(c x + b\right)}^{\frac{15}{2}} - 20790 \, {\left(c x + b\right)}^{\frac{13}{2}} b + 61425 \, {\left(c x + b\right)}^{\frac{11}{2}} b^{2} - 100100 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{3} + 96525 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{4} - 54054 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{5} + 15015 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{6}}{c^{7}}\right)} - \frac{2}{45045} \, A c^{2} {\left(\frac{1024 \, b^{\frac{15}{2}}}{c^{7}} - \frac{3003 \, {\left(c x + b\right)}^{\frac{15}{2}} - 20790 \, {\left(c x + b\right)}^{\frac{13}{2}} b + 61425 \, {\left(c x + b\right)}^{\frac{11}{2}} b^{2} - 100100 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{3} + 96525 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{4} - 54054 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{5} + 15015 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{6}}{c^{7}}\right)} + \frac{2}{9009} \, B b^{2} {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} + \frac{4}{9009} \, A b c {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} - \frac{2}{3465} \, A b^{2} {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)}"," ",0,"2/109395*B*c^2*(2048*b^(17/2)/c^8 + (6435*(c*x + b)^(17/2) - 51051*(c*x + b)^(15/2)*b + 176715*(c*x + b)^(13/2)*b^2 - 348075*(c*x + b)^(11/2)*b^3 + 425425*(c*x + b)^(9/2)*b^4 - 328185*(c*x + b)^(7/2)*b^5 + 153153*(c*x + b)^(5/2)*b^6 - 36465*(c*x + b)^(3/2)*b^7)/c^8) - 4/45045*B*b*c*(1024*b^(15/2)/c^7 - (3003*(c*x + b)^(15/2) - 20790*(c*x + b)^(13/2)*b + 61425*(c*x + b)^(11/2)*b^2 - 100100*(c*x + b)^(9/2)*b^3 + 96525*(c*x + b)^(7/2)*b^4 - 54054*(c*x + b)^(5/2)*b^5 + 15015*(c*x + b)^(3/2)*b^6)/c^7) - 2/45045*A*c^2*(1024*b^(15/2)/c^7 - (3003*(c*x + b)^(15/2) - 20790*(c*x + b)^(13/2)*b + 61425*(c*x + b)^(11/2)*b^2 - 100100*(c*x + b)^(9/2)*b^3 + 96525*(c*x + b)^(7/2)*b^4 - 54054*(c*x + b)^(5/2)*b^5 + 15015*(c*x + b)^(3/2)*b^6)/c^7) + 2/9009*B*b^2*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) + 4/9009*A*b*c*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) - 2/3465*A*b^2*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5)","B",0
215,1,488,0,0.277995," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)*x^(1/2),x, algorithm=""giac"")","-\frac{2}{45045} \, B c^{2} {\left(\frac{1024 \, b^{\frac{15}{2}}}{c^{7}} - \frac{3003 \, {\left(c x + b\right)}^{\frac{15}{2}} - 20790 \, {\left(c x + b\right)}^{\frac{13}{2}} b + 61425 \, {\left(c x + b\right)}^{\frac{11}{2}} b^{2} - 100100 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{3} + 96525 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{4} - 54054 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{5} + 15015 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{6}}{c^{7}}\right)} + \frac{4}{9009} \, B b c {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} + \frac{2}{9009} \, A c^{2} {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} - \frac{2}{3465} \, B b^{2} {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} - \frac{4}{3465} \, A b c {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} + \frac{2}{315} \, A b^{2} {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)}"," ",0,"-2/45045*B*c^2*(1024*b^(15/2)/c^7 - (3003*(c*x + b)^(15/2) - 20790*(c*x + b)^(13/2)*b + 61425*(c*x + b)^(11/2)*b^2 - 100100*(c*x + b)^(9/2)*b^3 + 96525*(c*x + b)^(7/2)*b^4 - 54054*(c*x + b)^(5/2)*b^5 + 15015*(c*x + b)^(3/2)*b^6)/c^7) + 4/9009*B*b*c*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) + 2/9009*A*c^2*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) - 2/3465*B*b^2*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) - 4/3465*A*b*c*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) + 2/315*A*b^2*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4)","B",0
216,1,416,0,0.266860," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{9009} \, B c^{2} {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} - \frac{4}{3465} \, B b c {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} - \frac{2}{3465} \, A c^{2} {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} + \frac{2}{315} \, B b^{2} {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} + \frac{4}{315} \, A b c {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} - \frac{2}{105} \, A b^{2} {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)}"," ",0,"2/9009*B*c^2*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) - 4/3465*B*b*c*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) - 2/3465*A*c^2*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) + 2/315*B*b^2*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) + 4/315*A*b*c*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) - 2/105*A*b^2*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3)","B",0
217,1,344,0,0.275290," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(3/2),x, algorithm=""giac"")","-\frac{2}{3465} \, B c^{2} {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} + \frac{4}{315} \, B b c {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} + \frac{2}{315} \, A c^{2} {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} - \frac{2}{105} \, B b^{2} {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} - \frac{4}{105} \, A b c {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} + \frac{2}{15} \, A b^{2} {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)}"," ",0,"-2/3465*B*c^2*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) + 4/315*B*b*c*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) + 2/315*A*c^2*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) - 2/105*B*b^2*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) - 4/105*A*b*c*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) + 2/15*A*b^2*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2)","B",0
218,1,270,0,0.235540," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(5/2),x, algorithm=""giac"")","\frac{2}{315} \, B c^{2} {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} - \frac{4}{105} \, B b c {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} - \frac{2}{105} \, A c^{2} {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} + \frac{2}{15} \, B b^{2} {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)} + \frac{4}{15} \, A b c {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)} + \frac{2}{3} \, A b^{2} {\left(\frac{{\left(c x + b\right)}^{\frac{3}{2}}}{c} - \frac{b^{\frac{3}{2}}}{c}\right)}"," ",0,"2/315*B*c^2*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) - 4/105*B*b*c*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) - 2/105*A*c^2*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) + 2/15*B*b^2*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2) + 4/15*A*b*c*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2) + 2/3*A*b^2*((c*x + b)^(3/2)/c - b^(3/2)/c)","B",0
219,1,139,0,0.221516," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(7/2),x, algorithm=""giac"")","\frac{2 \, A b^{3} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{2 \, {\left(105 \, A b^{3} c \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + 15 \, B \sqrt{-b} b^{\frac{7}{2}} + 161 \, A \sqrt{-b} b^{\frac{5}{2}} c\right)}}{105 \, \sqrt{-b} c} + \frac{2 \, {\left(15 \, {\left(c x + b\right)}^{\frac{7}{2}} B c^{6} + 21 \, {\left(c x + b\right)}^{\frac{5}{2}} A c^{7} + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{7} + 105 \, \sqrt{c x + b} A b^{2} c^{7}\right)}}{105 \, c^{7}}"," ",0,"2*A*b^3*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - 2/105*(105*A*b^3*c*arctan(sqrt(b)/sqrt(-b)) + 15*B*sqrt(-b)*b^(7/2) + 161*A*sqrt(-b)*b^(5/2)*c)/(sqrt(-b)*c) + 2/105*(15*(c*x + b)^(7/2)*B*c^6 + 21*(c*x + b)^(5/2)*A*c^7 + 35*(c*x + b)^(3/2)*A*b*c^7 + 105*sqrt(c*x + b)*A*b^2*c^7)/c^7","A",0
220,1,125,0,0.347247," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(9/2),x, algorithm=""giac"")","\frac{6 \, {\left(c x + b\right)}^{\frac{5}{2}} B c + 10 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c + 30 \, \sqrt{c x + b} B b^{2} c + 10 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{2} + 60 \, \sqrt{c x + b} A b c^{2} - \frac{15 \, \sqrt{c x + b} A b^{2} c}{x} + \frac{15 \, {\left(2 \, B b^{3} c + 5 \, A b^{2} c^{2}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}}}{15 \, c}"," ",0,"1/15*(6*(c*x + b)^(5/2)*B*c + 10*(c*x + b)^(3/2)*B*b*c + 30*sqrt(c*x + b)*B*b^2*c + 10*(c*x + b)^(3/2)*A*c^2 + 60*sqrt(c*x + b)*A*b*c^2 - 15*sqrt(c*x + b)*A*b^2*c/x + 15*(2*B*b^3*c + 5*A*b^2*c^2)*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b))/c","A",0
221,1,155,0,0.315228," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(11/2),x, algorithm=""giac"")","\frac{8 \, {\left(c x + b\right)}^{\frac{3}{2}} B c^{2} + 48 \, \sqrt{c x + b} B b c^{2} + 24 \, \sqrt{c x + b} A c^{3} + \frac{15 \, {\left(4 \, B b^{2} c^{2} + 3 \, A b c^{3}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{3 \, {\left(4 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{2} c^{2} - 4 \, \sqrt{c x + b} B b^{3} c^{2} + 9 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{3} - 7 \, \sqrt{c x + b} A b^{2} c^{3}\right)}}{c^{2} x^{2}}}{12 \, c}"," ",0,"1/12*(8*(c*x + b)^(3/2)*B*c^2 + 48*sqrt(c*x + b)*B*b*c^2 + 24*sqrt(c*x + b)*A*c^3 + 15*(4*B*b^2*c^2 + 3*A*b*c^3)*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - 3*(4*(c*x + b)^(3/2)*B*b^2*c^2 - 4*sqrt(c*x + b)*B*b^3*c^2 + 9*(c*x + b)^(3/2)*A*b*c^3 - 7*sqrt(c*x + b)*A*b^2*c^3)/(c^2*x^2))/c","A",0
222,1,151,0,0.352447," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(13/2),x, algorithm=""giac"")","\frac{48 \, \sqrt{c x + b} B c^{3} + \frac{15 \, {\left(6 \, B b c^{3} + A c^{4}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{54 \, {\left(c x + b\right)}^{\frac{5}{2}} B b c^{3} - 96 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{2} c^{3} + 42 \, \sqrt{c x + b} B b^{3} c^{3} + 33 \, {\left(c x + b\right)}^{\frac{5}{2}} A c^{4} - 40 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{4} + 15 \, \sqrt{c x + b} A b^{2} c^{4}}{c^{3} x^{3}}}{24 \, c}"," ",0,"1/24*(48*sqrt(c*x + b)*B*c^3 + 15*(6*B*b*c^3 + A*c^4)*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - (54*(c*x + b)^(5/2)*B*b*c^3 - 96*(c*x + b)^(3/2)*B*b^2*c^3 + 42*sqrt(c*x + b)*B*b^3*c^3 + 33*(c*x + b)^(5/2)*A*c^4 - 40*(c*x + b)^(3/2)*A*b*c^4 + 15*sqrt(c*x + b)*A*b^2*c^4)/(c^3*x^3))/c","A",0
223,1,177,0,0.339546," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(15/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(8 \, B b c^{4} - A c^{5}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} - \frac{264 \, {\left(c x + b\right)}^{\frac{7}{2}} B b c^{4} - 584 \, {\left(c x + b\right)}^{\frac{5}{2}} B b^{2} c^{4} + 440 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{3} c^{4} - 120 \, \sqrt{c x + b} B b^{4} c^{4} + 15 \, {\left(c x + b\right)}^{\frac{7}{2}} A c^{5} + 73 \, {\left(c x + b\right)}^{\frac{5}{2}} A b c^{5} - 55 \, {\left(c x + b\right)}^{\frac{3}{2}} A b^{2} c^{5} + 15 \, \sqrt{c x + b} A b^{3} c^{5}}{b c^{4} x^{4}}}{192 \, c}"," ",0,"1/192*(15*(8*B*b*c^4 - A*c^5)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) - (264*(c*x + b)^(7/2)*B*b*c^4 - 584*(c*x + b)^(5/2)*B*b^2*c^4 + 440*(c*x + b)^(3/2)*B*b^3*c^4 - 120*sqrt(c*x + b)*B*b^4*c^4 + 15*(c*x + b)^(7/2)*A*c^5 + 73*(c*x + b)^(5/2)*A*b*c^5 - 55*(c*x + b)^(3/2)*A*b^2*c^5 + 15*sqrt(c*x + b)*A*b^3*c^5)/(b*c^4*x^4))/c","A",0
224,1,208,0,0.440004," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(17/2),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(10 \, B b c^{5} - 3 \, A c^{6}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{150 \, {\left(c x + b\right)}^{\frac{9}{2}} B b c^{5} + 580 \, {\left(c x + b\right)}^{\frac{7}{2}} B b^{2} c^{5} - 1280 \, {\left(c x + b\right)}^{\frac{5}{2}} B b^{3} c^{5} + 700 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{4} c^{5} - 150 \, \sqrt{c x + b} B b^{5} c^{5} - 45 \, {\left(c x + b\right)}^{\frac{9}{2}} A c^{6} + 210 \, {\left(c x + b\right)}^{\frac{7}{2}} A b c^{6} + 384 \, {\left(c x + b\right)}^{\frac{5}{2}} A b^{2} c^{6} - 210 \, {\left(c x + b\right)}^{\frac{3}{2}} A b^{3} c^{6} + 45 \, \sqrt{c x + b} A b^{4} c^{6}}{b^{2} c^{5} x^{5}}}{1920 \, c}"," ",0,"-1/1920*(15*(10*B*b*c^5 - 3*A*c^6)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (150*(c*x + b)^(9/2)*B*b*c^5 + 580*(c*x + b)^(7/2)*B*b^2*c^5 - 1280*(c*x + b)^(5/2)*B*b^3*c^5 + 700*(c*x + b)^(3/2)*B*b^4*c^5 - 150*sqrt(c*x + b)*B*b^5*c^5 - 45*(c*x + b)^(9/2)*A*c^6 + 210*(c*x + b)^(7/2)*A*b*c^6 + 384*(c*x + b)^(5/2)*A*b^2*c^6 - 210*(c*x + b)^(3/2)*A*b^3*c^6 + 45*sqrt(c*x + b)*A*b^4*c^6)/(b^2*c^5*x^5))/c","A",0
225,1,135,0,0.188194," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(B b^{4} - A b^{3} c\right)} \sqrt{c x + b}}{c^{5}} + \frac{2 \, {\left(35 \, {\left(c x + b\right)}^{\frac{9}{2}} B - 180 \, {\left(c x + b\right)}^{\frac{7}{2}} B b + 378 \, {\left(c x + b\right)}^{\frac{5}{2}} B b^{2} - 420 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{3} + 45 \, {\left(c x + b\right)}^{\frac{7}{2}} A c - 189 \, {\left(c x + b\right)}^{\frac{5}{2}} A b c + 315 \, {\left(c x + b\right)}^{\frac{3}{2}} A b^{2} c\right)}}{315 \, c^{5}} - \frac{32 \, {\left(8 \, B b^{\frac{9}{2}} - 9 \, A b^{\frac{7}{2}} c\right)}}{315 \, c^{5}}"," ",0,"2*(B*b^4 - A*b^3*c)*sqrt(c*x + b)/c^5 + 2/315*(35*(c*x + b)^(9/2)*B - 180*(c*x + b)^(7/2)*B*b + 378*(c*x + b)^(5/2)*B*b^2 - 420*(c*x + b)^(3/2)*B*b^3 + 45*(c*x + b)^(7/2)*A*c - 189*(c*x + b)^(5/2)*A*b*c + 315*(c*x + b)^(3/2)*A*b^2*c)/c^5 - 32/315*(8*B*b^(9/2) - 9*A*b^(7/2)*c)/c^5","A",0
226,1,108,0,0.252030," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B b^{3} - A b^{2} c\right)} \sqrt{c x + b}}{c^{4}} + \frac{2 \, {\left(15 \, {\left(c x + b\right)}^{\frac{7}{2}} B - 63 \, {\left(c x + b\right)}^{\frac{5}{2}} B b + 105 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{2} + 21 \, {\left(c x + b\right)}^{\frac{5}{2}} A c - 70 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c\right)}}{105 \, c^{4}} + \frac{16 \, {\left(6 \, B b^{\frac{7}{2}} - 7 \, A b^{\frac{5}{2}} c\right)}}{105 \, c^{4}}"," ",0,"-2*(B*b^3 - A*b^2*c)*sqrt(c*x + b)/c^4 + 2/105*(15*(c*x + b)^(7/2)*B - 63*(c*x + b)^(5/2)*B*b + 105*(c*x + b)^(3/2)*B*b^2 + 21*(c*x + b)^(5/2)*A*c - 70*(c*x + b)^(3/2)*A*b*c)/c^4 + 16/105*(6*B*b^(7/2) - 7*A*b^(5/2)*c)/c^4","A",0
227,1,81,0,0.177916," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(B b^{2} - A b c\right)} \sqrt{c x + b}}{c^{3}} + \frac{2 \, {\left(3 \, {\left(c x + b\right)}^{\frac{5}{2}} B - 10 \, {\left(c x + b\right)}^{\frac{3}{2}} B b + 5 \, {\left(c x + b\right)}^{\frac{3}{2}} A c\right)}}{15 \, c^{3}} - \frac{4 \, {\left(4 \, B b^{\frac{5}{2}} - 5 \, A b^{\frac{3}{2}} c\right)}}{15 \, c^{3}}"," ",0,"2*(B*b^2 - A*b*c)*sqrt(c*x + b)/c^3 + 2/15*(3*(c*x + b)^(5/2)*B - 10*(c*x + b)^(3/2)*B*b + 5*(c*x + b)^(3/2)*A*c)/c^3 - 4/15*(4*B*b^(5/2) - 5*A*b^(3/2)*c)/c^3","A",0
228,1,53,0,0.177159," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(c x + b\right)}^{\frac{3}{2}} B}{3 \, c^{2}} - \frac{2 \, {\left(B b - A c\right)} \sqrt{c x + b}}{c^{2}} + \frac{2 \, {\left(2 \, B b^{\frac{3}{2}} - 3 \, A \sqrt{b} c\right)}}{3 \, c^{2}}"," ",0,"2/3*(c*x + b)^(3/2)*B/c^2 - 2*(B*b - A*c)*sqrt(c*x + b)/c^2 + 2/3*(2*B*b^(3/2) - 3*A*sqrt(b)*c)/c^2","A",0
229,1,103,0,0.206515," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","2 \, {\left(\frac{A \arctan\left(\frac{\sqrt{c x e + b e}}{\sqrt{-b e}}\right) e}{\sqrt{-b e}} + \frac{\sqrt{c x e + b e} B}{c}\right)} e^{\left(-1\right)} - \frac{2 \, {\left(A c \arctan\left(\frac{\sqrt{b} e^{\frac{1}{2}}}{\sqrt{-b e}}\right) e + \sqrt{-b e} B \sqrt{b} e^{\frac{1}{2}}\right)} e^{\left(-1\right)}}{\sqrt{-b e} c}"," ",0,"2*(A*arctan(sqrt(c*x*e + b*e)/sqrt(-b*e))*e/sqrt(-b*e) + sqrt(c*x*e + b*e)*B/c)*e^(-1) - 2*(A*c*arctan(sqrt(b)*e^(1/2)/sqrt(-b*e))*e + sqrt(-b*e)*B*sqrt(b)*e^(1/2))*e^(-1)/(sqrt(-b*e)*c)","A",0
230,1,58,0,0.228655," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{c x + b} A c}{b x} - \frac{{\left(2 \, B b c - A c^{2}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b}}{c}"," ",0,"-(sqrt(c*x + b)*A*c/(b*x) - (2*B*b*c - A*c^2)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b))/c","A",0
231,1,111,0,0.259910," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(4 \, B b c^{2} - 3 \, A c^{3}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{4 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c^{2} - 4 \, \sqrt{c x + b} B b^{2} c^{2} - 3 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{3} + 5 \, \sqrt{c x + b} A b c^{3}}{b^{2} c^{2} x^{2}}}{4 \, c}"," ",0,"-1/4*((4*B*b*c^2 - 3*A*c^3)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (4*(c*x + b)^(3/2)*B*b*c^2 - 4*sqrt(c*x + b)*B*b^2*c^2 - 3*(c*x + b)^(3/2)*A*c^3 + 5*sqrt(c*x + b)*A*b*c^3)/(b^2*c^2*x^2))/c","A",0
232,1,144,0,0.280879," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(6 \, B b c^{3} - 5 \, A c^{4}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} + \frac{18 \, {\left(c x + b\right)}^{\frac{5}{2}} B b c^{3} - 48 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{2} c^{3} + 30 \, \sqrt{c x + b} B b^{3} c^{3} - 15 \, {\left(c x + b\right)}^{\frac{5}{2}} A c^{4} + 40 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{4} - 33 \, \sqrt{c x + b} A b^{2} c^{4}}{b^{3} c^{3} x^{3}}}{24 \, c}"," ",0,"1/24*(3*(6*B*b*c^3 - 5*A*c^4)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + (18*(c*x + b)^(5/2)*B*b*c^3 - 48*(c*x + b)^(3/2)*B*b^2*c^3 + 30*sqrt(c*x + b)*B*b^3*c^3 - 15*(c*x + b)^(5/2)*A*c^4 + 40*(c*x + b)^(3/2)*A*b*c^4 - 33*sqrt(c*x + b)*A*b^2*c^4)/(b^3*c^3*x^3))/c","A",0
233,1,156,0,0.213156," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B b^{4} - A b^{3} c\right)}}{\sqrt{c x + b} c^{5}} + \frac{32 \, {\left(8 \, B b^{4} - 7 \, A b^{3} c\right)}}{35 \, \sqrt{b} c^{5}} + \frac{2 \, {\left(5 \, {\left(c x + b\right)}^{\frac{7}{2}} B c^{30} - 28 \, {\left(c x + b\right)}^{\frac{5}{2}} B b c^{30} + 70 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{2} c^{30} - 140 \, \sqrt{c x + b} B b^{3} c^{30} + 7 \, {\left(c x + b\right)}^{\frac{5}{2}} A c^{31} - 35 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{31} + 105 \, \sqrt{c x + b} A b^{2} c^{31}\right)}}{35 \, c^{35}}"," ",0,"-2*(B*b^4 - A*b^3*c)/(sqrt(c*x + b)*c^5) + 32/35*(8*B*b^4 - 7*A*b^3*c)/(sqrt(b)*c^5) + 2/35*(5*(c*x + b)^(7/2)*B*c^30 - 28*(c*x + b)^(5/2)*B*b*c^30 + 70*(c*x + b)^(3/2)*B*b^2*c^30 - 140*sqrt(c*x + b)*B*b^3*c^30 + 7*(c*x + b)^(5/2)*A*c^31 - 35*(c*x + b)^(3/2)*A*b*c^31 + 105*sqrt(c*x + b)*A*b^2*c^31)/c^35","A",0
234,1,124,0,0.191754," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(B b^{3} - A b^{2} c\right)}}{\sqrt{c x + b} c^{4}} - \frac{16 \, {\left(6 \, B b^{3} - 5 \, A b^{2} c\right)}}{15 \, \sqrt{b} c^{4}} + \frac{2 \, {\left(3 \, {\left(c x + b\right)}^{\frac{5}{2}} B c^{16} - 15 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c^{16} + 45 \, \sqrt{c x + b} B b^{2} c^{16} + 5 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{17} - 30 \, \sqrt{c x + b} A b c^{17}\right)}}{15 \, c^{20}}"," ",0,"2*(B*b^3 - A*b^2*c)/(sqrt(c*x + b)*c^4) - 16/15*(6*B*b^3 - 5*A*b^2*c)/(sqrt(b)*c^4) + 2/15*(3*(c*x + b)^(5/2)*B*c^16 - 15*(c*x + b)^(3/2)*B*b*c^16 + 45*sqrt(c*x + b)*B*b^2*c^16 + 5*(c*x + b)^(3/2)*A*c^17 - 30*sqrt(c*x + b)*A*b*c^17)/c^20","A",0
235,1,89,0,0.190728," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B b^{2} - A b c\right)}}{\sqrt{c x + b} c^{3}} + \frac{4 \, {\left(4 \, B b^{2} - 3 \, A b c\right)}}{3 \, \sqrt{b} c^{3}} + \frac{2 \, {\left({\left(c x + b\right)}^{\frac{3}{2}} B c^{6} - 6 \, \sqrt{c x + b} B b c^{6} + 3 \, \sqrt{c x + b} A c^{7}\right)}}{3 \, c^{9}}"," ",0,"-2*(B*b^2 - A*b*c)/(sqrt(c*x + b)*c^3) + 4/3*(4*B*b^2 - 3*A*b*c)/(sqrt(b)*c^3) + 2/3*((c*x + b)^(3/2)*B*c^6 - 6*sqrt(c*x + b)*B*b*c^6 + 3*sqrt(c*x + b)*A*c^7)/c^9","A",0
236,1,51,0,0.201654," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{c x + b} B}{c^{2}} + \frac{2 \, {\left(B b - A c\right)}}{\sqrt{c x + b} c^{2}} - \frac{2 \, {\left(2 \, B b - A c\right)}}{\sqrt{b} c^{2}}"," ",0,"2*sqrt(c*x + b)*B/c^2 + 2*(B*b - A*c)/(sqrt(c*x + b)*c^2) - 2*(2*B*b - A*c)/(sqrt(b)*c^2)","A",0
237,1,96,0,0.208766," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, A \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} - \frac{2 \, {\left(B b - A c\right)}}{\sqrt{c x + b} b c} - \frac{2 \, {\left(A \sqrt{b} c \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) - B \sqrt{-b} b + A \sqrt{-b} c\right)}}{\sqrt{-b} b^{\frac{3}{2}} c}"," ",0,"2*A*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) - 2*(B*b - A*c)/(sqrt(c*x + b)*b*c) - 2*(A*sqrt(b)*c*arctan(sqrt(b)/sqrt(-b)) - B*sqrt(-b)*b + A*sqrt(-b)*c)/(sqrt(-b)*b^(3/2)*c)","A",0
238,1,87,0,0.239627," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2)/x^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, B b - 3 \, A c\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{2 \, {\left(c x + b\right)} B b - 2 \, B b^{2} - 3 \, {\left(c x + b\right)} A c + 2 \, A b c}{{\left({\left(c x + b\right)}^{\frac{3}{2}} - \sqrt{c x + b} b\right)} b^{2}}"," ",0,"(2*B*b - 3*A*c)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (2*(c*x + b)*B*b - 2*B*b^2 - 3*(c*x + b)*A*c + 2*A*b*c)/(((c*x + b)^(3/2) - sqrt(c*x + b)*b)*b^2)","A",0
239,1,125,0,0.280797," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, B b c - 5 \, A c^{2}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{4 \, \sqrt{-b} b^{3}} - \frac{2 \, {\left(B b c - A c^{2}\right)}}{\sqrt{c x + b} b^{3}} - \frac{4 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c - 4 \, \sqrt{c x + b} B b^{2} c - 7 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{2} + 9 \, \sqrt{c x + b} A b c^{2}}{4 \, b^{3} c^{2} x^{2}}"," ",0,"-3/4*(4*B*b*c - 5*A*c^2)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) - 2*(B*b*c - A*c^2)/(sqrt(c*x + b)*b^3) - 1/4*(4*(c*x + b)^(3/2)*B*b*c - 4*sqrt(c*x + b)*B*b^2*c - 7*(c*x + b)^(3/2)*A*c^2 + 9*sqrt(c*x + b)*A*b*c^2)/(b^3*c^2*x^2)","A",0
240,1,165,0,0.327955," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{5 \, {\left(6 \, B b c^{2} - 7 \, A c^{3}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{8 \, \sqrt{-b} b^{4}} + \frac{2 \, {\left(B b c^{2} - A c^{3}\right)}}{\sqrt{c x + b} b^{4}} + \frac{42 \, {\left(c x + b\right)}^{\frac{5}{2}} B b c^{2} - 96 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{2} c^{2} + 54 \, \sqrt{c x + b} B b^{3} c^{2} - 57 \, {\left(c x + b\right)}^{\frac{5}{2}} A c^{3} + 136 \, {\left(c x + b\right)}^{\frac{3}{2}} A b c^{3} - 87 \, \sqrt{c x + b} A b^{2} c^{3}}{24 \, b^{4} c^{3} x^{3}}"," ",0,"5/8*(6*B*b*c^2 - 7*A*c^3)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^4) + 2*(B*b*c^2 - A*c^3)/(sqrt(c*x + b)*b^4) + 1/24*(42*(c*x + b)^(5/2)*B*b*c^2 - 96*(c*x + b)^(3/2)*B*b^2*c^2 + 54*sqrt(c*x + b)*B*b^3*c^2 - 57*(c*x + b)^(5/2)*A*c^3 + 136*(c*x + b)^(3/2)*A*b*c^3 - 87*sqrt(c*x + b)*A*b^2*c^3)/(b^4*c^3*x^3)","A",0
241,1,197,0,0.343304," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{35 \, {\left(8 \, B b c^{3} - 9 \, A c^{4}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{64 \, \sqrt{-b} b^{5}} - \frac{2 \, {\left(B b c^{3} - A c^{4}\right)}}{\sqrt{c x + b} b^{5}} - \frac{456 \, {\left(c x + b\right)}^{\frac{7}{2}} B b c^{3} - 1544 \, {\left(c x + b\right)}^{\frac{5}{2}} B b^{2} c^{3} + 1784 \, {\left(c x + b\right)}^{\frac{3}{2}} B b^{3} c^{3} - 696 \, \sqrt{c x + b} B b^{4} c^{3} - 561 \, {\left(c x + b\right)}^{\frac{7}{2}} A c^{4} + 1929 \, {\left(c x + b\right)}^{\frac{5}{2}} A b c^{4} - 2295 \, {\left(c x + b\right)}^{\frac{3}{2}} A b^{2} c^{4} + 975 \, \sqrt{c x + b} A b^{3} c^{4}}{192 \, b^{5} c^{4} x^{4}}"," ",0,"-35/64*(8*B*b*c^3 - 9*A*c^4)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^5) - 2*(B*b*c^3 - A*c^4)/(sqrt(c*x + b)*b^5) - 1/192*(456*(c*x + b)^(7/2)*B*b*c^3 - 1544*(c*x + b)^(5/2)*B*b^2*c^3 + 1784*(c*x + b)^(3/2)*B*b^3*c^3 - 696*sqrt(c*x + b)*B*b^4*c^3 - 561*(c*x + b)^(7/2)*A*c^4 + 1929*(c*x + b)^(5/2)*A*b*c^4 - 2295*(c*x + b)^(3/2)*A*b^2*c^4 + 975*sqrt(c*x + b)*A*b^3*c^4)/(b^5*c^4*x^4)","A",0
242,1,147,0,0.206249," ","integrate(x^(11/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{32 \, {\left(8 \, B b^{3} - 5 \, A b^{2} c\right)}}{15 \, \sqrt{b} c^{5}} + \frac{2 \, {\left(12 \, {\left(c x + b\right)} B b^{3} - B b^{4} - 9 \, {\left(c x + b\right)} A b^{2} c + A b^{3} c\right)}}{3 \, {\left(c x + b\right)}^{\frac{3}{2}} c^{5}} + \frac{2 \, {\left(3 \, {\left(c x + b\right)}^{\frac{5}{2}} B c^{20} - 20 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c^{20} + 90 \, \sqrt{c x + b} B b^{2} c^{20} + 5 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{21} - 45 \, \sqrt{c x + b} A b c^{21}\right)}}{15 \, c^{25}}"," ",0,"-32/15*(8*B*b^3 - 5*A*b^2*c)/(sqrt(b)*c^5) + 2/3*(12*(c*x + b)*B*b^3 - B*b^4 - 9*(c*x + b)*A*b^2*c + A*b^3*c)/((c*x + b)^(3/2)*c^5) + 2/15*(3*(c*x + b)^(5/2)*B*c^20 - 20*(c*x + b)^(3/2)*B*b*c^20 + 90*sqrt(c*x + b)*B*b^2*c^20 + 5*(c*x + b)^(3/2)*A*c^21 - 45*sqrt(c*x + b)*A*b*c^21)/c^25","A",0
243,1,112,0,0.197907," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{16 \, {\left(2 \, B b^{2} - A b c\right)}}{3 \, \sqrt{b} c^{4}} - \frac{2 \, {\left(9 \, {\left(c x + b\right)} B b^{2} - B b^{3} - 6 \, {\left(c x + b\right)} A b c + A b^{2} c\right)}}{3 \, {\left(c x + b\right)}^{\frac{3}{2}} c^{4}} + \frac{2 \, {\left({\left(c x + b\right)}^{\frac{3}{2}} B c^{8} - 9 \, \sqrt{c x + b} B b c^{8} + 3 \, \sqrt{c x + b} A c^{9}\right)}}{3 \, c^{12}}"," ",0,"16/3*(2*B*b^2 - A*b*c)/(sqrt(b)*c^4) - 2/3*(9*(c*x + b)*B*b^2 - B*b^3 - 6*(c*x + b)*A*b*c + A*b^2*c)/((c*x + b)^(3/2)*c^4) + 2/3*((c*x + b)^(3/2)*B*c^8 - 9*sqrt(c*x + b)*B*b*c^8 + 3*sqrt(c*x + b)*A*c^9)/c^12","A",0
244,1,72,0,0.220745," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{c x + b} B}{c^{3}} - \frac{4 \, {\left(4 \, B b - A c\right)}}{3 \, \sqrt{b} c^{3}} + \frac{2 \, {\left(6 \, {\left(c x + b\right)} B b - B b^{2} - 3 \, {\left(c x + b\right)} A c + A b c\right)}}{3 \, {\left(c x + b\right)}^{\frac{3}{2}} c^{3}}"," ",0,"2*sqrt(c*x + b)*B/c^3 - 4/3*(4*B*b - A*c)/(sqrt(b)*c^3) + 2/3*(6*(c*x + b)*B*b - B*b^2 - 3*(c*x + b)*A*c + A*b*c)/((c*x + b)^(3/2)*c^3)","A",0
245,1,45,0,0.194661," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, {\left(c x + b\right)} B - B b + A c\right)}}{3 \, {\left(c x + b\right)}^{\frac{3}{2}} c^{2}} + \frac{2 \, {\left(2 \, B b + A c\right)}}{3 \, b^{\frac{3}{2}} c^{2}}"," ",0,"-2/3*(3*(c*x + b)*B - B*b + A*c)/((c*x + b)^(3/2)*c^2) + 2/3*(2*B*b + A*c)/(b^(3/2)*c^2)","A",0
246,1,110,0,0.288859," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, A \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} - \frac{2 \, {\left(3 \, A \sqrt{b} c \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) - B \sqrt{-b} b + 4 \, A \sqrt{-b} c\right)}}{3 \, \sqrt{-b} b^{\frac{5}{2}} c} - \frac{2 \, {\left(B b^{2} - 3 \, {\left(c x + b\right)} A c - A b c\right)}}{3 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2} c}"," ",0,"2*A*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) - 2/3*(3*A*sqrt(b)*c*arctan(sqrt(b)/sqrt(-b)) - B*sqrt(-b)*b + 4*A*sqrt(-b)*c)/(sqrt(-b)*b^(5/2)*c) - 2/3*(B*b^2 - 3*(c*x + b)*A*c - A*b*c)/((c*x + b)^(3/2)*b^2*c)","A",0
247,1,90,0,0.295295," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{{\left(2 \, B b - 5 \, A c\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} - \frac{\sqrt{c x + b} A}{b^{3} x} + \frac{2 \, {\left(3 \, {\left(c x + b\right)} B b + B b^{2} - 6 \, {\left(c x + b\right)} A c - A b c\right)}}{3 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}"," ",0,"(2*B*b - 5*A*c)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) - sqrt(c*x + b)*A/(b^3*x) + 2/3*(3*(c*x + b)*B*b + B*b^2 - 6*(c*x + b)*A*c - A*b*c)/((c*x + b)^(3/2)*b^3)","A",0
248,1,149,0,0.303765," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2)/x^(1/2),x, algorithm=""giac"")","-\frac{5 \, {\left(4 \, B b c - 7 \, A c^{2}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{4 \, \sqrt{-b} b^{4}} - \frac{2 \, {\left(6 \, {\left(c x + b\right)} B b c + B b^{2} c - 9 \, {\left(c x + b\right)} A c^{2} - A b c^{2}\right)}}{3 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}} - \frac{4 \, {\left(c x + b\right)}^{\frac{3}{2}} B b c - 4 \, \sqrt{c x + b} B b^{2} c - 11 \, {\left(c x + b\right)}^{\frac{3}{2}} A c^{2} + 13 \, \sqrt{c x + b} A b c^{2}}{4 \, b^{4} c^{2} x^{2}}"," ",0,"-5/4*(4*B*b*c - 7*A*c^2)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^4) - 2/3*(6*(c*x + b)*B*b*c + B*b^2*c - 9*(c*x + b)*A*c^2 - A*b*c^2)/((c*x + b)^(3/2)*b^4) - 1/4*(4*(c*x + b)^(3/2)*B*b*c - 4*sqrt(c*x + b)*B*b^2*c - 11*(c*x + b)^(3/2)*A*c^2 + 13*sqrt(c*x + b)*A*b*c^2)/(b^4*c^2*x^2)","A",0
249,1,200,0,0.306325," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{35 \, {\left(2 \, B b c^{2} - 3 \, A c^{3}\right)} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{8 \, \sqrt{-b} b^{5}} + \frac{210 \, {\left(c x + b\right)}^{4} B b c^{2} - 560 \, {\left(c x + b\right)}^{3} B b^{2} c^{2} + 462 \, {\left(c x + b\right)}^{2} B b^{3} c^{2} - 96 \, {\left(c x + b\right)} B b^{4} c^{2} - 16 \, B b^{5} c^{2} - 315 \, {\left(c x + b\right)}^{4} A c^{3} + 840 \, {\left(c x + b\right)}^{3} A b c^{3} - 693 \, {\left(c x + b\right)}^{2} A b^{2} c^{3} + 144 \, {\left(c x + b\right)} A b^{3} c^{3} + 16 \, A b^{4} c^{3}}{24 \, {\left({\left(c x + b\right)}^{\frac{3}{2}} - \sqrt{c x + b} b\right)}^{3} b^{5}}"," ",0,"35/8*(2*B*b*c^2 - 3*A*c^3)*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^5) + 1/24*(210*(c*x + b)^4*B*b*c^2 - 560*(c*x + b)^3*B*b^2*c^2 + 462*(c*x + b)^2*B*b^3*c^2 - 96*(c*x + b)*B*b^4*c^2 - 16*B*b^5*c^2 - 315*(c*x + b)^4*A*c^3 + 840*(c*x + b)^3*A*b*c^3 - 693*(c*x + b)^2*A*b^2*c^3 + 144*(c*x + b)*A*b^3*c^3 + 16*A*b^4*c^3)/(((c*x + b)^(3/2) - sqrt(c*x + b)*b)^3*b^5)","A",0
250,1,49,0,0.265647," ","integrate(x^(1+p)*(3*c*x+2*b)*(c*x^2+b*x)^p,x, algorithm=""giac"")","\frac{c x^{2} e^{\left(p \log\left(c x + b\right) + 2 \, p \log\left(x\right) + \log\left(x\right)\right)} + b x e^{\left(p \log\left(c x + b\right) + 2 \, p \log\left(x\right) + \log\left(x\right)\right)}}{p + 1}"," ",0,"(c*x^2*e^(p*log(c*x + b) + 2*p*log(x) + log(x)) + b*x*e^(p*log(c*x + b) + 2*p*log(x) + log(x)))/(p + 1)","B",0
251,1,29,0,0.162382," ","integrate(x^3*(B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{7} \, B c x^{7} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{4} \, A a x^{4}"," ",0,"1/7*B*c*x^7 + 1/6*A*c*x^6 + 1/5*B*a*x^5 + 1/4*A*a*x^4","A",0
252,1,29,0,0.165585," ","integrate(x^2*(B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{6} \, B c x^{6} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{3} \, A a x^{3}"," ",0,"1/6*B*c*x^6 + 1/5*A*c*x^5 + 1/4*B*a*x^4 + 1/3*A*a*x^3","A",0
253,1,29,0,0.140334," ","integrate(x*(B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{5} \, B c x^{5} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{2} \, A a x^{2}"," ",0,"1/5*B*c*x^5 + 1/4*A*c*x^4 + 1/3*B*a*x^3 + 1/2*A*a*x^2","A",0
254,1,26,0,0.167913," ","integrate((B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{4} \, B c x^{4} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + A a x"," ",0,"1/4*B*c*x^4 + 1/3*A*c*x^3 + 1/2*B*a*x^2 + A*a*x","A",0
255,1,25,0,0.173880," ","integrate((B*x+A)*(c*x^2+a)/x,x, algorithm=""giac"")","\frac{1}{3} \, B c x^{3} + \frac{1}{2} \, A c x^{2} + B a x + A a \log\left({\left| x \right|}\right)"," ",0,"1/3*B*c*x^3 + 1/2*A*c*x^2 + B*a*x + A*a*log(abs(x))","A",0
256,1,25,0,0.163794," ","integrate((B*x+A)*(c*x^2+a)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, B c x^{2} + A c x + B a \log\left({\left| x \right|}\right) - \frac{A a}{x}"," ",0,"1/2*B*c*x^2 + A*c*x + B*a*log(abs(x)) - A*a/x","A",0
257,1,25,0,0.146922," ","integrate((B*x+A)*(c*x^2+a)/x^3,x, algorithm=""giac"")","B c x + A c \log\left({\left| x \right|}\right) - \frac{2 \, B a x + A a}{2 \, x^{2}}"," ",0,"B*c*x + A*c*log(abs(x)) - 1/2*(2*B*a*x + A*a)/x^2","A",0
258,1,53,0,0.151507," ","integrate(x^3*(B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, B c^{2} x^{9} + \frac{1}{8} \, A c^{2} x^{8} + \frac{2}{7} \, B a c x^{7} + \frac{1}{3} \, A a c x^{6} + \frac{1}{5} \, B a^{2} x^{5} + \frac{1}{4} \, A a^{2} x^{4}"," ",0,"1/9*B*c^2*x^9 + 1/8*A*c^2*x^8 + 2/7*B*a*c*x^7 + 1/3*A*a*c*x^6 + 1/5*B*a^2*x^5 + 1/4*A*a^2*x^4","A",0
259,1,53,0,0.177899," ","integrate(x^2*(B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, B c^{2} x^{8} + \frac{1}{7} \, A c^{2} x^{7} + \frac{1}{3} \, B a c x^{6} + \frac{2}{5} \, A a c x^{5} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{3} \, A a^{2} x^{3}"," ",0,"1/8*B*c^2*x^8 + 1/7*A*c^2*x^7 + 1/3*B*a*c*x^6 + 2/5*A*a*c*x^5 + 1/4*B*a^2*x^4 + 1/3*A*a^2*x^3","A",0
260,1,53,0,0.149825," ","integrate(x*(B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{7} \, B c^{2} x^{7} + \frac{1}{6} \, A c^{2} x^{6} + \frac{2}{5} \, B a c x^{5} + \frac{1}{2} \, A a c x^{4} + \frac{1}{3} \, B a^{2} x^{3} + \frac{1}{2} \, A a^{2} x^{2}"," ",0,"1/7*B*c^2*x^7 + 1/6*A*c^2*x^6 + 2/5*B*a*c*x^5 + 1/2*A*a*c*x^4 + 1/3*B*a^2*x^3 + 1/2*A*a^2*x^2","A",0
261,1,50,0,0.175299," ","integrate((B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{2} x^{6} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{2} \, B a c x^{4} + \frac{2}{3} \, A a c x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a^{2} x"," ",0,"1/6*B*c^2*x^6 + 1/5*A*c^2*x^5 + 1/2*B*a*c*x^4 + 2/3*A*a*c*x^3 + 1/2*B*a^2*x^2 + A*a^2*x","A",0
262,1,48,0,0.149466," ","integrate((B*x+A)*(c*x^2+a)^2/x,x, algorithm=""giac"")","\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({\left| x \right|}\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(abs(x))","A",0
263,1,49,0,0.222032," ","integrate((B*x+A)*(c*x^2+a)^2/x^2,x, algorithm=""giac"")","\frac{1}{4} \, B c^{2} x^{4} + \frac{1}{3} \, A c^{2} x^{3} + B a c x^{2} + 2 \, A a c x + B a^{2} \log\left({\left| x \right|}\right) - \frac{A a^{2}}{x}"," ",0,"1/4*B*c^2*x^4 + 1/3*A*c^2*x^3 + B*a*c*x^2 + 2*A*a*c*x + B*a^2*log(abs(x)) - A*a^2/x","A",0
264,1,51,0,0.166570," ","integrate((B*x+A)*(c*x^2+a)^2/x^3,x, algorithm=""giac"")","\frac{1}{3} \, B c^{2} x^{3} + \frac{1}{2} \, A c^{2} x^{2} + 2 \, B a c x + 2 \, A a c \log\left({\left| x \right|}\right) - \frac{2 \, B a^{2} x + A a^{2}}{2 \, x^{2}}"," ",0,"1/3*B*c^2*x^3 + 1/2*A*c^2*x^2 + 2*B*a*c*x + 2*A*a*c*log(abs(x)) - 1/2*(2*B*a^2*x + A*a^2)/x^2","A",0
265,1,77,0,0.150796," ","integrate(x^3*(B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{11} \, B c^{3} x^{11} + \frac{1}{10} \, A c^{3} x^{10} + \frac{1}{3} \, B a c^{2} x^{9} + \frac{3}{8} \, A a c^{2} x^{8} + \frac{3}{7} \, B a^{2} c x^{7} + \frac{1}{2} \, A a^{2} c x^{6} + \frac{1}{5} \, B a^{3} x^{5} + \frac{1}{4} \, A a^{3} x^{4}"," ",0,"1/11*B*c^3*x^11 + 1/10*A*c^3*x^10 + 1/3*B*a*c^2*x^9 + 3/8*A*a*c^2*x^8 + 3/7*B*a^2*c*x^7 + 1/2*A*a^2*c*x^6 + 1/5*B*a^3*x^5 + 1/4*A*a^3*x^4","A",0
266,1,77,0,0.154805," ","integrate(x^2*(B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{10} \, B c^{3} x^{10} + \frac{1}{9} \, A c^{3} x^{9} + \frac{3}{8} \, B a c^{2} x^{8} + \frac{3}{7} \, A a c^{2} x^{7} + \frac{1}{2} \, B a^{2} c x^{6} + \frac{3}{5} \, A a^{2} c x^{5} + \frac{1}{4} \, B a^{3} x^{4} + \frac{1}{3} \, A a^{3} x^{3}"," ",0,"1/10*B*c^3*x^10 + 1/9*A*c^3*x^9 + 3/8*B*a*c^2*x^8 + 3/7*A*a*c^2*x^7 + 1/2*B*a^2*c*x^6 + 3/5*A*a^2*c*x^5 + 1/4*B*a^3*x^4 + 1/3*A*a^3*x^3","A",0
267,1,77,0,0.150083," ","integrate(x*(B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{9} \, B c^{3} x^{9} + \frac{1}{8} \, A c^{3} x^{8} + \frac{3}{7} \, B a c^{2} x^{7} + \frac{1}{2} \, A a c^{2} x^{6} + \frac{3}{5} \, B a^{2} c x^{5} + \frac{3}{4} \, A a^{2} c x^{4} + \frac{1}{3} \, B a^{3} x^{3} + \frac{1}{2} \, A a^{3} x^{2}"," ",0,"1/9*B*c^3*x^9 + 1/8*A*c^3*x^8 + 3/7*B*a*c^2*x^7 + 1/2*A*a*c^2*x^6 + 3/5*B*a^2*c*x^5 + 3/4*A*a^2*c*x^4 + 1/3*B*a^3*x^3 + 1/2*A*a^3*x^2","A",0
268,1,73,0,0.152424," ","integrate((B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{8} \, B c^{3} x^{8} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{2} \, B a c^{2} x^{6} + \frac{3}{5} \, A a c^{2} x^{5} + \frac{3}{4} \, B a^{2} c x^{4} + A a^{2} c x^{3} + \frac{1}{2} \, B a^{3} x^{2} + A a^{3} x"," ",0,"1/8*B*c^3*x^8 + 1/7*A*c^3*x^7 + 1/2*B*a*c^2*x^6 + 3/5*A*a*c^2*x^5 + 3/4*B*a^2*c*x^4 + A*a^2*c*x^3 + 1/2*B*a^3*x^2 + A*a^3*x","A",0
269,1,72,0,0.147076," ","integrate((B*x+A)*(c*x^2+a)^3/x,x, algorithm=""giac"")","\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({\left| x \right|}\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(abs(x))","A",0
270,1,73,0,0.175759," ","integrate((B*x+A)*(c*x^2+a)^3/x^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{3} x^{6} + \frac{1}{5} \, A c^{3} x^{5} + \frac{3}{4} \, B a c^{2} x^{4} + A a c^{2} x^{3} + \frac{3}{2} \, B a^{2} c x^{2} + 3 \, A a^{2} c x + B a^{3} \log\left({\left| x \right|}\right) - \frac{A a^{3}}{x}"," ",0,"1/6*B*c^3*x^6 + 1/5*A*c^3*x^5 + 3/4*B*a*c^2*x^4 + A*a*c^2*x^3 + 3/2*B*a^2*c*x^2 + 3*A*a^2*c*x + B*a^3*log(abs(x)) - A*a^3/x","A",0
271,1,74,0,0.161660," ","integrate((B*x+A)*(c*x^2+a)^3/x^3,x, algorithm=""giac"")","\frac{1}{5} \, B c^{3} x^{5} + \frac{1}{4} \, A c^{3} x^{4} + B a c^{2} x^{3} + \frac{3}{2} \, A a c^{2} x^{2} + 3 \, B a^{2} c x + 3 \, A a^{2} c \log\left({\left| x \right|}\right) - \frac{2 \, B a^{3} x + A a^{3}}{2 \, x^{2}}"," ",0,"1/5*B*c^3*x^5 + 1/4*A*c^3*x^4 + B*a*c^2*x^3 + 3/2*A*a*c^2*x^2 + 3*B*a^2*c*x + 3*A*a^2*c*log(abs(x)) - 1/2*(2*B*a^3*x + A*a^3)/x^2","A",0
272,1,101,0,0.177828," ","integrate(x^3*(B*x+A)*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{13} \, B c^{4} x^{13} + \frac{1}{12} \, A c^{4} x^{12} + \frac{4}{11} \, B a c^{3} x^{11} + \frac{2}{5} \, A a c^{3} x^{10} + \frac{2}{3} \, B a^{2} c^{2} x^{9} + \frac{3}{4} \, A a^{2} c^{2} x^{8} + \frac{4}{7} \, B a^{3} c x^{7} + \frac{2}{3} \, A a^{3} c x^{6} + \frac{1}{5} \, B a^{4} x^{5} + \frac{1}{4} \, A a^{4} x^{4}"," ",0,"1/13*B*c^4*x^13 + 1/12*A*c^4*x^12 + 4/11*B*a*c^3*x^11 + 2/5*A*a*c^3*x^10 + 2/3*B*a^2*c^2*x^9 + 3/4*A*a^2*c^2*x^8 + 4/7*B*a^3*c*x^7 + 2/3*A*a^3*c*x^6 + 1/5*B*a^4*x^5 + 1/4*A*a^4*x^4","A",0
273,1,101,0,0.154426," ","integrate(x^2*(B*x+A)*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{12} \, B c^{4} x^{12} + \frac{1}{11} \, A c^{4} x^{11} + \frac{2}{5} \, B a c^{3} x^{10} + \frac{4}{9} \, A a c^{3} x^{9} + \frac{3}{4} \, B a^{2} c^{2} x^{8} + \frac{6}{7} \, A a^{2} c^{2} x^{7} + \frac{2}{3} \, B a^{3} c x^{6} + \frac{4}{5} \, A a^{3} c x^{5} + \frac{1}{4} \, B a^{4} x^{4} + \frac{1}{3} \, A a^{4} x^{3}"," ",0,"1/12*B*c^4*x^12 + 1/11*A*c^4*x^11 + 2/5*B*a*c^3*x^10 + 4/9*A*a*c^3*x^9 + 3/4*B*a^2*c^2*x^8 + 6/7*A*a^2*c^2*x^7 + 2/3*B*a^3*c*x^6 + 4/5*A*a^3*c*x^5 + 1/4*B*a^4*x^4 + 1/3*A*a^4*x^3","A",0
274,1,99,0,0.191021," ","integrate(x*(B*x+A)*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{11} \, B c^{4} x^{11} + \frac{1}{10} \, A c^{4} x^{10} + \frac{4}{9} \, B a c^{3} x^{9} + \frac{1}{2} \, A a c^{3} x^{8} + \frac{6}{7} \, B a^{2} c^{2} x^{7} + A a^{2} c^{2} x^{6} + \frac{4}{5} \, B a^{3} c x^{5} + A a^{3} c x^{4} + \frac{1}{3} \, B a^{4} x^{3} + \frac{1}{2} \, A a^{4} x^{2}"," ",0,"1/11*B*c^4*x^11 + 1/10*A*c^4*x^10 + 4/9*B*a*c^3*x^9 + 1/2*A*a*c^3*x^8 + 6/7*B*a^2*c^2*x^7 + A*a^2*c^2*x^6 + 4/5*B*a^3*c*x^5 + A*a^3*c*x^4 + 1/3*B*a^4*x^3 + 1/2*A*a^4*x^2","A",0
275,1,96,0,0.154876," ","integrate((B*x+A)*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{10} \, B c^{4} x^{10} + \frac{1}{9} \, A c^{4} x^{9} + \frac{1}{2} \, B a c^{3} x^{8} + \frac{4}{7} \, A a c^{3} x^{7} + B a^{2} c^{2} x^{6} + \frac{6}{5} \, A a^{2} c^{2} x^{5} + B a^{3} c x^{4} + \frac{4}{3} \, A a^{3} c x^{3} + \frac{1}{2} \, B a^{4} x^{2} + A a^{4} x"," ",0,"1/10*B*c^4*x^10 + 1/9*A*c^4*x^9 + 1/2*B*a*c^3*x^8 + 4/7*A*a*c^3*x^7 + B*a^2*c^2*x^6 + 6/5*A*a^2*c^2*x^5 + B*a^3*c*x^4 + 4/3*A*a^3*c*x^3 + 1/2*B*a^4*x^2 + A*a^4*x","A",0
276,1,97,0,0.152477," ","integrate((B*x+A)*(c*x^2+a)^4/x,x, algorithm=""giac"")","\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({\left| x \right|}\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(abs(x))","A",0
277,1,98,0,0.168991," ","integrate((B*x+A)*(c*x^2+a)^4/x^2,x, algorithm=""giac"")","\frac{1}{8} \, B c^{4} x^{8} + \frac{1}{7} \, A c^{4} x^{7} + \frac{2}{3} \, B a c^{3} x^{6} + \frac{4}{5} \, A a c^{3} x^{5} + \frac{3}{2} \, B a^{2} c^{2} x^{4} + 2 \, A a^{2} c^{2} x^{3} + 2 \, B a^{3} c x^{2} + 4 \, A a^{3} c x + B a^{4} \log\left({\left| x \right|}\right) - \frac{A a^{4}}{x}"," ",0,"1/8*B*c^4*x^8 + 1/7*A*c^4*x^7 + 2/3*B*a*c^3*x^6 + 4/5*A*a*c^3*x^5 + 3/2*B*a^2*c^2*x^4 + 2*A*a^2*c^2*x^3 + 2*B*a^3*c*x^2 + 4*A*a^3*c*x + B*a^4*log(abs(x)) - A*a^4/x","A",0
278,1,98,0,0.166262," ","integrate((B*x+A)*(c*x^2+a)^4/x^3,x, algorithm=""giac"")","\frac{1}{7} \, B c^{4} x^{7} + \frac{1}{6} \, A c^{4} x^{6} + \frac{4}{5} \, B a c^{3} x^{5} + A a c^{3} x^{4} + 2 \, B a^{2} c^{2} x^{3} + 3 \, A a^{2} c^{2} x^{2} + 4 \, B a^{3} c x + 4 \, A a^{3} c \log\left({\left| x \right|}\right) - \frac{2 \, B a^{4} x + A a^{4}}{2 \, x^{2}}"," ",0,"1/7*B*c^4*x^7 + 1/6*A*c^4*x^6 + 4/5*B*a*c^3*x^5 + A*a*c^3*x^4 + 2*B*a^2*c^2*x^3 + 3*A*a^2*c^2*x^2 + 4*B*a^3*c*x + 4*A*a^3*c*log(abs(x)) - 1/2*(2*B*a^4*x + A*a^4)/x^2","A",0
279,1,85,0,0.151227," ","integrate(x^4*(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{a^{2} d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{a^{2} e \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{3 \, c^{3} x^{4} e + 4 \, c^{3} d x^{3} - 6 \, a c^{2} x^{2} e - 12 \, a c^{2} d x}{12 \, c^{4}}"," ",0,"a^2*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/2*a^2*e*log(c*x^2 + a)/c^3 + 1/12*(3*c^3*x^4*e + 4*c^3*d*x^3 - 6*a*c^2*x^2*e - 12*a*c^2*d*x)/c^4","A",0
280,1,71,0,0.164539," ","integrate(x^3*(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{\sqrt{a c} c^{2}} - \frac{a d \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{2 \, c^{2} x^{3} e + 3 \, c^{2} d x^{2} - 6 \, a c x e}{6 \, c^{3}}"," ",0,"a^2*arctan(c*x/sqrt(a*c))*e/(sqrt(a*c)*c^2) - 1/2*a*d*log(c*x^2 + a)/c^2 + 1/6*(2*c^2*x^3*e + 3*c^2*d*x^2 - 6*a*c*x*e)/c^3","A",0
281,1,56,0,0.196661," ","integrate(x^2*(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","-\frac{a d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c} - \frac{a e \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{c x^{2} e + 2 \, c d x}{2 \, c^{2}}"," ",0,"-a*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) - 1/2*a*e*log(c*x^2 + a)/c^2 + 1/2*(c*x^2*e + 2*c*d*x)/c^2","A",0
282,1,44,0,0.148801," ","integrate(x*(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{\sqrt{a c} c} + \frac{x e}{c} + \frac{d \log\left(c x^{2} + a\right)}{2 \, c}"," ",0,"-a*arctan(c*x/sqrt(a*c))*e/(sqrt(a*c)*c) + x*e/c + 1/2*d*log(c*x^2 + a)/c","A",0
283,1,32,0,0.154107," ","integrate((e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}} + \frac{e \log\left(c x^{2} + a\right)}{2 \, c}"," ",0,"d*arctan(c*x/sqrt(a*c))/sqrt(a*c) + 1/2*e*log(c*x^2 + a)/c","A",0
284,1,40,0,0.152758," ","integrate((e*x+d)/x/(c*x^2+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{\sqrt{a c}} - \frac{d \log\left(c x^{2} + a\right)}{2 \, a} + \frac{d \log\left({\left| x \right|}\right)}{a}"," ",0,"arctan(c*x/sqrt(a*c))*e/sqrt(a*c) - 1/2*d*log(c*x^2 + a)/a + d*log(abs(x))/a","A",0
285,1,55,0,0.151307," ","integrate((e*x+d)/x^2/(c*x^2+a),x, algorithm=""giac"")","-\frac{c d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} a} - \frac{e \log\left(c x^{2} + a\right)}{2 \, a} + \frac{e \log\left({\left| x \right|}\right)}{a} - \frac{d}{a x}"," ",0,"-c*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a) - 1/2*e*log(c*x^2 + a)/a + e*log(abs(x))/a - d/(a*x)","A",0
286,1,66,0,0.153070," ","integrate((e*x+d)/x^3/(c*x^2+a),x, algorithm=""giac"")","-\frac{c \arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{\sqrt{a c} a} + \frac{c d \log\left(c x^{2} + a\right)}{2 \, a^{2}} - \frac{c d \log\left({\left| x \right|}\right)}{a^{2}} - \frac{2 \, a x e + a d}{2 \, a^{2} x^{2}}"," ",0,"-c*arctan(c*x/sqrt(a*c))*e/(sqrt(a*c)*a) + 1/2*c*d*log(c*x^2 + a)/a^2 - c*d*log(abs(x))/a^2 - 1/2*(2*a*x*e + a*d)/(a^2*x^2)","A",0
287,1,76,0,0.152539," ","integrate((e*x+d)/x^4/(c*x^2+a),x, algorithm=""giac"")","\frac{c^{2} d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} a^{2}} + \frac{c e \log\left(c x^{2} + a\right)}{2 \, a^{2}} - \frac{c e \log\left({\left| x \right|}\right)}{a^{2}} + \frac{6 \, c d x^{2} - 3 \, a x e - 2 \, a d}{6 \, a^{2} x^{3}}"," ",0,"c^2*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2) + 1/2*c*e*log(c*x^2 + a)/a^2 - c*e*log(abs(x))/a^2 + 1/6*(6*c*d*x^2 - 3*a*x*e - 2*a*d)/(a^2*x^3)","A",0
288,1,37,0,0.150411," ","integrate((e*x+d)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{d \arctan\left(\frac{c x}{\sqrt{-a c}}\right)}{\sqrt{-a c}} - \frac{e \log\left(c x^{2} - a\right)}{2 \, c}"," ",0,"-d*arctan(c*x/sqrt(-a*c))/sqrt(-a*c) - 1/2*e*log(c*x^2 - a)/c","A",0
289,1,87,0,0.197318," ","integrate(x^4*(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, a d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} c^{2}} - \frac{a e \log\left(c x^{2} + a\right)}{c^{3}} + \frac{c^{2} x^{2} e + 2 \, c^{2} d x}{2 \, c^{4}} + \frac{a c d x - a^{2} e}{2 \, {\left(c x^{2} + a\right)} c^{3}}"," ",0,"-3/2*a*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) - a*e*log(c*x^2 + a)/c^3 + 1/2*(c^2*x^2*e + 2*c^2*d*x)/c^4 + 1/2*(a*c*d*x - a^2*e)/((c*x^2 + a)*c^3)","A",0
290,1,67,0,0.154990," ","integrate(x^3*(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, a \arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{2 \, \sqrt{a c} c^{2}} + \frac{x e}{c^{2}} + \frac{d \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{a x e + a d}{2 \, {\left(c x^{2} + a\right)} c^{2}}"," ",0,"-3/2*a*arctan(c*x/sqrt(a*c))*e/(sqrt(a*c)*c^2) + x*e/c^2 + 1/2*d*log(c*x^2 + a)/c^2 + 1/2*(a*x*e + a*d)/((c*x^2 + a)*c^2)","A",0
291,1,62,0,0.188019," ","integrate(x^2*(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} c} + \frac{e \log\left(c x^{2} + a\right)}{2 \, c^{2}} - \frac{d x - \frac{a e}{c}}{2 \, {\left(c x^{2} + a\right)} c}"," ",0,"1/2*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) + 1/2*e*log(c*x^2 + a)/c^2 - 1/2*(d*x - a*e/c)/((c*x^2 + a)*c)","A",0
292,1,42,0,0.170099," ","integrate(x*(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{2 \, \sqrt{a c} c} - \frac{x e + d}{2 \, {\left(c x^{2} + a\right)} c}"," ",0,"1/2*arctan(c*x/sqrt(a*c))*e/(sqrt(a*c)*c) - 1/2*(x*e + d)/((c*x^2 + a)*c)","A",0
293,1,48,0,0.152414," ","integrate((e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a} + \frac{c d x - a e}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a) + 1/2*(c*d*x - a*e)/((c*x^2 + a)*a*c)","A",0
294,1,67,0,0.152369," ","integrate((e*x+d)/x/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{2 \, \sqrt{a c} a} - \frac{d \log\left(c x^{2} + a\right)}{2 \, a^{2}} + \frac{d \log\left({\left| x \right|}\right)}{a^{2}} + \frac{a x e + a d}{2 \, {\left(c x^{2} + a\right)} a^{2}}"," ",0,"1/2*arctan(c*x/sqrt(a*c))*e/(sqrt(a*c)*a) - 1/2*d*log(c*x^2 + a)/a^2 + d*log(abs(x))/a^2 + 1/2*(a*x*e + a*d)/((c*x^2 + a)*a^2)","A",0
295,1,80,0,0.158351," ","integrate((e*x+d)/x^2/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, c d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a^{2}} - \frac{e \log\left(c x^{2} + a\right)}{2 \, a^{2}} + \frac{e \log\left({\left| x \right|}\right)}{a^{2}} - \frac{3 \, c d x^{2} - a x e + 2 \, a d}{2 \, {\left(c x^{3} + a x\right)} a^{2}}"," ",0,"-3/2*c*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2) - 1/2*e*log(c*x^2 + a)/a^2 + e*log(abs(x))/a^2 - 1/2*(3*c*d*x^2 - a*x*e + 2*a*d)/((c*x^3 + a*x)*a^2)","A",0
296,1,95,0,0.158229," ","integrate((e*x+d)/x^3/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, c \arctan\left(\frac{c x}{\sqrt{a c}}\right) e}{2 \, \sqrt{a c} a^{2}} + \frac{c d \log\left(c x^{2} + a\right)}{a^{3}} - \frac{2 \, c d \log\left({\left| x \right|}\right)}{a^{3}} - \frac{3 \, a c x^{3} e + 2 \, a c d x^{2} + 2 \, a^{2} x e + a^{2} d}{2 \, {\left(c x^{2} + a\right)} a^{3} x^{2}}"," ",0,"-3/2*c*arctan(c*x/sqrt(a*c))*e/(sqrt(a*c)*a^2) + c*d*log(c*x^2 + a)/a^3 - 2*c*d*log(abs(x))/a^3 - 1/2*(3*a*c*x^3*e + 2*a*c*d*x^2 + 2*a^2*x*e + a^2*d)/((c*x^2 + a)*a^3*x^2)","A",0
297,1,102,0,0.166492," ","integrate(x^4*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""giac"")","\frac{{\left(a^{3} c d - a^{4} e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, c^{6}} - \frac{{\left(a^{3} c d + a^{4} e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, c^{6}} - \frac{3 \, c^{6} x^{4} e + 4 \, c^{6} d x^{3} + 6 \, a^{2} c^{4} x^{2} e + 12 \, a^{2} c^{4} d x}{12 \, c^{8}}"," ",0,"1/2*(a^3*c*d - a^4*e)*log(abs(c*x + a))/c^6 - 1/2*(a^3*c*d + a^4*e)*log(abs(c*x - a))/c^6 - 1/12*(3*c^6*x^4*e + 4*c^6*d*x^3 + 6*a^2*c^4*x^2*e + 12*a^2*c^4*d*x)/c^8","A",0
298,1,90,0,0.174194," ","integrate(x^3*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""giac"")","-\frac{{\left(a^{2} c d - a^{3} e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, c^{5}} - \frac{{\left(a^{2} c d + a^{3} e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, c^{5}} - \frac{2 \, c^{4} x^{3} e + 3 \, c^{4} d x^{2} + 6 \, a^{2} c^{2} x e}{6 \, c^{6}}"," ",0,"-1/2*(a^2*c*d - a^3*e)*log(abs(c*x + a))/c^5 - 1/2*(a^2*c*d + a^3*e)*log(abs(c*x - a))/c^5 - 1/6*(2*c^4*x^3*e + 3*c^4*d*x^2 + 6*a^2*c^2*x*e)/c^6","A",0
299,1,72,0,0.159258," ","integrate(x^2*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""giac"")","\frac{{\left(a c d - a^{2} e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, c^{4}} - \frac{{\left(a c d + a^{2} e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, c^{4}} - \frac{c^{2} x^{2} e + 2 \, c^{2} d x}{2 \, c^{4}}"," ",0,"1/2*(a*c*d - a^2*e)*log(abs(c*x + a))/c^4 - 1/2*(a*c*d + a^2*e)*log(abs(c*x - a))/c^4 - 1/2*(c^2*x^2*e + 2*c^2*d*x)/c^4","A",0
300,1,52,0,0.152967," ","integrate(x*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""giac"")","-\frac{x e}{c^{2}} - \frac{{\left(c d - a e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, c^{3}} - \frac{{\left(c d + a e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, c^{3}}"," ",0,"-x*e/c^2 - 1/2*(c*d - a*e)*log(abs(c*x + a))/c^3 - 1/2*(c*d + a*e)*log(abs(c*x - a))/c^3","A",0
301,1,50,0,0.152802," ","integrate((e*x+d)/(-c^2*x^2+a^2),x, algorithm=""giac"")","\frac{{\left(c d - a e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, a c^{2}} - \frac{{\left(c d + a e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, a c^{2}}"," ",0,"1/2*(c*d - a*e)*log(abs(c*x + a))/(a*c^2) - 1/2*(c*d + a*e)*log(abs(c*x - a))/(a*c^2)","A",0
302,1,64,0,0.168159," ","integrate((e*x+d)/x/(-c^2*x^2+a^2),x, algorithm=""giac"")","\frac{d \log\left({\left| x \right|}\right)}{a^{2}} - \frac{{\left(c^{2} d - a c e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, a^{2} c^{2}} - \frac{{\left(c^{2} d + a c e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, a^{2} c^{2}}"," ",0,"d*log(abs(x))/a^2 - 1/2*(c^2*d - a*c*e)*log(abs(c*x + a))/(a^2*c^2) - 1/2*(c^2*d + a*c*e)*log(abs(c*x - a))/(a^2*c^2)","A",0
303,1,74,0,0.153148," ","integrate((e*x+d)/x^2/(-c^2*x^2+a^2),x, algorithm=""giac"")","\frac{e \log\left({\left| x \right|}\right)}{a^{2}} - \frac{d}{a^{2} x} + \frac{{\left(c^{2} d - a c e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, a^{3} c} - \frac{{\left(c^{2} d + a c e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, a^{3} c}"," ",0,"e*log(abs(x))/a^2 - d/(a^2*x) + 1/2*(c^2*d - a*c*e)*log(abs(c*x + a))/(a^3*c) - 1/2*(c^2*d + a*c*e)*log(abs(c*x - a))/(a^3*c)","A",0
304,1,93,0,0.154688," ","integrate((e*x+d)/x^3/(-c^2*x^2+a^2),x, algorithm=""giac"")","\frac{c^{2} d \log\left({\left| x \right|}\right)}{a^{4}} - \frac{{\left(c^{3} d - a c^{2} e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, a^{4} c} - \frac{{\left(c^{3} d + a c^{2} e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, a^{4} c} - \frac{2 \, a^{2} x e + a^{2} d}{2 \, a^{4} x^{2}}"," ",0,"c^2*d*log(abs(x))/a^4 - 1/2*(c^3*d - a*c^2*e)*log(abs(c*x + a))/(a^4*c) - 1/2*(c^3*d + a*c^2*e)*log(abs(c*x - a))/(a^4*c) - 1/2*(2*a^2*x*e + a^2*d)/(a^4*x^2)","A",0
305,1,104,0,0.168699," ","integrate((e*x+d)/x^4/(-c^2*x^2+a^2),x, algorithm=""giac"")","\frac{c^{2} e \log\left({\left| x \right|}\right)}{a^{4}} + \frac{{\left(c^{4} d - a c^{3} e\right)} \log\left({\left| c x + a \right|}\right)}{2 \, a^{5} c} - \frac{{\left(c^{4} d + a c^{3} e\right)} \log\left({\left| c x - a \right|}\right)}{2 \, a^{5} c} - \frac{6 \, c^{2} d x^{2} + 3 \, a^{2} x e + 2 \, a^{2} d}{6 \, a^{4} x^{3}}"," ",0,"c^2*e*log(abs(x))/a^4 + 1/2*(c^4*d - a*c^3*e)*log(abs(c*x + a))/(a^5*c) - 1/2*(c^4*d + a*c^3*e)*log(abs(c*x - a))/(a^5*c) - 1/6*(6*c^2*d*x^2 + 3*a^2*x*e + 2*a^2*d)/(a^4*x^3)","A",0
306,1,112,0,0.156733," ","integrate(x^4*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, a c d - 4 \, a^{2} e\right)} \log\left({\left| c x + a \right|}\right)}{4 \, c^{6}} + \frac{{\left(3 \, a c d + 4 \, a^{2} e\right)} \log\left({\left| c x - a \right|}\right)}{4 \, c^{6}} + \frac{c^{4} x^{2} e + 2 \, c^{4} d x}{2 \, c^{8}} - \frac{a^{2} c^{2} d x + a^{4} e}{2 \, {\left(c x + a\right)} {\left(c x - a\right)} c^{6}}"," ",0,"-1/4*(3*a*c*d - 4*a^2*e)*log(abs(c*x + a))/c^6 + 1/4*(3*a*c*d + 4*a^2*e)*log(abs(c*x - a))/c^6 + 1/2*(c^4*x^2*e + 2*c^4*d*x)/c^8 - 1/2*(a^2*c^2*d*x + a^4*e)/((c*x + a)*(c*x - a)*c^6)","A",0
307,1,88,0,0.156482," ","integrate(x^3*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{x e}{c^{4}} + \frac{{\left(2 \, c d - 3 \, a e\right)} \log\left({\left| c x + a \right|}\right)}{4 \, c^{5}} + \frac{{\left(2 \, c d + 3 \, a e\right)} \log\left({\left| c x - a \right|}\right)}{4 \, c^{5}} - \frac{a^{2} x e + a^{2} d}{2 \, {\left(c x + a\right)} {\left(c x - a\right)} c^{4}}"," ",0,"x*e/c^4 + 1/4*(2*c*d - 3*a*e)*log(abs(c*x + a))/c^5 + 1/4*(2*c*d + 3*a*e)*log(abs(c*x - a))/c^5 - 1/2*(a^2*x*e + a^2*d)/((c*x + a)*(c*x - a)*c^4)","A",0
308,1,85,0,0.179257," ","integrate(x^2*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{d x + \frac{a^{2} e}{c^{2}}}{2 \, {\left(c x + a\right)} {\left(c x - a\right)} c^{2}} - \frac{{\left(c d - 2 \, a e\right)} \log\left({\left| c x + a \right|}\right)}{4 \, a c^{4}} + \frac{{\left(c d + 2 \, a e\right)} \log\left({\left| c x - a \right|}\right)}{4 \, a c^{4}}"," ",0,"-1/2*(d*x + a^2*e/c^2)/((c*x + a)*(c*x - a)*c^2) - 1/4*(c*d - 2*a*e)*log(abs(c*x + a))/(a*c^4) + 1/4*(c*d + 2*a*e)*log(abs(c*x - a))/(a*c^4)","A",0
309,1,63,0,0.164415," ","integrate(x*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{x e + d}{2 \, {\left(c^{2} x^{2} - a^{2}\right)} c^{2}} - \frac{e \log\left({\left| c x + a \right|}\right)}{4 \, a c^{3}} + \frac{e \log\left({\left| c x - a \right|}\right)}{4 \, a c^{3}}"," ",0,"-1/2*(x*e + d)/((c^2*x^2 - a^2)*c^2) - 1/4*e*log(abs(c*x + a))/(a*c^3) + 1/4*e*log(abs(c*x - a))/(a*c^3)","A",0
310,1,71,0,0.156065," ","integrate((e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{d \log\left({\left| c x + a \right|}\right)}{4 \, a^{3} c} - \frac{d \log\left({\left| c x - a \right|}\right)}{4 \, a^{3} c} - \frac{c^{2} d x + a^{2} e}{2 \, {\left(c^{2} x^{2} - a^{2}\right)} a^{2} c^{2}}"," ",0,"1/4*d*log(abs(c*x + a))/(a^3*c) - 1/4*d*log(abs(c*x - a))/(a^3*c) - 1/2*(c^2*d*x + a^2*e)/((c^2*x^2 - a^2)*a^2*c^2)","A",0
311,1,94,0,0.161940," ","integrate((e*x+d)/x/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{d \log\left({\left| x \right|}\right)}{a^{4}} - \frac{{\left(2 \, c d - a e\right)} \log\left({\left| c x + a \right|}\right)}{4 \, a^{4} c} - \frac{{\left(2 \, c d + a e\right)} \log\left({\left| c x - a \right|}\right)}{4 \, a^{4} c} - \frac{a^{2} x e + a^{2} d}{2 \, {\left(c x + a\right)} {\left(c x - a\right)} a^{4}}"," ",0,"d*log(abs(x))/a^4 - 1/4*(2*c*d - a*e)*log(abs(c*x + a))/(a^4*c) - 1/4*(2*c*d + a*e)*log(abs(c*x - a))/(a^4*c) - 1/2*(a^2*x*e + a^2*d)/((c*x + a)*(c*x - a)*a^4)","A",0
312,1,112,0,0.157078," ","integrate((e*x+d)/x^2/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{e \log\left({\left| x \right|}\right)}{a^{4}} - \frac{3 \, c^{2} d x^{2} + a^{2} x e - 2 \, a^{2} d}{2 \, {\left(c^{2} x^{3} - a^{2} x\right)} a^{4}} + \frac{{\left(3 \, c^{2} d - 2 \, a c e\right)} \log\left({\left| c x + a \right|}\right)}{4 \, a^{5} c} - \frac{{\left(3 \, c^{2} d + 2 \, a c e\right)} \log\left({\left| c x - a \right|}\right)}{4 \, a^{5} c}"," ",0,"e*log(abs(x))/a^4 - 1/2*(3*c^2*d*x^2 + a^2*x*e - 2*a^2*d)/((c^2*x^3 - a^2*x)*a^4) + 1/4*(3*c^2*d - 2*a*c*e)*log(abs(c*x + a))/(a^5*c) - 1/4*(3*c^2*d + 2*a*c*e)*log(abs(c*x - a))/(a^5*c)","A",0
313,1,139,0,0.193165," ","integrate((e*x+d)/x^3/(-c^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{2 \, c^{2} d \log\left({\left| x \right|}\right)}{a^{6}} - \frac{{\left(4 \, c^{3} d - 3 \, a c^{2} e\right)} \log\left({\left| c x + a \right|}\right)}{4 \, a^{6} c} - \frac{{\left(4 \, c^{3} d + 3 \, a c^{2} e\right)} \log\left({\left| c x - a \right|}\right)}{4 \, a^{6} c} - \frac{3 \, a^{2} c^{2} x^{3} e + 2 \, a^{2} c^{2} d x^{2} - 2 \, a^{4} x e - a^{4} d}{2 \, {\left(c x + a\right)} {\left(c x - a\right)} a^{6} x^{2}}"," ",0,"2*c^2*d*log(abs(x))/a^6 - 1/4*(4*c^3*d - 3*a*c^2*e)*log(abs(c*x + a))/(a^6*c) - 1/4*(4*c^3*d + 3*a*c^2*e)*log(abs(c*x - a))/(a^6*c) - 1/2*(3*a^2*c^2*x^3*e + 2*a^2*c^2*d*x^2 - 2*a^4*x*e - a^4*d)/((c*x + a)*(c*x - a)*a^6*x^2)","A",0
314,1,106,0,0.186746," ","integrate(x^4*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{A a^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{5}{2}}} + \frac{1}{1680} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(6 \, B x + 7 \, A\right)} x + \frac{6 \, B a}{c}\right)} x + \frac{35 \, A a}{c}\right)} x - \frac{32 \, B a^{2}}{c^{2}}\right)} x - \frac{105 \, A a^{2}}{c^{2}}\right)} x + \frac{128 \, B a^{3}}{c^{3}}\right)}"," ",0,"-1/16*A*a^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2) + 1/1680*sqrt(c*x^2 + a)*((2*((4*(5*(6*B*x + 7*A)*x + 6*B*a/c)*x + 35*A*a/c)*x - 32*B*a^2/c^2)*x - 105*A*a^2/c^2)*x + 128*B*a^3/c^3)","A",0
315,1,93,0,0.195288," ","integrate(x^3*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{B a^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{5}{2}}} + \frac{1}{240} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, B x + 6 \, A\right)} x + \frac{5 \, B a}{c}\right)} x + \frac{8 \, A a}{c}\right)} x - \frac{15 \, B a^{2}}{c^{2}}\right)} x - \frac{32 \, A a^{2}}{c^{2}}\right)}"," ",0,"-1/16*B*a^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2) + 1/240*sqrt(c*x^2 + a)*((2*((4*(5*B*x + 6*A)*x + 5*B*a/c)*x + 8*A*a/c)*x - 15*B*a^2/c^2)*x - 32*A*a^2/c^2)","A",0
316,1,81,0,0.526193," ","integrate(x^2*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{A a^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{3}{2}}} + \frac{1}{120} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(4 \, B x + 5 \, A\right)} x + \frac{4 \, B a}{c}\right)} x + \frac{15 \, A a}{c}\right)} x - \frac{16 \, B a^{2}}{c^{2}}\right)}"," ",0,"1/8*A*a^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2) + 1/120*sqrt(c*x^2 + a)*((2*(3*(4*B*x + 5*A)*x + 4*B*a/c)*x + 15*A*a/c)*x - 16*B*a^2/c^2)","A",0
317,1,68,0,0.179930," ","integrate(x*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{B a^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{3}{2}}} + \frac{1}{24} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, B x + 4 \, A\right)} x + \frac{3 \, B a}{c}\right)} x + \frac{8 \, A a}{c}\right)}"," ",0,"1/8*B*a^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2) + 1/24*sqrt(c*x^2 + a)*((2*(3*B*x + 4*A)*x + 3*B*a/c)*x + 8*A*a/c)","A",0
318,1,55,0,0.199692," ","integrate((B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{A a \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, \sqrt{c}} + \frac{1}{6} \, \sqrt{c x^{2} + a} {\left({\left(2 \, B x + 3 \, A\right)} x + \frac{2 \, B a}{c}\right)}"," ",0,"-1/2*A*a*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/6*sqrt(c*x^2 + a)*((2*B*x + 3*A)*x + 2*B*a/c)","A",0
319,1,78,0,0.200604," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, A a \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{B a \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, \sqrt{c}} + \frac{1}{2} \, \sqrt{c x^{2} + a} {\left(B x + 2 \, A\right)}"," ",0,"2*A*a*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 1/2*B*a*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/2*sqrt(c*x^2 + a)*(B*x + 2*A)","A",0
320,1,102,0,0.189804," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^2,x, algorithm=""giac"")","\frac{2 \, B a \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - A \sqrt{c} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \sqrt{c x^{2} + a} B + \frac{2 \, A a \sqrt{c}}{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a}"," ",0,"2*B*a*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - A*sqrt(c)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + sqrt(c*x^2 + a)*B + 2*A*a*sqrt(c)/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)","A",0
321,1,163,0,0.196530," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^3,x, algorithm=""giac"")","\frac{A c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - B \sqrt{c} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a \sqrt{c} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a c - 2 \, B a^{2} \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{2}}"," ",0,"A*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - B*sqrt(c)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + ((sqrt(c)*x - sqrt(c*x^2 + a))^3*A*c + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a*sqrt(c) + (sqrt(c)*x - sqrt(c*x^2 + a))*A*a*c - 2*B*a^2*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^2","B",0
322,1,143,0,0.215933," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^4,x, algorithm=""giac"")","\frac{B c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B c + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{2} c + 2 \, A a^{2} c^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"B*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) + 1/3*(3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*c + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*c^(3/2) - 3*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^2*c + 2*A*a^2*c^(3/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^3","B",0
323,1,267,0,0.191484," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{A c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a} + \frac{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A c^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} B a c^{\frac{3}{2}} + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a c^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} B a^{2} c^{\frac{3}{2}} + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{2} c^{2} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{3} c^{\frac{3}{2}} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{3} c^{2} - 8 \, B a^{4} c^{\frac{3}{2}}}{12 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{4} a}"," ",0,"-1/4*A*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/12*(3*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*c^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + a))^6*B*a*c^(3/2) + 21*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a*c^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + a))^4*B*a^2*c^(3/2) + 21*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^2*c^2 + 8*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^3*c^(3/2) + 3*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^3*c^2 - 8*B*a^4*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^4*a)","B",0
324,1,267,0,0.189800," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^6,x, algorithm=""giac"")","-\frac{B c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a} + \frac{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} B c^{2} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} B a c^{2} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} A a c^{\frac{5}{2}} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{2} c^{\frac{5}{2}} - 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} B a^{3} c^{2} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a^{3} c^{\frac{5}{2}} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{4} c^{2} - 16 \, A a^{4} c^{\frac{5}{2}}}{60 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{5} a}"," ",0,"-1/4*B*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/60*(15*(sqrt(c)*x - sqrt(c*x^2 + a))^9*B*c^2 + 90*(sqrt(c)*x - sqrt(c*x^2 + a))^7*B*a*c^2 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^6*A*a*c^(5/2) + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^2*c^(5/2) - 90*(sqrt(c)*x - sqrt(c*x^2 + a))^3*B*a^3*c^2 + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a^3*c^(5/2) - 15*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^4*c^2 - 16*A*a^4*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^5*a)","B",0
325,1,325,0,0.225703," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^7,x, algorithm=""giac"")","\frac{A c^{3} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{2}} - \frac{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} A c^{3} - 85 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} A a c^{3} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} B a^{2} c^{\frac{5}{2}} - 570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A a^{2} c^{3} + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} B a^{3} c^{\frac{5}{2}} - 570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a^{3} c^{3} - 85 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{4} c^{3} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{5} c^{\frac{5}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{5} c^{3} - 32 \, B a^{6} c^{\frac{5}{2}}}{120 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{6} a^{2}}"," ",0,"1/8*A*c^3*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) - 1/120*(15*(sqrt(c)*x - sqrt(c*x^2 + a))^11*A*c^3 - 85*(sqrt(c)*x - sqrt(c*x^2 + a))^9*A*a*c^3 - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*B*a^2*c^(5/2) - 570*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*a^2*c^3 + 320*(sqrt(c)*x - sqrt(c*x^2 + a))^6*B*a^3*c^(5/2) - 570*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a^3*c^3 - 85*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^4*c^3 + 192*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^5*c^(5/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^5*c^3 - 32*B*a^6*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^6*a^2)","B",0
326,1,130,0,0.215188," ","integrate(x^4*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, A a^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{5}{2}}} + \frac{1}{40320} \, \sqrt{c x^{2} + a} {\left(\frac{1024 \, B a^{4}}{c^{3}} - {\left(\frac{945 \, A a^{3}}{c^{2}} + 2 \, {\left(\frac{256 \, B a^{3}}{c^{2}} - {\left(\frac{315 \, A a^{2}}{c} + 4 \, {\left(\frac{48 \, B a^{2}}{c} + 5 \, {\left(189 \, A a + 2 \, {\left(80 \, B a + 7 \, {\left(8 \, B c x + 9 \, A c\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-3/128*A*a^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2) + 1/40320*sqrt(c*x^2 + a)*(1024*B*a^4/c^3 - (945*A*a^3/c^2 + 2*(256*B*a^3/c^2 - (315*A*a^2/c + 4*(48*B*a^2/c + 5*(189*A*a + 2*(80*B*a + 7*(8*B*c*x + 9*A*c)*x)*x)*x)*x)*x)*x)*x)","A",0
327,1,115,0,0.200523," ","integrate(x^3*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, B a^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{5}{2}}} - \frac{1}{4480} \, \sqrt{c x^{2} + a} {\left(\frac{256 \, A a^{3}}{c^{2}} + {\left(\frac{105 \, B a^{3}}{c^{2}} - 2 \, {\left(\frac{64 \, A a^{2}}{c} + {\left(\frac{35 \, B a^{2}}{c} + 4 \, {\left(128 \, A a + 5 \, {\left(21 \, B a + 2 \, {\left(7 \, B c x + 8 \, A c\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-3/128*B*a^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2) - 1/4480*sqrt(c*x^2 + a)*(256*A*a^3/c^2 + (105*B*a^3/c^2 - 2*(64*A*a^2/c + (35*B*a^2/c + 4*(128*A*a + 5*(21*B*a + 2*(7*B*c*x + 8*A*c)*x)*x)*x)*x)*x)*x)","A",0
328,1,103,0,0.198132," ","integrate(x^2*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{A a^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{3}{2}}} - \frac{1}{1680} \, \sqrt{c x^{2} + a} {\left(\frac{96 \, B a^{3}}{c^{2}} - {\left(\frac{105 \, A a^{2}}{c} + 2 \, {\left(\frac{24 \, B a^{2}}{c} + {\left(245 \, A a + 4 \, {\left(48 \, B a + 5 \, {\left(6 \, B c x + 7 \, A c\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"1/16*A*a^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2) - 1/1680*sqrt(c*x^2 + a)*(96*B*a^3/c^2 - (105*A*a^2/c + 2*(24*B*a^2/c + (245*A*a + 4*(48*B*a + 5*(6*B*c*x + 7*A*c)*x)*x)*x)*x)*x)","A",0
329,1,89,0,0.238324," ","integrate(x*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{B a^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{3}{2}}} + \frac{1}{240} \, \sqrt{c x^{2} + a} {\left(\frac{48 \, A a^{2}}{c} + {\left(\frac{15 \, B a^{2}}{c} + 2 \, {\left(48 \, A a + {\left(35 \, B a + 4 \, {\left(5 \, B c x + 6 \, A c\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"1/16*B*a^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2) + 1/240*sqrt(c*x^2 + a)*(48*A*a^2/c + (15*B*a^2/c + 2*(48*A*a + (35*B*a + 4*(5*B*c*x + 6*A*c)*x)*x)*x)*x)","A",0
330,1,76,0,0.187270," ","integrate((B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, A a^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, \sqrt{c}} + \frac{1}{40} \, \sqrt{c x^{2} + a} {\left(\frac{8 \, B a^{2}}{c} + {\left(25 \, A a + 2 \, {\left(8 \, B a + {\left(4 \, B c x + 5 \, A c\right)} x\right)} x\right)} x\right)}"," ",0,"-3/8*A*a^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/40*sqrt(c*x^2 + a)*(8*B*a^2/c + (25*A*a + 2*(8*B*a + (4*B*c*x + 5*A*c)*x)*x)*x)","A",0
331,1,100,0,0.204714," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x,x, algorithm=""giac"")","\frac{2 \, A a^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{3 \, B a^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, \sqrt{c}} + \frac{1}{24} \, \sqrt{c x^{2} + a} {\left(32 \, A a + {\left(15 \, B a + 2 \, {\left(3 \, B c x + 4 \, A c\right)} x\right)} x\right)}"," ",0,"2*A*a^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 3/8*B*a^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/24*sqrt(c*x^2 + a)*(32*A*a + (15*B*a + 2*(3*B*c*x + 4*A*c)*x)*x)","A",0
332,1,124,0,0.202015," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^2,x, algorithm=""giac"")","\frac{2 \, B a^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{3}{2} \, A a \sqrt{c} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{2 \, A a^{2} \sqrt{c}}{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a} + \frac{1}{6} \, \sqrt{c x^{2} + a} {\left(8 \, B a + {\left(2 \, B c x + 3 \, A c\right)} x\right)}"," ",0,"2*B*a^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 3/2*A*a*sqrt(c)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 2*A*a^2*sqrt(c)/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a) + 1/6*sqrt(c*x^2 + a)*(8*B*a + (2*B*c*x + 3*A*c)*x)","A",0
333,1,191,0,0.249959," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^3,x, algorithm=""giac"")","\frac{3 \, A a c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{3}{2} \, B a \sqrt{c} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{1}{2} \, {\left(B c x + 2 \, A c\right)} \sqrt{c x^{2} + a} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{2} \sqrt{c} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{2} c - 2 \, B a^{3} \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{2}}"," ",0,"3*A*a*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 3/2*B*a*sqrt(c)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 1/2*(B*c*x + 2*A*c)*sqrt(c*x^2 + a) + ((sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a*c + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^2*sqrt(c) + (sqrt(c)*x - sqrt(c*x^2 + a))*A*a^2*c - 2*B*a^3*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^2","B",0
334,1,211,0,0.217205," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^4,x, algorithm=""giac"")","\frac{3 \, B a c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - A c^{\frac{3}{2}} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \sqrt{c x^{2} + a} B c + \frac{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B a c + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a c^{\frac{3}{2}} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a^{2} c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{3} c + 8 \, A a^{3} c^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"3*B*a*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - A*c^(3/2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + sqrt(c*x^2 + a)*B*c + 1/3*(3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*a*c + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a*c^(3/2) - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a^2*c^(3/2) - 3*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^3*c + 8*A*a^3*c^(3/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^3","B",0
335,1,285,0,0.221242," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^5,x, algorithm=""giac"")","\frac{3 \, A c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a}} - B c^{\frac{3}{2}} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A c^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} B a c^{\frac{3}{2}} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a c^{2} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} B a^{2} c^{\frac{3}{2}} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{2} c^{2} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{3} c^{\frac{3}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{3} c^{2} - 32 \, B a^{4} c^{\frac{3}{2}}}{12 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{4}}"," ",0,"3/4*A*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - B*c^(3/2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 1/12*(15*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*c^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + a))^6*B*a*c^(3/2) + 9*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a*c^2 - 96*(sqrt(c)*x - sqrt(c*x^2 + a))^4*B*a^2*c^(3/2) + 9*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^2*c^2 + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^3*c^(3/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^3*c^2 - 32*B*a^4*c^(3/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^4","B",0
336,1,232,0,0.222320," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^6,x, algorithm=""giac"")","\frac{3 \, B c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a}} + \frac{25 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} B c^{2} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} A c^{\frac{5}{2}} - 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} B a c^{2} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{2} c^{\frac{5}{2}} + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} B a^{3} c^{2} - 25 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{4} c^{2} + 8 \, A a^{4} c^{\frac{5}{2}}}{20 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"3/4*B*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) + 1/20*(25*(sqrt(c)*x - sqrt(c*x^2 + a))^9*B*c^2 + 40*(sqrt(c)*x - sqrt(c*x^2 + a))^8*A*c^(5/2) - 10*(sqrt(c)*x - sqrt(c*x^2 + a))^7*B*a*c^2 + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^2*c^(5/2) + 10*(sqrt(c)*x - sqrt(c*x^2 + a))^3*B*a^3*c^2 - 25*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^4*c^2 + 8*A*a^4*c^(5/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^5","B",0
337,1,379,0,0.274375," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{A c^{3} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a} + \frac{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} A c^{3} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} B a c^{\frac{5}{2}} + 235 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} A a c^{3} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} B a^{2} c^{\frac{5}{2}} + 390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A a^{2} c^{3} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} B a^{3} c^{\frac{5}{2}} + 390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a^{3} c^{3} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} B a^{4} c^{\frac{5}{2}} + 235 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{4} c^{3} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{5} c^{\frac{5}{2}} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{5} c^{3} - 48 \, B a^{6} c^{\frac{5}{2}}}{120 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{6} a}"," ",0,"-1/8*A*c^3*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/120*(15*(sqrt(c)*x - sqrt(c*x^2 + a))^11*A*c^3 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^10*B*a*c^(5/2) + 235*(sqrt(c)*x - sqrt(c*x^2 + a))^9*A*a*c^3 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^8*B*a^2*c^(5/2) + 390*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*a^2*c^3 + 480*(sqrt(c)*x - sqrt(c*x^2 + a))^6*B*a^3*c^(5/2) + 390*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a^3*c^3 - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*B*a^4*c^(5/2) + 235*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^4*c^3 + 48*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^5*c^(5/2) + 15*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^5*c^3 - 48*B*a^6*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^6*a)","B",0
338,1,379,0,0.220478," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^8,x, algorithm=""giac"")","-\frac{B c^{3} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a} + \frac{105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} B c^{3} + 1540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} B a c^{3} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} A a c^{\frac{7}{2}} + 1085 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} B a^{2} c^{3} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} A a^{2} c^{\frac{7}{2}} + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} A a^{3} c^{\frac{7}{2}} - 1085 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B a^{4} c^{3} + 1344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{4} c^{\frac{7}{2}} - 1540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} B a^{5} c^{3} + 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a^{5} c^{\frac{7}{2}} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{6} c^{3} - 96 \, A a^{6} c^{\frac{7}{2}}}{840 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{7} a}"," ",0,"-1/8*B*c^3*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/840*(105*(sqrt(c)*x - sqrt(c*x^2 + a))^13*B*c^3 + 1540*(sqrt(c)*x - sqrt(c*x^2 + a))^11*B*a*c^3 + 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^10*A*a*c^(7/2) + 1085*(sqrt(c)*x - sqrt(c*x^2 + a))^9*B*a^2*c^3 + 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^8*A*a^2*c^(7/2) + 6720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*A*a^3*c^(7/2) - 1085*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*a^4*c^3 + 1344*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^4*c^(7/2) - 1540*(sqrt(c)*x - sqrt(c*x^2 + a))^3*B*a^5*c^3 + 672*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a^5*c^(7/2) - 105*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^6*c^3 - 96*A*a^6*c^(7/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^7*a)","B",0
339,1,155,0,0.212478," ","integrate(x^4*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{3 \, A a^{5} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{256 \, c^{\frac{5}{2}}} + \frac{1}{887040} \, {\left(\frac{10240 \, B a^{5}}{c^{3}} - {\left(\frac{10395 \, A a^{4}}{c^{2}} + 2 \, {\left(\frac{2560 \, B a^{4}}{c^{2}} - {\left(\frac{3465 \, A a^{3}}{c} + 4 \, {\left(\frac{480 \, B a^{3}}{c} + {\left(21483 \, A a^{2} + 2 \, {\left(9040 \, B a^{2} + 7 \, {\left(2079 \, A a c + 8 \, {\left(230 \, B a c + 9 \, {\left(10 \, B c^{2} x + 11 \, A c^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} + a}"," ",0,"-3/256*A*a^5*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2) + 1/887040*(10240*B*a^5/c^3 - (10395*A*a^4/c^2 + 2*(2560*B*a^4/c^2 - (3465*A*a^3/c + 4*(480*B*a^3/c + (21483*A*a^2 + 2*(9040*B*a^2 + 7*(2079*A*a*c + 8*(230*B*a*c + 9*(10*B*c^2*x + 11*A*c^2)*x)*x)*x)*x)*x)*x)*x)*x)*x)*sqrt(c*x^2 + a)","A",0
340,1,140,0,0.222967," ","integrate(x^3*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{3 \, B a^{5} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{256 \, c^{\frac{5}{2}}} - \frac{1}{80640} \, {\left(\frac{2560 \, A a^{4}}{c^{2}} + {\left(\frac{945 \, B a^{4}}{c^{2}} - 2 \, {\left(\frac{640 \, A a^{3}}{c} + {\left(\frac{315 \, B a^{3}}{c} + 4 \, {\left(2400 \, A a^{2} + {\left(1953 \, B a^{2} + 2 \, {\left(1520 \, A a c + 7 \, {\left(189 \, B a c + 8 \, {\left(9 \, B c^{2} x + 10 \, A c^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} + a}"," ",0,"-3/256*B*a^5*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2) - 1/80640*(2560*A*a^4/c^2 + (945*B*a^4/c^2 - 2*(640*A*a^3/c + (315*B*a^3/c + 4*(2400*A*a^2 + (1953*B*a^2 + 2*(1520*A*a*c + 7*(189*B*a*c + 8*(9*B*c^2*x + 10*A*c^2)*x)*x)*x)*x)*x)*x)*x)*x)*sqrt(c*x^2 + a)","A",0
341,1,128,0,0.213231," ","integrate(x^2*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{5 \, A a^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{3}{2}}} - \frac{1}{8064} \, {\left(\frac{256 \, B a^{4}}{c^{2}} - {\left(\frac{315 \, A a^{3}}{c} + 2 \, {\left(\frac{64 \, B a^{3}}{c} + {\left(1239 \, A a^{2} + 4 \, {\left(240 \, B a^{2} + {\left(357 \, A a c + 2 \, {\left(152 \, B a c + 7 \, {\left(8 \, B c^{2} x + 9 \, A c^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} + a}"," ",0,"5/128*A*a^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2) - 1/8064*(256*B*a^4/c^2 - (315*A*a^3/c + 2*(64*B*a^3/c + (1239*A*a^2 + 4*(240*B*a^2 + (357*A*a*c + 2*(152*B*a*c + 7*(8*B*c^2*x + 9*A*c^2)*x)*x)*x)*x)*x)*x)*x)*sqrt(c*x^2 + a)","A",0
342,1,114,0,0.197083," ","integrate(x*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{5 \, B a^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{3}{2}}} + \frac{1}{2688} \, {\left(\frac{384 \, A a^{3}}{c} + {\left(\frac{105 \, B a^{3}}{c} + 2 \, {\left(576 \, A a^{2} + {\left(413 \, B a^{2} + 4 \, {\left(144 \, A a c + {\left(119 \, B a c + 6 \, {\left(7 \, B c^{2} x + 8 \, A c^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} + a}"," ",0,"5/128*B*a^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2) + 1/2688*(384*A*a^3/c + (105*B*a^3/c + 2*(576*A*a^2 + (413*B*a^2 + 4*(144*A*a*c + (119*B*a*c + 6*(7*B*c^2*x + 8*A*c^2)*x)*x)*x)*x)*x)*x)*sqrt(c*x^2 + a)","A",0
343,1,101,0,0.196334," ","integrate((B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{5 \, A a^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, \sqrt{c}} + \frac{1}{336} \, {\left(\frac{48 \, B a^{3}}{c} + {\left(231 \, A a^{2} + 2 \, {\left(72 \, B a^{2} + {\left(91 \, A a c + 4 \, {\left(18 \, B a c + {\left(6 \, B c^{2} x + 7 \, A c^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} + a}"," ",0,"-5/16*A*a^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/336*(48*B*a^3/c + (231*A*a^2 + 2*(72*B*a^2 + (91*A*a*c + 4*(18*B*a*c + (6*B*c^2*x + 7*A*c^2)*x)*x)*x)*x)*x)*sqrt(c*x^2 + a)","A",0
344,1,125,0,0.212834," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x,x, algorithm=""giac"")","\frac{2 \, A a^{3} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{5 \, B a^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, \sqrt{c}} + \frac{1}{240} \, {\left(368 \, A a^{2} + {\left(165 \, B a^{2} + 2 \, {\left(88 \, A a c + {\left(65 \, B a c + 4 \, {\left(5 \, B c^{2} x + 6 \, A c^{2}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} + a}"," ",0,"2*A*a^3*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 5/16*B*a^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/240*(368*A*a^2 + (165*B*a^2 + 2*(88*A*a*c + (65*B*a*c + 4*(5*B*c^2*x + 6*A*c^2)*x)*x)*x)*x)*sqrt(c*x^2 + a)","A",0
345,1,150,0,0.256325," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^2,x, algorithm=""giac"")","\frac{2 \, B a^{3} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{15}{8} \, A a^{2} \sqrt{c} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{2 \, A a^{3} \sqrt{c}}{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a} + \frac{1}{120} \, {\left(184 \, B a^{2} + {\left(135 \, A a c + 2 \, {\left(44 \, B a c + 3 \, {\left(4 \, B c^{2} x + 5 \, A c^{2}\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} + a}"," ",0,"2*B*a^3*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 15/8*A*a^2*sqrt(c)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 2*A*a^3*sqrt(c)/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a) + 1/120*(184*B*a^2 + (135*A*a*c + 2*(44*B*a*c + 3*(4*B*c^2*x + 5*A*c^2)*x)*x)*x)*sqrt(c*x^2 + a)","A",0
346,1,219,0,0.221383," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^3,x, algorithm=""giac"")","\frac{5 \, A a^{2} c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{15}{8} \, B a^{2} \sqrt{c} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{1}{24} \, {\left(56 \, A a c + {\left(27 \, B a c + 2 \, {\left(3 \, B c^{2} x + 4 \, A c^{2}\right)} x\right)} x\right)} \sqrt{c x^{2} + a} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{3} \sqrt{c} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{3} c - 2 \, B a^{4} \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{2}}"," ",0,"5*A*a^2*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 15/8*B*a^2*sqrt(c)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 1/24*(56*A*a*c + (27*B*a*c + 2*(3*B*c^2*x + 4*A*c^2)*x)*x)*sqrt(c*x^2 + a) + ((sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^3*sqrt(c) + (sqrt(c)*x - sqrt(c*x^2 + a))*A*a^3*c - 2*B*a^4*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^2","A",0
347,1,239,0,0.231558," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^4,x, algorithm=""giac"")","\frac{5 \, B a^{2} c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{5}{2} \, A a c^{\frac{3}{2}} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{1}{6} \, {\left(14 \, B a c + {\left(2 \, B c^{2} x + 3 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + a} + \frac{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B a^{2} c + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{2} c^{\frac{3}{2}} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a^{3} c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{4} c + 14 \, A a^{4} c^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"5*B*a^2*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 5/2*A*a*c^(3/2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 1/6*(14*B*a*c + (2*B*c^2*x + 3*A*c^2)*x)*sqrt(c*x^2 + a) + 1/3*(3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*a^2*c + 18*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^2*c^(3/2) - 24*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a^3*c^(3/2) - 3*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^4*c + 14*A*a^4*c^(3/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^3","B",0
348,1,316,0,0.244858," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^5,x, algorithm=""giac"")","\frac{15 \, A a c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a}} - \frac{5}{2} \, B a c^{\frac{3}{2}} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{1}{2} \, {\left(B c^{2} x + 2 \, A c^{2}\right)} \sqrt{c x^{2} + a} + \frac{27 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A a c^{2} + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} B a^{2} c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a^{2} c^{2} - 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} B a^{3} c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{3} c^{2} + 152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{4} c^{\frac{3}{2}} + 27 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{4} c^{2} - 56 \, B a^{5} c^{\frac{3}{2}}}{12 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{4}}"," ",0,"15/4*A*a*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - 5/2*B*a*c^(3/2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 1/2*(B*c^2*x + 2*A*c^2)*sqrt(c*x^2 + a) + 1/12*(27*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*a*c^2 + 72*(sqrt(c)*x - sqrt(c*x^2 + a))^6*B*a^2*c^(3/2) - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a^2*c^2 - 168*(sqrt(c)*x - sqrt(c*x^2 + a))^4*B*a^3*c^(3/2) - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^3*c^2 + 152*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^4*c^(3/2) + 27*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^4*c^2 - 56*B*a^5*c^(3/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^4","B",0
349,1,331,0,0.264817," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^6,x, algorithm=""giac"")","\frac{15 \, B a c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a}} - A c^{\frac{5}{2}} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \sqrt{c x^{2} + a} B c^{2} + \frac{135 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} B a c^{2} + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} A a c^{\frac{5}{2}} - 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} B a^{2} c^{2} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} A a^{2} c^{\frac{5}{2}} + 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{3} c^{\frac{5}{2}} + 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} B a^{4} c^{2} - 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a^{4} c^{\frac{5}{2}} - 135 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{5} c^{2} + 184 \, A a^{5} c^{\frac{5}{2}}}{60 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"15/4*B*a*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - A*c^(5/2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + sqrt(c*x^2 + a)*B*c^2 + 1/60*(135*(sqrt(c)*x - sqrt(c*x^2 + a))^9*B*a*c^2 + 360*(sqrt(c)*x - sqrt(c*x^2 + a))^8*A*a*c^(5/2) - 150*(sqrt(c)*x - sqrt(c*x^2 + a))^7*B*a^2*c^2 - 720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*A*a^2*c^(5/2) + 1120*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^3*c^(5/2) + 150*(sqrt(c)*x - sqrt(c*x^2 + a))^3*B*a^4*c^2 - 560*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a^4*c^(5/2) - 135*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^5*c^2 + 184*A*a^5*c^(5/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^5","B",0
350,1,397,0,0.256827," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^7,x, algorithm=""giac"")","\frac{5 \, A c^{3} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a}} - B c^{\frac{5}{2}} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{165 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} A c^{3} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} B a c^{\frac{5}{2}} + 25 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} A a c^{3} - 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} B a^{2} c^{\frac{5}{2}} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A a^{2} c^{3} + 3680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} B a^{3} c^{\frac{5}{2}} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a^{3} c^{3} - 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} B a^{4} c^{\frac{5}{2}} + 25 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{4} c^{3} + 1488 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{5} c^{\frac{5}{2}} + 165 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{5} c^{3} - 368 \, B a^{6} c^{\frac{5}{2}}}{120 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{6}}"," ",0,"5/8*A*c^3*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - B*c^(5/2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 1/120*(165*(sqrt(c)*x - sqrt(c*x^2 + a))^11*A*c^3 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^10*B*a*c^(5/2) + 25*(sqrt(c)*x - sqrt(c*x^2 + a))^9*A*a*c^3 - 2160*(sqrt(c)*x - sqrt(c*x^2 + a))^8*B*a^2*c^(5/2) + 450*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*a^2*c^3 + 3680*(sqrt(c)*x - sqrt(c*x^2 + a))^6*B*a^3*c^(5/2) + 450*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a^3*c^3 - 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^4*B*a^4*c^(5/2) + 25*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^4*c^3 + 1488*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^5*c^(5/2) + 165*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^5*c^3 - 368*B*a^6*c^(5/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^6","B",0
351,1,316,0,0.243902," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^8,x, algorithm=""giac"")","\frac{5 \, B c^{3} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a}} + \frac{231 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} B c^{3} + 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} A c^{\frac{7}{2}} - 196 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} B a c^{3} + 595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} B a^{2} c^{3} + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} A a^{2} c^{\frac{7}{2}} - 595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B a^{4} c^{3} + 1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{4} c^{\frac{7}{2}} + 196 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} B a^{5} c^{3} - 231 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{6} c^{3} + 48 \, A a^{6} c^{\frac{7}{2}}}{168 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"5/8*B*c^3*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) + 1/168*(231*(sqrt(c)*x - sqrt(c*x^2 + a))^13*B*c^3 + 336*(sqrt(c)*x - sqrt(c*x^2 + a))^12*A*c^(7/2) - 196*(sqrt(c)*x - sqrt(c*x^2 + a))^11*B*a*c^3 + 595*(sqrt(c)*x - sqrt(c*x^2 + a))^9*B*a^2*c^3 + 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^8*A*a^2*c^(7/2) - 595*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*a^4*c^3 + 1008*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^4*c^(7/2) + 196*(sqrt(c)*x - sqrt(c*x^2 + a))^3*B*a^5*c^3 - 231*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^6*c^3 + 48*A*a^6*c^(7/2))/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^7","B",0
352,1,491,0,0.235996," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^9,x, algorithm=""giac"")","-\frac{5 \, A c^{4} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{64 \, \sqrt{-a} a} + \frac{105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{15} A c^{4} + 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{14} B a c^{\frac{7}{2}} + 2779 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} A a c^{4} - 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} B a^{2} c^{\frac{7}{2}} + 6265 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} A a^{2} c^{4} + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} B a^{3} c^{\frac{7}{2}} + 12355 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} A a^{3} c^{4} - 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} B a^{4} c^{\frac{7}{2}} + 12355 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A a^{4} c^{4} + 8064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} B a^{5} c^{\frac{7}{2}} + 6265 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a^{5} c^{4} - 8064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} B a^{6} c^{\frac{7}{2}} + 2779 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{6} c^{4} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{7} c^{\frac{7}{2}} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{7} c^{4} - 384 \, B a^{8} c^{\frac{7}{2}}}{1344 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{8} a}"," ",0,"-5/64*A*c^4*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/1344*(105*(sqrt(c)*x - sqrt(c*x^2 + a))^15*A*c^4 + 2688*(sqrt(c)*x - sqrt(c*x^2 + a))^14*B*a*c^(7/2) + 2779*(sqrt(c)*x - sqrt(c*x^2 + a))^13*A*a*c^4 - 2688*(sqrt(c)*x - sqrt(c*x^2 + a))^12*B*a^2*c^(7/2) + 6265*(sqrt(c)*x - sqrt(c*x^2 + a))^11*A*a^2*c^4 + 13440*(sqrt(c)*x - sqrt(c*x^2 + a))^10*B*a^3*c^(7/2) + 12355*(sqrt(c)*x - sqrt(c*x^2 + a))^9*A*a^3*c^4 - 13440*(sqrt(c)*x - sqrt(c*x^2 + a))^8*B*a^4*c^(7/2) + 12355*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*a^4*c^4 + 8064*(sqrt(c)*x - sqrt(c*x^2 + a))^6*B*a^5*c^(7/2) + 6265*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a^5*c^4 - 8064*(sqrt(c)*x - sqrt(c*x^2 + a))^4*B*a^6*c^(7/2) + 2779*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^6*c^4 + 384*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^7*c^(7/2) + 105*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^7*c^4 - 384*B*a^8*c^(7/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^8*a)","B",0
353,1,491,0,0.251152," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^10,x, algorithm=""giac"")","-\frac{5 \, B c^{4} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{64 \, \sqrt{-a} a} + \frac{315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{17} B c^{4} + 8022 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{15} B a c^{4} + 16128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{14} A a c^{\frac{9}{2}} + 10458 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} B a^{2} c^{4} + 26880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} A a^{2} c^{\frac{9}{2}} + 18270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} B a^{3} c^{4} + 80640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} A a^{3} c^{\frac{9}{2}} + 48384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} A a^{4} c^{\frac{9}{2}} - 18270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} B a^{5} c^{4} + 48384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} A a^{5} c^{\frac{9}{2}} - 10458 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B a^{6} c^{4} + 6912 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{6} c^{\frac{9}{2}} - 8022 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} B a^{7} c^{4} + 2304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a^{7} c^{\frac{9}{2}} - 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{8} c^{4} - 256 \, A a^{8} c^{\frac{9}{2}}}{4032 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{9} a}"," ",0,"-5/64*B*c^4*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/4032*(315*(sqrt(c)*x - sqrt(c*x^2 + a))^17*B*c^4 + 8022*(sqrt(c)*x - sqrt(c*x^2 + a))^15*B*a*c^4 + 16128*(sqrt(c)*x - sqrt(c*x^2 + a))^14*A*a*c^(9/2) + 10458*(sqrt(c)*x - sqrt(c*x^2 + a))^13*B*a^2*c^4 + 26880*(sqrt(c)*x - sqrt(c*x^2 + a))^12*A*a^2*c^(9/2) + 18270*(sqrt(c)*x - sqrt(c*x^2 + a))^11*B*a^3*c^4 + 80640*(sqrt(c)*x - sqrt(c*x^2 + a))^10*A*a^3*c^(9/2) + 48384*(sqrt(c)*x - sqrt(c*x^2 + a))^8*A*a^4*c^(9/2) - 18270*(sqrt(c)*x - sqrt(c*x^2 + a))^7*B*a^5*c^4 + 48384*(sqrt(c)*x - sqrt(c*x^2 + a))^6*A*a^5*c^(9/2) - 10458*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*a^6*c^4 + 6912*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^6*c^(9/2) - 8022*(sqrt(c)*x - sqrt(c*x^2 + a))^3*B*a^7*c^4 + 2304*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a^7*c^(9/2) - 315*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^8*c^4 - 256*A*a^8*c^(9/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^9*a)","B",0
354,1,87,0,0.194876," ","integrate(x^4*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{120} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(\frac{4 \, B x}{c} + \frac{5 \, A}{c}\right)} x - \frac{16 \, B a}{c^{2}}\right)} x - \frac{45 \, A a}{c^{2}}\right)} x + \frac{64 \, B a^{2}}{c^{3}}\right)} - \frac{3 \, A a^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/120*sqrt(c*x^2 + a)*((2*(3*(4*B*x/c + 5*A/c)*x - 16*B*a/c^2)*x - 45*A*a/c^2)*x + 64*B*a^2/c^3) - 3/8*A*a^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
355,1,74,0,0.217981," ","integrate(x^3*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(\frac{3 \, B x}{c} + \frac{4 \, A}{c}\right)} x - \frac{9 \, B a}{c^{2}}\right)} x - \frac{16 \, A a}{c^{2}}\right)} - \frac{3 \, B a^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + a)*((2*(3*B*x/c + 4*A/c)*x - 9*B*a/c^2)*x - 16*A*a/c^2) - 3/8*B*a^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
356,1,61,0,0.194710," ","integrate(x^2*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{c x^{2} + a} {\left({\left(\frac{2 \, B x}{c} + \frac{3 \, A}{c}\right)} x - \frac{4 \, B a}{c^{2}}\right)} + \frac{A a \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"1/6*sqrt(c*x^2 + a)*((2*B*x/c + 3*A/c)*x - 4*B*a/c^2) + 1/2*A*a*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
357,1,50,0,0.200135," ","integrate(x*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} + a} {\left(\frac{B x}{c} + \frac{2 \, A}{c}\right)} + \frac{B a \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"1/2*sqrt(c*x^2 + a)*(B*x/c + 2*A/c) + 1/2*B*a*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
358,1,39,0,0.189728," ","integrate((B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{A \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{\sqrt{c}} + \frac{\sqrt{c x^{2} + a} B}{c}"," ",0,"-A*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + sqrt(c*x^2 + a)*B/c","A",0
359,1,58,0,0.208594," ","integrate((B*x+A)/x/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, A \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{B \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{\sqrt{c}}"," ",0,"2*A*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) - B*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c)","A",0
360,1,65,0,0.190504," ","integrate((B*x+A)/x^2/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, B \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, A \sqrt{c}}{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a}"," ",0,"2*B*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/sqrt(-a) + 2*A*sqrt(c)/((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)","A",0
361,1,146,0,0.196881," ","integrate((B*x+A)/x^3/(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{A c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a \sqrt{c} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a c - 2 \, B a^{2} \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{2} a}"," ",0,"-A*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + ((sqrt(c)*x - sqrt(c*x^2 + a))^3*A*c + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a*sqrt(c) + (sqrt(c)*x - sqrt(c*x^2 + a))*A*a*c - 2*B*a^2*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^2*a)","B",0
362,1,151,0,0.220653," ","integrate((B*x+A)/x^4/(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{B c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B c + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{2} c - 4 \, A a^{2} c^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{3} a}"," ",0,"-B*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/3*(3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*c + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a*c^(3/2) - 3*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^2*c - 4*A*a^2*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^3*a)","A",0
363,1,241,0,0.210979," ","integrate((B*x+A)/x^5/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{3 \, A c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{2}} - \frac{9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} A c^{2} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} A a c^{2} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} B a^{2} c^{\frac{3}{2}} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A a^{2} c^{2} + 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a^{3} c^{\frac{3}{2}} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a^{3} c^{2} - 16 \, B a^{4} c^{\frac{3}{2}}}{12 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{4} a^{2}}"," ",0,"3/4*A*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) - 1/12*(9*(sqrt(c)*x - sqrt(c*x^2 + a))^7*A*c^2 - 33*(sqrt(c)*x - sqrt(c*x^2 + a))^5*A*a*c^2 - 48*(sqrt(c)*x - sqrt(c*x^2 + a))^4*B*a^2*c^(3/2) - 33*(sqrt(c)*x - sqrt(c*x^2 + a))^3*A*a^2*c^2 + 64*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a^3*c^(3/2) + 9*(sqrt(c)*x - sqrt(c*x^2 + a))*A*a^3*c^2 - 16*B*a^4*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^4*a^2)","B",0
364,1,241,0,0.209773," ","integrate((B*x+A)/x^6/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{3 \, B c^{2} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{2}} - \frac{45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} B c^{2} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} B a c^{2} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A a^{2} c^{\frac{5}{2}} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} B a^{3} c^{2} + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a^{3} c^{\frac{5}{2}} - 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{4} c^{2} - 64 \, A a^{4} c^{\frac{5}{2}}}{60 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{5} a^{2}}"," ",0,"3/4*B*c^2*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) - 1/60*(45*(sqrt(c)*x - sqrt(c*x^2 + a))^9*B*c^2 - 210*(sqrt(c)*x - sqrt(c*x^2 + a))^7*B*a*c^2 - 640*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*a^2*c^(5/2) + 210*(sqrt(c)*x - sqrt(c*x^2 + a))^3*B*a^3*c^2 + 320*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a^3*c^(5/2) - 45*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^4*c^2 - 64*A*a^4*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^5*a^2)","B",0
365,1,83,0,0.197996," ","integrate(x^4*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(\frac{2 \, B x}{c} + \frac{3 \, A}{c}\right)} x - \frac{8 \, B a}{c^{2}}\right)} x + \frac{9 \, A a}{c^{2}}\right)} x - \frac{16 \, B a^{2}}{c^{3}}}{6 \, \sqrt{c x^{2} + a}} + \frac{3 \, A a \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"1/6*((((2*B*x/c + 3*A/c)*x - 8*B*a/c^2)*x + 9*A*a/c^2)*x - 16*B*a^2/c^3)/sqrt(c*x^2 + a) + 3/2*A*a*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
366,1,70,0,0.208046," ","integrate(x^3*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{B x}{c} + \frac{2 \, A}{c}\right)} x + \frac{3 \, B a}{c^{2}}\right)} x + \frac{4 \, A a}{c^{2}}}{2 \, \sqrt{c x^{2} + a}} + \frac{3 \, B a \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"1/2*(((B*x/c + 2*A/c)*x + 3*B*a/c^2)*x + 4*A*a/c^2)/sqrt(c*x^2 + a) + 3/2*B*a*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
367,1,58,0,0.208625," ","integrate(x^2*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{B x}{c} - \frac{A}{c}\right)} x + \frac{2 \, B a}{c^{2}}}{\sqrt{c x^{2} + a}} - \frac{A \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"((B*x/c - A/c)*x + 2*B*a/c^2)/sqrt(c*x^2 + a) - A*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
368,1,48,0,0.236700," ","integrate(x*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{B x}{c} + \frac{A}{c}}{\sqrt{c x^{2} + a}} - \frac{B \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-(B*x/c + A/c)/sqrt(c*x^2 + a) - B*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
369,1,23,0,0.198293," ","integrate((B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{A x}{a} - \frac{B}{c}}{\sqrt{c x^{2} + a}}"," ",0,"(A*x/a - B/c)/sqrt(c*x^2 + a)","A",0
370,1,59,0,0.191637," ","integrate((B*x+A)/x/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{B x}{a} + \frac{A}{a}}{\sqrt{c x^{2} + a}} + \frac{2 \, A \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a}"," ",0,"(B*x/a + A/a)/sqrt(c*x^2 + a) + 2*A*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a)","A",0
371,1,96,0,0.206757," ","integrate((B*x+A)/x^2/(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{A c x}{a^{2}} - \frac{B}{a}}{\sqrt{c x^{2} + a}} + \frac{2 \, B \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{2 \, A \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)} a}"," ",0,"-(A*c*x/a^2 - B/a)/sqrt(c*x^2 + a) + 2*B*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 2*A*sqrt(c)/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)*a)","A",0
372,1,171,0,0.203340," ","integrate((B*x+A)/x^3/(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{B c x}{a^{2}} + \frac{A c}{a^{2}}}{\sqrt{c x^{2} + a}} - \frac{3 \, A c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a \sqrt{c} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a c - 2 \, B a^{2} \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{2} a^{2}}"," ",0,"-(B*c*x/a^2 + A*c/a^2)/sqrt(c*x^2 + a) - 3*A*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) + ((sqrt(c)*x - sqrt(c*x^2 + a))^3*A*c + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a*sqrt(c) + (sqrt(c)*x - sqrt(c*x^2 + a))*A*a*c - 2*B*a^2*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^2*a^2)","B",0
373,1,203,0,0.205303," ","integrate((B*x+A)/x^4/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{A c^{2} x}{a^{3}} - \frac{B c}{a^{2}}}{\sqrt{c x^{2} + a}} - \frac{3 \, B c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} B c - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} A c^{\frac{3}{2}} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} A a c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} B a^{2} c - 10 \, A a^{2} c^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{3} a^{2}}"," ",0,"(A*c^2*x/a^3 - B*c/a^2)/sqrt(c*x^2 + a) - 3*B*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) + 1/3*(3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*B*c - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*A*c^(3/2) + 24*(sqrt(c)*x - sqrt(c*x^2 + a))^2*A*a*c^(3/2) - 3*(sqrt(c)*x - sqrt(c*x^2 + a))*B*a^2*c - 10*A*a^2*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^3*a^2)","B",0
374,1,82,0,0.212051," ","integrate(x^4*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(\frac{3 \, B x}{c} - \frac{4 \, A}{c}\right)} x + \frac{12 \, B a}{c^{2}}\right)} x - \frac{3 \, A a}{c^{2}}\right)} x + \frac{8 \, B a^{2}}{c^{3}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}} - \frac{A \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"1/3*((((3*B*x/c - 4*A/c)*x + 12*B*a/c^2)*x - 3*A*a/c^2)*x + 8*B*a^2/c^3)/(c*x^2 + a)^(3/2) - A*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
375,1,70,0,0.223845," ","integrate(x^3*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(\frac{4 \, B x}{c} + \frac{3 \, A}{c}\right)} x + \frac{3 \, B a}{c^{2}}\right)} x + \frac{2 \, A a}{c^{2}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}} - \frac{B \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"-1/3*(((4*B*x/c + 3*A/c)*x + 3*B*a/c^2)*x + 2*A*a/c^2)/(c*x^2 + a)^(3/2) - B*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
376,1,36,0,0.196029," ","integrate(x^2*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{A x}{a} - \frac{3 \, B}{c}\right)} x^{2} - \frac{2 \, B a}{c^{2}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*((A*x/a - 3*B/c)*x^2 - 2*B*a/c^2)/(c*x^2 + a)^(3/2)","A",0
377,1,26,0,0.240184," ","integrate(x*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{\frac{B x^{3}}{a} - \frac{A}{c}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*(B*x^3/a - A/c)/(c*x^2 + a)^(3/2)","A",0
378,1,37,0,0.216614," ","integrate((B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{2 \, A c x^{2}}{a^{2}} + \frac{3 \, A}{a}\right)} x - \frac{B}{c}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*((2*A*c*x^2/a^2 + 3*A/a)*x - B/c)/(c*x^2 + a)^(3/2)","A",0
379,1,82,0,0.204258," ","integrate((B*x+A)/x/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, B c x}{a^{2}} + \frac{3 \, A c}{a^{2}}\right)} x + \frac{3 \, B}{a}\right)} x + \frac{4 \, A}{a}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}} + \frac{2 \, A \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}}"," ",0,"1/3*(((2*B*c*x/a^2 + 3*A*c/a^2)*x + 3*B/a)*x + 4*A/a)/(c*x^2 + a)^(3/2) + 2*A*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2)","A",0
380,1,119,0,0.206999," ","integrate((B*x+A)/x^2/(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(\frac{5 \, A c^{2} x}{a^{3}} - \frac{3 \, B c}{a^{2}}\right)} x + \frac{6 \, A c}{a^{2}}\right)} x - \frac{4 \, B}{a}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}} + \frac{2 \, B \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{2 \, A \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)} a^{2}}"," ",0,"-1/3*(((5*A*c^2*x/a^3 - 3*B*c/a^2)*x + 6*A*c/a^2)*x - 4*B/a)/(c*x^2 + a)^(3/2) + 2*B*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) + 2*A*sqrt(c)/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)*a^2)","A",0
381,1,197,0,0.220414," ","integrate((B*x+A)/x^3/(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(\frac{5 \, B c^{2} x}{a^{3}} + \frac{6 \, A c^{2}}{a^{3}}\right)} x + \frac{6 \, B c}{a^{2}}\right)} x + \frac{7 \, A c}{a^{2}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}} - \frac{5 \, A c \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} A c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} B a \sqrt{c} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} A a c - 2 \, B a^{2} \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} - a\right)}^{2} a^{3}}"," ",0,"-1/3*(((5*B*c^2*x/a^3 + 6*A*c^2/a^3)*x + 6*B*c/a^2)*x + 7*A*c/a^2)/(c*x^2 + a)^(3/2) - 5*A*c*arctan(-(sqrt(c)*x - sqrt(c*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^3) + ((sqrt(c)*x - sqrt(c*x^2 + a))^3*A*c + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*B*a*sqrt(c) + (sqrt(c)*x - sqrt(c*x^2 + a))*A*a*c - 2*B*a^2*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + a))^2 - a)^2*a^3)","A",0
382,1,53,0,0.250382," ","integrate((e*x+d)/(c*x^2+a)^(7/2),x, algorithm=""giac"")","\frac{{\left(4 \, {\left(\frac{2 \, c^{2} d x^{2}}{a^{3}} + \frac{5 \, c d}{a^{2}}\right)} x^{2} + \frac{15 \, d}{a}\right)} x - \frac{3 \, e}{c}}{15 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}}}"," ",0,"1/15*((4*(2*c^2*d*x^2/a^3 + 5*c*d/a^2)*x^2 + 15*d/a)*x - 3*e/c)/(c*x^2 + a)^(5/2)","A",0
383,1,68,0,0.226880," ","integrate((e*x+d)/(c*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left(2 \, {\left(4 \, {\left(\frac{2 \, c^{3} d x^{2}}{a^{4}} + \frac{7 \, c^{2} d}{a^{3}}\right)} x^{2} + \frac{35 \, c d}{a^{2}}\right)} x^{2} + \frac{35 \, d}{a}\right)} x - \frac{5 \, e}{c}}{35 \, {\left(c x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/35*((2*(4*(2*c^3*d*x^2/a^4 + 7*c^2*d/a^3)*x^2 + 35*c*d/a^2)*x^2 + 35*d/a)*x - 5*e/c)/(c*x^2 + a)^(7/2)","A",0
384,1,29,0,0.232833," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{2}{15} \, B c x^{\frac{15}{2}} + \frac{2}{13} \, A c x^{\frac{13}{2}} + \frac{2}{11} \, B a x^{\frac{11}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}}"," ",0,"2/15*B*c*x^(15/2) + 2/13*A*c*x^(13/2) + 2/11*B*a*x^(11/2) + 2/9*A*a*x^(9/2)","A",0
385,1,29,0,0.152355," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{2}{13} \, B c x^{\frac{13}{2}} + \frac{2}{11} \, A c x^{\frac{11}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}}"," ",0,"2/13*B*c*x^(13/2) + 2/11*A*c*x^(11/2) + 2/9*B*a*x^(9/2) + 2/7*A*a*x^(7/2)","A",0
386,1,29,0,0.149779," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{2}{11} \, B c x^{\frac{11}{2}} + \frac{2}{9} \, A c x^{\frac{9}{2}} + \frac{2}{7} \, B a x^{\frac{7}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}}"," ",0,"2/11*B*c*x^(11/2) + 2/9*A*c*x^(9/2) + 2/7*B*a*x^(7/2) + 2/5*A*a*x^(5/2)","A",0
387,1,29,0,0.149960," ","integrate((B*x+A)*(c*x^2+a)*x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{7} \, A c x^{\frac{7}{2}} + \frac{2}{5} \, B a x^{\frac{5}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}}"," ",0,"2/9*B*c*x^(9/2) + 2/7*A*c*x^(7/2) + 2/5*B*a*x^(5/2) + 2/3*A*a*x^(3/2)","A",0
388,1,29,0,0.147999," ","integrate((B*x+A)*(c*x^2+a)/x^(1/2),x, algorithm=""giac"")","\frac{2}{7} \, B c x^{\frac{7}{2}} + \frac{2}{5} \, A c x^{\frac{5}{2}} + \frac{2}{3} \, B a x^{\frac{3}{2}} + 2 \, A a \sqrt{x}"," ",0,"2/7*B*c*x^(7/2) + 2/5*A*c*x^(5/2) + 2/3*B*a*x^(3/2) + 2*A*a*sqrt(x)","A",0
389,1,29,0,0.151978," ","integrate((B*x+A)*(c*x^2+a)/x^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, B c x^{\frac{5}{2}} + \frac{2}{3} \, A c x^{\frac{3}{2}} + 2 \, B a \sqrt{x} - \frac{2 \, A a}{\sqrt{x}}"," ",0,"2/5*B*c*x^(5/2) + 2/3*A*c*x^(3/2) + 2*B*a*sqrt(x) - 2*A*a/sqrt(x)","A",0
390,1,29,0,0.150390," ","integrate((B*x+A)*(c*x^2+a)/x^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, B c x^{\frac{3}{2}} + 2 \, A c \sqrt{x} - \frac{2 \, {\left(3 \, B a x + A a\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*B*c*x^(3/2) + 2*A*c*sqrt(x) - 2/3*(3*B*a*x + A*a)/x^(3/2)","A",0
391,1,30,0,0.150766," ","integrate((B*x+A)*(c*x^2+a)/x^(7/2),x, algorithm=""giac"")","2 \, B c \sqrt{x} - \frac{2 \, {\left(15 \, A c x^{2} + 5 \, B a x + 3 \, A a\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2*B*c*sqrt(x) - 2/15*(15*A*c*x^2 + 5*B*a*x + 3*A*a)/x^(5/2)","A",0
392,1,29,0,0.156162," ","integrate((B*x+A)*(c*x^2+a)/x^(9/2),x, algorithm=""giac"")","-\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
393,1,53,0,0.156909," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{19} \, B c^{2} x^{\frac{19}{2}} + \frac{2}{17} \, A c^{2} x^{\frac{17}{2}} + \frac{4}{15} \, B a c x^{\frac{15}{2}} + \frac{4}{13} \, A a c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}}"," ",0,"2/19*B*c^2*x^(19/2) + 2/17*A*c^2*x^(17/2) + 4/15*B*a*c*x^(15/2) + 4/13*A*a*c*x^(13/2) + 2/11*B*a^2*x^(11/2) + 2/9*A*a^2*x^(9/2)","A",0
394,1,53,0,0.150404," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{17} \, B c^{2} x^{\frac{17}{2}} + \frac{2}{15} \, A c^{2} x^{\frac{15}{2}} + \frac{4}{13} \, B a c x^{\frac{13}{2}} + \frac{4}{11} \, A a c x^{\frac{11}{2}} + \frac{2}{9} \, B a^{2} x^{\frac{9}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}}"," ",0,"2/17*B*c^2*x^(17/2) + 2/15*A*c^2*x^(15/2) + 4/13*B*a*c*x^(13/2) + 4/11*A*a*c*x^(11/2) + 2/9*B*a^2*x^(9/2) + 2/7*A*a^2*x^(7/2)","A",0
395,1,53,0,0.152774," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{15} \, B c^{2} x^{\frac{15}{2}} + \frac{2}{13} \, A c^{2} x^{\frac{13}{2}} + \frac{4}{11} \, B a c x^{\frac{11}{2}} + \frac{4}{9} \, A a c x^{\frac{9}{2}} + \frac{2}{7} \, B a^{2} x^{\frac{7}{2}} + \frac{2}{5} \, A a^{2} x^{\frac{5}{2}}"," ",0,"2/15*B*c^2*x^(15/2) + 2/13*A*c^2*x^(13/2) + 4/11*B*a*c*x^(11/2) + 4/9*A*a*c*x^(9/2) + 2/7*B*a^2*x^(7/2) + 2/5*A*a^2*x^(5/2)","A",0
396,1,53,0,0.147542," ","integrate((B*x+A)*(c*x^2+a)^2*x^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, B c^{2} x^{\frac{13}{2}} + \frac{2}{11} \, A c^{2} x^{\frac{11}{2}} + \frac{4}{9} \, B a c x^{\frac{9}{2}} + \frac{4}{7} \, A a c x^{\frac{7}{2}} + \frac{2}{5} \, B a^{2} x^{\frac{5}{2}} + \frac{2}{3} \, A a^{2} x^{\frac{3}{2}}"," ",0,"2/13*B*c^2*x^(13/2) + 2/11*A*c^2*x^(11/2) + 4/9*B*a*c*x^(9/2) + 4/7*A*a*c*x^(7/2) + 2/5*B*a^2*x^(5/2) + 2/3*A*a^2*x^(3/2)","A",0
397,1,53,0,0.150300," ","integrate((B*x+A)*(c*x^2+a)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, B c^{2} x^{\frac{11}{2}} + \frac{2}{9} \, A c^{2} x^{\frac{9}{2}} + \frac{4}{7} \, B a c x^{\frac{7}{2}} + \frac{4}{5} \, A a c x^{\frac{5}{2}} + \frac{2}{3} \, B a^{2} x^{\frac{3}{2}} + 2 \, A a^{2} \sqrt{x}"," ",0,"2/11*B*c^2*x^(11/2) + 2/9*A*c^2*x^(9/2) + 4/7*B*a*c*x^(7/2) + 4/5*A*a*c*x^(5/2) + 2/3*B*a^2*x^(3/2) + 2*A*a^2*sqrt(x)","A",0
398,1,53,0,0.154446," ","integrate((B*x+A)*(c*x^2+a)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{9} \, B c^{2} x^{\frac{9}{2}} + \frac{2}{7} \, A c^{2} x^{\frac{7}{2}} + \frac{4}{5} \, B a c x^{\frac{5}{2}} + \frac{4}{3} \, A a c x^{\frac{3}{2}} + 2 \, B a^{2} \sqrt{x} - \frac{2 \, A a^{2}}{\sqrt{x}}"," ",0,"2/9*B*c^2*x^(9/2) + 2/7*A*c^2*x^(7/2) + 4/5*B*a*c*x^(5/2) + 4/3*A*a*c*x^(3/2) + 2*B*a^2*sqrt(x) - 2*A*a^2/sqrt(x)","A",0
399,1,53,0,0.170162," ","integrate((B*x+A)*(c*x^2+a)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, B c^{2} x^{\frac{7}{2}} + \frac{2}{5} \, A c^{2} x^{\frac{5}{2}} + \frac{4}{3} \, B a c x^{\frac{3}{2}} + 4 \, A a c \sqrt{x} - \frac{2 \, {\left(3 \, B a^{2} x + A a^{2}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/7*B*c^2*x^(7/2) + 2/5*A*c^2*x^(5/2) + 4/3*B*a*c*x^(3/2) + 4*A*a*c*sqrt(x) - 2/3*(3*B*a^2*x + A*a^2)/x^(3/2)","A",0
400,1,54,0,0.154887," ","integrate((B*x+A)*(c*x^2+a)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{5} \, B c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, A c^{2} x^{\frac{3}{2}} + 4 \, B a c \sqrt{x} - \frac{2 \, {\left(30 \, A a c x^{2} + 5 \, B a^{2} x + 3 \, A a^{2}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/5*B*c^2*x^(5/2) + 2/3*A*c^2*x^(3/2) + 4*B*a*c*sqrt(x) - 2/15*(30*A*a*c*x^2 + 5*B*a^2*x + 3*A*a^2)/x^(5/2)","A",0
401,1,54,0,0.152675," ","integrate((B*x+A)*(c*x^2+a)^2/x^(9/2),x, algorithm=""giac"")","\frac{2}{3} \, B c^{2} x^{\frac{3}{2}} + 2 \, A c^{2} \sqrt{x} - \frac{2 \, {\left(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,"2/3*B*c^2*x^(3/2) + 2*A*c^2*sqrt(x) - 2/105*(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
402,1,77,0,0.154414," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{23} \, B c^{3} x^{\frac{23}{2}} + \frac{2}{21} \, A c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B a c^{2} x^{\frac{19}{2}} + \frac{6}{17} \, A a c^{2} x^{\frac{17}{2}} + \frac{2}{5} \, B a^{2} c x^{\frac{15}{2}} + \frac{6}{13} \, A a^{2} c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} + \frac{2}{9} \, A a^{3} x^{\frac{9}{2}}"," ",0,"2/23*B*c^3*x^(23/2) + 2/21*A*c^3*x^(21/2) + 6/19*B*a*c^2*x^(19/2) + 6/17*A*a*c^2*x^(17/2) + 2/5*B*a^2*c*x^(15/2) + 6/13*A*a^2*c*x^(13/2) + 2/11*B*a^3*x^(11/2) + 2/9*A*a^3*x^(9/2)","A",0
403,1,77,0,0.154519," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{21} \, B c^{3} x^{\frac{21}{2}} + \frac{2}{19} \, A c^{3} x^{\frac{19}{2}} + \frac{6}{17} \, B a c^{2} x^{\frac{17}{2}} + \frac{2}{5} \, A a c^{2} x^{\frac{15}{2}} + \frac{6}{13} \, B a^{2} c x^{\frac{13}{2}} + \frac{6}{11} \, A a^{2} c x^{\frac{11}{2}} + \frac{2}{9} \, B a^{3} x^{\frac{9}{2}} + \frac{2}{7} \, A a^{3} x^{\frac{7}{2}}"," ",0,"2/21*B*c^3*x^(21/2) + 2/19*A*c^3*x^(19/2) + 6/17*B*a*c^2*x^(17/2) + 2/5*A*a*c^2*x^(15/2) + 6/13*B*a^2*c*x^(13/2) + 6/11*A*a^2*c*x^(11/2) + 2/9*B*a^3*x^(9/2) + 2/7*A*a^3*x^(7/2)","A",0
404,1,77,0,0.150245," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{19} \, B c^{3} x^{\frac{19}{2}} + \frac{2}{17} \, A c^{3} x^{\frac{17}{2}} + \frac{2}{5} \, B a c^{2} x^{\frac{15}{2}} + \frac{6}{13} \, A a c^{2} x^{\frac{13}{2}} + \frac{6}{11} \, B a^{2} c x^{\frac{11}{2}} + \frac{2}{3} \, A a^{2} c x^{\frac{9}{2}} + \frac{2}{7} \, B a^{3} x^{\frac{7}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}}"," ",0,"2/19*B*c^3*x^(19/2) + 2/17*A*c^3*x^(17/2) + 2/5*B*a*c^2*x^(15/2) + 6/13*A*a*c^2*x^(13/2) + 6/11*B*a^2*c*x^(11/2) + 2/3*A*a^2*c*x^(9/2) + 2/7*B*a^3*x^(7/2) + 2/5*A*a^3*x^(5/2)","A",0
405,1,77,0,0.155807," ","integrate((B*x+A)*(c*x^2+a)^3*x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, B c^{3} x^{\frac{17}{2}} + \frac{2}{15} \, A c^{3} x^{\frac{15}{2}} + \frac{6}{13} \, B a c^{2} x^{\frac{13}{2}} + \frac{6}{11} \, A a c^{2} x^{\frac{11}{2}} + \frac{2}{3} \, B a^{2} c x^{\frac{9}{2}} + \frac{6}{7} \, A a^{2} c x^{\frac{7}{2}} + \frac{2}{5} \, B a^{3} x^{\frac{5}{2}} + \frac{2}{3} \, A a^{3} x^{\frac{3}{2}}"," ",0,"2/17*B*c^3*x^(17/2) + 2/15*A*c^3*x^(15/2) + 6/13*B*a*c^2*x^(13/2) + 6/11*A*a*c^2*x^(11/2) + 2/3*B*a^2*c*x^(9/2) + 6/7*A*a^2*c*x^(7/2) + 2/5*B*a^3*x^(5/2) + 2/3*A*a^3*x^(3/2)","A",0
406,1,77,0,0.149606," ","integrate((B*x+A)*(c*x^2+a)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, B c^{3} x^{\frac{15}{2}} + \frac{2}{13} \, A c^{3} x^{\frac{13}{2}} + \frac{6}{11} \, B a c^{2} x^{\frac{11}{2}} + \frac{2}{3} \, A a c^{2} x^{\frac{9}{2}} + \frac{6}{7} \, B a^{2} c x^{\frac{7}{2}} + \frac{6}{5} \, A a^{2} c x^{\frac{5}{2}} + \frac{2}{3} \, B a^{3} x^{\frac{3}{2}} + 2 \, A a^{3} \sqrt{x}"," ",0,"2/15*B*c^3*x^(15/2) + 2/13*A*c^3*x^(13/2) + 6/11*B*a*c^2*x^(11/2) + 2/3*A*a*c^2*x^(9/2) + 6/7*B*a^2*c*x^(7/2) + 6/5*A*a^2*c*x^(5/2) + 2/3*B*a^3*x^(3/2) + 2*A*a^3*sqrt(x)","A",0
407,1,77,0,0.154155," ","integrate((B*x+A)*(c*x^2+a)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{13} \, B c^{3} x^{\frac{13}{2}} + \frac{2}{11} \, A c^{3} x^{\frac{11}{2}} + \frac{2}{3} \, B a c^{2} x^{\frac{9}{2}} + \frac{6}{7} \, A a c^{2} x^{\frac{7}{2}} + \frac{6}{5} \, B a^{2} c x^{\frac{5}{2}} + 2 \, A a^{2} c x^{\frac{3}{2}} + 2 \, B a^{3} \sqrt{x} - \frac{2 \, A a^{3}}{\sqrt{x}}"," ",0,"2/13*B*c^3*x^(13/2) + 2/11*A*c^3*x^(11/2) + 2/3*B*a*c^2*x^(9/2) + 6/7*A*a*c^2*x^(7/2) + 6/5*B*a^2*c*x^(5/2) + 2*A*a^2*c*x^(3/2) + 2*B*a^3*sqrt(x) - 2*A*a^3/sqrt(x)","A",0
408,1,77,0,0.195643," ","integrate((B*x+A)*(c*x^2+a)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{11} \, B c^{3} x^{\frac{11}{2}} + \frac{2}{9} \, A c^{3} x^{\frac{9}{2}} + \frac{6}{7} \, B a c^{2} x^{\frac{7}{2}} + \frac{6}{5} \, A a c^{2} x^{\frac{5}{2}} + 2 \, B a^{2} c x^{\frac{3}{2}} + 6 \, A a^{2} c \sqrt{x} - \frac{2 \, {\left(3 \, B a^{3} x + A a^{3}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/11*B*c^3*x^(11/2) + 2/9*A*c^3*x^(9/2) + 6/7*B*a*c^2*x^(7/2) + 6/5*A*a*c^2*x^(5/2) + 2*B*a^2*c*x^(3/2) + 6*A*a^2*c*sqrt(x) - 2/3*(3*B*a^3*x + A*a^3)/x^(3/2)","A",0
409,1,78,0,0.156974," ","integrate((B*x+A)*(c*x^2+a)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{9} \, B c^{3} x^{\frac{9}{2}} + \frac{2}{7} \, A c^{3} x^{\frac{7}{2}} + \frac{6}{5} \, B a c^{2} x^{\frac{5}{2}} + 2 \, A a c^{2} x^{\frac{3}{2}} + 6 \, B a^{2} c \sqrt{x} - \frac{2 \, {\left(45 \, A a^{2} c x^{2} + 5 \, B a^{3} x + 3 \, A a^{3}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/9*B*c^3*x^(9/2) + 2/7*A*c^3*x^(7/2) + 6/5*B*a*c^2*x^(5/2) + 2*A*a*c^2*x^(3/2) + 6*B*a^2*c*sqrt(x) - 2/15*(45*A*a^2*c*x^2 + 5*B*a^3*x + 3*A*a^3)/x^(5/2)","A",0
410,1,78,0,0.186329," ","integrate((B*x+A)*(c*x^2+a)^3/x^(9/2),x, algorithm=""giac"")","\frac{2}{7} \, B c^{3} x^{\frac{7}{2}} + \frac{2}{5} \, A c^{3} x^{\frac{5}{2}} + 2 \, B a c^{2} x^{\frac{3}{2}} + 6 \, A a c^{2} \sqrt{x} - \frac{2 \, {\left(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,"2/7*B*c^3*x^(7/2) + 2/5*A*c^3*x^(5/2) + 2*B*a*c^2*x^(3/2) + 6*A*a*c^2*sqrt(x) - 2/35*(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
411,1,78,0,0.188930," ","integrate((B*x+A)*(c*x^2+a)^3/x^(11/2),x, algorithm=""giac"")","\frac{2}{5} \, B c^{3} x^{\frac{5}{2}} + \frac{2}{3} \, A c^{3} x^{\frac{3}{2}} + 6 \, B a c^{2} \sqrt{x} - \frac{2 \, {\left(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,"2/5*B*c^3*x^(5/2) + 2/3*A*c^3*x^(3/2) + 6*B*a*c^2*sqrt(x) - 2/315*(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
412,1,262,0,0.202069," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, c^{4}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, c^{4}} + \frac{2 \, {\left(3 \, B c^{4} x^{\frac{5}{2}} + 5 \, A c^{4} x^{\frac{3}{2}} - 15 \, B a c^{3} \sqrt{x}\right)}}{15 \, c^{5}}"," ",0,"1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/c^4 + 1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/c^4 + 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/c^4 - 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/c^4 + 2/15*(3*B*c^4*x^(5/2) + 5*A*c^4*x^(3/2) - 15*B*a*c^3*sqrt(x))/c^5","A",0
413,1,255,0,0.185947," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{4}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{4}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, c^{4}} + \frac{2 \, {\left(B c^{2} x^{\frac{3}{2}} + 3 \, A c^{2} \sqrt{x}\right)}}{3 \, c^{3}}"," ",0,"-1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/c^4 - 1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/c^4 - 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/c^4 + 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/c^4 + 2/3*(B*c^2*x^(3/2) + 3*A*c^2*sqrt(x))/c^3","A",0
414,1,249,0,0.187144," ","integrate(x^(1/2)*(B*x+A)/(c*x^2+a),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{c} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a c^{3}}"," ",0,"2*B*sqrt(x)/c - 1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a*c^3) - 1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a*c^3) - 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^3) + 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^3)","A",0
415,1,244,0,0.178205," ","integrate((B*x+A)/x^(1/2)/(c*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a c^{3}}"," ",0,"1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a*c^3) + 1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a*c^3) + 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^3) - 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^3)","A",0
416,1,249,0,0.192566," ","integrate((B*x+A)/x^(3/2)/(c*x^2+a),x, algorithm=""giac"")","-\frac{2 \, A}{a \sqrt{x}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} c^{2}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} c^{2}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{2} c^{2}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{2} c^{2}}"," ",0,"-2*A/(a*sqrt(x)) + 1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^2) + 1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^2) + 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^2) - 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^2)","A",0
417,1,258,0,0.237559," ","integrate((B*x+A)/x^(5/2)/(c*x^2+a),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, B x + A\right)}}{3 \, a x^{\frac{3}{2}}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} c^{2}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} c^{2}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{2} c^{2}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{2} c^{2}}"," ",0,"-2/3*(3*B*x + A)/(a*x^(3/2)) - 1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^2) - 1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^2) - 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^2) + 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^2)","A",0
418,1,265,0,0.190555," ","integrate((B*x+A)/x^(7/2)/(c*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} c} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} c} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{3} c} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{3} c} + \frac{2 \, {\left(15 \, A c x^{2} - 5 \, B a x - 3 \, A a\right)}}{15 \, a^{2} x^{\frac{5}{2}}}"," ",0,"-1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^3*c) - 1/2*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^3*c) - 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c) + 1/4*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c) + 2/15*(15*A*c*x^2 - 5*B*a*x - 3*A*a)/(a^2*x^(5/2))","A",0
419,1,276,0,0.222393," ","integrate((B*x+A)/x^(9/2)/(c*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} c} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} c} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{3} c} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{4 \, a^{3} c} + \frac{2 \, {\left(105 \, B c x^{3} + 35 \, A c x^{2} - 21 \, B a x - 15 \, A a\right)}}{105 \, a^{2} x^{\frac{7}{2}}}"," ",0,"1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^3*c) + 1/2*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^3*c) + 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c) - 1/4*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c) + 2/105*(105*B*c*x^3 + 35*A*c*x^2 - 21*B*a*x - 15*A*a)/(a^2*x^(7/2))","A",0
420,1,283,0,0.196769," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{c^{2}} - \frac{A c x^{\frac{3}{2}} - B a \sqrt{x}}{2 \, {\left(c x^{2} + a\right)} c^{2}} - \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a c^{4}} - \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a c^{4}} - \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a c^{4}} + \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a c^{4}}"," ",0,"2*B*sqrt(x)/c^2 - 1/2*(A*c*x^(3/2) - B*a*sqrt(x))/((c*x^2 + a)*c^2) - 1/8*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c - 3*(a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a*c^4) - 1/8*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c - 3*(a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a*c^4) - 1/16*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c + 3*(a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^4) + 1/16*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c + 3*(a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^4)","A",0
421,1,271,0,0.202600," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{B x^{\frac{3}{2}} + A \sqrt{x}}{2 \, {\left(c x^{2} + a\right)} c} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a c^{4}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a c^{4}}"," ",0,"-1/2*(B*x^(3/2) + A*sqrt(x))/((c*x^2 + a)*c) + 1/8*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + 3*(a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a*c^4) + 1/8*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + 3*(a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a*c^4) + 1/16*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - 3*(a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^4) - 1/16*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - 3*(a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^4)","A",0
422,1,271,0,0.192160," ","integrate(x^(1/2)*(B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{A c x^{\frac{3}{2}} - B a \sqrt{x}}{2 \, {\left(c x^{2} + a\right)} a c} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c + \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{2} c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} B a c - \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{2} c^{3}}"," ",0,"1/2*(A*c*x^(3/2) - B*a*sqrt(x))/((c*x^2 + a)*a*c) + 1/8*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^3) + 1/8*sqrt(2)*((a*c^3)^(1/4)*B*a*c + (a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^3) + 1/16*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^3) - 1/16*sqrt(2)*((a*c^3)^(1/4)*B*a*c - (a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^3)","A",0
423,1,273,0,0.217533," ","integrate((B*x+A)/x^(1/2)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{B x^{\frac{3}{2}} + A \sqrt{x}}{2 \, {\left(c x^{2} + a\right)} a} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{2} c^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{2} c^{3}}"," ",0,"1/2*(B*x^(3/2) + A*sqrt(x))/((c*x^2 + a)*a) + 1/8*sqrt(2)*(3*(a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^3) + 1/8*sqrt(2)*(3*(a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^3) + 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^3) - 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^3)","A",0
424,1,281,0,0.223199," ","integrate((B*x+A)/x^(3/2)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{5 \, A c x^{2} - B a x + 4 \, A a}{2 \, {\left(c x^{\frac{5}{2}} + a \sqrt{x}\right)} a^{2}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} c^{2}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} c^{2}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{3} c^{2}} - \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{3} c^{2}}"," ",0,"-1/2*(5*A*c*x^2 - B*a*x + 4*A*a)/((c*x^(5/2) + a*sqrt(x))*a^2) + 1/8*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c - 5*(a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^2) + 1/8*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c - 5*(a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^2) + 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c + 5*(a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^2) - 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c + 5*(a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^2)","A",0
425,1,291,0,0.228118," ","integrate((B*x+A)/x^(5/2)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{B c x^{\frac{3}{2}} + A c \sqrt{x}}{2 \, {\left(c x^{2} + a\right)} a^{2}} - \frac{2 \, {\left(3 \, B x + A\right)}}{3 \, a^{2} x^{\frac{3}{2}}} - \frac{\sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} c^{2}} - \frac{\sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} c^{2}} - \frac{\sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{3} c^{2}} + \frac{\sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{16 \, a^{3} c^{2}}"," ",0,"-1/2*(B*c*x^(3/2) + A*c*sqrt(x))/((c*x^2 + a)*a^2) - 2/3*(3*B*x + A)/(a^2*x^(3/2)) - 1/8*sqrt(2)*(7*(a*c^3)^(1/4)*A*c^2 + 5*(a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^2) - 1/8*sqrt(2)*(7*(a*c^3)^(1/4)*A*c^2 + 5*(a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^2) - 1/16*sqrt(2)*(7*(a*c^3)^(1/4)*A*c^2 - 5*(a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^2) + 1/16*sqrt(2)*(7*(a*c^3)^(1/4)*A*c^2 - 5*(a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^2)","A",0
426,1,293,0,0.218872," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{11 \, B c x^{\frac{7}{2}} + 9 \, A c x^{\frac{5}{2}} + 7 \, B a x^{\frac{3}{2}} + 5 \, A a \sqrt{x}}{16 \, {\left(c x^{2} + a\right)}^{2} c^{2}} + \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 21 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a c^{5}} + \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 21 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a c^{5}} + \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 21 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a c^{5}} - \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 21 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a c^{5}}"," ",0,"-1/16*(11*B*c*x^(7/2) + 9*A*c*x^(5/2) + 7*B*a*x^(3/2) + 5*A*a*sqrt(x))/((c*x^2 + a)^2*c^2) + 1/64*sqrt(2)*(5*(a*c^3)^(1/4)*A*c^2 + 21*(a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a*c^5) + 1/64*sqrt(2)*(5*(a*c^3)^(1/4)*A*c^2 + 21*(a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a*c^5) + 1/128*sqrt(2)*(5*(a*c^3)^(1/4)*A*c^2 - 21*(a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^5) - 1/128*sqrt(2)*(5*(a*c^3)^(1/4)*A*c^2 - 21*(a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a*c^5)","A",0
427,1,298,0,0.200641," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} c^{4}} + \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} c^{4}} + \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{2} c^{4}} - \frac{\sqrt{2} {\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{2} c^{4}} + \frac{3 \, A c^{2} x^{\frac{7}{2}} - 9 \, B a c x^{\frac{5}{2}} - A a c x^{\frac{3}{2}} - 5 \, B a^{2} \sqrt{x}}{16 \, {\left(c x^{2} + a\right)}^{2} a c^{2}}"," ",0,"1/64*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c + 3*(a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^4) + 1/64*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c + 3*(a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^4) + 1/128*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c - 3*(a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^4) - 1/128*sqrt(2)*(5*(a*c^3)^(1/4)*B*a*c - 3*(a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^4) + 1/16*(3*A*c^2*x^(7/2) - 9*B*a*c*x^(5/2) - A*a*c*x^(3/2) - 5*B*a^2*sqrt(x))/((c*x^2 + a)^2*a*c^2)","A",0
428,1,289,0,0.215133," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, B c x^{\frac{7}{2}} + A c x^{\frac{5}{2}} - B a x^{\frac{3}{2}} - 3 \, A a \sqrt{x}}{16 \, {\left(c x^{2} + a\right)}^{2} a c} + \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} c^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} c^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{2} c^{4}} - \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{2} c^{4}}"," ",0,"1/16*(3*B*c*x^(7/2) + A*c*x^(5/2) - B*a*x^(3/2) - 3*A*a*sqrt(x))/((c*x^2 + a)^2*a*c) + 3/64*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^4) + 3/64*sqrt(2)*((a*c^3)^(1/4)*A*c^2 + (a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^2*c^4) + 3/128*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^4) - 3/128*sqrt(2)*((a*c^3)^(1/4)*A*c^2 - (a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^2*c^4)","A",0
429,1,297,0,0.212915," ","integrate(x^(1/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{3} c^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{3} c^{3}} + \frac{5 \, A c^{2} x^{\frac{7}{2}} + B a c x^{\frac{5}{2}} + 9 \, A a c x^{\frac{3}{2}} - 3 \, B a^{2} \sqrt{x}}{16 \, {\left(c x^{2} + a\right)}^{2} a^{2} c}"," ",0,"1/64*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c + 5*(a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^3) + 1/64*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c + 5*(a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^3) + 1/128*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c - 5*(a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^3) - 1/128*sqrt(2)*(3*(a*c^3)^(1/4)*B*a*c - 5*(a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^3) + 1/16*(5*A*c^2*x^(7/2) + B*a*c*x^(5/2) + 9*A*a*c*x^(3/2) - 3*B*a^2*sqrt(x))/((c*x^2 + a)^2*a^2*c)","A",0
430,1,293,0,0.231017," ","integrate((B*x+A)/x^(1/2)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{5 \, B c x^{\frac{7}{2}} + 7 \, A c x^{\frac{5}{2}} + 9 \, B a x^{\frac{3}{2}} + 11 \, A a \sqrt{x}}{16 \, {\left(c x^{2} + a\right)}^{2} a^{2}} + \frac{\sqrt{2} {\left(21 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} c^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} c^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{3} c^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a c^{3}\right)^{\frac{1}{4}} A c^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} B\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{3} c^{3}}"," ",0,"1/16*(5*B*c*x^(7/2) + 7*A*c*x^(5/2) + 9*B*a*x^(3/2) + 11*A*a*sqrt(x))/((c*x^2 + a)^2*a^2) + 1/64*sqrt(2)*(21*(a*c^3)^(1/4)*A*c^2 + 5*(a*c^3)^(3/4)*B)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^3) + 1/64*sqrt(2)*(21*(a*c^3)^(1/4)*A*c^2 + 5*(a*c^3)^(3/4)*B)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^3*c^3) + 1/128*sqrt(2)*(21*(a*c^3)^(1/4)*A*c^2 - 5*(a*c^3)^(3/4)*B)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^3) - 1/128*sqrt(2)*(21*(a*c^3)^(1/4)*A*c^2 - 5*(a*c^3)^(3/4)*B)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^3*c^3)","A",0
431,1,304,0,0.213540," ","integrate((B*x+A)/x^(3/2)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{2 \, A}{a^{3} \sqrt{x}} + \frac{3 \, \sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 15 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} c^{2}} + \frac{3 \, \sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c - 15 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} c^{2}} + \frac{3 \, \sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 15 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{4} c^{2}} - \frac{3 \, \sqrt{2} {\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} B a c + 15 \, \left(a c^{3}\right)^{\frac{3}{4}} A\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{c}}\right)}{128 \, a^{4} c^{2}} - \frac{13 \, A c^{2} x^{\frac{7}{2}} - 7 \, B a c x^{\frac{5}{2}} + 17 \, A a c x^{\frac{3}{2}} - 11 \, B a^{2} \sqrt{x}}{16 \, {\left(c x^{2} + a\right)}^{2} a^{3}}"," ",0,"-2*A/(a^3*sqrt(x)) + 3/64*sqrt(2)*(7*(a*c^3)^(1/4)*B*a*c - 15*(a*c^3)^(3/4)*A)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) + 2*sqrt(x))/(a/c)^(1/4))/(a^4*c^2) + 3/64*sqrt(2)*(7*(a*c^3)^(1/4)*B*a*c - 15*(a*c^3)^(3/4)*A)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/c)^(1/4) - 2*sqrt(x))/(a/c)^(1/4))/(a^4*c^2) + 3/128*sqrt(2)*(7*(a*c^3)^(1/4)*B*a*c + 15*(a*c^3)^(3/4)*A)*log(sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^4*c^2) - 3/128*sqrt(2)*(7*(a*c^3)^(1/4)*B*a*c + 15*(a*c^3)^(3/4)*A)*log(-sqrt(2)*sqrt(x)*(a/c)^(1/4) + x + sqrt(a/c))/(a^4*c^2) - 1/16*(13*A*c^2*x^(7/2) - 7*B*a*c*x^(5/2) + 17*A*a*c*x^(3/2) - 11*B*a^2*sqrt(x))/((c*x^2 + a)^2*a^3)","A",0
432,1,34,0,0.150916," ","integrate((1-x)/(x^2+1)/x^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} \sqrt{x} + x + 1\right) - \frac{1}{2} \, \sqrt{2} \log\left(-\sqrt{2} \sqrt{x} + x + 1\right)"," ",0,"1/2*sqrt(2)*log(sqrt(2)*sqrt(x) + x + 1) - 1/2*sqrt(2)*log(-sqrt(2)*sqrt(x) + x + 1)","A",0
433,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(B x + A\right)} \left(e x\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)*(e*x)^(7/2), x)","F",0
434,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(B x + A\right)} \left(e x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)*(e*x)^(5/2), x)","F",0
435,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(B x + A\right)} \left(e x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)*(e*x)^(3/2), x)","F",0
436,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x), x)","F",0
437,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{\sqrt{e x}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)/sqrt(e*x), x)","F",0
438,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)/(e*x)^(3/2), x)","F",0
439,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)/(e*x)^(5/2), x)","F",0
440,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{\left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)/(e*x)^(7/2), x)","F",0
441,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(9/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{\left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)/(e*x)^(9/2), x)","F",0
442,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)} \left(e x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)*(e*x)^(5/2), x)","F",0
443,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)} \left(e x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)*(e*x)^(3/2), x)","F",0
444,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)} \sqrt{e x}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)*sqrt(e*x), x)","F",0
445,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{\sqrt{e x}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/sqrt(e*x), x)","F",0
446,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/(e*x)^(3/2), x)","F",0
447,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/(e*x)^(5/2), x)","F",0
448,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/(e*x)^(7/2), x)","F",0
449,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/(e*x)^(9/2), x)","F",0
450,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)} \left(e x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)*(e*x)^(3/2), x)","F",0
451,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)} \sqrt{e x}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)*sqrt(e*x), x)","F",0
452,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)}}{\sqrt{e x}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)/sqrt(e*x), x)","F",0
453,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)/(e*x)^(3/2), x)","F",0
454,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)/(e*x)^(5/2), x)","F",0
455,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)/(e*x)^(7/2), x)","F",0
456,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)/(e*x)^(9/2), x)","F",0
457,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)}}{\left(e x\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)/(e*x)^(11/2), x)","F",0
458,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{7}{2}}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(7/2)/sqrt(c*x^2 + a), x)","F",0
459,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{5}{2}}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(5/2)/sqrt(c*x^2 + a), x)","F",0
460,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{3}{2}}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(3/2)/sqrt(c*x^2 + a), x)","F",0
461,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x)/sqrt(c*x^2 + a), x)","F",0
462,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + a} \sqrt{e x}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + a)*sqrt(e*x)), x)","F",0
463,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + a} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + a)*(e*x)^(3/2)), x)","F",0
464,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(5/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + a} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + a)*(e*x)^(5/2)), x)","F",0
465,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(7/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + a} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + a)*(e*x)^(7/2)), x)","F",0
466,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{7}{2}}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(7/2)/(c*x^2 + a)^(3/2), x)","F",0
467,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(5/2)/(c*x^2 + a)^(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(3/2)/(c*x^2 + a)^(3/2), x)","F",0
469,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x)/(c*x^2 + a)^(3/2), x)","F",0
470,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(3/2)*sqrt(e*x)), x)","F",0
471,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(3/2)*(e*x)^(3/2)), x)","F",0
472,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(5/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(3/2)*(e*x)^(5/2)), x)","F",0
473,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(7/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(3/2)*(e*x)^(7/2)), x)","F",0
474,0,0,0,0.000000," ","integrate((e*x)^(13/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{13}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(13/2)/(c*x^2 + a)^(5/2), x)","F",0
475,0,0,0,0.000000," ","integrate((e*x)^(11/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{11}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(11/2)/(c*x^2 + a)^(5/2), x)","F",0
476,0,0,0,0.000000," ","integrate((e*x)^(9/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{9}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(9/2)/(c*x^2 + a)^(5/2), x)","F",0
477,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{7}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(7/2)/(c*x^2 + a)^(5/2), x)","F",0
478,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(5/2)/(c*x^2 + a)^(5/2), x)","F",0
479,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^(3/2)/(c*x^2 + a)^(5/2), x)","F",0
480,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x)/(c*x^2 + a)^(5/2), x)","F",0
481,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{5}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(5/2)*sqrt(e*x)), x)","F",0
482,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(3/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(5/2)*(e*x)^(3/2)), x)","F",0
483,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(5/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(5/2)*(e*x)^(5/2)), x)","F",0
484,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(7/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(5/2)*(e*x)^(7/2)), x)","F",0
485,1,1778,0,0.244016," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{B c^{4} m^{9} x^{10} x^{m} e^{m} + A c^{4} m^{9} x^{9} x^{m} e^{m} + 45 \, B c^{4} m^{8} x^{10} x^{m} e^{m} + 4 \, B a c^{3} m^{9} x^{8} x^{m} e^{m} + 46 \, A c^{4} m^{8} x^{9} x^{m} e^{m} + 870 \, B c^{4} m^{7} x^{10} x^{m} e^{m} + 4 \, A a c^{3} m^{9} x^{7} x^{m} e^{m} + 188 \, B a c^{3} m^{8} x^{8} x^{m} e^{m} + 906 \, A c^{4} m^{7} x^{9} x^{m} e^{m} + 9450 \, B c^{4} m^{6} x^{10} x^{m} e^{m} + 6 \, B a^{2} c^{2} m^{9} x^{6} x^{m} e^{m} + 192 \, A a c^{3} m^{8} x^{7} x^{m} e^{m} + 3776 \, B a c^{3} m^{7} x^{8} x^{m} e^{m} + 9996 \, A c^{4} m^{6} x^{9} x^{m} e^{m} + 63273 \, B c^{4} m^{5} x^{10} x^{m} e^{m} + 6 \, A a^{2} c^{2} m^{9} x^{5} x^{m} e^{m} + 294 \, B a^{2} c^{2} m^{8} x^{6} x^{m} e^{m} + 3936 \, A a c^{3} m^{7} x^{7} x^{m} e^{m} + 42392 \, B a c^{3} m^{6} x^{8} x^{m} e^{m} + 67809 \, A c^{4} m^{5} x^{9} x^{m} e^{m} + 269325 \, B c^{4} m^{4} x^{10} x^{m} e^{m} + 4 \, B a^{3} c m^{9} x^{4} x^{m} e^{m} + 300 \, A a^{2} c^{2} m^{8} x^{5} x^{m} e^{m} + 6156 \, B a^{2} c^{2} m^{7} x^{6} x^{m} e^{m} + 45048 \, A a c^{3} m^{6} x^{7} x^{m} e^{m} + 291956 \, B a c^{3} m^{5} x^{8} x^{m} e^{m} + 291774 \, A c^{4} m^{4} x^{9} x^{m} e^{m} + 723680 \, B c^{4} m^{3} x^{10} x^{m} e^{m} + 4 \, A a^{3} c m^{9} x^{3} x^{m} e^{m} + 204 \, B a^{3} c m^{8} x^{4} x^{m} e^{m} + 6420 \, A a^{2} c^{2} m^{7} x^{5} x^{m} e^{m} + 71964 \, B a^{2} c^{2} m^{6} x^{6} x^{m} e^{m} + 315756 \, A a c^{3} m^{5} x^{7} x^{m} e^{m} + 1272572 \, B a c^{3} m^{4} x^{8} x^{m} e^{m} + 790964 \, A c^{4} m^{3} x^{9} x^{m} e^{m} + 1172700 \, B c^{4} m^{2} x^{10} x^{m} e^{m} + B a^{4} m^{9} x^{2} x^{m} e^{m} + 208 \, A a^{3} c m^{8} x^{3} x^{m} e^{m} + 4464 \, B a^{3} c m^{7} x^{4} x^{m} e^{m} + 76800 \, A a^{2} c^{2} m^{6} x^{5} x^{m} e^{m} + 514854 \, B a^{2} c^{2} m^{5} x^{6} x^{m} e^{m} + 1397928 \, A a c^{3} m^{4} x^{7} x^{m} e^{m} + 3487144 \, B a c^{3} m^{3} x^{8} x^{m} e^{m} + 1290824 \, A c^{4} m^{2} x^{9} x^{m} e^{m} + 1026576 \, B c^{4} m x^{10} x^{m} e^{m} + A a^{4} m^{9} x x^{m} e^{m} + 53 \, B a^{4} m^{8} x^{2} x^{m} e^{m} + 4656 \, A a^{3} c m^{7} x^{3} x^{m} e^{m} + 54744 \, B a^{3} c m^{6} x^{4} x^{m} e^{m} + 562638 \, A a^{2} c^{2} m^{5} x^{5} x^{m} e^{m} + 2323206 \, B a^{2} c^{2} m^{4} x^{6} x^{m} e^{m} + 3882224 \, A a c^{3} m^{3} x^{7} x^{m} e^{m} + 5740848 \, B a c^{3} m^{2} x^{8} x^{m} e^{m} + 1136160 \, A c^{4} m x^{9} x^{m} e^{m} + 362880 \, B c^{4} x^{10} x^{m} e^{m} + 54 \, A a^{4} m^{8} x x^{m} e^{m} + 1214 \, B a^{4} m^{7} x^{2} x^{m} e^{m} + 58632 \, A a^{3} c m^{6} x^{3} x^{m} e^{m} + 412116 \, B a^{3} c m^{5} x^{4} x^{m} e^{m} + 2599140 \, A a^{2} c^{2} m^{4} x^{5} x^{m} e^{m} + 6562344 \, B a^{2} c^{2} m^{3} x^{6} x^{m} e^{m} + 6462432 \, A a c^{3} m^{2} x^{7} x^{m} e^{m} + 5087520 \, B a c^{3} m x^{8} x^{m} e^{m} + 403200 \, A c^{4} x^{9} x^{m} e^{m} + 1266 \, A a^{4} m^{7} x x^{m} e^{m} + 15722 \, B a^{4} m^{6} x^{2} x^{m} e^{m} + 455196 \, A a^{3} c m^{5} x^{3} x^{m} e^{m} + 1959756 \, B a^{3} c m^{4} x^{4} x^{m} e^{m} + 7505880 \, A a^{2} c^{2} m^{3} x^{5} x^{m} e^{m} + 11082936 \, B a^{2} c^{2} m^{2} x^{6} x^{m} e^{m} + 5777280 \, A a c^{3} m x^{7} x^{m} e^{m} + 1814400 \, B a c^{3} x^{8} x^{m} e^{m} + 16884 \, A a^{4} m^{6} x x^{m} e^{m} + 126329 \, B a^{4} m^{5} x^{2} x^{m} e^{m} + 2242632 \, A a^{3} c m^{4} x^{3} x^{m} e^{m} + 5828696 \, B a^{3} c m^{3} x^{4} x^{m} e^{m} + 12927600 \, A a^{2} c^{2} m^{2} x^{5} x^{m} e^{m} + 10023840 \, B a^{2} c^{2} m x^{6} x^{m} e^{m} + 2073600 \, A a c^{3} x^{7} x^{m} e^{m} + 140889 \, A a^{4} m^{5} x x^{m} e^{m} + 649397 \, B a^{4} m^{4} x^{2} x^{m} e^{m} + 6939824 \, A a^{3} c m^{3} x^{3} x^{m} e^{m} + 10323216 \, B a^{3} c m^{2} x^{4} x^{m} e^{m} + 11883456 \, A a^{2} c^{2} m x^{5} x^{m} e^{m} + 3628800 \, B a^{2} c^{2} x^{6} x^{m} e^{m} + 761166 \, A a^{4} m^{4} x x^{m} e^{m} + 2118136 \, B a^{4} m^{3} x^{2} x^{m} e^{m} + 12818528 \, A a^{3} c m^{2} x^{3} x^{m} e^{m} + 9721440 \, B a^{3} c m x^{4} x^{m} e^{m} + 4354560 \, A a^{2} c^{2} x^{5} x^{m} e^{m} + 2655764 \, A a^{4} m^{3} x x^{m} e^{m} + 4173228 \, B a^{4} m^{2} x^{2} x^{m} e^{m} + 12558720 \, A a^{3} c m x^{3} x^{m} e^{m} + 3628800 \, B a^{3} c x^{4} x^{m} e^{m} + 5753736 \, A a^{4} m^{2} x x^{m} e^{m} + 4407120 \, B a^{4} m x^{2} x^{m} e^{m} + 4838400 \, A a^{3} c x^{3} x^{m} e^{m} + 6999840 \, A a^{4} m x x^{m} e^{m} + 1814400 \, B a^{4} x^{2} x^{m} e^{m} + 3628800 \, A a^{4} x x^{m} e^{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*x^10*x^m*e^m + A*c^4*m^9*x^9*x^m*e^m + 45*B*c^4*m^8*x^10*x^m*e^m + 4*B*a*c^3*m^9*x^8*x^m*e^m + 46*A*c^4*m^8*x^9*x^m*e^m + 870*B*c^4*m^7*x^10*x^m*e^m + 4*A*a*c^3*m^9*x^7*x^m*e^m + 188*B*a*c^3*m^8*x^8*x^m*e^m + 906*A*c^4*m^7*x^9*x^m*e^m + 9450*B*c^4*m^6*x^10*x^m*e^m + 6*B*a^2*c^2*m^9*x^6*x^m*e^m + 192*A*a*c^3*m^8*x^7*x^m*e^m + 3776*B*a*c^3*m^7*x^8*x^m*e^m + 9996*A*c^4*m^6*x^9*x^m*e^m + 63273*B*c^4*m^5*x^10*x^m*e^m + 6*A*a^2*c^2*m^9*x^5*x^m*e^m + 294*B*a^2*c^2*m^8*x^6*x^m*e^m + 3936*A*a*c^3*m^7*x^7*x^m*e^m + 42392*B*a*c^3*m^6*x^8*x^m*e^m + 67809*A*c^4*m^5*x^9*x^m*e^m + 269325*B*c^4*m^4*x^10*x^m*e^m + 4*B*a^3*c*m^9*x^4*x^m*e^m + 300*A*a^2*c^2*m^8*x^5*x^m*e^m + 6156*B*a^2*c^2*m^7*x^6*x^m*e^m + 45048*A*a*c^3*m^6*x^7*x^m*e^m + 291956*B*a*c^3*m^5*x^8*x^m*e^m + 291774*A*c^4*m^4*x^9*x^m*e^m + 723680*B*c^4*m^3*x^10*x^m*e^m + 4*A*a^3*c*m^9*x^3*x^m*e^m + 204*B*a^3*c*m^8*x^4*x^m*e^m + 6420*A*a^2*c^2*m^7*x^5*x^m*e^m + 71964*B*a^2*c^2*m^6*x^6*x^m*e^m + 315756*A*a*c^3*m^5*x^7*x^m*e^m + 1272572*B*a*c^3*m^4*x^8*x^m*e^m + 790964*A*c^4*m^3*x^9*x^m*e^m + 1172700*B*c^4*m^2*x^10*x^m*e^m + B*a^4*m^9*x^2*x^m*e^m + 208*A*a^3*c*m^8*x^3*x^m*e^m + 4464*B*a^3*c*m^7*x^4*x^m*e^m + 76800*A*a^2*c^2*m^6*x^5*x^m*e^m + 514854*B*a^2*c^2*m^5*x^6*x^m*e^m + 1397928*A*a*c^3*m^4*x^7*x^m*e^m + 3487144*B*a*c^3*m^3*x^8*x^m*e^m + 1290824*A*c^4*m^2*x^9*x^m*e^m + 1026576*B*c^4*m*x^10*x^m*e^m + A*a^4*m^9*x*x^m*e^m + 53*B*a^4*m^8*x^2*x^m*e^m + 4656*A*a^3*c*m^7*x^3*x^m*e^m + 54744*B*a^3*c*m^6*x^4*x^m*e^m + 562638*A*a^2*c^2*m^5*x^5*x^m*e^m + 2323206*B*a^2*c^2*m^4*x^6*x^m*e^m + 3882224*A*a*c^3*m^3*x^7*x^m*e^m + 5740848*B*a*c^3*m^2*x^8*x^m*e^m + 1136160*A*c^4*m*x^9*x^m*e^m + 362880*B*c^4*x^10*x^m*e^m + 54*A*a^4*m^8*x*x^m*e^m + 1214*B*a^4*m^7*x^2*x^m*e^m + 58632*A*a^3*c*m^6*x^3*x^m*e^m + 412116*B*a^3*c*m^5*x^4*x^m*e^m + 2599140*A*a^2*c^2*m^4*x^5*x^m*e^m + 6562344*B*a^2*c^2*m^3*x^6*x^m*e^m + 6462432*A*a*c^3*m^2*x^7*x^m*e^m + 5087520*B*a*c^3*m*x^8*x^m*e^m + 403200*A*c^4*x^9*x^m*e^m + 1266*A*a^4*m^7*x*x^m*e^m + 15722*B*a^4*m^6*x^2*x^m*e^m + 455196*A*a^3*c*m^5*x^3*x^m*e^m + 1959756*B*a^3*c*m^4*x^4*x^m*e^m + 7505880*A*a^2*c^2*m^3*x^5*x^m*e^m + 11082936*B*a^2*c^2*m^2*x^6*x^m*e^m + 5777280*A*a*c^3*m*x^7*x^m*e^m + 1814400*B*a*c^3*x^8*x^m*e^m + 16884*A*a^4*m^6*x*x^m*e^m + 126329*B*a^4*m^5*x^2*x^m*e^m + 2242632*A*a^3*c*m^4*x^3*x^m*e^m + 5828696*B*a^3*c*m^3*x^4*x^m*e^m + 12927600*A*a^2*c^2*m^2*x^5*x^m*e^m + 10023840*B*a^2*c^2*m*x^6*x^m*e^m + 2073600*A*a*c^3*x^7*x^m*e^m + 140889*A*a^4*m^5*x*x^m*e^m + 649397*B*a^4*m^4*x^2*x^m*e^m + 6939824*A*a^3*c*m^3*x^3*x^m*e^m + 10323216*B*a^3*c*m^2*x^4*x^m*e^m + 11883456*A*a^2*c^2*m*x^5*x^m*e^m + 3628800*B*a^2*c^2*x^6*x^m*e^m + 761166*A*a^4*m^4*x*x^m*e^m + 2118136*B*a^4*m^3*x^2*x^m*e^m + 12818528*A*a^3*c*m^2*x^3*x^m*e^m + 9721440*B*a^3*c*m*x^4*x^m*e^m + 4354560*A*a^2*c^2*x^5*x^m*e^m + 2655764*A*a^4*m^3*x*x^m*e^m + 4173228*B*a^4*m^2*x^2*x^m*e^m + 12558720*A*a^3*c*m*x^3*x^m*e^m + 3628800*B*a^3*c*x^4*x^m*e^m + 5753736*A*a^4*m^2*x*x^m*e^m + 4407120*B*a^4*m*x^2*x^m*e^m + 4838400*A*a^3*c*x^3*x^m*e^m + 6999840*A*a^4*m*x*x^m*e^m + 1814400*B*a^4*x^2*x^m*e^m + 3628800*A*a^4*x*x^m*e^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
486,1,1102,0,0.201968," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{B c^{3} m^{7} x^{8} x^{m} e^{m} + A c^{3} m^{7} x^{7} x^{m} e^{m} + 28 \, B c^{3} m^{6} x^{8} x^{m} e^{m} + 3 \, B a c^{2} m^{7} x^{6} x^{m} e^{m} + 29 \, A c^{3} m^{6} x^{7} x^{m} e^{m} + 322 \, B c^{3} m^{5} x^{8} x^{m} e^{m} + 3 \, A a c^{2} m^{7} x^{5} x^{m} e^{m} + 90 \, B a c^{2} m^{6} x^{6} x^{m} e^{m} + 343 \, A c^{3} m^{5} x^{7} x^{m} e^{m} + 1960 \, B c^{3} m^{4} x^{8} x^{m} e^{m} + 3 \, B a^{2} c m^{7} x^{4} x^{m} e^{m} + 93 \, A a c^{2} m^{6} x^{5} x^{m} e^{m} + 1098 \, B a c^{2} m^{5} x^{6} x^{m} e^{m} + 2135 \, A c^{3} m^{4} x^{7} x^{m} e^{m} + 6769 \, B c^{3} m^{3} x^{8} x^{m} e^{m} + 3 \, A a^{2} c m^{7} x^{3} x^{m} e^{m} + 96 \, B a^{2} c m^{6} x^{4} x^{m} e^{m} + 1173 \, A a c^{2} m^{5} x^{5} x^{m} e^{m} + 7020 \, B a c^{2} m^{4} x^{6} x^{m} e^{m} + 7504 \, A c^{3} m^{3} x^{7} x^{m} e^{m} + 13132 \, B c^{3} m^{2} x^{8} x^{m} e^{m} + B a^{3} m^{7} x^{2} x^{m} e^{m} + 99 \, A a^{2} c m^{6} x^{3} x^{m} e^{m} + 1254 \, B a^{2} c m^{5} x^{4} x^{m} e^{m} + 7743 \, A a c^{2} m^{4} x^{5} x^{m} e^{m} + 25227 \, B a c^{2} m^{3} x^{6} x^{m} e^{m} + 14756 \, A c^{3} m^{2} x^{7} x^{m} e^{m} + 13068 \, B c^{3} m x^{8} x^{m} e^{m} + A a^{3} m^{7} x x^{m} e^{m} + 34 \, B a^{3} m^{6} x^{2} x^{m} e^{m} + 1341 \, A a^{2} c m^{5} x^{3} x^{m} e^{m} + 8592 \, B a^{2} c m^{4} x^{4} x^{m} e^{m} + 28632 \, A a c^{2} m^{3} x^{5} x^{m} e^{m} + 50490 \, B a c^{2} m^{2} x^{6} x^{m} e^{m} + 14832 \, A c^{3} m x^{7} x^{m} e^{m} + 5040 \, B c^{3} x^{8} x^{m} e^{m} + 35 \, A a^{3} m^{6} x x^{m} e^{m} + 478 \, B a^{3} m^{5} x^{2} x^{m} e^{m} + 9585 \, A a^{2} c m^{4} x^{3} x^{m} e^{m} + 32979 \, B a^{2} c m^{3} x^{4} x^{m} e^{m} + 58692 \, A a c^{2} m^{2} x^{5} x^{m} e^{m} + 51432 \, B a c^{2} m x^{6} x^{m} e^{m} + 5760 \, A c^{3} x^{7} x^{m} e^{m} + 511 \, A a^{3} m^{5} x x^{m} e^{m} + 3580 \, B a^{3} m^{4} x^{2} x^{m} e^{m} + 38592 \, A a^{2} c m^{3} x^{3} x^{m} e^{m} + 69936 \, B a^{2} c m^{2} x^{4} x^{m} e^{m} + 60912 \, A a c^{2} m x^{5} x^{m} e^{m} + 20160 \, B a c^{2} x^{6} x^{m} e^{m} + 4025 \, A a^{3} m^{4} x x^{m} e^{m} + 15289 \, B a^{3} m^{3} x^{2} x^{m} e^{m} + 86076 \, A a^{2} c m^{2} x^{3} x^{m} e^{m} + 74628 \, B a^{2} c m x^{4} x^{m} e^{m} + 24192 \, A a c^{2} x^{5} x^{m} e^{m} + 18424 \, A a^{3} m^{3} x x^{m} e^{m} + 36706 \, B a^{3} m^{2} x^{2} x^{m} e^{m} + 96144 \, A a^{2} c m x^{3} x^{m} e^{m} + 30240 \, B a^{2} c x^{4} x^{m} e^{m} + 48860 \, A a^{3} m^{2} x x^{m} e^{m} + 44712 \, B a^{3} m x^{2} x^{m} e^{m} + 40320 \, A a^{2} c x^{3} x^{m} e^{m} + 69264 \, A a^{3} m x x^{m} e^{m} + 20160 \, B a^{3} x^{2} x^{m} e^{m} + 40320 \, A a^{3} x x^{m} e^{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*x^8*x^m*e^m + A*c^3*m^7*x^7*x^m*e^m + 28*B*c^3*m^6*x^8*x^m*e^m + 3*B*a*c^2*m^7*x^6*x^m*e^m + 29*A*c^3*m^6*x^7*x^m*e^m + 322*B*c^3*m^5*x^8*x^m*e^m + 3*A*a*c^2*m^7*x^5*x^m*e^m + 90*B*a*c^2*m^6*x^6*x^m*e^m + 343*A*c^3*m^5*x^7*x^m*e^m + 1960*B*c^3*m^4*x^8*x^m*e^m + 3*B*a^2*c*m^7*x^4*x^m*e^m + 93*A*a*c^2*m^6*x^5*x^m*e^m + 1098*B*a*c^2*m^5*x^6*x^m*e^m + 2135*A*c^3*m^4*x^7*x^m*e^m + 6769*B*c^3*m^3*x^8*x^m*e^m + 3*A*a^2*c*m^7*x^3*x^m*e^m + 96*B*a^2*c*m^6*x^4*x^m*e^m + 1173*A*a*c^2*m^5*x^5*x^m*e^m + 7020*B*a*c^2*m^4*x^6*x^m*e^m + 7504*A*c^3*m^3*x^7*x^m*e^m + 13132*B*c^3*m^2*x^8*x^m*e^m + B*a^3*m^7*x^2*x^m*e^m + 99*A*a^2*c*m^6*x^3*x^m*e^m + 1254*B*a^2*c*m^5*x^4*x^m*e^m + 7743*A*a*c^2*m^4*x^5*x^m*e^m + 25227*B*a*c^2*m^3*x^6*x^m*e^m + 14756*A*c^3*m^2*x^7*x^m*e^m + 13068*B*c^3*m*x^8*x^m*e^m + A*a^3*m^7*x*x^m*e^m + 34*B*a^3*m^6*x^2*x^m*e^m + 1341*A*a^2*c*m^5*x^3*x^m*e^m + 8592*B*a^2*c*m^4*x^4*x^m*e^m + 28632*A*a*c^2*m^3*x^5*x^m*e^m + 50490*B*a*c^2*m^2*x^6*x^m*e^m + 14832*A*c^3*m*x^7*x^m*e^m + 5040*B*c^3*x^8*x^m*e^m + 35*A*a^3*m^6*x*x^m*e^m + 478*B*a^3*m^5*x^2*x^m*e^m + 9585*A*a^2*c*m^4*x^3*x^m*e^m + 32979*B*a^2*c*m^3*x^4*x^m*e^m + 58692*A*a*c^2*m^2*x^5*x^m*e^m + 51432*B*a*c^2*m*x^6*x^m*e^m + 5760*A*c^3*x^7*x^m*e^m + 511*A*a^3*m^5*x*x^m*e^m + 3580*B*a^3*m^4*x^2*x^m*e^m + 38592*A*a^2*c*m^3*x^3*x^m*e^m + 69936*B*a^2*c*m^2*x^4*x^m*e^m + 60912*A*a*c^2*m*x^5*x^m*e^m + 20160*B*a*c^2*x^6*x^m*e^m + 4025*A*a^3*m^4*x*x^m*e^m + 15289*B*a^3*m^3*x^2*x^m*e^m + 86076*A*a^2*c*m^2*x^3*x^m*e^m + 74628*B*a^2*c*m*x^4*x^m*e^m + 24192*A*a*c^2*x^5*x^m*e^m + 18424*A*a^3*m^3*x*x^m*e^m + 36706*B*a^3*m^2*x^2*x^m*e^m + 96144*A*a^2*c*m*x^3*x^m*e^m + 30240*B*a^2*c*x^4*x^m*e^m + 48860*A*a^3*m^2*x*x^m*e^m + 44712*B*a^3*m*x^2*x^m*e^m + 40320*A*a^2*c*x^3*x^m*e^m + 69264*A*a^3*m*x*x^m*e^m + 20160*B*a^3*x^2*x^m*e^m + 40320*A*a^3*x*x^m*e^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
487,1,586,0,0.177809," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{B c^{2} m^{5} x^{6} x^{m} e^{m} + A c^{2} m^{5} x^{5} x^{m} e^{m} + 15 \, B c^{2} m^{4} x^{6} x^{m} e^{m} + 2 \, B a c m^{5} x^{4} x^{m} e^{m} + 16 \, A c^{2} m^{4} x^{5} x^{m} e^{m} + 85 \, B c^{2} m^{3} x^{6} x^{m} e^{m} + 2 \, A a c m^{5} x^{3} x^{m} e^{m} + 34 \, B a c m^{4} x^{4} x^{m} e^{m} + 95 \, A c^{2} m^{3} x^{5} x^{m} e^{m} + 225 \, B c^{2} m^{2} x^{6} x^{m} e^{m} + B a^{2} m^{5} x^{2} x^{m} e^{m} + 36 \, A a c m^{4} x^{3} x^{m} e^{m} + 214 \, B a c m^{3} x^{4} x^{m} e^{m} + 260 \, A c^{2} m^{2} x^{5} x^{m} e^{m} + 274 \, B c^{2} m x^{6} x^{m} e^{m} + A a^{2} m^{5} x x^{m} e^{m} + 19 \, B a^{2} m^{4} x^{2} x^{m} e^{m} + 242 \, A a c m^{3} x^{3} x^{m} e^{m} + 614 \, B a c m^{2} x^{4} x^{m} e^{m} + 324 \, A c^{2} m x^{5} x^{m} e^{m} + 120 \, B c^{2} x^{6} x^{m} e^{m} + 20 \, A a^{2} m^{4} x x^{m} e^{m} + 137 \, B a^{2} m^{3} x^{2} x^{m} e^{m} + 744 \, A a c m^{2} x^{3} x^{m} e^{m} + 792 \, B a c m x^{4} x^{m} e^{m} + 144 \, A c^{2} x^{5} x^{m} e^{m} + 155 \, A a^{2} m^{3} x x^{m} e^{m} + 461 \, B a^{2} m^{2} x^{2} x^{m} e^{m} + 1016 \, A a c m x^{3} x^{m} e^{m} + 360 \, B a c x^{4} x^{m} e^{m} + 580 \, A a^{2} m^{2} x x^{m} e^{m} + 702 \, B a^{2} m x^{2} x^{m} e^{m} + 480 \, A a c x^{3} x^{m} e^{m} + 1044 \, A a^{2} m x x^{m} e^{m} + 360 \, B a^{2} x^{2} x^{m} e^{m} + 720 \, A a^{2} x x^{m} e^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"(B*c^2*m^5*x^6*x^m*e^m + A*c^2*m^5*x^5*x^m*e^m + 15*B*c^2*m^4*x^6*x^m*e^m + 2*B*a*c*m^5*x^4*x^m*e^m + 16*A*c^2*m^4*x^5*x^m*e^m + 85*B*c^2*m^3*x^6*x^m*e^m + 2*A*a*c*m^5*x^3*x^m*e^m + 34*B*a*c*m^4*x^4*x^m*e^m + 95*A*c^2*m^3*x^5*x^m*e^m + 225*B*c^2*m^2*x^6*x^m*e^m + B*a^2*m^5*x^2*x^m*e^m + 36*A*a*c*m^4*x^3*x^m*e^m + 214*B*a*c*m^3*x^4*x^m*e^m + 260*A*c^2*m^2*x^5*x^m*e^m + 274*B*c^2*m*x^6*x^m*e^m + A*a^2*m^5*x*x^m*e^m + 19*B*a^2*m^4*x^2*x^m*e^m + 242*A*a*c*m^3*x^3*x^m*e^m + 614*B*a*c*m^2*x^4*x^m*e^m + 324*A*c^2*m*x^5*x^m*e^m + 120*B*c^2*x^6*x^m*e^m + 20*A*a^2*m^4*x*x^m*e^m + 137*B*a^2*m^3*x^2*x^m*e^m + 744*A*a*c*m^2*x^3*x^m*e^m + 792*B*a*c*m*x^4*x^m*e^m + 144*A*c^2*x^5*x^m*e^m + 155*A*a^2*m^3*x*x^m*e^m + 461*B*a^2*m^2*x^2*x^m*e^m + 1016*A*a*c*m*x^3*x^m*e^m + 360*B*a*c*x^4*x^m*e^m + 580*A*a^2*m^2*x*x^m*e^m + 702*B*a^2*m*x^2*x^m*e^m + 480*A*a*c*x^3*x^m*e^m + 1044*A*a^2*m*x*x^m*e^m + 360*B*a^2*x^2*x^m*e^m + 720*A*a^2*x*x^m*e^m)/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
488,1,230,0,0.163289," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{B c m^{3} x^{4} x^{m} e^{m} + A c m^{3} x^{3} x^{m} e^{m} + 6 \, B c m^{2} x^{4} x^{m} e^{m} + B a m^{3} x^{2} x^{m} e^{m} + 7 \, A c m^{2} x^{3} x^{m} e^{m} + 11 \, B c m x^{4} x^{m} e^{m} + A a m^{3} x x^{m} e^{m} + 8 \, B a m^{2} x^{2} x^{m} e^{m} + 14 \, A c m x^{3} x^{m} e^{m} + 6 \, B c x^{4} x^{m} e^{m} + 9 \, A a m^{2} x x^{m} e^{m} + 19 \, B a m x^{2} x^{m} e^{m} + 8 \, A c x^{3} x^{m} e^{m} + 26 \, A a m x x^{m} e^{m} + 12 \, B a x^{2} x^{m} e^{m} + 24 \, A a x x^{m} e^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"(B*c*m^3*x^4*x^m*e^m + A*c*m^3*x^3*x^m*e^m + 6*B*c*m^2*x^4*x^m*e^m + B*a*m^3*x^2*x^m*e^m + 7*A*c*m^2*x^3*x^m*e^m + 11*B*c*m*x^4*x^m*e^m + A*a*m^3*x*x^m*e^m + 8*B*a*m^2*x^2*x^m*e^m + 14*A*c*m*x^3*x^m*e^m + 6*B*c*x^4*x^m*e^m + 9*A*a*m^2*x*x^m*e^m + 19*B*a*m*x^2*x^m*e^m + 8*A*c*x^3*x^m*e^m + 26*A*a*m*x*x^m*e^m + 12*B*a*x^2*x^m*e^m + 24*A*a*x*x^m*e^m)/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
489,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{c x^{2} + a}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + a), x)","F",0
490,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{{\left(c x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + a)^2, x)","F",0
491,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{{\left(c x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + a)^3, x)","F",0
492,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(B x + A\right)} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*(B*x + A)*(e*x)^m, x)","F",0
493,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)*(e*x)^m, x)","F",0
494,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(B x + A\right)} \left(e x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)*(e*x)^m, x)","F",0
495,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/sqrt(c*x^2 + a), x)","F",0
496,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + a)^(3/2), x)","F",0
497,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + a)^(5/2), x)","F",0
498,0,0,0,0.000000," ","integrate(x^m*(a*x+1)/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/(a^2*x^2 - 1)^2, x)","F",0
499,0,0,0,0.000000," ","integrate(x^m/(-a*x+1)^2/(a*x+1),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(a x + 1\right)} {\left(a x - 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^m/((a*x + 1)*(a*x - 1)^2), x)","F",0
500,0,0,0,0.000000," ","integrate(x^m/(-a^2*x^2+1)^2+a*x^(1+m)/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{a x^{m + 1}}{{\left(a^{2} x^{2} - 1\right)}^{2}} + \frac{x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(a*x^(m + 1)/(a^2*x^2 - 1)^2 + x^m/(a^2*x^2 - 1)^2, x)","F",0
501,0,0,0,0.000000," ","integrate(x^m/(-a*x+1)/(-a^2*x^2+1),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(a^{2} x^{2} - 1\right)} {\left(a x - 1\right)}}\,{d x}"," ",0,"integrate(x^m/((a^2*x^2 - 1)*(a*x - 1)), x)","F",0
502,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + a\right)}^{p} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + a)^p*(e*x)^m, x)","F",0
503,0,0,0,0.000000," ","integrate(x^3*(e*x+d)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p*x^3, x)","F",0
504,0,0,0,0.000000," ","integrate(x^2*(e*x+d)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p*x^2, x)","F",0
505,0,0,0,0.000000," ","integrate(x*(e*x+d)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p} x\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p*x, x)","F",0
506,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p, x)","F",0
507,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+a)^p/x,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p/x, x)","F",0
508,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+a)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p/x^2, x)","F",0
509,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+a)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p/x^3, x)","F",0
510,1,53,0,0.146528," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{8} \, B b^{2} x^{8} + \frac{2}{7} \, B a b x^{7} + \frac{1}{7} \, A b^{2} x^{7} + \frac{1}{6} \, B a^{2} x^{6} + \frac{1}{3} \, A a b x^{6} + \frac{1}{5} \, A a^{2} x^{5}"," ",0,"1/8*B*b^2*x^8 + 2/7*B*a*b*x^7 + 1/7*A*b^2*x^7 + 1/6*B*a^2*x^6 + 1/3*A*a*b*x^6 + 1/5*A*a^2*x^5","A",0
511,1,53,0,0.210925," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{7} \, B b^{2} x^{7} + \frac{1}{3} \, B a b x^{6} + \frac{1}{6} \, A b^{2} x^{6} + \frac{1}{5} \, B a^{2} x^{5} + \frac{2}{5} \, A a b x^{5} + \frac{1}{4} \, A a^{2} x^{4}"," ",0,"1/7*B*b^2*x^7 + 1/3*B*a*b*x^6 + 1/6*A*b^2*x^6 + 1/5*B*a^2*x^5 + 2/5*A*a*b*x^5 + 1/4*A*a^2*x^4","A",0
512,1,53,0,0.151893," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{6} \, B b^{2} x^{6} + \frac{2}{5} \, B a b x^{5} + \frac{1}{5} \, A b^{2} x^{5} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{2} \, A a b x^{4} + \frac{1}{3} \, A a^{2} x^{3}"," ",0,"1/6*B*b^2*x^6 + 2/5*B*a*b*x^5 + 1/5*A*b^2*x^5 + 1/4*B*a^2*x^4 + 1/2*A*a*b*x^4 + 1/3*A*a^2*x^3","A",0
513,1,53,0,0.149883," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{5} \, B b^{2} x^{5} + \frac{1}{2} \, B a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{3} \, B a^{2} x^{3} + \frac{2}{3} \, A a b x^{3} + \frac{1}{2} \, A a^{2} x^{2}"," ",0,"1/5*B*b^2*x^5 + 1/2*B*a*b*x^4 + 1/4*A*b^2*x^4 + 1/3*B*a^2*x^3 + 2/3*A*a*b*x^3 + 1/2*A*a^2*x^2","A",0
514,1,49,0,0.153689," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{4} \, B b^{2} x^{4} + \frac{2}{3} \, B a b x^{3} + \frac{1}{3} \, A b^{2} x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a b x^{2} + A a^{2} x"," ",0,"1/4*B*b^2*x^4 + 2/3*B*a*b*x^3 + 1/3*A*b^2*x^3 + 1/2*B*a^2*x^2 + A*a*b*x^2 + A*a^2*x","A",0
515,1,46,0,0.148789," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x,x, algorithm=""giac"")","\frac{1}{3} \, B b^{2} x^{3} + B a b x^{2} + \frac{1}{2} \, A b^{2} x^{2} + B a^{2} x + 2 \, A a b x + A a^{2} \log\left({\left| x \right|}\right)"," ",0,"1/3*B*b^2*x^3 + B*a*b*x^2 + 1/2*A*b^2*x^2 + B*a^2*x + 2*A*a*b*x + A*a^2*log(abs(x))","A",0
516,1,46,0,0.148444," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, B b^{2} x^{2} + 2 \, B a b x + A b^{2} x - \frac{A a^{2}}{x} + {\left(B a^{2} + 2 \, A a b\right)} \log\left({\left| x \right|}\right)"," ",0,"1/2*B*b^2*x^2 + 2*B*a*b*x + A*b^2*x - A*a^2/x + (B*a^2 + 2*A*a*b)*log(abs(x))","A",0
517,1,47,0,0.149568," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^3,x, algorithm=""giac"")","B b^{2} x + {\left(2 \, B a b + A b^{2}\right)} \log\left({\left| x \right|}\right) - \frac{A a^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} x}{2 \, x^{2}}"," ",0,"B*b^2*x + (2*B*a*b + A*b^2)*log(abs(x)) - 1/2*(A*a^2 + 2*(B*a^2 + 2*A*a*b)*x)/x^2","A",0
518,1,51,0,0.155990," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^4,x, algorithm=""giac"")","B b^{2} \log\left({\left| x \right|}\right) - \frac{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,"B*b^2*log(abs(x)) - 1/6*(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
519,1,51,0,0.147831," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^5,x, algorithm=""giac"")","-\frac{12 \, B b^{2} x^{3} + 12 \, B a b x^{2} + 6 \, A b^{2} x^{2} + 4 \, B a^{2} x + 8 \, A a b x + 3 \, A a^{2}}{12 \, x^{4}}"," ",0,"-1/12*(12*B*b^2*x^3 + 12*B*a*b*x^2 + 6*A*b^2*x^2 + 4*B*a^2*x + 8*A*a*b*x + 3*A*a^2)/x^4","A",0
520,1,51,0,0.150930," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^6,x, algorithm=""giac"")","-\frac{30 \, B b^{2} x^{3} + 40 \, B a b x^{2} + 20 \, A b^{2} x^{2} + 15 \, B a^{2} x + 30 \, A a b x + 12 \, A a^{2}}{60 \, x^{5}}"," ",0,"-1/60*(30*B*b^2*x^3 + 40*B*a*b*x^2 + 20*A*b^2*x^2 + 15*B*a^2*x + 30*A*a*b*x + 12*A*a^2)/x^5","A",0
521,1,51,0,0.190346," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^7,x, algorithm=""giac"")","-\frac{20 \, B b^{2} x^{3} + 30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 12 \, B a^{2} x + 24 \, A a b x + 10 \, A a^{2}}{60 \, x^{6}}"," ",0,"-1/60*(20*B*b^2*x^3 + 30*B*a*b*x^2 + 15*A*b^2*x^2 + 12*B*a^2*x + 24*A*a*b*x + 10*A*a^2)/x^6","A",0
522,1,51,0,0.160053," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^8,x, algorithm=""giac"")","-\frac{105 \, B b^{2} x^{3} + 168 \, B a b x^{2} + 84 \, A b^{2} x^{2} + 70 \, B a^{2} x + 140 \, A a b x + 60 \, A a^{2}}{420 \, x^{7}}"," ",0,"-1/420*(105*B*b^2*x^3 + 168*B*a*b*x^2 + 84*A*b^2*x^2 + 70*B*a^2*x + 140*A*a*b*x + 60*A*a^2)/x^7","A",0
523,1,101,0,0.163912," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{10} \, B b^{4} x^{10} + \frac{4}{9} \, B a b^{3} x^{9} + \frac{1}{9} \, A b^{4} x^{9} + \frac{3}{4} \, B a^{2} b^{2} x^{8} + \frac{1}{2} \, A a b^{3} x^{8} + \frac{4}{7} \, B a^{3} b x^{7} + \frac{6}{7} \, A a^{2} b^{2} x^{7} + \frac{1}{6} \, B a^{4} x^{6} + \frac{2}{3} \, A a^{3} b x^{6} + \frac{1}{5} \, A a^{4} x^{5}"," ",0,"1/10*B*b^4*x^10 + 4/9*B*a*b^3*x^9 + 1/9*A*b^4*x^9 + 3/4*B*a^2*b^2*x^8 + 1/2*A*a*b^3*x^8 + 4/7*B*a^3*b*x^7 + 6/7*A*a^2*b^2*x^7 + 1/6*B*a^4*x^6 + 2/3*A*a^3*b*x^6 + 1/5*A*a^4*x^5","A",0
524,1,100,0,0.153739," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{9} \, B b^{4} x^{9} + \frac{1}{2} \, B a b^{3} x^{8} + \frac{1}{8} \, A b^{4} x^{8} + \frac{6}{7} \, B a^{2} b^{2} x^{7} + \frac{4}{7} \, A a b^{3} x^{7} + \frac{2}{3} \, B a^{3} b x^{6} + A a^{2} b^{2} x^{6} + \frac{1}{5} \, B a^{4} x^{5} + \frac{4}{5} \, A a^{3} b x^{5} + \frac{1}{4} \, A a^{4} x^{4}"," ",0,"1/9*B*b^4*x^9 + 1/2*B*a*b^3*x^8 + 1/8*A*b^4*x^8 + 6/7*B*a^2*b^2*x^7 + 4/7*A*a*b^3*x^7 + 2/3*B*a^3*b*x^6 + A*a^2*b^2*x^6 + 1/5*B*a^4*x^5 + 4/5*A*a^3*b*x^5 + 1/4*A*a^4*x^4","A",0
525,1,99,0,0.165431," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{8} \, B b^{4} x^{8} + \frac{4}{7} \, B a b^{3} x^{7} + \frac{1}{7} \, A b^{4} x^{7} + B a^{2} b^{2} x^{6} + \frac{2}{3} \, A a b^{3} x^{6} + \frac{4}{5} \, B a^{3} b x^{5} + \frac{6}{5} \, A a^{2} b^{2} x^{5} + \frac{1}{4} \, B a^{4} x^{4} + A a^{3} b x^{4} + \frac{1}{3} \, A a^{4} x^{3}"," ",0,"1/8*B*b^4*x^8 + 4/7*B*a*b^3*x^7 + 1/7*A*b^4*x^7 + B*a^2*b^2*x^6 + 2/3*A*a*b^3*x^6 + 4/5*B*a^3*b*x^5 + 6/5*A*a^2*b^2*x^5 + 1/4*B*a^4*x^4 + A*a^3*b*x^4 + 1/3*A*a^4*x^3","A",0
526,1,100,0,0.152421," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{7} \, B b^{4} x^{7} + \frac{2}{3} \, B a b^{3} x^{6} + \frac{1}{6} \, A b^{4} x^{6} + \frac{6}{5} \, B a^{2} b^{2} x^{5} + \frac{4}{5} \, A a b^{3} x^{5} + B a^{3} b x^{4} + \frac{3}{2} \, A a^{2} b^{2} x^{4} + \frac{1}{3} \, B a^{4} x^{3} + \frac{4}{3} \, A a^{3} b x^{3} + \frac{1}{2} \, A a^{4} x^{2}"," ",0,"1/7*B*b^4*x^7 + 2/3*B*a*b^3*x^6 + 1/6*A*b^4*x^6 + 6/5*B*a^2*b^2*x^5 + 4/5*A*a*b^3*x^5 + B*a^3*b*x^4 + 3/2*A*a^2*b^2*x^4 + 1/3*B*a^4*x^3 + 4/3*A*a^3*b*x^3 + 1/2*A*a^4*x^2","A",0
527,1,97,0,0.182799," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, B b^{4} x^{6} + \frac{4}{5} \, B a b^{3} x^{5} + \frac{1}{5} \, A b^{4} x^{5} + \frac{3}{2} \, B a^{2} b^{2} x^{4} + A a b^{3} x^{4} + \frac{4}{3} \, B a^{3} b x^{3} + 2 \, A a^{2} b^{2} x^{3} + \frac{1}{2} \, B a^{4} x^{2} + 2 \, A a^{3} b x^{2} + A a^{4} x"," ",0,"1/6*B*b^4*x^6 + 4/5*B*a*b^3*x^5 + 1/5*A*b^4*x^5 + 3/2*B*a^2*b^2*x^4 + A*a*b^3*x^4 + 4/3*B*a^3*b*x^3 + 2*A*a^2*b^2*x^3 + 1/2*B*a^4*x^2 + 2*A*a^3*b*x^2 + A*a^4*x","B",0
528,1,94,0,0.170773," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x,x, algorithm=""giac"")","\frac{1}{5} \, B b^{4} x^{5} + B a b^{3} x^{4} + \frac{1}{4} \, A b^{4} x^{4} + 2 \, B a^{2} b^{2} x^{3} + \frac{4}{3} \, A a b^{3} x^{3} + 2 \, B a^{3} b x^{2} + 3 \, A a^{2} b^{2} x^{2} + B a^{4} x + 4 \, A a^{3} b x + A a^{4} \log\left({\left| x \right|}\right)"," ",0,"1/5*B*b^4*x^5 + B*a*b^3*x^4 + 1/4*A*b^4*x^4 + 2*B*a^2*b^2*x^3 + 4/3*A*a*b^3*x^3 + 2*B*a^3*b*x^2 + 3*A*a^2*b^2*x^2 + B*a^4*x + 4*A*a^3*b*x + A*a^4*log(abs(x))","A",0
529,1,95,0,0.156580," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^2,x, algorithm=""giac"")","\frac{1}{4} \, B b^{4} x^{4} + \frac{4}{3} \, B a b^{3} x^{3} + \frac{1}{3} \, A b^{4} x^{3} + 3 \, B a^{2} b^{2} x^{2} + 2 \, A a b^{3} x^{2} + 4 \, B a^{3} b x + 6 \, A a^{2} b^{2} x - \frac{A a^{4}}{x} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \log\left({\left| x \right|}\right)"," ",0,"1/4*B*b^4*x^4 + 4/3*B*a*b^3*x^3 + 1/3*A*b^4*x^3 + 3*B*a^2*b^2*x^2 + 2*A*a*b^3*x^2 + 4*B*a^3*b*x + 6*A*a^2*b^2*x - A*a^4/x + (B*a^4 + 4*A*a^3*b)*log(abs(x))","A",0
530,1,96,0,0.152806," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^3,x, algorithm=""giac"")","\frac{1}{3} \, B b^{4} x^{3} + 2 \, B a b^{3} x^{2} + \frac{1}{2} \, A b^{4} x^{2} + 6 \, B a^{2} b^{2} x + 4 \, A a b^{3} x + 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} \log\left({\left| x \right|}\right) - \frac{A a^{4} + 2 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{2 \, x^{2}}"," ",0,"1/3*B*b^4*x^3 + 2*B*a*b^3*x^2 + 1/2*A*b^4*x^2 + 6*B*a^2*b^2*x + 4*A*a*b^3*x + 2*(2*B*a^3*b + 3*A*a^2*b^2)*log(abs(x)) - 1/2*(A*a^4 + 2*(B*a^4 + 4*A*a^3*b)*x)/x^2","A",0
531,1,96,0,0.159770," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^4,x, algorithm=""giac"")","\frac{1}{2} \, B b^{4} x^{2} + 4 \, B a b^{3} x + A b^{4} x + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \log\left({\left| x \right|}\right) - \frac{2 \, A a^{4} + 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,"1/2*B*b^4*x^2 + 4*B*a*b^3*x + A*b^4*x + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*log(abs(x)) - 1/6*(2*A*a^4 + 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
532,1,96,0,0.167220," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^5,x, algorithm=""giac"")","B b^{4} x + {\left(4 \, B a b^{3} + A b^{4}\right)} \log\left({\left| x \right|}\right) - \frac{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,"B*b^4*x + (4*B*a*b^3 + A*b^4)*log(abs(x)) - 1/12*(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
533,1,99,0,0.165330," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^6,x, algorithm=""giac"")","B b^{4} \log\left({\left| x \right|}\right) - \frac{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,"B*b^4*log(abs(x)) - 1/60*(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
534,1,99,0,0.171269," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^7,x, algorithm=""giac"")","-\frac{30 \, B b^{4} x^{5} + 60 \, B a b^{3} x^{4} + 15 \, A b^{4} x^{4} + 60 \, B a^{2} b^{2} x^{3} + 40 \, A a b^{3} x^{3} + 30 \, B a^{3} b x^{2} + 45 \, A a^{2} b^{2} x^{2} + 6 \, B a^{4} x + 24 \, A a^{3} b x + 5 \, A a^{4}}{30 \, x^{6}}"," ",0,"-1/30*(30*B*b^4*x^5 + 60*B*a*b^3*x^4 + 15*A*b^4*x^4 + 60*B*a^2*b^2*x^3 + 40*A*a*b^3*x^3 + 30*B*a^3*b*x^2 + 45*A*a^2*b^2*x^2 + 6*B*a^4*x + 24*A*a^3*b*x + 5*A*a^4)/x^6","B",0
535,1,99,0,0.155804," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^8,x, algorithm=""giac"")","-\frac{105 \, B b^{4} x^{5} + 280 \, B a b^{3} x^{4} + 70 \, A b^{4} x^{4} + 315 \, B a^{2} b^{2} x^{3} + 210 \, A a b^{3} x^{3} + 168 \, B a^{3} b x^{2} + 252 \, A a^{2} b^{2} x^{2} + 35 \, B a^{4} x + 140 \, A a^{3} b x + 30 \, A a^{4}}{210 \, x^{7}}"," ",0,"-1/210*(105*B*b^4*x^5 + 280*B*a*b^3*x^4 + 70*A*b^4*x^4 + 315*B*a^2*b^2*x^3 + 210*A*a*b^3*x^3 + 168*B*a^3*b*x^2 + 252*A*a^2*b^2*x^2 + 35*B*a^4*x + 140*A*a^3*b*x + 30*A*a^4)/x^7","A",0
536,1,99,0,0.160905," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^9,x, algorithm=""giac"")","-\frac{280 \, B b^{4} x^{5} + 840 \, B a b^{3} x^{4} + 210 \, A b^{4} x^{4} + 1008 \, B a^{2} b^{2} x^{3} + 672 \, A a b^{3} x^{3} + 560 \, B a^{3} b x^{2} + 840 \, A a^{2} b^{2} x^{2} + 120 \, B a^{4} x + 480 \, A a^{3} b x + 105 \, A a^{4}}{840 \, x^{8}}"," ",0,"-1/840*(280*B*b^4*x^5 + 840*B*a*b^3*x^4 + 210*A*b^4*x^4 + 1008*B*a^2*b^2*x^3 + 672*A*a*b^3*x^3 + 560*B*a^3*b*x^2 + 840*A*a^2*b^2*x^2 + 120*B*a^4*x + 480*A*a^3*b*x + 105*A*a^4)/x^8","A",0
537,1,99,0,0.184292," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^10,x, algorithm=""giac"")","-\frac{630 \, B b^{4} x^{5} + 2016 \, B a b^{3} x^{4} + 504 \, A b^{4} x^{4} + 2520 \, B a^{2} b^{2} x^{3} + 1680 \, A a b^{3} x^{3} + 1440 \, B a^{3} b x^{2} + 2160 \, A a^{2} b^{2} x^{2} + 315 \, B a^{4} x + 1260 \, A a^{3} b x + 280 \, A a^{4}}{2520 \, x^{9}}"," ",0,"-1/2520*(630*B*b^4*x^5 + 2016*B*a*b^3*x^4 + 504*A*b^4*x^4 + 2520*B*a^2*b^2*x^3 + 1680*A*a*b^3*x^3 + 1440*B*a^3*b*x^2 + 2160*A*a^2*b^2*x^2 + 315*B*a^4*x + 1260*A*a^3*b*x + 280*A*a^4)/x^9","A",0
538,1,99,0,0.152355," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^11,x, algorithm=""giac"")","-\frac{252 \, B b^{4} x^{5} + 840 \, B a b^{3} x^{4} + 210 \, A b^{4} x^{4} + 1080 \, B a^{2} b^{2} x^{3} + 720 \, A a b^{3} x^{3} + 630 \, B a^{3} b x^{2} + 945 \, A a^{2} b^{2} x^{2} + 140 \, B a^{4} x + 560 \, A a^{3} b x + 126 \, A a^{4}}{1260 \, x^{10}}"," ",0,"-1/1260*(252*B*b^4*x^5 + 840*B*a*b^3*x^4 + 210*A*b^4*x^4 + 1080*B*a^2*b^2*x^3 + 720*A*a*b^3*x^3 + 630*B*a^3*b*x^2 + 945*A*a^2*b^2*x^2 + 140*B*a^4*x + 560*A*a^3*b*x + 126*A*a^4)/x^10","A",0
539,1,149,0,0.166833," ","integrate(x^5*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{13} \, B b^{6} x^{13} + \frac{1}{2} \, B a b^{5} x^{12} + \frac{1}{12} \, A b^{6} x^{12} + \frac{15}{11} \, B a^{2} b^{4} x^{11} + \frac{6}{11} \, A a b^{5} x^{11} + 2 \, B a^{3} b^{3} x^{10} + \frac{3}{2} \, A a^{2} b^{4} x^{10} + \frac{5}{3} \, B a^{4} b^{2} x^{9} + \frac{20}{9} \, A a^{3} b^{3} x^{9} + \frac{3}{4} \, B a^{5} b x^{8} + \frac{15}{8} \, A a^{4} b^{2} x^{8} + \frac{1}{7} \, B a^{6} x^{7} + \frac{6}{7} \, A a^{5} b x^{7} + \frac{1}{6} \, A a^{6} x^{6}"," ",0,"1/13*B*b^6*x^13 + 1/2*B*a*b^5*x^12 + 1/12*A*b^6*x^12 + 15/11*B*a^2*b^4*x^11 + 6/11*A*a*b^5*x^11 + 2*B*a^3*b^3*x^10 + 3/2*A*a^2*b^4*x^10 + 5/3*B*a^4*b^2*x^9 + 20/9*A*a^3*b^3*x^9 + 3/4*B*a^5*b*x^8 + 15/8*A*a^4*b^2*x^8 + 1/7*B*a^6*x^7 + 6/7*A*a^5*b*x^7 + 1/6*A*a^6*x^6","A",0
540,1,148,0,0.157207," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{12} \, B b^{6} x^{12} + \frac{6}{11} \, B a b^{5} x^{11} + \frac{1}{11} \, A b^{6} x^{11} + \frac{3}{2} \, B a^{2} b^{4} x^{10} + \frac{3}{5} \, A a b^{5} x^{10} + \frac{20}{9} \, B a^{3} b^{3} x^{9} + \frac{5}{3} \, A a^{2} b^{4} x^{9} + \frac{15}{8} \, B a^{4} b^{2} x^{8} + \frac{5}{2} \, A a^{3} b^{3} x^{8} + \frac{6}{7} \, B a^{5} b x^{7} + \frac{15}{7} \, A a^{4} b^{2} x^{7} + \frac{1}{6} \, B a^{6} x^{6} + A a^{5} b x^{6} + \frac{1}{5} \, A a^{6} x^{5}"," ",0,"1/12*B*b^6*x^12 + 6/11*B*a*b^5*x^11 + 1/11*A*b^6*x^11 + 3/2*B*a^2*b^4*x^10 + 3/5*A*a*b^5*x^10 + 20/9*B*a^3*b^3*x^9 + 5/3*A*a^2*b^4*x^9 + 15/8*B*a^4*b^2*x^8 + 5/2*A*a^3*b^3*x^8 + 6/7*B*a^5*b*x^7 + 15/7*A*a^4*b^2*x^7 + 1/6*B*a^6*x^6 + A*a^5*b*x^6 + 1/5*A*a^6*x^5","A",0
541,1,148,0,0.202967," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{11} \, B b^{6} x^{11} + \frac{3}{5} \, B a b^{5} x^{10} + \frac{1}{10} \, A b^{6} x^{10} + \frac{5}{3} \, B a^{2} b^{4} x^{9} + \frac{2}{3} \, A a b^{5} x^{9} + \frac{5}{2} \, B a^{3} b^{3} x^{8} + \frac{15}{8} \, A a^{2} b^{4} x^{8} + \frac{15}{7} \, B a^{4} b^{2} x^{7} + \frac{20}{7} \, A a^{3} b^{3} x^{7} + B a^{5} b x^{6} + \frac{5}{2} \, A a^{4} b^{2} x^{6} + \frac{1}{5} \, B a^{6} x^{5} + \frac{6}{5} \, A a^{5} b x^{5} + \frac{1}{4} \, A a^{6} x^{4}"," ",0,"1/11*B*b^6*x^11 + 3/5*B*a*b^5*x^10 + 1/10*A*b^6*x^10 + 5/3*B*a^2*b^4*x^9 + 2/3*A*a*b^5*x^9 + 5/2*B*a^3*b^3*x^8 + 15/8*A*a^2*b^4*x^8 + 15/7*B*a^4*b^2*x^7 + 20/7*A*a^3*b^3*x^7 + B*a^5*b*x^6 + 5/2*A*a^4*b^2*x^6 + 1/5*B*a^6*x^5 + 6/5*A*a^5*b*x^5 + 1/4*A*a^6*x^4","A",0
542,1,149,0,0.188923," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{10} \, B b^{6} x^{10} + \frac{2}{3} \, B a b^{5} x^{9} + \frac{1}{9} \, A b^{6} x^{9} + \frac{15}{8} \, B a^{2} b^{4} x^{8} + \frac{3}{4} \, A a b^{5} x^{8} + \frac{20}{7} \, B a^{3} b^{3} x^{7} + \frac{15}{7} \, A a^{2} b^{4} x^{7} + \frac{5}{2} \, B a^{4} b^{2} x^{6} + \frac{10}{3} \, A a^{3} b^{3} x^{6} + \frac{6}{5} \, B a^{5} b x^{5} + 3 \, A a^{4} b^{2} x^{5} + \frac{1}{4} \, B a^{6} x^{4} + \frac{3}{2} \, A a^{5} b x^{4} + \frac{1}{3} \, A a^{6} x^{3}"," ",0,"1/10*B*b^6*x^10 + 2/3*B*a*b^5*x^9 + 1/9*A*b^6*x^9 + 15/8*B*a^2*b^4*x^8 + 3/4*A*a*b^5*x^8 + 20/7*B*a^3*b^3*x^7 + 15/7*A*a^2*b^4*x^7 + 5/2*B*a^4*b^2*x^6 + 10/3*A*a^3*b^3*x^6 + 6/5*B*a^5*b*x^5 + 3*A*a^4*b^2*x^5 + 1/4*B*a^6*x^4 + 3/2*A*a^5*b*x^4 + 1/3*A*a^6*x^3","A",0
543,1,149,0,0.151059," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{9} \, B b^{6} x^{9} + \frac{3}{4} \, B a b^{5} x^{8} + \frac{1}{8} \, A b^{6} x^{8} + \frac{15}{7} \, B a^{2} b^{4} x^{7} + \frac{6}{7} \, A a b^{5} x^{7} + \frac{10}{3} \, B a^{3} b^{3} x^{6} + \frac{5}{2} \, A a^{2} b^{4} x^{6} + 3 \, B a^{4} b^{2} x^{5} + 4 \, A a^{3} b^{3} x^{5} + \frac{3}{2} \, B a^{5} b x^{4} + \frac{15}{4} \, A a^{4} b^{2} x^{4} + \frac{1}{3} \, B a^{6} x^{3} + 2 \, A a^{5} b x^{3} + \frac{1}{2} \, A a^{6} x^{2}"," ",0,"1/9*B*b^6*x^9 + 3/4*B*a*b^5*x^8 + 1/8*A*b^6*x^8 + 15/7*B*a^2*b^4*x^7 + 6/7*A*a*b^5*x^7 + 10/3*B*a^3*b^3*x^6 + 5/2*A*a^2*b^4*x^6 + 3*B*a^4*b^2*x^5 + 4*A*a^3*b^3*x^5 + 3/2*B*a^5*b*x^4 + 15/4*A*a^4*b^2*x^4 + 1/3*B*a^6*x^3 + 2*A*a^5*b*x^3 + 1/2*A*a^6*x^2","B",0
544,1,145,0,0.154280," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{8} \, B b^{6} x^{8} + \frac{6}{7} \, B a b^{5} x^{7} + \frac{1}{7} \, A b^{6} x^{7} + \frac{5}{2} \, B a^{2} b^{4} x^{6} + A a b^{5} x^{6} + 4 \, B a^{3} b^{3} x^{5} + 3 \, A a^{2} b^{4} x^{5} + \frac{15}{4} \, B a^{4} b^{2} x^{4} + 5 \, A a^{3} b^{3} x^{4} + 2 \, B a^{5} b x^{3} + 5 \, A a^{4} b^{2} x^{3} + \frac{1}{2} \, B a^{6} x^{2} + 3 \, A a^{5} b x^{2} + A a^{6} x"," ",0,"1/8*B*b^6*x^8 + 6/7*B*a*b^5*x^7 + 1/7*A*b^6*x^7 + 5/2*B*a^2*b^4*x^6 + A*a*b^5*x^6 + 4*B*a^3*b^3*x^5 + 3*A*a^2*b^4*x^5 + 15/4*B*a^4*b^2*x^4 + 5*A*a^3*b^3*x^4 + 2*B*a^5*b*x^3 + 5*A*a^4*b^2*x^3 + 1/2*B*a^6*x^2 + 3*A*a^5*b*x^2 + A*a^6*x","B",0
545,1,142,0,0.171088," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x,x, algorithm=""giac"")","\frac{1}{7} \, B b^{6} x^{7} + B a b^{5} x^{6} + \frac{1}{6} \, A b^{6} x^{6} + 3 \, B a^{2} b^{4} x^{5} + \frac{6}{5} \, A a b^{5} x^{5} + 5 \, B a^{3} b^{3} x^{4} + \frac{15}{4} \, A a^{2} b^{4} x^{4} + 5 \, B a^{4} b^{2} x^{3} + \frac{20}{3} \, A a^{3} b^{3} x^{3} + 3 \, B a^{5} b x^{2} + \frac{15}{2} \, A a^{4} b^{2} x^{2} + B a^{6} x + 6 \, A a^{5} b x + A a^{6} \log\left({\left| x \right|}\right)"," ",0,"1/7*B*b^6*x^7 + B*a*b^5*x^6 + 1/6*A*b^6*x^6 + 3*B*a^2*b^4*x^5 + 6/5*A*a*b^5*x^5 + 5*B*a^3*b^3*x^4 + 15/4*A*a^2*b^4*x^4 + 5*B*a^4*b^2*x^3 + 20/3*A*a^3*b^3*x^3 + 3*B*a^5*b*x^2 + 15/2*A*a^4*b^2*x^2 + B*a^6*x + 6*A*a^5*b*x + A*a^6*log(abs(x))","A",0
546,1,143,0,0.156475," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^2,x, algorithm=""giac"")","\frac{1}{6} \, B b^{6} x^{6} + \frac{6}{5} \, B a b^{5} x^{5} + \frac{1}{5} \, A b^{6} x^{5} + \frac{15}{4} \, B a^{2} b^{4} x^{4} + \frac{3}{2} \, A a b^{5} x^{4} + \frac{20}{3} \, B a^{3} b^{3} x^{3} + 5 \, A a^{2} b^{4} x^{3} + \frac{15}{2} \, B a^{4} b^{2} x^{2} + 10 \, A a^{3} b^{3} x^{2} + 6 \, B a^{5} b x + 15 \, A a^{4} b^{2} x - \frac{A a^{6}}{x} + {\left(B a^{6} + 6 \, A a^{5} b\right)} \log\left({\left| x \right|}\right)"," ",0,"1/6*B*b^6*x^6 + 6/5*B*a*b^5*x^5 + 1/5*A*b^6*x^5 + 15/4*B*a^2*b^4*x^4 + 3/2*A*a*b^5*x^4 + 20/3*B*a^3*b^3*x^3 + 5*A*a^2*b^4*x^3 + 15/2*B*a^4*b^2*x^2 + 10*A*a^3*b^3*x^2 + 6*B*a^5*b*x + 15*A*a^4*b^2*x - A*a^6/x + (B*a^6 + 6*A*a^5*b)*log(abs(x))","A",0
547,1,144,0,0.172193," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^3,x, algorithm=""giac"")","\frac{1}{5} \, B b^{6} x^{5} + \frac{3}{2} \, B a b^{5} x^{4} + \frac{1}{4} \, A b^{6} x^{4} + 5 \, B a^{2} b^{4} x^{3} + 2 \, A a b^{5} x^{3} + 10 \, B a^{3} b^{3} x^{2} + \frac{15}{2} \, A a^{2} b^{4} x^{2} + 15 \, B a^{4} b^{2} x + 20 \, A a^{3} b^{3} x + 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} \log\left({\left| x \right|}\right) - \frac{A a^{6} + 2 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{2 \, x^{2}}"," ",0,"1/5*B*b^6*x^5 + 3/2*B*a*b^5*x^4 + 1/4*A*b^6*x^4 + 5*B*a^2*b^4*x^3 + 2*A*a*b^5*x^3 + 10*B*a^3*b^3*x^2 + 15/2*A*a^2*b^4*x^2 + 15*B*a^4*b^2*x + 20*A*a^3*b^3*x + 3*(2*B*a^5*b + 5*A*a^4*b^2)*log(abs(x)) - 1/2*(A*a^6 + 2*(B*a^6 + 6*A*a^5*b)*x)/x^2","A",0
548,1,145,0,0.166721," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^4,x, algorithm=""giac"")","\frac{1}{4} \, B b^{6} x^{4} + 2 \, B a b^{5} x^{3} + \frac{1}{3} \, A b^{6} x^{3} + \frac{15}{2} \, B a^{2} b^{4} x^{2} + 3 \, A a b^{5} x^{2} + 20 \, B a^{3} b^{3} x + 15 \, A a^{2} b^{4} x + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} \log\left({\left| x \right|}\right) - \frac{2 \, A a^{6} + 18 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 3 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{6 \, x^{3}}"," ",0,"1/4*B*b^6*x^4 + 2*B*a*b^5*x^3 + 1/3*A*b^6*x^3 + 15/2*B*a^2*b^4*x^2 + 3*A*a*b^5*x^2 + 20*B*a^3*b^3*x + 15*A*a^2*b^4*x + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*log(abs(x)) - 1/6*(2*A*a^6 + 18*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 3*(B*a^6 + 6*A*a^5*b)*x)/x^3","A",0
549,1,145,0,0.185452," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^5,x, algorithm=""giac"")","\frac{1}{3} \, B b^{6} x^{3} + 3 \, B a b^{5} x^{2} + \frac{1}{2} \, A b^{6} x^{2} + 15 \, B a^{2} b^{4} x + 6 \, A a b^{5} x + 5 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} \log\left({\left| x \right|}\right) - \frac{3 \, A a^{6} + 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,"1/3*B*b^6*x^3 + 3*B*a*b^5*x^2 + 1/2*A*b^6*x^2 + 15*B*a^2*b^4*x + 6*A*a*b^5*x + 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*log(abs(x)) - 1/12*(3*A*a^6 + 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
550,1,144,0,0.178566," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^6,x, algorithm=""giac"")","\frac{1}{2} \, B b^{6} x^{2} + 6 \, B a b^{5} x + A b^{6} x + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} \log\left({\left| x \right|}\right) - \frac{4 \, A a^{6} + 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,"1/2*B*b^6*x^2 + 6*B*a*b^5*x + A*b^6*x + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*log(abs(x)) - 1/20*(4*A*a^6 + 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
551,1,144,0,0.155966," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^7,x, algorithm=""giac"")","B b^{6} x + {\left(6 \, B a b^{5} + A b^{6}\right)} \log\left({\left| x \right|}\right) - \frac{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,"B*b^6*x + (6*B*a*b^5 + A*b^6)*log(abs(x)) - 1/60*(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
552,1,147,0,0.165831," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^8,x, algorithm=""giac"")","B b^{6} \log\left({\left| x \right|}\right) - \frac{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,"B*b^6*log(abs(x)) - 1/420*(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
553,1,147,0,0.154272," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^9,x, algorithm=""giac"")","-\frac{56 \, B b^{6} x^{7} + 168 \, B a b^{5} x^{6} + 28 \, A b^{6} x^{6} + 280 \, B a^{2} b^{4} x^{5} + 112 \, A a b^{5} x^{5} + 280 \, B a^{3} b^{3} x^{4} + 210 \, A a^{2} b^{4} x^{4} + 168 \, B a^{4} b^{2} x^{3} + 224 \, A a^{3} b^{3} x^{3} + 56 \, B a^{5} b x^{2} + 140 \, A a^{4} b^{2} x^{2} + 8 \, B a^{6} x + 48 \, A a^{5} b x + 7 \, A a^{6}}{56 \, x^{8}}"," ",0,"-1/56*(56*B*b^6*x^7 + 168*B*a*b^5*x^6 + 28*A*b^6*x^6 + 280*B*a^2*b^4*x^5 + 112*A*a*b^5*x^5 + 280*B*a^3*b^3*x^4 + 210*A*a^2*b^4*x^4 + 168*B*a^4*b^2*x^3 + 224*A*a^3*b^3*x^3 + 56*B*a^5*b*x^2 + 140*A*a^4*b^2*x^2 + 8*B*a^6*x + 48*A*a^5*b*x + 7*A*a^6)/x^8","B",0
554,1,147,0,0.177317," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^10,x, algorithm=""giac"")","-\frac{252 \, B b^{6} x^{7} + 1008 \, B a b^{5} x^{6} + 168 \, A b^{6} x^{6} + 1890 \, B a^{2} b^{4} x^{5} + 756 \, A a b^{5} x^{5} + 2016 \, B a^{3} b^{3} x^{4} + 1512 \, A a^{2} b^{4} x^{4} + 1260 \, B a^{4} b^{2} x^{3} + 1680 \, A a^{3} b^{3} x^{3} + 432 \, B a^{5} b x^{2} + 1080 \, A a^{4} b^{2} x^{2} + 63 \, B a^{6} x + 378 \, A a^{5} b x + 56 \, A a^{6}}{504 \, x^{9}}"," ",0,"-1/504*(252*B*b^6*x^7 + 1008*B*a*b^5*x^6 + 168*A*b^6*x^6 + 1890*B*a^2*b^4*x^5 + 756*A*a*b^5*x^5 + 2016*B*a^3*b^3*x^4 + 1512*A*a^2*b^4*x^4 + 1260*B*a^4*b^2*x^3 + 1680*A*a^3*b^3*x^3 + 432*B*a^5*b*x^2 + 1080*A*a^4*b^2*x^2 + 63*B*a^6*x + 378*A*a^5*b*x + 56*A*a^6)/x^9","B",0
555,1,147,0,0.162405," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^11,x, algorithm=""giac"")","-\frac{840 \, B b^{6} x^{7} + 3780 \, B a b^{5} x^{6} + 630 \, A b^{6} x^{6} + 7560 \, B a^{2} b^{4} x^{5} + 3024 \, A a b^{5} x^{5} + 8400 \, B a^{3} b^{3} x^{4} + 6300 \, A a^{2} b^{4} x^{4} + 5400 \, B a^{4} b^{2} x^{3} + 7200 \, A a^{3} b^{3} x^{3} + 1890 \, B a^{5} b x^{2} + 4725 \, A a^{4} b^{2} x^{2} + 280 \, B a^{6} x + 1680 \, A a^{5} b x + 252 \, A a^{6}}{2520 \, x^{10}}"," ",0,"-1/2520*(840*B*b^6*x^7 + 3780*B*a*b^5*x^6 + 630*A*b^6*x^6 + 7560*B*a^2*b^4*x^5 + 3024*A*a*b^5*x^5 + 8400*B*a^3*b^3*x^4 + 6300*A*a^2*b^4*x^4 + 5400*B*a^4*b^2*x^3 + 7200*A*a^3*b^3*x^3 + 1890*B*a^5*b*x^2 + 4725*A*a^4*b^2*x^2 + 280*B*a^6*x + 1680*A*a^5*b*x + 252*A*a^6)/x^10","A",0
556,1,147,0,0.189390," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^12,x, algorithm=""giac"")","-\frac{2310 \, B b^{6} x^{7} + 11088 \, B a b^{5} x^{6} + 1848 \, A b^{6} x^{6} + 23100 \, B a^{2} b^{4} x^{5} + 9240 \, A a b^{5} x^{5} + 26400 \, B a^{3} b^{3} x^{4} + 19800 \, A a^{2} b^{4} x^{4} + 17325 \, B a^{4} b^{2} x^{3} + 23100 \, A a^{3} b^{3} x^{3} + 6160 \, B a^{5} b x^{2} + 15400 \, A a^{4} b^{2} x^{2} + 924 \, B a^{6} x + 5544 \, A a^{5} b x + 840 \, A a^{6}}{9240 \, x^{11}}"," ",0,"-1/9240*(2310*B*b^6*x^7 + 11088*B*a*b^5*x^6 + 1848*A*b^6*x^6 + 23100*B*a^2*b^4*x^5 + 9240*A*a*b^5*x^5 + 26400*B*a^3*b^3*x^4 + 19800*A*a^2*b^4*x^4 + 17325*B*a^4*b^2*x^3 + 23100*A*a^3*b^3*x^3 + 6160*B*a^5*b*x^2 + 15400*A*a^4*b^2*x^2 + 924*B*a^6*x + 5544*A*a^5*b*x + 840*A*a^6)/x^11","A",0
557,1,147,0,0.157074," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^13,x, algorithm=""giac"")","-\frac{5544 \, B b^{6} x^{7} + 27720 \, B a b^{5} x^{6} + 4620 \, A b^{6} x^{6} + 59400 \, B a^{2} b^{4} x^{5} + 23760 \, A a b^{5} x^{5} + 69300 \, B a^{3} b^{3} x^{4} + 51975 \, A a^{2} b^{4} x^{4} + 46200 \, B a^{4} b^{2} x^{3} + 61600 \, A a^{3} b^{3} x^{3} + 16632 \, B a^{5} b x^{2} + 41580 \, A a^{4} b^{2} x^{2} + 2520 \, B a^{6} x + 15120 \, A a^{5} b x + 2310 \, A a^{6}}{27720 \, x^{12}}"," ",0,"-1/27720*(5544*B*b^6*x^7 + 27720*B*a*b^5*x^6 + 4620*A*b^6*x^6 + 59400*B*a^2*b^4*x^5 + 23760*A*a*b^5*x^5 + 69300*B*a^3*b^3*x^4 + 51975*A*a^2*b^4*x^4 + 46200*B*a^4*b^2*x^3 + 61600*A*a^3*b^3*x^3 + 16632*B*a^5*b*x^2 + 41580*A*a^4*b^2*x^2 + 2520*B*a^6*x + 15120*A*a^5*b*x + 2310*A*a^6)/x^12","A",0
558,1,147,0,0.152264," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^14,x, algorithm=""giac"")","-\frac{12012 \, B b^{6} x^{7} + 61776 \, B a b^{5} x^{6} + 10296 \, A b^{6} x^{6} + 135135 \, B a^{2} b^{4} x^{5} + 54054 \, A a b^{5} x^{5} + 160160 \, B a^{3} b^{3} x^{4} + 120120 \, A a^{2} b^{4} x^{4} + 108108 \, B a^{4} b^{2} x^{3} + 144144 \, A a^{3} b^{3} x^{3} + 39312 \, B a^{5} b x^{2} + 98280 \, A a^{4} b^{2} x^{2} + 6006 \, B a^{6} x + 36036 \, A a^{5} b x + 5544 \, A a^{6}}{72072 \, x^{13}}"," ",0,"-1/72072*(12012*B*b^6*x^7 + 61776*B*a*b^5*x^6 + 10296*A*b^6*x^6 + 135135*B*a^2*b^4*x^5 + 54054*A*a*b^5*x^5 + 160160*B*a^3*b^3*x^4 + 120120*A*a^2*b^4*x^4 + 108108*B*a^4*b^2*x^3 + 144144*A*a^3*b^3*x^3 + 39312*B*a^5*b*x^2 + 98280*A*a^4*b^2*x^2 + 6006*B*a^6*x + 36036*A*a^5*b*x + 5544*A*a^6)/x^13","A",0
559,1,143,0,0.168704," ","integrate(x^7*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{19} \, x^{19} e + \frac{1}{18} \, d x^{18} + \frac{5}{9} \, x^{18} e + \frac{10}{17} \, d x^{17} + \frac{45}{17} \, x^{17} e + \frac{45}{16} \, d x^{16} + \frac{15}{2} \, x^{16} e + 8 \, d x^{15} + 14 \, x^{15} e + 15 \, d x^{14} + 18 \, x^{14} e + \frac{252}{13} \, d x^{13} + \frac{210}{13} \, x^{13} e + \frac{35}{2} \, d x^{12} + 10 \, x^{12} e + \frac{120}{11} \, d x^{11} + \frac{45}{11} \, x^{11} e + \frac{9}{2} \, d x^{10} + x^{10} e + \frac{10}{9} \, d x^{9} + \frac{1}{9} \, x^{9} e + \frac{1}{8} \, d x^{8}"," ",0,"1/19*x^19*e + 1/18*d*x^18 + 5/9*x^18*e + 10/17*d*x^17 + 45/17*x^17*e + 45/16*d*x^16 + 15/2*x^16*e + 8*d*x^15 + 14*x^15*e + 15*d*x^14 + 18*x^14*e + 252/13*d*x^13 + 210/13*x^13*e + 35/2*d*x^12 + 10*x^12*e + 120/11*d*x^11 + 45/11*x^11*e + 9/2*d*x^10 + x^10*e + 10/9*d*x^9 + 1/9*x^9*e + 1/8*d*x^8","A",0
560,1,144,0,0.152121," ","integrate(x^6*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{18} \, x^{18} e + \frac{1}{17} \, d x^{17} + \frac{10}{17} \, x^{17} e + \frac{5}{8} \, d x^{16} + \frac{45}{16} \, x^{16} e + 3 \, d x^{15} + 8 \, x^{15} e + \frac{60}{7} \, d x^{14} + 15 \, x^{14} e + \frac{210}{13} \, d x^{13} + \frac{252}{13} \, x^{13} e + 21 \, d x^{12} + \frac{35}{2} \, x^{12} e + \frac{210}{11} \, d x^{11} + \frac{120}{11} \, x^{11} e + 12 \, d x^{10} + \frac{9}{2} \, x^{10} e + 5 \, d x^{9} + \frac{10}{9} \, x^{9} e + \frac{5}{4} \, d x^{8} + \frac{1}{8} \, x^{8} e + \frac{1}{7} \, d x^{7}"," ",0,"1/18*x^18*e + 1/17*d*x^17 + 10/17*x^17*e + 5/8*d*x^16 + 45/16*x^16*e + 3*d*x^15 + 8*x^15*e + 60/7*d*x^14 + 15*x^14*e + 210/13*d*x^13 + 252/13*x^13*e + 21*d*x^12 + 35/2*x^12*e + 210/11*d*x^11 + 120/11*x^11*e + 12*d*x^10 + 9/2*x^10*e + 5*d*x^9 + 10/9*x^9*e + 5/4*d*x^8 + 1/8*x^8*e + 1/7*d*x^7","A",0
561,1,144,0,0.193478," ","integrate(x^5*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{17} \, x^{17} e + \frac{1}{16} \, d x^{16} + \frac{5}{8} \, x^{16} e + \frac{2}{3} \, d x^{15} + 3 \, x^{15} e + \frac{45}{14} \, d x^{14} + \frac{60}{7} \, x^{14} e + \frac{120}{13} \, d x^{13} + \frac{210}{13} \, x^{13} e + \frac{35}{2} \, d x^{12} + 21 \, x^{12} e + \frac{252}{11} \, d x^{11} + \frac{210}{11} \, x^{11} e + 21 \, d x^{10} + 12 \, x^{10} e + \frac{40}{3} \, d x^{9} + 5 \, x^{9} e + \frac{45}{8} \, d x^{8} + \frac{5}{4} \, x^{8} e + \frac{10}{7} \, d x^{7} + \frac{1}{7} \, x^{7} e + \frac{1}{6} \, d x^{6}"," ",0,"1/17*x^17*e + 1/16*d*x^16 + 5/8*x^16*e + 2/3*d*x^15 + 3*x^15*e + 45/14*d*x^14 + 60/7*x^14*e + 120/13*d*x^13 + 210/13*x^13*e + 35/2*d*x^12 + 21*x^12*e + 252/11*d*x^11 + 210/11*x^11*e + 21*d*x^10 + 12*x^10*e + 40/3*d*x^9 + 5*x^9*e + 45/8*d*x^8 + 5/4*x^8*e + 10/7*d*x^7 + 1/7*x^7*e + 1/6*d*x^6","A",0
562,1,144,0,0.155015," ","integrate(x^4*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{16} \, x^{16} e + \frac{1}{15} \, d x^{15} + \frac{2}{3} \, x^{15} e + \frac{5}{7} \, d x^{14} + \frac{45}{14} \, x^{14} e + \frac{45}{13} \, d x^{13} + \frac{120}{13} \, x^{13} e + 10 \, d x^{12} + \frac{35}{2} \, x^{12} e + \frac{210}{11} \, d x^{11} + \frac{252}{11} \, x^{11} e + \frac{126}{5} \, d x^{10} + 21 \, x^{10} e + \frac{70}{3} \, d x^{9} + \frac{40}{3} \, x^{9} e + 15 \, d x^{8} + \frac{45}{8} \, x^{8} e + \frac{45}{7} \, d x^{7} + \frac{10}{7} \, x^{7} e + \frac{5}{3} \, d x^{6} + \frac{1}{6} \, x^{6} e + \frac{1}{5} \, d x^{5}"," ",0,"1/16*x^16*e + 1/15*d*x^15 + 2/3*x^15*e + 5/7*d*x^14 + 45/14*x^14*e + 45/13*d*x^13 + 120/13*x^13*e + 10*d*x^12 + 35/2*x^12*e + 210/11*d*x^11 + 252/11*x^11*e + 126/5*d*x^10 + 21*x^10*e + 70/3*d*x^9 + 40/3*x^9*e + 15*d*x^8 + 45/8*x^8*e + 45/7*d*x^7 + 10/7*x^7*e + 5/3*d*x^6 + 1/6*x^6*e + 1/5*d*x^5","A",0
563,1,144,0,0.153646," ","integrate(x^3*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{15} \, x^{15} e + \frac{1}{14} \, d x^{14} + \frac{5}{7} \, x^{14} e + \frac{10}{13} \, d x^{13} + \frac{45}{13} \, x^{13} e + \frac{15}{4} \, d x^{12} + 10 \, x^{12} e + \frac{120}{11} \, d x^{11} + \frac{210}{11} \, x^{11} e + 21 \, d x^{10} + \frac{126}{5} \, x^{10} e + 28 \, d x^{9} + \frac{70}{3} \, x^{9} e + \frac{105}{4} \, d x^{8} + 15 \, x^{8} e + \frac{120}{7} \, d x^{7} + \frac{45}{7} \, x^{7} e + \frac{15}{2} \, d x^{6} + \frac{5}{3} \, x^{6} e + 2 \, d x^{5} + \frac{1}{5} \, x^{5} e + \frac{1}{4} \, d x^{4}"," ",0,"1/15*x^15*e + 1/14*d*x^14 + 5/7*x^14*e + 10/13*d*x^13 + 45/13*x^13*e + 15/4*d*x^12 + 10*x^12*e + 120/11*d*x^11 + 210/11*x^11*e + 21*d*x^10 + 126/5*x^10*e + 28*d*x^9 + 70/3*x^9*e + 105/4*d*x^8 + 15*x^8*e + 120/7*d*x^7 + 45/7*x^7*e + 15/2*d*x^6 + 5/3*x^6*e + 2*d*x^5 + 1/5*x^5*e + 1/4*d*x^4","B",0
564,1,144,0,0.177311," ","integrate(x^2*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{14} \, x^{14} e + \frac{1}{13} \, d x^{13} + \frac{10}{13} \, x^{13} e + \frac{5}{6} \, d x^{12} + \frac{15}{4} \, x^{12} e + \frac{45}{11} \, d x^{11} + \frac{120}{11} \, x^{11} e + 12 \, d x^{10} + 21 \, x^{10} e + \frac{70}{3} \, d x^{9} + 28 \, x^{9} e + \frac{63}{2} \, d x^{8} + \frac{105}{4} \, x^{8} e + 30 \, d x^{7} + \frac{120}{7} \, x^{7} e + 20 \, d x^{6} + \frac{15}{2} \, x^{6} e + 9 \, d x^{5} + 2 \, x^{5} e + \frac{5}{2} \, d x^{4} + \frac{1}{4} \, x^{4} e + \frac{1}{3} \, d x^{3}"," ",0,"1/14*x^14*e + 1/13*d*x^13 + 10/13*x^13*e + 5/6*d*x^12 + 15/4*x^12*e + 45/11*d*x^11 + 120/11*x^11*e + 12*d*x^10 + 21*x^10*e + 70/3*d*x^9 + 28*x^9*e + 63/2*d*x^8 + 105/4*x^8*e + 30*d*x^7 + 120/7*x^7*e + 20*d*x^6 + 15/2*x^6*e + 9*d*x^5 + 2*x^5*e + 5/2*d*x^4 + 1/4*x^4*e + 1/3*d*x^3","B",0
565,1,144,0,0.154051," ","integrate(x*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{13} \, x^{13} e + \frac{1}{12} \, d x^{12} + \frac{5}{6} \, x^{12} e + \frac{10}{11} \, d x^{11} + \frac{45}{11} \, x^{11} e + \frac{9}{2} \, d x^{10} + 12 \, x^{10} e + \frac{40}{3} \, d x^{9} + \frac{70}{3} \, x^{9} e + \frac{105}{4} \, d x^{8} + \frac{63}{2} \, x^{8} e + 36 \, d x^{7} + 30 \, x^{7} e + 35 \, d x^{6} + 20 \, x^{6} e + 24 \, d x^{5} + 9 \, x^{5} e + \frac{45}{4} \, d x^{4} + \frac{5}{2} \, x^{4} e + \frac{10}{3} \, d x^{3} + \frac{1}{3} \, x^{3} e + \frac{1}{2} \, d x^{2}"," ",0,"1/13*x^13*e + 1/12*d*x^12 + 5/6*x^12*e + 10/11*d*x^11 + 45/11*x^11*e + 9/2*d*x^10 + 12*x^10*e + 40/3*d*x^9 + 70/3*x^9*e + 105/4*d*x^8 + 63/2*x^8*e + 36*d*x^7 + 30*x^7*e + 35*d*x^6 + 20*x^6*e + 24*d*x^5 + 9*x^5*e + 45/4*d*x^4 + 5/2*x^4*e + 10/3*d*x^3 + 1/3*x^3*e + 1/2*d*x^2","B",0
566,1,140,0,0.190897," ","integrate((e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{12} \, x^{12} e + \frac{1}{11} \, d x^{11} + \frac{10}{11} \, x^{11} e + d x^{10} + \frac{9}{2} \, x^{10} e + 5 \, d x^{9} + \frac{40}{3} \, x^{9} e + 15 \, d x^{8} + \frac{105}{4} \, x^{8} e + 30 \, d x^{7} + 36 \, x^{7} e + 42 \, d x^{6} + 35 \, x^{6} e + 42 \, d x^{5} + 24 \, x^{5} e + 30 \, d x^{4} + \frac{45}{4} \, x^{4} e + 15 \, d x^{3} + \frac{10}{3} \, x^{3} e + 5 \, d x^{2} + \frac{1}{2} \, x^{2} e + d x"," ",0,"1/12*x^12*e + 1/11*d*x^11 + 10/11*x^11*e + d*x^10 + 9/2*x^10*e + 5*d*x^9 + 40/3*x^9*e + 15*d*x^8 + 105/4*x^8*e + 30*d*x^7 + 36*x^7*e + 42*d*x^6 + 35*x^6*e + 42*d*x^5 + 24*x^5*e + 30*d*x^4 + 45/4*x^4*e + 15*d*x^3 + 10/3*x^3*e + 5*d*x^2 + 1/2*x^2*e + d*x","B",0
567,1,137,0,0.170761," ","integrate((e*x+d)*(x^2+2*x+1)^5/x,x, algorithm=""giac"")","\frac{1}{11} \, x^{11} e + \frac{1}{10} \, d x^{10} + x^{10} e + \frac{10}{9} \, d x^{9} + 5 \, x^{9} e + \frac{45}{8} \, d x^{8} + 15 \, x^{8} e + \frac{120}{7} \, d x^{7} + 30 \, x^{7} e + 35 \, d x^{6} + 42 \, x^{6} e + \frac{252}{5} \, d x^{5} + 42 \, x^{5} e + \frac{105}{2} \, d x^{4} + 30 \, x^{4} e + 40 \, d x^{3} + 15 \, x^{3} e + \frac{45}{2} \, d x^{2} + 5 \, x^{2} e + 10 \, d x + x e + d \log\left({\left| x \right|}\right)"," ",0,"1/11*x^11*e + 1/10*d*x^10 + x^10*e + 10/9*d*x^9 + 5*x^9*e + 45/8*d*x^8 + 15*x^8*e + 120/7*d*x^7 + 30*x^7*e + 35*d*x^6 + 42*x^6*e + 252/5*d*x^5 + 42*x^5*e + 105/2*d*x^4 + 30*x^4*e + 40*d*x^3 + 15*x^3*e + 45/2*d*x^2 + 5*x^2*e + 10*d*x + x*e + d*log(abs(x))","A",0
568,1,137,0,0.155908," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^2,x, algorithm=""giac"")","\frac{1}{10} \, x^{10} e + \frac{1}{9} \, d x^{9} + \frac{10}{9} \, x^{9} e + \frac{5}{4} \, d x^{8} + \frac{45}{8} \, x^{8} e + \frac{45}{7} \, d x^{7} + \frac{120}{7} \, x^{7} e + 20 \, d x^{6} + 35 \, x^{6} e + 42 \, d x^{5} + \frac{252}{5} \, x^{5} e + 63 \, d x^{4} + \frac{105}{2} \, x^{4} e + 70 \, d x^{3} + 40 \, x^{3} e + 60 \, d x^{2} + \frac{45}{2} \, x^{2} e + 45 \, d x + 10 \, x e + {\left(10 \, d + e\right)} \log\left({\left| x \right|}\right) - \frac{d}{x}"," ",0,"1/10*x^10*e + 1/9*d*x^9 + 10/9*x^9*e + 5/4*d*x^8 + 45/8*x^8*e + 45/7*d*x^7 + 120/7*x^7*e + 20*d*x^6 + 35*x^6*e + 42*d*x^5 + 252/5*x^5*e + 63*d*x^4 + 105/2*x^4*e + 70*d*x^3 + 40*x^3*e + 60*d*x^2 + 45/2*x^2*e + 45*d*x + 10*x*e + (10*d + e)*log(abs(x)) - d/x","A",0
569,1,137,0,0.157295," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^3,x, algorithm=""giac"")","\frac{1}{9} \, x^{9} e + \frac{1}{8} \, d x^{8} + \frac{5}{4} \, x^{8} e + \frac{10}{7} \, d x^{7} + \frac{45}{7} \, x^{7} e + \frac{15}{2} \, d x^{6} + 20 \, x^{6} e + 24 \, d x^{5} + 42 \, x^{5} e + \frac{105}{2} \, d x^{4} + 63 \, x^{4} e + 84 \, d x^{3} + 70 \, x^{3} e + 105 \, d x^{2} + 60 \, x^{2} e + 120 \, d x + 45 \, x e + 5 \, {\left(9 \, d + 2 \, e\right)} \log\left({\left| x \right|}\right) - \frac{2 \, {\left(10 \, d + e\right)} x + d}{2 \, x^{2}}"," ",0,"1/9*x^9*e + 1/8*d*x^8 + 5/4*x^8*e + 10/7*d*x^7 + 45/7*x^7*e + 15/2*d*x^6 + 20*x^6*e + 24*d*x^5 + 42*x^5*e + 105/2*d*x^4 + 63*x^4*e + 84*d*x^3 + 70*x^3*e + 105*d*x^2 + 60*x^2*e + 120*d*x + 45*x*e + 5*(9*d + 2*e)*log(abs(x)) - 1/2*(2*(10*d + e)*x + d)/x^2","A",0
570,1,139,0,0.157192," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^4,x, algorithm=""giac"")","\frac{1}{8} \, x^{8} e + \frac{1}{7} \, d x^{7} + \frac{10}{7} \, x^{7} e + \frac{5}{3} \, d x^{6} + \frac{15}{2} \, x^{6} e + 9 \, d x^{5} + 24 \, x^{5} e + 30 \, d x^{4} + \frac{105}{2} \, x^{4} e + 70 \, d x^{3} + 84 \, x^{3} e + 126 \, d x^{2} + 105 \, x^{2} e + 210 \, d x + 120 \, x e + 15 \, {\left(8 \, d + 3 \, e\right)} \log\left({\left| x \right|}\right) - \frac{30 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 3 \, {\left(10 \, d + e\right)} x + 2 \, d}{6 \, x^{3}}"," ",0,"1/8*x^8*e + 1/7*d*x^7 + 10/7*x^7*e + 5/3*d*x^6 + 15/2*x^6*e + 9*d*x^5 + 24*x^5*e + 30*d*x^4 + 105/2*x^4*e + 70*d*x^3 + 84*x^3*e + 126*d*x^2 + 105*x^2*e + 210*d*x + 120*x*e + 15*(8*d + 3*e)*log(abs(x)) - 1/6*(30*(9*d + 2*e)*x^2 + 3*(10*d + e)*x + 2*d)/x^3","A",0
571,1,139,0,0.194425," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^5,x, algorithm=""giac"")","\frac{1}{7} \, x^{7} e + \frac{1}{6} \, d x^{6} + \frac{5}{3} \, x^{6} e + 2 \, d x^{5} + 9 \, x^{5} e + \frac{45}{4} \, d x^{4} + 30 \, x^{4} e + 40 \, d x^{3} + 70 \, x^{3} e + 105 \, d x^{2} + 126 \, x^{2} e + 252 \, d x + 210 \, x e + 30 \, {\left(7 \, d + 4 \, e\right)} \log\left({\left| x \right|}\right) - \frac{180 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 30 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 4 \, {\left(10 \, d + e\right)} x + 3 \, d}{12 \, x^{4}}"," ",0,"1/7*x^7*e + 1/6*d*x^6 + 5/3*x^6*e + 2*d*x^5 + 9*x^5*e + 45/4*d*x^4 + 30*x^4*e + 40*d*x^3 + 70*x^3*e + 105*d*x^2 + 126*x^2*e + 252*d*x + 210*x*e + 30*(7*d + 4*e)*log(abs(x)) - 1/12*(180*(8*d + 3*e)*x^3 + 30*(9*d + 2*e)*x^2 + 4*(10*d + e)*x + 3*d)/x^4","A",0
572,1,139,0,0.150102," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^6,x, algorithm=""giac"")","\frac{1}{6} \, x^{6} e + \frac{1}{5} \, d x^{5} + 2 \, x^{5} e + \frac{5}{2} \, d x^{4} + \frac{45}{4} \, x^{4} e + 15 \, d x^{3} + 40 \, x^{3} e + 60 \, d x^{2} + 105 \, x^{2} e + 210 \, d x + 252 \, x e + 42 \, {\left(6 \, d + 5 \, e\right)} \log\left({\left| x \right|}\right) - \frac{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,"1/6*x^6*e + 1/5*d*x^5 + 2*x^5*e + 5/2*d*x^4 + 45/4*x^4*e + 15*d*x^3 + 40*x^3*e + 60*d*x^2 + 105*x^2*e + 210*d*x + 252*x*e + 42*(6*d + 5*e)*log(abs(x)) - 1/60*(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
573,1,139,0,0.154161," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^7,x, algorithm=""giac"")","\frac{1}{5} \, x^{5} e + \frac{1}{4} \, d x^{4} + \frac{5}{2} \, x^{4} e + \frac{10}{3} \, d x^{3} + 15 \, x^{3} e + \frac{45}{2} \, d x^{2} + 60 \, x^{2} e + 120 \, d x + 210 \, x e + 42 \, {\left(5 \, d + 6 \, e\right)} \log\left({\left| x \right|}\right) - \frac{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,"1/5*x^5*e + 1/4*d*x^4 + 5/2*x^4*e + 10/3*d*x^3 + 15*x^3*e + 45/2*d*x^2 + 60*x^2*e + 120*d*x + 210*x*e + 42*(5*d + 6*e)*log(abs(x)) - 1/60*(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
574,1,139,0,0.147640," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^8,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} e + \frac{1}{3} \, d x^{3} + \frac{10}{3} \, x^{3} e + 5 \, d x^{2} + \frac{45}{2} \, x^{2} e + 45 \, d x + 120 \, x e + 30 \, {\left(4 \, d + 7 \, e\right)} \log\left({\left| x \right|}\right) - \frac{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,"1/4*x^4*e + 1/3*d*x^3 + 10/3*x^3*e + 5*d*x^2 + 45/2*x^2*e + 45*d*x + 120*x*e + 30*(4*d + 7*e)*log(abs(x)) - 1/84*(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
575,1,139,0,0.157655," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^9,x, algorithm=""giac"")","\frac{1}{3} \, x^{3} e + \frac{1}{2} \, d x^{2} + 5 \, x^{2} e + 10 \, d x + 45 \, x e + 15 \, {\left(3 \, d + 8 \, e\right)} \log\left({\left| x \right|}\right) - \frac{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,"1/3*x^3*e + 1/2*d*x^2 + 5*x^2*e + 10*d*x + 45*x*e + 15*(3*d + 8*e)*log(abs(x)) - 1/168*(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
576,1,138,0,0.174617," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^10,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} e + d x + 10 \, x e + 5 \, {\left(2 \, d + 9 \, e\right)} \log\left({\left| x \right|}\right) - \frac{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,"1/2*x^2*e + d*x + 10*x*e + 5*(2*d + 9*e)*log(abs(x)) - 1/504*(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
577,1,137,0,0.153362," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^11,x, algorithm=""giac"")","x e + {\left(d + 10 \, e\right)} \log\left({\left| x \right|}\right) - \frac{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,"x*e + (d + 10*e)*log(abs(x)) - 1/2520*(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
578,1,140,0,0.179946," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^12,x, algorithm=""giac"")","e \log\left({\left| x \right|}\right) - \frac{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,"e*log(abs(x)) - 1/27720*(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
579,1,142,0,0.155915," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^13,x, algorithm=""giac"")","-\frac{132 \, x^{11} e + 66 \, d x^{10} + 660 \, x^{10} e + 440 \, d x^{9} + 1980 \, x^{9} e + 1485 \, d x^{8} + 3960 \, x^{8} e + 3168 \, d x^{7} + 5544 \, x^{7} e + 4620 \, d x^{6} + 5544 \, x^{6} e + 4752 \, d x^{5} + 3960 \, x^{5} e + 3465 \, d x^{4} + 1980 \, x^{4} e + 1760 \, d x^{3} + 660 \, x^{3} e + 594 \, d x^{2} + 132 \, x^{2} e + 120 \, d x + 12 \, x e + 11 \, d}{132 \, x^{12}}"," ",0,"-1/132*(132*x^11*e + 66*d*x^10 + 660*x^10*e + 440*d*x^9 + 1980*x^9*e + 1485*d*x^8 + 3960*x^8*e + 3168*d*x^7 + 5544*x^7*e + 4620*d*x^6 + 5544*x^6*e + 4752*d*x^5 + 3960*x^5*e + 3465*d*x^4 + 1980*x^4*e + 1760*d*x^3 + 660*x^3*e + 594*d*x^2 + 132*x^2*e + 120*d*x + 12*x*e + 11*d)/x^12","B",0
580,1,142,0,0.157410," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^14,x, algorithm=""giac"")","-\frac{858 \, x^{11} e + 572 \, d x^{10} + 5720 \, x^{10} e + 4290 \, d x^{9} + 19305 \, x^{9} e + 15444 \, d x^{8} + 41184 \, x^{8} e + 34320 \, d x^{7} + 60060 \, x^{7} e + 51480 \, d x^{6} + 61776 \, x^{6} e + 54054 \, d x^{5} + 45045 \, x^{5} e + 40040 \, d x^{4} + 22880 \, x^{4} e + 20592 \, d x^{3} + 7722 \, x^{3} e + 7020 \, d x^{2} + 1560 \, x^{2} e + 1430 \, d x + 143 \, x e + 132 \, d}{1716 \, x^{13}}"," ",0,"-1/1716*(858*x^11*e + 572*d*x^10 + 5720*x^10*e + 4290*d*x^9 + 19305*x^9*e + 15444*d*x^8 + 41184*x^8*e + 34320*d*x^7 + 60060*x^7*e + 51480*d*x^6 + 61776*x^6*e + 54054*d*x^5 + 45045*x^5*e + 40040*d*x^4 + 22880*x^4*e + 20592*d*x^3 + 7722*x^3*e + 7020*d*x^2 + 1560*x^2*e + 1430*d*x + 143*x*e + 132*d)/x^13","B",0
581,1,142,0,0.174726," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^15,x, algorithm=""giac"")","-\frac{4004 \, x^{11} e + 3003 \, d x^{10} + 30030 \, x^{10} e + 24024 \, d x^{9} + 108108 \, x^{9} e + 90090 \, d x^{8} + 240240 \, x^{8} e + 205920 \, d x^{7} + 360360 \, x^{7} e + 315315 \, d x^{6} + 378378 \, x^{6} e + 336336 \, d x^{5} + 280280 \, x^{5} e + 252252 \, d x^{4} + 144144 \, x^{4} e + 131040 \, d x^{3} + 49140 \, x^{3} e + 45045 \, d x^{2} + 10010 \, x^{2} e + 9240 \, d x + 924 \, x e + 858 \, d}{12012 \, x^{14}}"," ",0,"-1/12012*(4004*x^11*e + 3003*d*x^10 + 30030*x^10*e + 24024*d*x^9 + 108108*x^9*e + 90090*d*x^8 + 240240*x^8*e + 205920*d*x^7 + 360360*x^7*e + 315315*d*x^6 + 378378*x^6*e + 336336*d*x^5 + 280280*x^5*e + 252252*d*x^4 + 144144*x^4*e + 131040*d*x^3 + 49140*x^3*e + 45045*d*x^2 + 10010*x^2*e + 9240*d*x + 924*x*e + 858*d)/x^14","B",0
582,1,142,0,0.155159," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^16,x, algorithm=""giac"")","-\frac{15015 \, x^{11} e + 12012 \, d x^{10} + 120120 \, x^{10} e + 100100 \, d x^{9} + 450450 \, x^{9} e + 386100 \, d x^{8} + 1029600 \, x^{8} e + 900900 \, d x^{7} + 1576575 \, x^{7} e + 1401400 \, d x^{6} + 1681680 \, x^{6} e + 1513512 \, d x^{5} + 1261260 \, x^{5} e + 1146600 \, d x^{4} + 655200 \, x^{4} e + 600600 \, d x^{3} + 225225 \, x^{3} e + 207900 \, d x^{2} + 46200 \, x^{2} e + 42900 \, d x + 4290 \, x e + 4004 \, d}{60060 \, x^{15}}"," ",0,"-1/60060*(15015*x^11*e + 12012*d*x^10 + 120120*x^10*e + 100100*d*x^9 + 450450*x^9*e + 386100*d*x^8 + 1029600*x^8*e + 900900*d*x^7 + 1576575*x^7*e + 1401400*d*x^6 + 1681680*x^6*e + 1513512*d*x^5 + 1261260*x^5*e + 1146600*d*x^4 + 655200*x^4*e + 600600*d*x^3 + 225225*x^3*e + 207900*d*x^2 + 46200*x^2*e + 42900*d*x + 4290*x*e + 4004*d)/x^15","A",0
583,1,142,0,0.156400," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^17,x, algorithm=""giac"")","-\frac{48048 \, x^{11} e + 40040 \, d x^{10} + 400400 \, x^{10} e + 343200 \, d x^{9} + 1544400 \, x^{9} e + 1351350 \, d x^{8} + 3603600 \, x^{8} e + 3203200 \, d x^{7} + 5605600 \, x^{7} e + 5045040 \, d x^{6} + 6054048 \, x^{6} e + 5503680 \, d x^{5} + 4586400 \, x^{5} e + 4204200 \, d x^{4} + 2402400 \, x^{4} e + 2217600 \, d x^{3} + 831600 \, x^{3} e + 772200 \, d x^{2} + 171600 \, x^{2} e + 160160 \, d x + 16016 \, x e + 15015 \, d}{240240 \, x^{16}}"," ",0,"-1/240240*(48048*x^11*e + 40040*d*x^10 + 400400*x^10*e + 343200*d*x^9 + 1544400*x^9*e + 1351350*d*x^8 + 3603600*x^8*e + 3203200*d*x^7 + 5605600*x^7*e + 5045040*d*x^6 + 6054048*x^6*e + 5503680*d*x^5 + 4586400*x^5*e + 4204200*d*x^4 + 2402400*x^4*e + 2217600*d*x^3 + 831600*x^3*e + 772200*d*x^2 + 171600*x^2*e + 160160*d*x + 16016*x*e + 15015*d)/x^16","A",0
584,1,142,0,0.158859," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^18,x, algorithm=""giac"")","-\frac{136136 \, x^{11} e + 116688 \, d x^{10} + 1166880 \, x^{10} e + 1021020 \, d x^{9} + 4594590 \, x^{9} e + 4084080 \, d x^{8} + 10890880 \, x^{8} e + 9801792 \, d x^{7} + 17153136 \, x^{7} e + 15593760 \, d x^{6} + 18712512 \, x^{6} e + 17153136 \, d x^{5} + 14294280 \, x^{5} e + 13194720 \, d x^{4} + 7539840 \, x^{4} e + 7001280 \, d x^{3} + 2625480 \, x^{3} e + 2450448 \, d x^{2} + 544544 \, x^{2} e + 510510 \, d x + 51051 \, x e + 48048 \, d}{816816 \, x^{17}}"," ",0,"-1/816816*(136136*x^11*e + 116688*d*x^10 + 1166880*x^10*e + 1021020*d*x^9 + 4594590*x^9*e + 4084080*d*x^8 + 10890880*x^8*e + 9801792*d*x^7 + 17153136*x^7*e + 15593760*d*x^6 + 18712512*x^6*e + 17153136*d*x^5 + 14294280*x^5*e + 13194720*d*x^4 + 7539840*x^4*e + 7001280*d*x^3 + 2625480*x^3*e + 2450448*d*x^2 + 544544*x^2*e + 510510*d*x + 51051*x*e + 48048*d)/x^17","A",0
585,1,142,0,0.162601," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^19,x, algorithm=""giac"")","-\frac{350064 \, x^{11} e + 306306 \, d x^{10} + 3063060 \, x^{10} e + 2722720 \, d x^{9} + 12252240 \, x^{9} e + 11027016 \, d x^{8} + 29405376 \, x^{8} e + 26732160 \, d x^{7} + 46781280 \, x^{7} e + 42882840 \, d x^{6} + 51459408 \, x^{6} e + 47500992 \, d x^{5} + 39584160 \, x^{5} e + 36756720 \, d x^{4} + 21003840 \, x^{4} e + 19603584 \, d x^{3} + 7351344 \, x^{3} e + 6891885 \, d x^{2} + 1531530 \, x^{2} e + 1441440 \, d x + 144144 \, x e + 136136 \, d}{2450448 \, x^{18}}"," ",0,"-1/2450448*(350064*x^11*e + 306306*d*x^10 + 3063060*x^10*e + 2722720*d*x^9 + 12252240*x^9*e + 11027016*d*x^8 + 29405376*x^8*e + 26732160*d*x^7 + 46781280*x^7*e + 42882840*d*x^6 + 51459408*x^6*e + 47500992*d*x^5 + 39584160*x^5*e + 36756720*d*x^4 + 21003840*x^4*e + 19603584*d*x^3 + 7351344*x^3*e + 6891885*d*x^2 + 1531530*x^2*e + 1441440*d*x + 144144*x*e + 136136*d)/x^18","A",0
586,1,142,0,0.153945," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^20,x, algorithm=""giac"")","-\frac{831402 \, x^{11} e + 739024 \, d x^{10} + 7390240 \, x^{10} e + 6651216 \, d x^{9} + 29930472 \, x^{9} e + 27209520 \, d x^{8} + 72558720 \, x^{8} e + 66512160 \, d x^{7} + 116396280 \, x^{7} e + 107442720 \, d x^{6} + 128931264 \, x^{6} e + 119721888 \, d x^{5} + 99768240 \, x^{5} e + 93117024 \, d x^{4} + 53209728 \, x^{4} e + 49884120 \, d x^{3} + 18706545 \, x^{3} e + 17606160 \, d x^{2} + 3912480 \, x^{2} e + 3695120 \, d x + 369512 \, x e + 350064 \, d}{6651216 \, x^{19}}"," ",0,"-1/6651216*(831402*x^11*e + 739024*d*x^10 + 7390240*x^10*e + 6651216*d*x^9 + 29930472*x^9*e + 27209520*d*x^8 + 72558720*x^8*e + 66512160*d*x^7 + 116396280*x^7*e + 107442720*d*x^6 + 128931264*x^6*e + 119721888*d*x^5 + 99768240*x^5*e + 93117024*d*x^4 + 53209728*x^4*e + 49884120*d*x^3 + 18706545*x^3*e + 17606160*d*x^2 + 3912480*x^2*e + 3695120*d*x + 369512*x*e + 350064*d)/x^19","A",0
587,1,142,0,0.178774," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^21,x, algorithm=""giac"")","-\frac{1847560 \, x^{11} e + 1662804 \, d x^{10} + 16628040 \, x^{10} e + 15116400 \, d x^{9} + 68023800 \, x^{9} e + 62355150 \, d x^{8} + 166280400 \, x^{8} e + 153489600 \, d x^{7} + 268606800 \, x^{7} e + 249420600 \, d x^{6} + 299304720 \, x^{6} e + 279351072 \, d x^{5} + 232792560 \, x^{5} e + 218243025 \, d x^{4} + 124710300 \, x^{4} e + 117374400 \, d x^{3} + 44015400 \, x^{3} e + 41570100 \, d x^{2} + 9237800 \, x^{2} e + 8751600 \, d x + 875160 \, x e + 831402 \, d}{16628040 \, x^{20}}"," ",0,"-1/16628040*(1847560*x^11*e + 1662804*d*x^10 + 16628040*x^10*e + 15116400*d*x^9 + 68023800*x^9*e + 62355150*d*x^8 + 166280400*x^8*e + 153489600*d*x^7 + 268606800*x^7*e + 249420600*d*x^6 + 299304720*x^6*e + 279351072*d*x^5 + 232792560*x^5*e + 218243025*d*x^4 + 124710300*x^4*e + 117374400*d*x^3 + 44015400*x^3*e + 41570100*d*x^2 + 9237800*x^2*e + 8751600*d*x + 875160*x*e + 831402*d)/x^20","A",0
588,1,61,0,0.181165," ","integrate(x^11*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
589,1,61,0,0.169014," ","integrate(x^10*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
590,1,59,0,0.161829," ","integrate(x^9*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
591,1,61,0,0.149990," ","integrate(x^8*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
592,1,61,0,0.151952," ","integrate(x^7*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
593,1,61,0,0.149812," ","integrate(x^6*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
594,1,61,0,0.151983," ","integrate(x^5*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
595,1,61,0,0.148096," ","integrate(x^4*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
596,1,61,0,0.147808," ","integrate(x^3*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
597,1,61,0,0.150081," ","integrate(x^2*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
598,1,61,0,0.174523," ","integrate(x*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\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
599,1,62,0,0.149141," ","integrate((1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{1}{12} \, {\left(x^{2} + 2 \, x\right)}^{6} + \frac{1}{2} \, {\left(x^{2} + 2 \, x\right)}^{5} + \frac{5}{4} \, {\left(x^{2} + 2 \, x\right)}^{4} + \frac{5}{3} \, {\left(x^{2} + 2 \, x\right)}^{3} + \frac{5}{4} \, {\left(x^{2} + 2 \, x\right)}^{2} + \frac{1}{2} \, x^{2} + x"," ",0,"1/12*(x^2 + 2*x)^6 + 1/2*(x^2 + 2*x)^5 + 5/4*(x^2 + 2*x)^4 + 5/3*(x^2 + 2*x)^3 + 5/4*(x^2 + 2*x)^2 + 1/2*x^2 + x","B",0
600,1,57,0,0.154069," ","integrate((1+x)*(x^2+2*x+1)^5/x,x, algorithm=""giac"")","\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({\left| x \right|}\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(abs(x))","A",0
601,1,59,0,0.155940," ","integrate((1+x)*(x^2+2*x+1)^5/x^2,x, algorithm=""giac"")","\frac{1}{10} \, x^{10} + \frac{11}{9} \, x^{9} + \frac{55}{8} \, x^{8} + \frac{165}{7} \, x^{7} + 55 \, x^{6} + \frac{462}{5} \, x^{5} + \frac{231}{2} \, x^{4} + 110 \, x^{3} + \frac{165}{2} \, x^{2} + 55 \, x - \frac{1}{x} + 11 \, \log\left({\left| x \right|}\right)"," ",0,"1/10*x^10 + 11/9*x^9 + 55/8*x^8 + 165/7*x^7 + 55*x^6 + 462/5*x^5 + 231/2*x^4 + 110*x^3 + 165/2*x^2 + 55*x - 1/x + 11*log(abs(x))","A",0
602,1,59,0,0.165963," ","integrate((1+x)*(x^2+2*x+1)^5/x^3,x, algorithm=""giac"")","\frac{1}{9} \, x^{9} + \frac{11}{8} \, x^{8} + \frac{55}{7} \, x^{7} + \frac{55}{2} \, x^{6} + 66 \, x^{5} + \frac{231}{2} \, x^{4} + 154 \, x^{3} + 165 \, x^{2} + 165 \, x - \frac{22 \, x + 1}{2 \, x^{2}} + 55 \, \log\left({\left| x \right|}\right)"," ",0,"1/9*x^9 + 11/8*x^8 + 55/7*x^7 + 55/2*x^6 + 66*x^5 + 231/2*x^4 + 154*x^3 + 165*x^2 + 165*x - 1/2*(22*x + 1)/x^2 + 55*log(abs(x))","A",0
603,1,59,0,0.147791," ","integrate((1+x)*(x^2+2*x+1)^5/x^4,x, algorithm=""giac"")","\frac{1}{8} \, x^{8} + \frac{11}{7} \, x^{7} + \frac{55}{6} \, x^{6} + 33 \, x^{5} + \frac{165}{2} \, x^{4} + 154 \, x^{3} + 231 \, x^{2} + 330 \, x - \frac{330 \, x^{2} + 33 \, x + 2}{6 \, x^{3}} + 165 \, \log\left({\left| x \right|}\right)"," ",0,"1/8*x^8 + 11/7*x^7 + 55/6*x^6 + 33*x^5 + 165/2*x^4 + 154*x^3 + 231*x^2 + 330*x - 1/6*(330*x^2 + 33*x + 2)/x^3 + 165*log(abs(x))","A",0
604,1,59,0,0.150594," ","integrate((1+x)*(x^2+2*x+1)^5/x^5,x, algorithm=""giac"")","\frac{1}{7} \, x^{7} + \frac{11}{6} \, x^{6} + 11 \, x^{5} + \frac{165}{4} \, x^{4} + 110 \, x^{3} + 231 \, x^{2} + 462 \, x - \frac{1980 \, x^{3} + 330 \, x^{2} + 44 \, x + 3}{12 \, x^{4}} + 330 \, \log\left({\left| x \right|}\right)"," ",0,"1/7*x^7 + 11/6*x^6 + 11*x^5 + 165/4*x^4 + 110*x^3 + 231*x^2 + 462*x - 1/12*(1980*x^3 + 330*x^2 + 44*x + 3)/x^4 + 330*log(abs(x))","A",0
605,1,59,0,0.162471," ","integrate((1+x)*(x^2+2*x+1)^5/x^6,x, algorithm=""giac"")","\frac{1}{6} \, x^{6} + \frac{11}{5} \, x^{5} + \frac{55}{4} \, x^{4} + 55 \, x^{3} + 165 \, x^{2} + 462 \, x - \frac{19800 \, x^{4} + 4950 \, x^{3} + 1100 \, x^{2} + 165 \, x + 12}{60 \, x^{5}} + 462 \, \log\left({\left| x \right|}\right)"," ",0,"1/6*x^6 + 11/5*x^5 + 55/4*x^4 + 55*x^3 + 165*x^2 + 462*x - 1/60*(19800*x^4 + 4950*x^3 + 1100*x^2 + 165*x + 12)/x^5 + 462*log(abs(x))","A",0
606,1,59,0,0.152791," ","integrate((1+x)*(x^2+2*x+1)^5/x^7,x, algorithm=""giac"")","\frac{1}{5} \, x^{5} + \frac{11}{4} \, x^{4} + \frac{55}{3} \, x^{3} + \frac{165}{2} \, x^{2} + 330 \, x - \frac{27720 \, x^{5} + 9900 \, x^{4} + 3300 \, x^{3} + 825 \, x^{2} + 132 \, x + 10}{60 \, x^{6}} + 462 \, \log\left({\left| x \right|}\right)"," ",0,"1/5*x^5 + 11/4*x^4 + 55/3*x^3 + 165/2*x^2 + 330*x - 1/60*(27720*x^5 + 9900*x^4 + 3300*x^3 + 825*x^2 + 132*x + 10)/x^6 + 462*log(abs(x))","A",0
607,1,59,0,0.150173," ","integrate((1+x)*(x^2+2*x+1)^5/x^8,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{55}{2} \, x^{2} + 165 \, x - \frac{38808 \, x^{6} + 19404 \, x^{5} + 9240 \, x^{4} + 3465 \, x^{3} + 924 \, x^{2} + 154 \, x + 12}{84 \, x^{7}} + 330 \, \log\left({\left| x \right|}\right)"," ",0,"1/4*x^4 + 11/3*x^3 + 55/2*x^2 + 165*x - 1/84*(38808*x^6 + 19404*x^5 + 9240*x^4 + 3465*x^3 + 924*x^2 + 154*x + 12)/x^7 + 330*log(abs(x))","A",0
608,1,59,0,0.150864," ","integrate((1+x)*(x^2+2*x+1)^5/x^9,x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{11}{2} \, x^{2} + 55 \, x - \frac{55440 \, x^{7} + 38808 \, x^{6} + 25872 \, x^{5} + 13860 \, x^{4} + 5544 \, x^{3} + 1540 \, x^{2} + 264 \, x + 21}{168 \, x^{8}} + 165 \, \log\left({\left| x \right|}\right)"," ",0,"1/3*x^3 + 11/2*x^2 + 55*x - 1/168*(55440*x^7 + 38808*x^6 + 25872*x^5 + 13860*x^4 + 5544*x^3 + 1540*x^2 + 264*x + 21)/x^8 + 165*log(abs(x))","A",0
609,1,59,0,0.168262," ","integrate((1+x)*(x^2+2*x+1)^5/x^10,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 11 \, x - \frac{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}} + 55 \, \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 + 11*x - 1/504*(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 + 55*log(abs(x))","A",0
610,1,57,0,0.149432," ","integrate((1+x)*(x^2+2*x+1)^5/x^11,x, algorithm=""giac"")","x - \frac{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}} + 11 \, \log\left({\left| x \right|}\right)"," ",0,"x - 1/2520*(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 + 11*log(abs(x))","A",0
611,1,59,0,0.188905," ","integrate((1+x)*(x^2+2*x+1)^5/x^12,x, algorithm=""giac"")","-\frac{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}} + \log\left({\left| x \right|}\right)"," ",0,"-1/27720*(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 + log(abs(x))","A",0
612,1,60,0,0.166597," ","integrate((1+x)*(x^2+2*x+1)^5/x^13,x, algorithm=""giac"")","-\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
613,1,60,0,0.177519," ","integrate((1+x)*(x^2+2*x+1)^5/x^14,x, algorithm=""giac"")","-\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
614,1,60,0,0.169349," ","integrate((1+x)*(x^2+2*x+1)^5/x^15,x, algorithm=""giac"")","-\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
615,1,60,0,0.154039," ","integrate((1+x)*(x^2+2*x+1)^5/x^16,x, algorithm=""giac"")","-\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
616,1,60,0,0.151047," ","integrate((1+x)*(x^2+2*x+1)^5/x^17,x, algorithm=""giac"")","-\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
617,1,60,0,0.153034," ","integrate((1+x)*(x^2+2*x+1)^5/x^18,x, algorithm=""giac"")","-\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
618,1,60,0,0.154381," ","integrate((1+x)*(x^2+2*x+1)^5/x^19,x, algorithm=""giac"")","-\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
619,1,60,0,0.163855," ","integrate((1+x)*(x^2+2*x+1)^5/x^20,x, algorithm=""giac"")","-\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
620,1,60,0,0.152012," ","integrate((1+x)*(x^2+2*x+1)^5/x^21,x, algorithm=""giac"")","-\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
621,1,60,0,0.158553," ","integrate((1+x)*(x^2+2*x+1)^5/x^22,x, algorithm=""giac"")","-\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
622,1,152,0,0.163520," ","integrate(x^5*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{{\left(6 \, B a^{5} - 5 \, A a^{4} b\right)} \log\left({\left| b x + a \right|}\right)}{b^{7}} - \frac{B a^{6} - A a^{5} b}{{\left(b x + a\right)} b^{7}} + \frac{12 \, B b^{8} x^{5} - 30 \, B a b^{7} x^{4} + 15 \, A b^{8} x^{4} + 60 \, B a^{2} b^{6} x^{3} - 40 \, A a b^{7} x^{3} - 120 \, B a^{3} b^{5} x^{2} + 90 \, A a^{2} b^{6} x^{2} + 300 \, B a^{4} b^{4} x - 240 \, A a^{3} b^{5} x}{60 \, b^{10}}"," ",0,"-(6*B*a^5 - 5*A*a^4*b)*log(abs(b*x + a))/b^7 - (B*a^6 - A*a^5*b)/((b*x + a)*b^7) + 1/60*(12*B*b^8*x^5 - 30*B*a*b^7*x^4 + 15*A*b^8*x^4 + 60*B*a^2*b^6*x^3 - 40*A*a*b^7*x^3 - 120*B*a^3*b^5*x^2 + 90*A*a^2*b^6*x^2 + 300*B*a^4*b^4*x - 240*A*a^3*b^5*x)/b^10","A",0
623,1,126,0,0.163324," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(5 \, B a^{4} - 4 \, A a^{3} b\right)} \log\left({\left| b x + a \right|}\right)}{b^{6}} + \frac{B a^{5} - A a^{4} b}{{\left(b x + a\right)} b^{6}} + \frac{3 \, B b^{6} x^{4} - 8 \, B a b^{5} x^{3} + 4 \, A b^{6} x^{3} + 18 \, B a^{2} b^{4} x^{2} - 12 \, A a b^{5} x^{2} - 48 \, B a^{3} b^{3} x + 36 \, A a^{2} b^{4} x}{12 \, b^{8}}"," ",0,"(5*B*a^4 - 4*A*a^3*b)*log(abs(b*x + a))/b^6 + (B*a^5 - A*a^4*b)/((b*x + a)*b^6) + 1/12*(3*B*b^6*x^4 - 8*B*a*b^5*x^3 + 4*A*b^6*x^3 + 18*B*a^2*b^4*x^2 - 12*A*a*b^5*x^2 - 48*B*a^3*b^3*x + 36*A*a^2*b^4*x)/b^8","A",0
624,1,104,0,0.175998," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{{\left(4 \, B a^{3} - 3 \, A a^{2} b\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}} + \frac{2 \, B b^{4} x^{3} - 6 \, B a b^{3} x^{2} + 3 \, A b^{4} x^{2} + 18 \, B a^{2} b^{2} x - 12 \, A a b^{3} x}{6 \, b^{6}} - \frac{B a^{4} - A a^{3} b}{{\left(b x + a\right)} b^{5}}"," ",0,"-(4*B*a^3 - 3*A*a^2*b)*log(abs(b*x + a))/b^5 + 1/6*(2*B*b^4*x^3 - 6*B*a*b^3*x^2 + 3*A*b^4*x^2 + 18*B*a^2*b^2*x - 12*A*a*b^3*x)/b^6 - (B*a^4 - A*a^3*b)/((b*x + a)*b^5)","A",0
625,1,75,0,0.156705," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(3 \, B a^{2} - 2 \, A a b\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}} + \frac{B b^{2} x^{2} - 4 \, B a b x + 2 \, A b^{2} x}{2 \, b^{4}} + \frac{B a^{3} - A a^{2} b}{{\left(b x + a\right)} b^{4}}"," ",0,"(3*B*a^2 - 2*A*a*b)*log(abs(b*x + a))/b^4 + 1/2*(B*b^2*x^2 - 4*B*a*b*x + 2*A*b^2*x)/b^4 + (B*a^3 - A*a^2*b)/((b*x + a)*b^4)","A",0
626,1,51,0,0.178692," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{B x}{b^{2}} - \frac{{\left(2 \, B a - A b\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}} - \frac{B a^{2} - A a b}{{\left(b x + a\right)} b^{3}}"," ",0,"B*x/b^2 - (2*B*a - A*b)*log(abs(b*x + a))/b^3 - (B*a^2 - A*a*b)/((b*x + a)*b^3)","A",0
627,1,32,0,0.154289," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{B \log\left({\left| b x + a \right|}\right)}{b^{2}} + \frac{B a - A b}{{\left(b x + a\right)} b^{2}}"," ",0,"B*log(abs(b*x + a))/b^2 + (B*a - A*b)/((b*x + a)*b^2)","A",0
628,1,48,0,0.153550," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{A \log\left({\left| b x + a \right|}\right)}{a^{2}} + \frac{A \log\left({\left| x \right|}\right)}{a^{2}} - \frac{B a^{2} - A a b}{{\left(b x + a\right)} a^{2} b}"," ",0,"-A*log(abs(b*x + a))/a^2 + A*log(abs(x))/a^2 - (B*a^2 - A*a*b)/((b*x + a)*a^2*b)","A",0
629,1,71,0,0.151101," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B a - 2 \, A b\right)} \log\left({\left| x \right|}\right)}{a^{3}} + \frac{B a x - 2 \, A b x - A a}{{\left(b x^{2} + a x\right)} a^{2}} - \frac{{\left(B a b - 2 \, A b^{2}\right)} \log\left({\left| b x + a \right|}\right)}{a^{3} b}"," ",0,"(B*a - 2*A*b)*log(abs(x))/a^3 + (B*a*x - 2*A*b*x - A*a)/((b*x^2 + a*x)*a^2) - (B*a*b - 2*A*b^2)*log(abs(b*x + a))/(a^3*b)","A",0
630,1,106,0,0.157462," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{{\left(2 \, B a b - 3 \, A b^{2}\right)} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{{\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} \log\left({\left| b x + a \right|}\right)}{a^{4} b} - \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(b x + a\right)} a^{4} x^{2}}"," ",0,"-(2*B*a*b - 3*A*b^2)*log(abs(x))/a^4 + (2*B*a*b^2 - 3*A*b^3)*log(abs(b*x + a))/(a^4*b) - 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)/((b*x + a)*a^4*x^2)","A",0
631,1,133,0,0.156085," ","integrate((B*x+A)/x^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(3 \, B a b^{2} - 4 \, A b^{3}\right)} \log\left({\left| x \right|}\right)}{a^{5}} - \frac{{\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} \log\left({\left| b x + a \right|}\right)}{a^{5} b} - \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(b x + a\right)} a^{5} x^{3}}"," ",0,"(3*B*a*b^2 - 4*A*b^3)*log(abs(x))/a^5 - (3*B*a*b^3 - 4*A*b^4)*log(abs(b*x + a))/(a^5*b) - 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)/((b*x + a)*a^5*x^3)","A",0
632,1,157,0,0.180534," ","integrate((B*x+A)/x^5/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{{\left(4 \, B a b^{3} - 5 \, A b^{4}\right)} \log\left({\left| x \right|}\right)}{a^{6}} + \frac{{\left(4 \, B a b^{4} - 5 \, A b^{5}\right)} \log\left({\left| b x + a \right|}\right)}{a^{6} b} - \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(b x + a\right)} a^{6} x^{4}}"," ",0,"-(4*B*a*b^3 - 5*A*b^4)*log(abs(x))/a^6 + (4*B*a*b^4 - 5*A*b^5)*log(abs(b*x + a))/(a^6*b) - 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)/((b*x + a)*a^6*x^4)","A",0
633,1,149,0,0.154375," ","integrate(x^5*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{10 \, {\left(2 \, B a^{3} - A a^{2} b\right)} \log\left({\left| b x + a \right|}\right)}{b^{7}} - \frac{74 \, B a^{6} - 47 \, A a^{5} b + 30 \, {\left(3 \, B a^{4} b^{2} - 2 \, A a^{3} b^{3}\right)} x^{2} + 3 \, {\left(54 \, B a^{5} b - 35 \, A a^{4} b^{2}\right)} x}{6 \, {\left(b x + a\right)}^{3} b^{7}} + \frac{2 \, B b^{8} x^{3} - 12 \, B a b^{7} x^{2} + 3 \, A b^{8} x^{2} + 60 \, B a^{2} b^{6} x - 24 \, A a b^{7} x}{6 \, b^{12}}"," ",0,"-10*(2*B*a^3 - A*a^2*b)*log(abs(b*x + a))/b^7 - 1/6*(74*B*a^6 - 47*A*a^5*b + 30*(3*B*a^4*b^2 - 2*A*a^3*b^3)*x^2 + 3*(54*B*a^5*b - 35*A*a^4*b^2)*x)/((b*x + a)^3*b^7) + 1/6*(2*B*b^8*x^3 - 12*B*a*b^7*x^2 + 3*A*b^8*x^2 + 60*B*a^2*b^6*x - 24*A*a*b^7*x)/b^12","A",0
634,1,124,0,0.160422," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2 \, {\left(5 \, B a^{2} - 2 \, A a b\right)} \log\left({\left| b x + a \right|}\right)}{b^{6}} + \frac{B b^{4} x^{2} - 8 \, B a b^{3} x + 2 \, A b^{4} x}{2 \, b^{8}} + \frac{47 \, B a^{5} - 26 \, A a^{4} b + 12 \, {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} + 15 \, {\left(7 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} x}{6 \, {\left(b x + a\right)}^{3} b^{6}}"," ",0,"2*(5*B*a^2 - 2*A*a*b)*log(abs(b*x + a))/b^6 + 1/2*(B*b^4*x^2 - 8*B*a*b^3*x + 2*A*b^4*x)/b^8 + 1/6*(47*B*a^5 - 26*A*a^4*b + 12*(5*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 + 15*(7*B*a^4*b - 4*A*a^3*b^2)*x)/((b*x + a)^3*b^6)","A",0
635,1,96,0,0.157509," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{B x}{b^{4}} - \frac{{\left(4 \, B a - A b\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}} - \frac{26 \, B a^{4} - 11 \, A a^{3} b + 18 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 3 \, {\left(20 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x}{6 \, {\left(b x + a\right)}^{3} b^{5}}"," ",0,"B*x/b^4 - (4*B*a - A*b)*log(abs(b*x + a))/b^5 - 1/6*(26*B*a^4 - 11*A*a^3*b + 18*(2*B*a^2*b^2 - A*a*b^3)*x^2 + 3*(20*B*a^3*b - 9*A*a^2*b^2)*x)/((b*x + a)^3*b^5)","A",0
636,1,76,0,0.154421," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{B \log\left({\left| b x + a \right|}\right)}{b^{4}} + \frac{6 \, {\left(3 \, B a b - A b^{2}\right)} x^{2} + 3 \, {\left(9 \, B a^{2} - 2 \, A a b\right)} x + \frac{11 \, B a^{3} - 2 \, A a^{2} b}{b}}{6 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"B*log(abs(b*x + a))/b^4 + 1/6*(6*(3*B*a*b - A*b^2)*x^2 + 3*(9*B*a^2 - 2*A*a*b)*x + (11*B*a^3 - 2*A*a^2*b)/b)/((b*x + a)^3*b^3)","A",0
637,1,45,0,0.191867," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{6 \, B b^{2} x^{2} + 6 \, B a b x + 3 \, A b^{2} x + 2 \, B a^{2} + A a b}{6 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"-1/6*(6*B*b^2*x^2 + 6*B*a*b*x + 3*A*b^2*x + 2*B*a^2 + A*a*b)/((b*x + a)^3*b^3)","A",0
638,1,25,0,0.149406," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{3 \, B b x + B a + 2 \, A b}{6 \, {\left(b x + a\right)}^{3} b^{2}}"," ",0,"-1/6*(3*B*b*x + B*a + 2*A*b)/((b*x + a)^3*b^2)","A",0
639,1,71,0,0.149908," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{A \log\left({\left| b x + a \right|}\right)}{a^{4}} + \frac{A \log\left({\left| x \right|}\right)}{a^{4}} + \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(b x + a\right)}^{3} a^{4} b}"," ",0,"-A*log(abs(b*x + a))/a^4 + A*log(abs(x))/a^4 + 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)/((b*x + a)^3*a^4*b)","A",0
640,1,122,0,0.169470," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(B a - 4 \, A b\right)} \log\left({\left| x \right|}\right)}{a^{5}} - \frac{{\left(B a b - 4 \, A b^{2}\right)} \log\left({\left| b x + a \right|}\right)}{a^{5} b} - \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(b x + a\right)}^{3} a^{5} x}"," ",0,"(B*a - 4*A*b)*log(abs(x))/a^5 - (B*a*b - 4*A*b^2)*log(abs(b*x + a))/(a^5*b) - 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)/((b*x + a)^3*a^5*x)","A",0
641,1,157,0,0.154475," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, B a b - 5 \, A b^{2}\right)} \log\left({\left| x \right|}\right)}{a^{6}} + \frac{2 \, {\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} \log\left({\left| b x + a \right|}\right)}{a^{6} b} - \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}{6 \, {\left(b x + a\right)}^{3} a^{6} x^{2}}"," ",0,"-2*(2*B*a*b - 5*A*b^2)*log(abs(x))/a^6 + 2*(2*B*a*b^2 - 5*A*b^3)*log(abs(b*x + a))/(a^6*b) - 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)/((b*x + a)^3*a^6*x^2)","A",0
642,1,175,0,0.154227," ","integrate((B*x+A)/x^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{10 \, {\left(B a b^{2} - 2 \, A b^{3}\right)} \log\left({\left| x \right|}\right)}{a^{7}} - \frac{10 \, {\left(B a b^{3} - 2 \, A b^{4}\right)} \log\left({\left| b x + a \right|}\right)}{a^{7} b} + \frac{60 \, B a b^{4} x^{5} - 120 \, A b^{5} x^{5} + 150 \, B a^{2} b^{3} x^{4} - 300 \, A a b^{4} x^{4} + 110 \, B a^{3} b^{2} x^{3} - 220 \, A a^{2} b^{3} x^{3} + 15 \, B a^{4} b x^{2} - 30 \, A a^{3} b^{2} x^{2} - 3 \, B a^{5} x + 6 \, A a^{4} b x - 2 \, A a^{5}}{6 \, {\left(b x^{2} + a x\right)}^{3} a^{6}}"," ",0,"10*(B*a*b^2 - 2*A*b^3)*log(abs(x))/a^7 - 10*(B*a*b^3 - 2*A*b^4)*log(abs(b*x + a))/(a^7*b) + 1/6*(60*B*a*b^4*x^5 - 120*A*b^5*x^5 + 150*B*a^2*b^3*x^4 - 300*A*a*b^4*x^4 + 110*B*a^3*b^2*x^3 - 220*A*a^2*b^3*x^3 + 15*B*a^4*b*x^2 - 30*A*a^3*b^2*x^2 - 3*B*a^5*x + 6*A*a^4*b*x - 2*A*a^5)/((b*x^2 + a*x)^3*a^6)","A",0
643,1,172,0,0.161089," ","integrate(x^6*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(7 \, B a^{2} - 2 \, A a b\right)} \log\left({\left| b x + a \right|}\right)}{b^{8}} + \frac{B b^{6} x^{2} - 12 \, B a b^{5} x + 2 \, A b^{6} x}{2 \, b^{12}} + \frac{459 \, B a^{7} - 174 \, A a^{6} b + 100 \, {\left(7 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} x^{4} + 50 \, {\left(49 \, B a^{4} b^{3} - 20 \, A a^{3} b^{4}\right)} x^{3} + 10 \, {\left(329 \, B a^{5} b^{2} - 130 \, A a^{4} b^{3}\right)} x^{2} + 35 \, {\left(57 \, B a^{6} b - 22 \, A a^{5} b^{2}\right)} x}{20 \, {\left(b x + a\right)}^{5} b^{8}}"," ",0,"3*(7*B*a^2 - 2*A*a*b)*log(abs(b*x + a))/b^8 + 1/2*(B*b^6*x^2 - 12*B*a*b^5*x + 2*A*b^6*x)/b^12 + 1/20*(459*B*a^7 - 174*A*a^6*b + 100*(7*B*a^3*b^4 - 3*A*a^2*b^5)*x^4 + 50*(49*B*a^4*b^3 - 20*A*a^3*b^4)*x^3 + 10*(329*B*a^5*b^2 - 130*A*a^4*b^3)*x^2 + 35*(57*B*a^6*b - 22*A*a^5*b^2)*x)/((b*x + a)^5*b^8)","A",0
644,1,144,0,0.154828," ","integrate(x^5*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{B x}{b^{6}} - \frac{{\left(6 \, B a - A b\right)} \log\left({\left| b x + a \right|}\right)}{b^{7}} - \frac{522 \, B a^{6} - 137 \, A a^{5} b + 300 \, {\left(3 \, B a^{2} b^{4} - A a b^{5}\right)} x^{4} + 300 \, {\left(10 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} x^{3} + 100 \, {\left(39 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(462 \, B a^{5} b - 125 \, A a^{4} b^{2}\right)} x}{60 \, {\left(b x + a\right)}^{5} b^{7}}"," ",0,"B*x/b^6 - (6*B*a - A*b)*log(abs(b*x + a))/b^7 - 1/60*(522*B*a^6 - 137*A*a^5*b + 300*(3*B*a^2*b^4 - A*a*b^5)*x^4 + 300*(10*B*a^3*b^3 - 3*A*a^2*b^4)*x^3 + 100*(39*B*a^4*b^2 - 11*A*a^3*b^3)*x^2 + 5*(462*B*a^5*b - 125*A*a^4*b^2)*x)/((b*x + a)^5*b^7)","A",0
645,1,124,0,0.152778," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{B \log\left({\left| b x + a \right|}\right)}{b^{6}} + \frac{60 \, {\left(5 \, B a b^{3} - A b^{4}\right)} x^{4} + 60 \, {\left(15 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + 20 \, {\left(55 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} x^{2} + 5 \, {\left(125 \, B a^{4} - 12 \, A a^{3} b\right)} x + \frac{137 \, B a^{5} - 12 \, A a^{4} b}{b}}{60 \, {\left(b x + a\right)}^{5} b^{5}}"," ",0,"B*log(abs(b*x + a))/b^6 + 1/60*(60*(5*B*a*b^3 - A*b^4)*x^4 + 60*(15*B*a^2*b^2 - 2*A*a*b^3)*x^3 + 20*(55*B*a^3*b - 6*A*a^2*b^2)*x^2 + 5*(125*B*a^4 - 12*A*a^3*b)*x + (137*B*a^5 - 12*A*a^4*b)/b)/((b*x + a)^5*b^5)","A",0
646,1,93,0,0.168999," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{20 \, B b^{4} x^{4} + 40 \, B a b^{3} x^{3} + 10 \, A b^{4} x^{3} + 40 \, B a^{2} b^{2} x^{2} + 10 \, A a b^{3} x^{2} + 20 \, B a^{3} b x + 5 \, A a^{2} b^{2} x + 4 \, B a^{4} + A a^{3} b}{20 \, {\left(b x + a\right)}^{5} b^{5}}"," ",0,"-1/20*(20*B*b^4*x^4 + 40*B*a*b^3*x^3 + 10*A*b^4*x^3 + 40*B*a^2*b^2*x^2 + 10*A*a*b^3*x^2 + 20*B*a^3*b*x + 5*A*a^2*b^2*x + 4*B*a^4 + A*a^3*b)/((b*x + a)^5*b^5)","A",0
647,1,70,0,0.164285," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{30 \, B b^{3} x^{3} + 30 \, B a b^{2} x^{2} + 20 \, A b^{3} x^{2} + 15 \, B a^{2} b x + 10 \, A a b^{2} x + 3 \, B a^{3} + 2 \, A a^{2} b}{60 \, {\left(b x + a\right)}^{5} b^{4}}"," ",0,"-1/60*(30*B*b^3*x^3 + 30*B*a*b^2*x^2 + 20*A*b^3*x^2 + 15*B*a^2*b*x + 10*A*a*b^2*x + 3*B*a^3 + 2*A*a^2*b)/((b*x + a)^5*b^4)","A",0
648,1,46,0,0.176417," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{20 \, B b^{2} x^{2} + 10 \, B a b x + 15 \, A b^{2} x + 2 \, B a^{2} + 3 \, A a b}{60 \, {\left(b x + a\right)}^{5} b^{3}}"," ",0,"-1/60*(20*B*b^2*x^2 + 10*B*a*b*x + 15*A*b^2*x + 2*B*a^2 + 3*A*a*b)/((b*x + a)^5*b^3)","A",0
649,1,25,0,0.155096," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{5 \, B b x + B a + 4 \, A b}{20 \, {\left(b x + a\right)}^{5} b^{2}}"," ",0,"-1/20*(5*B*b*x + B*a + 4*A*b)/((b*x + a)^5*b^2)","A",0
650,1,95,0,0.155329," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{A \log\left({\left| b x + a \right|}\right)}{a^{6}} + \frac{A \log\left({\left| x \right|}\right)}{a^{6}} + \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(b x + a\right)}^{5} a^{6} b}"," ",0,"-A*log(abs(b*x + a))/a^6 + A*log(abs(x))/a^6 + 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)/((b*x + a)^5*a^6*b)","A",0
651,1,168,0,0.163730," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{{\left(B a - 6 \, A b\right)} \log\left({\left| x \right|}\right)}{a^{7}} - \frac{{\left(B a b - 6 \, A b^{2}\right)} \log\left({\left| b x + a \right|}\right)}{a^{7} b} - \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(b x + a\right)}^{5} a^{7} x}"," ",0,"(B*a - 6*A*b)*log(abs(x))/a^7 - (B*a*b - 6*A*b^2)*log(abs(b*x + a))/(a^7*b) - 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)/((b*x + a)^5*a^7*x)","A",0
652,1,205,0,0.159578," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, B a b - 7 \, A b^{2}\right)} \log\left({\left| x \right|}\right)}{a^{8}} + \frac{3 \, {\left(2 \, B a b^{2} - 7 \, A b^{3}\right)} \log\left({\left| b x + a \right|}\right)}{a^{8} b} - \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}{20 \, {\left(b x + a\right)}^{5} a^{8} x^{2}}"," ",0,"-3*(2*B*a*b - 7*A*b^2)*log(abs(x))/a^8 + 3*(2*B*a*b^2 - 7*A*b^3)*log(abs(b*x + a))/(a^8*b) - 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)/((b*x + a)^5*a^8*x^2)","A",0
653,1,78,0,0.197267," ","integrate(x^4*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{7} \, B b x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, B a x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A a x^{5} \mathrm{sgn}\left(b x + a\right) - \frac{{\left(5 \, B a^{7} - 7 \, A a^{6} b\right)} \mathrm{sgn}\left(b x + a\right)}{210 \, b^{6}}"," ",0,"1/7*B*b*x^7*sgn(b*x + a) + 1/6*B*a*x^6*sgn(b*x + a) + 1/6*A*b*x^6*sgn(b*x + a) + 1/5*A*a*x^5*sgn(b*x + a) - 1/210*(5*B*a^7 - 7*A*a^6*b)*sgn(b*x + a)/b^6","A",0
654,1,78,0,0.153519," ","integrate(x^3*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, B b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B a x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A a x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(2 \, B a^{6} - 3 \, A a^{5} b\right)} \mathrm{sgn}\left(b x + a\right)}{60 \, b^{5}}"," ",0,"1/6*B*b*x^6*sgn(b*x + a) + 1/5*B*a*x^5*sgn(b*x + a) + 1/5*A*b*x^5*sgn(b*x + a) + 1/4*A*a*x^4*sgn(b*x + a) + 1/60*(2*B*a^6 - 3*A*a^5*b)*sgn(b*x + a)/b^5","A",0
655,1,78,0,0.216233," ","integrate(x^2*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, B b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, B a x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A a x^{3} \mathrm{sgn}\left(b x + a\right) - \frac{{\left(3 \, B a^{5} - 5 \, A a^{4} b\right)} \mathrm{sgn}\left(b x + a\right)}{60 \, b^{4}}"," ",0,"1/5*B*b*x^5*sgn(b*x + a) + 1/4*B*a*x^4*sgn(b*x + a) + 1/4*A*b*x^4*sgn(b*x + a) + 1/3*A*a*x^3*sgn(b*x + a) - 1/60*(3*B*a^5 - 5*A*a^4*b)*sgn(b*x + a)/b^4","A",0
656,1,77,0,0.191016," ","integrate(x*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, B b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(B a^{4} - 2 \, A a^{3} b\right)} \mathrm{sgn}\left(b x + a\right)}{12 \, b^{3}}"," ",0,"1/4*B*b*x^4*sgn(b*x + a) + 1/3*B*a*x^3*sgn(b*x + a) + 1/3*A*b*x^3*sgn(b*x + a) + 1/2*A*a*x^2*sgn(b*x + a) + 1/12*(B*a^4 - 2*A*a^3*b)*sgn(b*x + a)/b^3","A",0
657,1,74,0,0.218567," ","integrate((B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, B b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b x^{2} \mathrm{sgn}\left(b x + a\right) + A a x \mathrm{sgn}\left(b x + a\right) - \frac{{\left(B a^{3} - 3 \, A a^{2} b\right)} \mathrm{sgn}\left(b x + a\right)}{6 \, b^{2}}"," ",0,"1/3*B*b*x^3*sgn(b*x + a) + 1/2*B*a*x^2*sgn(b*x + a) + 1/2*A*b*x^2*sgn(b*x + a) + A*a*x*sgn(b*x + a) - 1/6*(B*a^3 - 3*A*a^2*b)*sgn(b*x + a)/b^2","A",0
658,1,46,0,0.164117," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{2} \, B b x^{2} \mathrm{sgn}\left(b x + a\right) + B a x \mathrm{sgn}\left(b x + a\right) + A b x \mathrm{sgn}\left(b x + a\right) + A a \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right)"," ",0,"1/2*B*b*x^2*sgn(b*x + a) + B*a*x*sgn(b*x + a) + A*b*x*sgn(b*x + a) + A*a*log(abs(x))*sgn(b*x + a)","A",0
659,1,47,0,0.183634," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^2,x, algorithm=""giac"")","B b x \mathrm{sgn}\left(b x + a\right) + {\left(B a \mathrm{sgn}\left(b x + a\right) + A b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right) - \frac{A a \mathrm{sgn}\left(b x + a\right)}{x}"," ",0,"B*b*x*sgn(b*x + a) + (B*a*sgn(b*x + a) + A*b*sgn(b*x + a))*log(abs(x)) - A*a*sgn(b*x + a)/x","A",0
660,1,50,0,0.192840," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^3,x, algorithm=""giac"")","B b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{A a \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(B a \mathrm{sgn}\left(b x + a\right) + A b \mathrm{sgn}\left(b x + a\right)\right)} x}{2 \, x^{2}}"," ",0,"B*b*log(abs(x))*sgn(b*x + a) - 1/2*(A*a*sgn(b*x + a) + 2*(B*a*sgn(b*x + a) + A*b*sgn(b*x + a))*x)/x^2","A",0
661,1,77,0,0.160895," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{{\left(3 \, B a b^{2} - A b^{3}\right)} \mathrm{sgn}\left(b x + a\right)}{6 \, a^{2}} - \frac{6 \, B b x^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a x \mathrm{sgn}\left(b x + a\right) + 3 \, A b x \mathrm{sgn}\left(b x + a\right) + 2 \, A a \mathrm{sgn}\left(b x + a\right)}{6 \, x^{3}}"," ",0,"-1/6*(3*B*a*b^2 - A*b^3)*sgn(b*x + a)/a^2 - 1/6*(6*B*b*x^2*sgn(b*x + a) + 3*B*a*x*sgn(b*x + a) + 3*A*b*x*sgn(b*x + a) + 2*A*a*sgn(b*x + a))/x^3","A",0
662,1,77,0,0.158792," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^5,x, algorithm=""giac"")","\frac{{\left(2 \, B a b^{3} - A b^{4}\right)} \mathrm{sgn}\left(b x + a\right)}{12 \, a^{3}} - \frac{6 \, B b x^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, B a x \mathrm{sgn}\left(b x + a\right) + 4 \, A b x \mathrm{sgn}\left(b x + a\right) + 3 \, A a \mathrm{sgn}\left(b x + a\right)}{12 \, x^{4}}"," ",0,"1/12*(2*B*a*b^3 - A*b^4)*sgn(b*x + a)/a^3 - 1/12*(6*B*b*x^2*sgn(b*x + a) + 4*B*a*x*sgn(b*x + a) + 4*A*b*x*sgn(b*x + a) + 3*A*a*sgn(b*x + a))/x^4","A",0
663,1,77,0,0.223488," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^6,x, algorithm=""giac"")","-\frac{{\left(5 \, B a b^{4} - 3 \, A b^{5}\right)} \mathrm{sgn}\left(b x + a\right)}{60 \, a^{4}} - \frac{20 \, B b x^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, B a x \mathrm{sgn}\left(b x + a\right) + 15 \, A b x \mathrm{sgn}\left(b x + a\right) + 12 \, A a \mathrm{sgn}\left(b x + a\right)}{60 \, x^{5}}"," ",0,"-1/60*(5*B*a*b^4 - 3*A*b^5)*sgn(b*x + a)/a^4 - 1/60*(20*B*b*x^2*sgn(b*x + a) + 15*B*a*x*sgn(b*x + a) + 15*A*b*x*sgn(b*x + a) + 12*A*a*sgn(b*x + a))/x^5","A",0
664,1,77,0,0.156243," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^7,x, algorithm=""giac"")","\frac{{\left(3 \, B a b^{5} - 2 \, A b^{6}\right)} \mathrm{sgn}\left(b x + a\right)}{60 \, a^{5}} - \frac{15 \, B b x^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B a x \mathrm{sgn}\left(b x + a\right) + 12 \, A b x \mathrm{sgn}\left(b x + a\right) + 10 \, A a \mathrm{sgn}\left(b x + a\right)}{60 \, x^{6}}"," ",0,"1/60*(3*B*a*b^5 - 2*A*b^6)*sgn(b*x + a)/a^5 - 1/60*(15*B*b*x^2*sgn(b*x + a) + 12*B*a*x*sgn(b*x + a) + 12*A*b*x*sgn(b*x + a) + 10*A*a*sgn(b*x + a))/x^6","A",0
665,1,150,0,0.180831," ","integrate(x^5*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{10} \, B b^{3} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a b^{2} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{1}{9} \, A b^{3} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, B a^{2} b x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, A a b^{2} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B a^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, A a^{2} b x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A a^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(3 \, B a^{10} - 5 \, A a^{9} b\right)} \mathrm{sgn}\left(b x + a\right)}{2520 \, b^{7}}"," ",0,"1/10*B*b^3*x^10*sgn(b*x + a) + 1/3*B*a*b^2*x^9*sgn(b*x + a) + 1/9*A*b^3*x^9*sgn(b*x + a) + 3/8*B*a^2*b*x^8*sgn(b*x + a) + 3/8*A*a*b^2*x^8*sgn(b*x + a) + 1/7*B*a^3*x^7*sgn(b*x + a) + 3/7*A*a^2*b*x^7*sgn(b*x + a) + 1/6*A*a^3*x^6*sgn(b*x + a) + 1/2520*(3*B*a^10 - 5*A*a^9*b)*sgn(b*x + a)/b^7","A",0
666,1,150,0,0.214174," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, B b^{3} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, B a b^{2} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, A b^{3} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, B a^{2} b x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, A a b^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, B a^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a^{2} b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A a^{3} x^{5} \mathrm{sgn}\left(b x + a\right) - \frac{{\left(5 \, B a^{9} - 9 \, A a^{8} b\right)} \mathrm{sgn}\left(b x + a\right)}{2520 \, b^{6}}"," ",0,"1/9*B*b^3*x^9*sgn(b*x + a) + 3/8*B*a*b^2*x^8*sgn(b*x + a) + 1/8*A*b^3*x^8*sgn(b*x + a) + 3/7*B*a^2*b*x^7*sgn(b*x + a) + 3/7*A*a*b^2*x^7*sgn(b*x + a) + 1/6*B*a^3*x^6*sgn(b*x + a) + 1/2*A*a^2*b*x^6*sgn(b*x + a) + 1/5*A*a^3*x^5*sgn(b*x + a) - 1/2520*(5*B*a^9 - 9*A*a^8*b)*sgn(b*x + a)/b^6","A",0
667,1,149,0,0.196458," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, B b^{3} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, B a b^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, A b^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{2} b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a b^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B a^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, A a^{2} b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A a^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(B a^{8} - 2 \, A a^{7} b\right)} \mathrm{sgn}\left(b x + a\right)}{280 \, b^{5}}"," ",0,"1/8*B*b^3*x^8*sgn(b*x + a) + 3/7*B*a*b^2*x^7*sgn(b*x + a) + 1/7*A*b^3*x^7*sgn(b*x + a) + 1/2*B*a^2*b*x^6*sgn(b*x + a) + 1/2*A*a*b^2*x^6*sgn(b*x + a) + 1/5*B*a^3*x^5*sgn(b*x + a) + 3/5*A*a^2*b*x^5*sgn(b*x + a) + 1/4*A*a^3*x^4*sgn(b*x + a) + 1/280*(B*a^8 - 2*A*a^7*b)*sgn(b*x + a)/b^5","A",0
668,1,150,0,0.161866," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7} \, B b^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a b^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, B a^{2} b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, A a b^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, B a^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, A a^{2} b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A a^{3} x^{3} \mathrm{sgn}\left(b x + a\right) - \frac{{\left(3 \, B a^{7} - 7 \, A a^{6} b\right)} \mathrm{sgn}\left(b x + a\right)}{420 \, b^{4}}"," ",0,"1/7*B*b^3*x^7*sgn(b*x + a) + 1/2*B*a*b^2*x^6*sgn(b*x + a) + 1/6*A*b^3*x^6*sgn(b*x + a) + 3/5*B*a^2*b*x^5*sgn(b*x + a) + 3/5*A*a*b^2*x^5*sgn(b*x + a) + 1/4*B*a^3*x^4*sgn(b*x + a) + 3/4*A*a^2*b*x^4*sgn(b*x + a) + 1/3*A*a^3*x^3*sgn(b*x + a) - 1/420*(3*B*a^7 - 7*A*a^6*b)*sgn(b*x + a)/b^4","A",0
669,1,148,0,0.162372," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, B b^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, B a b^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a^{2} b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, A a b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + A a^{2} b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(B a^{6} - 3 \, A a^{5} b\right)} \mathrm{sgn}\left(b x + a\right)}{60 \, b^{3}}"," ",0,"1/6*B*b^3*x^6*sgn(b*x + a) + 3/5*B*a*b^2*x^5*sgn(b*x + a) + 1/5*A*b^3*x^5*sgn(b*x + a) + 3/4*B*a^2*b*x^4*sgn(b*x + a) + 3/4*A*a*b^2*x^4*sgn(b*x + a) + 1/3*B*a^3*x^3*sgn(b*x + a) + A*a^2*b*x^3*sgn(b*x + a) + 1/2*A*a^3*x^2*sgn(b*x + a) + 1/60*(B*a^6 - 3*A*a^5*b)*sgn(b*x + a)/b^3","A",0
670,1,144,0,0.170105," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{5} \, B b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + B a^{2} b x^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + A a^{3} x \mathrm{sgn}\left(b x + a\right) - \frac{{\left(B a^{5} - 5 \, A a^{4} b\right)} \mathrm{sgn}\left(b x + a\right)}{20 \, b^{2}}"," ",0,"1/5*B*b^3*x^5*sgn(b*x + a) + 3/4*B*a*b^2*x^4*sgn(b*x + a) + 1/4*A*b^3*x^4*sgn(b*x + a) + B*a^2*b*x^3*sgn(b*x + a) + A*a*b^2*x^3*sgn(b*x + a) + 1/2*B*a^3*x^2*sgn(b*x + a) + 3/2*A*a^2*b*x^2*sgn(b*x + a) + A*a^3*x*sgn(b*x + a) - 1/20*(B*a^5 - 5*A*a^4*b)*sgn(b*x + a)/b^2","B",0
671,1,118,0,0.161913," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{4} \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + B a^{3} x \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + A a^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right)"," ",0,"1/4*B*b^3*x^4*sgn(b*x + a) + B*a*b^2*x^3*sgn(b*x + a) + 1/3*A*b^3*x^3*sgn(b*x + a) + 3/2*B*a^2*b*x^2*sgn(b*x + a) + 3/2*A*a*b^2*x^2*sgn(b*x + a) + B*a^3*x*sgn(b*x + a) + 3*A*a^2*b*x*sgn(b*x + a) + A*a^3*log(abs(x))*sgn(b*x + a)","A",0
672,1,119,0,0.182606," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, B b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, B a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{2} b x \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{2} x \mathrm{sgn}\left(b x + a\right) - \frac{A a^{3} \mathrm{sgn}\left(b x + a\right)}{x} + {\left(B a^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right)"," ",0,"1/3*B*b^3*x^3*sgn(b*x + a) + 3/2*B*a*b^2*x^2*sgn(b*x + a) + 1/2*A*b^3*x^2*sgn(b*x + a) + 3*B*a^2*b*x*sgn(b*x + a) + 3*A*a*b^2*x*sgn(b*x + a) - A*a^3*sgn(b*x + a)/x + (B*a^3*sgn(b*x + a) + 3*A*a^2*b*sgn(b*x + a))*log(abs(x))","A",0
673,1,117,0,0.159128," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, B b^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} x \mathrm{sgn}\left(b x + a\right) + A b^{3} x \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(B a^{2} b \mathrm{sgn}\left(b x + a\right) + A a b^{2} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right) - \frac{A a^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(B a^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b \mathrm{sgn}\left(b x + a\right)\right)} x}{2 \, x^{2}}"," ",0,"1/2*B*b^3*x^2*sgn(b*x + a) + 3*B*a*b^2*x*sgn(b*x + a) + A*b^3*x*sgn(b*x + a) + 3*(B*a^2*b*sgn(b*x + a) + A*a*b^2*sgn(b*x + a))*log(abs(x)) - 1/2*(A*a^3*sgn(b*x + a) + 2*(B*a^3*sgn(b*x + a) + 3*A*a^2*b*sgn(b*x + a))*x)/x^2","A",0
674,1,118,0,0.167270," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^4,x, algorithm=""giac"")","B b^{3} x \mathrm{sgn}\left(b x + a\right) + {\left(3 \, B a b^{2} \mathrm{sgn}\left(b x + a\right) + A b^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right) - \frac{2 \, A a^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(B a^{2} b \mathrm{sgn}\left(b x + a\right) + A a b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 3 \, {\left(B a^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b \mathrm{sgn}\left(b x + a\right)\right)} x}{6 \, x^{3}}"," ",0,"B*b^3*x*sgn(b*x + a) + (3*B*a*b^2*sgn(b*x + a) + A*b^3*sgn(b*x + a))*log(abs(x)) - 1/6*(2*A*a^3*sgn(b*x + a) + 18*(B*a^2*b*sgn(b*x + a) + A*a*b^2*sgn(b*x + a))*x^2 + 3*(B*a^3*sgn(b*x + a) + 3*A*a^2*b*sgn(b*x + a))*x)/x^3","A",0
675,1,121,0,0.175487," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^5,x, algorithm=""giac"")","B b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{3 \, A a^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(3 \, B a b^{2} \mathrm{sgn}\left(b x + a\right) + A b^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 18 \, {\left(B a^{2} b \mathrm{sgn}\left(b x + a\right) + A a b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 4 \, {\left(B a^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b \mathrm{sgn}\left(b x + a\right)\right)} x}{12 \, x^{4}}"," ",0,"B*b^3*log(abs(x))*sgn(b*x + a) - 1/12*(3*A*a^3*sgn(b*x + a) + 12*(3*B*a*b^2*sgn(b*x + a) + A*b^3*sgn(b*x + a))*x^3 + 18*(B*a^2*b*sgn(b*x + a) + A*a*b^2*sgn(b*x + a))*x^2 + 4*(B*a^3*sgn(b*x + a) + 3*A*a^2*b*sgn(b*x + a))*x)/x^4","A",0
676,1,149,0,0.161136," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^6,x, algorithm=""giac"")","-\frac{{\left(5 \, B a b^{4} - A b^{5}\right)} \mathrm{sgn}\left(b x + a\right)}{20 \, a^{2}} - \frac{20 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{20 \, x^{5}}"," ",0,"-1/20*(5*B*a*b^4 - A*b^5)*sgn(b*x + a)/a^2 - 1/20*(20*B*b^3*x^4*sgn(b*x + a) + 30*B*a*b^2*x^3*sgn(b*x + a) + 10*A*b^3*x^3*sgn(b*x + a) + 20*B*a^2*b*x^2*sgn(b*x + a) + 20*A*a*b^2*x^2*sgn(b*x + a) + 5*B*a^3*x*sgn(b*x + a) + 15*A*a^2*b*x*sgn(b*x + a) + 4*A*a^3*sgn(b*x + a))/x^5","B",0
677,1,149,0,0.161072," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^7,x, algorithm=""giac"")","\frac{{\left(3 \, B a b^{5} - A b^{6}\right)} \mathrm{sgn}\left(b x + a\right)}{60 \, a^{3}} - \frac{30 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 45 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 36 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{60 \, x^{6}}"," ",0,"1/60*(3*B*a*b^5 - A*b^6)*sgn(b*x + a)/a^3 - 1/60*(30*B*b^3*x^4*sgn(b*x + a) + 60*B*a*b^2*x^3*sgn(b*x + a) + 20*A*b^3*x^3*sgn(b*x + a) + 45*B*a^2*b*x^2*sgn(b*x + a) + 45*A*a*b^2*x^2*sgn(b*x + a) + 12*B*a^3*x*sgn(b*x + a) + 36*A*a^2*b*x*sgn(b*x + a) + 10*A*a^3*sgn(b*x + a))/x^6","A",0
678,1,149,0,0.232880," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^8,x, algorithm=""giac"")","-\frac{{\left(7 \, B a b^{6} - 3 \, A b^{7}\right)} \mathrm{sgn}\left(b x + a\right)}{420 \, a^{4}} - \frac{140 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 315 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 105 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 252 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 252 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 70 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 210 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 60 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{420 \, x^{7}}"," ",0,"-1/420*(7*B*a*b^6 - 3*A*b^7)*sgn(b*x + a)/a^4 - 1/420*(140*B*b^3*x^4*sgn(b*x + a) + 315*B*a*b^2*x^3*sgn(b*x + a) + 105*A*b^3*x^3*sgn(b*x + a) + 252*B*a^2*b*x^2*sgn(b*x + a) + 252*A*a*b^2*x^2*sgn(b*x + a) + 70*B*a^3*x*sgn(b*x + a) + 210*A*a^2*b*x*sgn(b*x + a) + 60*A*a^3*sgn(b*x + a))/x^7","A",0
679,1,149,0,0.172744," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^9,x, algorithm=""giac"")","\frac{{\left(2 \, B a b^{7} - A b^{8}\right)} \mathrm{sgn}\left(b x + a\right)}{280 \, a^{5}} - \frac{70 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 168 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 56 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 140 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 40 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 120 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 35 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{280 \, x^{8}}"," ",0,"1/280*(2*B*a*b^7 - A*b^8)*sgn(b*x + a)/a^5 - 1/280*(70*B*b^3*x^4*sgn(b*x + a) + 168*B*a*b^2*x^3*sgn(b*x + a) + 56*A*b^3*x^3*sgn(b*x + a) + 140*B*a^2*b*x^2*sgn(b*x + a) + 140*A*a*b^2*x^2*sgn(b*x + a) + 40*B*a^3*x*sgn(b*x + a) + 120*A*a^2*b*x*sgn(b*x + a) + 35*A*a^3*sgn(b*x + a))/x^8","A",0
680,1,149,0,0.182628," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^10,x, algorithm=""giac"")","-\frac{{\left(9 \, B a b^{8} - 5 \, A b^{9}\right)} \mathrm{sgn}\left(b x + a\right)}{2520 \, a^{6}} - \frac{504 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 1260 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 420 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 1080 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 1080 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 315 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 945 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 280 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{2520 \, x^{9}}"," ",0,"-1/2520*(9*B*a*b^8 - 5*A*b^9)*sgn(b*x + a)/a^6 - 1/2520*(504*B*b^3*x^4*sgn(b*x + a) + 1260*B*a*b^2*x^3*sgn(b*x + a) + 420*A*b^3*x^3*sgn(b*x + a) + 1080*B*a^2*b*x^2*sgn(b*x + a) + 1080*A*a*b^2*x^2*sgn(b*x + a) + 315*B*a^3*x*sgn(b*x + a) + 945*A*a^2*b*x*sgn(b*x + a) + 280*A*a^3*sgn(b*x + a))/x^9","A",0
681,1,149,0,0.162488," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^11,x, algorithm=""giac"")","\frac{{\left(5 \, B a b^{9} - 3 \, A b^{10}\right)} \mathrm{sgn}\left(b x + a\right)}{2520 \, a^{7}} - \frac{420 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 1080 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 360 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 945 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 945 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 280 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 840 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 252 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{2520 \, x^{10}}"," ",0,"1/2520*(5*B*a*b^9 - 3*A*b^10)*sgn(b*x + a)/a^7 - 1/2520*(420*B*b^3*x^4*sgn(b*x + a) + 1080*B*a*b^2*x^3*sgn(b*x + a) + 360*A*b^3*x^3*sgn(b*x + a) + 945*B*a^2*b*x^2*sgn(b*x + a) + 945*A*a*b^2*x^2*sgn(b*x + a) + 280*B*a^3*x*sgn(b*x + a) + 840*A*a^2*b*x*sgn(b*x + a) + 252*A*a^3*sgn(b*x + a))/x^10","A",0
682,1,149,0,0.197184," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^12,x, algorithm=""giac"")","-\frac{{\left(11 \, B a b^{10} - 7 \, A b^{11}\right)} \mathrm{sgn}\left(b x + a\right)}{9240 \, a^{8}} - \frac{1320 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 3465 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 1155 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 3080 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 3080 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 924 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 2772 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 840 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{9240 \, x^{11}}"," ",0,"-1/9240*(11*B*a*b^10 - 7*A*b^11)*sgn(b*x + a)/a^8 - 1/9240*(1320*B*b^3*x^4*sgn(b*x + a) + 3465*B*a*b^2*x^3*sgn(b*x + a) + 1155*A*b^3*x^3*sgn(b*x + a) + 3080*B*a^2*b*x^2*sgn(b*x + a) + 3080*A*a*b^2*x^2*sgn(b*x + a) + 924*B*a^3*x*sgn(b*x + a) + 2772*A*a^2*b*x*sgn(b*x + a) + 840*A*a^3*sgn(b*x + a))/x^11","A",0
683,1,220,0,0.184427," ","integrate(x^6*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{13} \, B b^{5} x^{13} \mathrm{sgn}\left(b x + a\right) + \frac{5}{12} \, B a b^{4} x^{12} \mathrm{sgn}\left(b x + a\right) + \frac{1}{12} \, A b^{5} x^{12} \mathrm{sgn}\left(b x + a\right) + \frac{10}{11} \, B a^{2} b^{3} x^{11} \mathrm{sgn}\left(b x + a\right) + \frac{5}{11} \, A a b^{4} x^{11} \mathrm{sgn}\left(b x + a\right) + B a^{3} b^{2} x^{10} \mathrm{sgn}\left(b x + a\right) + A a^{2} b^{3} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, B a^{4} b x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, A a^{3} b^{2} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, B a^{5} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, A a^{4} b x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, A a^{5} x^{7} \mathrm{sgn}\left(b x + a\right) - \frac{{\left(7 \, B a^{13} - 13 \, A a^{12} b\right)} \mathrm{sgn}\left(b x + a\right)}{72072 \, b^{8}}"," ",0,"1/13*B*b^5*x^13*sgn(b*x + a) + 5/12*B*a*b^4*x^12*sgn(b*x + a) + 1/12*A*b^5*x^12*sgn(b*x + a) + 10/11*B*a^2*b^3*x^11*sgn(b*x + a) + 5/11*A*a*b^4*x^11*sgn(b*x + a) + B*a^3*b^2*x^10*sgn(b*x + a) + A*a^2*b^3*x^10*sgn(b*x + a) + 5/9*B*a^4*b*x^9*sgn(b*x + a) + 10/9*A*a^3*b^2*x^9*sgn(b*x + a) + 1/8*B*a^5*x^8*sgn(b*x + a) + 5/8*A*a^4*b*x^8*sgn(b*x + a) + 1/7*A*a^5*x^7*sgn(b*x + a) - 1/72072*(7*B*a^13 - 13*A*a^12*b)*sgn(b*x + a)/b^8","A",0
684,1,220,0,0.173367," ","integrate(x^5*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{12} \, B b^{5} x^{12} \mathrm{sgn}\left(b x + a\right) + \frac{5}{11} \, B a b^{4} x^{11} \mathrm{sgn}\left(b x + a\right) + \frac{1}{11} \, A b^{5} x^{11} \mathrm{sgn}\left(b x + a\right) + B a^{2} b^{3} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a b^{4} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, B a^{3} b^{2} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, A a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, B a^{4} b x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A a^{3} b^{2} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B a^{5} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, A a^{4} b x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A a^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(B a^{12} - 2 \, A a^{11} b\right)} \mathrm{sgn}\left(b x + a\right)}{5544 \, b^{7}}"," ",0,"1/12*B*b^5*x^12*sgn(b*x + a) + 5/11*B*a*b^4*x^11*sgn(b*x + a) + 1/11*A*b^5*x^11*sgn(b*x + a) + B*a^2*b^3*x^10*sgn(b*x + a) + 1/2*A*a*b^4*x^10*sgn(b*x + a) + 10/9*B*a^3*b^2*x^9*sgn(b*x + a) + 10/9*A*a^2*b^3*x^9*sgn(b*x + a) + 5/8*B*a^4*b*x^8*sgn(b*x + a) + 5/4*A*a^3*b^2*x^8*sgn(b*x + a) + 1/7*B*a^5*x^7*sgn(b*x + a) + 5/7*A*a^4*b*x^7*sgn(b*x + a) + 1/6*A*a^5*x^6*sgn(b*x + a) + 1/5544*(B*a^12 - 2*A*a^11*b)*sgn(b*x + a)/b^7","A",0
685,1,222,0,0.169006," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{11} \, B b^{5} x^{11} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a b^{4} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{1}{10} \, A b^{5} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, B a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, A a b^{4} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B a^{3} b^{2} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A a^{2} b^{3} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, B a^{4} b x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, A a^{3} b^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, B a^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, A a^{4} b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A a^{5} x^{5} \mathrm{sgn}\left(b x + a\right) - \frac{{\left(5 \, B a^{11} - 11 \, A a^{10} b\right)} \mathrm{sgn}\left(b x + a\right)}{13860 \, b^{6}}"," ",0,"1/11*B*b^5*x^11*sgn(b*x + a) + 1/2*B*a*b^4*x^10*sgn(b*x + a) + 1/10*A*b^5*x^10*sgn(b*x + a) + 10/9*B*a^2*b^3*x^9*sgn(b*x + a) + 5/9*A*a*b^4*x^9*sgn(b*x + a) + 5/4*B*a^3*b^2*x^8*sgn(b*x + a) + 5/4*A*a^2*b^3*x^8*sgn(b*x + a) + 5/7*B*a^4*b*x^7*sgn(b*x + a) + 10/7*A*a^3*b^2*x^7*sgn(b*x + a) + 1/6*B*a^5*x^6*sgn(b*x + a) + 5/6*A*a^4*b*x^6*sgn(b*x + a) + 1/5*A*a^5*x^5*sgn(b*x + a) - 1/13860*(5*B*a^11 - 11*A*a^10*b)*sgn(b*x + a)/b^6","A",0
686,1,221,0,0.171216," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{10} \, B b^{5} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, B a b^{4} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{1}{9} \, A b^{5} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B a^{2} b^{3} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, A a b^{4} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B a^{3} b^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, A a^{2} b^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a^{4} b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B a^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + A a^{4} b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A a^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(2 \, B a^{10} - 5 \, A a^{9} b\right)} \mathrm{sgn}\left(b x + a\right)}{2520 \, b^{5}}"," ",0,"1/10*B*b^5*x^10*sgn(b*x + a) + 5/9*B*a*b^4*x^9*sgn(b*x + a) + 1/9*A*b^5*x^9*sgn(b*x + a) + 5/4*B*a^2*b^3*x^8*sgn(b*x + a) + 5/8*A*a*b^4*x^8*sgn(b*x + a) + 10/7*B*a^3*b^2*x^7*sgn(b*x + a) + 10/7*A*a^2*b^3*x^7*sgn(b*x + a) + 5/6*B*a^4*b*x^6*sgn(b*x + a) + 5/3*A*a^3*b^2*x^6*sgn(b*x + a) + 1/5*B*a^5*x^5*sgn(b*x + a) + A*a^4*b*x^5*sgn(b*x + a) + 1/4*A*a^5*x^4*sgn(b*x + a) + 1/2520*(2*B*a^10 - 5*A*a^9*b)*sgn(b*x + a)/b^5","A",0
687,1,220,0,0.191710," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{9} \, B b^{5} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, B a b^{4} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, A b^{5} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B a^{2} b^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, A a b^{4} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + B a^{4} b x^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, B a^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A a^{4} b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A a^{5} x^{3} \mathrm{sgn}\left(b x + a\right) - \frac{{\left(B a^{9} - 3 \, A a^{8} b\right)} \mathrm{sgn}\left(b x + a\right)}{504 \, b^{4}}"," ",0,"1/9*B*b^5*x^9*sgn(b*x + a) + 5/8*B*a*b^4*x^8*sgn(b*x + a) + 1/8*A*b^5*x^8*sgn(b*x + a) + 10/7*B*a^2*b^3*x^7*sgn(b*x + a) + 5/7*A*a*b^4*x^7*sgn(b*x + a) + 5/3*B*a^3*b^2*x^6*sgn(b*x + a) + 5/3*A*a^2*b^3*x^6*sgn(b*x + a) + B*a^4*b*x^5*sgn(b*x + a) + 2*A*a^3*b^2*x^5*sgn(b*x + a) + 1/4*B*a^5*x^4*sgn(b*x + a) + 5/4*A*a^4*b*x^4*sgn(b*x + a) + 1/3*A*a^5*x^3*sgn(b*x + a) - 1/504*(B*a^9 - 3*A*a^8*b)*sgn(b*x + a)/b^4","A",0
688,1,221,0,0.169487," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, B b^{5} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, B a b^{4} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, A b^{5} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, A a b^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{3} b^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{2} b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B a^{4} b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a^{4} b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{{\left(B a^{8} - 4 \, A a^{7} b\right)} \mathrm{sgn}\left(b x + a\right)}{168 \, b^{3}}"," ",0,"1/8*B*b^5*x^8*sgn(b*x + a) + 5/7*B*a*b^4*x^7*sgn(b*x + a) + 1/7*A*b^5*x^7*sgn(b*x + a) + 5/3*B*a^2*b^3*x^6*sgn(b*x + a) + 5/6*A*a*b^4*x^6*sgn(b*x + a) + 2*B*a^3*b^2*x^5*sgn(b*x + a) + 2*A*a^2*b^3*x^5*sgn(b*x + a) + 5/4*B*a^4*b*x^4*sgn(b*x + a) + 5/2*A*a^3*b^2*x^4*sgn(b*x + a) + 1/3*B*a^5*x^3*sgn(b*x + a) + 5/3*A*a^4*b*x^3*sgn(b*x + a) + 1/2*A*a^5*x^2*sgn(b*x + a) + 1/168*(B*a^8 - 4*A*a^7*b)*sgn(b*x + a)/b^3","B",0
689,1,217,0,0.198004," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{7} \, B b^{5} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + A a^{5} x \mathrm{sgn}\left(b x + a\right) - \frac{{\left(B a^{7} - 7 \, A a^{6} b\right)} \mathrm{sgn}\left(b x + a\right)}{42 \, b^{2}}"," ",0,"1/7*B*b^5*x^7*sgn(b*x + a) + 5/6*B*a*b^4*x^6*sgn(b*x + a) + 1/6*A*b^5*x^6*sgn(b*x + a) + 2*B*a^2*b^3*x^5*sgn(b*x + a) + A*a*b^4*x^5*sgn(b*x + a) + 5/2*B*a^3*b^2*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*x^4*sgn(b*x + a) + 5/3*B*a^4*b*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*x^3*sgn(b*x + a) + 1/2*B*a^5*x^2*sgn(b*x + a) + 5/2*A*a^4*b*x^2*sgn(b*x + a) + A*a^5*x*sgn(b*x + a) - 1/42*(B*a^7 - 7*A*a^6*b)*sgn(b*x + a)/b^2","B",0
690,1,190,0,0.209481," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x,x, algorithm=""giac"")","\frac{1}{6} \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + B a^{5} x \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + A a^{5} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*B*b^5*x^6*sgn(b*x + a) + B*a*b^4*x^5*sgn(b*x + a) + 1/5*A*b^5*x^5*sgn(b*x + a) + 5/2*B*a^2*b^3*x^4*sgn(b*x + a) + 5/4*A*a*b^4*x^4*sgn(b*x + a) + 10/3*B*a^3*b^2*x^3*sgn(b*x + a) + 10/3*A*a^2*b^3*x^3*sgn(b*x + a) + 5/2*B*a^4*b*x^2*sgn(b*x + a) + 5*A*a^3*b^2*x^2*sgn(b*x + a) + B*a^5*x*sgn(b*x + a) + 5*A*a^4*b*x*sgn(b*x + a) + A*a^5*log(abs(x))*sgn(b*x + a)","A",0
691,1,191,0,0.219964," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^2,x, algorithm=""giac"")","\frac{1}{5} \, B b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, B a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a b^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{2} b^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{4} b x \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} b^{2} x \mathrm{sgn}\left(b x + a\right) - \frac{A a^{5} \mathrm{sgn}\left(b x + a\right)}{x} + {\left(B a^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right)"," ",0,"1/5*B*b^5*x^5*sgn(b*x + a) + 5/4*B*a*b^4*x^4*sgn(b*x + a) + 1/4*A*b^5*x^4*sgn(b*x + a) + 10/3*B*a^2*b^3*x^3*sgn(b*x + a) + 5/3*A*a*b^4*x^3*sgn(b*x + a) + 5*B*a^3*b^2*x^2*sgn(b*x + a) + 5*A*a^2*b^3*x^2*sgn(b*x + a) + 5*B*a^4*b*x*sgn(b*x + a) + 10*A*a^3*b^2*x*sgn(b*x + a) - A*a^5*sgn(b*x + a)/x + (B*a^5*sgn(b*x + a) + 5*A*a^4*b*sgn(b*x + a))*log(abs(x))","A",0
692,1,191,0,0.166858," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, B b^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a b^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A b^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{2} b^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a b^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{3} b^{2} x \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{2} b^{3} x \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(B a^{4} b \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right) - \frac{A a^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(B a^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} x}{2 \, x^{2}}"," ",0,"1/4*B*b^5*x^4*sgn(b*x + a) + 5/3*B*a*b^4*x^3*sgn(b*x + a) + 1/3*A*b^5*x^3*sgn(b*x + a) + 5*B*a^2*b^3*x^2*sgn(b*x + a) + 5/2*A*a*b^4*x^2*sgn(b*x + a) + 10*B*a^3*b^2*x*sgn(b*x + a) + 10*A*a^2*b^3*x*sgn(b*x + a) + 5*(B*a^4*b*sgn(b*x + a) + 2*A*a^3*b^2*sgn(b*x + a))*log(abs(x)) - 1/2*(A*a^5*sgn(b*x + a) + 2*(B*a^5*sgn(b*x + a) + 5*A*a^4*b*sgn(b*x + a))*x)/x^2","A",0
693,1,190,0,0.204256," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, B b^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a b^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{2} b^{3} x \mathrm{sgn}\left(b x + a\right) + 5 \, A a b^{4} x \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(B a^{3} b^{2} \mathrm{sgn}\left(b x + a\right) + A a^{2} b^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right) - \frac{2 \, A a^{5} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(B a^{4} b \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 3 \, {\left(B a^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} x}{6 \, x^{3}}"," ",0,"1/3*B*b^5*x^3*sgn(b*x + a) + 5/2*B*a*b^4*x^2*sgn(b*x + a) + 1/2*A*b^5*x^2*sgn(b*x + a) + 10*B*a^2*b^3*x*sgn(b*x + a) + 5*A*a*b^4*x*sgn(b*x + a) + 10*(B*a^3*b^2*sgn(b*x + a) + A*a^2*b^3*sgn(b*x + a))*log(abs(x)) - 1/6*(2*A*a^5*sgn(b*x + a) + 30*(B*a^4*b*sgn(b*x + a) + 2*A*a^3*b^2*sgn(b*x + a))*x^2 + 3*(B*a^5*sgn(b*x + a) + 5*A*a^4*b*sgn(b*x + a))*x)/x^3","A",0
694,1,188,0,0.169533," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, B b^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a b^{4} x \mathrm{sgn}\left(b x + a\right) + A b^{5} x \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(2 \, B a^{2} b^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{4} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right) - \frac{3 \, A a^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(B a^{3} b^{2} \mathrm{sgn}\left(b x + a\right) + A a^{2} b^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 30 \, {\left(B a^{4} b \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 4 \, {\left(B a^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} x}{12 \, x^{4}}"," ",0,"1/2*B*b^5*x^2*sgn(b*x + a) + 5*B*a*b^4*x*sgn(b*x + a) + A*b^5*x*sgn(b*x + a) + 5*(2*B*a^2*b^3*sgn(b*x + a) + A*a*b^4*sgn(b*x + a))*log(abs(x)) - 1/12*(3*A*a^5*sgn(b*x + a) + 120*(B*a^3*b^2*sgn(b*x + a) + A*a^2*b^3*sgn(b*x + a))*x^3 + 30*(B*a^4*b*sgn(b*x + a) + 2*A*a^3*b^2*sgn(b*x + a))*x^2 + 4*(B*a^5*sgn(b*x + a) + 5*A*a^4*b*sgn(b*x + a))*x)/x^4","A",0
695,1,188,0,0.192879," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^6,x, algorithm=""giac"")","B b^{5} x \mathrm{sgn}\left(b x + a\right) + {\left(5 \, B a b^{4} \mathrm{sgn}\left(b x + a\right) + A b^{5} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right) - \frac{12 \, A a^{5} \mathrm{sgn}\left(b x + a\right) + 300 \, {\left(2 \, B a^{2} b^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{4} + 300 \, {\left(B a^{3} b^{2} \mathrm{sgn}\left(b x + a\right) + A a^{2} b^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 100 \, {\left(B a^{4} b \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 15 \, {\left(B a^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} x}{60 \, x^{5}}"," ",0,"B*b^5*x*sgn(b*x + a) + (5*B*a*b^4*sgn(b*x + a) + A*b^5*sgn(b*x + a))*log(abs(x)) - 1/60*(12*A*a^5*sgn(b*x + a) + 300*(2*B*a^2*b^3*sgn(b*x + a) + A*a*b^4*sgn(b*x + a))*x^4 + 300*(B*a^3*b^2*sgn(b*x + a) + A*a^2*b^3*sgn(b*x + a))*x^3 + 100*(B*a^4*b*sgn(b*x + a) + 2*A*a^3*b^2*sgn(b*x + a))*x^2 + 15*(B*a^5*sgn(b*x + a) + 5*A*a^4*b*sgn(b*x + a))*x)/x^5","A",0
696,1,191,0,0.169038," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^7,x, algorithm=""giac"")","B b^{5} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{10 \, A a^{5} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(5 \, B a b^{4} \mathrm{sgn}\left(b x + a\right) + A b^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{5} + 150 \, {\left(2 \, B a^{2} b^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{4} + 200 \, {\left(B a^{3} b^{2} \mathrm{sgn}\left(b x + a\right) + A a^{2} b^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 75 \, {\left(B a^{4} b \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 12 \, {\left(B a^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} x}{60 \, x^{6}}"," ",0,"B*b^5*log(abs(x))*sgn(b*x + a) - 1/60*(10*A*a^5*sgn(b*x + a) + 60*(5*B*a*b^4*sgn(b*x + a) + A*b^5*sgn(b*x + a))*x^5 + 150*(2*B*a^2*b^3*sgn(b*x + a) + A*a*b^4*sgn(b*x + a))*x^4 + 200*(B*a^3*b^2*sgn(b*x + a) + A*a^2*b^3*sgn(b*x + a))*x^3 + 75*(B*a^4*b*sgn(b*x + a) + 2*A*a^3*b^2*sgn(b*x + a))*x^2 + 12*(B*a^5*sgn(b*x + a) + 5*A*a^4*b*sgn(b*x + a))*x)/x^6","A",0
697,1,221,0,0.222916," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^8,x, algorithm=""giac"")","-\frac{{\left(7 \, B a b^{6} - A b^{7}\right)} \mathrm{sgn}\left(b x + a\right)}{42 \, a^{2}} - \frac{42 \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 105 \, B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 21 \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 70 \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 105 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 42 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 84 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 35 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{42 \, x^{7}}"," ",0,"-1/42*(7*B*a*b^6 - A*b^7)*sgn(b*x + a)/a^2 - 1/42*(42*B*b^5*x^6*sgn(b*x + a) + 105*B*a*b^4*x^5*sgn(b*x + a) + 21*A*b^5*x^5*sgn(b*x + a) + 140*B*a^2*b^3*x^4*sgn(b*x + a) + 70*A*a*b^4*x^4*sgn(b*x + a) + 105*B*a^3*b^2*x^3*sgn(b*x + a) + 105*A*a^2*b^3*x^3*sgn(b*x + a) + 42*B*a^4*b*x^2*sgn(b*x + a) + 84*A*a^3*b^2*x^2*sgn(b*x + a) + 7*B*a^5*x*sgn(b*x + a) + 35*A*a^4*b*x*sgn(b*x + a) + 6*A*a^5*sgn(b*x + a))/x^7","B",0
698,1,221,0,0.170680," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^9,x, algorithm=""giac"")","\frac{{\left(4 \, B a b^{7} - A b^{8}\right)} \mathrm{sgn}\left(b x + a\right)}{168 \, a^{3}} - \frac{84 \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 280 \, B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 56 \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 420 \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 210 \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 336 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 336 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 280 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 24 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 120 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 21 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{168 \, x^{8}}"," ",0,"1/168*(4*B*a*b^7 - A*b^8)*sgn(b*x + a)/a^3 - 1/168*(84*B*b^5*x^6*sgn(b*x + a) + 280*B*a*b^4*x^5*sgn(b*x + a) + 56*A*b^5*x^5*sgn(b*x + a) + 420*B*a^2*b^3*x^4*sgn(b*x + a) + 210*A*a*b^4*x^4*sgn(b*x + a) + 336*B*a^3*b^2*x^3*sgn(b*x + a) + 336*A*a^2*b^3*x^3*sgn(b*x + a) + 140*B*a^4*b*x^2*sgn(b*x + a) + 280*A*a^3*b^2*x^2*sgn(b*x + a) + 24*B*a^5*x*sgn(b*x + a) + 120*A*a^4*b*x*sgn(b*x + a) + 21*A*a^5*sgn(b*x + a))/x^8","B",0
699,1,221,0,0.174164," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^10,x, algorithm=""giac"")","-\frac{{\left(3 \, B a b^{8} - A b^{9}\right)} \mathrm{sgn}\left(b x + a\right)}{504 \, a^{4}} - \frac{168 \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 630 \, B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 1008 \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 504 \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 840 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 840 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 360 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 720 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 63 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 315 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 56 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{504 \, x^{9}}"," ",0,"-1/504*(3*B*a*b^8 - A*b^9)*sgn(b*x + a)/a^4 - 1/504*(168*B*b^5*x^6*sgn(b*x + a) + 630*B*a*b^4*x^5*sgn(b*x + a) + 126*A*b^5*x^5*sgn(b*x + a) + 1008*B*a^2*b^3*x^4*sgn(b*x + a) + 504*A*a*b^4*x^4*sgn(b*x + a) + 840*B*a^3*b^2*x^3*sgn(b*x + a) + 840*A*a^2*b^3*x^3*sgn(b*x + a) + 360*B*a^4*b*x^2*sgn(b*x + a) + 720*A*a^3*b^2*x^2*sgn(b*x + a) + 63*B*a^5*x*sgn(b*x + a) + 315*A*a^4*b*x*sgn(b*x + a) + 56*A*a^5*sgn(b*x + a))/x^9","A",0
700,1,221,0,0.218454," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^11,x, algorithm=""giac"")","\frac{{\left(5 \, B a b^{9} - 2 \, A b^{10}\right)} \mathrm{sgn}\left(b x + a\right)}{2520 \, a^{5}} - \frac{630 \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 2520 \, B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 504 \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 4200 \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 2100 \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 3600 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 3600 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 1575 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 3150 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 280 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 1400 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 252 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{2520 \, x^{10}}"," ",0,"1/2520*(5*B*a*b^9 - 2*A*b^10)*sgn(b*x + a)/a^5 - 1/2520*(630*B*b^5*x^6*sgn(b*x + a) + 2520*B*a*b^4*x^5*sgn(b*x + a) + 504*A*b^5*x^5*sgn(b*x + a) + 4200*B*a^2*b^3*x^4*sgn(b*x + a) + 2100*A*a*b^4*x^4*sgn(b*x + a) + 3600*B*a^3*b^2*x^3*sgn(b*x + a) + 3600*A*a^2*b^3*x^3*sgn(b*x + a) + 1575*B*a^4*b*x^2*sgn(b*x + a) + 3150*A*a^3*b^2*x^2*sgn(b*x + a) + 280*B*a^5*x*sgn(b*x + a) + 1400*A*a^4*b*x*sgn(b*x + a) + 252*A*a^5*sgn(b*x + a))/x^10","A",0
701,1,221,0,0.203389," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^12,x, algorithm=""giac"")","-\frac{{\left(11 \, B a b^{10} - 5 \, A b^{11}\right)} \mathrm{sgn}\left(b x + a\right)}{13860 \, a^{6}} - \frac{2772 \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 11550 \, B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 2310 \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 19800 \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 9900 \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 17325 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 17325 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 7700 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 15400 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 1386 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 6930 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 1260 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{13860 \, x^{11}}"," ",0,"-1/13860*(11*B*a*b^10 - 5*A*b^11)*sgn(b*x + a)/a^6 - 1/13860*(2772*B*b^5*x^6*sgn(b*x + a) + 11550*B*a*b^4*x^5*sgn(b*x + a) + 2310*A*b^5*x^5*sgn(b*x + a) + 19800*B*a^2*b^3*x^4*sgn(b*x + a) + 9900*A*a*b^4*x^4*sgn(b*x + a) + 17325*B*a^3*b^2*x^3*sgn(b*x + a) + 17325*A*a^2*b^3*x^3*sgn(b*x + a) + 7700*B*a^4*b*x^2*sgn(b*x + a) + 15400*A*a^3*b^2*x^2*sgn(b*x + a) + 1386*B*a^5*x*sgn(b*x + a) + 6930*A*a^4*b*x*sgn(b*x + a) + 1260*A*a^5*sgn(b*x + a))/x^11","A",0
702,1,221,0,0.221020," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^13,x, algorithm=""giac"")","\frac{{\left(2 \, B a b^{11} - A b^{12}\right)} \mathrm{sgn}\left(b x + a\right)}{5544 \, a^{7}} - \frac{924 \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 3960 \, B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 792 \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 6930 \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 3465 \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 6160 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 6160 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 2772 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 5544 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 504 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 2520 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 462 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{5544 \, x^{12}}"," ",0,"1/5544*(2*B*a*b^11 - A*b^12)*sgn(b*x + a)/a^7 - 1/5544*(924*B*b^5*x^6*sgn(b*x + a) + 3960*B*a*b^4*x^5*sgn(b*x + a) + 792*A*b^5*x^5*sgn(b*x + a) + 6930*B*a^2*b^3*x^4*sgn(b*x + a) + 3465*A*a*b^4*x^4*sgn(b*x + a) + 6160*B*a^3*b^2*x^3*sgn(b*x + a) + 6160*A*a^2*b^3*x^3*sgn(b*x + a) + 2772*B*a^4*b*x^2*sgn(b*x + a) + 5544*A*a^3*b^2*x^2*sgn(b*x + a) + 504*B*a^5*x*sgn(b*x + a) + 2520*A*a^4*b*x*sgn(b*x + a) + 462*A*a^5*sgn(b*x + a))/x^12","A",0
703,1,221,0,0.199532," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^14,x, algorithm=""giac"")","-\frac{{\left(13 \, B a b^{12} - 7 \, A b^{13}\right)} \mathrm{sgn}\left(b x + a\right)}{72072 \, a^{8}} - \frac{10296 \, B b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 45045 \, B a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 9009 \, A b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 80080 \, B a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 40040 \, A a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 72072 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 72072 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 32760 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 65520 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 6006 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 30030 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 5544 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{72072 \, x^{13}}"," ",0,"-1/72072*(13*B*a*b^12 - 7*A*b^13)*sgn(b*x + a)/a^8 - 1/72072*(10296*B*b^5*x^6*sgn(b*x + a) + 45045*B*a*b^4*x^5*sgn(b*x + a) + 9009*A*b^5*x^5*sgn(b*x + a) + 80080*B*a^2*b^3*x^4*sgn(b*x + a) + 40040*A*a*b^4*x^4*sgn(b*x + a) + 72072*B*a^3*b^2*x^3*sgn(b*x + a) + 72072*A*a^2*b^3*x^3*sgn(b*x + a) + 32760*B*a^4*b*x^2*sgn(b*x + a) + 65520*A*a^3*b^2*x^2*sgn(b*x + a) + 6006*B*a^5*x*sgn(b*x + a) + 30030*A*a^4*b*x*sgn(b*x + a) + 5544*A*a^5*sgn(b*x + a))/x^13","A",0
704,1,185,0,0.164481," ","integrate(x^4*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{12 \, B b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) - 15 \, B a b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, A b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, B a^{2} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) - 20 \, A a b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, B a^{3} b x^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{2} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 60 \, B a^{4} x \mathrm{sgn}\left(b x + a\right) - 60 \, A a^{3} b x \mathrm{sgn}\left(b x + a\right)}{60 \, b^{5}} - \frac{{\left(B a^{5} \mathrm{sgn}\left(b x + a\right) - A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{6}}"," ",0,"1/60*(12*B*b^4*x^5*sgn(b*x + a) - 15*B*a*b^3*x^4*sgn(b*x + a) + 15*A*b^4*x^4*sgn(b*x + a) + 20*B*a^2*b^2*x^3*sgn(b*x + a) - 20*A*a*b^3*x^3*sgn(b*x + a) - 30*B*a^3*b*x^2*sgn(b*x + a) + 30*A*a^2*b^2*x^2*sgn(b*x + a) + 60*B*a^4*x*sgn(b*x + a) - 60*A*a^3*b*x*sgn(b*x + a))/b^5 - (B*a^5*sgn(b*x + a) - A*a^4*b*sgn(b*x + a))*log(abs(b*x + a))/b^6","A",0
705,1,148,0,0.160101," ","integrate(x^3*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{3 \, B b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) - 12 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 12 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right)}{12 \, b^{4}} + \frac{{\left(B a^{4} \mathrm{sgn}\left(b x + a\right) - A a^{3} b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}}"," ",0,"1/12*(3*B*b^3*x^4*sgn(b*x + a) - 4*B*a*b^2*x^3*sgn(b*x + a) + 4*A*b^3*x^3*sgn(b*x + a) + 6*B*a^2*b*x^2*sgn(b*x + a) - 6*A*a*b^2*x^2*sgn(b*x + a) - 12*B*a^3*x*sgn(b*x + a) + 12*A*a^2*b*x*sgn(b*x + a))/b^4 + (B*a^4*sgn(b*x + a) - A*a^3*b*sgn(b*x + a))*log(abs(b*x + a))/b^5","A",0
706,1,113,0,0.153263," ","integrate(x^2*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, B b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b x^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} x \mathrm{sgn}\left(b x + a\right) - 6 \, A a b x \mathrm{sgn}\left(b x + a\right)}{6 \, b^{3}} - \frac{{\left(B a^{3} \mathrm{sgn}\left(b x + a\right) - A a^{2} b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}}"," ",0,"1/6*(2*B*b^2*x^3*sgn(b*x + a) - 3*B*a*b*x^2*sgn(b*x + a) + 3*A*b^2*x^2*sgn(b*x + a) + 6*B*a^2*x*sgn(b*x + a) - 6*A*a*b*x*sgn(b*x + a))/b^3 - (B*a^3*sgn(b*x + a) - A*a^2*b*sgn(b*x + a))*log(abs(b*x + a))/b^4","A",0
707,1,75,0,0.151863," ","integrate(x*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{B b x^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, B a x \mathrm{sgn}\left(b x + a\right) + 2 \, A b x \mathrm{sgn}\left(b x + a\right)}{2 \, b^{2}} + \frac{{\left(B a^{2} \mathrm{sgn}\left(b x + a\right) - A a b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}}"," ",0,"1/2*(B*b*x^2*sgn(b*x + a) - 2*B*a*x*sgn(b*x + a) + 2*A*b*x*sgn(b*x + a))/b^2 + (B*a^2*sgn(b*x + a) - A*a*b*sgn(b*x + a))*log(abs(b*x + a))/b^3","A",0
708,1,45,0,0.163345," ","integrate((B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{B x \mathrm{sgn}\left(b x + a\right)}{b} - \frac{{\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{2}}"," ",0,"B*x*sgn(b*x + a)/b - (B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*log(abs(b*x + a))/b^2","A",0
709,1,49,0,0.156276," ","integrate((B*x+A)/x/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{A \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right)}{a} + \frac{{\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{a b}"," ",0,"A*log(abs(x))*sgn(b*x + a)/a + (B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*log(abs(b*x + a))/(a*b)","A",0
710,1,81,0,0.156938," ","integrate((B*x+A)/x^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right)}{a^{2}} - \frac{A \mathrm{sgn}\left(b x + a\right)}{a x} - \frac{{\left(B a b \mathrm{sgn}\left(b x + a\right) - A b^{2} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{a^{2} b}"," ",0,"(B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*log(abs(x))/a^2 - A*sgn(b*x + a)/(a*x) - (B*a*b*sgn(b*x + a) - A*b^2*sgn(b*x + a))*log(abs(b*x + a))/(a^2*b)","A",0
711,1,117,0,0.154637," ","integrate((B*x+A)/x^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(B a b \mathrm{sgn}\left(b x + a\right) - A b^{2} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right)}{a^{3}} + \frac{{\left(B a b^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{a^{3} b} - \frac{A a^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(B a^{2} \mathrm{sgn}\left(b x + a\right) - A a b \mathrm{sgn}\left(b x + a\right)\right)} x}{2 \, a^{3} x^{2}}"," ",0,"-(B*a*b*sgn(b*x + a) - A*b^2*sgn(b*x + a))*log(abs(x))/a^3 + (B*a*b^2*sgn(b*x + a) - A*b^3*sgn(b*x + a))*log(abs(b*x + a))/(a^3*b) - 1/2*(A*a^2*sgn(b*x + a) + 2*(B*a^2*sgn(b*x + a) - A*a*b*sgn(b*x + a))*x)/(a^3*x^2)","A",0
712,1,153,0,0.159863," ","integrate((B*x+A)/x^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(B a b^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right)}{a^{4}} - \frac{{\left(B a b^{3} \mathrm{sgn}\left(b x + a\right) - A b^{4} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{a^{4} b} - \frac{2 \, A a^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(B a^{2} b \mathrm{sgn}\left(b x + a\right) - A a b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 3 \, {\left(B a^{3} \mathrm{sgn}\left(b x + a\right) - A a^{2} b \mathrm{sgn}\left(b x + a\right)\right)} x}{6 \, a^{4} x^{3}}"," ",0,"(B*a*b^2*sgn(b*x + a) - A*b^3*sgn(b*x + a))*log(abs(x))/a^4 - (B*a*b^3*sgn(b*x + a) - A*b^4*sgn(b*x + a))*log(abs(b*x + a))/(a^4*b) - 1/6*(2*A*a^3*sgn(b*x + a) - 6*(B*a^2*b*sgn(b*x + a) - A*a*b^2*sgn(b*x + a))*x^2 + 3*(B*a^3*sgn(b*x + a) - A*a^2*b*sgn(b*x + a))*x)/(a^4*x^3)","A",0
713,1,188,0,0.231353," ","integrate((B*x+A)/x^5/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(B a b^{3} \mathrm{sgn}\left(b x + a\right) - A b^{4} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x \right|}\right)}{a^{5}} + \frac{{\left(B a b^{4} \mathrm{sgn}\left(b x + a\right) - A b^{5} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{a^{5} b} - \frac{3 \, A a^{4} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(B a^{2} b^{2} \mathrm{sgn}\left(b x + a\right) - A a b^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} - 6 \, {\left(B a^{3} b \mathrm{sgn}\left(b x + a\right) - A a^{2} b^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 4 \, {\left(B a^{4} \mathrm{sgn}\left(b x + a\right) - A a^{3} b \mathrm{sgn}\left(b x + a\right)\right)} x}{12 \, a^{5} x^{4}}"," ",0,"-(B*a*b^3*sgn(b*x + a) - A*b^4*sgn(b*x + a))*log(abs(x))/a^5 + (B*a*b^4*sgn(b*x + a) - A*b^5*sgn(b*x + a))*log(abs(b*x + a))/(a^5*b) - 1/12*(3*A*a^4*sgn(b*x + a) + 12*(B*a^2*b^2*sgn(b*x + a) - A*a*b^3*sgn(b*x + a))*x^3 - 6*(B*a^3*b*sgn(b*x + a) - A*a^2*b^2*sgn(b*x + a))*x^2 + 4*(B*a^4*sgn(b*x + a) - A*a^3*b*sgn(b*x + a))*x)/(a^5*x^4)","A",0
714,0,0,0,0.000000," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
715,0,0,0,0.000000," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
716,0,0,0,0.000000," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
717,0,0,0,0.000000," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
718,0,0,0,0.000000," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
719,0,0,0,0.000000," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
720,0,0,0,0.000000," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
721,0,0,0,0.000000," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
722,0,0,0,0.000000," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
723,0,0,0,0.000000," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
724,0,0,0,0.000000," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
725,0,0,0,0.000000," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
726,0,0,0,0.000000," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
727,0,0,0,0.000000," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
728,0,0,0,0.000000," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
729,1,53,0,0.149692," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{4}{13} \, B a b x^{\frac{13}{2}} + \frac{2}{13} \, A b^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{4}{11} \, A a b x^{\frac{11}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}}"," ",0,"2/15*B*b^2*x^(15/2) + 4/13*B*a*b*x^(13/2) + 2/13*A*b^2*x^(13/2) + 2/11*B*a^2*x^(11/2) + 4/11*A*a*b*x^(11/2) + 2/9*A*a^2*x^(9/2)","A",0
730,1,53,0,0.163562," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{4}{11} \, B a b x^{\frac{11}{2}} + \frac{2}{11} \, A b^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B a^{2} x^{\frac{9}{2}} + \frac{4}{9} \, A a b x^{\frac{9}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}}"," ",0,"2/13*B*b^2*x^(13/2) + 4/11*B*a*b*x^(11/2) + 2/11*A*b^2*x^(11/2) + 2/9*B*a^2*x^(9/2) + 4/9*A*a*b*x^(9/2) + 2/7*A*a^2*x^(7/2)","A",0
731,1,53,0,0.152351," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{11} \, B b^{2} x^{\frac{11}{2}} + \frac{4}{9} \, B a b x^{\frac{9}{2}} + \frac{2}{9} \, A b^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B a^{2} x^{\frac{7}{2}} + \frac{4}{7} \, A a b x^{\frac{7}{2}} + \frac{2}{5} \, A a^{2} x^{\frac{5}{2}}"," ",0,"2/11*B*b^2*x^(11/2) + 4/9*B*a*b*x^(9/2) + 2/9*A*b^2*x^(9/2) + 2/7*B*a^2*x^(7/2) + 4/7*A*a*b*x^(7/2) + 2/5*A*a^2*x^(5/2)","A",0
732,1,53,0,0.152989," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)*x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, B b^{2} x^{\frac{9}{2}} + \frac{4}{7} \, B a b x^{\frac{7}{2}} + \frac{2}{7} \, A b^{2} x^{\frac{7}{2}} + \frac{2}{5} \, B a^{2} x^{\frac{5}{2}} + \frac{4}{5} \, A a b x^{\frac{5}{2}} + \frac{2}{3} \, A a^{2} x^{\frac{3}{2}}"," ",0,"2/9*B*b^2*x^(9/2) + 4/7*B*a*b*x^(7/2) + 2/7*A*b^2*x^(7/2) + 2/5*B*a^2*x^(5/2) + 4/5*A*a*b*x^(5/2) + 2/3*A*a^2*x^(3/2)","A",0
733,1,53,0,0.179900," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{7} \, B b^{2} x^{\frac{7}{2}} + \frac{4}{5} \, B a b x^{\frac{5}{2}} + \frac{2}{5} \, A b^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B a^{2} x^{\frac{3}{2}} + \frac{4}{3} \, A a b x^{\frac{3}{2}} + 2 \, A a^{2} \sqrt{x}"," ",0,"2/7*B*b^2*x^(7/2) + 4/5*B*a*b*x^(5/2) + 2/5*A*b^2*x^(5/2) + 2/3*B*a^2*x^(3/2) + 4/3*A*a*b*x^(3/2) + 2*A*a^2*sqrt(x)","A",0
734,1,53,0,0.158206," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, B b^{2} x^{\frac{5}{2}} + \frac{4}{3} \, B a b x^{\frac{3}{2}} + \frac{2}{3} \, A b^{2} x^{\frac{3}{2}} + 2 \, B a^{2} \sqrt{x} + 4 \, A a b \sqrt{x} - \frac{2 \, A a^{2}}{\sqrt{x}}"," ",0,"2/5*B*b^2*x^(5/2) + 4/3*B*a*b*x^(3/2) + 2/3*A*b^2*x^(3/2) + 2*B*a^2*sqrt(x) + 4*A*a*b*sqrt(x) - 2*A*a^2/sqrt(x)","A",0
735,1,51,0,0.151440," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, B b^{2} x^{\frac{3}{2}} + 4 \, B a b \sqrt{x} + 2 \, A b^{2} \sqrt{x} - \frac{2 \, {\left(3 \, B a^{2} x + 6 \, A a b x + A a^{2}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*B*b^2*x^(3/2) + 4*B*a*b*sqrt(x) + 2*A*b^2*sqrt(x) - 2/3*(3*B*a^2*x + 6*A*a*b*x + A*a^2)/x^(3/2)","A",0
736,1,52,0,0.151835," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(7/2),x, algorithm=""giac"")","2 \, B b^{2} \sqrt{x} - \frac{2 \, {\left(30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 5 \, B a^{2} x + 10 \, A a b x + 3 \, A a^{2}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2*B*b^2*sqrt(x) - 2/15*(30*B*a*b*x^2 + 15*A*b^2*x^2 + 5*B*a^2*x + 10*A*a*b*x + 3*A*a^2)/x^(5/2)","A",0
737,1,51,0,0.176615," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, B b^{2} x^{3} + 70 \, B a b x^{2} + 35 \, A b^{2} x^{2} + 21 \, B a^{2} x + 42 \, A a b x + 15 \, A a^{2}\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(105*B*b^2*x^3 + 70*B*a*b*x^2 + 35*A*b^2*x^2 + 21*B*a^2*x + 42*A*a*b*x + 15*A*a^2)/x^(7/2)","A",0
738,1,101,0,0.187693," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{19} \, B b^{4} x^{\frac{19}{2}} + \frac{8}{17} \, B a b^{3} x^{\frac{17}{2}} + \frac{2}{17} \, A b^{4} x^{\frac{17}{2}} + \frac{4}{5} \, B a^{2} b^{2} x^{\frac{15}{2}} + \frac{8}{15} \, A a b^{3} x^{\frac{15}{2}} + \frac{8}{13} \, B a^{3} b x^{\frac{13}{2}} + \frac{12}{13} \, A a^{2} b^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B a^{4} x^{\frac{11}{2}} + \frac{8}{11} \, A a^{3} b x^{\frac{11}{2}} + \frac{2}{9} \, A a^{4} x^{\frac{9}{2}}"," ",0,"2/19*B*b^4*x^(19/2) + 8/17*B*a*b^3*x^(17/2) + 2/17*A*b^4*x^(17/2) + 4/5*B*a^2*b^2*x^(15/2) + 8/15*A*a*b^3*x^(15/2) + 8/13*B*a^3*b*x^(13/2) + 12/13*A*a^2*b^2*x^(13/2) + 2/11*B*a^4*x^(11/2) + 8/11*A*a^3*b*x^(11/2) + 2/9*A*a^4*x^(9/2)","A",0
739,1,101,0,0.155852," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{17} \, B b^{4} x^{\frac{17}{2}} + \frac{8}{15} \, B a b^{3} x^{\frac{15}{2}} + \frac{2}{15} \, A b^{4} x^{\frac{15}{2}} + \frac{12}{13} \, B a^{2} b^{2} x^{\frac{13}{2}} + \frac{8}{13} \, A a b^{3} x^{\frac{13}{2}} + \frac{8}{11} \, B a^{3} b x^{\frac{11}{2}} + \frac{12}{11} \, A a^{2} b^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B a^{4} x^{\frac{9}{2}} + \frac{8}{9} \, A a^{3} b x^{\frac{9}{2}} + \frac{2}{7} \, A a^{4} x^{\frac{7}{2}}"," ",0,"2/17*B*b^4*x^(17/2) + 8/15*B*a*b^3*x^(15/2) + 2/15*A*b^4*x^(15/2) + 12/13*B*a^2*b^2*x^(13/2) + 8/13*A*a*b^3*x^(13/2) + 8/11*B*a^3*b*x^(11/2) + 12/11*A*a^2*b^2*x^(11/2) + 2/9*B*a^4*x^(9/2) + 8/9*A*a^3*b*x^(9/2) + 2/7*A*a^4*x^(7/2)","A",0
740,1,101,0,0.153007," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{15} \, B b^{4} x^{\frac{15}{2}} + \frac{8}{13} \, B a b^{3} x^{\frac{13}{2}} + \frac{2}{13} \, A b^{4} x^{\frac{13}{2}} + \frac{12}{11} \, B a^{2} b^{2} x^{\frac{11}{2}} + \frac{8}{11} \, A a b^{3} x^{\frac{11}{2}} + \frac{8}{9} \, B a^{3} b x^{\frac{9}{2}} + \frac{4}{3} \, A a^{2} b^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B a^{4} x^{\frac{7}{2}} + \frac{8}{7} \, A a^{3} b x^{\frac{7}{2}} + \frac{2}{5} \, A a^{4} x^{\frac{5}{2}}"," ",0,"2/15*B*b^4*x^(15/2) + 8/13*B*a*b^3*x^(13/2) + 2/13*A*b^4*x^(13/2) + 12/11*B*a^2*b^2*x^(11/2) + 8/11*A*a*b^3*x^(11/2) + 8/9*B*a^3*b*x^(9/2) + 4/3*A*a^2*b^2*x^(9/2) + 2/7*B*a^4*x^(7/2) + 8/7*A*a^3*b*x^(7/2) + 2/5*A*a^4*x^(5/2)","A",0
741,1,101,0,0.152271," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2*x^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, B b^{4} x^{\frac{13}{2}} + \frac{8}{11} \, B a b^{3} x^{\frac{11}{2}} + \frac{2}{11} \, A b^{4} x^{\frac{11}{2}} + \frac{4}{3} \, B a^{2} b^{2} x^{\frac{9}{2}} + \frac{8}{9} \, A a b^{3} x^{\frac{9}{2}} + \frac{8}{7} \, B a^{3} b x^{\frac{7}{2}} + \frac{12}{7} \, A a^{2} b^{2} x^{\frac{7}{2}} + \frac{2}{5} \, B a^{4} x^{\frac{5}{2}} + \frac{8}{5} \, A a^{3} b x^{\frac{5}{2}} + \frac{2}{3} \, A a^{4} x^{\frac{3}{2}}"," ",0,"2/13*B*b^4*x^(13/2) + 8/11*B*a*b^3*x^(11/2) + 2/11*A*b^4*x^(11/2) + 4/3*B*a^2*b^2*x^(9/2) + 8/9*A*a*b^3*x^(9/2) + 8/7*B*a^3*b*x^(7/2) + 12/7*A*a^2*b^2*x^(7/2) + 2/5*B*a^4*x^(5/2) + 8/5*A*a^3*b*x^(5/2) + 2/3*A*a^4*x^(3/2)","A",0
742,1,101,0,0.153588," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, B b^{4} x^{\frac{11}{2}} + \frac{8}{9} \, B a b^{3} x^{\frac{9}{2}} + \frac{2}{9} \, A b^{4} x^{\frac{9}{2}} + \frac{12}{7} \, B a^{2} b^{2} x^{\frac{7}{2}} + \frac{8}{7} \, A a b^{3} x^{\frac{7}{2}} + \frac{8}{5} \, B a^{3} b x^{\frac{5}{2}} + \frac{12}{5} \, A a^{2} b^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B a^{4} x^{\frac{3}{2}} + \frac{8}{3} \, A a^{3} b x^{\frac{3}{2}} + 2 \, A a^{4} \sqrt{x}"," ",0,"2/11*B*b^4*x^(11/2) + 8/9*B*a*b^3*x^(9/2) + 2/9*A*b^4*x^(9/2) + 12/7*B*a^2*b^2*x^(7/2) + 8/7*A*a*b^3*x^(7/2) + 8/5*B*a^3*b*x^(5/2) + 12/5*A*a^2*b^2*x^(5/2) + 2/3*B*a^4*x^(3/2) + 8/3*A*a^3*b*x^(3/2) + 2*A*a^4*sqrt(x)","A",0
743,1,101,0,0.198354," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{9} \, B b^{4} x^{\frac{9}{2}} + \frac{8}{7} \, B a b^{3} x^{\frac{7}{2}} + \frac{2}{7} \, A b^{4} x^{\frac{7}{2}} + \frac{12}{5} \, B a^{2} b^{2} x^{\frac{5}{2}} + \frac{8}{5} \, A a b^{3} x^{\frac{5}{2}} + \frac{8}{3} \, B a^{3} b x^{\frac{3}{2}} + 4 \, A a^{2} b^{2} x^{\frac{3}{2}} + 2 \, B a^{4} \sqrt{x} + 8 \, A a^{3} b \sqrt{x} - \frac{2 \, A a^{4}}{\sqrt{x}}"," ",0,"2/9*B*b^4*x^(9/2) + 8/7*B*a*b^3*x^(7/2) + 2/7*A*b^4*x^(7/2) + 12/5*B*a^2*b^2*x^(5/2) + 8/5*A*a*b^3*x^(5/2) + 8/3*B*a^3*b*x^(3/2) + 4*A*a^2*b^2*x^(3/2) + 2*B*a^4*sqrt(x) + 8*A*a^3*b*sqrt(x) - 2*A*a^4/sqrt(x)","A",0
744,1,99,0,0.163130," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, B b^{4} x^{\frac{7}{2}} + \frac{8}{5} \, B a b^{3} x^{\frac{5}{2}} + \frac{2}{5} \, A b^{4} x^{\frac{5}{2}} + 4 \, B a^{2} b^{2} x^{\frac{3}{2}} + \frac{8}{3} \, A a b^{3} x^{\frac{3}{2}} + 8 \, B a^{3} b \sqrt{x} + 12 \, A a^{2} b^{2} \sqrt{x} - \frac{2 \, {\left(3 \, B a^{4} x + 12 \, A a^{3} b x + A a^{4}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/7*B*b^4*x^(7/2) + 8/5*B*a*b^3*x^(5/2) + 2/5*A*b^4*x^(5/2) + 4*B*a^2*b^2*x^(3/2) + 8/3*A*a*b^3*x^(3/2) + 8*B*a^3*b*sqrt(x) + 12*A*a^2*b^2*sqrt(x) - 2/3*(3*B*a^4*x + 12*A*a^3*b*x + A*a^4)/x^(3/2)","A",0
745,1,100,0,0.194057," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{5} \, B b^{4} x^{\frac{5}{2}} + \frac{8}{3} \, B a b^{3} x^{\frac{3}{2}} + \frac{2}{3} \, A b^{4} x^{\frac{3}{2}} + 12 \, B a^{2} b^{2} \sqrt{x} + 8 \, A a b^{3} \sqrt{x} - \frac{2 \, {\left(60 \, B a^{3} b x^{2} + 90 \, A a^{2} b^{2} x^{2} + 5 \, B a^{4} x + 20 \, A a^{3} b x + 3 \, A a^{4}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/5*B*b^4*x^(5/2) + 8/3*B*a*b^3*x^(3/2) + 2/3*A*b^4*x^(3/2) + 12*B*a^2*b^2*sqrt(x) + 8*A*a*b^3*sqrt(x) - 2/15*(60*B*a^3*b*x^2 + 90*A*a^2*b^2*x^2 + 5*B*a^4*x + 20*A*a^3*b*x + 3*A*a^4)/x^(5/2)","A",0
746,1,100,0,0.174015," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(9/2),x, algorithm=""giac"")","\frac{2}{3} \, B b^{4} x^{\frac{3}{2}} + 8 \, B a b^{3} \sqrt{x} + 2 \, A b^{4} \sqrt{x} - \frac{2 \, {\left(630 \, B a^{2} b^{2} x^{3} + 420 \, A a b^{3} x^{3} + 140 \, B a^{3} b x^{2} + 210 \, A a^{2} b^{2} x^{2} + 21 \, B a^{4} x + 84 \, A a^{3} b x + 15 \, A a^{4}\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"2/3*B*b^4*x^(3/2) + 8*B*a*b^3*sqrt(x) + 2*A*b^4*sqrt(x) - 2/105*(630*B*a^2*b^2*x^3 + 420*A*a*b^3*x^3 + 140*B*a^3*b*x^2 + 210*A*a^2*b^2*x^2 + 21*B*a^4*x + 84*A*a^3*b*x + 15*A*a^4)/x^(7/2)","A",0
747,1,149,0,0.165216," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{23} \, B b^{6} x^{\frac{23}{2}} + \frac{4}{7} \, B a b^{5} x^{\frac{21}{2}} + \frac{2}{21} \, A b^{6} x^{\frac{21}{2}} + \frac{30}{19} \, B a^{2} b^{4} x^{\frac{19}{2}} + \frac{12}{19} \, A a b^{5} x^{\frac{19}{2}} + \frac{40}{17} \, B a^{3} b^{3} x^{\frac{17}{2}} + \frac{30}{17} \, A a^{2} b^{4} x^{\frac{17}{2}} + 2 \, B a^{4} b^{2} x^{\frac{15}{2}} + \frac{8}{3} \, A a^{3} b^{3} x^{\frac{15}{2}} + \frac{12}{13} \, B a^{5} b x^{\frac{13}{2}} + \frac{30}{13} \, A a^{4} b^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B a^{6} x^{\frac{11}{2}} + \frac{12}{11} \, A a^{5} b x^{\frac{11}{2}} + \frac{2}{9} \, A a^{6} x^{\frac{9}{2}}"," ",0,"2/23*B*b^6*x^(23/2) + 4/7*B*a*b^5*x^(21/2) + 2/21*A*b^6*x^(21/2) + 30/19*B*a^2*b^4*x^(19/2) + 12/19*A*a*b^5*x^(19/2) + 40/17*B*a^3*b^3*x^(17/2) + 30/17*A*a^2*b^4*x^(17/2) + 2*B*a^4*b^2*x^(15/2) + 8/3*A*a^3*b^3*x^(15/2) + 12/13*B*a^5*b*x^(13/2) + 30/13*A*a^4*b^2*x^(13/2) + 2/11*B*a^6*x^(11/2) + 12/11*A*a^5*b*x^(11/2) + 2/9*A*a^6*x^(9/2)","A",0
748,1,149,0,0.155807," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{21} \, B b^{6} x^{\frac{21}{2}} + \frac{12}{19} \, B a b^{5} x^{\frac{19}{2}} + \frac{2}{19} \, A b^{6} x^{\frac{19}{2}} + \frac{30}{17} \, B a^{2} b^{4} x^{\frac{17}{2}} + \frac{12}{17} \, A a b^{5} x^{\frac{17}{2}} + \frac{8}{3} \, B a^{3} b^{3} x^{\frac{15}{2}} + 2 \, A a^{2} b^{4} x^{\frac{15}{2}} + \frac{30}{13} \, B a^{4} b^{2} x^{\frac{13}{2}} + \frac{40}{13} \, A a^{3} b^{3} x^{\frac{13}{2}} + \frac{12}{11} \, B a^{5} b x^{\frac{11}{2}} + \frac{30}{11} \, A a^{4} b^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B a^{6} x^{\frac{9}{2}} + \frac{4}{3} \, A a^{5} b x^{\frac{9}{2}} + \frac{2}{7} \, A a^{6} x^{\frac{7}{2}}"," ",0,"2/21*B*b^6*x^(21/2) + 12/19*B*a*b^5*x^(19/2) + 2/19*A*b^6*x^(19/2) + 30/17*B*a^2*b^4*x^(17/2) + 12/17*A*a*b^5*x^(17/2) + 8/3*B*a^3*b^3*x^(15/2) + 2*A*a^2*b^4*x^(15/2) + 30/13*B*a^4*b^2*x^(13/2) + 40/13*A*a^3*b^3*x^(13/2) + 12/11*B*a^5*b*x^(11/2) + 30/11*A*a^4*b^2*x^(11/2) + 2/9*B*a^6*x^(9/2) + 4/3*A*a^5*b*x^(9/2) + 2/7*A*a^6*x^(7/2)","A",0
749,1,149,0,0.158693," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{19} \, B b^{6} x^{\frac{19}{2}} + \frac{12}{17} \, B a b^{5} x^{\frac{17}{2}} + \frac{2}{17} \, A b^{6} x^{\frac{17}{2}} + 2 \, B a^{2} b^{4} x^{\frac{15}{2}} + \frac{4}{5} \, A a b^{5} x^{\frac{15}{2}} + \frac{40}{13} \, B a^{3} b^{3} x^{\frac{13}{2}} + \frac{30}{13} \, A a^{2} b^{4} x^{\frac{13}{2}} + \frac{30}{11} \, B a^{4} b^{2} x^{\frac{11}{2}} + \frac{40}{11} \, A a^{3} b^{3} x^{\frac{11}{2}} + \frac{4}{3} \, B a^{5} b x^{\frac{9}{2}} + \frac{10}{3} \, A a^{4} b^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B a^{6} x^{\frac{7}{2}} + \frac{12}{7} \, A a^{5} b x^{\frac{7}{2}} + \frac{2}{5} \, A a^{6} x^{\frac{5}{2}}"," ",0,"2/19*B*b^6*x^(19/2) + 12/17*B*a*b^5*x^(17/2) + 2/17*A*b^6*x^(17/2) + 2*B*a^2*b^4*x^(15/2) + 4/5*A*a*b^5*x^(15/2) + 40/13*B*a^3*b^3*x^(13/2) + 30/13*A*a^2*b^4*x^(13/2) + 30/11*B*a^4*b^2*x^(11/2) + 40/11*A*a^3*b^3*x^(11/2) + 4/3*B*a^5*b*x^(9/2) + 10/3*A*a^4*b^2*x^(9/2) + 2/7*B*a^6*x^(7/2) + 12/7*A*a^5*b*x^(7/2) + 2/5*A*a^6*x^(5/2)","A",0
750,1,149,0,0.174414," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3*x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, B b^{6} x^{\frac{17}{2}} + \frac{4}{5} \, B a b^{5} x^{\frac{15}{2}} + \frac{2}{15} \, A b^{6} x^{\frac{15}{2}} + \frac{30}{13} \, B a^{2} b^{4} x^{\frac{13}{2}} + \frac{12}{13} \, A a b^{5} x^{\frac{13}{2}} + \frac{40}{11} \, B a^{3} b^{3} x^{\frac{11}{2}} + \frac{30}{11} \, A a^{2} b^{4} x^{\frac{11}{2}} + \frac{10}{3} \, B a^{4} b^{2} x^{\frac{9}{2}} + \frac{40}{9} \, A a^{3} b^{3} x^{\frac{9}{2}} + \frac{12}{7} \, B a^{5} b x^{\frac{7}{2}} + \frac{30}{7} \, A a^{4} b^{2} x^{\frac{7}{2}} + \frac{2}{5} \, B a^{6} x^{\frac{5}{2}} + \frac{12}{5} \, A a^{5} b x^{\frac{5}{2}} + \frac{2}{3} \, A a^{6} x^{\frac{3}{2}}"," ",0,"2/17*B*b^6*x^(17/2) + 4/5*B*a*b^5*x^(15/2) + 2/15*A*b^6*x^(15/2) + 30/13*B*a^2*b^4*x^(13/2) + 12/13*A*a*b^5*x^(13/2) + 40/11*B*a^3*b^3*x^(11/2) + 30/11*A*a^2*b^4*x^(11/2) + 10/3*B*a^4*b^2*x^(9/2) + 40/9*A*a^3*b^3*x^(9/2) + 12/7*B*a^5*b*x^(7/2) + 30/7*A*a^4*b^2*x^(7/2) + 2/5*B*a^6*x^(5/2) + 12/5*A*a^5*b*x^(5/2) + 2/3*A*a^6*x^(3/2)","A",0
751,1,149,0,0.158247," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, B b^{6} x^{\frac{15}{2}} + \frac{12}{13} \, B a b^{5} x^{\frac{13}{2}} + \frac{2}{13} \, A b^{6} x^{\frac{13}{2}} + \frac{30}{11} \, B a^{2} b^{4} x^{\frac{11}{2}} + \frac{12}{11} \, A a b^{5} x^{\frac{11}{2}} + \frac{40}{9} \, B a^{3} b^{3} x^{\frac{9}{2}} + \frac{10}{3} \, A a^{2} b^{4} x^{\frac{9}{2}} + \frac{30}{7} \, B a^{4} b^{2} x^{\frac{7}{2}} + \frac{40}{7} \, A a^{3} b^{3} x^{\frac{7}{2}} + \frac{12}{5} \, B a^{5} b x^{\frac{5}{2}} + 6 \, A a^{4} b^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B a^{6} x^{\frac{3}{2}} + 4 \, A a^{5} b x^{\frac{3}{2}} + 2 \, A a^{6} \sqrt{x}"," ",0,"2/15*B*b^6*x^(15/2) + 12/13*B*a*b^5*x^(13/2) + 2/13*A*b^6*x^(13/2) + 30/11*B*a^2*b^4*x^(11/2) + 12/11*A*a*b^5*x^(11/2) + 40/9*B*a^3*b^3*x^(9/2) + 10/3*A*a^2*b^4*x^(9/2) + 30/7*B*a^4*b^2*x^(7/2) + 40/7*A*a^3*b^3*x^(7/2) + 12/5*B*a^5*b*x^(5/2) + 6*A*a^4*b^2*x^(5/2) + 2/3*B*a^6*x^(3/2) + 4*A*a^5*b*x^(3/2) + 2*A*a^6*sqrt(x)","A",0
752,1,149,0,0.161584," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{13} \, B b^{6} x^{\frac{13}{2}} + \frac{12}{11} \, B a b^{5} x^{\frac{11}{2}} + \frac{2}{11} \, A b^{6} x^{\frac{11}{2}} + \frac{10}{3} \, B a^{2} b^{4} x^{\frac{9}{2}} + \frac{4}{3} \, A a b^{5} x^{\frac{9}{2}} + \frac{40}{7} \, B a^{3} b^{3} x^{\frac{7}{2}} + \frac{30}{7} \, A a^{2} b^{4} x^{\frac{7}{2}} + 6 \, B a^{4} b^{2} x^{\frac{5}{2}} + 8 \, A a^{3} b^{3} x^{\frac{5}{2}} + 4 \, B a^{5} b x^{\frac{3}{2}} + 10 \, A a^{4} b^{2} x^{\frac{3}{2}} + 2 \, B a^{6} \sqrt{x} + 12 \, A a^{5} b \sqrt{x} - \frac{2 \, A a^{6}}{\sqrt{x}}"," ",0,"2/13*B*b^6*x^(13/2) + 12/11*B*a*b^5*x^(11/2) + 2/11*A*b^6*x^(11/2) + 10/3*B*a^2*b^4*x^(9/2) + 4/3*A*a*b^5*x^(9/2) + 40/7*B*a^3*b^3*x^(7/2) + 30/7*A*a^2*b^4*x^(7/2) + 6*B*a^4*b^2*x^(5/2) + 8*A*a^3*b^3*x^(5/2) + 4*B*a^5*b*x^(3/2) + 10*A*a^4*b^2*x^(3/2) + 2*B*a^6*sqrt(x) + 12*A*a^5*b*sqrt(x) - 2*A*a^6/sqrt(x)","A",0
753,1,147,0,0.166167," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{11} \, B b^{6} x^{\frac{11}{2}} + \frac{4}{3} \, B a b^{5} x^{\frac{9}{2}} + \frac{2}{9} \, A b^{6} x^{\frac{9}{2}} + \frac{30}{7} \, B a^{2} b^{4} x^{\frac{7}{2}} + \frac{12}{7} \, A a b^{5} x^{\frac{7}{2}} + 8 \, B a^{3} b^{3} x^{\frac{5}{2}} + 6 \, A a^{2} b^{4} x^{\frac{5}{2}} + 10 \, B a^{4} b^{2} x^{\frac{3}{2}} + \frac{40}{3} \, A a^{3} b^{3} x^{\frac{3}{2}} + 12 \, B a^{5} b \sqrt{x} + 30 \, A a^{4} b^{2} \sqrt{x} - \frac{2 \, {\left(3 \, B a^{6} x + 18 \, A a^{5} b x + A a^{6}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/11*B*b^6*x^(11/2) + 4/3*B*a*b^5*x^(9/2) + 2/9*A*b^6*x^(9/2) + 30/7*B*a^2*b^4*x^(7/2) + 12/7*A*a*b^5*x^(7/2) + 8*B*a^3*b^3*x^(5/2) + 6*A*a^2*b^4*x^(5/2) + 10*B*a^4*b^2*x^(3/2) + 40/3*A*a^3*b^3*x^(3/2) + 12*B*a^5*b*sqrt(x) + 30*A*a^4*b^2*sqrt(x) - 2/3*(3*B*a^6*x + 18*A*a^5*b*x + A*a^6)/x^(3/2)","A",0
754,1,148,0,0.195319," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{9} \, B b^{6} x^{\frac{9}{2}} + \frac{12}{7} \, B a b^{5} x^{\frac{7}{2}} + \frac{2}{7} \, A b^{6} x^{\frac{7}{2}} + 6 \, B a^{2} b^{4} x^{\frac{5}{2}} + \frac{12}{5} \, A a b^{5} x^{\frac{5}{2}} + \frac{40}{3} \, B a^{3} b^{3} x^{\frac{3}{2}} + 10 \, A a^{2} b^{4} x^{\frac{3}{2}} + 30 \, B a^{4} b^{2} \sqrt{x} + 40 \, A a^{3} b^{3} \sqrt{x} - \frac{2 \, {\left(90 \, B a^{5} b x^{2} + 225 \, A a^{4} b^{2} x^{2} + 5 \, B a^{6} x + 30 \, A a^{5} b x + 3 \, A a^{6}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/9*B*b^6*x^(9/2) + 12/7*B*a*b^5*x^(7/2) + 2/7*A*b^6*x^(7/2) + 6*B*a^2*b^4*x^(5/2) + 12/5*A*a*b^5*x^(5/2) + 40/3*B*a^3*b^3*x^(3/2) + 10*A*a^2*b^4*x^(3/2) + 30*B*a^4*b^2*sqrt(x) + 40*A*a^3*b^3*sqrt(x) - 2/15*(90*B*a^5*b*x^2 + 225*A*a^4*b^2*x^2 + 5*B*a^6*x + 30*A*a^5*b*x + 3*A*a^6)/x^(5/2)","A",0
755,1,148,0,0.179318," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(9/2),x, algorithm=""giac"")","\frac{2}{7} \, B b^{6} x^{\frac{7}{2}} + \frac{12}{5} \, B a b^{5} x^{\frac{5}{2}} + \frac{2}{5} \, A b^{6} x^{\frac{5}{2}} + 10 \, B a^{2} b^{4} x^{\frac{3}{2}} + 4 \, A a b^{5} x^{\frac{3}{2}} + 40 \, B a^{3} b^{3} \sqrt{x} + 30 \, A a^{2} b^{4} \sqrt{x} - \frac{2 \, {\left(525 \, B a^{4} b^{2} x^{3} + 700 \, A a^{3} b^{3} x^{3} + 70 \, B a^{5} b x^{2} + 175 \, A a^{4} b^{2} x^{2} + 7 \, B a^{6} x + 42 \, A a^{5} b x + 5 \, A a^{6}\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"2/7*B*b^6*x^(7/2) + 12/5*B*a*b^5*x^(5/2) + 2/5*A*b^6*x^(5/2) + 10*B*a^2*b^4*x^(3/2) + 4*A*a*b^5*x^(3/2) + 40*B*a^3*b^3*sqrt(x) + 30*A*a^2*b^4*sqrt(x) - 2/35*(525*B*a^4*b^2*x^3 + 700*A*a^3*b^3*x^3 + 70*B*a^5*b*x^2 + 175*A*a^4*b^2*x^2 + 7*B*a^6*x + 42*A*a^5*b*x + 5*A*a^6)/x^(7/2)","A",0
756,1,148,0,0.160352," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(11/2),x, algorithm=""giac"")","\frac{2}{5} \, B b^{6} x^{\frac{5}{2}} + 4 \, B a b^{5} x^{\frac{3}{2}} + \frac{2}{3} \, A b^{6} x^{\frac{3}{2}} + 30 \, B a^{2} b^{4} \sqrt{x} + 12 \, A a b^{5} \sqrt{x} - \frac{2 \, {\left(6300 \, B a^{3} b^{3} x^{4} + 4725 \, A a^{2} b^{4} x^{4} + 1575 \, B a^{4} b^{2} x^{3} + 2100 \, A a^{3} b^{3} x^{3} + 378 \, B a^{5} b x^{2} + 945 \, A a^{4} b^{2} x^{2} + 45 \, B a^{6} x + 270 \, A a^{5} b x + 35 \, A a^{6}\right)}}{315 \, x^{\frac{9}{2}}}"," ",0,"2/5*B*b^6*x^(5/2) + 4*B*a*b^5*x^(3/2) + 2/3*A*b^6*x^(3/2) + 30*B*a^2*b^4*sqrt(x) + 12*A*a*b^5*sqrt(x) - 2/315*(6300*B*a^3*b^3*x^4 + 4725*A*a^2*b^4*x^4 + 1575*B*a^4*b^2*x^3 + 2100*A*a^3*b^3*x^3 + 378*B*a^5*b*x^2 + 945*A*a^4*b^2*x^2 + 45*B*a^6*x + 270*A*a^5*b*x + 35*A*a^6)/x^(9/2)","A",0
757,1,146,0,0.185628," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{5}} - \frac{B a^{4} \sqrt{x} - A a^{3} b \sqrt{x}}{{\left(b x + a\right)} b^{5}} + \frac{2 \, {\left(15 \, B b^{12} x^{\frac{7}{2}} - 42 \, B a b^{11} x^{\frac{5}{2}} + 21 \, A b^{12} x^{\frac{5}{2}} + 105 \, B a^{2} b^{10} x^{\frac{3}{2}} - 70 \, A a b^{11} x^{\frac{3}{2}} - 420 \, B a^{3} b^{9} \sqrt{x} + 315 \, A a^{2} b^{10} \sqrt{x}\right)}}{105 \, b^{14}}"," ",0,"(9*B*a^4 - 7*A*a^3*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^5) - (B*a^4*sqrt(x) - A*a^3*b*sqrt(x))/((b*x + a)*b^5) + 2/105*(15*B*b^12*x^(7/2) - 42*B*a*b^11*x^(5/2) + 21*A*b^12*x^(5/2) + 105*B*a^2*b^10*x^(3/2) - 70*A*a*b^11*x^(3/2) - 420*B*a^3*b^9*sqrt(x) + 315*A*a^2*b^10*sqrt(x))/b^14","A",0
758,1,122,0,0.181288," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{{\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{B a^{3} \sqrt{x} - A a^{2} b \sqrt{x}}{{\left(b x + a\right)} b^{4}} + \frac{2 \, {\left(3 \, B b^{8} x^{\frac{5}{2}} - 10 \, B a b^{7} x^{\frac{3}{2}} + 5 \, A b^{8} x^{\frac{3}{2}} + 45 \, B a^{2} b^{6} \sqrt{x} - 30 \, A a b^{7} \sqrt{x}\right)}}{15 \, b^{10}}"," ",0,"-(7*B*a^3 - 5*A*a^2*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^4) + (B*a^3*sqrt(x) - A*a^2*b*sqrt(x))/((b*x + a)*b^4) + 2/15*(3*B*b^8*x^(5/2) - 10*B*a*b^7*x^(3/2) + 5*A*b^8*x^(3/2) + 45*B*a^2*b^6*sqrt(x) - 30*A*a*b^7*sqrt(x))/b^10","A",0
759,1,95,0,0.190448," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(5 \, B a^{2} - 3 \, A a b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} - \frac{B a^{2} \sqrt{x} - A a b \sqrt{x}}{{\left(b x + a\right)} b^{3}} + \frac{2 \, {\left(B b^{4} x^{\frac{3}{2}} - 6 \, B a b^{3} \sqrt{x} + 3 \, A b^{4} \sqrt{x}\right)}}{3 \, b^{6}}"," ",0,"(5*B*a^2 - 3*A*a*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^3) - (B*a^2*sqrt(x) - A*a*b*sqrt(x))/((b*x + a)*b^3) + 2/3*(B*b^4*x^(3/2) - 6*B*a*b^3*sqrt(x) + 3*A*b^4*sqrt(x))/b^6","A",0
760,1,65,0,0.156140," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b^{2}} - \frac{{\left(3 \, B a - A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{B a \sqrt{x} - A b \sqrt{x}}{{\left(b x + a\right)} b^{2}}"," ",0,"2*B*sqrt(x)/b^2 - (3*B*a - A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^2) + (B*a*sqrt(x) - A*b*sqrt(x))/((b*x + a)*b^2)","A",0
761,1,60,0,0.187813," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)/x^(1/2),x, algorithm=""giac"")","\frac{{\left(B a + A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a b} - \frac{B a \sqrt{x} - A b \sqrt{x}}{{\left(b x + a\right)} a b}"," ",0,"(B*a + A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a*b) - (B*a*sqrt(x) - A*b*sqrt(x))/((b*x + a)*a*b)","A",0
762,1,60,0,0.157378," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B a - 3 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{B a x - 3 \, A b x - 2 \, A a}{{\left(b x^{\frac{3}{2}} + a \sqrt{x}\right)} a^{2}}"," ",0,"(B*a - 3*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2) + (B*a*x - 3*A*b*x - 2*A*a)/((b*x^(3/2) + a*sqrt(x))*a^2)","A",0
763,1,85,0,0.157953," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{{\left(3 \, B a b - 5 \, A b^{2}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} - \frac{B a b \sqrt{x} - A b^{2} \sqrt{x}}{{\left(b x + a\right)} a^{3}} - \frac{2 \, {\left(3 \, B a x - 6 \, A b x + A a\right)}}{3 \, a^{3} x^{\frac{3}{2}}}"," ",0,"-(3*B*a*b - 5*A*b^2)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3) - (B*a*b*sqrt(x) - A*b^2*sqrt(x))/((b*x + a)*a^3) - 2/3*(3*B*a*x - 6*A*b*x + A*a)/(a^3*x^(3/2))","A",0
764,1,110,0,0.161912," ","integrate((B*x+A)/x^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} + \frac{B a b^{2} \sqrt{x} - A b^{3} \sqrt{x}}{{\left(b x + a\right)} a^{4}} + \frac{2 \, {\left(30 \, B a b x^{2} - 45 \, A b^{2} x^{2} - 5 \, B a^{2} x + 10 \, A a b x - 3 \, A a^{2}\right)}}{15 \, a^{4} x^{\frac{5}{2}}}"," ",0,"(5*B*a*b^2 - 7*A*b^3)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4) + (B*a*b^2*sqrt(x) - A*b^3*sqrt(x))/((b*x + a)*a^4) + 2/15*(30*B*a*b*x^2 - 45*A*b^2*x^2 - 5*B*a^2*x + 10*A*a*b*x - 3*A*a^2)/(a^4*x^(5/2))","A",0
765,1,136,0,0.166150," ","integrate((B*x+A)/x^(9/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{{\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{5}} - \frac{B a b^{3} \sqrt{x} - A b^{4} \sqrt{x}}{{\left(b x + a\right)} a^{5}} - \frac{2 \, {\left(315 \, B a b^{2} x^{3} - 420 \, A b^{3} x^{3} - 70 \, B a^{2} b x^{2} + 105 \, A a b^{2} x^{2} + 21 \, B a^{3} x - 42 \, A a^{2} b x + 15 \, A a^{3}\right)}}{105 \, a^{5} x^{\frac{7}{2}}}"," ",0,"-(7*B*a*b^3 - 9*A*b^4)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^5) - (B*a*b^3*sqrt(x) - A*b^4*sqrt(x))/((b*x + a)*a^5) - 2/105*(315*B*a*b^2*x^3 - 420*A*b^3*x^3 - 70*B*a^2*b*x^2 + 105*A*a*b^2*x^2 + 21*B*a^3*x - 42*A*a^2*b*x + 15*A*a^3)/(a^5*x^(7/2))","A",0
766,1,143,0,0.168800," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{35 \, {\left(3 \, B a^{2} - A a b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{5}} - \frac{165 \, B a^{2} b^{2} x^{\frac{5}{2}} - 87 \, A a b^{3} x^{\frac{5}{2}} + 280 \, B a^{3} b x^{\frac{3}{2}} - 136 \, A a^{2} b^{2} x^{\frac{3}{2}} + 123 \, B a^{4} \sqrt{x} - 57 \, A a^{3} b \sqrt{x}}{24 \, {\left(b x + a\right)}^{3} b^{5}} + \frac{2 \, {\left(B b^{8} x^{\frac{3}{2}} - 12 \, B a b^{7} \sqrt{x} + 3 \, A b^{8} \sqrt{x}\right)}}{3 \, b^{12}}"," ",0,"35/8*(3*B*a^2 - A*a*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^5) - 1/24*(165*B*a^2*b^2*x^(5/2) - 87*A*a*b^3*x^(5/2) + 280*B*a^3*b*x^(3/2) - 136*A*a^2*b^2*x^(3/2) + 123*B*a^4*sqrt(x) - 57*A*a^3*b*sqrt(x))/((b*x + a)^3*b^5) + 2/3*(B*b^8*x^(3/2) - 12*B*a*b^7*sqrt(x) + 3*A*b^8*sqrt(x))/b^12","A",0
767,1,111,0,0.165305," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b^{4}} - \frac{5 \, {\left(7 \, B a - A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{4}} + \frac{87 \, B a b^{2} x^{\frac{5}{2}} - 33 \, A b^{3} x^{\frac{5}{2}} + 136 \, B a^{2} b x^{\frac{3}{2}} - 40 \, A a b^{2} x^{\frac{3}{2}} + 57 \, B a^{3} \sqrt{x} - 15 \, A a^{2} b \sqrt{x}}{24 \, {\left(b x + a\right)}^{3} b^{4}}"," ",0,"2*B*sqrt(x)/b^4 - 5/8*(7*B*a - A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/24*(87*B*a*b^2*x^(5/2) - 33*A*b^3*x^(5/2) + 136*B*a^2*b*x^(3/2) - 40*A*a*b^2*x^(3/2) + 57*B*a^3*sqrt(x) - 15*A*a^2*b*sqrt(x))/((b*x + a)^3*b^4)","A",0
768,1,107,0,0.162076," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(5 \, B a + A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{3}} - \frac{33 \, B a b^{2} x^{\frac{5}{2}} - 3 \, A b^{3} x^{\frac{5}{2}} + 40 \, B a^{2} b x^{\frac{3}{2}} + 8 \, A a b^{2} x^{\frac{3}{2}} + 15 \, B a^{3} \sqrt{x} + 3 \, A a^{2} b \sqrt{x}}{24 \, {\left(b x + a\right)}^{3} a b^{3}}"," ",0,"1/8*(5*B*a + A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a*b^3) - 1/24*(33*B*a*b^2*x^(5/2) - 3*A*b^3*x^(5/2) + 40*B*a^2*b*x^(3/2) + 8*A*a*b^2*x^(3/2) + 15*B*a^3*sqrt(x) + 3*A*a^2*b*sqrt(x))/((b*x + a)^3*a*b^3)","A",0
769,1,106,0,0.161383," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(B a + A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{2}} + \frac{3 \, B a b^{2} x^{\frac{5}{2}} + 3 \, A b^{3} x^{\frac{5}{2}} - 8 \, B a^{2} b x^{\frac{3}{2}} + 8 \, A a b^{2} x^{\frac{3}{2}} - 3 \, B a^{3} \sqrt{x} - 3 \, A a^{2} b \sqrt{x}}{24 \, {\left(b x + a\right)}^{3} a^{2} b^{2}}"," ",0,"1/8*(B*a + A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2*b^2) + 1/24*(3*B*a*b^2*x^(5/2) + 3*A*b^3*x^(5/2) - 8*B*a^2*b*x^(3/2) + 8*A*a*b^2*x^(3/2) - 3*B*a^3*sqrt(x) - 3*A*a^2*b*sqrt(x))/((b*x + a)^3*a^2*b^2)","A",0
770,1,107,0,0.206631," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2/x^(1/2),x, algorithm=""giac"")","\frac{{\left(B a + 5 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3} b} + \frac{3 \, B a b^{2} x^{\frac{5}{2}} + 15 \, A b^{3} x^{\frac{5}{2}} + 8 \, B a^{2} b x^{\frac{3}{2}} + 40 \, A a b^{2} x^{\frac{3}{2}} - 3 \, B a^{3} \sqrt{x} + 33 \, A a^{2} b \sqrt{x}}{24 \, {\left(b x + a\right)}^{3} a^{3} b}"," ",0,"1/8*(B*a + 5*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3*b) + 1/24*(3*B*a*b^2*x^(5/2) + 15*A*b^3*x^(5/2) + 8*B*a^2*b*x^(3/2) + 40*A*a*b^2*x^(3/2) - 3*B*a^3*sqrt(x) + 33*A*a^2*b*sqrt(x))/((b*x + a)^3*a^3*b)","A",0
771,1,110,0,0.164963," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{5 \, {\left(B a - 7 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{4}} - \frac{2 \, A}{a^{4} \sqrt{x}} + \frac{15 \, B a b^{2} x^{\frac{5}{2}} - 57 \, A b^{3} x^{\frac{5}{2}} + 40 \, B a^{2} b x^{\frac{3}{2}} - 136 \, A a b^{2} x^{\frac{3}{2}} + 33 \, B a^{3} \sqrt{x} - 87 \, A a^{2} b \sqrt{x}}{24 \, {\left(b x + a\right)}^{3} a^{4}}"," ",0,"5/8*(B*a - 7*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4) - 2*A/(a^4*sqrt(x)) + 1/24*(15*B*a*b^2*x^(5/2) - 57*A*b^3*x^(5/2) + 40*B*a^2*b*x^(3/2) - 136*A*a*b^2*x^(3/2) + 33*B*a^3*sqrt(x) - 87*A*a^2*b*sqrt(x))/((b*x + a)^3*a^4)","A",0
772,1,136,0,0.168252," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{35 \, {\left(B a b - 3 \, A b^{2}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{5}} - \frac{105 \, B a b^{3} x^{4} - 315 \, A b^{4} x^{4} + 280 \, B a^{2} b^{2} x^{3} - 840 \, A a b^{3} x^{3} + 231 \, B a^{3} b x^{2} - 693 \, A a^{2} b^{2} x^{2} + 48 \, B a^{4} x - 144 \, A a^{3} b x + 16 \, A a^{4}}{24 \, {\left(b x^{\frac{3}{2}} + a \sqrt{x}\right)}^{3} a^{5}}"," ",0,"-35/8*(B*a*b - 3*A*b^2)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^5) - 1/24*(105*B*a*b^3*x^4 - 315*A*b^4*x^4 + 280*B*a^2*b^2*x^3 - 840*A*a*b^3*x^3 + 231*B*a^3*b*x^2 - 693*A*a^2*b^2*x^2 + 48*B*a^4*x - 144*A*a^3*b*x + 16*A*a^4)/((b*x^(3/2) + a*sqrt(x))^3*a^5)","A",0
773,1,191,0,0.181952," ","integrate(x^(11/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{231 \, {\left(13 \, B a^{2} - 3 \, A a b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} b^{7}} - \frac{35595 \, B a^{2} b^{4} x^{\frac{9}{2}} - 12645 \, A a b^{5} x^{\frac{9}{2}} + 121310 \, B a^{3} b^{3} x^{\frac{7}{2}} - 39810 \, A a^{2} b^{4} x^{\frac{7}{2}} + 160384 \, B a^{4} b^{2} x^{\frac{5}{2}} - 50304 \, A a^{3} b^{3} x^{\frac{5}{2}} + 96290 \, B a^{5} b x^{\frac{3}{2}} - 29310 \, A a^{4} b^{2} x^{\frac{3}{2}} + 22005 \, B a^{6} \sqrt{x} - 6555 \, A a^{5} b \sqrt{x}}{1920 \, {\left(b x + a\right)}^{5} b^{7}} + \frac{2 \, {\left(B b^{12} x^{\frac{3}{2}} - 18 \, B a b^{11} \sqrt{x} + 3 \, A b^{12} \sqrt{x}\right)}}{3 \, b^{18}}"," ",0,"231/128*(13*B*a^2 - 3*A*a*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^7) - 1/1920*(35595*B*a^2*b^4*x^(9/2) - 12645*A*a*b^5*x^(9/2) + 121310*B*a^3*b^3*x^(7/2) - 39810*A*a^2*b^4*x^(7/2) + 160384*B*a^4*b^2*x^(5/2) - 50304*A*a^3*b^3*x^(5/2) + 96290*B*a^5*b*x^(3/2) - 29310*A*a^4*b^2*x^(3/2) + 22005*B*a^6*sqrt(x) - 6555*A*a^5*b*sqrt(x))/((b*x + a)^5*b^7) + 2/3*(B*b^12*x^(3/2) - 18*B*a*b^11*sqrt(x) + 3*A*b^12*sqrt(x))/b^18","A",0
774,1,159,0,0.169427," ","integrate(x^(9/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b^{6}} - \frac{63 \, {\left(11 \, B a - A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} b^{6}} + \frac{4215 \, B a b^{4} x^{\frac{9}{2}} - 965 \, A b^{5} x^{\frac{9}{2}} + 13270 \, B a^{2} b^{3} x^{\frac{7}{2}} - 2370 \, A a b^{4} x^{\frac{7}{2}} + 16768 \, B a^{3} b^{2} x^{\frac{5}{2}} - 2688 \, A a^{2} b^{3} x^{\frac{5}{2}} + 9770 \, B a^{4} b x^{\frac{3}{2}} - 1470 \, A a^{3} b^{2} x^{\frac{3}{2}} + 2185 \, B a^{5} \sqrt{x} - 315 \, A a^{4} b \sqrt{x}}{640 \, {\left(b x + a\right)}^{5} b^{6}}"," ",0,"2*B*sqrt(x)/b^6 - 63/128*(11*B*a - A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/640*(4215*B*a*b^4*x^(9/2) - 965*A*b^5*x^(9/2) + 13270*B*a^2*b^3*x^(7/2) - 2370*A*a*b^4*x^(7/2) + 16768*B*a^3*b^2*x^(5/2) - 2688*A*a^2*b^3*x^(5/2) + 9770*B*a^4*b*x^(3/2) - 1470*A*a^3*b^2*x^(3/2) + 2185*B*a^5*sqrt(x) - 315*A*a^4*b*sqrt(x))/((b*x + a)^5*b^6)","A",0
775,1,155,0,0.168765," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{7 \, {\left(9 \, B a + A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a b^{5}} - \frac{2895 \, B a b^{4} x^{\frac{9}{2}} - 105 \, A b^{5} x^{\frac{9}{2}} + 7110 \, B a^{2} b^{3} x^{\frac{7}{2}} + 790 \, A a b^{4} x^{\frac{7}{2}} + 8064 \, B a^{3} b^{2} x^{\frac{5}{2}} + 896 \, A a^{2} b^{3} x^{\frac{5}{2}} + 4410 \, B a^{4} b x^{\frac{3}{2}} + 490 \, A a^{3} b^{2} x^{\frac{3}{2}} + 945 \, B a^{5} \sqrt{x} + 105 \, A a^{4} b \sqrt{x}}{1920 \, {\left(b x + a\right)}^{5} a b^{5}}"," ",0,"7/128*(9*B*a + A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a*b^5) - 1/1920*(2895*B*a*b^4*x^(9/2) - 105*A*b^5*x^(9/2) + 7110*B*a^2*b^3*x^(7/2) + 790*A*a*b^4*x^(7/2) + 8064*B*a^3*b^2*x^(5/2) + 896*A*a^2*b^3*x^(5/2) + 4410*B*a^4*b*x^(3/2) + 490*A*a^3*b^2*x^(3/2) + 945*B*a^5*sqrt(x) + 105*A*a^4*b*sqrt(x))/((b*x + a)^5*a*b^5)","A",0
776,1,156,0,0.168343," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{{\left(7 \, B a + 3 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{2} b^{4}} + \frac{105 \, B a b^{4} x^{\frac{9}{2}} + 45 \, A b^{5} x^{\frac{9}{2}} - 790 \, B a^{2} b^{3} x^{\frac{7}{2}} + 210 \, A a b^{4} x^{\frac{7}{2}} - 896 \, B a^{3} b^{2} x^{\frac{5}{2}} - 384 \, A a^{2} b^{3} x^{\frac{5}{2}} - 490 \, B a^{4} b x^{\frac{3}{2}} - 210 \, A a^{3} b^{2} x^{\frac{3}{2}} - 105 \, B a^{5} \sqrt{x} - 45 \, A a^{4} b \sqrt{x}}{1920 \, {\left(b x + a\right)}^{5} a^{2} b^{4}}"," ",0,"1/128*(7*B*a + 3*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2*b^4) + 1/1920*(105*B*a*b^4*x^(9/2) + 45*A*b^5*x^(9/2) - 790*B*a^2*b^3*x^(7/2) + 210*A*a*b^4*x^(7/2) - 896*B*a^3*b^2*x^(5/2) - 384*A*a^2*b^3*x^(5/2) - 490*B*a^4*b*x^(3/2) - 210*A*a^3*b^2*x^(3/2) - 105*B*a^5*sqrt(x) - 45*A*a^4*b*sqrt(x))/((b*x + a)^5*a^2*b^4)","A",0
777,1,154,0,0.164407," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(B a + A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{3} b^{3}} + \frac{15 \, B a b^{4} x^{\frac{9}{2}} + 15 \, A b^{5} x^{\frac{9}{2}} + 70 \, B a^{2} b^{3} x^{\frac{7}{2}} + 70 \, A a b^{4} x^{\frac{7}{2}} - 128 \, B a^{3} b^{2} x^{\frac{5}{2}} + 128 \, A a^{2} b^{3} x^{\frac{5}{2}} - 70 \, B a^{4} b x^{\frac{3}{2}} - 70 \, A a^{3} b^{2} x^{\frac{3}{2}} - 15 \, B a^{5} \sqrt{x} - 15 \, A a^{4} b \sqrt{x}}{640 \, {\left(b x + a\right)}^{5} a^{3} b^{3}}"," ",0,"3/128*(B*a + A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3*b^3) + 1/640*(15*B*a*b^4*x^(9/2) + 15*A*b^5*x^(9/2) + 70*B*a^2*b^3*x^(7/2) + 70*A*a*b^4*x^(7/2) - 128*B*a^3*b^2*x^(5/2) + 128*A*a^2*b^3*x^(5/2) - 70*B*a^4*b*x^(3/2) - 70*A*a^3*b^2*x^(3/2) - 15*B*a^5*sqrt(x) - 15*A*a^4*b*sqrt(x))/((b*x + a)^5*a^3*b^3)","A",0
778,1,156,0,0.179978," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{{\left(3 \, B a + 7 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{4} b^{2}} + \frac{45 \, B a b^{4} x^{\frac{9}{2}} + 105 \, A b^{5} x^{\frac{9}{2}} + 210 \, B a^{2} b^{3} x^{\frac{7}{2}} + 490 \, A a b^{4} x^{\frac{7}{2}} + 384 \, B a^{3} b^{2} x^{\frac{5}{2}} + 896 \, A a^{2} b^{3} x^{\frac{5}{2}} - 210 \, B a^{4} b x^{\frac{3}{2}} + 790 \, A a^{3} b^{2} x^{\frac{3}{2}} - 45 \, B a^{5} \sqrt{x} - 105 \, A a^{4} b \sqrt{x}}{1920 \, {\left(b x + a\right)}^{5} a^{4} b^{2}}"," ",0,"1/128*(3*B*a + 7*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4*b^2) + 1/1920*(45*B*a*b^4*x^(9/2) + 105*A*b^5*x^(9/2) + 210*B*a^2*b^3*x^(7/2) + 490*A*a*b^4*x^(7/2) + 384*B*a^3*b^2*x^(5/2) + 896*A*a^2*b^3*x^(5/2) - 210*B*a^4*b*x^(3/2) + 790*A*a^3*b^2*x^(3/2) - 45*B*a^5*sqrt(x) - 105*A*a^4*b*sqrt(x))/((b*x + a)^5*a^4*b^2)","A",0
779,1,155,0,0.176797," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3/x^(1/2),x, algorithm=""giac"")","\frac{7 \, {\left(B a + 9 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{5} b} + \frac{105 \, B a b^{4} x^{\frac{9}{2}} + 945 \, A b^{5} x^{\frac{9}{2}} + 490 \, B a^{2} b^{3} x^{\frac{7}{2}} + 4410 \, A a b^{4} x^{\frac{7}{2}} + 896 \, B a^{3} b^{2} x^{\frac{5}{2}} + 8064 \, A a^{2} b^{3} x^{\frac{5}{2}} + 790 \, B a^{4} b x^{\frac{3}{2}} + 7110 \, A a^{3} b^{2} x^{\frac{3}{2}} - 105 \, B a^{5} \sqrt{x} + 2895 \, A a^{4} b \sqrt{x}}{1920 \, {\left(b x + a\right)}^{5} a^{5} b}"," ",0,"7/128*(B*a + 9*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^5*b) + 1/1920*(105*B*a*b^4*x^(9/2) + 945*A*b^5*x^(9/2) + 490*B*a^2*b^3*x^(7/2) + 4410*A*a*b^4*x^(7/2) + 896*B*a^3*b^2*x^(5/2) + 8064*A*a^2*b^3*x^(5/2) + 790*B*a^4*b*x^(3/2) + 7110*A*a^3*b^2*x^(3/2) - 105*B*a^5*sqrt(x) + 2895*A*a^4*b*sqrt(x))/((b*x + a)^5*a^5*b)","A",0
780,1,158,0,0.207220," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{63 \, {\left(B a - 11 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{6}} - \frac{2 \, A}{a^{6} \sqrt{x}} + \frac{315 \, B a b^{4} x^{\frac{9}{2}} - 2185 \, A b^{5} x^{\frac{9}{2}} + 1470 \, B a^{2} b^{3} x^{\frac{7}{2}} - 9770 \, A a b^{4} x^{\frac{7}{2}} + 2688 \, B a^{3} b^{2} x^{\frac{5}{2}} - 16768 \, A a^{2} b^{3} x^{\frac{5}{2}} + 2370 \, B a^{4} b x^{\frac{3}{2}} - 13270 \, A a^{3} b^{2} x^{\frac{3}{2}} + 965 \, B a^{5} \sqrt{x} - 4215 \, A a^{4} b \sqrt{x}}{640 \, {\left(b x + a\right)}^{5} a^{6}}"," ",0,"63/128*(B*a - 11*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^6) - 2*A/(a^6*sqrt(x)) + 1/640*(315*B*a*b^4*x^(9/2) - 2185*A*b^5*x^(9/2) + 1470*B*a^2*b^3*x^(7/2) - 9770*A*a*b^4*x^(7/2) + 2688*B*a^3*b^2*x^(5/2) - 16768*A*a^2*b^3*x^(5/2) + 2370*B*a^4*b*x^(3/2) - 13270*A*a^3*b^2*x^(3/2) + 965*B*a^5*sqrt(x) - 4215*A*a^4*b*sqrt(x))/((b*x + a)^5*a^6)","A",0
781,1,180,0,0.175737," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{231 \, {\left(3 \, B a b - 13 \, A b^{2}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{7}} - \frac{2 \, {\left(3 \, B a x - 18 \, A b x + A a\right)}}{3 \, a^{7} x^{\frac{3}{2}}} - \frac{6555 \, B a b^{5} x^{\frac{9}{2}} - 22005 \, A b^{6} x^{\frac{9}{2}} + 29310 \, B a^{2} b^{4} x^{\frac{7}{2}} - 96290 \, A a b^{5} x^{\frac{7}{2}} + 50304 \, B a^{3} b^{3} x^{\frac{5}{2}} - 160384 \, A a^{2} b^{4} x^{\frac{5}{2}} + 39810 \, B a^{4} b^{2} x^{\frac{3}{2}} - 121310 \, A a^{3} b^{3} x^{\frac{3}{2}} + 12645 \, B a^{5} b \sqrt{x} - 35595 \, A a^{4} b^{2} \sqrt{x}}{1920 \, {\left(b x + a\right)}^{5} a^{7}}"," ",0,"-231/128*(3*B*a*b - 13*A*b^2)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^7) - 2/3*(3*B*a*x - 18*A*b*x + A*a)/(a^7*x^(3/2)) - 1/1920*(6555*B*a*b^5*x^(9/2) - 22005*A*b^6*x^(9/2) + 29310*B*a^2*b^4*x^(7/2) - 96290*A*a*b^5*x^(7/2) + 50304*B*a^3*b^3*x^(5/2) - 160384*A*a^2*b^4*x^(5/2) + 39810*B*a^4*b^2*x^(3/2) - 121310*A*a^3*b^3*x^(3/2) + 12645*B*a^5*b*sqrt(x) - 35595*A*a^4*b^2*sqrt(x))/((b*x + a)^5*a^7)","A",0
782,1,53,0,0.182010," ","integrate(x^(7/2)*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, B b x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{11} \, B a x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{11} \, A b x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, A a x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/13*B*b*x^(13/2)*sgn(b*x + a) + 2/11*B*a*x^(11/2)*sgn(b*x + a) + 2/11*A*b*x^(11/2)*sgn(b*x + a) + 2/9*A*a*x^(9/2)*sgn(b*x + a)","A",0
783,1,53,0,0.226212," ","integrate(x^(5/2)*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, B b x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, B a x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, A b x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, A a x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/11*B*b*x^(11/2)*sgn(b*x + a) + 2/9*B*a*x^(9/2)*sgn(b*x + a) + 2/9*A*b*x^(9/2)*sgn(b*x + a) + 2/7*A*a*x^(7/2)*sgn(b*x + a)","A",0
784,1,53,0,0.208546," ","integrate(x^(3/2)*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, B b x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, B a x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, A b x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, A a x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/9*B*b*x^(9/2)*sgn(b*x + a) + 2/7*B*a*x^(7/2)*sgn(b*x + a) + 2/7*A*b*x^(7/2)*sgn(b*x + a) + 2/5*A*a*x^(5/2)*sgn(b*x + a)","A",0
785,1,53,0,0.154855," ","integrate((B*x+A)*x^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{7} \, B b x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, B a x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, A b x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A a x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/7*B*b*x^(7/2)*sgn(b*x + a) + 2/5*B*a*x^(5/2)*sgn(b*x + a) + 2/5*A*b*x^(5/2)*sgn(b*x + a) + 2/3*A*a*x^(3/2)*sgn(b*x + a)","A",0
786,1,53,0,0.162704," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{5} \, B b x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A b x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, A a \sqrt{x} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/5*B*b*x^(5/2)*sgn(b*x + a) + 2/3*B*a*x^(3/2)*sgn(b*x + a) + 2/3*A*b*x^(3/2)*sgn(b*x + a) + 2*A*a*sqrt(x)*sgn(b*x + a)","A",0
787,1,53,0,0.183774," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, B b x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, B a \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 2 \, A b \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, A a \mathrm{sgn}\left(b x + a\right)}{\sqrt{x}}"," ",0,"2/3*B*b*x^(3/2)*sgn(b*x + a) + 2*B*a*sqrt(x)*sgn(b*x + a) + 2*A*b*sqrt(x)*sgn(b*x + a) - 2*A*a*sgn(b*x + a)/sqrt(x)","A",0
788,1,51,0,0.161351," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(5/2),x, algorithm=""giac"")","2 \, B b \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, {\left(3 \, B a x \mathrm{sgn}\left(b x + a\right) + 3 \, A b x \mathrm{sgn}\left(b x + a\right) + A a \mathrm{sgn}\left(b x + a\right)\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2*B*b*sqrt(x)*sgn(b*x + a) - 2/3*(3*B*a*x*sgn(b*x + a) + 3*A*b*x*sgn(b*x + a) + A*a*sgn(b*x + a))/x^(3/2)","A",0
789,1,51,0,0.173678," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, B b x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a x \mathrm{sgn}\left(b x + a\right) + 5 \, A b x \mathrm{sgn}\left(b x + a\right) + 3 \, A a \mathrm{sgn}\left(b x + a\right)\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*B*b*x^2*sgn(b*x + a) + 5*B*a*x*sgn(b*x + a) + 5*A*b*x*sgn(b*x + a) + 3*A*a*sgn(b*x + a))/x^(5/2)","A",0
790,1,51,0,0.192326," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, B b x^{2} \mathrm{sgn}\left(b x + a\right) + 21 \, B a x \mathrm{sgn}\left(b x + a\right) + 21 \, A b x \mathrm{sgn}\left(b x + a\right) + 15 \, A a \mathrm{sgn}\left(b x + a\right)\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(35*B*b*x^2*sgn(b*x + a) + 21*B*a*x*sgn(b*x + a) + 21*A*b*x*sgn(b*x + a) + 15*A*a*sgn(b*x + a))/x^(7/2)","A",0
791,1,125,0,0.196967," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{17} \, B b^{3} x^{\frac{17}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, B a b^{2} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{15} \, A b^{3} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{13} \, B a^{2} b x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{13} \, A a b^{2} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{11} \, A a^{2} b x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, A a^{3} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/17*B*b^3*x^(17/2)*sgn(b*x + a) + 2/5*B*a*b^2*x^(15/2)*sgn(b*x + a) + 2/15*A*b^3*x^(15/2)*sgn(b*x + a) + 6/13*B*a^2*b*x^(13/2)*sgn(b*x + a) + 6/13*A*a*b^2*x^(13/2)*sgn(b*x + a) + 2/11*B*a^3*x^(11/2)*sgn(b*x + a) + 6/11*A*a^2*b*x^(11/2)*sgn(b*x + a) + 2/9*A*a^3*x^(9/2)*sgn(b*x + a)","A",0
792,1,125,0,0.171901," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, B b^{3} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{13} \, B a b^{2} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{13} \, A b^{3} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{11} \, B a^{2} b x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{11} \, A a b^{2} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, B a^{3} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A a^{2} b x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, A a^{3} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/15*B*b^3*x^(15/2)*sgn(b*x + a) + 6/13*B*a*b^2*x^(13/2)*sgn(b*x + a) + 2/13*A*b^3*x^(13/2)*sgn(b*x + a) + 6/11*B*a^2*b*x^(11/2)*sgn(b*x + a) + 6/11*A*a*b^2*x^(11/2)*sgn(b*x + a) + 2/9*B*a^3*x^(9/2)*sgn(b*x + a) + 2/3*A*a^2*b*x^(9/2)*sgn(b*x + a) + 2/7*A*a^3*x^(7/2)*sgn(b*x + a)","A",0
793,1,125,0,0.160508," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{13} \, B b^{3} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{11} \, B a b^{2} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{11} \, A b^{3} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a^{2} b x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A a b^{2} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, B a^{3} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, A a^{2} b x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/13*B*b^3*x^(13/2)*sgn(b*x + a) + 6/11*B*a*b^2*x^(11/2)*sgn(b*x + a) + 2/11*A*b^3*x^(11/2)*sgn(b*x + a) + 2/3*B*a^2*b*x^(9/2)*sgn(b*x + a) + 2/3*A*a*b^2*x^(9/2)*sgn(b*x + a) + 2/7*B*a^3*x^(7/2)*sgn(b*x + a) + 6/7*A*a^2*b*x^(7/2)*sgn(b*x + a) + 2/5*A*a^3*x^(5/2)*sgn(b*x + a)","A",0
794,1,125,0,0.332291," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)*x^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, B b^{3} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a b^{2} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, A b^{3} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, B a^{2} b x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, A a b^{2} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, B a^{3} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, A a^{2} b x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A a^{3} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/11*B*b^3*x^(11/2)*sgn(b*x + a) + 2/3*B*a*b^2*x^(9/2)*sgn(b*x + a) + 2/9*A*b^3*x^(9/2)*sgn(b*x + a) + 6/7*B*a^2*b*x^(7/2)*sgn(b*x + a) + 6/7*A*a*b^2*x^(7/2)*sgn(b*x + a) + 2/5*B*a^3*x^(5/2)*sgn(b*x + a) + 6/5*A*a^2*b*x^(5/2)*sgn(b*x + a) + 2/3*A*a^3*x^(3/2)*sgn(b*x + a)","A",0
795,1,125,0,0.190043," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, B b^{3} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, B a b^{2} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, A b^{3} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, B a^{2} b x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, A a b^{2} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a^{3} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{2} b x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/9*B*b^3*x^(9/2)*sgn(b*x + a) + 6/7*B*a*b^2*x^(7/2)*sgn(b*x + a) + 2/7*A*b^3*x^(7/2)*sgn(b*x + a) + 6/5*B*a^2*b*x^(5/2)*sgn(b*x + a) + 6/5*A*a*b^2*x^(5/2)*sgn(b*x + a) + 2/3*B*a^3*x^(3/2)*sgn(b*x + a) + 2*A*a^2*b*x^(3/2)*sgn(b*x + a) + 2*A*a^3*sqrt(x)*sgn(b*x + a)","A",0
796,1,125,0,0.168820," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(3/2),x, algorithm=""giac"")","\frac{2}{7} \, B b^{3} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, B a b^{2} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, A b^{3} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{2} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{2} b \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, A a^{3} \mathrm{sgn}\left(b x + a\right)}{\sqrt{x}}"," ",0,"2/7*B*b^3*x^(7/2)*sgn(b*x + a) + 6/5*B*a*b^2*x^(5/2)*sgn(b*x + a) + 2/5*A*b^3*x^(5/2)*sgn(b*x + a) + 2*B*a^2*b*x^(3/2)*sgn(b*x + a) + 2*A*a*b^2*x^(3/2)*sgn(b*x + a) + 2*B*a^3*sqrt(x)*sgn(b*x + a) + 6*A*a^2*b*sqrt(x)*sgn(b*x + a) - 2*A*a^3*sgn(b*x + a)/sqrt(x)","A",0
797,1,123,0,0.164100," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(5/2),x, algorithm=""giac"")","\frac{2}{5} \, B b^{3} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, B a b^{2} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A b^{3} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{2} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, {\left(3 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 9 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + A a^{3} \mathrm{sgn}\left(b x + a\right)\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/5*B*b^3*x^(5/2)*sgn(b*x + a) + 2*B*a*b^2*x^(3/2)*sgn(b*x + a) + 2/3*A*b^3*x^(3/2)*sgn(b*x + a) + 6*B*a^2*b*sqrt(x)*sgn(b*x + a) + 6*A*a*b^2*sqrt(x)*sgn(b*x + a) - 2/3*(3*B*a^3*x*sgn(b*x + a) + 9*A*a^2*b*x*sgn(b*x + a) + A*a^3*sgn(b*x + a))/x^(3/2)","A",0
798,1,124,0,0.169656," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, B b^{3} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 6 \, B a b^{2} \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 2 \, A b^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, {\left(45 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 45 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{3} \mathrm{sgn}\left(b x + a\right)\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/3*B*b^3*x^(3/2)*sgn(b*x + a) + 6*B*a*b^2*sqrt(x)*sgn(b*x + a) + 2*A*b^3*sqrt(x)*sgn(b*x + a) - 2/15*(45*B*a^2*b*x^2*sgn(b*x + a) + 45*A*a*b^2*x^2*sgn(b*x + a) + 5*B*a^3*x*sgn(b*x + a) + 15*A*a^2*b*x*sgn(b*x + a) + 3*A*a^3*sgn(b*x + a))/x^(5/2)","A",0
799,1,124,0,0.179492," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(9/2),x, algorithm=""giac"")","2 \, B b^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, {\left(105 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) + 21 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{3} \mathrm{sgn}\left(b x + a\right)\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"2*B*b^3*sqrt(x)*sgn(b*x + a) - 2/35*(105*B*a*b^2*x^3*sgn(b*x + a) + 35*A*b^3*x^3*sgn(b*x + a) + 35*B*a^2*b*x^2*sgn(b*x + a) + 35*A*a*b^2*x^2*sgn(b*x + a) + 7*B*a^3*x*sgn(b*x + a) + 21*A*a^2*b*x*sgn(b*x + a) + 5*A*a^3*sgn(b*x + a))/x^(7/2)","A",0
800,1,197,0,0.207947," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{21} \, B b^{5} x^{\frac{21}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{19} \, B a b^{4} x^{\frac{19}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{19} \, A b^{5} x^{\frac{19}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{17} \, B a^{2} b^{3} x^{\frac{17}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{17} \, A a b^{4} x^{\frac{17}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, B a^{3} b^{2} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, A a^{2} b^{3} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{13} \, B a^{4} b x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{13} \, A a^{3} b^{2} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{11} \, B a^{5} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{11} \, A a^{4} b x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, A a^{5} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/21*B*b^5*x^(21/2)*sgn(b*x + a) + 10/19*B*a*b^4*x^(19/2)*sgn(b*x + a) + 2/19*A*b^5*x^(19/2)*sgn(b*x + a) + 20/17*B*a^2*b^3*x^(17/2)*sgn(b*x + a) + 10/17*A*a*b^4*x^(17/2)*sgn(b*x + a) + 4/3*B*a^3*b^2*x^(15/2)*sgn(b*x + a) + 4/3*A*a^2*b^3*x^(15/2)*sgn(b*x + a) + 10/13*B*a^4*b*x^(13/2)*sgn(b*x + a) + 20/13*A*a^3*b^2*x^(13/2)*sgn(b*x + a) + 2/11*B*a^5*x^(11/2)*sgn(b*x + a) + 10/11*A*a^4*b*x^(11/2)*sgn(b*x + a) + 2/9*A*a^5*x^(9/2)*sgn(b*x + a)","A",0
801,1,197,0,0.185643," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{19} \, B b^{5} x^{\frac{19}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{17} \, B a b^{4} x^{\frac{17}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{17} \, A b^{5} x^{\frac{17}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, B a^{2} b^{3} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A a b^{4} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{13} \, B a^{3} b^{2} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{13} \, A a^{2} b^{3} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{11} \, B a^{4} b x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{11} \, A a^{3} b^{2} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, B a^{5} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, A a^{4} b x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, A a^{5} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/19*B*b^5*x^(19/2)*sgn(b*x + a) + 10/17*B*a*b^4*x^(17/2)*sgn(b*x + a) + 2/17*A*b^5*x^(17/2)*sgn(b*x + a) + 4/3*B*a^2*b^3*x^(15/2)*sgn(b*x + a) + 2/3*A*a*b^4*x^(15/2)*sgn(b*x + a) + 20/13*B*a^3*b^2*x^(13/2)*sgn(b*x + a) + 20/13*A*a^2*b^3*x^(13/2)*sgn(b*x + a) + 10/11*B*a^4*b*x^(11/2)*sgn(b*x + a) + 20/11*A*a^3*b^2*x^(11/2)*sgn(b*x + a) + 2/9*B*a^5*x^(9/2)*sgn(b*x + a) + 10/9*A*a^4*b*x^(9/2)*sgn(b*x + a) + 2/7*A*a^5*x^(7/2)*sgn(b*x + a)","A",0
802,1,197,0,0.169306," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{17} \, B b^{5} x^{\frac{17}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a b^{4} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{15} \, A b^{5} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{13} \, B a^{2} b^{3} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{13} \, A a b^{4} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{11} \, B a^{3} b^{2} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{11} \, A a^{2} b^{3} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, B a^{4} b x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{9} \, A a^{3} b^{2} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, B a^{5} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, A a^{4} b x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, A a^{5} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/17*B*b^5*x^(17/2)*sgn(b*x + a) + 2/3*B*a*b^4*x^(15/2)*sgn(b*x + a) + 2/15*A*b^5*x^(15/2)*sgn(b*x + a) + 20/13*B*a^2*b^3*x^(13/2)*sgn(b*x + a) + 10/13*A*a*b^4*x^(13/2)*sgn(b*x + a) + 20/11*B*a^3*b^2*x^(11/2)*sgn(b*x + a) + 20/11*A*a^2*b^3*x^(11/2)*sgn(b*x + a) + 10/9*B*a^4*b*x^(9/2)*sgn(b*x + a) + 20/9*A*a^3*b^2*x^(9/2)*sgn(b*x + a) + 2/7*B*a^5*x^(7/2)*sgn(b*x + a) + 10/7*A*a^4*b*x^(7/2)*sgn(b*x + a) + 2/5*A*a^5*x^(5/2)*sgn(b*x + a)","A",0
803,1,197,0,0.170902," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)*x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, B b^{5} x^{\frac{15}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{13} \, B a b^{4} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{13} \, A b^{5} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{11} \, B a^{2} b^{3} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{11} \, A a b^{4} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{9} \, B a^{3} b^{2} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{9} \, A a^{2} b^{3} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B a^{4} b x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{7} \, A a^{3} b^{2} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, B a^{5} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{4} b x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A a^{5} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/15*B*b^5*x^(15/2)*sgn(b*x + a) + 10/13*B*a*b^4*x^(13/2)*sgn(b*x + a) + 2/13*A*b^5*x^(13/2)*sgn(b*x + a) + 20/11*B*a^2*b^3*x^(11/2)*sgn(b*x + a) + 10/11*A*a*b^4*x^(11/2)*sgn(b*x + a) + 20/9*B*a^3*b^2*x^(9/2)*sgn(b*x + a) + 20/9*A*a^2*b^3*x^(9/2)*sgn(b*x + a) + 10/7*B*a^4*b*x^(7/2)*sgn(b*x + a) + 20/7*A*a^3*b^2*x^(7/2)*sgn(b*x + a) + 2/5*B*a^5*x^(5/2)*sgn(b*x + a) + 2*A*a^4*b*x^(5/2)*sgn(b*x + a) + 2/3*A*a^5*x^(3/2)*sgn(b*x + a)","A",0
804,1,197,0,0.170103," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, B b^{5} x^{\frac{13}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{11} \, B a b^{4} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{11} \, A b^{5} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{9} \, B a^{2} b^{3} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, A a b^{4} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{7} \, B a^{3} b^{2} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{7} \, A a^{2} b^{3} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{4} b x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{3} b^{2} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a^{5} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{4} b x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{5} \sqrt{x} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/13*B*b^5*x^(13/2)*sgn(b*x + a) + 10/11*B*a*b^4*x^(11/2)*sgn(b*x + a) + 2/11*A*b^5*x^(11/2)*sgn(b*x + a) + 20/9*B*a^2*b^3*x^(9/2)*sgn(b*x + a) + 10/9*A*a*b^4*x^(9/2)*sgn(b*x + a) + 20/7*B*a^3*b^2*x^(7/2)*sgn(b*x + a) + 20/7*A*a^2*b^3*x^(7/2)*sgn(b*x + a) + 2*B*a^4*b*x^(5/2)*sgn(b*x + a) + 4*A*a^3*b^2*x^(5/2)*sgn(b*x + a) + 2/3*B*a^5*x^(3/2)*sgn(b*x + a) + 10/3*A*a^4*b*x^(3/2)*sgn(b*x + a) + 2*A*a^5*sqrt(x)*sgn(b*x + a)","A",0
805,1,197,0,0.178711," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(3/2),x, algorithm=""giac"")","\frac{2}{11} \, B b^{5} x^{\frac{11}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, B a b^{4} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{9} \, A b^{5} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{7} \, B a^{2} b^{3} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, A a b^{4} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{3} b^{2} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{2} b^{3} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, B a^{4} b x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, A a^{3} b^{2} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{5} \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{4} b \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, A a^{5} \mathrm{sgn}\left(b x + a\right)}{\sqrt{x}}"," ",0,"2/11*B*b^5*x^(11/2)*sgn(b*x + a) + 10/9*B*a*b^4*x^(9/2)*sgn(b*x + a) + 2/9*A*b^5*x^(9/2)*sgn(b*x + a) + 20/7*B*a^2*b^3*x^(7/2)*sgn(b*x + a) + 10/7*A*a*b^4*x^(7/2)*sgn(b*x + a) + 4*B*a^3*b^2*x^(5/2)*sgn(b*x + a) + 4*A*a^2*b^3*x^(5/2)*sgn(b*x + a) + 10/3*B*a^4*b*x^(3/2)*sgn(b*x + a) + 20/3*A*a^3*b^2*x^(3/2)*sgn(b*x + a) + 2*B*a^5*sqrt(x)*sgn(b*x + a) + 10*A*a^4*b*sqrt(x)*sgn(b*x + a) - 2*A*a^5*sgn(b*x + a)/sqrt(x)","A",0
806,1,195,0,0.177922," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(5/2),x, algorithm=""giac"")","\frac{2}{9} \, B b^{5} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B a b^{4} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, A b^{5} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{2} b^{3} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{4} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, B a^{3} b^{2} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, A a^{2} b^{3} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, {\left(3 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + A a^{5} \mathrm{sgn}\left(b x + a\right)\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/9*B*b^5*x^(9/2)*sgn(b*x + a) + 10/7*B*a*b^4*x^(7/2)*sgn(b*x + a) + 2/7*A*b^5*x^(7/2)*sgn(b*x + a) + 4*B*a^2*b^3*x^(5/2)*sgn(b*x + a) + 2*A*a*b^4*x^(5/2)*sgn(b*x + a) + 20/3*B*a^3*b^2*x^(3/2)*sgn(b*x + a) + 20/3*A*a^2*b^3*x^(3/2)*sgn(b*x + a) + 10*B*a^4*b*sqrt(x)*sgn(b*x + a) + 20*A*a^3*b^2*sqrt(x)*sgn(b*x + a) - 2/3*(3*B*a^5*x*sgn(b*x + a) + 15*A*a^4*b*x*sgn(b*x + a) + A*a^5*sgn(b*x + a))/x^(3/2)","A",0
807,1,196,0,0.177189," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(7/2),x, algorithm=""giac"")","\frac{2}{7} \, B b^{5} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + 2 \, B a b^{4} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, A b^{5} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, B a^{2} b^{3} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a b^{4} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 20 \, B a^{3} b^{2} \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{2} b^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, {\left(75 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 150 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 25 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{5} \mathrm{sgn}\left(b x + a\right)\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/7*B*b^5*x^(7/2)*sgn(b*x + a) + 2*B*a*b^4*x^(5/2)*sgn(b*x + a) + 2/5*A*b^5*x^(5/2)*sgn(b*x + a) + 20/3*B*a^2*b^3*x^(3/2)*sgn(b*x + a) + 10/3*A*a*b^4*x^(3/2)*sgn(b*x + a) + 20*B*a^3*b^2*sqrt(x)*sgn(b*x + a) + 20*A*a^2*b^3*sqrt(x)*sgn(b*x + a) - 2/15*(75*B*a^4*b*x^2*sgn(b*x + a) + 150*A*a^3*b^2*x^2*sgn(b*x + a) + 5*B*a^5*x*sgn(b*x + a) + 25*A*a^4*b*x*sgn(b*x + a) + 3*A*a^5*sgn(b*x + a))/x^(5/2)","A",0
808,1,196,0,0.175780," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(9/2),x, algorithm=""giac"")","\frac{2}{5} \, B b^{5} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, B a b^{4} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A b^{5} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 20 \, B a^{2} b^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 10 \, A a b^{4} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - \frac{2 \, {\left(1050 \, B a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 1050 \, A a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 175 \, B a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + 350 \, A a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 21 \, B a^{5} x \mathrm{sgn}\left(b x + a\right) + 105 \, A a^{4} b x \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{5} \mathrm{sgn}\left(b x + a\right)\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"2/5*B*b^5*x^(5/2)*sgn(b*x + a) + 10/3*B*a*b^4*x^(3/2)*sgn(b*x + a) + 2/3*A*b^5*x^(3/2)*sgn(b*x + a) + 20*B*a^2*b^3*sqrt(x)*sgn(b*x + a) + 10*A*a*b^4*sqrt(x)*sgn(b*x + a) - 2/105*(1050*B*a^3*b^2*x^3*sgn(b*x + a) + 1050*A*a^2*b^3*x^3*sgn(b*x + a) + 175*B*a^4*b*x^2*sgn(b*x + a) + 350*A*a^3*b^2*x^2*sgn(b*x + a) + 21*B*a^5*x*sgn(b*x + a) + 105*A*a^4*b*x*sgn(b*x + a) + 15*A*a^5*sgn(b*x + a))/x^(7/2)","A",0
809,1,205,0,0.373727," ","integrate(x^(7/2)*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a^{5} \mathrm{sgn}\left(b x + a\right) - A a^{4} b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{5}} + \frac{2 \, {\left(35 \, B b^{8} x^{\frac{9}{2}} \mathrm{sgn}\left(b x + a\right) - 45 \, B a b^{7} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + 45 \, A b^{8} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) + 63 \, B a^{2} b^{6} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) - 63 \, A a b^{7} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) - 105 \, B a^{3} b^{5} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 105 \, A a^{2} b^{6} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 315 \, B a^{4} b^{4} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - 315 \, A a^{3} b^{5} \sqrt{x} \mathrm{sgn}\left(b x + a\right)\right)}}{315 \, b^{9}}"," ",0,"-2*(B*a^5*sgn(b*x + a) - A*a^4*b*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^5) + 2/315*(35*B*b^8*x^(9/2)*sgn(b*x + a) - 45*B*a*b^7*x^(7/2)*sgn(b*x + a) + 45*A*b^8*x^(7/2)*sgn(b*x + a) + 63*B*a^2*b^6*x^(5/2)*sgn(b*x + a) - 63*A*a*b^7*x^(5/2)*sgn(b*x + a) - 105*B*a^3*b^5*x^(3/2)*sgn(b*x + a) + 105*A*a^2*b^6*x^(3/2)*sgn(b*x + a) + 315*B*a^4*b^4*sqrt(x)*sgn(b*x + a) - 315*A*a^3*b^5*sqrt(x)*sgn(b*x + a))/b^9","A",0
810,1,169,0,0.198800," ","integrate(x^(5/2)*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(B a^{4} \mathrm{sgn}\left(b x + a\right) - A a^{3} b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{2 \, {\left(15 \, B b^{6} x^{\frac{7}{2}} \mathrm{sgn}\left(b x + a\right) - 21 \, B a b^{5} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 21 \, A b^{6} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) + 35 \, B a^{2} b^{4} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) - 35 \, A a b^{5} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) - 105 \, B a^{3} b^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 105 \, A a^{2} b^{4} \sqrt{x} \mathrm{sgn}\left(b x + a\right)\right)}}{105 \, b^{7}}"," ",0,"2*(B*a^4*sgn(b*x + a) - A*a^3*b*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^4) + 2/105*(15*B*b^6*x^(7/2)*sgn(b*x + a) - 21*B*a*b^5*x^(5/2)*sgn(b*x + a) + 21*A*b^6*x^(5/2)*sgn(b*x + a) + 35*B*a^2*b^4*x^(3/2)*sgn(b*x + a) - 35*A*a*b^5*x^(3/2)*sgn(b*x + a) - 105*B*a^3*b^3*sqrt(x)*sgn(b*x + a) + 105*A*a^2*b^4*sqrt(x)*sgn(b*x + a))/b^7","A",0
811,1,133,0,0.172603," ","integrate(x^(3/2)*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a^{3} \mathrm{sgn}\left(b x + a\right) - A a^{2} b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{2 \, {\left(3 \, B b^{4} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{3} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 5 \, A b^{4} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) + 15 \, B a^{2} b^{2} \sqrt{x} \mathrm{sgn}\left(b x + a\right) - 15 \, A a b^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right)\right)}}{15 \, b^{5}}"," ",0,"-2*(B*a^3*sgn(b*x + a) - A*a^2*b*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^3) + 2/15*(3*B*b^4*x^(5/2)*sgn(b*x + a) - 5*B*a*b^3*x^(3/2)*sgn(b*x + a) + 5*A*b^4*x^(3/2)*sgn(b*x + a) + 15*B*a^2*b^2*sqrt(x)*sgn(b*x + a) - 15*A*a*b^3*sqrt(x)*sgn(b*x + a))/b^5","A",0
812,1,94,0,0.159470," ","integrate((B*x+A)*x^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(B a^{2} \mathrm{sgn}\left(b x + a\right) - A a b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{2 \, {\left(B b^{2} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b \sqrt{x} \mathrm{sgn}\left(b x + a\right) + 3 \, A b^{2} \sqrt{x} \mathrm{sgn}\left(b x + a\right)\right)}}{3 \, b^{3}}"," ",0,"2*(B*a^2*sgn(b*x + a) - A*a*b*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^2) + 2/3*(B*b^2*x^(3/2)*sgn(b*x + a) - 3*B*a*b*sqrt(x)*sgn(b*x + a) + 3*A*b^2*sqrt(x)*sgn(b*x + a))/b^3","A",0
813,1,57,0,0.160097," ","integrate((B*x+A)/x^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x} \mathrm{sgn}\left(b x + a\right)}{b} - \frac{2 \, {\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b}"," ",0,"2*B*sqrt(x)*sgn(b*x + a)/b - 2*(B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b)","A",0
814,1,57,0,0.157988," ","integrate((B*x+A)/x^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{2 \, A \mathrm{sgn}\left(b x + a\right)}{a \sqrt{x}}"," ",0,"2*(B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a) - 2*A*sgn(b*x + a)/(a*sqrt(x))","A",0
815,1,85,0,0.168659," ","integrate((B*x+A)/x^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a b \mathrm{sgn}\left(b x + a\right) - A b^{2} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} - \frac{2 \, {\left(3 \, B a x \mathrm{sgn}\left(b x + a\right) - 3 \, A b x \mathrm{sgn}\left(b x + a\right) + A a \mathrm{sgn}\left(b x + a\right)\right)}}{3 \, a^{2} x^{\frac{3}{2}}}"," ",0,"-2*(B*a*b*sgn(b*x + a) - A*b^2*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2) - 2/3*(3*B*a*x*sgn(b*x + a) - 3*A*b*x*sgn(b*x + a) + A*a*sgn(b*x + a))/(a^2*x^(3/2))","A",0
816,1,122,0,0.164603," ","integrate((B*x+A)/x^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(B a b^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} + \frac{2 \, {\left(15 \, B a b x^{2} \mathrm{sgn}\left(b x + a\right) - 15 \, A b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, B a^{2} x \mathrm{sgn}\left(b x + a\right) + 5 \, A a b x \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} \mathrm{sgn}\left(b x + a\right)\right)}}{15 \, a^{3} x^{\frac{5}{2}}}"," ",0,"2*(B*a*b^2*sgn(b*x + a) - A*b^3*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3) + 2/15*(15*B*a*b*x^2*sgn(b*x + a) - 15*A*b^2*x^2*sgn(b*x + a) - 5*B*a^2*x*sgn(b*x + a) + 5*A*a*b*x*sgn(b*x + a) - 3*A*a^2*sgn(b*x + a))/(a^3*x^(5/2))","A",0
817,1,158,0,0.181911," ","integrate((B*x+A)/x^(9/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a b^{3} \mathrm{sgn}\left(b x + a\right) - A b^{4} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} - \frac{2 \, {\left(105 \, B a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) - 105 \, A b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) - 35 \, B a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, A a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 21 \, B a^{3} x \mathrm{sgn}\left(b x + a\right) - 21 \, A a^{2} b x \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{3} \mathrm{sgn}\left(b x + a\right)\right)}}{105 \, a^{4} x^{\frac{7}{2}}}"," ",0,"-2*(B*a*b^3*sgn(b*x + a) - A*b^4*sgn(b*x + a))*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4) - 2/105*(105*B*a*b^2*x^3*sgn(b*x + a) - 105*A*b^3*x^3*sgn(b*x + a) - 35*B*a^2*b*x^2*sgn(b*x + a) + 35*A*a*b^2*x^2*sgn(b*x + a) + 21*B*a^3*x*sgn(b*x + a) - 21*A*a^2*b*x*sgn(b*x + a) + 15*A*a^3*sgn(b*x + a))/(a^4*x^(7/2))","A",0
818,1,170,0,0.222342," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{7 \, {\left(9 \, B a^{3} - 5 \, A a^{2} b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} b^{5} \mathrm{sgn}\left(b x + a\right)} + \frac{17 \, B a^{3} b x^{\frac{3}{2}} - 13 \, A a^{2} b^{2} x^{\frac{3}{2}} + 15 \, B a^{4} \sqrt{x} - 11 \, A a^{3} b \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} b^{5} \mathrm{sgn}\left(b x + a\right)} + \frac{2 \, {\left(3 \, B b^{12} x^{\frac{5}{2}} - 15 \, B a b^{11} x^{\frac{3}{2}} + 5 \, A b^{12} x^{\frac{3}{2}} + 90 \, B a^{2} b^{10} \sqrt{x} - 45 \, A a b^{11} \sqrt{x}\right)}}{15 \, b^{15} \mathrm{sgn}\left(b x + a\right)}"," ",0,"-7/4*(9*B*a^3 - 5*A*a^2*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^5*sgn(b*x + a)) + 1/4*(17*B*a^3*b*x^(3/2) - 13*A*a^2*b^2*x^(3/2) + 15*B*a^4*sqrt(x) - 11*A*a^3*b*sqrt(x))/((b*x + a)^2*b^5*sgn(b*x + a)) + 2/15*(3*B*b^12*x^(5/2) - 15*B*a*b^11*x^(3/2) + 5*A*b^12*x^(3/2) + 90*B*a^2*b^10*sqrt(x) - 45*A*a*b^11*sqrt(x))/(b^15*sgn(b*x + a))","A",0
819,1,143,0,0.258318," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{5 \, {\left(7 \, B a^{2} - 3 \, A a b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} b^{4} \mathrm{sgn}\left(b x + a\right)} - \frac{13 \, B a^{2} b x^{\frac{3}{2}} - 9 \, A a b^{2} x^{\frac{3}{2}} + 11 \, B a^{3} \sqrt{x} - 7 \, A a^{2} b \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} b^{4} \mathrm{sgn}\left(b x + a\right)} + \frac{2 \, {\left(B b^{6} x^{\frac{3}{2}} - 9 \, B a b^{5} \sqrt{x} + 3 \, A b^{6} \sqrt{x}\right)}}{3 \, b^{9} \mathrm{sgn}\left(b x + a\right)}"," ",0,"5/4*(7*B*a^2 - 3*A*a*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^4*sgn(b*x + a)) - 1/4*(13*B*a^2*b*x^(3/2) - 9*A*a*b^2*x^(3/2) + 11*B*a^3*sqrt(x) - 7*A*a^2*b*sqrt(x))/((b*x + a)^2*b^4*sgn(b*x + a)) + 2/3*(B*b^6*x^(3/2) - 9*B*a*b^5*sqrt(x) + 3*A*b^6*sqrt(x))/(b^9*sgn(b*x + a))","A",0
820,1,111,0,0.207305," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b^{3} \mathrm{sgn}\left(b x + a\right)} - \frac{3 \, {\left(5 \, B a - A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} b^{3} \mathrm{sgn}\left(b x + a\right)} + \frac{9 \, B a b x^{\frac{3}{2}} - 5 \, A b^{2} x^{\frac{3}{2}} + 7 \, B a^{2} \sqrt{x} - 3 \, A a b \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} b^{3} \mathrm{sgn}\left(b x + a\right)}"," ",0,"2*B*sqrt(x)/(b^3*sgn(b*x + a)) - 3/4*(5*B*a - A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^3*sgn(b*x + a)) + 1/4*(9*B*a*b*x^(3/2) - 5*A*b^2*x^(3/2) + 7*B*a^2*sqrt(x) - 3*A*a*b*sqrt(x))/((b*x + a)^2*b^3*sgn(b*x + a))","A",0
821,1,98,0,0.302313," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(3 \, B a + A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a b^{2} \mathrm{sgn}\left(b x + a\right)} - \frac{5 \, B a b x^{\frac{3}{2}} - A b^{2} x^{\frac{3}{2}} + 3 \, B a^{2} \sqrt{x} + A a b \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} a b^{2} \mathrm{sgn}\left(b x + a\right)}"," ",0,"1/4*(3*B*a + A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a*b^2*sgn(b*x + a)) - 1/4*(5*B*a*b*x^(3/2) - A*b^2*x^(3/2) + 3*B*a^2*sqrt(x) + A*a*b*sqrt(x))/((b*x + a)^2*a*b^2*sgn(b*x + a))","A",0
822,1,98,0,0.233334," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(1/2),x, algorithm=""giac"")","\frac{{\left(B a + 3 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{2} b \mathrm{sgn}\left(b x + a\right)} + \frac{B a b x^{\frac{3}{2}} + 3 \, A b^{2} x^{\frac{3}{2}} - B a^{2} \sqrt{x} + 5 \, A a b \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} a^{2} b \mathrm{sgn}\left(b x + a\right)}"," ",0,"1/4*(B*a + 3*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2*b*sgn(b*x + a)) + 1/4*(B*a*b*x^(3/2) + 3*A*b^2*x^(3/2) - B*a^2*sqrt(x) + 5*A*a*b*sqrt(x))/((b*x + a)^2*a^2*b*sgn(b*x + a))","A",0
823,1,110,0,0.208736," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, {\left(B a - 5 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{3} \mathrm{sgn}\left(b x + a\right)} - \frac{2 \, A}{a^{3} \sqrt{x} \mathrm{sgn}\left(b x + a\right)} + \frac{3 \, B a b x^{\frac{3}{2}} - 7 \, A b^{2} x^{\frac{3}{2}} + 5 \, B a^{2} \sqrt{x} - 9 \, A a b \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} a^{3} \mathrm{sgn}\left(b x + a\right)}"," ",0,"3/4*(B*a - 5*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3*sgn(b*x + a)) - 2*A/(a^3*sqrt(x)*sgn(b*x + a)) + 1/4*(3*B*a*b*x^(3/2) - 7*A*b^2*x^(3/2) + 5*B*a^2*sqrt(x) - 9*A*a*b*sqrt(x))/((b*x + a)^2*a^3*sgn(b*x + a))","A",0
824,1,132,0,0.207124," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{5 \, {\left(3 \, B a b - 7 \, A b^{2}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{4} \mathrm{sgn}\left(b x + a\right)} - \frac{2 \, {\left(3 \, B a x - 9 \, A b x + A a\right)}}{3 \, a^{4} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right)} - \frac{7 \, B a b^{2} x^{\frac{3}{2}} - 11 \, A b^{3} x^{\frac{3}{2}} + 9 \, B a^{2} b \sqrt{x} - 13 \, A a b^{2} \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} a^{4} \mathrm{sgn}\left(b x + a\right)}"," ",0,"-5/4*(3*B*a*b - 7*A*b^2)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4*sgn(b*x + a)) - 2/3*(3*B*a*x - 9*A*b*x + A*a)/(a^4*x^(3/2)*sgn(b*x + a)) - 1/4*(7*B*a*b^2*x^(3/2) - 11*A*b^3*x^(3/2) + 9*B*a^2*b*sqrt(x) - 13*A*a*b^2*sqrt(x))/((b*x + a)^2*a^4*sgn(b*x + a))","A",0
825,1,159,0,0.210708," ","integrate((B*x+A)/x^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{7 \, {\left(5 \, B a b^{2} - 9 \, A b^{3}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{5} \mathrm{sgn}\left(b x + a\right)} + \frac{11 \, B a b^{3} x^{\frac{3}{2}} - 15 \, A b^{4} x^{\frac{3}{2}} + 13 \, B a^{2} b^{2} \sqrt{x} - 17 \, A a b^{3} \sqrt{x}}{4 \, {\left(b x + a\right)}^{2} a^{5} \mathrm{sgn}\left(b x + a\right)} + \frac{2 \, {\left(45 \, B a b x^{2} - 90 \, A b^{2} x^{2} - 5 \, B a^{2} x + 15 \, A a b x - 3 \, A a^{2}\right)}}{15 \, a^{5} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right)}"," ",0,"7/4*(5*B*a*b^2 - 9*A*b^3)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^5*sgn(b*x + a)) + 1/4*(11*B*a*b^3*x^(3/2) - 15*A*b^4*x^(3/2) + 13*B*a^2*b^2*sqrt(x) - 17*A*a*b^3*sqrt(x))/((b*x + a)^2*a^5*sgn(b*x + a)) + 2/15*(45*B*a*b*x^2 - 90*A*b^2*x^2 - 5*B*a^2*x + 15*A*a*b*x - 3*A*a^2)/(a^5*x^(5/2)*sgn(b*x + a))","A",0
826,1,218,0,0.293291," ","integrate(x^(11/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{231 \, {\left(13 \, B a^{3} - 5 \, A a^{2} b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} b^{7} \mathrm{sgn}\left(b x + a\right)} + \frac{4431 \, B a^{3} b^{3} x^{\frac{7}{2}} - 2295 \, A a^{2} b^{4} x^{\frac{7}{2}} + 11767 \, B a^{4} b^{2} x^{\frac{5}{2}} - 5855 \, A a^{3} b^{3} x^{\frac{5}{2}} + 10633 \, B a^{5} b x^{\frac{3}{2}} - 5153 \, A a^{4} b^{2} x^{\frac{3}{2}} + 3249 \, B a^{6} \sqrt{x} - 1545 \, A a^{5} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} b^{7} \mathrm{sgn}\left(b x + a\right)} + \frac{2 \, {\left(3 \, B b^{20} x^{\frac{5}{2}} - 25 \, B a b^{19} x^{\frac{3}{2}} + 5 \, A b^{20} x^{\frac{3}{2}} + 225 \, B a^{2} b^{18} \sqrt{x} - 75 \, A a b^{19} \sqrt{x}\right)}}{15 \, b^{25} \mathrm{sgn}\left(b x + a\right)}"," ",0,"-231/64*(13*B*a^3 - 5*A*a^2*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^7*sgn(b*x + a)) + 1/192*(4431*B*a^3*b^3*x^(7/2) - 2295*A*a^2*b^4*x^(7/2) + 11767*B*a^4*b^2*x^(5/2) - 5855*A*a^3*b^3*x^(5/2) + 10633*B*a^5*b*x^(3/2) - 5153*A*a^4*b^2*x^(3/2) + 3249*B*a^6*sqrt(x) - 1545*A*a^5*b*sqrt(x))/((b*x + a)^4*b^7*sgn(b*x + a)) + 2/15*(3*B*b^20*x^(5/2) - 25*B*a*b^19*x^(3/2) + 5*A*b^20*x^(3/2) + 225*B*a^2*b^18*sqrt(x) - 75*A*a*b^19*sqrt(x))/(b^25*sgn(b*x + a))","A",0
827,1,191,0,0.227766," ","integrate(x^(9/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{105 \, {\left(11 \, B a^{2} - 3 \, A a b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} b^{6} \mathrm{sgn}\left(b x + a\right)} - \frac{2295 \, B a^{2} b^{3} x^{\frac{7}{2}} - 975 \, A a b^{4} x^{\frac{7}{2}} + 5855 \, B a^{3} b^{2} x^{\frac{5}{2}} - 2295 \, A a^{2} b^{3} x^{\frac{5}{2}} + 5153 \, B a^{4} b x^{\frac{3}{2}} - 1929 \, A a^{3} b^{2} x^{\frac{3}{2}} + 1545 \, B a^{5} \sqrt{x} - 561 \, A a^{4} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} b^{6} \mathrm{sgn}\left(b x + a\right)} + \frac{2 \, {\left(B b^{10} x^{\frac{3}{2}} - 15 \, B a b^{9} \sqrt{x} + 3 \, A b^{10} \sqrt{x}\right)}}{3 \, b^{15} \mathrm{sgn}\left(b x + a\right)}"," ",0,"105/64*(11*B*a^2 - 3*A*a*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^6*sgn(b*x + a)) - 1/192*(2295*B*a^2*b^3*x^(7/2) - 975*A*a*b^4*x^(7/2) + 5855*B*a^3*b^2*x^(5/2) - 2295*A*a^2*b^3*x^(5/2) + 5153*B*a^4*b*x^(3/2) - 1929*A*a^3*b^2*x^(3/2) + 1545*B*a^5*sqrt(x) - 561*A*a^4*b*sqrt(x))/((b*x + a)^4*b^6*sgn(b*x + a)) + 2/3*(B*b^10*x^(3/2) - 15*B*a*b^9*sqrt(x) + 3*A*b^10*sqrt(x))/(b^15*sgn(b*x + a))","A",0
828,1,159,0,0.384171," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b^{5} \mathrm{sgn}\left(b x + a\right)} - \frac{35 \, {\left(9 \, B a - A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} b^{5} \mathrm{sgn}\left(b x + a\right)} + \frac{975 \, B a b^{3} x^{\frac{7}{2}} - 279 \, A b^{4} x^{\frac{7}{2}} + 2295 \, B a^{2} b^{2} x^{\frac{5}{2}} - 511 \, A a b^{3} x^{\frac{5}{2}} + 1929 \, B a^{3} b x^{\frac{3}{2}} - 385 \, A a^{2} b^{2} x^{\frac{3}{2}} + 561 \, B a^{4} \sqrt{x} - 105 \, A a^{3} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} b^{5} \mathrm{sgn}\left(b x + a\right)}"," ",0,"2*B*sqrt(x)/(b^5*sgn(b*x + a)) - 35/64*(9*B*a - A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^5*sgn(b*x + a)) + 1/192*(975*B*a*b^3*x^(7/2) - 279*A*b^4*x^(7/2) + 2295*B*a^2*b^2*x^(5/2) - 511*A*a*b^3*x^(5/2) + 1929*B*a^3*b*x^(3/2) - 385*A*a^2*b^2*x^(3/2) + 561*B*a^4*sqrt(x) - 105*A*a^3*b*sqrt(x))/((b*x + a)^4*b^5*sgn(b*x + a))","A",0
829,1,147,0,0.356839," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{5 \, {\left(7 \, B a + A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} a b^{4} \mathrm{sgn}\left(b x + a\right)} - \frac{279 \, B a b^{3} x^{\frac{7}{2}} - 15 \, A b^{4} x^{\frac{7}{2}} + 511 \, B a^{2} b^{2} x^{\frac{5}{2}} + 73 \, A a b^{3} x^{\frac{5}{2}} + 385 \, B a^{3} b x^{\frac{3}{2}} + 55 \, A a^{2} b^{2} x^{\frac{3}{2}} + 105 \, B a^{4} \sqrt{x} + 15 \, A a^{3} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} a b^{4} \mathrm{sgn}\left(b x + a\right)}"," ",0,"5/64*(7*B*a + A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a*b^4*sgn(b*x + a)) - 1/192*(279*B*a*b^3*x^(7/2) - 15*A*b^4*x^(7/2) + 511*B*a^2*b^2*x^(5/2) + 73*A*a*b^3*x^(5/2) + 385*B*a^3*b*x^(3/2) + 55*A*a^2*b^2*x^(3/2) + 105*B*a^4*sqrt(x) + 15*A*a^3*b*sqrt(x))/((b*x + a)^4*a*b^4*sgn(b*x + a))","A",0
830,1,148,0,0.265993," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(5 \, B a + 3 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} a^{2} b^{3} \mathrm{sgn}\left(b x + a\right)} + \frac{15 \, B a b^{3} x^{\frac{7}{2}} + 9 \, A b^{4} x^{\frac{7}{2}} - 73 \, B a^{2} b^{2} x^{\frac{5}{2}} + 33 \, A a b^{3} x^{\frac{5}{2}} - 55 \, B a^{3} b x^{\frac{3}{2}} - 33 \, A a^{2} b^{2} x^{\frac{3}{2}} - 15 \, B a^{4} \sqrt{x} - 9 \, A a^{3} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} a^{2} b^{3} \mathrm{sgn}\left(b x + a\right)}"," ",0,"1/64*(5*B*a + 3*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2*b^3*sgn(b*x + a)) + 1/192*(15*B*a*b^3*x^(7/2) + 9*A*b^4*x^(7/2) - 73*B*a^2*b^2*x^(5/2) + 33*A*a*b^3*x^(5/2) - 55*B*a^3*b*x^(3/2) - 33*A*a^2*b^2*x^(3/2) - 15*B*a^4*sqrt(x) - 9*A*a^3*b*sqrt(x))/((b*x + a)^4*a^2*b^3*sgn(b*x + a))","A",0
831,1,148,0,0.217119," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(3 \, B a + 5 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} a^{3} b^{2} \mathrm{sgn}\left(b x + a\right)} + \frac{9 \, B a b^{3} x^{\frac{7}{2}} + 15 \, A b^{4} x^{\frac{7}{2}} + 33 \, B a^{2} b^{2} x^{\frac{5}{2}} + 55 \, A a b^{3} x^{\frac{5}{2}} - 33 \, B a^{3} b x^{\frac{3}{2}} + 73 \, A a^{2} b^{2} x^{\frac{3}{2}} - 9 \, B a^{4} \sqrt{x} - 15 \, A a^{3} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} a^{3} b^{2} \mathrm{sgn}\left(b x + a\right)}"," ",0,"1/64*(3*B*a + 5*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3*b^2*sgn(b*x + a)) + 1/192*(9*B*a*b^3*x^(7/2) + 15*A*b^4*x^(7/2) + 33*B*a^2*b^2*x^(5/2) + 55*A*a*b^3*x^(5/2) - 33*B*a^3*b*x^(3/2) + 73*A*a^2*b^2*x^(3/2) - 9*B*a^4*sqrt(x) - 15*A*a^3*b*sqrt(x))/((b*x + a)^4*a^3*b^2*sgn(b*x + a))","A",0
832,1,147,0,0.239774," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(1/2),x, algorithm=""giac"")","\frac{5 \, {\left(B a + 7 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} a^{4} b \mathrm{sgn}\left(b x + a\right)} + \frac{15 \, B a b^{3} x^{\frac{7}{2}} + 105 \, A b^{4} x^{\frac{7}{2}} + 55 \, B a^{2} b^{2} x^{\frac{5}{2}} + 385 \, A a b^{3} x^{\frac{5}{2}} + 73 \, B a^{3} b x^{\frac{3}{2}} + 511 \, A a^{2} b^{2} x^{\frac{3}{2}} - 15 \, B a^{4} \sqrt{x} + 279 \, A a^{3} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} a^{4} b \mathrm{sgn}\left(b x + a\right)}"," ",0,"5/64*(B*a + 7*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4*b*sgn(b*x + a)) + 1/192*(15*B*a*b^3*x^(7/2) + 105*A*b^4*x^(7/2) + 55*B*a^2*b^2*x^(5/2) + 385*A*a*b^3*x^(5/2) + 73*B*a^3*b*x^(3/2) + 511*A*a^2*b^2*x^(3/2) - 15*B*a^4*sqrt(x) + 279*A*a^3*b*sqrt(x))/((b*x + a)^4*a^4*b*sgn(b*x + a))","A",0
833,1,158,0,0.266783," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{35 \, {\left(B a - 9 \, A b\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} a^{5} \mathrm{sgn}\left(b x + a\right)} - \frac{2 \, A}{a^{5} \sqrt{x} \mathrm{sgn}\left(b x + a\right)} + \frac{105 \, B a b^{3} x^{\frac{7}{2}} - 561 \, A b^{4} x^{\frac{7}{2}} + 385 \, B a^{2} b^{2} x^{\frac{5}{2}} - 1929 \, A a b^{3} x^{\frac{5}{2}} + 511 \, B a^{3} b x^{\frac{3}{2}} - 2295 \, A a^{2} b^{2} x^{\frac{3}{2}} + 279 \, B a^{4} \sqrt{x} - 975 \, A a^{3} b \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} a^{5} \mathrm{sgn}\left(b x + a\right)}"," ",0,"35/64*(B*a - 9*A*b)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^5*sgn(b*x + a)) - 2*A/(a^5*sqrt(x)*sgn(b*x + a)) + 1/192*(105*B*a*b^3*x^(7/2) - 561*A*b^4*x^(7/2) + 385*B*a^2*b^2*x^(5/2) - 1929*A*a*b^3*x^(5/2) + 511*B*a^3*b*x^(3/2) - 2295*A*a^2*b^2*x^(3/2) + 279*B*a^4*sqrt(x) - 975*A*a^3*b*sqrt(x))/((b*x + a)^4*a^5*sgn(b*x + a))","A",0
834,1,180,0,0.241003," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{105 \, {\left(3 \, B a b - 11 \, A b^{2}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} a^{6} \mathrm{sgn}\left(b x + a\right)} - \frac{2 \, {\left(3 \, B a x - 15 \, A b x + A a\right)}}{3 \, a^{6} x^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right)} - \frac{561 \, B a b^{4} x^{\frac{7}{2}} - 1545 \, A b^{5} x^{\frac{7}{2}} + 1929 \, B a^{2} b^{3} x^{\frac{5}{2}} - 5153 \, A a b^{4} x^{\frac{5}{2}} + 2295 \, B a^{3} b^{2} x^{\frac{3}{2}} - 5855 \, A a^{2} b^{3} x^{\frac{3}{2}} + 975 \, B a^{4} b \sqrt{x} - 2295 \, A a^{3} b^{2} \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} a^{6} \mathrm{sgn}\left(b x + a\right)}"," ",0,"-105/64*(3*B*a*b - 11*A*b^2)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^6*sgn(b*x + a)) - 2/3*(3*B*a*x - 15*A*b*x + A*a)/(a^6*x^(3/2)*sgn(b*x + a)) - 1/192*(561*B*a*b^4*x^(7/2) - 1545*A*b^5*x^(7/2) + 1929*B*a^2*b^3*x^(5/2) - 5153*A*a*b^4*x^(5/2) + 2295*B*a^3*b^2*x^(3/2) - 5855*A*a^2*b^3*x^(3/2) + 975*B*a^4*b*sqrt(x) - 2295*A*a^3*b^2*sqrt(x))/((b*x + a)^4*a^6*sgn(b*x + a))","A",0
835,1,207,0,0.229763," ","integrate((B*x+A)/x^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{231 \, {\left(5 \, B a b^{2} - 13 \, A b^{3}\right)} \arctan\left(\frac{b \sqrt{x}}{\sqrt{a b}}\right)}{64 \, \sqrt{a b} a^{7} \mathrm{sgn}\left(b x + a\right)} + \frac{2 \, {\left(75 \, B a b x^{2} - 225 \, A b^{2} x^{2} - 5 \, B a^{2} x + 25 \, A a b x - 3 \, A a^{2}\right)}}{15 \, a^{7} x^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right)} + \frac{1545 \, B a b^{5} x^{\frac{7}{2}} - 3249 \, A b^{6} x^{\frac{7}{2}} + 5153 \, B a^{2} b^{4} x^{\frac{5}{2}} - 10633 \, A a b^{5} x^{\frac{5}{2}} + 5855 \, B a^{3} b^{3} x^{\frac{3}{2}} - 11767 \, A a^{2} b^{4} x^{\frac{3}{2}} + 2295 \, B a^{4} b^{2} \sqrt{x} - 4431 \, A a^{3} b^{3} \sqrt{x}}{192 \, {\left(b x + a\right)}^{4} a^{7} \mathrm{sgn}\left(b x + a\right)}"," ",0,"231/64*(5*B*a*b^2 - 13*A*b^3)*arctan(b*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^7*sgn(b*x + a)) + 2/15*(75*B*a*b*x^2 - 225*A*b^2*x^2 - 5*B*a^2*x + 25*A*a*b*x - 3*A*a^2)/(a^7*x^(5/2)*sgn(b*x + a)) + 1/192*(1545*B*a*b^5*x^(7/2) - 3249*A*b^6*x^(7/2) + 5153*B*a^2*b^4*x^(5/2) - 10633*A*a*b^5*x^(5/2) + 5855*B*a^3*b^3*x^(3/2) - 11767*A*a^2*b^4*x^(3/2) + 2295*B*a^4*b^2*sqrt(x) - 4431*A*a^3*b^3*sqrt(x))/((b*x + a)^4*a^7*sgn(b*x + a))","A",0
836,1,1808,0,0.266938," ","integrate(x^m*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{B b^{6} m^{7} x^{8} x^{m} + 6 \, B a b^{5} m^{7} x^{7} x^{m} + A b^{6} m^{7} x^{7} x^{m} + 28 \, B b^{6} m^{6} x^{8} x^{m} + 15 \, B a^{2} b^{4} m^{7} x^{6} x^{m} + 6 \, A a b^{5} m^{7} x^{6} x^{m} + 174 \, B a b^{5} m^{6} x^{7} x^{m} + 29 \, A b^{6} m^{6} x^{7} x^{m} + 322 \, B b^{6} m^{5} x^{8} x^{m} + 20 \, B a^{3} b^{3} m^{7} x^{5} x^{m} + 15 \, A a^{2} b^{4} m^{7} x^{5} x^{m} + 450 \, B a^{2} b^{4} m^{6} x^{6} x^{m} + 180 \, A a b^{5} m^{6} x^{6} x^{m} + 2058 \, B a b^{5} m^{5} x^{7} x^{m} + 343 \, A b^{6} m^{5} x^{7} x^{m} + 1960 \, B b^{6} m^{4} x^{8} x^{m} + 15 \, B a^{4} b^{2} m^{7} x^{4} x^{m} + 20 \, A a^{3} b^{3} m^{7} x^{4} x^{m} + 620 \, B a^{3} b^{3} m^{6} x^{5} x^{m} + 465 \, A a^{2} b^{4} m^{6} x^{5} x^{m} + 5490 \, B a^{2} b^{4} m^{5} x^{6} x^{m} + 2196 \, A a b^{5} m^{5} x^{6} x^{m} + 12810 \, B a b^{5} m^{4} x^{7} x^{m} + 2135 \, A b^{6} m^{4} x^{7} x^{m} + 6769 \, B b^{6} m^{3} x^{8} x^{m} + 6 \, B a^{5} b m^{7} x^{3} x^{m} + 15 \, A a^{4} b^{2} m^{7} x^{3} x^{m} + 480 \, B a^{4} b^{2} m^{6} x^{4} x^{m} + 640 \, A a^{3} b^{3} m^{6} x^{4} x^{m} + 7820 \, B a^{3} b^{3} m^{5} x^{5} x^{m} + 5865 \, A a^{2} b^{4} m^{5} x^{5} x^{m} + 35100 \, B a^{2} b^{4} m^{4} x^{6} x^{m} + 14040 \, A a b^{5} m^{4} x^{6} x^{m} + 45024 \, B a b^{5} m^{3} x^{7} x^{m} + 7504 \, A b^{6} m^{3} x^{7} x^{m} + 13132 \, B b^{6} m^{2} x^{8} x^{m} + B a^{6} m^{7} x^{2} x^{m} + 6 \, A a^{5} b m^{7} x^{2} x^{m} + 198 \, B a^{5} b m^{6} x^{3} x^{m} + 495 \, A a^{4} b^{2} m^{6} x^{3} x^{m} + 6270 \, B a^{4} b^{2} m^{5} x^{4} x^{m} + 8360 \, A a^{3} b^{3} m^{5} x^{4} x^{m} + 51620 \, B a^{3} b^{3} m^{4} x^{5} x^{m} + 38715 \, A a^{2} b^{4} m^{4} x^{5} x^{m} + 126135 \, B a^{2} b^{4} m^{3} x^{6} x^{m} + 50454 \, A a b^{5} m^{3} x^{6} x^{m} + 88536 \, B a b^{5} m^{2} x^{7} x^{m} + 14756 \, A b^{6} m^{2} x^{7} x^{m} + 13068 \, B b^{6} m x^{8} x^{m} + A a^{6} m^{7} x x^{m} + 34 \, B a^{6} m^{6} x^{2} x^{m} + 204 \, A a^{5} b m^{6} x^{2} x^{m} + 2682 \, B a^{5} b m^{5} x^{3} x^{m} + 6705 \, A a^{4} b^{2} m^{5} x^{3} x^{m} + 42960 \, B a^{4} b^{2} m^{4} x^{4} x^{m} + 57280 \, A a^{3} b^{3} m^{4} x^{4} x^{m} + 190880 \, B a^{3} b^{3} m^{3} x^{5} x^{m} + 143160 \, A a^{2} b^{4} m^{3} x^{5} x^{m} + 252450 \, B a^{2} b^{4} m^{2} x^{6} x^{m} + 100980 \, A a b^{5} m^{2} x^{6} x^{m} + 88992 \, B a b^{5} m x^{7} x^{m} + 14832 \, A b^{6} m x^{7} x^{m} + 5040 \, B b^{6} x^{8} x^{m} + 35 \, A a^{6} m^{6} x x^{m} + 478 \, B a^{6} m^{5} x^{2} x^{m} + 2868 \, A a^{5} b m^{5} x^{2} x^{m} + 19170 \, B a^{5} b m^{4} x^{3} x^{m} + 47925 \, A a^{4} b^{2} m^{4} x^{3} x^{m} + 164895 \, B a^{4} b^{2} m^{3} x^{4} x^{m} + 219860 \, A a^{3} b^{3} m^{3} x^{4} x^{m} + 391280 \, B a^{3} b^{3} m^{2} x^{5} x^{m} + 293460 \, A a^{2} b^{4} m^{2} x^{5} x^{m} + 257160 \, B a^{2} b^{4} m x^{6} x^{m} + 102864 \, A a b^{5} m x^{6} x^{m} + 34560 \, B a b^{5} x^{7} x^{m} + 5760 \, A b^{6} x^{7} x^{m} + 511 \, A a^{6} m^{5} x x^{m} + 3580 \, B a^{6} m^{4} x^{2} x^{m} + 21480 \, A a^{5} b m^{4} x^{2} x^{m} + 77184 \, B a^{5} b m^{3} x^{3} x^{m} + 192960 \, A a^{4} b^{2} m^{3} x^{3} x^{m} + 349680 \, B a^{4} b^{2} m^{2} x^{4} x^{m} + 466240 \, A a^{3} b^{3} m^{2} x^{4} x^{m} + 406080 \, B a^{3} b^{3} m x^{5} x^{m} + 304560 \, A a^{2} b^{4} m x^{5} x^{m} + 100800 \, B a^{2} b^{4} x^{6} x^{m} + 40320 \, A a b^{5} x^{6} x^{m} + 4025 \, A a^{6} m^{4} x x^{m} + 15289 \, B a^{6} m^{3} x^{2} x^{m} + 91734 \, A a^{5} b m^{3} x^{2} x^{m} + 172152 \, B a^{5} b m^{2} x^{3} x^{m} + 430380 \, A a^{4} b^{2} m^{2} x^{3} x^{m} + 373140 \, B a^{4} b^{2} m x^{4} x^{m} + 497520 \, A a^{3} b^{3} m x^{4} x^{m} + 161280 \, B a^{3} b^{3} x^{5} x^{m} + 120960 \, A a^{2} b^{4} x^{5} x^{m} + 18424 \, A a^{6} m^{3} x x^{m} + 36706 \, B a^{6} m^{2} x^{2} x^{m} + 220236 \, A a^{5} b m^{2} x^{2} x^{m} + 192288 \, B a^{5} b m x^{3} x^{m} + 480720 \, A a^{4} b^{2} m x^{3} x^{m} + 151200 \, B a^{4} b^{2} x^{4} x^{m} + 201600 \, A a^{3} b^{3} x^{4} x^{m} + 48860 \, A a^{6} m^{2} x x^{m} + 44712 \, B a^{6} m x^{2} x^{m} + 268272 \, A a^{5} b m x^{2} x^{m} + 80640 \, B a^{5} b x^{3} x^{m} + 201600 \, A a^{4} b^{2} x^{3} x^{m} + 69264 \, A a^{6} m x x^{m} + 20160 \, B a^{6} x^{2} x^{m} + 120960 \, A a^{5} b x^{2} x^{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}"," ",0,"(B*b^6*m^7*x^8*x^m + 6*B*a*b^5*m^7*x^7*x^m + A*b^6*m^7*x^7*x^m + 28*B*b^6*m^6*x^8*x^m + 15*B*a^2*b^4*m^7*x^6*x^m + 6*A*a*b^5*m^7*x^6*x^m + 174*B*a*b^5*m^6*x^7*x^m + 29*A*b^6*m^6*x^7*x^m + 322*B*b^6*m^5*x^8*x^m + 20*B*a^3*b^3*m^7*x^5*x^m + 15*A*a^2*b^4*m^7*x^5*x^m + 450*B*a^2*b^4*m^6*x^6*x^m + 180*A*a*b^5*m^6*x^6*x^m + 2058*B*a*b^5*m^5*x^7*x^m + 343*A*b^6*m^5*x^7*x^m + 1960*B*b^6*m^4*x^8*x^m + 15*B*a^4*b^2*m^7*x^4*x^m + 20*A*a^3*b^3*m^7*x^4*x^m + 620*B*a^3*b^3*m^6*x^5*x^m + 465*A*a^2*b^4*m^6*x^5*x^m + 5490*B*a^2*b^4*m^5*x^6*x^m + 2196*A*a*b^5*m^5*x^6*x^m + 12810*B*a*b^5*m^4*x^7*x^m + 2135*A*b^6*m^4*x^7*x^m + 6769*B*b^6*m^3*x^8*x^m + 6*B*a^5*b*m^7*x^3*x^m + 15*A*a^4*b^2*m^7*x^3*x^m + 480*B*a^4*b^2*m^6*x^4*x^m + 640*A*a^3*b^3*m^6*x^4*x^m + 7820*B*a^3*b^3*m^5*x^5*x^m + 5865*A*a^2*b^4*m^5*x^5*x^m + 35100*B*a^2*b^4*m^4*x^6*x^m + 14040*A*a*b^5*m^4*x^6*x^m + 45024*B*a*b^5*m^3*x^7*x^m + 7504*A*b^6*m^3*x^7*x^m + 13132*B*b^6*m^2*x^8*x^m + B*a^6*m^7*x^2*x^m + 6*A*a^5*b*m^7*x^2*x^m + 198*B*a^5*b*m^6*x^3*x^m + 495*A*a^4*b^2*m^6*x^3*x^m + 6270*B*a^4*b^2*m^5*x^4*x^m + 8360*A*a^3*b^3*m^5*x^4*x^m + 51620*B*a^3*b^3*m^4*x^5*x^m + 38715*A*a^2*b^4*m^4*x^5*x^m + 126135*B*a^2*b^4*m^3*x^6*x^m + 50454*A*a*b^5*m^3*x^6*x^m + 88536*B*a*b^5*m^2*x^7*x^m + 14756*A*b^6*m^2*x^7*x^m + 13068*B*b^6*m*x^8*x^m + A*a^6*m^7*x*x^m + 34*B*a^6*m^6*x^2*x^m + 204*A*a^5*b*m^6*x^2*x^m + 2682*B*a^5*b*m^5*x^3*x^m + 6705*A*a^4*b^2*m^5*x^3*x^m + 42960*B*a^4*b^2*m^4*x^4*x^m + 57280*A*a^3*b^3*m^4*x^4*x^m + 190880*B*a^3*b^3*m^3*x^5*x^m + 143160*A*a^2*b^4*m^3*x^5*x^m + 252450*B*a^2*b^4*m^2*x^6*x^m + 100980*A*a*b^5*m^2*x^6*x^m + 88992*B*a*b^5*m*x^7*x^m + 14832*A*b^6*m*x^7*x^m + 5040*B*b^6*x^8*x^m + 35*A*a^6*m^6*x*x^m + 478*B*a^6*m^5*x^2*x^m + 2868*A*a^5*b*m^5*x^2*x^m + 19170*B*a^5*b*m^4*x^3*x^m + 47925*A*a^4*b^2*m^4*x^3*x^m + 164895*B*a^4*b^2*m^3*x^4*x^m + 219860*A*a^3*b^3*m^3*x^4*x^m + 391280*B*a^3*b^3*m^2*x^5*x^m + 293460*A*a^2*b^4*m^2*x^5*x^m + 257160*B*a^2*b^4*m*x^6*x^m + 102864*A*a*b^5*m*x^6*x^m + 34560*B*a*b^5*x^7*x^m + 5760*A*b^6*x^7*x^m + 511*A*a^6*m^5*x*x^m + 3580*B*a^6*m^4*x^2*x^m + 21480*A*a^5*b*m^4*x^2*x^m + 77184*B*a^5*b*m^3*x^3*x^m + 192960*A*a^4*b^2*m^3*x^3*x^m + 349680*B*a^4*b^2*m^2*x^4*x^m + 466240*A*a^3*b^3*m^2*x^4*x^m + 406080*B*a^3*b^3*m*x^5*x^m + 304560*A*a^2*b^4*m*x^5*x^m + 100800*B*a^2*b^4*x^6*x^m + 40320*A*a*b^5*x^6*x^m + 4025*A*a^6*m^4*x*x^m + 15289*B*a^6*m^3*x^2*x^m + 91734*A*a^5*b*m^3*x^2*x^m + 172152*B*a^5*b*m^2*x^3*x^m + 430380*A*a^4*b^2*m^2*x^3*x^m + 373140*B*a^4*b^2*m*x^4*x^m + 497520*A*a^3*b^3*m*x^4*x^m + 161280*B*a^3*b^3*x^5*x^m + 120960*A*a^2*b^4*x^5*x^m + 18424*A*a^6*m^3*x*x^m + 36706*B*a^6*m^2*x^2*x^m + 220236*A*a^5*b*m^2*x^2*x^m + 192288*B*a^5*b*m*x^3*x^m + 480720*A*a^4*b^2*m*x^3*x^m + 151200*B*a^4*b^2*x^4*x^m + 201600*A*a^3*b^3*x^4*x^m + 48860*A*a^6*m^2*x*x^m + 44712*B*a^6*m*x^2*x^m + 268272*A*a^5*b*m*x^2*x^m + 80640*B*a^5*b*x^3*x^m + 201600*A*a^4*b^2*x^3*x^m + 69264*A*a^6*m*x*x^m + 20160*B*a^6*x^2*x^m + 120960*A*a^5*b*x^2*x^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
837,1,926,0,0.195292," ","integrate(x^m*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{B b^{4} m^{5} x^{6} x^{m} + 4 \, B a b^{3} m^{5} x^{5} x^{m} + A b^{4} m^{5} x^{5} x^{m} + 15 \, B b^{4} m^{4} x^{6} x^{m} + 6 \, B a^{2} b^{2} m^{5} x^{4} x^{m} + 4 \, A a b^{3} m^{5} x^{4} x^{m} + 64 \, B a b^{3} m^{4} x^{5} x^{m} + 16 \, A b^{4} m^{4} x^{5} x^{m} + 85 \, B b^{4} m^{3} x^{6} x^{m} + 4 \, B a^{3} b m^{5} x^{3} x^{m} + 6 \, A a^{2} b^{2} m^{5} x^{3} x^{m} + 102 \, B a^{2} b^{2} m^{4} x^{4} x^{m} + 68 \, A a b^{3} m^{4} x^{4} x^{m} + 380 \, B a b^{3} m^{3} x^{5} x^{m} + 95 \, A b^{4} m^{3} x^{5} x^{m} + 225 \, B b^{4} m^{2} x^{6} x^{m} + B a^{4} m^{5} x^{2} x^{m} + 4 \, A a^{3} b m^{5} x^{2} x^{m} + 72 \, B a^{3} b m^{4} x^{3} x^{m} + 108 \, A a^{2} b^{2} m^{4} x^{3} x^{m} + 642 \, B a^{2} b^{2} m^{3} x^{4} x^{m} + 428 \, A a b^{3} m^{3} x^{4} x^{m} + 1040 \, B a b^{3} m^{2} x^{5} x^{m} + 260 \, A b^{4} m^{2} x^{5} x^{m} + 274 \, B b^{4} m x^{6} x^{m} + A a^{4} m^{5} x x^{m} + 19 \, B a^{4} m^{4} x^{2} x^{m} + 76 \, A a^{3} b m^{4} x^{2} x^{m} + 484 \, B a^{3} b m^{3} x^{3} x^{m} + 726 \, A a^{2} b^{2} m^{3} x^{3} x^{m} + 1842 \, B a^{2} b^{2} m^{2} x^{4} x^{m} + 1228 \, A a b^{3} m^{2} x^{4} x^{m} + 1296 \, B a b^{3} m x^{5} x^{m} + 324 \, A b^{4} m x^{5} x^{m} + 120 \, B b^{4} x^{6} x^{m} + 20 \, A a^{4} m^{4} x x^{m} + 137 \, B a^{4} m^{3} x^{2} x^{m} + 548 \, A a^{3} b m^{3} x^{2} x^{m} + 1488 \, B a^{3} b m^{2} x^{3} x^{m} + 2232 \, A a^{2} b^{2} m^{2} x^{3} x^{m} + 2376 \, B a^{2} b^{2} m x^{4} x^{m} + 1584 \, A a b^{3} m x^{4} x^{m} + 576 \, B a b^{3} x^{5} x^{m} + 144 \, A b^{4} x^{5} x^{m} + 155 \, A a^{4} m^{3} x x^{m} + 461 \, B a^{4} m^{2} x^{2} x^{m} + 1844 \, A a^{3} b m^{2} x^{2} x^{m} + 2032 \, B a^{3} b m x^{3} x^{m} + 3048 \, A a^{2} b^{2} m x^{3} x^{m} + 1080 \, B a^{2} b^{2} x^{4} x^{m} + 720 \, A a b^{3} x^{4} x^{m} + 580 \, A a^{4} m^{2} x x^{m} + 702 \, B a^{4} m x^{2} x^{m} + 2808 \, A a^{3} b m x^{2} x^{m} + 960 \, B a^{3} b x^{3} x^{m} + 1440 \, A a^{2} b^{2} x^{3} x^{m} + 1044 \, A a^{4} m x x^{m} + 360 \, B a^{4} x^{2} x^{m} + 1440 \, A a^{3} b x^{2} x^{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}"," ",0,"(B*b^4*m^5*x^6*x^m + 4*B*a*b^3*m^5*x^5*x^m + A*b^4*m^5*x^5*x^m + 15*B*b^4*m^4*x^6*x^m + 6*B*a^2*b^2*m^5*x^4*x^m + 4*A*a*b^3*m^5*x^4*x^m + 64*B*a*b^3*m^4*x^5*x^m + 16*A*b^4*m^4*x^5*x^m + 85*B*b^4*m^3*x^6*x^m + 4*B*a^3*b*m^5*x^3*x^m + 6*A*a^2*b^2*m^5*x^3*x^m + 102*B*a^2*b^2*m^4*x^4*x^m + 68*A*a*b^3*m^4*x^4*x^m + 380*B*a*b^3*m^3*x^5*x^m + 95*A*b^4*m^3*x^5*x^m + 225*B*b^4*m^2*x^6*x^m + B*a^4*m^5*x^2*x^m + 4*A*a^3*b*m^5*x^2*x^m + 72*B*a^3*b*m^4*x^3*x^m + 108*A*a^2*b^2*m^4*x^3*x^m + 642*B*a^2*b^2*m^3*x^4*x^m + 428*A*a*b^3*m^3*x^4*x^m + 1040*B*a*b^3*m^2*x^5*x^m + 260*A*b^4*m^2*x^5*x^m + 274*B*b^4*m*x^6*x^m + A*a^4*m^5*x*x^m + 19*B*a^4*m^4*x^2*x^m + 76*A*a^3*b*m^4*x^2*x^m + 484*B*a^3*b*m^3*x^3*x^m + 726*A*a^2*b^2*m^3*x^3*x^m + 1842*B*a^2*b^2*m^2*x^4*x^m + 1228*A*a*b^3*m^2*x^4*x^m + 1296*B*a*b^3*m*x^5*x^m + 324*A*b^4*m*x^5*x^m + 120*B*b^4*x^6*x^m + 20*A*a^4*m^4*x*x^m + 137*B*a^4*m^3*x^2*x^m + 548*A*a^3*b*m^3*x^2*x^m + 1488*B*a^3*b*m^2*x^3*x^m + 2232*A*a^2*b^2*m^2*x^3*x^m + 2376*B*a^2*b^2*m*x^4*x^m + 1584*A*a*b^3*m*x^4*x^m + 576*B*a*b^3*x^5*x^m + 144*A*b^4*x^5*x^m + 155*A*a^4*m^3*x*x^m + 461*B*a^4*m^2*x^2*x^m + 1844*A*a^3*b*m^2*x^2*x^m + 2032*B*a^3*b*m*x^3*x^m + 3048*A*a^2*b^2*m*x^3*x^m + 1080*B*a^2*b^2*x^4*x^m + 720*A*a*b^3*x^4*x^m + 580*A*a^4*m^2*x*x^m + 702*B*a^4*m*x^2*x^m + 2808*A*a^3*b*m*x^2*x^m + 960*B*a^3*b*x^3*x^m + 1440*A*a^2*b^2*x^3*x^m + 1044*A*a^4*m*x*x^m + 360*B*a^4*x^2*x^m + 1440*A*a^3*b*x^2*x^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
838,1,332,0,0.175096," ","integrate(x^m*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{B b^{2} m^{3} x^{4} x^{m} + 2 \, B a b m^{3} x^{3} x^{m} + A b^{2} m^{3} x^{3} x^{m} + 6 \, B b^{2} m^{2} x^{4} x^{m} + B a^{2} m^{3} x^{2} x^{m} + 2 \, A a b m^{3} x^{2} x^{m} + 14 \, B a b m^{2} x^{3} x^{m} + 7 \, A b^{2} m^{2} x^{3} x^{m} + 11 \, B b^{2} m x^{4} x^{m} + A a^{2} m^{3} x x^{m} + 8 \, B a^{2} m^{2} x^{2} x^{m} + 16 \, A a b m^{2} x^{2} x^{m} + 28 \, B a b m x^{3} x^{m} + 14 \, A b^{2} m x^{3} x^{m} + 6 \, B b^{2} x^{4} x^{m} + 9 \, A a^{2} m^{2} x x^{m} + 19 \, B a^{2} m x^{2} x^{m} + 38 \, A a b m x^{2} x^{m} + 16 \, B a b x^{3} x^{m} + 8 \, A b^{2} x^{3} x^{m} + 26 \, A a^{2} m x x^{m} + 12 \, B a^{2} x^{2} x^{m} + 24 \, A a b x^{2} x^{m} + 24 \, A a^{2} x x^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"(B*b^2*m^3*x^4*x^m + 2*B*a*b*m^3*x^3*x^m + A*b^2*m^3*x^3*x^m + 6*B*b^2*m^2*x^4*x^m + B*a^2*m^3*x^2*x^m + 2*A*a*b*m^3*x^2*x^m + 14*B*a*b*m^2*x^3*x^m + 7*A*b^2*m^2*x^3*x^m + 11*B*b^2*m*x^4*x^m + A*a^2*m^3*x*x^m + 8*B*a^2*m^2*x^2*x^m + 16*A*a*b*m^2*x^2*x^m + 28*B*a*b*m*x^3*x^m + 14*A*b^2*m*x^3*x^m + 6*B*b^2*x^4*x^m + 9*A*a^2*m^2*x*x^m + 19*B*a^2*m*x^2*x^m + 38*A*a*b*m*x^2*x^m + 16*B*a*b*x^3*x^m + 8*A*b^2*x^3*x^m + 26*A*a^2*m*x*x^m + 12*B*a^2*x^2*x^m + 24*A*a*b*x^2*x^m + 24*A*a^2*x*x^m)/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
839,0,0,0,0.000000," ","integrate(x^m*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} x^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}\,{d x}"," ",0,"integrate((B*x + A)*x^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
840,0,0,0,0.000000," ","integrate(x^m*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} x^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((B*x + A)*x^m/(b^2*x^2 + 2*a*b*x + a^2)^2, x)","F",0
841,1,1560,0,0.237762," ","integrate(x^m*(1+x)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{m^{11} x^{12} x^{m} + 11 \, m^{11} x^{11} x^{m} + 66 \, m^{10} x^{12} x^{m} + 55 \, m^{11} x^{10} x^{m} + 737 \, m^{10} x^{11} x^{m} + 1925 \, m^{9} x^{12} x^{m} + 165 \, m^{11} x^{9} x^{m} + 3740 \, m^{10} x^{10} x^{m} + 21780 \, m^{9} x^{11} x^{m} + 32670 \, m^{8} x^{12} x^{m} + 330 \, m^{11} x^{8} x^{m} + 11385 \, m^{10} x^{9} x^{m} + 112035 \, m^{9} x^{10} x^{m} + 373890 \, m^{8} x^{11} x^{m} + 357423 \, m^{7} x^{12} x^{m} + 462 \, m^{11} x^{7} x^{m} + 23100 \, m^{10} x^{8} x^{m} + 345840 \, m^{9} x^{9} x^{m} + 1947000 \, m^{8} x^{10} x^{m} + 4131303 \, m^{7} x^{11} x^{m} + 2637558 \, m^{6} x^{12} x^{m} + 462 \, m^{11} x^{6} x^{m} + 32802 \, m^{10} x^{7} x^{m} + 711810 \, m^{9} x^{8} x^{m} + 6089490 \, m^{8} x^{9} x^{m} + 21750465 \, m^{7} x^{10} x^{m} + 30748641 \, m^{6} x^{11} x^{m} + 13339535 \, m^{5} x^{12} x^{m} + 330 \, m^{11} x^{5} x^{m} + 33264 \, m^{10} x^{6} x^{m} + 1025640 \, m^{9} x^{7} x^{m} + 12709620 \, m^{8} x^{8} x^{m} + 68855985 \, m^{7} x^{9} x^{m} + 163460220 \, m^{6} x^{10} x^{m} + 156657490 \, m^{5} x^{11} x^{m} + 45995730 \, m^{4} x^{12} x^{m} + 165 \, m^{11} x^{4} x^{m} + 24090 \, m^{10} x^{5} x^{m} + 1055670 \, m^{9} x^{6} x^{m} + 18586260 \, m^{8} x^{7} x^{m} + 145645830 \, m^{7} x^{8} x^{m} + 523190745 \, m^{6} x^{9} x^{m} + 839860505 \, m^{5} x^{10} x^{m} + 543539260 \, m^{4} x^{11} x^{m} + 105258076 \, m^{3} x^{12} x^{m} + 55 \, m^{11} x^{3} x^{m} + 12210 \, m^{10} x^{4} x^{m} + 776160 \, m^{9} x^{5} x^{m} + 19431720 \, m^{8} x^{6} x^{m} + 216148086 \, m^{7} x^{7} x^{m} + 1120622580 \, m^{6} x^{8} x^{m} + 2714671410 \, m^{5} x^{9} x^{m} + 2935253200 \, m^{4} x^{10} x^{m} + 1250343336 \, m^{3} x^{11} x^{m} + 150917976 \, m^{2} x^{12} x^{m} + 11 \, m^{11} x^{2} x^{m} + 4125 \, m^{10} x^{3} x^{m} + 399465 \, m^{9} x^{4} x^{m} + 14523300 \, m^{8} x^{5} x^{m} + 229661586 \, m^{7} x^{6} x^{m} + 1687068306 \, m^{6} x^{7} x^{m} + 5881795590 \, m^{5} x^{8} x^{m} + 9569532060 \, m^{4} x^{9} x^{m} + 6793843980 \, m^{3} x^{10} x^{m} + 1800387072 \, m^{2} x^{11} x^{m} + 120543840 \, m x^{12} x^{m} + m^{11} x x^{m} + 836 \, m^{10} x^{2} x^{m} + 137060 \, m^{9} x^{3} x^{m} + 7604190 \, m^{8} x^{4} x^{m} + 174706290 \, m^{7} x^{5} x^{m} + 1822135392 \, m^{6} x^{6} x^{m} + 8976008580 \, m^{5} x^{7} x^{m} + 20948784780 \, m^{4} x^{8} x^{m} + 22313339400 \, m^{3} x^{9} x^{m} + 9832379040 \, m^{2} x^{10} x^{m} + 1442897280 \, m x^{11} x^{m} + 39916800 \, x^{12} x^{m} + 77 \, m^{10} x x^{m} + 28215 \, m^{9} x^{2} x^{m} + 2656170 \, m^{8} x^{3} x^{m} + 93244635 \, m^{7} x^{4} x^{m} + 1412257770 \, m^{6} x^{5} x^{m} + 9852674370 \, m^{5} x^{6} x^{m} + 32372349240 \, m^{4} x^{7} x^{m} + 49287977640 \, m^{3} x^{8} x^{m} + 32492401920 \, m^{2} x^{9} x^{m} + 7911984960 \, m x^{10} x^{m} + 479001600 \, x^{11} x^{m} + 2640 \, m^{9} x x^{m} + 557040 \, m^{8} x^{2} x^{m} + 33251955 \, m^{7} x^{3} x^{m} + 769916070 \, m^{6} x^{4} x^{m} + 7785487380 \, m^{5} x^{5} x^{m} + 36088363080 \, m^{4} x^{6} x^{m} + 77023113552 \, m^{3} x^{7} x^{m} + 72321091920 \, m^{2} x^{8} x^{m} + 26275708800 \, m x^{9} x^{m} + 2634508800 \, x^{10} x^{m} + 53130 \, m^{8} x x^{m} + 7130013 \, m^{7} x^{2} x^{m} + 281209005 \, m^{6} x^{3} x^{m} + 4343723835 \, m^{5} x^{4} x^{m} + 29075712600 \, m^{4} x^{5} x^{m} + 87099379752 \, m^{3} x^{6} x^{m} + 114113083392 \, m^{2} x^{7} x^{m} + 58845916800 \, m x^{8} x^{m} + 8781696000 \, x^{9} x^{m} + 696333 \, m^{7} x x^{m} + 61932948 \, m^{6} x^{2} x^{m} + 1630835690 \, m^{5} x^{3} x^{m} + 16626679410 \, m^{4} x^{4} x^{m} + 71499692880 \, m^{3} x^{5} x^{m} + 130678599744 \, m^{2} x^{6} x^{m} + 93588929280 \, m x^{7} x^{m} + 19758816000 \, x^{8} x^{m} + 6230301 \, m^{6} x x^{m} + 371026645 \, m^{5} x^{2} x^{m} + 6441351180 \, m^{4} x^{3} x^{m} + 41932410300 \, m^{3} x^{4} x^{m} + 109126448640 \, m^{2} x^{5} x^{m} + 108308914560 \, m x^{6} x^{m} + 31614105600 \, x^{7} x^{m} + 38759930 \, m^{5} x x^{m} + 1524718360 \, m^{4} x^{2} x^{m} + 16822322440 \, m^{3} x^{3} x^{m} + 65582815320 \, m^{2} x^{4} x^{m} + 91782408960 \, m x^{5} x^{m} + 36883123200 \, x^{6} x^{m} + 167310220 \, m^{4} x x^{m} + 4179838476 \, m^{3} x^{2} x^{m} + 27303851520 \, m^{2} x^{3} x^{m} + 56376064800 \, m x^{4} x^{m} + 31614105600 \, x^{5} x^{m} + 489896616 \, m^{3} x x^{m} + 7194486816 \, m^{2} x^{2} x^{m} + 24324220800 \, m x^{3} x^{m} + 19758816000 \, x^{4} x^{m} + 924118272 \, m^{2} x x^{m} + 6858181440 \, m x^{2} x^{m} + 8781696000 \, x^{3} x^{m} + 1007441280 \, m x x^{m} + 2634508800 \, x^{2} x^{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}"," ",0,"(m^11*x^12*x^m + 11*m^11*x^11*x^m + 66*m^10*x^12*x^m + 55*m^11*x^10*x^m + 737*m^10*x^11*x^m + 1925*m^9*x^12*x^m + 165*m^11*x^9*x^m + 3740*m^10*x^10*x^m + 21780*m^9*x^11*x^m + 32670*m^8*x^12*x^m + 330*m^11*x^8*x^m + 11385*m^10*x^9*x^m + 112035*m^9*x^10*x^m + 373890*m^8*x^11*x^m + 357423*m^7*x^12*x^m + 462*m^11*x^7*x^m + 23100*m^10*x^8*x^m + 345840*m^9*x^9*x^m + 1947000*m^8*x^10*x^m + 4131303*m^7*x^11*x^m + 2637558*m^6*x^12*x^m + 462*m^11*x^6*x^m + 32802*m^10*x^7*x^m + 711810*m^9*x^8*x^m + 6089490*m^8*x^9*x^m + 21750465*m^7*x^10*x^m + 30748641*m^6*x^11*x^m + 13339535*m^5*x^12*x^m + 330*m^11*x^5*x^m + 33264*m^10*x^6*x^m + 1025640*m^9*x^7*x^m + 12709620*m^8*x^8*x^m + 68855985*m^7*x^9*x^m + 163460220*m^6*x^10*x^m + 156657490*m^5*x^11*x^m + 45995730*m^4*x^12*x^m + 165*m^11*x^4*x^m + 24090*m^10*x^5*x^m + 1055670*m^9*x^6*x^m + 18586260*m^8*x^7*x^m + 145645830*m^7*x^8*x^m + 523190745*m^6*x^9*x^m + 839860505*m^5*x^10*x^m + 543539260*m^4*x^11*x^m + 105258076*m^3*x^12*x^m + 55*m^11*x^3*x^m + 12210*m^10*x^4*x^m + 776160*m^9*x^5*x^m + 19431720*m^8*x^6*x^m + 216148086*m^7*x^7*x^m + 1120622580*m^6*x^8*x^m + 2714671410*m^5*x^9*x^m + 2935253200*m^4*x^10*x^m + 1250343336*m^3*x^11*x^m + 150917976*m^2*x^12*x^m + 11*m^11*x^2*x^m + 4125*m^10*x^3*x^m + 399465*m^9*x^4*x^m + 14523300*m^8*x^5*x^m + 229661586*m^7*x^6*x^m + 1687068306*m^6*x^7*x^m + 5881795590*m^5*x^8*x^m + 9569532060*m^4*x^9*x^m + 6793843980*m^3*x^10*x^m + 1800387072*m^2*x^11*x^m + 120543840*m*x^12*x^m + m^11*x*x^m + 836*m^10*x^2*x^m + 137060*m^9*x^3*x^m + 7604190*m^8*x^4*x^m + 174706290*m^7*x^5*x^m + 1822135392*m^6*x^6*x^m + 8976008580*m^5*x^7*x^m + 20948784780*m^4*x^8*x^m + 22313339400*m^3*x^9*x^m + 9832379040*m^2*x^10*x^m + 1442897280*m*x^11*x^m + 39916800*x^12*x^m + 77*m^10*x*x^m + 28215*m^9*x^2*x^m + 2656170*m^8*x^3*x^m + 93244635*m^7*x^4*x^m + 1412257770*m^6*x^5*x^m + 9852674370*m^5*x^6*x^m + 32372349240*m^4*x^7*x^m + 49287977640*m^3*x^8*x^m + 32492401920*m^2*x^9*x^m + 7911984960*m*x^10*x^m + 479001600*x^11*x^m + 2640*m^9*x*x^m + 557040*m^8*x^2*x^m + 33251955*m^7*x^3*x^m + 769916070*m^6*x^4*x^m + 7785487380*m^5*x^5*x^m + 36088363080*m^4*x^6*x^m + 77023113552*m^3*x^7*x^m + 72321091920*m^2*x^8*x^m + 26275708800*m*x^9*x^m + 2634508800*x^10*x^m + 53130*m^8*x*x^m + 7130013*m^7*x^2*x^m + 281209005*m^6*x^3*x^m + 4343723835*m^5*x^4*x^m + 29075712600*m^4*x^5*x^m + 87099379752*m^3*x^6*x^m + 114113083392*m^2*x^7*x^m + 58845916800*m*x^8*x^m + 8781696000*x^9*x^m + 696333*m^7*x*x^m + 61932948*m^6*x^2*x^m + 1630835690*m^5*x^3*x^m + 16626679410*m^4*x^4*x^m + 71499692880*m^3*x^5*x^m + 130678599744*m^2*x^6*x^m + 93588929280*m*x^7*x^m + 19758816000*x^8*x^m + 6230301*m^6*x*x^m + 371026645*m^5*x^2*x^m + 6441351180*m^4*x^3*x^m + 41932410300*m^3*x^4*x^m + 109126448640*m^2*x^5*x^m + 108308914560*m*x^6*x^m + 31614105600*x^7*x^m + 38759930*m^5*x*x^m + 1524718360*m^4*x^2*x^m + 16822322440*m^3*x^3*x^m + 65582815320*m^2*x^4*x^m + 91782408960*m*x^5*x^m + 36883123200*x^6*x^m + 167310220*m^4*x*x^m + 4179838476*m^3*x^2*x^m + 27303851520*m^2*x^3*x^m + 56376064800*m*x^4*x^m + 31614105600*x^5*x^m + 489896616*m^3*x*x^m + 7194486816*m^2*x^2*x^m + 24324220800*m*x^3*x^m + 19758816000*x^4*x^m + 924118272*m^2*x*x^m + 6858181440*m*x^2*x^m + 8781696000*x^3*x^m + 1007441280*m*x*x^m + 2634508800*x^2*x^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
842,1,3224,0,0.334967," ","integrate(x^m*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""giac"")","\frac{m^{11} x^{12} x^{m} e + d m^{11} x^{11} x^{m} + 10 \, m^{11} x^{11} x^{m} e + 66 \, m^{10} x^{12} x^{m} e + 10 \, d m^{11} x^{10} x^{m} + 67 \, d m^{10} x^{11} x^{m} + 45 \, m^{11} x^{10} x^{m} e + 670 \, m^{10} x^{11} x^{m} e + 1925 \, m^{9} x^{12} x^{m} e + 45 \, d m^{11} x^{9} x^{m} + 680 \, d m^{10} x^{10} x^{m} + 1980 \, d m^{9} x^{11} x^{m} + 120 \, m^{11} x^{9} x^{m} e + 3060 \, m^{10} x^{10} x^{m} e + 19800 \, m^{9} x^{11} x^{m} e + 32670 \, m^{8} x^{12} x^{m} e + 120 \, d m^{11} x^{8} x^{m} + 3105 \, d m^{10} x^{9} x^{m} + 20370 \, d m^{9} x^{10} x^{m} + 33990 \, d m^{8} x^{11} x^{m} + 210 \, m^{11} x^{8} x^{m} e + 8280 \, m^{10} x^{9} x^{m} e + 91665 \, m^{9} x^{10} x^{m} e + 339900 \, m^{8} x^{11} x^{m} e + 357423 \, m^{7} x^{12} x^{m} e + 210 \, d m^{11} x^{7} x^{m} + 8400 \, d m^{10} x^{8} x^{m} + 94320 \, d m^{9} x^{9} x^{m} + 354000 \, d m^{8} x^{10} x^{m} + 375573 \, d m^{7} x^{11} x^{m} + 252 \, m^{11} x^{7} x^{m} e + 14700 \, m^{10} x^{8} x^{m} e + 251520 \, m^{9} x^{9} x^{m} e + 1593000 \, m^{8} x^{10} x^{m} e + 3755730 \, m^{7} x^{11} x^{m} e + 2637558 \, m^{6} x^{12} x^{m} e + 252 \, d m^{11} x^{6} x^{m} + 14910 \, d m^{10} x^{7} x^{m} + 258840 \, d m^{9} x^{8} x^{m} + 1660770 \, d m^{8} x^{9} x^{m} + 3954630 \, d m^{7} x^{10} x^{m} + 2795331 \, d m^{6} x^{11} x^{m} + 210 \, m^{11} x^{6} x^{m} e + 17892 \, m^{10} x^{7} x^{m} e + 452970 \, m^{9} x^{8} x^{m} e + 4428720 \, m^{8} x^{9} x^{m} e + 17795835 \, m^{7} x^{10} x^{m} e + 27953310 \, m^{6} x^{11} x^{m} e + 13339535 \, m^{5} x^{12} x^{m} e + 210 \, d m^{11} x^{5} x^{m} + 18144 \, d m^{10} x^{6} x^{m} + 466200 \, d m^{9} x^{7} x^{m} + 4621680 \, d m^{8} x^{8} x^{m} + 18778905 \, d m^{7} x^{9} x^{m} + 29720040 \, d m^{6} x^{10} x^{m} + 14241590 \, d m^{5} x^{11} x^{m} + 120 \, m^{11} x^{5} x^{m} e + 15120 \, m^{10} x^{6} x^{m} e + 559440 \, m^{9} x^{7} x^{m} e + 8087940 \, m^{8} x^{8} x^{m} e + 50077080 \, m^{7} x^{9} x^{m} e + 133740180 \, m^{6} x^{10} x^{m} e + 142415900 \, m^{5} x^{11} x^{m} e + 45995730 \, m^{4} x^{12} x^{m} e + 120 \, d m^{11} x^{4} x^{m} + 15330 \, d m^{10} x^{5} x^{m} + 575820 \, d m^{9} x^{6} x^{m} + 8448300 \, d m^{8} x^{7} x^{m} + 52962120 \, d m^{7} x^{8} x^{m} + 142688385 \, d m^{6} x^{9} x^{m} + 152701910 \, d m^{5} x^{10} x^{m} + 49412660 \, d m^{4} x^{11} x^{m} + 45 \, m^{11} x^{4} x^{m} e + 8760 \, m^{10} x^{5} x^{m} e + 479850 \, m^{9} x^{6} x^{m} e + 10137960 \, m^{8} x^{7} x^{m} e + 92683710 \, m^{7} x^{8} x^{m} e + 380502360 \, m^{6} x^{9} x^{m} e + 687158595 \, m^{5} x^{10} x^{m} e + 494126600 \, m^{4} x^{11} x^{m} e + 105258076 \, m^{3} x^{12} x^{m} e + 45 \, d m^{11} x^{3} x^{m} + 8880 \, d m^{10} x^{4} x^{m} + 493920 \, d m^{9} x^{5} x^{m} + 10599120 \, d m^{8} x^{6} x^{m} + 98249130 \, d m^{7} x^{7} x^{m} + 407499120 \, d m^{6} x^{8} x^{m} + 740364930 \, d m^{5} x^{9} x^{m} + 533682400 \, d m^{4} x^{10} x^{m} + 113667576 \, d m^{3} x^{11} x^{m} + 10 \, m^{11} x^{3} x^{m} e + 3330 \, m^{10} x^{4} x^{m} e + 282240 \, m^{9} x^{5} x^{m} e + 8832600 \, m^{8} x^{6} x^{m} e + 117898956 \, m^{7} x^{7} x^{m} e + 713123460 \, m^{6} x^{8} x^{m} e + 1974306480 \, m^{5} x^{9} x^{m} e + 2401570800 \, m^{4} x^{10} x^{m} e + 1136675760 \, m^{3} x^{11} x^{m} e + 150917976 \, m^{2} x^{12} x^{m} e + 10 \, d m^{11} x^{2} x^{m} + 3375 \, d m^{10} x^{3} x^{m} + 290520 \, d m^{9} x^{4} x^{m} + 9242100 \, d m^{8} x^{5} x^{m} + 125269956 \, d m^{7} x^{6} x^{m} + 766849230 \, d m^{6} x^{7} x^{m} + 2138834760 \, d m^{5} x^{8} x^{m} + 2609872380 \, d m^{4} x^{9} x^{m} + 1235244360 \, d m^{3} x^{10} x^{m} + 163671552 \, d m^{2} x^{11} x^{m} + m^{11} x^{2} x^{m} e + 750 \, m^{10} x^{3} x^{m} e + 108945 \, m^{9} x^{4} x^{m} e + 5281200 \, m^{8} x^{5} x^{m} e + 104391630 \, m^{7} x^{6} x^{m} e + 920219076 \, m^{6} x^{7} x^{m} e + 3742960830 \, m^{5} x^{8} x^{m} e + 6959659680 \, m^{4} x^{9} x^{m} e + 5558599620 \, m^{3} x^{10} x^{m} e + 1636715520 \, m^{2} x^{11} x^{m} e + 120543840 \, m x^{12} x^{m} e + d m^{11} x x^{m} + 760 \, d m^{10} x^{2} x^{m} + 112140 \, d m^{9} x^{3} x^{m} + 5530320 \, d m^{8} x^{4} x^{m} + 111176730 \, d m^{7} x^{5} x^{m} + 993892032 \, d m^{6} x^{6} x^{m} + 4080003900 \, d m^{5} x^{7} x^{m} + 7617739920 \, d m^{4} x^{8} x^{m} + 6085456200 \, d m^{3} x^{9} x^{m} + 1787705280 \, d m^{2} x^{10} x^{m} + 131172480 \, d m x^{11} x^{m} + 76 \, m^{10} x^{2} x^{m} e + 24920 \, m^{9} x^{3} x^{m} e + 2073870 \, m^{8} x^{4} x^{m} e + 63529560 \, m^{7} x^{5} x^{m} e + 828243360 \, m^{6} x^{6} x^{m} e + 4896004680 \, m^{5} x^{7} x^{m} e + 13331044860 \, m^{4} x^{8} x^{m} e + 16227883200 \, m^{3} x^{9} x^{m} e + 8044673760 \, m^{2} x^{10} x^{m} e + 1311724800 \, m x^{11} x^{m} e + 39916800 \, x^{12} x^{m} e + 77 \, d m^{10} x x^{m} + 25650 \, d m^{9} x^{2} x^{m} + 2173230 \, d m^{8} x^{3} x^{m} + 67814280 \, d m^{7} x^{4} x^{m} + 898709490 \, d m^{6} x^{5} x^{m} + 5374186020 \, d m^{5} x^{6} x^{m} + 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843,1,43,0,0.171402," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{7} \, B c x^{7} + \frac{1}{6} \, B b x^{6} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{4} \, A a x^{4}"," ",0,"1/7*B*c*x^7 + 1/6*B*b*x^6 + 1/6*A*c*x^6 + 1/5*B*a*x^5 + 1/5*A*b*x^5 + 1/4*A*a*x^4","A",0
844,1,43,0,0.215088," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{6} \, B c x^{6} + \frac{1}{5} \, B b x^{5} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{4} \, A b x^{4} + \frac{1}{3} \, A a x^{3}"," ",0,"1/6*B*c*x^6 + 1/5*B*b*x^5 + 1/5*A*c*x^5 + 1/4*B*a*x^4 + 1/4*A*b*x^4 + 1/3*A*a*x^3","A",0
845,1,43,0,0.150599," ","integrate(x*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{5} \, B c x^{5} + \frac{1}{4} \, B b x^{4} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{3} \, A b x^{3} + \frac{1}{2} \, A a x^{2}"," ",0,"1/5*B*c*x^5 + 1/4*B*b*x^4 + 1/4*A*c*x^4 + 1/3*B*a*x^3 + 1/3*A*b*x^3 + 1/2*A*a*x^2","A",0
846,1,40,0,0.146576," ","integrate((B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{4} \, B c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + \frac{1}{2} \, A b x^{2} + A a x"," ",0,"1/4*B*c*x^4 + 1/3*B*b*x^3 + 1/3*A*c*x^3 + 1/2*B*a*x^2 + 1/2*A*b*x^2 + A*a*x","A",0
847,1,36,0,0.146382," ","integrate((B*x+A)*(c*x^2+b*x+a)/x,x, algorithm=""giac"")","\frac{1}{3} \, B c x^{3} + \frac{1}{2} \, B b x^{2} + \frac{1}{2} \, A c x^{2} + B a x + A b x + A a \log\left({\left| x \right|}\right)"," ",0,"1/3*B*c*x^3 + 1/2*B*b*x^2 + 1/2*A*c*x^2 + B*a*x + A*b*x + A*a*log(abs(x))","A",0
848,1,34,0,0.180550," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, B c x^{2} + B b x + A c x + {\left(B a + A b\right)} \log\left({\left| x \right|}\right) - \frac{A a}{x}"," ",0,"1/2*B*c*x^2 + B*b*x + A*c*x + (B*a + A*b)*log(abs(x)) - A*a/x","A",0
849,1,35,0,0.150140," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^3,x, algorithm=""giac"")","B c x + {\left(B b + A c\right)} \log\left({\left| x \right|}\right) - \frac{A a + 2 \, {\left(B a + A b\right)} x}{2 \, x^{2}}"," ",0,"B*c*x + (B*b + A*c)*log(abs(x)) - 1/2*(A*a + 2*(B*a + A*b)*x)/x^2","A",0
850,1,39,0,0.165575," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^4,x, algorithm=""giac"")","B c \log\left({\left| x \right|}\right) - \frac{6 \, {\left(B b + A c\right)} x^{2} + 2 \, A a + 3 \, {\left(B a + A b\right)} x}{6 \, x^{3}}"," ",0,"B*c*log(abs(x)) - 1/6*(6*(B*b + A*c)*x^2 + 2*A*a + 3*(B*a + A*b)*x)/x^3","A",0
851,1,41,0,0.165774," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^5,x, algorithm=""giac"")","-\frac{12 \, B c x^{3} + 6 \, B b x^{2} + 6 \, A c x^{2} + 4 \, B a x + 4 \, A b x + 3 \, A a}{12 \, x^{4}}"," ",0,"-1/12*(12*B*c*x^3 + 6*B*b*x^2 + 6*A*c*x^2 + 4*B*a*x + 4*A*b*x + 3*A*a)/x^4","A",0
852,1,41,0,0.152479," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^6,x, algorithm=""giac"")","-\frac{30 \, B c x^{3} + 20 \, B b x^{2} + 20 \, A c x^{2} + 15 \, B a x + 15 \, A b x + 12 \, A a}{60 \, x^{5}}"," ",0,"-1/60*(30*B*c*x^3 + 20*B*b*x^2 + 20*A*c*x^2 + 15*B*a*x + 15*A*b*x + 12*A*a)/x^5","A",0
853,1,41,0,0.148284," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^7,x, algorithm=""giac"")","-\frac{20 \, B c x^{3} + 15 \, B b x^{2} + 15 \, A c x^{2} + 12 \, B a x + 12 \, A b x + 10 \, A a}{60 \, x^{6}}"," ",0,"-1/60*(20*B*c*x^3 + 15*B*b*x^2 + 15*A*c*x^2 + 12*B*a*x + 12*A*b*x + 10*A*a)/x^6","A",0
854,1,41,0,0.166296," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^8,x, algorithm=""giac"")","-\frac{105 \, B c x^{3} + 84 \, B b x^{2} + 84 \, A c x^{2} + 70 \, B a x + 70 \, A b x + 60 \, A a}{420 \, x^{7}}"," ",0,"-1/420*(105*B*c*x^3 + 84*B*b*x^2 + 84*A*c*x^2 + 70*B*a*x + 70*A*b*x + 60*A*a)/x^7","A",0
855,1,103,0,0.151141," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, B c^{2} x^{8} + \frac{2}{7} \, B b c x^{7} + \frac{1}{7} \, A c^{2} x^{7} + \frac{1}{6} \, B b^{2} x^{6} + \frac{1}{3} \, B a c x^{6} + \frac{1}{3} \, A b c x^{6} + \frac{2}{5} \, B a b x^{5} + \frac{1}{5} \, A b^{2} x^{5} + \frac{2}{5} \, A a c x^{5} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{2} \, A a b x^{4} + \frac{1}{3} \, A a^{2} x^{3}"," ",0,"1/8*B*c^2*x^8 + 2/7*B*b*c*x^7 + 1/7*A*c^2*x^7 + 1/6*B*b^2*x^6 + 1/3*B*a*c*x^6 + 1/3*A*b*c*x^6 + 2/5*B*a*b*x^5 + 1/5*A*b^2*x^5 + 2/5*A*a*c*x^5 + 1/4*B*a^2*x^4 + 1/2*A*a*b*x^4 + 1/3*A*a^2*x^3","A",0
856,1,103,0,0.153340," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{7} \, B c^{2} x^{7} + \frac{1}{3} \, B b c x^{6} + \frac{1}{6} \, A c^{2} x^{6} + \frac{1}{5} \, B b^{2} x^{5} + \frac{2}{5} \, B a c x^{5} + \frac{2}{5} \, A b c x^{5} + \frac{1}{2} \, B a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{2} \, A a c x^{4} + \frac{1}{3} \, B a^{2} x^{3} + \frac{2}{3} \, A a b x^{3} + \frac{1}{2} \, A a^{2} x^{2}"," ",0,"1/7*B*c^2*x^7 + 1/3*B*b*c*x^6 + 1/6*A*c^2*x^6 + 1/5*B*b^2*x^5 + 2/5*B*a*c*x^5 + 2/5*A*b*c*x^5 + 1/2*B*a*b*x^4 + 1/4*A*b^2*x^4 + 1/2*A*a*c*x^4 + 1/3*B*a^2*x^3 + 2/3*A*a*b*x^3 + 1/2*A*a^2*x^2","A",0
857,1,99,0,0.150962," ","integrate((B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{2} x^{6} + \frac{2}{5} \, B b c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{4} \, B b^{2} x^{4} + \frac{1}{2} \, B a c x^{4} + \frac{1}{2} \, A b c x^{4} + \frac{2}{3} \, B a b x^{3} + \frac{1}{3} \, A b^{2} x^{3} + \frac{2}{3} \, A a c x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a b x^{2} + A a^{2} x"," ",0,"1/6*B*c^2*x^6 + 2/5*B*b*c*x^5 + 1/5*A*c^2*x^5 + 1/4*B*b^2*x^4 + 1/2*B*a*c*x^4 + 1/2*A*b*c*x^4 + 2/3*B*a*b*x^3 + 1/3*A*b^2*x^3 + 2/3*A*a*c*x^3 + 1/2*B*a^2*x^2 + A*a*b*x^2 + A*a^2*x","A",0
858,1,95,0,0.159188," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x,x, algorithm=""giac"")","\frac{1}{5} \, B c^{2} x^{5} + \frac{1}{2} \, B b c x^{4} + \frac{1}{4} \, A c^{2} x^{4} + \frac{1}{3} \, B b^{2} x^{3} + \frac{2}{3} \, B a c x^{3} + \frac{2}{3} \, A b c x^{3} + B a b x^{2} + \frac{1}{2} \, A b^{2} x^{2} + A a c x^{2} + B a^{2} x + 2 \, A a b x + A a^{2} \log\left({\left| x \right|}\right)"," ",0,"1/5*B*c^2*x^5 + 1/2*B*b*c*x^4 + 1/4*A*c^2*x^4 + 1/3*B*b^2*x^3 + 2/3*B*a*c*x^3 + 2/3*A*b*c*x^3 + B*a*b*x^2 + 1/2*A*b^2*x^2 + A*a*c*x^2 + B*a^2*x + 2*A*a*b*x + A*a^2*log(abs(x))","A",0
859,1,92,0,0.195572," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^2,x, algorithm=""giac"")","\frac{1}{4} \, B c^{2} x^{4} + \frac{2}{3} \, B b c x^{3} + \frac{1}{3} \, A c^{2} x^{3} + \frac{1}{2} \, B b^{2} x^{2} + B a c x^{2} + A b c x^{2} + 2 \, B a b x + A b^{2} x + 2 \, A a c x - \frac{A a^{2}}{x} + {\left(B a^{2} + 2 \, A a b\right)} \log\left({\left| x \right|}\right)"," ",0,"1/4*B*c^2*x^4 + 2/3*B*b*c*x^3 + 1/3*A*c^2*x^3 + 1/2*B*b^2*x^2 + B*a*c*x^2 + A*b*c*x^2 + 2*B*a*b*x + A*b^2*x + 2*A*a*c*x - A*a^2/x + (B*a^2 + 2*A*a*b)*log(abs(x))","A",0
860,1,89,0,0.159082," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^3,x, algorithm=""giac"")","\frac{1}{3} \, B c^{2} x^{3} + B b c x^{2} + \frac{1}{2} \, A c^{2} x^{2} + B b^{2} x + 2 \, B a c x + 2 \, A b c x + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} \log\left({\left| x \right|}\right) - \frac{A a^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} x}{2 \, x^{2}}"," ",0,"1/3*B*c^2*x^3 + B*b*c*x^2 + 1/2*A*c^2*x^2 + B*b^2*x + 2*B*a*c*x + 2*A*b*c*x + (2*B*a*b + A*b^2 + 2*A*a*c)*log(abs(x)) - 1/2*(A*a^2 + 2*(B*a^2 + 2*A*a*b)*x)/x^2","A",0
861,1,89,0,0.167063," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^4,x, algorithm=""giac"")","\frac{1}{2} \, B c^{2} x^{2} + 2 \, B b c x + A c^{2} x + {\left(B b^{2} + 2 \, B a c + 2 \, A b c\right)} \log\left({\left| x \right|}\right) - \frac{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,"1/2*B*c^2*x^2 + 2*B*b*c*x + A*c^2*x + (B*b^2 + 2*B*a*c + 2*A*b*c)*log(abs(x)) - 1/6*(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
862,1,90,0,0.152306," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^5,x, algorithm=""giac"")","B c^{2} x + {\left(2 \, B b c + A c^{2}\right)} \log\left({\left| x \right|}\right) - \frac{12 \, {\left(B b^{2} + 2 \, B a c + 2 \, A b 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,"B*c^2*x + (2*B*b*c + A*c^2)*log(abs(x)) - 1/12*(12*(B*b^2 + 2*B*a*c + 2*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
863,1,93,0,0.184049," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^6,x, algorithm=""giac"")","B c^{2} \log\left({\left| x \right|}\right) - \frac{60 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 30 \, {\left(B b^{2} + 2 \, B a c + 2 \, A b 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,"B*c^2*log(abs(x)) - 1/60*(60*(2*B*b*c + A*c^2)*x^4 + 30*(B*b^2 + 2*B*a*c + 2*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
864,1,101,0,0.151526," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^7,x, algorithm=""giac"")","-\frac{60 \, B c^{2} x^{5} + 60 \, B b c x^{4} + 30 \, A c^{2} x^{4} + 20 \, B b^{2} x^{3} + 40 \, B a c x^{3} + 40 \, A b c x^{3} + 30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 30 \, A a c x^{2} + 12 \, B a^{2} x + 24 \, A a b x + 10 \, A a^{2}}{60 \, x^{6}}"," ",0,"-1/60*(60*B*c^2*x^5 + 60*B*b*c*x^4 + 30*A*c^2*x^4 + 20*B*b^2*x^3 + 40*B*a*c*x^3 + 40*A*b*c*x^3 + 30*B*a*b*x^2 + 15*A*b^2*x^2 + 30*A*a*c*x^2 + 12*B*a^2*x + 24*A*a*b*x + 10*A*a^2)/x^6","A",0
865,1,101,0,0.154808," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^8,x, algorithm=""giac"")","-\frac{210 \, B c^{2} x^{5} + 280 \, B b c x^{4} + 140 \, A c^{2} x^{4} + 105 \, B b^{2} x^{3} + 210 \, B a c x^{3} + 210 \, A b c x^{3} + 168 \, B a b x^{2} + 84 \, A b^{2} x^{2} + 168 \, A a c x^{2} + 70 \, B a^{2} x + 140 \, A a b x + 60 \, A a^{2}}{420 \, x^{7}}"," ",0,"-1/420*(210*B*c^2*x^5 + 280*B*b*c*x^4 + 140*A*c^2*x^4 + 105*B*b^2*x^3 + 210*B*a*c*x^3 + 210*A*b*c*x^3 + 168*B*a*b*x^2 + 84*A*b^2*x^2 + 168*A*a*c*x^2 + 70*B*a^2*x + 140*A*a*b*x + 60*A*a^2)/x^7","A",0
866,1,101,0,0.192718," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^9,x, algorithm=""giac"")","-\frac{280 \, B c^{2} x^{5} + 420 \, B b c x^{4} + 210 \, A c^{2} x^{4} + 168 \, B b^{2} x^{3} + 336 \, B a c x^{3} + 336 \, A b c x^{3} + 280 \, B a b x^{2} + 140 \, A b^{2} x^{2} + 280 \, A a c x^{2} + 120 \, B a^{2} x + 240 \, A a b x + 105 \, A a^{2}}{840 \, x^{8}}"," ",0,"-1/840*(280*B*c^2*x^5 + 420*B*b*c*x^4 + 210*A*c^2*x^4 + 168*B*b^2*x^3 + 336*B*a*c*x^3 + 336*A*b*c*x^3 + 280*B*a*b*x^2 + 140*A*b^2*x^2 + 280*A*a*c*x^2 + 120*B*a^2*x + 240*A*a*b*x + 105*A*a^2)/x^8","A",0
867,1,192,0,0.204278," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{10} \, B c^{3} x^{10} + \frac{1}{3} \, B b c^{2} x^{9} + \frac{1}{9} \, A c^{3} x^{9} + \frac{3}{8} \, B b^{2} c x^{8} + \frac{3}{8} \, B a c^{2} x^{8} + \frac{3}{8} \, A b c^{2} x^{8} + \frac{1}{7} \, B b^{3} x^{7} + \frac{6}{7} \, B a b c x^{7} + \frac{3}{7} \, A b^{2} c x^{7} + \frac{3}{7} \, A a c^{2} x^{7} + \frac{1}{2} \, B a b^{2} x^{6} + \frac{1}{6} \, A b^{3} x^{6} + \frac{1}{2} \, B a^{2} c x^{6} + A a b c x^{6} + \frac{3}{5} \, B a^{2} b x^{5} + \frac{3}{5} \, A a b^{2} x^{5} + \frac{3}{5} \, A a^{2} c x^{5} + \frac{1}{4} \, B a^{3} x^{4} + \frac{3}{4} \, A a^{2} b x^{4} + \frac{1}{3} \, A a^{3} x^{3}"," ",0,"1/10*B*c^3*x^10 + 1/3*B*b*c^2*x^9 + 1/9*A*c^3*x^9 + 3/8*B*b^2*c*x^8 + 3/8*B*a*c^2*x^8 + 3/8*A*b*c^2*x^8 + 1/7*B*b^3*x^7 + 6/7*B*a*b*c*x^7 + 3/7*A*b^2*c*x^7 + 3/7*A*a*c^2*x^7 + 1/2*B*a*b^2*x^6 + 1/6*A*b^3*x^6 + 1/2*B*a^2*c*x^6 + A*a*b*c*x^6 + 3/5*B*a^2*b*x^5 + 3/5*A*a*b^2*x^5 + 3/5*A*a^2*c*x^5 + 1/4*B*a^3*x^4 + 3/4*A*a^2*b*x^4 + 1/3*A*a^3*x^3","A",0
868,1,191,0,0.153002," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{9} \, B c^{3} x^{9} + \frac{3}{8} \, B b c^{2} x^{8} + \frac{1}{8} \, A c^{3} x^{8} + \frac{3}{7} \, B b^{2} c x^{7} + \frac{3}{7} \, B a c^{2} x^{7} + \frac{3}{7} \, A b c^{2} x^{7} + \frac{1}{6} \, B b^{3} x^{6} + B a b c x^{6} + \frac{1}{2} \, A b^{2} c x^{6} + \frac{1}{2} \, A a c^{2} x^{6} + \frac{3}{5} \, B a b^{2} x^{5} + \frac{1}{5} \, A b^{3} x^{5} + \frac{3}{5} \, B a^{2} c x^{5} + \frac{6}{5} \, A a b c x^{5} + \frac{3}{4} \, B a^{2} b x^{4} + \frac{3}{4} \, A a b^{2} x^{4} + \frac{3}{4} \, A a^{2} c x^{4} + \frac{1}{3} \, B a^{3} x^{3} + A a^{2} b x^{3} + \frac{1}{2} \, A a^{3} x^{2}"," ",0,"1/9*B*c^3*x^9 + 3/8*B*b*c^2*x^8 + 1/8*A*c^3*x^8 + 3/7*B*b^2*c*x^7 + 3/7*B*a*c^2*x^7 + 3/7*A*b*c^2*x^7 + 1/6*B*b^3*x^6 + B*a*b*c*x^6 + 1/2*A*b^2*c*x^6 + 1/2*A*a*c^2*x^6 + 3/5*B*a*b^2*x^5 + 1/5*A*b^3*x^5 + 3/5*B*a^2*c*x^5 + 6/5*A*a*b*c*x^5 + 3/4*B*a^2*b*x^4 + 3/4*A*a*b^2*x^4 + 3/4*A*a^2*c*x^4 + 1/3*B*a^3*x^3 + A*a^2*b*x^3 + 1/2*A*a^3*x^2","A",0
869,1,187,0,0.152582," ","integrate((B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{8} \, B c^{3} x^{8} + \frac{3}{7} \, B b c^{2} x^{7} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{2} \, B b^{2} c x^{6} + \frac{1}{2} \, B a c^{2} x^{6} + \frac{1}{2} \, A b c^{2} x^{6} + \frac{1}{5} \, B b^{3} x^{5} + \frac{6}{5} \, B a b c x^{5} + \frac{3}{5} \, A b^{2} c x^{5} + \frac{3}{5} \, A a c^{2} x^{5} + \frac{3}{4} \, B a b^{2} x^{4} + \frac{1}{4} \, A b^{3} x^{4} + \frac{3}{4} \, B a^{2} c x^{4} + \frac{3}{2} \, A a b c x^{4} + B a^{2} b x^{3} + A a b^{2} x^{3} + A a^{2} c x^{3} + \frac{1}{2} \, B a^{3} x^{2} + \frac{3}{2} \, A a^{2} b x^{2} + A a^{3} x"," ",0,"1/8*B*c^3*x^8 + 3/7*B*b*c^2*x^7 + 1/7*A*c^3*x^7 + 1/2*B*b^2*c*x^6 + 1/2*B*a*c^2*x^6 + 1/2*A*b*c^2*x^6 + 1/5*B*b^3*x^5 + 6/5*B*a*b*c*x^5 + 3/5*A*b^2*c*x^5 + 3/5*A*a*c^2*x^5 + 3/4*B*a*b^2*x^4 + 1/4*A*b^3*x^4 + 3/4*B*a^2*c*x^4 + 3/2*A*a*b*c*x^4 + B*a^2*b*x^3 + A*a*b^2*x^3 + A*a^2*c*x^3 + 1/2*B*a^3*x^2 + 3/2*A*a^2*b*x^2 + A*a^3*x","A",0
870,1,185,0,0.153372," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x,x, algorithm=""giac"")","\frac{1}{7} \, B c^{3} x^{7} + \frac{1}{2} \, B b c^{2} x^{6} + \frac{1}{6} \, A c^{3} x^{6} + \frac{3}{5} \, B b^{2} c x^{5} + \frac{3}{5} \, B a c^{2} x^{5} + \frac{3}{5} \, A b c^{2} x^{5} + \frac{1}{4} \, B b^{3} x^{4} + \frac{3}{2} \, B a b c x^{4} + \frac{3}{4} \, A b^{2} c x^{4} + \frac{3}{4} \, A a c^{2} x^{4} + B a b^{2} x^{3} + \frac{1}{3} \, A b^{3} x^{3} + B a^{2} c x^{3} + 2 \, A a b c x^{3} + \frac{3}{2} \, B a^{2} b x^{2} + \frac{3}{2} \, A a b^{2} x^{2} + \frac{3}{2} \, A a^{2} c x^{2} + B a^{3} x + 3 \, A a^{2} b x + A a^{3} \log\left({\left| x \right|}\right)"," ",0,"1/7*B*c^3*x^7 + 1/2*B*b*c^2*x^6 + 1/6*A*c^3*x^6 + 3/5*B*b^2*c*x^5 + 3/5*B*a*c^2*x^5 + 3/5*A*b*c^2*x^5 + 1/4*B*b^3*x^4 + 3/2*B*a*b*c*x^4 + 3/4*A*b^2*c*x^4 + 3/4*A*a*c^2*x^4 + B*a*b^2*x^3 + 1/3*A*b^3*x^3 + B*a^2*c*x^3 + 2*A*a*b*c*x^3 + 3/2*B*a^2*b*x^2 + 3/2*A*a*b^2*x^2 + 3/2*A*a^2*c*x^2 + B*a^3*x + 3*A*a^2*b*x + A*a^3*log(abs(x))","A",0
871,1,183,0,0.153504," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{3} x^{6} + \frac{3}{5} \, B b c^{2} x^{5} + \frac{1}{5} \, A c^{3} x^{5} + \frac{3}{4} \, B b^{2} c x^{4} + \frac{3}{4} \, B a c^{2} x^{4} + \frac{3}{4} \, A b c^{2} x^{4} + \frac{1}{3} \, B b^{3} x^{3} + 2 \, B a b c x^{3} + A b^{2} c x^{3} + A a c^{2} x^{3} + \frac{3}{2} \, B a b^{2} x^{2} + \frac{1}{2} \, A b^{3} x^{2} + \frac{3}{2} \, B a^{2} c x^{2} + 3 \, A a b c x^{2} + 3 \, B a^{2} b x + 3 \, A a b^{2} x + 3 \, A a^{2} c x - \frac{A a^{3}}{x} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \log\left({\left| x \right|}\right)"," ",0,"1/6*B*c^3*x^6 + 3/5*B*b*c^2*x^5 + 1/5*A*c^3*x^5 + 3/4*B*b^2*c*x^4 + 3/4*B*a*c^2*x^4 + 3/4*A*b*c^2*x^4 + 1/3*B*b^3*x^3 + 2*B*a*b*c*x^3 + A*b^2*c*x^3 + A*a*c^2*x^3 + 3/2*B*a*b^2*x^2 + 1/2*A*b^3*x^2 + 3/2*B*a^2*c*x^2 + 3*A*a*b*c*x^2 + 3*B*a^2*b*x + 3*A*a*b^2*x + 3*A*a^2*c*x - A*a^3/x + (B*a^3 + 3*A*a^2*b)*log(abs(x))","A",0
872,1,174,0,0.165546," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^3,x, algorithm=""giac"")","\frac{1}{5} \, B c^{3} x^{5} + \frac{3}{4} \, B b c^{2} x^{4} + \frac{1}{4} \, A c^{3} x^{4} + B b^{2} c x^{3} + B a c^{2} x^{3} + A b c^{2} x^{3} + \frac{1}{2} \, B b^{3} x^{2} + 3 \, B a b c x^{2} + \frac{3}{2} \, A b^{2} c x^{2} + \frac{3}{2} \, A a c^{2} x^{2} + 3 \, B a b^{2} x + A b^{3} x + 3 \, B a^{2} c x + 6 \, A a b c x + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} \log\left({\left| x \right|}\right) - \frac{A a^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2 \, x^{2}}"," ",0,"1/5*B*c^3*x^5 + 3/4*B*b*c^2*x^4 + 1/4*A*c^3*x^4 + B*b^2*c*x^3 + B*a*c^2*x^3 + A*b*c^2*x^3 + 1/2*B*b^3*x^2 + 3*B*a*b*c*x^2 + 3/2*A*b^2*c*x^2 + 3/2*A*a*c^2*x^2 + 3*B*a*b^2*x + A*b^3*x + 3*B*a^2*c*x + 6*A*a*b*c*x + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*log(abs(x)) - 1/2*(A*a^3 + 2*(B*a^3 + 3*A*a^2*b)*x)/x^2","A",0
873,1,169,0,0.166631," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^4,x, algorithm=""giac"")","\frac{1}{4} \, B c^{3} x^{4} + B b c^{2} x^{3} + \frac{1}{3} \, A c^{3} x^{3} + \frac{3}{2} \, B b^{2} c x^{2} + \frac{3}{2} \, B a c^{2} x^{2} + \frac{3}{2} \, A b c^{2} x^{2} + B b^{3} x + 6 \, B a b c x + 3 \, A b^{2} c x + 3 \, A a c^{2} x + {\left(3 \, B a b^{2} + A b^{3} + 3 \, B a^{2} c + 6 \, A a b c\right)} \log\left({\left| x \right|}\right) - \frac{2 \, A a^{3} + 18 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{6 \, x^{3}}"," ",0,"1/4*B*c^3*x^4 + B*b*c^2*x^3 + 1/3*A*c^3*x^3 + 3/2*B*b^2*c*x^2 + 3/2*B*a*c^2*x^2 + 3/2*A*b*c^2*x^2 + B*b^3*x + 6*B*a*b*c*x + 3*A*b^2*c*x + 3*A*a*c^2*x + (3*B*a*b^2 + A*b^3 + 3*B*a^2*c + 6*A*a*b*c)*log(abs(x)) - 1/6*(2*A*a^3 + 18*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + 3*(B*a^3 + 3*A*a^2*b)*x)/x^3","A",0
874,1,166,0,0.184428," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^5,x, algorithm=""giac"")","\frac{1}{3} \, B c^{3} x^{3} + \frac{3}{2} \, B b c^{2} x^{2} + \frac{1}{2} \, A c^{3} x^{2} + 3 \, B b^{2} c x + 3 \, B a c^{2} x + 3 \, A b c^{2} x + {\left(B b^{3} + 6 \, B a b c + 3 \, A b^{2} c + 3 \, A a c^{2}\right)} \log\left({\left| x \right|}\right) - \frac{3 \, A a^{3} + 12 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, B a^{2} c + 6 \, A a b 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,"1/3*B*c^3*x^3 + 3/2*B*b*c^2*x^2 + 1/2*A*c^3*x^2 + 3*B*b^2*c*x + 3*B*a*c^2*x + 3*A*b*c^2*x + (B*b^3 + 6*B*a*b*c + 3*A*b^2*c + 3*A*a*c^2)*log(abs(x)) - 1/12*(3*A*a^3 + 12*(3*B*a*b^2 + A*b^3 + 3*B*a^2*c + 6*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
875,1,162,0,0.160835," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^6,x, algorithm=""giac"")","\frac{1}{2} \, B c^{3} x^{2} + 3 \, B b c^{2} x + A c^{3} x + 3 \, {\left(B b^{2} c + B a c^{2} + A b c^{2}\right)} \log\left({\left| x \right|}\right) - \frac{20 \, {\left(B b^{3} + 6 \, B a b c + 3 \, A b^{2} c + 3 \, A a c^{2}\right)} x^{4} + 4 \, A a^{3} + 10 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, B a^{2} c + 6 \, A a b 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,"1/2*B*c^3*x^2 + 3*B*b*c^2*x + A*c^3*x + 3*(B*b^2*c + B*a*c^2 + A*b*c^2)*log(abs(x)) - 1/20*(20*(B*b^3 + 6*B*a*b*c + 3*A*b^2*c + 3*A*a*c^2)*x^4 + 4*A*a^3 + 10*(3*B*a*b^2 + A*b^3 + 3*B*a^2*c + 6*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
876,1,162,0,0.152282," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^7,x, algorithm=""giac"")","B c^{3} x + {\left(3 \, B b c^{2} + A c^{3}\right)} \log\left({\left| x \right|}\right) - \frac{180 \, {\left(B b^{2} c + B a c^{2} + A b c^{2}\right)} x^{5} + 30 \, {\left(B b^{3} + 6 \, B a b c + 3 \, A b^{2} c + 3 \, A a c^{2}\right)} x^{4} + 10 \, A a^{3} + 20 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, B a^{2} c + 6 \, A a b 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,"B*c^3*x + (3*B*b*c^2 + A*c^3)*log(abs(x)) - 1/60*(180*(B*b^2*c + B*a*c^2 + A*b*c^2)*x^5 + 30*(B*b^3 + 6*B*a*b*c + 3*A*b^2*c + 3*A*a*c^2)*x^4 + 10*A*a^3 + 20*(3*B*a*b^2 + A*b^3 + 3*B*a^2*c + 6*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
877,1,165,0,0.192942," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^8,x, algorithm=""giac"")","B c^{3} \log\left({\left| x \right|}\right) - \frac{420 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 630 \, {\left(B b^{2} c + B a c^{2} + A b c^{2}\right)} x^{5} + 140 \, {\left(B b^{3} + 6 \, B a b c + 3 \, A b^{2} c + 3 \, A a c^{2}\right)} x^{4} + 60 \, A a^{3} + 105 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, B a^{2} c + 6 \, A a b 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,"B*c^3*log(abs(x)) - 1/420*(420*(3*B*b*c^2 + A*c^3)*x^6 + 630*(B*b^2*c + B*a*c^2 + A*b*c^2)*x^5 + 140*(B*b^3 + 6*B*a*b*c + 3*A*b^2*c + 3*A*a*c^2)*x^4 + 60*A*a^3 + 105*(3*B*a*b^2 + A*b^3 + 3*B*a^2*c + 6*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
878,1,191,0,0.172350," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^9,x, algorithm=""giac"")","-\frac{280 \, B c^{3} x^{7} + 420 \, B b c^{2} x^{6} + 140 \, A c^{3} x^{6} + 280 \, B b^{2} c x^{5} + 280 \, B a c^{2} x^{5} + 280 \, A b c^{2} x^{5} + 70 \, B b^{3} x^{4} + 420 \, B a b c x^{4} + 210 \, A b^{2} c x^{4} + 210 \, A a c^{2} x^{4} + 168 \, B a b^{2} x^{3} + 56 \, A b^{3} x^{3} + 168 \, B a^{2} c x^{3} + 336 \, A a b c x^{3} + 140 \, B a^{2} b x^{2} + 140 \, A a b^{2} x^{2} + 140 \, A a^{2} c x^{2} + 40 \, B a^{3} x + 120 \, A a^{2} b x + 35 \, A a^{3}}{280 \, x^{8}}"," ",0,"-1/280*(280*B*c^3*x^7 + 420*B*b*c^2*x^6 + 140*A*c^3*x^6 + 280*B*b^2*c*x^5 + 280*B*a*c^2*x^5 + 280*A*b*c^2*x^5 + 70*B*b^3*x^4 + 420*B*a*b*c*x^4 + 210*A*b^2*c*x^4 + 210*A*a*c^2*x^4 + 168*B*a*b^2*x^3 + 56*A*b^3*x^3 + 168*B*a^2*c*x^3 + 336*A*a*b*c*x^3 + 140*B*a^2*b*x^2 + 140*A*a*b^2*x^2 + 140*A*a^2*c*x^2 + 40*B*a^3*x + 120*A*a^2*b*x + 35*A*a^3)/x^8","A",0
879,1,191,0,0.157367," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^10,x, algorithm=""giac"")","-\frac{1260 \, B c^{3} x^{7} + 2520 \, B b c^{2} x^{6} + 840 \, A c^{3} x^{6} + 1890 \, B b^{2} c x^{5} + 1890 \, B a c^{2} x^{5} + 1890 \, A b c^{2} x^{5} + 504 \, B b^{3} x^{4} + 3024 \, B a b c x^{4} + 1512 \, A b^{2} c x^{4} + 1512 \, A a c^{2} x^{4} + 1260 \, B a b^{2} x^{3} + 420 \, A b^{3} x^{3} + 1260 \, B a^{2} c x^{3} + 2520 \, A a b c x^{3} + 1080 \, B a^{2} b x^{2} + 1080 \, A a b^{2} x^{2} + 1080 \, A a^{2} c x^{2} + 315 \, B a^{3} x + 945 \, A a^{2} b x + 280 \, A a^{3}}{2520 \, x^{9}}"," ",0,"-1/2520*(1260*B*c^3*x^7 + 2520*B*b*c^2*x^6 + 840*A*c^3*x^6 + 1890*B*b^2*c*x^5 + 1890*B*a*c^2*x^5 + 1890*A*b*c^2*x^5 + 504*B*b^3*x^4 + 3024*B*a*b*c*x^4 + 1512*A*b^2*c*x^4 + 1512*A*a*c^2*x^4 + 1260*B*a*b^2*x^3 + 420*A*b^3*x^3 + 1260*B*a^2*c*x^3 + 2520*A*a*b*c*x^3 + 1080*B*a^2*b*x^2 + 1080*A*a*b^2*x^2 + 1080*A*a^2*c*x^2 + 315*B*a^3*x + 945*A*a^2*b*x + 280*A*a^3)/x^9","A",0
880,1,191,0,0.156465," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^11,x, algorithm=""giac"")","-\frac{840 \, B c^{3} x^{7} + 1890 \, B b c^{2} x^{6} + 630 \, A c^{3} x^{6} + 1512 \, B b^{2} c x^{5} + 1512 \, B a c^{2} x^{5} + 1512 \, A b c^{2} x^{5} + 420 \, B b^{3} x^{4} + 2520 \, B a b c x^{4} + 1260 \, A b^{2} c x^{4} + 1260 \, A a c^{2} x^{4} + 1080 \, B a b^{2} x^{3} + 360 \, A b^{3} x^{3} + 1080 \, B a^{2} c x^{3} + 2160 \, A a b c x^{3} + 945 \, B a^{2} b x^{2} + 945 \, A a b^{2} x^{2} + 945 \, A a^{2} c x^{2} + 280 \, B a^{3} x + 840 \, A a^{2} b x + 252 \, A a^{3}}{2520 \, x^{10}}"," ",0,"-1/2520*(840*B*c^3*x^7 + 1890*B*b*c^2*x^6 + 630*A*c^3*x^6 + 1512*B*b^2*c*x^5 + 1512*B*a*c^2*x^5 + 1512*A*b*c^2*x^5 + 420*B*b^3*x^4 + 2520*B*a*b*c*x^4 + 1260*A*b^2*c*x^4 + 1260*A*a*c^2*x^4 + 1080*B*a*b^2*x^3 + 360*A*b^3*x^3 + 1080*B*a^2*c*x^3 + 2160*A*a*b*c*x^3 + 945*B*a^2*b*x^2 + 945*A*a*b^2*x^2 + 945*A*a^2*c*x^2 + 280*B*a^3*x + 840*A*a^2*b*x + 252*A*a^3)/x^10","A",0
881,1,247,0,0.182420," ","integrate(x^4*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{3 \, c^{3} x^{4} e + 4 \, c^{3} d x^{3} - 4 \, b c^{2} x^{3} e - 6 \, b c^{2} d x^{2} + 6 \, b^{2} c x^{2} e - 6 \, a c^{2} x^{2} e + 12 \, b^{2} c d x - 12 \, a c^{2} d x - 12 \, b^{3} x e + 24 \, a b c x e}{12 \, c^{4}} - \frac{{\left(b^{3} c d - 2 \, a b c^{2} d - b^{4} e + 3 \, a b^{2} c e - a^{2} c^{2} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{5}} + \frac{{\left(b^{4} c d - 4 \, a b^{2} c^{2} d + 2 \, a^{2} c^{3} d - b^{5} e + 5 \, a b^{3} c e - 5 \, a^{2} b c^{2} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{5}}"," ",0,"1/12*(3*c^3*x^4*e + 4*c^3*d*x^3 - 4*b*c^2*x^3*e - 6*b*c^2*d*x^2 + 6*b^2*c*x^2*e - 6*a*c^2*x^2*e + 12*b^2*c*d*x - 12*a*c^2*d*x - 12*b^3*x*e + 24*a*b*c*x*e)/c^4 - 1/2*(b^3*c*d - 2*a*b*c^2*d - b^4*e + 3*a*b^2*c*e - a^2*c^2*e)*log(c*x^2 + b*x + a)/c^5 + (b^4*c*d - 4*a*b^2*c^2*d + 2*a^2*c^3*d - b^5*e + 5*a*b^3*c*e - 5*a^2*b*c^2*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^5)","A",0
882,1,178,0,0.161508," ","integrate(x^3*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, c^{2} x^{3} e + 3 \, c^{2} d x^{2} - 3 \, b c x^{2} e - 6 \, b c d x + 6 \, b^{2} x e - 6 \, a c x e}{6 \, c^{3}} + \frac{{\left(b^{2} c d - a c^{2} d - b^{3} e + 2 \, a b c e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} - \frac{{\left(b^{3} c d - 3 \, a b c^{2} d - b^{4} e + 4 \, a b^{2} c e - 2 \, a^{2} c^{2} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{4}}"," ",0,"1/6*(2*c^2*x^3*e + 3*c^2*d*x^2 - 3*b*c*x^2*e - 6*b*c*d*x + 6*b^2*x*e - 6*a*c*x*e)/c^3 + 1/2*(b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e)*log(c*x^2 + b*x + a)/c^4 - (b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4)","A",0
883,1,122,0,0.171181," ","integrate(x^2*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{c x^{2} e + 2 \, c d x - 2 \, b x e}{2 \, c^{2}} - \frac{{\left(b c d - b^{2} e + a c e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} + \frac{{\left(b^{2} c d - 2 \, a c^{2} d - b^{3} e + 3 \, a b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/2*(c*x^2*e + 2*c*d*x - 2*b*x*e)/c^2 - 1/2*(b*c*d - b^2*e + a*c*e)*log(c*x^2 + b*x + a)/c^3 + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
884,1,88,0,0.158674," ","integrate(x*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{x e}{c} + \frac{{\left(c d - b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} - \frac{{\left(b c d - b^{2} e + 2 \, a c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"x*e/c + 1/2*(c*d - b*e)*log(c*x^2 + b*x + a)/c^2 - (b*c*d - b^2*e + 2*a*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
885,1,65,0,0.170964," ","integrate((e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{e \log\left(c x^{2} + b x + a\right)}{2 \, c} + \frac{{\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c}"," ",0,"1/2*e*log(c*x^2 + b*x + a)/c + (2*c*d - b*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c)","A",0
886,1,72,0,0.163340," ","integrate((e*x+d)/x/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{d \log\left(c x^{2} + b x + a\right)}{2 \, a} + \frac{d \log\left({\left| x \right|}\right)}{a} - \frac{{\left(b d - 2 \, a e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a}"," ",0,"-1/2*d*log(c*x^2 + b*x + a)/a + d*log(abs(x))/a - (b*d - 2*a*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a)","A",0
887,1,105,0,0.152591," ","integrate((e*x+d)/x^2/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(b d - a e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{2}} - \frac{{\left(b d - a e\right)} \log\left({\left| x \right|}\right)}{a^{2}} + \frac{{\left(b^{2} d - 2 \, a c d - a b e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a^{2}} - \frac{d}{a x}"," ",0,"1/2*(b*d - a*e)*log(c*x^2 + b*x + a)/a^2 - (b*d - a*e)*log(abs(x))/a^2 + (b^2*d - 2*a*c*d - a*b*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) - d/(a*x)","A",0
888,1,152,0,0.183842," ","integrate((e*x+d)/x^3/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} d - a c d - a b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{3}} + \frac{{\left(b^{2} d - a c d - a b e\right)} \log\left({\left| x \right|}\right)}{a^{3}} - \frac{{\left(b^{3} d - 3 \, a b c d - a b^{2} e + 2 \, a^{2} c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a^{3}} - \frac{a^{2} d - 2 \, {\left(a b d - a^{2} e\right)} x}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(b^2*d - a*c*d - a*b*e)*log(c*x^2 + b*x + a)/a^3 + (b^2*d - a*c*d - a*b*e)*log(abs(x))/a^3 - (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^3) - 1/2*(a^2*d - 2*(a*b*d - a^2*e)*x)/(a^3*x^2)","A",0
889,1,214,0,0.177812," ","integrate((e*x+d)/x^4/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(b^{3} d - 2 \, a b c d - a b^{2} e + a^{2} c e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{4}} - \frac{{\left(b^{3} d - 2 \, a b c d - a b^{2} e + a^{2} c e\right)} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{{\left(b^{4} d - 4 \, a b^{2} c d + 2 \, a^{2} c^{2} d - a b^{3} e + 3 \, a^{2} b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a^{4}} - \frac{2 \, a^{3} d + 6 \, {\left(a b^{2} d - a^{2} c d - a^{2} b e\right)} x^{2} - 3 \, {\left(a^{2} b d - a^{3} e\right)} x}{6 \, a^{4} x^{3}}"," ",0,"1/2*(b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*log(c*x^2 + b*x + a)/a^4 - (b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*log(abs(x))/a^4 + (b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - a*b^3*e + 3*a^2*b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^4) - 1/6*(2*a^3*d + 6*(a*b^2*d - a^2*c*d - a^2*b*e)*x^2 - 3*(a^2*b*d - a^3*e)*x)/(a^4*x^3)","A",0
890,1,297,0,0.162071," ","integrate(x^4*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, b^{4} c d - 12 \, a b^{2} c^{2} d + 12 \, a^{2} c^{3} d - 3 \, b^{5} e + 20 \, a b^{3} c e - 30 \, a^{2} b c^{2} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(2 \, b c d - 3 \, b^{2} e + 2 \, a c e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{c^{2} x^{2} e + 2 \, c^{2} d x - 4 \, b c x e}{2 \, c^{4}} - \frac{a b^{3} c d - 3 \, a^{2} b c^{2} d - a b^{4} e + 4 \, a^{2} b^{2} c e - 2 \, a^{3} c^{2} e + {\left(b^{4} c d - 4 \, a b^{2} c^{2} d + 2 \, a^{2} c^{3} d - b^{5} e + 5 \, a b^{3} c e - 5 \, a^{2} b c^{2} e\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{4}}"," ",0,"(2*b^4*c*d - 12*a*b^2*c^2*d + 12*a^2*c^3*d - 3*b^5*e + 20*a*b^3*c*e - 30*a^2*b*c^2*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4 - 4*a*c^5)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*b*c*d - 3*b^2*e + 2*a*c*e)*log(c*x^2 + b*x + a)/c^4 + 1/2*(c^2*x^2*e + 2*c^2*d*x - 4*b*c*x*e)/c^4 - (a*b^3*c*d - 3*a^2*b*c^2*d - a*b^4*e + 4*a^2*b^2*c*e - 2*a^3*c^2*e + (b^4*c*d - 4*a*b^2*c^2*d + 2*a^2*c^3*d - b^5*e + 5*a*b^3*c*e - 5*a^2*b*c^2*e)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^4)","A",0
891,1,235,0,0.161806," ","integrate(x^3*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(b^{3} c d - 6 \, a b c^{2} d - 2 \, b^{4} e + 12 \, a b^{2} c e - 12 \, a^{2} c^{2} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{x e}{c^{2}} + \frac{{\left(c d - 2 \, b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} + \frac{\frac{{\left(b^{3} c d - 3 \, a b c^{2} d - b^{4} e + 4 \, a b^{2} c e - 2 \, a^{2} c^{2} e\right)} x}{c} + \frac{a b^{2} c d - 2 \, a^{2} c^{2} d - a b^{3} e + 3 \, a^{2} b c e}{c}}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"-(b^3*c*d - 6*a*b*c^2*d - 2*b^4*e + 12*a*b^2*c*e - 12*a^2*c^2*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^3 - 4*a*c^4)*sqrt(-b^2 + 4*a*c)) + x*e/c^2 + 1/2*(c*d - 2*b*e)*log(c*x^2 + b*x + a)/c^3 + ((b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)*x/c + (a*b^2*c*d - 2*a^2*c^2*d - a*b^3*e + 3*a^2*b*c*e)/c)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
892,1,169,0,0.202933," ","integrate(x^2*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, a c^{2} d + b^{3} e - 6 \, a b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{e \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} - \frac{a b c d - a b^{2} e + 2 \, a^{2} c e + {\left(b^{2} c d - 2 \, a c^{2} d - b^{3} e + 3 \, a b c e\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"-(4*a*c^2*d + b^3*e - 6*a*b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2 - 4*a*c^3)*sqrt(-b^2 + 4*a*c)) + 1/2*e*log(c*x^2 + b*x + a)/c^2 - (a*b*c*d - a*b^2*e + 2*a^2*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
893,1,113,0,0.164334," ","integrate(x*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2 \, {\left(b d - 2 \, a e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{b c d x - b^{2} x e + 2 \, a c x e + 2 \, a c d - a b e}{{\left(b^{2} c - 4 \, a c^{2}\right)} {\left(c x^{2} + b x + a\right)}}"," ",0,"2*(b*d - 2*a*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) + (b*c*d*x - b^2*x*e + 2*a*c*x*e + 2*a*c*d - a*b*e)/((b^2*c - 4*a*c^2)*(c*x^2 + b*x + a))","A",0
894,1,99,0,0.155088," ","integrate((e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c d x - b x e + b d - 2 \, a e}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-2*(2*c*d - b*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (2*c*d*x - b*x*e + b*d - 2*a*e)/((c*x^2 + b*x + a)*(b^2 - 4*a*c))","A",0
895,1,160,0,0.159597," ","integrate((e*x+d)/x/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(b^{3} d - 6 \, a b c d + 4 \, a^{2} c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{d \log\left(c x^{2} + b x + a\right)}{2 \, a^{2}} + \frac{d \log\left({\left| x \right|}\right)}{a^{2}} + \frac{a b^{2} d - 2 \, a^{2} c d - a^{2} b e + {\left(a b c d - 2 \, a^{2} c e\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{2}}"," ",0,"-(b^3*d - 6*a*b*c*d + 4*a^2*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^2*b^2 - 4*a^3*c)*sqrt(-b^2 + 4*a*c)) - 1/2*d*log(c*x^2 + b*x + a)/a^2 + d*log(abs(x))/a^2 + (a*b^2*d - 2*a^2*c*d - a^2*b*e + (a*b*c*d - 2*a^2*c*e)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*a^2)","A",0
896,1,245,0,0.160250," ","integrate((e*x+d)/x^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, b^{4} d - 12 \, a b^{2} c d + 12 \, a^{2} c^{2} d - a b^{3} e + 6 \, a^{2} b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{2} c d x^{2} - 6 \, a c^{2} d x^{2} - a b c x^{2} e + 2 \, b^{3} d x - 7 \, a b c d x - a b^{2} x e + 2 \, a^{2} c x e + a b^{2} d - 4 \, a^{2} c d}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(c x^{3} + b x^{2} + a x\right)}} + \frac{{\left(2 \, b d - a e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{3}} - \frac{{\left(2 \, b d - a e\right)} \log\left({\left| x \right|}\right)}{a^{3}}"," ",0,"(2*b^4*d - 12*a*b^2*c*d + 12*a^2*c^2*d - a*b^3*e + 6*a^2*b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^3*b^2 - 4*a^4*c)*sqrt(-b^2 + 4*a*c)) - (2*b^2*c*d*x^2 - 6*a*c^2*d*x^2 - a*b*c*x^2*e + 2*b^3*d*x - 7*a*b*c*d*x - a*b^2*x*e + 2*a^2*c*x*e + a*b^2*d - 4*a^2*c*d)/((a^2*b^2 - 4*a^3*c)*(c*x^3 + b*x^2 + a*x)) + 1/2*(2*b*d - a*e)*log(c*x^2 + b*x + a)/a^3 - (2*b*d - a*e)*log(abs(x))/a^3","A",0
897,1,345,0,0.169251," ","integrate((e*x+d)/x^3/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{5} d - 20 \, a b^{3} c d + 30 \, a^{2} b c^{2} d - 2 \, a b^{4} e + 12 \, a^{2} b^{2} c e - 12 \, a^{3} c^{2} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(3 \, b^{2} d - 2 \, a c d - 2 \, a b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{4}} + \frac{{\left(3 \, b^{2} d - 2 \, a c d - 2 \, a b e\right)} \log\left({\left| x \right|}\right)}{a^{4}} - \frac{a^{3} b^{2} d - 4 \, a^{4} c d - 2 \, {\left(3 \, a b^{3} c d - 11 \, a^{2} b c^{2} d - 2 \, a^{2} b^{2} c e + 6 \, a^{3} c^{2} e\right)} x^{3} - {\left(6 \, a b^{4} d - 25 \, a^{2} b^{2} c d + 8 \, a^{3} c^{2} d - 4 \, a^{2} b^{3} e + 14 \, a^{3} b c e\right)} x^{2} - {\left(3 \, a^{2} b^{3} d - 12 \, a^{3} b c d - 2 \, a^{3} b^{2} e + 8 \, a^{4} c e\right)} x}{2 \, {\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{4} x^{2}}"," ",0,"-(3*b^5*d - 20*a*b^3*c*d + 30*a^2*b*c^2*d - 2*a*b^4*e + 12*a^2*b^2*c*e - 12*a^3*c^2*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^4*b^2 - 4*a^5*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(3*b^2*d - 2*a*c*d - 2*a*b*e)*log(c*x^2 + b*x + a)/a^4 + (3*b^2*d - 2*a*c*d - 2*a*b*e)*log(abs(x))/a^4 - 1/2*(a^3*b^2*d - 4*a^4*c*d - 2*(3*a*b^3*c*d - 11*a^2*b*c^2*d - 2*a^2*b^2*c*e + 6*a^3*c^2*e)*x^3 - (6*a*b^4*d - 25*a^2*b^2*c*d + 8*a^3*c^2*d - 4*a^2*b^3*e + 14*a^3*b*c*e)*x^2 - (3*a^2*b^3*d - 12*a^3*b*c*d - 2*a^3*b^2*e + 8*a^4*c*e)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*a^4*x^2)","A",0
898,1,10,0,0.191403," ","integrate((5+2*x)/(x^2+5*x+4),x, algorithm=""giac"")","\log\left({\left| x^{2} + 5 \, x + 4 \right|}\right)"," ",0,"log(abs(x^2 + 5*x + 4))","A",0
899,1,15,0,0.146883," ","integrate((7+3*x)/(x^2+6*x+8),x, algorithm=""giac"")","\frac{5}{2} \, \log\left({\left| x + 4 \right|}\right) + \frac{1}{2} \, \log\left({\left| x + 2 \right|}\right)"," ",0,"5/2*log(abs(x + 4)) + 1/2*log(abs(x + 2))","A",0
900,1,14,0,0.148391," ","integrate((5+2*x)/(x^2+4*x+5),x, algorithm=""giac"")","\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
901,1,26,0,0.151650," ","integrate((-2+7*x)/(2*x^2-16*x+42),x, algorithm=""giac"")","\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
902,1,42,0,0.148936," ","integrate((3+x)/(x^2+3*x+1),x, algorithm=""giac"")","\frac{3}{10} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x - \sqrt{5} + 3 \right|}}{{\left| 2 \, x + \sqrt{5} + 3 \right|}}\right) + \frac{1}{2} \, \log\left({\left| x^{2} + 3 \, x + 1 \right|}\right)"," ",0,"3/10*sqrt(5)*log(abs(2*x - sqrt(5) + 3)/abs(2*x + sqrt(5) + 3)) + 1/2*log(abs(x^2 + 3*x + 1))","A",0
903,1,46,0,0.154721," ","integrate((-1+2*x)/(4*x^2+8*x+1),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{3} \log\left(\frac{{\left| 8 \, x - 4 \, \sqrt{3} + 8 \right|}}{{\left| 8 \, x + 4 \, \sqrt{3} + 8 \right|}}\right) + \frac{1}{4} \, \log\left({\left| 4 \, x^{2} + 8 \, x + 1 \right|}\right)"," ",0,"-1/4*sqrt(3)*log(abs(8*x - 4*sqrt(3) + 8)/abs(8*x + 4*sqrt(3) + 8)) + 1/4*log(abs(4*x^2 + 8*x + 1))","A",0
904,1,14,0,0.148900," ","integrate((3+2*x)/(4*x^2+12*x+13)^2,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(4 \, x^{2} + 12 \, x + 13\right)}}"," ",0,"-1/4/(4*x^2 + 12*x + 13)","A",0
905,1,22,0,0.164595," ","integrate((4+x)/(x^2+4*x+5)^2,x, algorithm=""giac"")","\frac{2 \, x + 3}{2 \, {\left(x^{2} + 4 \, x + 5\right)}} + \arctan\left(x + 2\right)"," ",0,"1/2*(2*x + 3)/(x^2 + 4*x + 5) + arctan(x + 2)","A",0
906,1,32,0,0.150481," ","integrate((-1+3*x)/(x^2+x+1)^2,x, algorithm=""giac"")","-\frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{5 \, x + 7}{3 \, {\left(x^{2} + x + 1\right)}}"," ",0,"-10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/3*(5*x + 7)/(x^2 + x + 1)","A",0
907,1,44,0,0.150016," ","integrate((1+x)/(x^2-x+1)^3,x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{2 \, x^{3} - 3 \, x^{2} + 4 \, x - 2}{2 \, {\left(x^{2} - x + 1\right)}^{2}}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/2*(2*x^3 - 3*x^2 + 4*x - 2)/(x^2 - x + 1)^2","A",0
908,1,11,0,0.146024," ","integrate(1/(B*x+A),x, algorithm=""giac"")","\frac{\log\left({\left| B x + A \right|}\right)}{B}"," ",0,"log(abs(B*x + A))/B","A",0
909,1,22,0,0.152176," ","integrate((B*x+A)/(B^2*x^2+2*A*B*x+A^2),x, algorithm=""giac"")","\frac{\log\left(A^{2} + {\left(B x^{2} + 2 \, A x\right)} B\right)}{2 \, B}"," ",0,"1/2*log(A^2 + (B*x^2 + 2*A*x)*B)/B","B",0
910,1,414,0,0.240774," ","integrate(x^4*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{107520} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, B x + \frac{B b c^{5} + 14 \, A c^{6}}{c^{6}}\right)} x - \frac{11 \, B b^{2} c^{4} - 24 \, B a c^{5} - 14 \, A b c^{5}}{c^{6}}\right)} x + \frac{99 \, B b^{3} c^{3} - 316 \, B a b c^{4} - 126 \, A b^{2} c^{4} + 280 \, A a c^{5}}{c^{6}}\right)} x - \frac{231 \, B b^{4} c^{2} - 972 \, B a b^{2} c^{3} - 294 \, A b^{3} c^{3} + 512 \, B a^{2} c^{4} + 952 \, A a b c^{4}}{c^{6}}\right)} x + \frac{1155 \, B b^{5} c - 6048 \, B a b^{3} c^{2} - 1470 \, A b^{4} c^{2} + 6352 \, B a^{2} b c^{3} + 6272 \, A a b^{2} c^{3} - 3360 \, A a^{2} c^{4}}{c^{6}}\right)} x - \frac{3465 \, B b^{6} - 21840 \, B a b^{4} c - 4410 \, A b^{5} c + 34608 \, B a^{2} b^{2} c^{2} + 23520 \, A a b^{3} c^{2} - 8192 \, B a^{3} c^{3} - 25312 \, A a^{2} b c^{3}}{c^{6}}\right)} - \frac{{\left(33 \, B b^{7} - 252 \, B a b^{5} c - 42 \, A b^{6} c + 560 \, B a^{2} b^{3} c^{2} + 280 \, A a b^{4} c^{2} - 320 \, B a^{3} b c^{3} - 480 \, A a^{2} b^{2} c^{3} + 128 \, A a^{3} c^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{13}{2}}}"," ",0,"1/107520*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(12*B*x + (B*b*c^5 + 14*A*c^6)/c^6)*x - (11*B*b^2*c^4 - 24*B*a*c^5 - 14*A*b*c^5)/c^6)*x + (99*B*b^3*c^3 - 316*B*a*b*c^4 - 126*A*b^2*c^4 + 280*A*a*c^5)/c^6)*x - (231*B*b^4*c^2 - 972*B*a*b^2*c^3 - 294*A*b^3*c^3 + 512*B*a^2*c^4 + 952*A*a*b*c^4)/c^6)*x + (1155*B*b^5*c - 6048*B*a*b^3*c^2 - 1470*A*b^4*c^2 + 6352*B*a^2*b*c^3 + 6272*A*a*b^2*c^3 - 3360*A*a^2*c^4)/c^6)*x - (3465*B*b^6 - 21840*B*a*b^4*c - 4410*A*b^5*c + 34608*B*a^2*b^2*c^2 + 23520*A*a*b^3*c^2 - 8192*B*a^3*c^3 - 25312*A*a^2*b*c^3)/c^6) - 1/2048*(33*B*b^7 - 252*B*a*b^5*c - 42*A*b^6*c + 560*B*a^2*b^3*c^2 + 280*A*a*b^4*c^2 - 320*B*a^3*b*c^3 - 480*A*a^2*b^2*c^3 + 128*A*a^3*c^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","A",0
911,1,323,0,0.258443," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B x + \frac{B b c^{4} + 12 \, A c^{5}}{c^{5}}\right)} x - \frac{9 \, B b^{2} c^{3} - 20 \, B a c^{4} - 12 \, A b c^{4}}{c^{5}}\right)} x + \frac{21 \, B b^{3} c^{2} - 68 \, B a b c^{3} - 28 \, A b^{2} c^{3} + 64 \, A a c^{4}}{c^{5}}\right)} x - \frac{105 \, B b^{4} c - 448 \, B a b^{2} c^{2} - 140 \, A b^{3} c^{2} + 240 \, B a^{2} c^{3} + 464 \, A a b c^{3}}{c^{5}}\right)} x + \frac{315 \, B b^{5} - 1680 \, B a b^{3} c - 420 \, A b^{4} c + 1808 \, B a^{2} b c^{2} + 1840 \, A a b^{2} c^{2} - 1024 \, A a^{2} c^{3}}{c^{5}}\right)} + \frac{{\left(21 \, B b^{6} - 140 \, B a b^{4} c - 28 \, A b^{5} c + 240 \, B a^{2} b^{2} c^{2} + 160 \, A a b^{3} c^{2} - 64 \, B a^{3} c^{3} - 192 \, A a^{2} b c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{11}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*B*x + (B*b*c^4 + 12*A*c^5)/c^5)*x - (9*B*b^2*c^3 - 20*B*a*c^4 - 12*A*b*c^4)/c^5)*x + (21*B*b^3*c^2 - 68*B*a*b*c^3 - 28*A*b^2*c^3 + 64*A*a*c^4)/c^5)*x - (105*B*b^4*c - 448*B*a*b^2*c^2 - 140*A*b^3*c^2 + 240*B*a^2*c^3 + 464*A*a*b*c^3)/c^5)*x + (315*B*b^5 - 1680*B*a*b^3*c - 420*A*b^4*c + 1808*B*a^2*b*c^2 + 1840*A*a*b^2*c^2 - 1024*A*a^2*c^3)/c^5) + 1/1024*(21*B*b^6 - 140*B*a*b^4*c - 28*A*b^5*c + 240*B*a^2*b^2*c^2 + 160*A*a*b^3*c^2 - 64*B*a^3*c^3 - 192*A*a^2*b*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
912,1,245,0,0.226416," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, B x + \frac{B b c^{3} + 10 \, A c^{4}}{c^{4}}\right)} x - \frac{7 \, B b^{2} c^{2} - 16 \, B a c^{3} - 10 \, A b c^{3}}{c^{4}}\right)} x + \frac{35 \, B b^{3} c - 116 \, B a b c^{2} - 50 \, A b^{2} c^{2} + 120 \, A a c^{3}}{c^{4}}\right)} x - \frac{105 \, B b^{4} - 460 \, B a b^{2} c - 150 \, A b^{3} c + 256 \, B a^{2} c^{2} + 520 \, A a b c^{2}}{c^{4}}\right)} - \frac{{\left(7 \, B b^{5} - 40 \, B a b^{3} c - 10 \, A b^{4} c + 48 \, B a^{2} b c^{2} + 48 \, A a b^{2} c^{2} - 32 \, A a^{2} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x + a)*(2*(4*(6*(8*B*x + (B*b*c^3 + 10*A*c^4)/c^4)*x - (7*B*b^2*c^2 - 16*B*a*c^3 - 10*A*b*c^3)/c^4)*x + (35*B*b^3*c - 116*B*a*b*c^2 - 50*A*b^2*c^2 + 120*A*a*c^3)/c^4)*x - (105*B*b^4 - 460*B*a*b^2*c - 150*A*b^3*c + 256*B*a^2*c^2 + 520*A*a*b*c^2)/c^4) - 1/256*(7*B*b^5 - 40*B*a*b^3*c - 10*A*b^4*c + 48*B*a^2*b*c^2 + 48*A*a*b^2*c^2 - 32*A*a^2*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
913,1,178,0,0.249916," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, B x + \frac{B b c^{2} + 8 \, A c^{3}}{c^{3}}\right)} x - \frac{5 \, B b^{2} c - 12 \, B a c^{2} - 8 \, A b c^{2}}{c^{3}}\right)} x + \frac{15 \, B b^{3} - 52 \, B a b c - 24 \, A b^{2} c + 64 \, A a c^{2}}{c^{3}}\right)} + \frac{{\left(5 \, B b^{4} - 24 \, B a b^{2} c - 8 \, A b^{3} c + 16 \, B a^{2} c^{2} + 32 \, A a b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*B*x + (B*b*c^2 + 8*A*c^3)/c^3)*x - (5*B*b^2*c - 12*B*a*c^2 - 8*A*b*c^2)/c^3)*x + (15*B*b^3 - 52*B*a*b*c - 24*A*b^2*c + 64*A*a*c^2)/c^3) + 1/128*(5*B*b^4 - 24*B*a*b^2*c - 8*A*b^3*c + 16*B*a^2*c^2 + 32*A*a*b*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
914,1,123,0,0.245448," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, B x + \frac{B b c + 6 \, A c^{2}}{c^{2}}\right)} x - \frac{3 \, B b^{2} - 8 \, B a c - 6 \, A b c}{c^{2}}\right)} - \frac{{\left(B b^{3} - 4 \, B a b c - 2 \, A b^{2} c + 8 \, A a c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*(4*B*x + (B*b*c + 6*A*c^2)/c^2)*x - (3*B*b^2 - 8*B*a*c - 6*A*b*c)/c^2) - 1/16*(B*b^3 - 4*B*a*b*c - 2*A*b^2*c + 8*A*a*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
915,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
916,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{2,[4,4,0]%%%}+%%%{%%%{-16,[1]%%%},[4,2,1]%%%}+%%%{%%%{32,[2]%%%},[4,0,2]%%%}+%%%{-4,[2,4,1]%%%}+%%%{%%%{32,[1]%%%},[2,2,2]%%%}+%%%{%%%{-64,[2]%%%},[2,0,3]%%%}+%%%{2,[0,4,2]%%%}+%%%{%%%{-16,[1]%%%},[0,2,3]%%%}+%%%{%%%{32,[2]%%%},[0,0,4]%%%} / %%%{4,[4,0,0]%%%}+%%%{-8,[2,0,1]%%%}+%%%{4,[0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
917,1,359,0,0.303005," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^3,x, algorithm=""giac"")","-B \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c - b \sqrt{c} \right|}\right) + \frac{{\left(4 \, B a b - A b^{2} + 4 \, A a c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a} + \frac{4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} \sqrt{c} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b \sqrt{c} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c - 8 \, B a^{3} \sqrt{c}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{2} a}"," ",0,"-B*sqrt(c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c - b*sqrt(c))) + 1/4*(4*B*a*b - A*b^2 + 4*A*a*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a) + 1/4*(4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*sqrt(c) + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b*sqrt(c) - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c - 8*B*a^3*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^2*a)","B",0
918,1,524,0,0.219607," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{{\left(2 \, B a b^{2} - A b^{3} - 8 \, B a^{2} c + 4 \, A a b c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{2}} + \frac{6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a b^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b^{3} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} c + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b c + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{2} b \sqrt{c} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{2} c^{\frac{3}{2}} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{3} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b c - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} b \sqrt{c} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{2} b^{2} \sqrt{c} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} c + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b c + 16 \, A a^{4} c^{\frac{3}{2}}}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{3} a^{2}}"," ",0,"-1/8*(2*B*a*b^2 - A*b^3 - 8*B*a^2*c + 4*A*a*b*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^2) + 1/24*(6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*b^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b^3 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*c + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b*c + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^2*b*sqrt(c) + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^2*c^(3/2) + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^3 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b*c - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*b*sqrt(c) + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^2*b^2*sqrt(c) - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*c + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b*c + 16*A*a^4*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^3*a^2)","B",0
919,1,991,0,0.273537," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^5,x, algorithm=""giac"")","\frac{{\left(8 \, B a b^{3} - 5 \, A b^{4} - 32 \, B a^{2} b c + 24 \, A a b^{2} c - 16 \, A a^{2} c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{64 \, \sqrt{-a} a^{3}} - \frac{24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a b^{3} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A b^{4} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b c + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{2} c - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} c^{2} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{3} c^{\frac{3}{2}} - 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} b^{3} + 55 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b^{4} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{3} b c - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{2} c - 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} c^{2} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{3} b^{2} \sqrt{c} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{4} c^{\frac{3}{2}} - 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{3} b c^{\frac{3}{2}} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{3} b^{3} - 73 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b^{4} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b c - 648 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{2} c - 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} c^{2} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{4} b^{2} \sqrt{c} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{3} b^{3} \sqrt{c} - 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{5} c^{\frac{3}{2}} - 256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{4} b c^{\frac{3}{2}} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} b^{3} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b^{4} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b c - 312 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{2} c - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} c^{2} + 128 \, B a^{6} c^{\frac{3}{2}} - 128 \, A a^{5} b c^{\frac{3}{2}}}{192 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{4} a^{3}}"," ",0,"1/64*(8*B*a*b^3 - 5*A*b^4 - 32*B*a^2*b*c + 24*A*a*b^2*c - 16*A*a^2*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^3) - 1/192*(24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a*b^3 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*b^4 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b*c + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^2*c - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*c^2 - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^3*c^(3/2) - 88*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*b^3 + 55*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b^4 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^3*b*c - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^2*c - 336*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*c^2 - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^3*b^2*sqrt(c) + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^4*c^(3/2) - 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^3*b*c^(3/2) + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^3*b^3 - 73*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b^4 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b*c - 648*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^2*c - 336*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*c^2 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^4*b^2*sqrt(c) - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^3*b^3*sqrt(c) - 128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^5*c^(3/2) - 256*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^4*b*c^(3/2) + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*b^3 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b^4 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b*c - 312*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^2*c - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*c^2 + 128*B*a^6*c^(3/2) - 128*A*a^5*b*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^4*a^3)","B",0
920,1,1407,0,0.261864," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^6,x, algorithm=""giac"")","-\frac{{\left(10 \, B a b^{4} - 7 \, A b^{5} - 48 \, B a^{2} b^{2} c + 40 \, A a b^{3} c + 32 \, B a^{3} c^{2} - 48 \, A a^{2} b c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{128 \, \sqrt{-a} a^{4}} + \frac{150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a b^{4} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A b^{5} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{2} b^{2} c + 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a b^{3} c + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} c^{2} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b c^{2} - 700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b^{4} + 490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{5} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{3} b^{2} c - 2800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} b^{3} c + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} c^{2} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b c^{2} + 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{4} b c^{\frac{3}{2}} + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{4} c^{\frac{5}{2}} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{3} b^{4} - 896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{5} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{4} b^{2} c + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} b^{3} c + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b c^{2} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{4} b^{3} \sqrt{c} - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{5} b c^{\frac{3}{2}} + 24320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{4} b^{2} c^{\frac{3}{2}} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} c^{\frac{5}{2}} - 580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b^{4} + 790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{5} - 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{5} b^{2} c + 9200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} b^{3} c - 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} c^{2} + 12000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b c^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{5} b^{3} \sqrt{c} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{4} b^{4} \sqrt{c} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{6} b c^{\frac{3}{2}} + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{5} b^{2} c^{\frac{3}{2}} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{6} c^{\frac{5}{2}} - 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b^{4} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{5} - 3120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{6} b^{2} c + 3240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} b^{3} c - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} c^{2} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b c^{2} - 1280 \, B a^{7} b c^{\frac{3}{2}} + 1280 \, A a^{6} b^{2} c^{\frac{3}{2}} - 512 \, A a^{7} c^{\frac{5}{2}}}{1920 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{5} a^{4}}"," ",0,"-1/128*(10*B*a*b^4 - 7*A*b^5 - 48*B*a^2*b^2*c + 40*A*a*b^3*c + 32*B*a^3*c^2 - 48*A*a^2*b*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^4) + 1/1920*(150*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a*b^4 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*b^5 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^2*b^2*c + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a*b^3*c + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*c^2 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b*c^2 - 700*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b^4 + 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^5 + 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^3*b^2*c - 2800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*b^3*c + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*c^2 + 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b*c^2 + 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^4*b*c^(3/2) + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^4*c^(5/2) + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^3*b^4 - 896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^5 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^4*b^2*c + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*b^3*c + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b*c^2 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^4*b^3*sqrt(c) - 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^5*b*c^(3/2) + 24320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^4*b^2*c^(3/2) + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*c^(5/2) - 580*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b^4 + 790*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^5 - 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^5*b^2*c + 9200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*b^3*c - 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*c^2 + 12000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b*c^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^5*b^3*sqrt(c) + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^4*b^4*sqrt(c) - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^6*b*c^(3/2) + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^5*b^2*c^(3/2) + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^6*c^(5/2) - 150*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b^4 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^5 - 3120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^6*b^2*c + 3240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*b^3*c - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*c^2 + 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b*c^2 - 1280*B*a^7*b*c^(3/2) + 1280*A*a^6*b^2*c^(3/2) - 512*A*a^7*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^5*a^4)","B",0
921,1,1955,0,0.324202," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^7,x, algorithm=""giac"")","\frac{{\left(28 \, B a b^{5} - 21 \, A b^{6} - 160 \, B a^{2} b^{3} c + 140 \, A a b^{4} c + 192 \, B a^{3} b c^{2} - 240 \, A a^{2} b^{2} c^{2} + 64 \, A a^{3} c^{3}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{512 \, \sqrt{-a} a^{5}} - \frac{420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a b^{5} - 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A b^{6} - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{2} b^{3} c + 2100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a b^{4} c + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{3} b c^{2} - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{2} b^{2} c^{2} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{3} c^{3} - 2380 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{2} b^{5} + 1785 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a b^{6} + 13600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} b^{3} c - 11900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b^{4} c - 16320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{4} b c^{2} + 20400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{3} b^{2} c^{2} - 5440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{4} c^{3} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{5} c^{\frac{5}{2}} + 5544 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{3} b^{5} - 4158 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} b^{6} - 31680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} b^{3} c + 27720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b^{4} c - 48000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{5} b c^{2} - 47520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{4} b^{2} c^{2} - 36480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{5} c^{3} - 97280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{5} b^{2} c^{\frac{3}{2}} + 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{6} c^{\frac{5}{2}} - 163840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{5} b c^{\frac{5}{2}} - 6744 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{4} b^{5} + 5058 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} b^{6} - 16320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{5} b^{3} c - 33720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b^{4} c + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{6} b c^{2} - 170400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{5} b^{2} c^{2} - 36480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{6} c^{3} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{5} b^{4} \sqrt{c} + 76800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{6} b^{2} c^{\frac{3}{2}} - 168960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} b^{3} c^{\frac{3}{2}} - 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{6} b c^{\frac{5}{2}} + 2740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{5} b^{5} - 3335 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} b^{6} + 23840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} b^{3} c - 47740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b^{4} c + 45120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{7} b c^{2} - 102480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{6} b^{2} c^{2} - 5440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{7} c^{3} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{6} b^{4} \sqrt{c} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{5} b^{5} \sqrt{c} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{7} b^{2} c^{\frac{3}{2}} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{6} b^{3} c^{\frac{3}{2}} + 12288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{8} c^{\frac{5}{2}} - 24576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{7} b c^{\frac{5}{2}} + 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{6} b^{5} - 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} b^{6} + 12960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} b^{3} c - 13260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b^{4} c + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{8} b c^{2} - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{7} b^{2} c^{2} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{8} c^{3} + 5120 \, B a^{8} b^{2} c^{\frac{3}{2}} - 5120 \, A a^{7} b^{3} c^{\frac{3}{2}} - 2048 \, B a^{9} c^{\frac{5}{2}} + 4096 \, A a^{8} b c^{\frac{5}{2}}}{7680 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{6} a^{5}}"," ",0,"1/512*(28*B*a*b^5 - 21*A*b^6 - 160*B*a^2*b^3*c + 140*A*a*b^4*c + 192*B*a^3*b*c^2 - 240*A*a^2*b^2*c^2 + 64*A*a^3*c^3)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^5) - 1/7680*(420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a*b^5 - 315*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*b^6 - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^2*b^3*c + 2100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a*b^4*c + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^3*b*c^2 - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^2*b^2*c^2 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^3*c^3 - 2380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^2*b^5 + 1785*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a*b^6 + 13600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*b^3*c - 11900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b^4*c - 16320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^4*b*c^2 + 20400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^3*b^2*c^2 - 5440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^4*c^3 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^5*c^(5/2) + 5544*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^3*b^5 - 4158*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*b^6 - 31680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*b^3*c + 27720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b^4*c - 48000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^5*b*c^2 - 47520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^4*b^2*c^2 - 36480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^5*c^3 - 97280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^5*b^2*c^(3/2) + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^6*c^(5/2) - 163840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^5*b*c^(5/2) - 6744*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^4*b^5 + 5058*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*b^6 - 16320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^5*b^3*c - 33720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b^4*c + 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^6*b*c^2 - 170400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^5*b^2*c^2 - 36480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^6*c^3 - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^5*b^4*sqrt(c) + 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^6*b^2*c^(3/2) - 168960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*b^3*c^(3/2) - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^6*b*c^(5/2) + 2740*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^5*b^5 - 3335*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*b^6 + 23840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*b^3*c - 47740*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b^4*c + 45120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^7*b*c^2 - 102480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^6*b^2*c^2 - 5440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^7*c^3 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^6*b^4*sqrt(c) - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^5*b^5*sqrt(c) + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^7*b^2*c^(3/2) - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^6*b^3*c^(3/2) + 12288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^8*c^(5/2) - 24576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^7*b*c^(5/2) + 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^6*b^5 - 315*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*b^6 + 12960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*b^3*c - 13260*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b^4*c + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^8*b*c^2 - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^7*b^2*c^2 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^8*c^3 + 5120*B*a^8*b^2*c^(3/2) - 5120*A*a^7*b^3*c^(3/2) - 2048*B*a^9*c^(5/2) + 4096*A*a^8*b*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^6*a^5)","B",0
922,1,639,0,0.324115," ","integrate(x^4*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{10321920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, {\left(16 \, B c x + \frac{19 \, B b c^{8} + 18 \, A c^{9}}{c^{8}}\right)} x + \frac{3 \, B b^{2} c^{7} + 320 \, B a c^{8} + 306 \, A b c^{8}}{c^{8}}\right)} x - \frac{13 \, B b^{3} c^{6} - 60 \, B a b c^{7} - 18 \, A b^{2} c^{7} - 1512 \, A a c^{8}}{c^{8}}\right)} x + \frac{143 \, B b^{4} c^{5} - 804 \, B a b^{2} c^{6} - 198 \, A b^{3} c^{6} + 768 \, B a^{2} c^{7} + 936 \, A a b c^{7}}{c^{8}}\right)} x - \frac{1287 \, B b^{5} c^{4} - 8536 \, B a b^{3} c^{5} - 1782 \, A b^{4} c^{5} + 12912 \, B a^{2} b c^{6} + 10224 \, A a b^{2} c^{6} - 10080 \, A a^{2} c^{7}}{c^{8}}\right)} x + \frac{3003 \, B b^{6} c^{3} - 22968 \, B a b^{4} c^{4} - 4158 \, A b^{5} c^{4} + 47280 \, B a^{2} b^{2} c^{5} + 28080 \, A a b^{3} c^{5} - 16384 \, B a^{3} c^{6} - 43488 \, A a^{2} b c^{6}}{c^{8}}\right)} x - \frac{15015 \, B b^{7} c^{2} - 130284 \, B a b^{5} c^{3} - 20790 \, A b^{6} c^{3} + 338832 \, B a^{2} b^{3} c^{4} + 161784 \, A a b^{4} c^{4} - 236864 \, B a^{3} b c^{5} - 340128 \, A a^{2} b^{2} c^{5} + 120960 \, A a^{3} c^{6}}{c^{8}}\right)} x + \frac{45045 \, B b^{8} c - 438900 \, B a b^{6} c^{2} - 62370 \, A b^{7} c^{2} + 1383984 \, B a^{2} b^{4} c^{3} + 551880 \, A a b^{5} c^{3} - 1467072 \, B a^{3} b^{2} c^{4} - 1469664 \, A a^{2} b^{3} c^{4} + 262144 \, B a^{4} c^{5} + 1058688 \, A a^{3} b c^{5}}{c^{8}}\right)} + \frac{{\left(143 \, B b^{9} - 1584 \, B a b^{7} c - 198 \, A b^{8} c + 6048 \, B a^{2} b^{5} c^{2} + 2016 \, A a b^{6} c^{2} - 8960 \, B a^{3} b^{3} c^{3} - 6720 \, A a^{2} b^{4} c^{3} + 3840 \, B a^{4} b c^{4} + 7680 \, A a^{3} b^{2} c^{4} - 1536 \, A a^{4} c^{5}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{65536 \, c^{\frac{15}{2}}}"," ",0,"1/10321920*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(4*(14*(16*B*c*x + (19*B*b*c^8 + 18*A*c^9)/c^8)*x + (3*B*b^2*c^7 + 320*B*a*c^8 + 306*A*b*c^8)/c^8)*x - (13*B*b^3*c^6 - 60*B*a*b*c^7 - 18*A*b^2*c^7 - 1512*A*a*c^8)/c^8)*x + (143*B*b^4*c^5 - 804*B*a*b^2*c^6 - 198*A*b^3*c^6 + 768*B*a^2*c^7 + 936*A*a*b*c^7)/c^8)*x - (1287*B*b^5*c^4 - 8536*B*a*b^3*c^5 - 1782*A*b^4*c^5 + 12912*B*a^2*b*c^6 + 10224*A*a*b^2*c^6 - 10080*A*a^2*c^7)/c^8)*x + (3003*B*b^6*c^3 - 22968*B*a*b^4*c^4 - 4158*A*b^5*c^4 + 47280*B*a^2*b^2*c^5 + 28080*A*a*b^3*c^5 - 16384*B*a^3*c^6 - 43488*A*a^2*b*c^6)/c^8)*x - (15015*B*b^7*c^2 - 130284*B*a*b^5*c^3 - 20790*A*b^6*c^3 + 338832*B*a^2*b^3*c^4 + 161784*A*a*b^4*c^4 - 236864*B*a^3*b*c^5 - 340128*A*a^2*b^2*c^5 + 120960*A*a^3*c^6)/c^8)*x + (45045*B*b^8*c - 438900*B*a*b^6*c^2 - 62370*A*b^7*c^2 + 1383984*B*a^2*b^4*c^3 + 551880*A*a*b^5*c^3 - 1467072*B*a^3*b^2*c^4 - 1469664*A*a^2*b^3*c^4 + 262144*B*a^4*c^5 + 1058688*A*a^3*b*c^5)/c^8) + 1/65536*(143*B*b^9 - 1584*B*a*b^7*c - 198*A*b^8*c + 6048*B*a^2*b^5*c^2 + 2016*A*a*b^6*c^2 - 8960*B*a^3*b^3*c^3 - 6720*A*a^2*b^4*c^3 + 3840*B*a^4*b*c^4 + 7680*A*a^3*b^2*c^4 - 1536*A*a^4*c^5)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(15/2)","A",0
923,1,524,0,0.273926," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{573440} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, B c x + \frac{17 \, B b c^{7} + 16 \, A c^{8}}{c^{7}}\right)} x + \frac{B b^{2} c^{6} + 84 \, B a c^{7} + 80 \, A b c^{7}}{c^{7}}\right)} x - \frac{11 \, B b^{3} c^{5} - 52 \, B a b c^{6} - 16 \, A b^{2} c^{6} - 1024 \, A a c^{7}}{c^{7}}\right)} x + \frac{99 \, B b^{4} c^{4} - 568 \, B a b^{2} c^{5} - 144 \, A b^{3} c^{5} + 560 \, B a^{2} c^{6} + 704 \, A a b c^{6}}{c^{7}}\right)} x - \frac{231 \, B b^{5} c^{3} - 1560 \, B a b^{3} c^{4} - 336 \, A b^{4} c^{4} + 2416 \, B a^{2} b c^{5} + 1984 \, A a b^{2} c^{5} - 2048 \, A a^{2} c^{6}}{c^{7}}\right)} x + \frac{1155 \, B b^{6} c^{2} - 8988 \, B a b^{4} c^{3} - 1680 \, A b^{5} c^{3} + 18896 \, B a^{2} b^{2} c^{4} + 11648 \, A a b^{3} c^{4} - 6720 \, B a^{3} c^{5} - 18688 \, A a^{2} b c^{5}}{c^{7}}\right)} x - \frac{3465 \, B b^{7} c - 30660 \, B a b^{5} c^{2} - 5040 \, A b^{6} c^{2} + 81648 \, B a^{2} b^{3} c^{3} + 40320 \, A a b^{4} c^{3} - 58816 \, B a^{3} b c^{4} - 87808 \, A a^{2} b^{2} c^{4} + 32768 \, A a^{3} c^{5}}{c^{7}}\right)} - \frac{3 \, {\left(33 \, B b^{8} - 336 \, B a b^{6} c - 48 \, A b^{7} c + 1120 \, B a^{2} b^{4} c^{2} + 448 \, A a b^{5} c^{2} - 1280 \, B a^{3} b^{2} c^{3} - 1280 \, A a^{2} b^{3} c^{3} + 256 \, B a^{4} c^{4} + 1024 \, A a^{3} b c^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{13}{2}}}"," ",0,"1/573440*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(4*(14*B*c*x + (17*B*b*c^7 + 16*A*c^8)/c^7)*x + (B*b^2*c^6 + 84*B*a*c^7 + 80*A*b*c^7)/c^7)*x - (11*B*b^3*c^5 - 52*B*a*b*c^6 - 16*A*b^2*c^6 - 1024*A*a*c^7)/c^7)*x + (99*B*b^4*c^4 - 568*B*a*b^2*c^5 - 144*A*b^3*c^5 + 560*B*a^2*c^6 + 704*A*a*b*c^6)/c^7)*x - (231*B*b^5*c^3 - 1560*B*a*b^3*c^4 - 336*A*b^4*c^4 + 2416*B*a^2*b*c^5 + 1984*A*a*b^2*c^5 - 2048*A*a^2*c^6)/c^7)*x + (1155*B*b^6*c^2 - 8988*B*a*b^4*c^3 - 1680*A*b^5*c^3 + 18896*B*a^2*b^2*c^4 + 11648*A*a*b^3*c^4 - 6720*B*a^3*c^5 - 18688*A*a^2*b*c^5)/c^7)*x - (3465*B*b^7*c - 30660*B*a*b^5*c^2 - 5040*A*b^6*c^2 + 81648*B*a^2*b^3*c^3 + 40320*A*a*b^4*c^3 - 58816*B*a^3*b*c^4 - 87808*A*a^2*b^2*c^4 + 32768*A*a^3*c^5)/c^7) - 3/32768*(33*B*b^8 - 336*B*a*b^6*c - 48*A*b^7*c + 1120*B*a^2*b^4*c^2 + 448*A*a*b^5*c^2 - 1280*B*a^3*b^2*c^3 - 1280*A*a^2*b^3*c^3 + 256*B*a^4*c^4 + 1024*A*a^3*b*c^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","A",0
924,1,422,0,0.243232," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{107520} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, B c x + \frac{15 \, B b c^{6} + 14 \, A c^{7}}{c^{6}}\right)} x + \frac{3 \, B b^{2} c^{5} + 192 \, B a c^{6} + 182 \, A b c^{6}}{c^{6}}\right)} x - \frac{27 \, B b^{3} c^{4} - 132 \, B a b c^{5} - 42 \, A b^{2} c^{5} - 1960 \, A a c^{6}}{c^{6}}\right)} x + \frac{63 \, B b^{4} c^{3} - 372 \, B a b^{2} c^{4} - 98 \, A b^{3} c^{4} + 384 \, B a^{2} c^{5} + 504 \, A a b c^{5}}{c^{6}}\right)} x - \frac{315 \, B b^{5} c^{2} - 2184 \, B a b^{3} c^{3} - 490 \, A b^{4} c^{3} + 3504 \, B a^{2} b c^{4} + 3024 \, A a b^{2} c^{4} - 3360 \, A a^{2} c^{5}}{c^{6}}\right)} x + \frac{945 \, B b^{6} c - 7560 \, B a b^{4} c^{2} - 1470 \, A b^{5} c^{2} + 16464 \, B a^{2} b^{2} c^{3} + 10640 \, A a b^{3} c^{3} - 6144 \, B a^{3} c^{4} - 18144 \, A a^{2} b c^{4}}{c^{6}}\right)} + \frac{{\left(9 \, B b^{7} - 84 \, B a b^{5} c - 14 \, A b^{6} c + 240 \, B a^{2} b^{3} c^{2} + 120 \, A a b^{4} c^{2} - 192 \, B a^{3} b c^{3} - 288 \, A a^{2} b^{2} c^{3} + 128 \, A a^{3} c^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{11}{2}}}"," ",0,"1/107520*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(12*B*c*x + (15*B*b*c^6 + 14*A*c^7)/c^6)*x + (3*B*b^2*c^5 + 192*B*a*c^6 + 182*A*b*c^6)/c^6)*x - (27*B*b^3*c^4 - 132*B*a*b*c^5 - 42*A*b^2*c^5 - 1960*A*a*c^6)/c^6)*x + (63*B*b^4*c^3 - 372*B*a*b^2*c^4 - 98*A*b^3*c^4 + 384*B*a^2*c^5 + 504*A*a*b*c^5)/c^6)*x - (315*B*b^5*c^2 - 2184*B*a*b^3*c^3 - 490*A*b^4*c^3 + 3504*B*a^2*b*c^4 + 3024*A*a*b^2*c^4 - 3360*A*a^2*c^5)/c^6)*x + (945*B*b^6*c - 7560*B*a*b^4*c^2 - 1470*A*b^5*c^2 + 16464*B*a^2*b^2*c^3 + 10640*A*a*b^3*c^3 - 6144*B*a^3*c^4 - 18144*A*a^2*b*c^4)/c^6) + 1/2048*(9*B*b^7 - 84*B*a*b^5*c - 14*A*b^6*c + 240*B*a^2*b^3*c^2 + 120*A*a*b^4*c^2 - 192*B*a^3*b*c^3 - 288*A*a^2*b^2*c^3 + 128*A*a^3*c^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
925,1,332,0,0.272637," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B c x + \frac{13 \, B b c^{5} + 12 \, A c^{6}}{c^{5}}\right)} x + \frac{3 \, B b^{2} c^{4} + 140 \, B a c^{5} + 132 \, A b c^{5}}{c^{5}}\right)} x - \frac{7 \, B b^{3} c^{3} - 36 \, B a b c^{4} - 12 \, A b^{2} c^{4} - 384 \, A a c^{5}}{c^{5}}\right)} x + \frac{35 \, B b^{4} c^{2} - 216 \, B a b^{2} c^{3} - 60 \, A b^{3} c^{3} + 240 \, B a^{2} c^{4} + 336 \, A a b c^{4}}{c^{5}}\right)} x - \frac{105 \, B b^{5} c - 760 \, B a b^{3} c^{2} - 180 \, A b^{4} c^{2} + 1296 \, B a^{2} b c^{3} + 1200 \, A a b^{2} c^{3} - 1536 \, A a^{2} c^{4}}{c^{5}}\right)} - \frac{{\left(7 \, B b^{6} - 60 \, B a b^{4} c - 12 \, A b^{5} c + 144 \, B a^{2} b^{2} c^{2} + 96 \, A a b^{3} c^{2} - 64 \, B a^{3} c^{3} - 192 \, A a^{2} b c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*B*c*x + (13*B*b*c^5 + 12*A*c^6)/c^5)*x + (3*B*b^2*c^4 + 140*B*a*c^5 + 132*A*b*c^5)/c^5)*x - (7*B*b^3*c^3 - 36*B*a*b*c^4 - 12*A*b^2*c^4 - 384*A*a*c^5)/c^5)*x + (35*B*b^4*c^2 - 216*B*a*b^2*c^3 - 60*A*b^3*c^3 + 240*B*a^2*c^4 + 336*A*a*b*c^4)/c^5)*x - (105*B*b^5*c - 760*B*a*b^3*c^2 - 180*A*b^4*c^2 + 1296*B*a^2*b*c^3 + 1200*A*a*b^2*c^3 - 1536*A*a^2*c^4)/c^5) - 1/1024*(7*B*b^6 - 60*B*a*b^4*c - 12*A*b^5*c + 144*B*a^2*b^2*c^2 + 96*A*a*b^3*c^2 - 64*B*a^3*c^3 - 192*A*a^2*b*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
926,1,251,0,0.228531," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{640} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, B c x + \frac{11 \, B b c^{4} + 10 \, A c^{5}}{c^{4}}\right)} x + \frac{B b^{2} c^{3} + 32 \, B a c^{4} + 30 \, A b c^{4}}{c^{4}}\right)} x - \frac{5 \, B b^{3} c^{2} - 28 \, B a b c^{3} - 10 \, A b^{2} c^{3} - 200 \, A a c^{4}}{c^{4}}\right)} x + \frac{15 \, B b^{4} c - 100 \, B a b^{2} c^{2} - 30 \, A b^{3} c^{2} + 128 \, B a^{2} c^{3} + 200 \, A a b c^{3}}{c^{4}}\right)} + \frac{3 \, {\left(B b^{5} - 8 \, B a b^{3} c - 2 \, A b^{4} c + 16 \, B a^{2} b c^{2} + 16 \, A a b^{2} c^{2} - 32 \, A a^{2} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/640*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*B*c*x + (11*B*b*c^4 + 10*A*c^5)/c^4)*x + (B*b^2*c^3 + 32*B*a*c^4 + 30*A*b*c^4)/c^4)*x - (5*B*b^3*c^2 - 28*B*a*b*c^3 - 10*A*b^2*c^3 - 200*A*a*c^4)/c^4)*x + (15*B*b^4*c - 100*B*a*b^2*c^2 - 30*A*b^3*c^2 + 128*B*a^2*c^3 + 200*A*a*b*c^3)/c^4) + 3/256*(B*b^5 - 8*B*a*b^3*c - 2*A*b^4*c + 16*B*a^2*b*c^2 + 16*A*a*b^2*c^2 - 32*A*a^2*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
927,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
928,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,0,0]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,0,0]%%%}+%%%{%%{[1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,0,0]%%%} / %%%{%%%{1,[1]%%%},[4,0,0,0,0]%%%}+%%%{%%%{-2,[1]%%%},[2,0,1,0,0]%%%}+%%%{%%%{1,[1]%%%},[0,0,2,0,0]%%%} Error: Bad Argument Value","F(-2)",0
929,1,412,0,0.376674," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, B c x + \frac{5 \, B b c + 4 \, A c^{2}}{c}\right)} \sqrt{c x^{2} + b x + a} + \frac{3 \, {\left(4 \, B a b + A b^{2} + 4 \, A a c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a}} - \frac{3 \, {\left(B b^{2} + 4 \, B a c + 4 \, A b c\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{8 \, \sqrt{c}} + \frac{4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} \sqrt{c} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b \sqrt{c} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c - 8 \, B a^{3} \sqrt{c} - 8 \, A a^{2} b \sqrt{c}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{2}}"," ",0,"1/4*(2*B*c*x + (5*B*b*c + 4*A*c^2)/c)*sqrt(c*x^2 + b*x + a) + 3/4*(4*B*a*b + A*b^2 + 4*A*a*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/sqrt(-a) - 3/8*(B*b^2 + 4*B*a*c + 4*A*b*c)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/sqrt(c) + 1/4*(4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*sqrt(c) + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b*sqrt(c) - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c - 8*B*a^3*sqrt(c) - 8*A*a^2*b*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^2","B",0
930,1,630,0,0.436232," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^4,x, algorithm=""giac"")","\sqrt{c x^{2} + b x + a} B c - \frac{{\left(3 \, B b c^{\frac{3}{2}} + 2 \, A c^{\frac{5}{2}}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c - b \sqrt{c} \right|}\right)}{2 \, c} + \frac{{\left(6 \, B a b^{2} - A b^{3} + 24 \, B a^{2} c + 12 \, A a b c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a} + \frac{30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a b^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b^{3} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} c + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b c + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{2} b \sqrt{c} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a b^{2} \sqrt{c} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{2} c^{\frac{3}{2}} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} b^{2} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{3} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} b \sqrt{c} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{3} c^{\frac{3}{2}} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} c + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b c + 48 \, B a^{4} b \sqrt{c} + 64 \, A a^{4} c^{\frac{3}{2}}}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{3} a}"," ",0,"sqrt(c*x^2 + b*x + a)*B*c - 1/2*(3*B*b*c^(3/2) + 2*A*c^(5/2))*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c - b*sqrt(c)))/c + 1/8*(6*B*a*b^2 - A*b^3 + 24*B*a^2*c + 12*A*a*b*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a) + 1/24*(30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*b^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b^3 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*c + 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b*c + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^2*b*sqrt(c) + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a*b^2*sqrt(c) + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^2*c^(3/2) - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*b^2 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^3 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*b*sqrt(c) - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^3*c^(3/2) + 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*c + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b*c + 48*B*a^4*b*sqrt(c) + 64*A*a^4*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^3*a)","B",0
931,1,1019,0,0.590666," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^5,x, algorithm=""giac"")","-B c^{\frac{3}{2}} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c - b \sqrt{c} \right|}\right) - \frac{{\left(8 \, B a b^{3} - 3 \, A b^{4} - 96 \, B a^{2} b c + 24 \, A a b^{2} c - 48 \, A a^{2} c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{64 \, \sqrt{-a} a^{2}} + \frac{24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a b^{3} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A b^{4} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b c + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{2} c + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} c^{2} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{2} b^{2} \sqrt{c} + 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{3} c^{\frac{3}{2}} + 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{2} b c^{\frac{3}{2}} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} b^{3} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b^{4} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{3} b c + 504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{2} c + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} c^{2} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{3} b^{2} \sqrt{c} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{2} b^{3} \sqrt{c} - 1536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{4} c^{\frac{3}{2}} - 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{3} b^{3} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b^{4} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b c + 504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{2} c + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} c^{2} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{5} c^{\frac{3}{2}} + 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{4} b c^{\frac{3}{2}} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} b^{3} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b^{4} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b c + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{2} c + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} c^{2} - 512 \, B a^{6} c^{\frac{3}{2}}}{192 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{4} a^{2}}"," ",0,"-B*c^(3/2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c - b*sqrt(c))) - 1/64*(8*B*a*b^3 - 3*A*b^4 - 96*B*a^2*b*c + 24*A*a*b^2*c - 48*A*a^2*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^2) + 1/192*(24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a*b^3 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*b^4 + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b*c + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^2*c + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*c^2 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^2*b^2*sqrt(c) + 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^3*c^(3/2) + 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^2*b*c^(3/2) + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*b^3 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b^4 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^3*b*c + 504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^2*c + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*c^2 - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^3*b^2*sqrt(c) + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^2*b^3*sqrt(c) - 1536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^4*c^(3/2) - 88*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^3*b^3 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b^4 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b*c + 504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^2*c + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*c^2 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^5*c^(3/2) + 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^4*b*c^(3/2) + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*b^3 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b^4 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b*c + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^2*c + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*c^2 - 512*B*a^6*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^4*a^2)","B",0
932,1,1357,0,0.293392," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^6,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B a b^{4} - A b^{5} - 16 \, B a^{2} b^{2} c + 8 \, A a b^{3} c + 32 \, B a^{3} c^{2} - 16 \, A a^{2} b c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{128 \, \sqrt{-a} a^{3}} - \frac{30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a b^{4} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A b^{5} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{2} b^{2} c + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a b^{3} c - 800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} c^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b c^{2} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{3} b c^{\frac{3}{2}} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{3} c^{\frac{5}{2}} - 140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b^{4} + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{5} - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{3} b^{2} c - 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} b^{3} c + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} c^{2} - 2720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b c^{2} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{3} b^{3} \sqrt{c} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{4} b c^{\frac{3}{2}} - 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{3} b^{2} c^{\frac{3}{2}} - 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{5} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} b^{3} c - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b c^{2} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{4} b^{3} \sqrt{c} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{3} b^{4} \sqrt{c} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{5} b c^{\frac{3}{2}} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{4} b^{2} c^{\frac{3}{2}} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} c^{\frac{5}{2}} + 140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b^{4} - 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{5} + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{5} b^{2} c - 2000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} b^{3} c - 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} c^{2} - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b c^{2} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{6} b c^{\frac{3}{2}} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{5} b^{2} c^{\frac{3}{2}} - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b^{4} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{5} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{6} b^{2} c - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} b^{3} c + 800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} c^{2} - 1040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b c^{2} - 256 \, A a^{7} c^{\frac{5}{2}}}{640 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{5} a^{3}}"," ",0,"3/128*(2*B*a*b^4 - A*b^5 - 16*B*a^2*b^2*c + 8*A*a*b^3*c + 32*B*a^3*c^2 - 16*A*a^2*b*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^3) - 1/640*(30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a*b^4 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*b^5 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^2*b^2*c + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a*b^3*c - 800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*c^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b*c^2 - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^3*b*c^(3/2) - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^3*c^(5/2) - 140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b^4 + 70*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^5 - 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^3*b^2*c - 560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*b^3*c + 320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*c^2 - 2720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b*c^2 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^3*b^3*sqrt(c) + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^4*b*c^(3/2) - 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^3*b^2*c^(3/2) - 128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^5 - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*b^3*c - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b*c^2 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^4*b^3*sqrt(c) - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^3*b^4*sqrt(c) - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^5*b*c^(3/2) - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^4*b^2*c^(3/2) - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*c^(5/2) + 140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b^4 - 70*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^5 + 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^5*b^2*c - 2000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*b^3*c - 320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*c^2 - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b*c^2 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^6*b*c^(3/2) - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^5*b^2*c^(3/2) - 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b^4 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^5 + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^6*b^2*c - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*b^3*c + 800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*c^2 - 1040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b*c^2 - 256*A*a^7*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^5*a^3)","B",0
933,1,2059,0,0.358556," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{{\left(12 \, B a b^{5} - 7 \, A b^{6} - 96 \, B a^{2} b^{3} c + 60 \, A a b^{4} c + 192 \, B a^{3} b c^{2} - 144 \, A a^{2} b^{2} c^{2} + 64 \, A a^{3} c^{3}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{512 \, \sqrt{-a} a^{4}} + \frac{180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a b^{5} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A b^{6} - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{2} b^{3} c + 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a b^{4} c + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{3} b c^{2} - 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{2} b^{2} c^{2} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{3} c^{3} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{4} c^{\frac{5}{2}} - 1020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{2} b^{5} + 595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a b^{6} + 8160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} b^{3} c - 5100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b^{4} c + 29760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{4} b c^{2} + 12240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{3} b^{2} c^{2} + 15040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{4} c^{3} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{4} b^{2} c^{\frac{3}{2}} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{5} c^{\frac{5}{2}} + 76800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{4} b c^{\frac{5}{2}} + 2376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{3} b^{5} - 1386 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} b^{6} + 24000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} b^{3} c + 11880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b^{4} c + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{5} b c^{2} + 97440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{4} b^{2} c^{2} + 24960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{5} c^{3} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{4} b^{4} \sqrt{c} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{5} b^{2} c^{\frac{3}{2}} + 112640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{4} b^{3} c^{\frac{3}{2}} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{6} c^{\frac{5}{2}} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{5} b c^{\frac{5}{2}} - 696 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{4} b^{5} + 1686 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} b^{6} - 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{5} b^{3} c + 42600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b^{4} c - 17280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{6} b c^{2} + 128160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{5} b^{2} c^{2} + 24960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{6} c^{3} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{5} b^{4} \sqrt{c} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{4} b^{5} \sqrt{c} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} b^{3} c^{\frac{3}{2}} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{7} c^{\frac{5}{2}} + 92160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{6} b c^{\frac{5}{2}} - 1020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{5} b^{5} + 595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} b^{6} - 22560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} b^{3} c + 25620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b^{4} c - 16320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{7} b c^{2} + 58320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{6} b^{2} c^{2} + 15040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{7} c^{3} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{7} b^{2} c^{\frac{3}{2}} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{6} b^{3} c^{\frac{3}{2}} + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{8} c^{\frac{5}{2}} + 12288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{7} b c^{\frac{5}{2}} + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{6} b^{5} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} b^{6} - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} b^{3} c + 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b^{4} c - 12480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{8} b c^{2} + 13200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{7} b^{2} c^{2} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{8} c^{3} - 3072 \, B a^{9} c^{\frac{5}{2}} + 3072 \, A a^{8} b c^{\frac{5}{2}}}{7680 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{6} a^{4}}"," ",0,"-1/512*(12*B*a*b^5 - 7*A*b^6 - 96*B*a^2*b^3*c + 60*A*a*b^4*c + 192*B*a^3*b*c^2 - 144*A*a^2*b^2*c^2 + 64*A*a^3*c^3)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^4) + 1/7680*(180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a*b^5 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*b^6 - 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^2*b^3*c + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a*b^4*c + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^3*b*c^2 - 2160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^2*b^2*c^2 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^3*c^3 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^4*c^(5/2) - 1020*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^2*b^5 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a*b^6 + 8160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*b^3*c - 5100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b^4*c + 29760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^4*b*c^2 + 12240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^3*b^2*c^2 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^4*c^3 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^4*b^2*c^(3/2) - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^5*c^(5/2) + 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^4*b*c^(5/2) + 2376*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^3*b^5 - 1386*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*b^6 + 24000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*b^3*c + 11880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b^4*c + 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^5*b*c^2 + 97440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^4*b^2*c^2 + 24960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^5*c^3 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^4*b^4*sqrt(c) - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^5*b^2*c^(3/2) + 112640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^4*b^3*c^(3/2) + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^6*c^(5/2) + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^5*b*c^(5/2) - 696*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^4*b^5 + 1686*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*b^6 - 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^5*b^3*c + 42600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b^4*c - 17280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^6*b*c^2 + 128160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^5*b^2*c^2 + 24960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^6*c^3 - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^5*b^4*sqrt(c) + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^4*b^5*sqrt(c) + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*b^3*c^(3/2) - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^7*c^(5/2) + 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^6*b*c^(5/2) - 1020*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^5*b^5 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*b^6 - 22560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*b^3*c + 25620*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b^4*c - 16320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^7*b*c^2 + 58320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^6*b^2*c^2 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^7*c^3 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^7*b^2*c^(3/2) + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^6*b^3*c^(3/2) + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^8*c^(5/2) + 12288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^7*b*c^(5/2) + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^6*b^5 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*b^6 - 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*b^3*c + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b^4*c - 12480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^8*b*c^2 + 13200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^7*b^2*c^2 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^8*c^3 - 3072*B*a^9*c^(5/2) + 3072*A*a^8*b*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^6*a^4)","B",0
934,1,2713,0,0.357459," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^8,x, algorithm=""giac"")","\frac{{\left(14 \, B a b^{6} - 9 \, A b^{7} - 120 \, B a^{2} b^{4} c + 84 \, A a b^{5} c + 288 \, B a^{3} b^{2} c^{2} - 240 \, A a^{2} b^{3} c^{2} - 128 \, B a^{4} c^{3} + 192 \, A a^{3} b c^{3}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{1024 \, \sqrt{-a} a^{5}} - \frac{1470 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a b^{6} - 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A b^{7} - 12600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{2} b^{4} c + 8820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a b^{5} c + 30240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{3} b^{2} c^{2} - 25200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{2} b^{3} c^{2} - 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{4} c^{3} + 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{3} b c^{3} - 9800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{2} b^{6} + 6300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a b^{7} + 84000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{3} b^{4} c - 58800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{2} b^{5} c - 201600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{4} b^{2} c^{2} + 168000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{3} b^{3} c^{2} - 197120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{5} c^{3} - 134400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{4} b c^{3} - 1075200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{5} b c^{\frac{5}{2}} - 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{5} c^{\frac{7}{2}} + 27734 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} b^{6} - 17829 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b^{7} - 237720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{4} b^{4} c + 166404 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{3} b^{5} c - 1192800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{5} b^{2} c^{2} - 475440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{4} b^{3} c^{2} - 138880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{6} c^{3} - 1512000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{5} b c^{3} - 1576960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{5} b^{3} c^{\frac{3}{2}} + 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{6} b c^{\frac{5}{2}} - 3655680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{5} b^{2} c^{\frac{5}{2}} - 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{6} c^{\frac{7}{2}} - 43008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} b^{6} + 27648 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b^{7} - 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{5} b^{4} c - 258048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{4} b^{5} c - 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{6} b^{2} c^{2} - 3225600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{5} b^{3} c^{2} - 2580480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{6} b c^{3} - 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{5} b^{5} \sqrt{c} + 716800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{6} b^{3} c^{\frac{3}{2}} - 2580480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{5} b^{4} c^{\frac{3}{2}} - 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{7} b c^{\frac{5}{2}} - 3440640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{6} b^{2} c^{\frac{5}{2}} - 860160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{7} c^{\frac{7}{2}} + 15274 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{5} b^{6} - 25179 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b^{7} + 237720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{6} b^{4} c - 768516 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{5} b^{5} c + 977760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{7} b^{2} c^{2} - 3610320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{6} b^{3} c^{2} + 138880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{8} c^{3} - 1928640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{7} b c^{3} + 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{6} b^{5} \sqrt{c} - 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} b^{6} \sqrt{c} + 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{7} b^{3} c^{\frac{3}{2}} - 1290240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{6} b^{4} c^{\frac{3}{2}} + 1118208 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{8} b c^{\frac{5}{2}} - 2838528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{7} b^{2} c^{\frac{5}{2}} - 172032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{8} c^{\frac{7}{2}} + 9800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} b^{6} - 6300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b^{7} + 346080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{7} b^{4} c - 371280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{6} b^{5} c + 631680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{8} b^{2} c^{2} - 1243200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{7} b^{3} c^{2} + 197120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{9} c^{3} - 725760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{8} b c^{3} + 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{8} b^{3} c^{\frac{3}{2}} - 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{7} b^{4} c^{\frac{3}{2}} + 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{9} b c^{\frac{5}{2}} - 344064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{8} b^{2} c^{\frac{5}{2}} - 86016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{9} c^{\frac{7}{2}} - 1470 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} b^{6} + 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b^{7} + 12600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{8} b^{4} c - 8820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{7} b^{5} c + 184800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{9} b^{2} c^{2} - 189840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{8} b^{3} c^{2} + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{10} c^{3} - 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{9} b c^{3} + 43008 \, B a^{10} b c^{\frac{5}{2}} - 43008 \, A a^{9} b^{2} c^{\frac{5}{2}} + 12288 \, A a^{10} c^{\frac{7}{2}}}{107520 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{7} a^{5}}"," ",0,"1/1024*(14*B*a*b^6 - 9*A*b^7 - 120*B*a^2*b^4*c + 84*A*a*b^5*c + 288*B*a^3*b^2*c^2 - 240*A*a^2*b^3*c^2 - 128*B*a^4*c^3 + 192*A*a^3*b*c^3)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^5) - 1/107520*(1470*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a*b^6 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*b^7 - 12600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^2*b^4*c + 8820*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a*b^5*c + 30240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^3*b^2*c^2 - 25200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^2*b^3*c^2 - 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^4*c^3 + 20160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^3*b*c^3 - 9800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^2*b^6 + 6300*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a*b^7 + 84000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^3*b^4*c - 58800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^2*b^5*c - 201600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^4*b^2*c^2 + 168000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^3*b^3*c^2 - 197120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^5*c^3 - 134400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^4*b*c^3 - 1075200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^5*b*c^(5/2) - 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^5*c^(7/2) + 27734*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*b^6 - 17829*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b^7 - 237720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^4*b^4*c + 166404*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^3*b^5*c - 1192800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^5*b^2*c^2 - 475440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^4*b^3*c^2 - 138880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^6*c^3 - 1512000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^5*b*c^3 - 1576960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^5*b^3*c^(3/2) + 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^6*b*c^(5/2) - 3655680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^5*b^2*c^(5/2) - 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^6*c^(7/2) - 43008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*b^6 + 27648*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b^7 - 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^5*b^4*c - 258048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^4*b^5*c - 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^6*b^2*c^2 - 3225600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^5*b^3*c^2 - 2580480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^6*b*c^3 - 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^5*b^5*sqrt(c) + 716800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^6*b^3*c^(3/2) - 2580480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^5*b^4*c^(3/2) - 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^7*b*c^(5/2) - 3440640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^6*b^2*c^(5/2) - 860160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^7*c^(7/2) + 15274*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^5*b^6 - 25179*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b^7 + 237720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^6*b^4*c - 768516*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^5*b^5*c + 977760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^7*b^2*c^2 - 3610320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^6*b^3*c^2 + 138880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^8*c^3 - 1928640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^7*b*c^3 + 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^6*b^5*sqrt(c) - 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*b^6*sqrt(c) + 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^7*b^3*c^(3/2) - 1290240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^6*b^4*c^(3/2) + 1118208*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^8*b*c^(5/2) - 2838528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^7*b^2*c^(5/2) - 172032*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^8*c^(7/2) + 9800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*b^6 - 6300*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b^7 + 346080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^7*b^4*c - 371280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^6*b^5*c + 631680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^8*b^2*c^2 - 1243200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^7*b^3*c^2 + 197120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^9*c^3 - 725760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^8*b*c^3 + 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^8*b^3*c^(3/2) - 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^7*b^4*c^(3/2) + 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^9*b*c^(5/2) - 344064*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^8*b^2*c^(5/2) - 86016*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^9*c^(7/2) - 1470*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*b^6 + 945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b^7 + 12600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^8*b^4*c - 8820*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^7*b^5*c + 184800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^9*b^2*c^2 - 189840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^8*b^3*c^2 + 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^10*c^3 - 20160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^9*b*c^3 + 43008*B*a^10*b*c^(5/2) - 43008*A*a^9*b^2*c^(5/2) + 12288*A*a^10*c^(7/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^7*a^5)","B",0
935,1,908,0,0.308622," ","integrate(x^4*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{908328960} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, {\left(18 \, {\left(20 \, B c^{2} x + \frac{45 \, B b c^{11} + 22 \, A c^{12}}{c^{10}}\right)} x + \frac{465 \, B b^{2} c^{10} + 920 \, B a c^{11} + 902 \, A b c^{11}}{c^{10}}\right)} x + \frac{15 \, B b^{3} c^{9} + 17300 \, B a b c^{10} + 8426 \, A b^{2} c^{10} + 16632 \, A a c^{11}}{c^{10}}\right)} x - \frac{225 \, B b^{4} c^{8} - 1620 \, B a b^{2} c^{9} - 330 \, A b^{3} c^{9} - 144640 \, B a^{2} c^{10} - 279928 \, A a b c^{10}}{c^{10}}\right)} x + \frac{975 \, B b^{5} c^{7} - 8000 \, B a b^{3} c^{8} - 1430 \, A b^{4} c^{8} + 17040 \, B a^{2} b c^{9} + 10560 \, A a b^{2} c^{9} + 687456 \, A a^{2} c^{10}}{c^{10}}\right)} x - \frac{2145 \, B b^{6} c^{6} - 19760 \, B a b^{4} c^{7} - 3146 \, A b^{5} c^{7} + 53040 \, B a^{2} b^{2} c^{8} + 26400 \, A a b^{3} c^{8} - 30720 \, B a^{3} c^{9} - 58080 \, A a^{2} b c^{9}}{c^{10}}\right)} x + \frac{19305 \, B b^{7} c^{5} - 197340 \, B a b^{5} c^{6} - 28314 \, A b^{6} c^{6} + 637360 \, B a^{2} b^{3} c^{7} + 266200 \, A a b^{4} c^{7} - 617280 \, B a^{3} b c^{8} - 733920 \, A a^{2} b^{2} c^{8} + 443520 \, A a^{3} c^{9}}{c^{10}}\right)} x - \frac{45045 \, B b^{8} c^{4} - 506220 \, B a b^{6} c^{5} - 66066 \, A b^{7} c^{5} + 1908720 \, B a^{2} b^{4} c^{6} + 688248 \, A a b^{5} c^{6} - 2571840 \, B a^{3} b^{2} c^{7} - 2275680 \, A a^{2} b^{3} c^{7} + 655360 \, B a^{4} c^{8} + 2273920 \, A a^{3} b c^{8}}{c^{10}}\right)} x + \frac{225225 \, B b^{9} c^{3} - 2762760 \, B a b^{7} c^{4} - 330330 \, A b^{8} c^{4} + 11911680 \, B a^{2} b^{5} c^{5} + 3781008 \, A a b^{6} c^{5} - 20507520 \, B a^{3} b^{3} c^{6} - 14572800 \, A a^{2} b^{4} c^{6} + 10684160 \, B a^{4} b c^{7} + 20176640 \, A a^{3} b^{2} c^{7} - 5322240 \, A a^{4} c^{8}}{c^{10}}\right)} x - \frac{675675 \, B b^{10} c^{2} - 9009000 \, B a b^{8} c^{3} - 990990 \, A b^{9} c^{3} + 43834560 \, B a^{2} b^{6} c^{4} + 12400080 \, A a b^{7} c^{4} - 92062080 \, B a^{3} b^{4} c^{5} - 54730368 \, A a^{2} b^{5} c^{5} + 73201920 \, B a^{4} b^{2} c^{6} + 96940800 \, A a^{3} b^{3} c^{6} - 10485760 \, B a^{5} c^{7} - 52349440 \, A a^{4} b c^{7}}{c^{10}}\right)} - \frac{{\left(195 \, B b^{11} - 2860 \, B a b^{9} c - 286 \, A b^{10} c + 15840 \, B a^{2} b^{7} c^{2} + 3960 \, A a b^{8} c^{2} - 40320 \, B a^{3} b^{5} c^{3} - 20160 \, A a^{2} b^{6} c^{3} + 44800 \, B a^{4} b^{3} c^{4} + 44800 \, A a^{3} b^{4} c^{4} - 15360 \, B a^{5} b c^{5} - 38400 \, A a^{4} b^{2} c^{5} + 6144 \, A a^{5} c^{6}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{524288 \, c^{\frac{17}{2}}}"," ",0,"1/908328960*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(14*(16*(18*(20*B*c^2*x + (45*B*b*c^11 + 22*A*c^12)/c^10)*x + (465*B*b^2*c^10 + 920*B*a*c^11 + 902*A*b*c^11)/c^10)*x + (15*B*b^3*c^9 + 17300*B*a*b*c^10 + 8426*A*b^2*c^10 + 16632*A*a*c^11)/c^10)*x - (225*B*b^4*c^8 - 1620*B*a*b^2*c^9 - 330*A*b^3*c^9 - 144640*B*a^2*c^10 - 279928*A*a*b*c^10)/c^10)*x + (975*B*b^5*c^7 - 8000*B*a*b^3*c^8 - 1430*A*b^4*c^8 + 17040*B*a^2*b*c^9 + 10560*A*a*b^2*c^9 + 687456*A*a^2*c^10)/c^10)*x - (2145*B*b^6*c^6 - 19760*B*a*b^4*c^7 - 3146*A*b^5*c^7 + 53040*B*a^2*b^2*c^8 + 26400*A*a*b^3*c^8 - 30720*B*a^3*c^9 - 58080*A*a^2*b*c^9)/c^10)*x + (19305*B*b^7*c^5 - 197340*B*a*b^5*c^6 - 28314*A*b^6*c^6 + 637360*B*a^2*b^3*c^7 + 266200*A*a*b^4*c^7 - 617280*B*a^3*b*c^8 - 733920*A*a^2*b^2*c^8 + 443520*A*a^3*c^9)/c^10)*x - (45045*B*b^8*c^4 - 506220*B*a*b^6*c^5 - 66066*A*b^7*c^5 + 1908720*B*a^2*b^4*c^6 + 688248*A*a*b^5*c^6 - 2571840*B*a^3*b^2*c^7 - 2275680*A*a^2*b^3*c^7 + 655360*B*a^4*c^8 + 2273920*A*a^3*b*c^8)/c^10)*x + (225225*B*b^9*c^3 - 2762760*B*a*b^7*c^4 - 330330*A*b^8*c^4 + 11911680*B*a^2*b^5*c^5 + 3781008*A*a*b^6*c^5 - 20507520*B*a^3*b^3*c^6 - 14572800*A*a^2*b^4*c^6 + 10684160*B*a^4*b*c^7 + 20176640*A*a^3*b^2*c^7 - 5322240*A*a^4*c^8)/c^10)*x - (675675*B*b^10*c^2 - 9009000*B*a*b^8*c^3 - 990990*A*b^9*c^3 + 43834560*B*a^2*b^6*c^4 + 12400080*A*a*b^7*c^4 - 92062080*B*a^3*b^4*c^5 - 54730368*A*a^2*b^5*c^5 + 73201920*B*a^4*b^2*c^6 + 96940800*A*a^3*b^3*c^6 - 10485760*B*a^5*c^7 - 52349440*A*a^4*b*c^7)/c^10) - 1/524288*(195*B*b^11 - 2860*B*a*b^9*c - 286*A*b^10*c + 15840*B*a^2*b^7*c^2 + 3960*A*a*b^8*c^2 - 40320*B*a^3*b^5*c^3 - 20160*A*a^2*b^6*c^3 + 44800*B*a^4*b^3*c^4 + 44800*A*a^3*b^4*c^4 - 15360*B*a^5*b*c^5 - 38400*A*a^4*b^2*c^5 + 6144*A*a^5*c^6)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(17/2)","A",0
936,1,769,0,0.322610," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{41287680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, {\left(18 \, B c^{2} x + \frac{41 \, B b c^{10} + 20 \, A c^{11}}{c^{9}}\right)} x + \frac{383 \, B b^{2} c^{9} + 756 \, B a c^{10} + 740 \, A b c^{10}}{c^{9}}\right)} x + \frac{15 \, B b^{3} c^{8} + 12724 \, B a b c^{9} + 6180 \, A b^{2} c^{9} + 12160 \, A a c^{10}}{c^{9}}\right)} x - \frac{65 \, B b^{4} c^{7} - 480 \, B a b^{2} c^{8} - 100 \, A b^{3} c^{8} - 31248 \, B a^{2} c^{9} - 60240 \, A a b c^{9}}{c^{9}}\right)} x + \frac{143 \, B b^{5} c^{6} - 1200 \, B a b^{3} c^{7} - 220 \, A b^{4} c^{7} + 2640 \, B a^{2} b c^{8} + 1680 \, A a b^{2} c^{8} + 76800 \, A a^{2} c^{9}}{c^{9}}\right)} x - \frac{1287 \, B b^{6} c^{5} - 12100 \, B a b^{4} c^{6} - 1980 \, A b^{5} c^{6} + 33360 \, B a^{2} b^{2} c^{7} + 17120 \, A a b^{3} c^{7} - 20160 \, B a^{3} c^{8} - 39360 \, A a^{2} b c^{8}}{c^{9}}\right)} x + \frac{3003 \, B b^{7} c^{4} - 31284 \, B a b^{5} c^{5} - 4620 \, A b^{6} c^{5} + 103440 \, B a^{2} b^{3} c^{6} + 44640 \, A a b^{4} c^{6} - 103360 \, B a^{3} b c^{7} - 127680 \, A a^{2} b^{2} c^{7} + 81920 \, A a^{3} c^{8}}{c^{9}}\right)} x - \frac{15015 \, B b^{8} c^{3} - 171864 \, B a b^{6} c^{4} - 23100 \, A b^{7} c^{4} + 662400 \, B a^{2} b^{4} c^{5} + 246960 \, A a b^{5} c^{5} - 917120 \, B a^{3} b^{2} c^{6} - 843840 \, A a^{2} b^{3} c^{6} + 241920 \, B a^{4} c^{7} + 881920 \, A a^{3} b c^{7}}{c^{9}}\right)} x + \frac{45045 \, B b^{9} c^{2} - 563640 \, B a b^{7} c^{3} - 69300 \, A b^{8} c^{3} + 2487744 \, B a^{2} b^{5} c^{4} + 814800 \, A a b^{6} c^{4} - 4406400 \, B a^{3} b^{3} c^{5} - 3245760 \, A a^{2} b^{4} c^{5} + 2379520 \, B a^{4} b c^{6} + 4688640 \, A a^{3} b^{2} c^{6} - 1310720 \, A a^{4} c^{7}}{c^{9}}\right)} + \frac{{\left(143 \, B b^{10} - 1980 \, B a b^{8} c - 220 \, A b^{9} c + 10080 \, B a^{2} b^{6} c^{2} + 2880 \, A a b^{7} c^{2} - 22400 \, B a^{3} b^{4} c^{3} - 13440 \, A a^{2} b^{5} c^{3} + 19200 \, B a^{4} b^{2} c^{4} + 25600 \, A a^{3} b^{3} c^{4} - 3072 \, B a^{5} c^{5} - 15360 \, A a^{4} b c^{5}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{262144 \, c^{\frac{15}{2}}}"," ",0,"1/41287680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(14*(16*(18*B*c^2*x + (41*B*b*c^10 + 20*A*c^11)/c^9)*x + (383*B*b^2*c^9 + 756*B*a*c^10 + 740*A*b*c^10)/c^9)*x + (15*B*b^3*c^8 + 12724*B*a*b*c^9 + 6180*A*b^2*c^9 + 12160*A*a*c^10)/c^9)*x - (65*B*b^4*c^7 - 480*B*a*b^2*c^8 - 100*A*b^3*c^8 - 31248*B*a^2*c^9 - 60240*A*a*b*c^9)/c^9)*x + (143*B*b^5*c^6 - 1200*B*a*b^3*c^7 - 220*A*b^4*c^7 + 2640*B*a^2*b*c^8 + 1680*A*a*b^2*c^8 + 76800*A*a^2*c^9)/c^9)*x - (1287*B*b^6*c^5 - 12100*B*a*b^4*c^6 - 1980*A*b^5*c^6 + 33360*B*a^2*b^2*c^7 + 17120*A*a*b^3*c^7 - 20160*B*a^3*c^8 - 39360*A*a^2*b*c^8)/c^9)*x + (3003*B*b^7*c^4 - 31284*B*a*b^5*c^5 - 4620*A*b^6*c^5 + 103440*B*a^2*b^3*c^6 + 44640*A*a*b^4*c^6 - 103360*B*a^3*b*c^7 - 127680*A*a^2*b^2*c^7 + 81920*A*a^3*c^8)/c^9)*x - (15015*B*b^8*c^3 - 171864*B*a*b^6*c^4 - 23100*A*b^7*c^4 + 662400*B*a^2*b^4*c^5 + 246960*A*a*b^5*c^5 - 917120*B*a^3*b^2*c^6 - 843840*A*a^2*b^3*c^6 + 241920*B*a^4*c^7 + 881920*A*a^3*b*c^7)/c^9)*x + (45045*B*b^9*c^2 - 563640*B*a*b^7*c^3 - 69300*A*b^8*c^3 + 2487744*B*a^2*b^5*c^4 + 814800*A*a*b^6*c^4 - 4406400*B*a^3*b^3*c^5 - 3245760*A*a^2*b^4*c^5 + 2379520*B*a^4*b*c^6 + 4688640*A*a^3*b^2*c^6 - 1310720*A*a^4*c^7)/c^9) + 1/262144*(143*B*b^10 - 1980*B*a*b^8*c - 220*A*b^9*c + 10080*B*a^2*b^6*c^2 + 2880*A*a*b^7*c^2 - 22400*B*a^3*b^4*c^3 - 13440*A*a^2*b^5*c^3 + 19200*B*a^4*b^2*c^4 + 25600*A*a^3*b^3*c^4 - 3072*B*a^5*c^5 - 15360*A*a^4*b*c^5)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(15/2)","A",0
937,1,643,0,0.270222," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{2064384} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, B c^{2} x + \frac{37 \, B b c^{9} + 18 \, A c^{10}}{c^{8}}\right)} x + \frac{309 \, B b^{2} c^{8} + 608 \, B a c^{9} + 594 \, A b c^{9}}{c^{8}}\right)} x + \frac{5 \, B b^{3} c^{7} + 3012 \, B a b c^{8} + 1458 \, A b^{2} c^{8} + 2856 \, A a c^{9}}{c^{8}}\right)} x - \frac{11 \, B b^{4} c^{6} - 84 \, B a b^{2} c^{7} - 18 \, A b^{3} c^{7} - 3840 \, B a^{2} c^{8} - 7368 \, A a b c^{8}}{c^{8}}\right)} x + \frac{99 \, B b^{5} c^{5} - 856 \, B a b^{3} c^{6} - 162 \, A b^{4} c^{6} + 1968 \, B a^{2} b c^{7} + 1296 \, A a b^{2} c^{7} + 39648 \, A a^{2} c^{8}}{c^{8}}\right)} x - \frac{231 \, B b^{6} c^{4} - 2232 \, B a b^{4} c^{5} - 378 \, A b^{5} c^{5} + 6384 \, B a^{2} b^{2} c^{6} + 3408 \, A a b^{3} c^{6} - 4096 \, B a^{3} c^{7} - 8352 \, A a^{2} b c^{7}}{c^{8}}\right)} x + \frac{1155 \, B b^{7} c^{3} - 12348 \, B a b^{5} c^{4} - 1890 \, A b^{6} c^{4} + 42192 \, B a^{2} b^{3} c^{5} + 18984 \, A a b^{4} c^{5} - 44096 \, B a^{3} b c^{6} - 57312 \, A a^{2} b^{2} c^{6} + 40320 \, A a^{3} c^{7}}{c^{8}}\right)} x - \frac{3465 \, B b^{8} c^{2} - 40740 \, B a b^{6} c^{3} - 5670 \, A b^{7} c^{3} + 162288 \, B a^{2} b^{4} c^{4} + 63000 \, A a b^{5} c^{4} - 234432 \, B a^{3} b^{2} c^{5} - 226464 \, A a^{2} b^{3} c^{5} + 65536 \, B a^{4} c^{6} + 254592 \, A a^{3} b c^{6}}{c^{8}}\right)} - \frac{5 \, {\left(11 \, B b^{9} - 144 \, B a b^{7} c - 18 \, A b^{8} c + 672 \, B a^{2} b^{5} c^{2} + 224 \, A a b^{6} c^{2} - 1280 \, B a^{3} b^{3} c^{3} - 960 \, A a^{2} b^{4} c^{3} + 768 \, B a^{4} b c^{4} + 1536 \, A a^{3} b^{2} c^{4} - 512 \, A a^{4} c^{5}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{65536 \, c^{\frac{13}{2}}}"," ",0,"1/2064384*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(14*(16*B*c^2*x + (37*B*b*c^9 + 18*A*c^10)/c^8)*x + (309*B*b^2*c^8 + 608*B*a*c^9 + 594*A*b*c^9)/c^8)*x + (5*B*b^3*c^7 + 3012*B*a*b*c^8 + 1458*A*b^2*c^8 + 2856*A*a*c^9)/c^8)*x - (11*B*b^4*c^6 - 84*B*a*b^2*c^7 - 18*A*b^3*c^7 - 3840*B*a^2*c^8 - 7368*A*a*b*c^8)/c^8)*x + (99*B*b^5*c^5 - 856*B*a*b^3*c^6 - 162*A*b^4*c^6 + 1968*B*a^2*b*c^7 + 1296*A*a*b^2*c^7 + 39648*A*a^2*c^8)/c^8)*x - (231*B*b^6*c^4 - 2232*B*a*b^4*c^5 - 378*A*b^5*c^5 + 6384*B*a^2*b^2*c^6 + 3408*A*a*b^3*c^6 - 4096*B*a^3*c^7 - 8352*A*a^2*b*c^7)/c^8)*x + (1155*B*b^7*c^3 - 12348*B*a*b^5*c^4 - 1890*A*b^6*c^4 + 42192*B*a^2*b^3*c^5 + 18984*A*a*b^4*c^5 - 44096*B*a^3*b*c^6 - 57312*A*a^2*b^2*c^6 + 40320*A*a^3*c^7)/c^8)*x - (3465*B*b^8*c^2 - 40740*B*a*b^6*c^3 - 5670*A*b^7*c^3 + 162288*B*a^2*b^4*c^4 + 63000*A*a*b^5*c^4 - 234432*B*a^3*b^2*c^5 - 226464*A*a^2*b^3*c^5 + 65536*B*a^4*c^6 + 254592*A*a^3*b*c^6)/c^8) - 5/65536*(11*B*b^9 - 144*B*a*b^7*c - 18*A*b^8*c + 672*B*a^2*b^5*c^2 + 224*A*a*b^6*c^2 - 1280*B*a^3*b^3*c^3 - 960*A*a^2*b^4*c^3 + 768*B*a^4*b*c^4 + 1536*A*a^3*b^2*c^4 - 512*A*a^4*c^5)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","B",0
938,1,528,0,0.308983," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{344064} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, B c^{2} x + \frac{33 \, B b c^{8} + 16 \, A c^{9}}{c^{7}}\right)} x + \frac{243 \, B b^{2} c^{7} + 476 \, B a c^{8} + 464 \, A b c^{8}}{c^{7}}\right)} x + \frac{3 \, B b^{3} c^{6} + 1228 \, B a b c^{7} + 592 \, A b^{2} c^{7} + 1152 \, A a c^{8}}{c^{7}}\right)} x - \frac{27 \, B b^{4} c^{5} - 216 \, B a b^{2} c^{6} - 48 \, A b^{3} c^{6} - 6608 \, B a^{2} c^{7} - 12608 \, A a b c^{7}}{c^{7}}\right)} x + \frac{63 \, B b^{5} c^{4} - 568 \, B a b^{3} c^{5} - 112 \, A b^{4} c^{5} + 1392 \, B a^{2} b c^{6} + 960 \, A a b^{2} c^{6} + 18432 \, A a^{2} c^{7}}{c^{7}}\right)} x - \frac{315 \, B b^{6} c^{3} - 3164 \, B a b^{4} c^{4} - 560 \, A b^{5} c^{4} + 9552 \, B a^{2} b^{2} c^{5} + 5376 \, A a b^{3} c^{5} - 6720 \, B a^{3} c^{6} - 14592 \, A a^{2} b c^{6}}{c^{7}}\right)} x + \frac{945 \, B b^{7} c^{2} - 10500 \, B a b^{5} c^{3} - 1680 \, A b^{6} c^{3} + 37744 \, B a^{2} b^{3} c^{4} + 17920 \, A a b^{4} c^{4} - 42432 \, B a^{3} b c^{5} - 59136 \, A a^{2} b^{2} c^{5} + 49152 \, A a^{3} c^{6}}{c^{7}}\right)} + \frac{5 \, {\left(9 \, B b^{8} - 112 \, B a b^{6} c - 16 \, A b^{7} c + 480 \, B a^{2} b^{4} c^{2} + 192 \, A a b^{5} c^{2} - 768 \, B a^{3} b^{2} c^{3} - 768 \, A a^{2} b^{3} c^{3} + 256 \, B a^{4} c^{4} + 1024 \, A a^{3} b c^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{11}{2}}}"," ",0,"1/344064*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(12*(14*B*c^2*x + (33*B*b*c^8 + 16*A*c^9)/c^7)*x + (243*B*b^2*c^7 + 476*B*a*c^8 + 464*A*b*c^8)/c^7)*x + (3*B*b^3*c^6 + 1228*B*a*b*c^7 + 592*A*b^2*c^7 + 1152*A*a*c^8)/c^7)*x - (27*B*b^4*c^5 - 216*B*a*b^2*c^6 - 48*A*b^3*c^6 - 6608*B*a^2*c^7 - 12608*A*a*b*c^7)/c^7)*x + (63*B*b^5*c^4 - 568*B*a*b^3*c^5 - 112*A*b^4*c^5 + 1392*B*a^2*b*c^6 + 960*A*a*b^2*c^6 + 18432*A*a^2*c^7)/c^7)*x - (315*B*b^6*c^3 - 3164*B*a*b^4*c^4 - 560*A*b^5*c^4 + 9552*B*a^2*b^2*c^5 + 5376*A*a*b^3*c^5 - 6720*B*a^3*c^6 - 14592*A*a^2*b*c^6)/c^7)*x + (945*B*b^7*c^2 - 10500*B*a*b^5*c^3 - 1680*A*b^6*c^3 + 37744*B*a^2*b^3*c^4 + 17920*A*a*b^4*c^4 - 42432*B*a^3*b*c^5 - 59136*A*a^2*b^2*c^5 + 49152*A*a^3*c^6)/c^7) + 5/32768*(9*B*b^8 - 112*B*a*b^6*c - 16*A*b^7*c + 480*B*a^2*b^4*c^2 + 192*A*a*b^5*c^2 - 768*B*a^3*b^2*c^3 - 768*A*a^2*b^3*c^3 + 256*B*a^4*c^4 + 1024*A*a^3*b*c^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","B",0
939,1,425,0,0.306588," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{21504} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, B c^{2} x + \frac{29 \, B b c^{7} + 14 \, A c^{8}}{c^{6}}\right)} x + \frac{37 \, B b^{2} c^{6} + 72 \, B a c^{7} + 70 \, A b c^{7}}{c^{6}}\right)} x + \frac{3 \, B b^{3} c^{5} + 788 \, B a b c^{6} + 378 \, A b^{2} c^{6} + 728 \, A a c^{7}}{c^{6}}\right)} x - \frac{7 \, B b^{4} c^{4} - 60 \, B a b^{2} c^{5} - 14 \, A b^{3} c^{5} - 1152 \, B a^{2} c^{6} - 2184 \, A a b c^{6}}{c^{6}}\right)} x + \frac{35 \, B b^{5} c^{3} - 336 \, B a b^{3} c^{4} - 70 \, A b^{4} c^{4} + 912 \, B a^{2} b c^{5} + 672 \, A a b^{2} c^{5} + 7392 \, A a^{2} c^{6}}{c^{6}}\right)} x - \frac{105 \, B b^{6} c^{2} - 1120 \, B a b^{4} c^{3} - 210 \, A b^{5} c^{3} + 3696 \, B a^{2} b^{2} c^{4} + 2240 \, A a b^{3} c^{4} - 3072 \, B a^{3} c^{5} - 7392 \, A a^{2} b c^{5}}{c^{6}}\right)} - \frac{5 \, {\left(B b^{7} - 12 \, B a b^{5} c - 2 \, A b^{6} c + 48 \, B a^{2} b^{3} c^{2} + 24 \, A a b^{4} c^{2} - 64 \, B a^{3} b c^{3} - 96 \, A a^{2} b^{2} c^{3} + 128 \, A a^{3} c^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{9}{2}}}"," ",0,"1/21504*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(12*B*c^2*x + (29*B*b*c^7 + 14*A*c^8)/c^6)*x + (37*B*b^2*c^6 + 72*B*a*c^7 + 70*A*b*c^7)/c^6)*x + (3*B*b^3*c^5 + 788*B*a*b*c^6 + 378*A*b^2*c^6 + 728*A*a*c^7)/c^6)*x - (7*B*b^4*c^4 - 60*B*a*b^2*c^5 - 14*A*b^3*c^5 - 1152*B*a^2*c^6 - 2184*A*a*b*c^6)/c^6)*x + (35*B*b^5*c^3 - 336*B*a*b^3*c^4 - 70*A*b^4*c^4 + 912*B*a^2*b*c^5 + 672*A*a*b^2*c^5 + 7392*A*a^2*c^6)/c^6)*x - (105*B*b^6*c^2 - 1120*B*a*b^4*c^3 - 210*A*b^5*c^3 + 3696*B*a^2*b^2*c^4 + 2240*A*a*b^3*c^4 - 3072*B*a^3*c^5 - 7392*A*a^2*b*c^5)/c^6) - 5/2048*(B*b^7 - 12*B*a*b^5*c - 2*A*b^6*c + 48*B*a^2*b^3*c^2 + 24*A*a*b^4*c^2 - 64*B*a^3*b*c^3 - 96*A*a^2*b^2*c^3 + 128*A*a^3*c^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","B",0
940,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
941,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,0,0]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,0,0]%%%}+%%%{%%{[1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,0,0]%%%} / %%%{%%%{1,[1]%%%},[4,0,0,0,0]%%%}+%%%{%%%{-2,[1]%%%},[2,0,1,0,0]%%%}+%%%{%%%{1,[1]%%%},[0,0,2,0,0]%%%} Error: Bad Argument Value","F(-2)",0
942,1,527,0,0.415414," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^3,x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, B c^{2} x + \frac{17 \, B b c^{4} + 8 \, A c^{5}}{c^{3}}\right)} x + \frac{59 \, B b^{2} c^{3} + 108 \, B a c^{4} + 104 \, A b c^{4}}{c^{3}}\right)} x + \frac{15 \, B b^{3} c^{2} + 556 \, B a b c^{3} + 264 \, A b^{2} c^{3} + 448 \, A a c^{4}}{c^{3}}\right)} + \frac{5 \, {\left(4 \, B a^{2} b + 3 \, A a b^{2} + 4 \, A a^{2} c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a}} + \frac{5 \, {\left(B b^{4} - 24 \, B a b^{2} c - 8 \, A b^{3} c - 48 \, B a^{2} c^{2} - 96 \, A a b c^{2}\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{128 \, c^{\frac{3}{2}}} + \frac{4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} b + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} c + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} \sqrt{c} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{2} b \sqrt{c} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} c - 8 \, B a^{4} \sqrt{c} - 16 \, A a^{3} b \sqrt{c}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{2}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*B*c^2*x + (17*B*b*c^4 + 8*A*c^5)/c^3)*x + (59*B*b^2*c^3 + 108*B*a*c^4 + 104*A*b*c^4)/c^3)*x + (15*B*b^3*c^2 + 556*B*a*b*c^3 + 264*A*b^2*c^3 + 448*A*a*c^4)/c^3) + 5/4*(4*B*a^2*b + 3*A*a*b^2 + 4*A*a^2*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/sqrt(-a) + 5/128*(B*b^4 - 24*B*a*b^2*c - 8*A*b^3*c - 48*B*a^2*c^2 - 96*A*a*b*c^2)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/c^(3/2) + 1/4*(4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*b + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*c + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*sqrt(c) + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^2*b*sqrt(c) - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*c - 8*B*a^4*sqrt(c) - 16*A*a^3*b*sqrt(c))/((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^2","B",0
943,1,784,0,0.621903," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^4,x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, B c^{2} x + \frac{13 \, B b c^{3} + 6 \, A c^{4}}{c^{2}}\right)} x + \frac{33 \, B b^{2} c^{2} + 56 \, B a c^{3} + 54 \, A b c^{3}}{c^{2}}\right)} + \frac{5 \, {\left(6 \, B a b^{2} + A b^{3} + 8 \, B a^{2} c + 12 \, A a b c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a}} - \frac{5 \, {\left(B b^{3} + 12 \, B a b c + 6 \, A b^{2} c + 8 \, A a c^{2}\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{16 \, \sqrt{c}} + \frac{54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a b^{2} \sqrt{c} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b^{3} \sqrt{c} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} c^{\frac{3}{2}} + 108 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b c^{\frac{3}{2}} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{2} b c + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a b^{2} c + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{2} c^{2} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} b^{2} \sqrt{c} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{3} \sqrt{c} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b c^{\frac{3}{2}} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} b c - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{2} b^{2} c - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{3} c^{2} + 42 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b^{2} \sqrt{c} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{3} \sqrt{c} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} c^{\frac{3}{2}} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b c^{\frac{3}{2}} + 96 \, B a^{4} b c + 48 \, A a^{3} b^{2} c + 112 \, A a^{4} c^{2}}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{3} \sqrt{c}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*(4*B*c^2*x + (13*B*b*c^3 + 6*A*c^4)/c^2)*x + (33*B*b^2*c^2 + 56*B*a*c^3 + 54*A*b*c^3)/c^2) + 5/8*(6*B*a*b^2 + A*b^3 + 8*B*a^2*c + 12*A*a*b*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/sqrt(-a) - 5/16*(B*b^3 + 12*B*a*b*c + 6*A*b^2*c + 8*A*a*c^2)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/sqrt(c) + 1/24*(54*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*b^2*sqrt(c) + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b^3*sqrt(c) + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*c^(3/2) + 108*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b*c^(3/2) + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^2*b*c + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a*b^2*c + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^2*c^2 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*b^2*sqrt(c) - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^3*sqrt(c) - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b*c^(3/2) - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*b*c - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^2*b^2*c - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^3*c^2 + 42*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b^2*sqrt(c) + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^3*sqrt(c) - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*c^(3/2) + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b*c^(3/2) + 96*B*a^4*b*c + 48*A*a^3*b^2*c + 112*A*a^4*c^2)/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^3*sqrt(c))","B",0
944,1,1163,0,0.668693," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^5,x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, B c^{2} x + \frac{9 \, B b c^{2} + 4 \, A c^{3}}{c}\right)} \sqrt{c x^{2} + b x + a} - \frac{5 \, {\left(3 \, B b^{2} c + 4 \, B a c^{2} + 4 \, A b c^{2}\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{8 \, \sqrt{c}} + \frac{5 \, {\left(8 \, B a b^{3} - A b^{4} + 96 \, B a^{2} b c + 24 \, A a b^{2} c + 48 \, A a^{2} c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{64 \, \sqrt{-a} a} + \frac{264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a b^{3} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A b^{4} + 864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b c + 792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{2} c + 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} c^{2} + 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{2} b^{2} \sqrt{c} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a b^{3} \sqrt{c} + 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{3} c^{\frac{3}{2}} + 2304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{2} b c^{\frac{3}{2}} - 584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} b^{3} + 73 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b^{4} - 1248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{3} b c - 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{2} c - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} c^{2} - 2304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{3} b^{2} \sqrt{c} - 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{4} c^{\frac{3}{2}} - 3456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{3} b c^{\frac{3}{2}} + 440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{3} b^{3} - 55 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b^{4} + 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b c + 1320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{2} c - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} c^{2} + 1536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{4} b^{2} \sqrt{c} + 2432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{5} c^{\frac{3}{2}} + 3584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{4} b c^{\frac{3}{2}} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} b^{3} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b^{4} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b c - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{2} c + 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} c^{2} - 384 \, B a^{5} b^{2} \sqrt{c} - 896 \, B a^{6} c^{\frac{3}{2}} - 896 \, A a^{5} b c^{\frac{3}{2}}}{192 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{4} a}"," ",0,"1/4*(2*B*c^2*x + (9*B*b*c^2 + 4*A*c^3)/c)*sqrt(c*x^2 + b*x + a) - 5/8*(3*B*b^2*c + 4*B*a*c^2 + 4*A*b*c^2)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/sqrt(c) + 5/64*(8*B*a*b^3 - A*b^4 + 96*B*a^2*b*c + 24*A*a*b^2*c + 48*A*a^2*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a) + 1/192*(264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a*b^3 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*b^4 + 864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b*c + 792*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^2*c + 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*c^2 + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^2*b^2*sqrt(c) + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a*b^3*sqrt(c) + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^3*c^(3/2) + 2304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^2*b*c^(3/2) - 584*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*b^3 + 73*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b^4 - 1248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^3*b*c - 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^2*c - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*c^2 - 2304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^3*b^2*sqrt(c) - 2688*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^4*c^(3/2) - 3456*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^3*b*c^(3/2) + 440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^3*b^3 - 55*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b^4 + 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b*c + 1320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^2*c - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*c^2 + 1536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^4*b^2*sqrt(c) + 2432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^5*c^(3/2) + 3584*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^4*b*c^(3/2) - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*b^3 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b^4 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b*c - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^2*c + 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*c^2 - 384*B*a^5*b^2*sqrt(c) - 896*B*a^6*c^(3/2) - 896*A*a^5*b*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^4*a)","B",0
945,1,1526,0,0.989575," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^6,x, algorithm=""giac"")","\sqrt{c x^{2} + b x + a} B c^{2} - \frac{{\left(5 \, B b c^{\frac{5}{2}} + 2 \, A c^{\frac{7}{2}}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c - b \sqrt{c} \right|}\right)}{2 \, c} - \frac{{\left(10 \, B a b^{4} - 3 \, A b^{5} - 240 \, B a^{2} b^{2} c + 40 \, A a b^{3} c - 480 \, B a^{3} c^{2} - 240 \, A a^{2} b c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{128 \, \sqrt{-a} a^{2}} + \frac{150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a b^{4} - 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A b^{5} + 7920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{2} b^{2} c + 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a b^{3} c + 4320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} c^{2} + 7920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b c^{2} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{2} b^{3} \sqrt{c} + 23040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{3} b c^{\frac{3}{2}} + 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{2} b^{2} c^{\frac{3}{2}} + 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{3} c^{\frac{5}{2}} + 580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b^{4} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{5} - 13920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{3} b^{2} c + 6160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} b^{3} c - 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} c^{2} - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b c^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{3} b^{3} \sqrt{c} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{2} b^{4} \sqrt{c} - 57600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{4} b c^{\frac{3}{2}} - 23040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{4} c^{\frac{5}{2}} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{3} b^{4} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{5} + 19200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{4} b^{2} c + 6400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} b^{3} c + 19200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b c^{2} + 70400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{5} b c^{\frac{3}{2}} + 19200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{4} b^{2} c^{\frac{3}{2}} + 35840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} c^{\frac{5}{2}} + 700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b^{4} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{5} - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{5} b^{2} c + 2800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} b^{3} c + 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} c^{2} + 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b c^{2} - 44800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{6} b c^{\frac{3}{2}} - 17920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{6} c^{\frac{5}{2}} - 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b^{4} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{5} + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{6} b^{2} c - 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} b^{3} c - 4320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} c^{2} + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b c^{2} + 8960 \, B a^{7} b c^{\frac{3}{2}} + 5888 \, A a^{7} c^{\frac{5}{2}}}{1920 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{5} a^{2}}"," ",0,"sqrt(c*x^2 + b*x + a)*B*c^2 - 1/2*(5*B*b*c^(5/2) + 2*A*c^(7/2))*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c - b*sqrt(c)))/c - 1/128*(10*B*a*b^4 - 3*A*b^5 - 240*B*a^2*b^2*c + 40*A*a*b^3*c - 480*B*a^3*c^2 - 240*A*a^2*b*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^2) + 1/1920*(150*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a*b^4 - 45*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*b^5 + 7920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^2*b^2*c + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a*b^3*c + 4320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*c^2 + 7920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b*c^2 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^2*b^3*sqrt(c) + 23040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^3*b*c^(3/2) + 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^2*b^2*c^(3/2) + 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^3*c^(5/2) + 580*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b^4 + 210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^5 - 13920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^3*b^2*c + 6160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*b^3*c - 4800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*c^2 - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b*c^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^3*b^3*sqrt(c) + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^2*b^4*sqrt(c) - 57600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^4*b*c^(3/2) - 23040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^4*c^(5/2) - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^3*b^4 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^5 + 19200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^4*b^2*c + 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*b^3*c + 19200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b*c^2 + 70400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^5*b*c^(3/2) + 19200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^4*b^2*c^(3/2) + 35840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*c^(5/2) + 700*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b^4 - 210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^5 - 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^5*b^2*c + 2800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*b^3*c + 4800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*c^2 + 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b*c^2 - 44800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^6*b*c^(3/2) - 17920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^6*c^(5/2) - 150*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b^4 + 45*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^5 + 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^6*b^2*c - 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*b^3*c - 4320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*c^2 + 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b*c^2 + 8960*B*a^7*b*c^(3/2) + 5888*A*a^7*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^5*a^2)","B",0
946,1,2089,0,1.450381," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^7,x, algorithm=""giac"")","-B c^{\frac{5}{2}} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c - b \sqrt{c} \right|}\right) + \frac{{\left(12 \, B a b^{5} - 5 \, A b^{6} - 160 \, B a^{2} b^{3} c + 60 \, A a b^{4} c + 960 \, B a^{3} b c^{2} - 240 \, A a^{2} b^{2} c^{2} + 320 \, A a^{3} c^{3}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{512 \, \sqrt{-a} a^{3}} - \frac{180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a b^{5} - 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A b^{6} - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{2} b^{3} c + 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a b^{4} c - 31680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{3} b c^{2} - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{2} b^{2} c^{2} - 10560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{3} c^{3} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{3} b^{2} c^{\frac{3}{2}} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{4} c^{\frac{5}{2}} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{3} b c^{\frac{5}{2}} - 1020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{2} b^{5} + 425 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a b^{6} - 22240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} b^{3} c - 5100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b^{4} c + 41280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{4} b c^{2} - 56400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{3} b^{2} c^{2} - 1600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{4} c^{3} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{3} b^{4} \sqrt{c} + 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{4} b^{2} c^{\frac{3}{2}} - 76800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{3} b^{3} c^{\frac{3}{2}} + 138240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{5} c^{\frac{5}{2}} - 696 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{3} b^{5} - 990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} b^{6} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} b^{3} c - 34200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b^{4} c - 86400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{5} b c^{2} - 93600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{4} b^{2} c^{2} - 28800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{5} c^{3} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{4} b^{4} \sqrt{c} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{3} b^{5} \sqrt{c} - 76800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{5} b^{2} c^{\frac{3}{2}} - 51200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{4} b^{3} c^{\frac{3}{2}} - 235520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{6} c^{\frac{5}{2}} - 153600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{5} b c^{\frac{5}{2}} + 2376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{4} b^{5} - 990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} b^{6} + 14400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{5} b^{3} c - 34200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b^{4} c + 67200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{6} b c^{2} - 93600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{5} b^{2} c^{2} - 28800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{6} c^{3} + 76800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{6} b^{2} c^{\frac{3}{2}} - 76800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} b^{3} c^{\frac{3}{2}} + 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{7} c^{\frac{5}{2}} - 1020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{5} b^{5} + 425 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} b^{6} + 13600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} b^{3} c - 5100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b^{4} c - 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{7} b c^{2} - 56400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{6} b^{2} c^{2} - 1600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{7} c^{3} - 95232 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{8} c^{\frac{5}{2}} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{7} b c^{\frac{5}{2}} + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{6} b^{5} - 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} b^{6} - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} b^{3} c + 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b^{4} c + 14400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{8} b c^{2} - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{7} b^{2} c^{2} - 10560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{8} c^{3} + 23552 \, B a^{9} c^{\frac{5}{2}}}{7680 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{6} a^{3}}"," ",0,"-B*c^(5/2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c - b*sqrt(c))) + 1/512*(12*B*a*b^5 - 5*A*b^6 - 160*B*a^2*b^3*c + 60*A*a*b^4*c + 960*B*a^3*b*c^2 - 240*A*a^2*b^2*c^2 + 320*A*a^3*c^3)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^3) - 1/7680*(180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a*b^5 - 75*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*b^6 - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^2*b^3*c + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a*b^4*c - 31680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^3*b*c^2 - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^2*b^2*c^2 - 10560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^3*c^3 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^3*b^2*c^(3/2) - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^4*c^(5/2) - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^3*b*c^(5/2) - 1020*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^2*b^5 + 425*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a*b^6 - 22240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*b^3*c - 5100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b^4*c + 41280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^4*b*c^2 - 56400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^3*b^2*c^2 - 1600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^4*c^3 - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^3*b^4*sqrt(c) + 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^4*b^2*c^(3/2) - 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^3*b^3*c^(3/2) + 138240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^5*c^(5/2) - 696*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^3*b^5 - 990*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*b^6 - 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*b^3*c - 34200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b^4*c - 86400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^5*b*c^2 - 93600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^4*b^2*c^2 - 28800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^5*c^3 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^4*b^4*sqrt(c) - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^3*b^5*sqrt(c) - 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^5*b^2*c^(3/2) - 51200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^4*b^3*c^(3/2) - 235520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^6*c^(5/2) - 153600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^5*b*c^(5/2) + 2376*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^4*b^5 - 990*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*b^6 + 14400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^5*b^3*c - 34200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b^4*c + 67200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^6*b*c^2 - 93600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^5*b^2*c^2 - 28800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^6*c^3 + 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^6*b^2*c^(3/2) - 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*b^3*c^(3/2) + 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^7*c^(5/2) - 1020*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^5*b^5 + 425*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*b^6 + 13600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*b^3*c - 5100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b^4*c - 4800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^7*b*c^2 - 56400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^6*b^2*c^2 - 1600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^7*c^3 - 95232*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^8*c^(5/2) - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^7*b*c^(5/2) + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^6*b^5 - 75*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*b^6 - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*b^3*c + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b^4*c + 14400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^8*b*c^2 - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^7*b^2*c^2 - 10560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^8*c^3 + 23552*B*a^9*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^6*a^3)","B",0
947,1,2598,0,0.427486," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^8,x, algorithm=""giac"")","-\frac{5 \, {\left(2 \, B a b^{6} - A b^{7} - 24 \, B a^{2} b^{4} c + 12 \, A a b^{5} c + 96 \, B a^{3} b^{2} c^{2} - 48 \, A a^{2} b^{3} c^{2} - 128 \, B a^{4} c^{3} + 64 \, A a^{3} b c^{3}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{1024 \, \sqrt{-a} a^{4}} + \frac{210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a b^{6} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A b^{7} - 2520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{2} b^{4} c + 1260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a b^{5} c + 10080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{3} b^{2} c^{2} - 5040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{2} b^{3} c^{2} + 29568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{4} c^{3} + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{3} b c^{3} + 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} B a^{4} b c^{\frac{5}{2}} + 43008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} A a^{4} c^{\frac{7}{2}} - 1400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{2} b^{6} + 700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a b^{7} + 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{3} b^{4} c - 8400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{2} b^{5} c + 147840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{4} b^{2} c^{2} + 33600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{3} b^{3} c^{2} - 25088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{5} c^{3} + 141568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{4} b c^{3} + 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{4} b^{3} c^{\frac{3}{2}} - 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{5} b c^{\frac{5}{2}} + 387072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{4} b^{2} c^{\frac{5}{2}} + 3962 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} b^{6} - 1981 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b^{7} + 81480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{4} b^{4} c + 23772 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{3} b^{5} c + 104160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{5} b^{2} c^{2} + 378000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{4} b^{3} c^{2} + 76160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{6} c^{3} + 284480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{5} b c^{3} + 43008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{4} b^{5} \sqrt{c} - 71680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{5} b^{3} c^{\frac{3}{2}} + 358400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{4} b^{4} c^{\frac{3}{2}} + 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{6} b c^{\frac{5}{2}} + 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{5} b^{2} c^{\frac{5}{2}} + 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{6} c^{\frac{7}{2}} + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b^{7} + 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{4} b^{5} c + 645120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{5} b^{3} c^{2} + 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{6} b c^{3} - 43008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{5} b^{5} \sqrt{c} + 43008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{4} b^{6} \sqrt{c} + 71680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{6} b^{3} c^{\frac{3}{2}} + 286720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{5} b^{4} c^{\frac{3}{2}} - 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{7} b c^{\frac{5}{2}} + 860160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{6} b^{2} c^{\frac{5}{2}} - 3962 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{5} b^{6} + 1981 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b^{7} - 81480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{6} b^{4} c + 105252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{5} b^{5} c - 104160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{7} b^{2} c^{2} + 482160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{6} b^{3} c^{2} - 76160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{8} c^{3} + 360640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{7} b c^{3} - 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{7} b^{3} c^{\frac{3}{2}} + 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{6} b^{4} c^{\frac{3}{2}} + 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{8} b c^{\frac{5}{2}} + 258048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{7} b^{2} c^{\frac{5}{2}} + 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{8} c^{\frac{7}{2}} + 1400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} b^{6} - 700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b^{7} - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{7} b^{4} c + 8400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{6} b^{5} c - 147840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{8} b^{2} c^{2} + 181440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{7} b^{3} c^{2} + 25088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{9} c^{3} + 116480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{8} b c^{3} - 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{9} b c^{\frac{5}{2}} + 129024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{8} b^{2} c^{\frac{5}{2}} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} b^{6} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b^{7} + 2520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{8} b^{4} c - 1260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{7} b^{5} c - 10080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{9} b^{2} c^{2} + 5040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{8} b^{3} c^{2} - 29568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{10} c^{3} + 36288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{9} b c^{3} + 6144 \, A a^{10} c^{\frac{7}{2}}}{21504 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{7} a^{4}}"," ",0,"-5/1024*(2*B*a*b^6 - A*b^7 - 24*B*a^2*b^4*c + 12*A*a*b^5*c + 96*B*a^3*b^2*c^2 - 48*A*a^2*b^3*c^2 - 128*B*a^4*c^3 + 64*A*a^3*b*c^3)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^4) + 1/21504*(210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a*b^6 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*b^7 - 2520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^2*b^4*c + 1260*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a*b^5*c + 10080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^3*b^2*c^2 - 5040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^2*b^3*c^2 + 29568*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^4*c^3 + 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^3*b*c^3 + 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*B*a^4*b*c^(5/2) + 43008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*A*a^4*c^(7/2) - 1400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^2*b^6 + 700*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a*b^7 + 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^3*b^4*c - 8400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^2*b^5*c + 147840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^4*b^2*c^2 + 33600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^3*b^3*c^2 - 25088*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^5*c^3 + 141568*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^4*b*c^3 + 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^4*b^3*c^(3/2) - 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^5*b*c^(5/2) + 387072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^4*b^2*c^(5/2) + 3962*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*b^6 - 1981*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b^7 + 81480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^4*b^4*c + 23772*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^3*b^5*c + 104160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^5*b^2*c^2 + 378000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^4*b^3*c^2 + 76160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^6*c^3 + 284480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^5*b*c^3 + 43008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^4*b^5*sqrt(c) - 71680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^5*b^3*c^(3/2) + 358400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^4*b^4*c^(3/2) + 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^6*b*c^(5/2) + 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^5*b^2*c^(5/2) + 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^6*c^(7/2) + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b^7 + 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^4*b^5*c + 645120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^5*b^3*c^2 + 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^6*b*c^3 - 43008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^5*b^5*sqrt(c) + 43008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^4*b^6*sqrt(c) + 71680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^6*b^3*c^(3/2) + 286720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^5*b^4*c^(3/2) - 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^7*b*c^(5/2) + 860160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^6*b^2*c^(5/2) - 3962*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^5*b^6 + 1981*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b^7 - 81480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^6*b^4*c + 105252*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^5*b^5*c - 104160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^7*b^2*c^2 + 482160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^6*b^3*c^2 - 76160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^8*c^3 + 360640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^7*b*c^3 - 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^7*b^3*c^(3/2) + 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^6*b^4*c^(3/2) + 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^8*b*c^(5/2) + 258048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^7*b^2*c^(5/2) + 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^8*c^(7/2) + 1400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*b^6 - 700*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b^7 - 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^7*b^4*c + 8400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^6*b^5*c - 147840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^8*b^2*c^2 + 181440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^7*b^3*c^2 + 25088*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^9*c^3 + 116480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^8*b*c^3 - 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^9*b*c^(5/2) + 129024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^8*b^2*c^(5/2) - 210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*b^6 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b^7 + 2520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^8*b^4*c - 1260*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^7*b^5*c - 10080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^9*b^2*c^2 + 5040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^8*b^3*c^2 - 29568*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^10*c^3 + 36288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^9*b*c^3 + 6144*A*a^10*c^(7/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^7*a^4)","B",0
948,1,3603,0,0.471413," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^9,x, algorithm=""giac"")","\frac{5 \, {\left(16 \, B a b^{7} - 9 \, A b^{8} - 192 \, B a^{2} b^{5} c + 112 \, A a b^{6} c + 768 \, B a^{3} b^{3} c^{2} - 480 \, A a^{2} b^{4} c^{2} - 1024 \, B a^{4} b c^{3} + 768 \, A a^{3} b^{2} c^{3} - 256 \, A a^{4} c^{4}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{16384 \, \sqrt{-a} a^{5}} - \frac{1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a b^{7} - 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A b^{8} - 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{2} b^{5} c + 11760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a b^{6} c + 80640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{3} b^{3} c^{2} - 50400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a^{2} b^{4} c^{2} - 107520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{4} b c^{3} + 80640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a^{3} b^{2} c^{3} - 26880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a^{4} c^{4} - 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{14} B a^{5} c^{\frac{7}{2}} - 12880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{2} b^{7} + 7245 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a b^{8} + 154560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{3} b^{5} c - 90160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{2} b^{6} c - 618240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{4} b^{3} c^{2} + 386400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{3} b^{4} c^{2} - 2157568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{5} b c^{3} - 618240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{4} b^{2} c^{3} - 711424 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{5} c^{4} - 6193152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} B a^{5} b^{2} c^{\frac{5}{2}} + 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} B a^{6} c^{\frac{7}{2}} - 4816896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} A a^{5} b c^{\frac{7}{2}} + 42896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{3} b^{7} - 24129 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{2} b^{8} - 514752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{4} b^{5} c + 300272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{3} b^{6} c - 5510400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{5} b^{3} c^{2} - 1286880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{4} b^{4} c^{2} - 2286592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{6} b c^{3} - 9639168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{5} b^{2} c^{3} - 1603840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{6} c^{4} - 5734400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{5} b^{4} c^{\frac{3}{2}} - 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{6} b^{2} c^{\frac{5}{2}} - 16744448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{5} b^{3} c^{\frac{5}{2}} - 3440640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{7} c^{\frac{7}{2}} - 6881280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{6} b c^{\frac{7}{2}} - 80848 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{4} b^{7} + 45477 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{3} b^{8} - 1684032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{5} b^{5} c - 565936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{4} b^{6} c - 4273920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{6} b^{3} c^{2} - 12811680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{5} b^{4} c^{2} - 2329600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{7} b c^{3} - 21477120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{6} b^{2} c^{3} - 3162880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{7} c^{4} - 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{5} b^{6} \sqrt{c} + 1146880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{6} b^{4} c^{\frac{3}{2}} - 8945664 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{5} b^{5} c^{\frac{3}{2}} - 6881280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{7} b^{2} c^{\frac{5}{2}} - 22937600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{6} b^{3} c^{\frac{5}{2}} + 3440640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} B a^{8} c^{\frac{7}{2}} - 17203200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} A a^{7} b c^{\frac{7}{2}} + 17456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{5} b^{7} - 52827 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{4} b^{8} + 380352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{6} b^{5} c - 2630320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{5} b^{6} c + 2607360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{7} b^{3} c^{2} - 19692960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{6} b^{4} c^{2} + 1111040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{8} b c^{3} - 24917760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{7} b^{2} c^{3} - 3162880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{8} c^{4} + 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{6} b^{6} \sqrt{c} - 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{5} b^{7} \sqrt{c} + 1146880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{7} b^{4} c^{\frac{3}{2}} - 6881280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{6} b^{5} c^{\frac{3}{2}} + 9633792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{8} b^{2} c^{\frac{5}{2}} - 27066368 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{7} b^{3} c^{\frac{5}{2}} - 2064384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} B a^{9} c^{\frac{7}{2}} - 8257536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} A a^{8} b c^{\frac{7}{2}} + 42896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{6} b^{7} - 24129 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{5} b^{8} + 1549632 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{7} b^{5} c - 1764112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{6} b^{6} c + 4811520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{8} b^{3} c^{2} - 11608800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{7} b^{4} c^{2} + 3906560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{9} b c^{3} - 15832320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{8} b^{2} c^{3} - 1603840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{9} c^{4} + 3440640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{8} b^{4} c^{\frac{3}{2}} - 3440640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{7} b^{5} c^{\frac{3}{2}} + 2064384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{9} b^{2} c^{\frac{5}{2}} - 8257536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{8} b^{3} c^{\frac{5}{2}} + 2064384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{10} c^{\frac{7}{2}} - 6193152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{9} b c^{\frac{7}{2}} - 12880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{7} b^{7} + 7245 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{6} b^{8} + 154560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{8} b^{5} c - 90160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{7} b^{6} c + 2822400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{9} b^{3} c^{2} - 3054240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{8} b^{4} c^{2} + 1283072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{10} b c^{3} - 4058880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{9} b^{2} c^{3} - 711424 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{10} c^{4} + 2064384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{10} b^{2} c^{\frac{5}{2}} - 2064384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{9} b^{3} c^{\frac{5}{2}} - 98304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{11} c^{\frac{7}{2}} - 589824 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{10} b c^{\frac{7}{2}} + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{8} b^{7} - 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{7} b^{8} - 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{9} b^{5} c + 11760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{8} b^{6} c + 80640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{10} b^{3} c^{2} - 50400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{9} b^{4} c^{2} + 580608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{11} b c^{3} - 607488 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{10} b^{2} c^{3} - 26880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{11} c^{4} + 98304 \, B a^{12} c^{\frac{7}{2}} - 98304 \, A a^{11} b c^{\frac{7}{2}}}{344064 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{8} a^{5}}"," ",0,"5/16384*(16*B*a*b^7 - 9*A*b^8 - 192*B*a^2*b^5*c + 112*A*a*b^6*c + 768*B*a^3*b^3*c^2 - 480*A*a^2*b^4*c^2 - 1024*B*a^4*b*c^3 + 768*A*a^3*b^2*c^3 - 256*A*a^4*c^4)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^5) - 1/344064*(1680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*B*a*b^7 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*A*b^8 - 20160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*B*a^2*b^5*c + 11760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*A*a*b^6*c + 80640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*B*a^3*b^3*c^2 - 50400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*A*a^2*b^4*c^2 - 107520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*B*a^4*b*c^3 + 80640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*A*a^3*b^2*c^3 - 26880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*A*a^4*c^4 - 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^14*B*a^5*c^(7/2) - 12880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^2*b^7 + 7245*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a*b^8 + 154560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^3*b^5*c - 90160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^2*b^6*c - 618240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^4*b^3*c^2 + 386400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^3*b^4*c^2 - 2157568*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*B*a^5*b*c^3 - 618240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^4*b^2*c^3 - 711424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*A*a^5*c^4 - 6193152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*B*a^5*b^2*c^(5/2) + 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*B*a^6*c^(7/2) - 4816896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*A*a^5*b*c^(7/2) + 42896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^3*b^7 - 24129*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^2*b^8 - 514752*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^4*b^5*c + 300272*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^3*b^6*c - 5510400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^5*b^3*c^2 - 1286880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^4*b^4*c^2 - 2286592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*B*a^6*b*c^3 - 9639168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^5*b^2*c^3 - 1603840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*A*a^6*c^4 - 5734400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^5*b^4*c^(3/2) - 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^6*b^2*c^(5/2) - 16744448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^5*b^3*c^(5/2) - 3440640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^7*c^(7/2) - 6881280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^6*b*c^(7/2) - 80848*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^4*b^7 + 45477*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^3*b^8 - 1684032*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^5*b^5*c - 565936*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^4*b^6*c - 4273920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^6*b^3*c^2 - 12811680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^5*b^4*c^2 - 2329600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^7*b*c^3 - 21477120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^6*b^2*c^3 - 3162880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^7*c^4 - 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^5*b^6*sqrt(c) + 1146880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^6*b^4*c^(3/2) - 8945664*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^5*b^5*c^(3/2) - 6881280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^7*b^2*c^(5/2) - 22937600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^6*b^3*c^(5/2) + 3440640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^8*c^(7/2) - 17203200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^7*b*c^(7/2) + 17456*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^5*b^7 - 52827*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^4*b^8 + 380352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^6*b^5*c - 2630320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^5*b^6*c + 2607360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^7*b^3*c^2 - 19692960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^6*b^4*c^2 + 1111040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^8*b*c^3 - 24917760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^7*b^2*c^3 - 3162880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^8*c^4 + 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^6*b^6*sqrt(c) - 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^5*b^7*sqrt(c) + 1146880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^7*b^4*c^(3/2) - 6881280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^6*b^5*c^(3/2) + 9633792*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^8*b^2*c^(5/2) - 27066368*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^7*b^3*c^(5/2) - 2064384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^9*c^(7/2) - 8257536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^8*b*c^(7/2) + 42896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^6*b^7 - 24129*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^5*b^8 + 1549632*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^7*b^5*c - 1764112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^6*b^6*c + 4811520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^8*b^3*c^2 - 11608800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^7*b^4*c^2 + 3906560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^9*b*c^3 - 15832320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^8*b^2*c^3 - 1603840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^9*c^4 + 3440640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^8*b^4*c^(3/2) - 3440640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^7*b^5*c^(3/2) + 2064384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^9*b^2*c^(5/2) - 8257536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^8*b^3*c^(5/2) + 2064384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^10*c^(7/2) - 6193152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^9*b*c^(7/2) - 12880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^7*b^7 + 7245*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^6*b^8 + 154560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^8*b^5*c - 90160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^7*b^6*c + 2822400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^9*b^3*c^2 - 3054240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^8*b^4*c^2 + 1283072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^10*b*c^3 - 4058880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^9*b^2*c^3 - 711424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^10*c^4 + 2064384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^10*b^2*c^(5/2) - 2064384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^9*b^3*c^(5/2) - 98304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^11*c^(7/2) - 589824*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^10*b*c^(7/2) + 1680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^8*b^7 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^7*b^8 - 20160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^9*b^5*c + 11760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^8*b^6*c + 80640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^10*b^3*c^2 - 50400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^9*b^4*c^2 + 580608*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^11*b*c^3 - 607488*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^10*b^2*c^3 - 26880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^11*c^4 + 98304*B*a^12*c^(7/2) - 98304*A*a^11*b*c^(7/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^8*a^5)","B",0
949,1,4427,0,0.583136," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^10,x, algorithm=""giac"")","-\frac{5 \, {\left(18 \, B a b^{8} - 11 \, A b^{9} - 224 \, B a^{2} b^{6} c + 144 \, A a b^{7} c + 960 \, B a^{3} b^{4} c^{2} - 672 \, A a^{2} b^{5} c^{2} - 1536 \, B a^{4} b^{2} c^{3} + 1280 \, A a^{3} b^{3} c^{3} + 512 \, B a^{5} c^{4} - 768 \, A a^{4} b c^{4}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{32768 \, \sqrt{-a} a^{6}} + \frac{5670 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} B a b^{8} - 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} A b^{9} - 70560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} B a^{2} b^{6} c + 45360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} A a b^{7} c + 302400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} B a^{3} b^{4} c^{2} - 211680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} A a^{2} b^{5} c^{2} - 483840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} B a^{4} b^{2} c^{3} + 403200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} A a^{3} b^{3} c^{3} + 161280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} B a^{5} c^{4} - 241920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{17} A a^{4} b c^{4} - 49140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{2} b^{8} + 30030 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a b^{9} + 611520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{3} b^{6} c - 393120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a^{2} b^{7} c - 2620800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{4} b^{4} c^{2} + 1834560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a^{3} b^{5} c^{2} + 4193280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{5} b^{2} c^{3} - 3494400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a^{4} b^{3} c^{3} + 4107264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} B a^{6} c^{4} + 2096640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} A a^{5} b c^{4} + 28901376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{14} B a^{6} b c^{\frac{7}{2}} + 8257536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{14} A a^{6} c^{\frac{9}{2}} + 188244 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{3} b^{8} - 115038 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{2} b^{9} - 2342592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{4} b^{6} c + 1505952 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{3} b^{7} c + 10039680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{5} b^{4} c^{2} - 7027776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{4} b^{5} c^{2} + 54125568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{6} b^{2} c^{3} + 13386240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{5} b^{3} c^{3} + 5354496 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} B a^{7} c^{4} + 41513472 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} A a^{6} b c^{4} + 100466688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} B a^{6} b^{3} c^{\frac{5}{2}} + 12386304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} B a^{7} b c^{\frac{7}{2}} + 136249344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} A a^{6} b^{2} c^{\frac{7}{2}} + 13762560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} A a^{7} c^{\frac{9}{2}} - 417636 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{4} b^{8} + 255222 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{3} b^{9} + 5197248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{5} b^{6} c - 3341088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{4} b^{7} c + 69148800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{6} b^{4} c^{2} + 15591744 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{5} b^{5} c^{2} + 71027712 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{7} b^{2} c^{3} + 192665088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{6} b^{3} c^{3} + 9354240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} B a^{8} c^{4} + 109831680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} A a^{7} b c^{4} + 53673984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{6} b^{5} c^{\frac{3}{2}} + 37158912 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{7} b^{3} c^{\frac{5}{2}} + 235339776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{6} b^{4} c^{\frac{5}{2}} + 61931520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} B a^{8} b c^{\frac{7}{2}} + 247726080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{7} b^{2} c^{\frac{7}{2}} + 41287680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} A a^{8} c^{\frac{9}{2}} + 589824 \, {\left(\sqrt{c} x - 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5670 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{9} b^{8} + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{8} b^{9} + 70560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{10} b^{6} c - 45360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{9} b^{7} c - 302400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{11} b^{4} c^{2} + 211680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{10} b^{5} c^{2} - 3644928 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{12} b^{2} c^{3} + 3725568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{11} b^{3} c^{3} - 161280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{13} c^{4} + 241920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{12} b c^{4} - 589824 \, B a^{13} b c^{\frac{7}{2}} + 589824 \, A a^{12} b^{2} c^{\frac{7}{2}} - 131072 \, A a^{13} c^{\frac{9}{2}}}{2064384 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - 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sqrt(c*x^2 + b*x + a))^11*A*a^7*b*c^4 + 53673984*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^6*b^5*c^(3/2) + 37158912*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^7*b^3*c^(5/2) + 235339776*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^6*b^4*c^(5/2) + 61931520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*B*a^8*b*c^(7/2) + 247726080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^7*b^2*c^(7/2) + 41287680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*A*a^8*c^(9/2) + 589824*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^5*b^8 - 360448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^4*b^9 + 12386304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^6*b^6*c + 4718592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^5*b^7*c + 41287680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^7*b^4*c^2 + 144506880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^6*b^5*c^2 + 20643840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^8*b^2*c^3 + 405995520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^7*b^3*c^3 + 165150720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^8*b*c^4 + 4128768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^6*b^7*sqrt(c) - 12386304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^7*b^5*c^(3/2) + 78446592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^6*b^6*c^(3/2) + 24772608*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^8*b^3*c^(5/2) + 322043904*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^7*b^4*c^(5/2) - 53673984*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*B*a^9*b*c^(7/2) + 383975424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^8*b^2*c^(7/2) + 24772608*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*A*a^9*c^(9/2) - 172188*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^6*b^8 + 334602*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^5*b^9 - 5197248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^7*b^6*c + 19266336*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^6*b^7*c - 48504960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^8*b^4*c^2 + 194975424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^7*b^5*c^2 - 54512640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^9*b^2*c^3 + 389491200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^8*b^3*c^3 - 9354240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^10*c^4 + 137894400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^9*b*c^4 - 4128768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^7*b^7*sqrt(c) + 4128768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^6*b^8*sqrt(c) - 20643840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^8*b^5*c^(3/2) + 55050240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^7*b^6*c^(3/2) - 112852992*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^9*b^3*c^(5/2) + 280756224*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^8*b^4*c^(5/2) - 12386304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*B*a^10*b*c^(7/2) + 198180864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^9*b^2*c^(7/2) + 24772608*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*A*a^10*c^(9/2) - 188244*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^7*b^8 + 115038*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^6*b^9 - 10043712*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^8*b^6*c + 10880352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^7*b^7*c - 51327360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^9*b^4*c^2 + 93731904*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^8*b^5*c^2 - 70640640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^10*b^2*c^3 + 193052160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^9*b^3*c^3 - 5354496*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^11*c^4 + 57576960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^10*b*c^4 - 20643840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^9*b^5*c^(3/2) + 20643840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^8*b^6*c^(3/2) - 37158912*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^10*b^3*c^(5/2) + 74317824*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^9*b^4*c^(5/2) - 33619968*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^11*b*c^(7/2) + 83165184*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^10*b^2*c^(7/2) + 3538944*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^11*c^(9/2) + 49140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^8*b^8 - 30030*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^7*b^9 - 611520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^9*b^6*c + 393120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^8*b^7*c - 18023040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^10*b^4*c^2 + 18809280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^9*b^5*c^2 - 20708352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^11*b^2*c^3 + 37900800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^10*b^3*c^3 - 4107264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^12*c^4 + 14418432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^11*b*c^4 - 12386304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^11*b^3*c^(5/2) + 12386304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^10*b^4*c^(5/2) - 2949120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^12*b*c^(7/2) + 7077888*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^11*b^2*c^(7/2) + 1179648*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^12*c^(9/2) - 5670*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^9*b^8 + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^8*b^9 + 70560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^10*b^6*c - 45360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^9*b^7*c - 302400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^11*b^4*c^2 + 211680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^10*b^5*c^2 - 3644928*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^12*b^2*c^3 + 3725568*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^11*b^3*c^3 - 161280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^13*c^4 + 241920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^12*b*c^4 - 589824*B*a^13*b*c^(7/2) + 589824*A*a^12*b^2*c^(7/2) - 131072*A*a^13*c^(9/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^9*a^6)","B",0
950,1,249,0,0.255631," ","integrate(x^4*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(\frac{8 \, B x}{c} - \frac{9 \, B b c^{3} - 10 \, A c^{4}}{c^{5}}\right)} x + \frac{63 \, B b^{2} c^{2} - 64 \, B a c^{3} - 70 \, A b c^{3}}{c^{5}}\right)} x - \frac{315 \, B b^{3} c - 644 \, B a b c^{2} - 350 \, A b^{2} c^{2} + 360 \, A a c^{3}}{c^{5}}\right)} x + \frac{945 \, B b^{4} - 2940 \, B a b^{2} c - 1050 \, A b^{3} c + 1024 \, B a^{2} c^{2} + 2200 \, A a b c^{2}}{c^{5}}\right)} + \frac{{\left(63 \, B b^{5} - 280 \, B a b^{3} c - 70 \, A b^{4} c + 240 \, B a^{2} b c^{2} + 240 \, A a b^{2} c^{2} - 96 \, A a^{2} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{11}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x + a)*(2*(4*(6*(8*B*x/c - (9*B*b*c^3 - 10*A*c^4)/c^5)*x + (63*B*b^2*c^2 - 64*B*a*c^3 - 70*A*b*c^3)/c^5)*x - (315*B*b^3*c - 644*B*a*b*c^2 - 350*A*b^2*c^2 + 360*A*a*c^3)/c^5)*x + (945*B*b^4 - 2940*B*a*b^2*c - 1050*A*b^3*c + 1024*B*a^2*c^2 + 2200*A*a*b*c^2)/c^5) + 1/256*(63*B*b^5 - 280*B*a*b^3*c - 70*A*b^4*c + 240*B*a^2*b*c^2 + 240*A*a*b^2*c^2 - 96*A*a^2*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
951,1,183,0,0.265209," ","integrate(x^3*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(\frac{6 \, B x}{c} - \frac{7 \, B b c^{2} - 8 \, A c^{3}}{c^{4}}\right)} x + \frac{35 \, B b^{2} c - 36 \, B a c^{2} - 40 \, A b c^{2}}{c^{4}}\right)} x - \frac{105 \, B b^{3} - 220 \, B a b c - 120 \, A b^{2} c + 128 \, A a c^{2}}{c^{4}}\right)} - \frac{{\left(35 \, B b^{4} - 120 \, B a b^{2} c - 40 \, A b^{3} c + 48 \, B a^{2} c^{2} + 96 \, A a b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*B*x/c - (7*B*b*c^2 - 8*A*c^3)/c^4)*x + (35*B*b^2*c - 36*B*a*c^2 - 40*A*b*c^2)/c^4)*x - (105*B*b^3 - 220*B*a*b*c - 120*A*b^2*c + 128*A*a*c^2)/c^4) - 1/128*(35*B*b^4 - 120*B*a*b^2*c - 40*A*b^3*c + 48*B*a^2*c^2 + 96*A*a*b*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
952,1,128,0,0.247936," ","integrate(x^2*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(\frac{4 \, B x}{c} - \frac{5 \, B b c - 6 \, A c^{2}}{c^{3}}\right)} x + \frac{15 \, B b^{2} - 16 \, B a c - 18 \, A b c}{c^{3}}\right)} + \frac{{\left(5 \, B b^{3} - 12 \, B a b c - 6 \, A b^{2} c + 8 \, A a c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*(4*B*x/c - (5*B*b*c - 6*A*c^2)/c^3)*x + (15*B*b^2 - 16*B*a*c - 18*A*b*c)/c^3) + 1/16*(5*B*b^3 - 12*B*a*b*c - 6*A*b^2*c + 8*A*a*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
953,1,90,0,0.239100," ","integrate(x*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(\frac{2 \, B x}{c} - \frac{3 \, B b - 4 \, A c}{c^{2}}\right)} - \frac{{\left(3 \, B b^{2} - 4 \, B a c - 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*B*x/c - (3*B*b - 4*A*c)/c^2) - 1/8*(3*B*b^2 - 4*B*a*c - 4*A*b*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
954,1,62,0,0.236191," ","integrate((B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x + a} B}{c} + \frac{{\left(B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"sqrt(c*x^2 + b*x + a)*B/c + 1/2*(B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
955,-2,0,0,0.000000," ","integrate((B*x+A)/x/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
956,1,110,0,0.232174," ","integrate((B*x+A)/x^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, B a - A b\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b + 2 \, A a \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)} a}"," ",0,"(2*B*a - A*b)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a) + ((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b + 2*A*a*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)*a)","A",0
957,1,303,0,0.287119," ","integrate((B*x+A)/x^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{2}} + \frac{4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} \sqrt{c} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c - 8 \, B a^{3} \sqrt{c} + 8 \, A a^{2} b \sqrt{c}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{2} a^{2}}"," ",0,"-1/4*(4*B*a*b - 3*A*b^2 + 4*A*a*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^2) + 1/4*(4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*sqrt(c) - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c - 8*B*a^3*sqrt(c) + 8*A*a^2*b*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^2*a^2)","B",0
958,1,511,0,0.243186," ","integrate((B*x+A)/x^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(6 \, B a b^{2} - 5 \, A b^{3} - 8 \, B a^{2} c + 12 \, A a b c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{3}} - \frac{18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a b^{2} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} c + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b c - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} b^{2} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{3} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b c - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} b \sqrt{c} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{3} c^{\frac{3}{2}} + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b^{2} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{3} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} c - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b c + 48 \, B a^{4} b \sqrt{c} - 48 \, A a^{3} b^{2} \sqrt{c} + 32 \, A a^{4} c^{\frac{3}{2}}}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{3} a^{3}}"," ",0,"1/8*(6*B*a*b^2 - 5*A*b^3 - 8*B*a^2*c + 12*A*a*b*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^3) - 1/24*(18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*b^2 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*c + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b*c - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*b^2 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^3 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b*c - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*b*sqrt(c) - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^3*c^(3/2) + 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b^2 - 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^3 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*c - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b*c + 48*B*a^4*b*sqrt(c) - 48*A*a^3*b^2*sqrt(c) + 32*A*a^4*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^3*a^3)","B",0
959,1,884,0,0.296917," ","integrate((B*x+A)/x^5/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(40 \, B a b^{3} - 35 \, A b^{4} - 96 \, B a^{2} b c + 120 \, A a b^{2} c - 48 \, A a^{2} c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{64 \, \sqrt{-a} a^{4}} + \frac{120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a b^{3} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A b^{4} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b c + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{2} c - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} c^{2} - 440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} b^{3} + 385 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b^{4} + 1056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{3} b c - 1320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{2} c + 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} c^{2} + 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{4} c^{\frac{3}{2}} + 584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{3} b^{3} - 511 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b^{4} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b c + 1752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{2} c + 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} c^{2} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{4} b^{2} \sqrt{c} - 1024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{5} c^{\frac{3}{2}} + 2048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{4} b c^{\frac{3}{2}} - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} b^{3} + 279 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b^{4} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b c + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{2} c - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} c^{2} - 384 \, B a^{5} b^{2} \sqrt{c} + 384 \, A a^{4} b^{3} \sqrt{c} + 256 \, B a^{6} c^{\frac{3}{2}} - 512 \, A a^{5} b c^{\frac{3}{2}}}{192 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{4} a^{4}}"," ",0,"-1/64*(40*B*a*b^3 - 35*A*b^4 - 96*B*a^2*b*c + 120*A*a*b^2*c - 48*A*a^2*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^4) + 1/192*(120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a*b^3 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*b^4 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b*c + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^2*c - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*c^2 - 440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*b^3 + 385*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b^4 + 1056*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^3*b*c - 1320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^2*c + 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*c^2 + 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^4*c^(3/2) + 584*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^3*b^3 - 511*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b^4 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b*c + 1752*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^2*c + 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*c^2 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^4*b^2*sqrt(c) - 1024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^5*c^(3/2) + 2048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^4*b*c^(3/2) - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*b^3 + 279*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b^4 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b*c + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^2*c - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*c^2 - 384*B*a^5*b^2*sqrt(c) + 384*A*a^4*b^3*sqrt(c) + 256*B*a^6*c^(3/2) - 512*A*a^5*b*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^4*a^4)","B",0
960,1,1266,0,0.266575," ","integrate((B*x+A)/x^6/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(70 \, B a b^{4} - 63 \, A b^{5} - 240 \, B a^{2} b^{2} c + 280 \, A a b^{3} c + 96 \, B a^{3} c^{2} - 240 \, A a^{2} b c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{128 \, \sqrt{-a} a^{5}} - \frac{1050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a b^{4} - 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A b^{5} - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{2} b^{2} c + 4200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a b^{3} c + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} B a^{3} c^{2} - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} A a^{2} b c^{2} - 4900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{2} b^{4} + 4410 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a b^{5} + 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{3} b^{2} c - 19600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{2} b^{3} c - 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} B a^{4} c^{2} + 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} A a^{3} b c^{2} + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{3} b^{4} - 8064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{2} b^{5} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{4} b^{2} c + 35840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{3} b^{3} c - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a^{4} b c^{2} - 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{5} b c^{\frac{3}{2}} - 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{5} c^{\frac{5}{2}} - 7900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{4} b^{4} + 7110 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{3} b^{5} + 13920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{5} b^{2} c - 31600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{4} b^{3} c + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{6} c^{2} - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{5} b c^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{5} b^{3} \sqrt{c} + 25600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{6} b c^{\frac{3}{2}} - 38400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{5} b^{2} c^{\frac{3}{2}} + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{6} c^{\frac{5}{2}} + 2790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{5} b^{4} - 2895 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{4} b^{5} + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{6} b^{2} c - 4200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{5} b^{3} c - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{7} c^{2} + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{6} b c^{2} + 3840 \, B a^{6} b^{3} \sqrt{c} - 3840 \, A a^{5} b^{4} \sqrt{c} - 5120 \, B a^{7} b c^{\frac{3}{2}} + 7680 \, A a^{6} b^{2} c^{\frac{3}{2}} - 2048 \, A a^{7} c^{\frac{5}{2}}}{1920 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{5} a^{5}}"," ",0,"1/128*(70*B*a*b^4 - 63*A*b^5 - 240*B*a^2*b^2*c + 280*A*a*b^3*c + 96*B*a^3*c^2 - 240*A*a^2*b*c^2)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^5) - 1/1920*(1050*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a*b^4 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*b^5 - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^2*b^2*c + 4200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a*b^3*c + 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*B*a^3*c^2 - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*A*a^2*b*c^2 - 4900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^2*b^4 + 4410*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a*b^5 + 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^3*b^2*c - 19600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^2*b^3*c - 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*B*a^4*c^2 + 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*A*a^3*b*c^2 + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^3*b^4 - 8064*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^2*b^5 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^4*b^2*c + 35840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^3*b^3*c - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a^4*b*c^2 - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^5*b*c^(3/2) - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^5*c^(5/2) - 7900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^4*b^4 + 7110*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^3*b^5 + 13920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^5*b^2*c - 31600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^4*b^3*c + 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^6*c^2 - 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^5*b*c^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^5*b^3*sqrt(c) + 25600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^6*b*c^(3/2) - 38400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^5*b^2*c^(3/2) + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^6*c^(5/2) + 2790*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^5*b^4 - 2895*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^4*b^5 + 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^6*b^2*c - 4200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^5*b^3*c - 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^7*c^2 + 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^6*b*c^2 + 3840*B*a^6*b^3*sqrt(c) - 3840*A*a^5*b^4*sqrt(c) - 5120*B*a^7*b*c^(3/2) + 7680*A*a^6*b^2*c^(3/2) - 2048*A*a^7*c^(5/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^5*a^5)","B",0
961,1,367,0,0.309825," ","integrate(x^4*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left(\frac{4 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} x}{b^{2} c^{4} - 4 \, a c^{5}} - \frac{7 \, B b^{3} c^{2} - 28 \, B a b c^{3} - 6 \, A b^{2} c^{3} + 24 \, A a c^{4}}{b^{2} c^{4} - 4 \, a c^{5}}\right)} x + \frac{35 \, B b^{4} c - 172 \, B a b^{2} c^{2} - 30 \, A b^{3} c^{2} + 128 \, B a^{2} c^{3} + 120 \, A a b c^{3}}{b^{2} c^{4} - 4 \, a c^{5}}\right)} x + \frac{105 \, B b^{5} - 530 \, B a b^{3} c - 90 \, A b^{4} c + 488 \, B a^{2} b c^{2} + 372 \, A a b^{2} c^{2} - 144 \, A a^{2} c^{3}}{b^{2} c^{4} - 4 \, a c^{5}}\right)} x + \frac{105 \, B a b^{4} - 460 \, B a^{2} b^{2} c - 90 \, A a b^{3} c + 256 \, B a^{3} c^{2} + 312 \, A a^{2} b c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}{24 \, \sqrt{c x^{2} + b x + a}} + \frac{{\left(35 \, B b^{3} - 60 \, B a b c - 30 \, A b^{2} c + 24 \, A a c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{9}{2}}}"," ",0,"1/24*(((2*(4*(B*b^2*c^3 - 4*B*a*c^4)*x/(b^2*c^4 - 4*a*c^5) - (7*B*b^3*c^2 - 28*B*a*b*c^3 - 6*A*b^2*c^3 + 24*A*a*c^4)/(b^2*c^4 - 4*a*c^5))*x + (35*B*b^4*c - 172*B*a*b^2*c^2 - 30*A*b^3*c^2 + 128*B*a^2*c^3 + 120*A*a*b*c^3)/(b^2*c^4 - 4*a*c^5))*x + (105*B*b^5 - 530*B*a*b^3*c - 90*A*b^4*c + 488*B*a^2*b*c^2 + 372*A*a*b^2*c^2 - 144*A*a^2*c^3)/(b^2*c^4 - 4*a*c^5))*x + (105*B*a*b^4 - 460*B*a^2*b^2*c - 90*A*a*b^3*c + 256*B*a^3*c^2 + 312*A*a^2*b*c^2)/(b^2*c^4 - 4*a*c^5))/sqrt(c*x^2 + b*x + a) + 1/16*(35*B*b^3 - 60*B*a*b*c - 30*A*b^2*c + 24*A*a*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
962,1,268,0,0.252432," ","integrate(x^3*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} x}{b^{2} c^{3} - 4 \, a c^{4}} - \frac{5 \, B b^{3} c - 20 \, B a b c^{2} - 4 \, A b^{2} c^{2} + 16 \, A a c^{3}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{15 \, B b^{4} - 62 \, B a b^{2} c - 12 \, A b^{3} c + 24 \, B a^{2} c^{2} + 40 \, A a b c^{2}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{15 \, B a b^{3} - 52 \, B a^{2} b c - 12 \, A a b^{2} c + 32 \, A a^{2} c^{2}}{b^{2} c^{3} - 4 \, a c^{4}}}{4 \, \sqrt{c x^{2} + b x + a}} - \frac{3 \, {\left(5 \, B b^{2} - 4 \, B a c - 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{7}{2}}}"," ",0,"1/4*(((2*(B*b^2*c^2 - 4*B*a*c^3)*x/(b^2*c^3 - 4*a*c^4) - (5*B*b^3*c - 20*B*a*b*c^2 - 4*A*b^2*c^2 + 16*A*a*c^3)/(b^2*c^3 - 4*a*c^4))*x - (15*B*b^4 - 62*B*a*b^2*c - 12*A*b^3*c + 24*B*a^2*c^2 + 40*A*a*b*c^2)/(b^2*c^3 - 4*a*c^4))*x - (15*B*a*b^3 - 52*B*a^2*b*c - 12*A*a*b^2*c + 32*A*a^2*c^2)/(b^2*c^3 - 4*a*c^4))/sqrt(c*x^2 + b*x + a) - 3/8*(5*B*b^2 - 4*B*a*c - 4*A*b*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
963,1,177,0,0.258709," ","integrate(x^2*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{{\left(B b^{2} c - 4 \, B a c^{2}\right)} x}{b^{2} c^{2} - 4 \, a c^{3}} + \frac{3 \, B b^{3} - 10 \, B a b c - 2 \, A b^{2} c + 4 \, A a c^{2}}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x + \frac{3 \, B a b^{2} - 8 \, B a^{2} c - 2 \, A a b c}{b^{2} c^{2} - 4 \, a c^{3}}}{\sqrt{c x^{2} + b x + a}} + \frac{{\left(3 \, B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"(((B*b^2*c - 4*B*a*c^2)*x/(b^2*c^2 - 4*a*c^3) + (3*B*b^3 - 10*B*a*b*c - 2*A*b^2*c + 4*A*a*c^2)/(b^2*c^2 - 4*a*c^3))*x + (3*B*a*b^2 - 8*B*a^2*c - 2*A*a*b*c)/(b^2*c^2 - 4*a*c^3))/sqrt(c*x^2 + b*x + a) + 1/2*(3*B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
964,1,110,0,0.246973," ","integrate(x*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(B b^{2} - 2 \, B a c - A b c\right)} x}{b^{2} c - 4 \, a c^{2}} + \frac{B a b - 2 \, A a c}{b^{2} c - 4 \, a c^{2}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{B \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-2*((B*b^2 - 2*B*a*c - A*b*c)*x/(b^2*c - 4*a*c^2) + (B*a*b - 2*A*a*c)/(b^2*c - 4*a*c^2))/sqrt(c*x^2 + b*x + a) - B*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
965,1,55,0,0.238648," ","integrate((B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B b - 2 \, A c\right)} x}{b^{2} - 4 \, a c} + \frac{2 \, B a - A b}{b^{2} - 4 \, a c}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"2*((B*b - 2*A*c)*x/(b^2 - 4*a*c) + (2*B*a - A*b)/(b^2 - 4*a*c))/sqrt(c*x^2 + b*x + a)","A",0
966,1,125,0,0.269396," ","integrate((B*x+A)/x/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, B a^{2} c - A a b c\right)} x}{a^{2} b^{2} - 4 \, a^{3} c} + \frac{B a^{2} b - A a b^{2} + 2 \, A a^{2} c}{a^{2} b^{2} - 4 \, a^{3} c}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{2 \, A \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a}"," ",0,"-2*((2*B*a^2*c - A*a*b*c)*x/(a^2*b^2 - 4*a^3*c) + (B*a^2*b - A*a*b^2 + 2*A*a^2*c)/(a^2*b^2 - 4*a^3*c))/sqrt(c*x^2 + b*x + a) + 2*A*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a)","A",0
967,1,220,0,0.271716," ","integrate((B*x+A)/x^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B a^{3} b c - A a^{2} b^{2} c + 2 \, A a^{3} c^{2}\right)} x}{a^{4} b^{2} - 4 \, a^{5} c} + \frac{B a^{3} b^{2} - A a^{2} b^{3} - 2 \, B a^{4} c + 3 \, A a^{3} b c}{a^{4} b^{2} - 4 \, a^{5} c}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{{\left(2 \, B a - 3 \, A b\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b + 2 \, A a \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)} a^{2}}"," ",0,"2*((B*a^3*b*c - A*a^2*b^2*c + 2*A*a^3*c^2)*x/(a^4*b^2 - 4*a^5*c) + (B*a^3*b^2 - A*a^2*b^3 - 2*B*a^4*c + 3*A*a^3*b*c)/(a^4*b^2 - 4*a^5*c))/sqrt(c*x^2 + b*x + a) + (2*B*a - 3*A*b)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^2) + ((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b + 2*A*a*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)*a^2)","A",0
968,1,467,0,0.257338," ","integrate((B*x+A)/x^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(B a^{4} b^{2} c - A a^{3} b^{3} c - 2 \, B a^{5} c^{2} + 3 \, A a^{4} b c^{2}\right)} x}{a^{6} b^{2} - 4 \, a^{7} c} + \frac{B a^{4} b^{3} - A a^{3} b^{4} - 3 \, B a^{5} b c + 4 \, A a^{4} b^{2} c - 2 \, A a^{5} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{3 \, {\left(4 \, B a b - 5 \, A b^{2} + 4 \, A a c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{3}} + \frac{4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} \sqrt{c} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b \sqrt{c} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c - 8 \, B a^{3} \sqrt{c} + 16 \, A a^{2} b \sqrt{c}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{2} a^{3}}"," ",0,"-2*((B*a^4*b^2*c - A*a^3*b^3*c - 2*B*a^5*c^2 + 3*A*a^4*b*c^2)*x/(a^6*b^2 - 4*a^7*c) + (B*a^4*b^3 - A*a^3*b^4 - 3*B*a^5*b*c + 4*A*a^4*b^2*c - 2*A*a^5*c^2)/(a^6*b^2 - 4*a^7*c))/sqrt(c*x^2 + b*x + a) - 3/4*(4*B*a*b - 5*A*b^2 + 4*A*a*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^3) + 1/4*(4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*sqrt(c) - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b*sqrt(c) - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c - 8*B*a^3*sqrt(c) + 16*A*a^2*b*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^2*a^3)","B",0
969,1,798,0,0.275366," ","integrate((B*x+A)/x^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B a^{5} b^{3} c - A a^{4} b^{4} c - 3 \, B a^{6} b c^{2} + 4 \, A a^{5} b^{2} c^{2} - 2 \, A a^{6} c^{3}\right)} x}{a^{8} b^{2} - 4 \, a^{9} c} + \frac{B a^{5} b^{4} - A a^{4} b^{5} - 4 \, B a^{6} b^{2} c + 5 \, A a^{5} b^{3} c + 2 \, B a^{7} c^{2} - 5 \, A a^{6} b c^{2}}{a^{8} b^{2} - 4 \, a^{9} c}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{{\left(30 \, B a b^{2} - 35 \, A b^{3} - 24 \, B a^{2} c + 60 \, A a b c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{4}} - \frac{42 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a b^{2} - 57 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} c + 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b c + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{2} b \sqrt{c} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a b^{2} \sqrt{c} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a^{2} c^{\frac{3}{2}} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} b^{2} + 136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{3} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b c - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} b \sqrt{c} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{2} b^{2} \sqrt{c} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{3} c^{\frac{3}{2}} + 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b^{2} - 87 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{3} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} c - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b c + 96 \, B a^{4} b \sqrt{c} - 144 \, A a^{3} b^{2} \sqrt{c} + 80 \, A a^{4} c^{\frac{3}{2}}}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{3} a^{4}}"," ",0,"2*((B*a^5*b^3*c - A*a^4*b^4*c - 3*B*a^6*b*c^2 + 4*A*a^5*b^2*c^2 - 2*A*a^6*c^3)*x/(a^8*b^2 - 4*a^9*c) + (B*a^5*b^4 - A*a^4*b^5 - 4*B*a^6*b^2*c + 5*A*a^5*b^3*c + 2*B*a^7*c^2 - 5*A*a^6*b*c^2)/(a^8*b^2 - 4*a^9*c))/sqrt(c*x^2 + b*x + a) + 1/8*(30*B*a*b^2 - 35*A*b^3 - 24*B*a^2*c + 60*A*a*b*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^4) - 1/24*(42*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*b^2 - 57*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*c + 84*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b*c + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^2*b*sqrt(c) - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a*b^2*sqrt(c) + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a^2*c^(3/2) - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*b^2 + 136*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^3 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b*c - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*b*sqrt(c) + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^2*b^2*sqrt(c) - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^3*c^(3/2) + 54*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b^2 - 87*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^3 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*c - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b*c + 96*B*a^4*b*sqrt(c) - 144*A*a^3*b^2*sqrt(c) + 80*A*a^4*c^(3/2))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^3*a^4)","B",0
970,1,458,0,0.287659," ","integrate(x^4*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(\frac{3 \, {\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} x}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}} + \frac{4 \, {\left(5 \, B b^{5} c - 37 \, B a b^{3} c^{2} - 2 \, A b^{4} c^{2} + 64 \, B a^{2} b c^{3} + 14 \, A a b^{2} c^{3} - 16 \, A a^{2} c^{4}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x + \frac{3 \, {\left(5 \, B b^{6} - 30 \, B a b^{4} c - 2 \, A b^{5} c + 16 \, B a^{2} b^{2} c^{2} + 12 \, A a b^{3} c^{2} + 64 \, B a^{3} c^{3}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x + \frac{6 \, {\left(5 \, B a b^{5} - 35 \, B a^{2} b^{3} c - 2 \, A a b^{4} c + 52 \, B a^{3} b c^{2} + 14 \, A a^{2} b^{2} c^{2} - 8 \, A a^{3} c^{3}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x + \frac{15 \, B a^{2} b^{4} - 100 \, B a^{3} b^{2} c - 6 \, A a^{2} b^{3} c + 128 \, B a^{4} c^{2} + 40 \, A a^{3} b c^{2}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} + \frac{{\left(5 \, B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{7}{2}}}"," ",0,"1/3*((((3*(B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5) + 4*(5*B*b^5*c - 37*B*a*b^3*c^2 - 2*A*b^4*c^2 + 64*B*a^2*b*c^3 + 14*A*a*b^2*c^3 - 16*A*a^2*c^4)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + 3*(5*B*b^6 - 30*B*a*b^4*c - 2*A*b^5*c + 16*B*a^2*b^2*c^2 + 12*A*a*b^3*c^2 + 64*B*a^3*c^3)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + 6*(5*B*a*b^5 - 35*B*a^2*b^3*c - 2*A*a*b^4*c + 52*B*a^3*b*c^2 + 14*A*a^2*b^2*c^2 - 8*A*a^3*c^3)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + (15*B*a^2*b^4 - 100*B*a^3*b^2*c - 6*A*a^2*b^3*c + 128*B*a^4*c^2 + 40*A*a^3*b*c^2)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))/(c*x^2 + b*x + a)^(3/2) + 1/2*(5*B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
971,1,314,0,0.279210," ","integrate(x^3*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(\frac{{\left(4 \, B b^{4} c - 28 \, B a b^{2} c^{2} - A b^{3} c^{2} + 32 \, B a^{2} c^{3} + 12 \, A a b c^{3}\right)} x}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}} + \frac{3 \, {\left(B b^{5} - 6 \, B a b^{3} c + 2 \, A a b^{2} c^{2} + 8 \, A a^{2} c^{3}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{6 \, {\left(B a b^{4} - 7 \, B a^{2} b^{2} c + 4 \, B a^{3} c^{2} + 4 \, A a^{2} b c^{2}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{3 \, B a^{2} b^{3} - 20 \, B a^{3} b c + 16 \, A a^{3} c^{2}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} - \frac{B \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"-2/3*((((4*B*b^4*c - 28*B*a*b^2*c^2 - A*b^3*c^2 + 32*B*a^2*c^3 + 12*A*a*b*c^3)*x/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4) + 3*(B*b^5 - 6*B*a*b^3*c + 2*A*a*b^2*c^2 + 8*A*a^2*c^3)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x + 6*(B*a*b^4 - 7*B*a^2*b^2*c + 4*B*a^3*c^2 + 4*A*a^2*b*c^2)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x + (3*B*a^2*b^3 - 20*B*a^3*b*c + 16*A*a^3*c^2)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))/(c*x^2 + b*x + a)^(3/2) - B*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
972,1,195,0,0.259565," ","integrate(x^2*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{{\left(B b^{3} - 12 \, B a b c + 2 \, A b^{2} c + 8 \, A a c^{2}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} - \frac{3 \, {\left(2 \, B a b^{2} - A b^{3} + 8 \, B a^{2} c - 4 \, A a b c\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x - \frac{12 \, {\left(2 \, B a^{2} b - A a b^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x - \frac{8 \, {\left(2 \, B a^{3} - A a^{2} b\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*((((B*b^3 - 12*B*a*b*c + 2*A*b^2*c + 8*A*a*c^2)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) - 3*(2*B*a*b^2 - A*b^3 + 8*B*a^2*c - 4*A*a*b*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x - 12*(2*B*a^2*b - A*a*b^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x - 8*(2*B*a^3 - A*a^2*b)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
973,1,196,0,0.253213," ","integrate(x*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{2 \, {\left(B b^{2} c + 4 \, B a c^{2} - 4 \, A b c^{2}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(B b^{3} + 4 \, B a b c - 4 \, A b^{2} c\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(4 \, B a b^{2} - A b^{3} - 4 \, A a b c\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{2 \, {\left(4 \, B a^{2} b - A a b^{2} - 4 \, A a^{2} c\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*(((2*(B*b^2*c + 4*B*a*c^2 - 4*A*b*c^2)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(B*b^3 + 4*B*a*b*c - 4*A*b^2*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(4*B*a*b^2 - A*b^3 - 4*A*a*b*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 2*(4*B*a^2*b - A*a*b^2 - 4*A*a^2*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","A",0
974,1,193,0,0.305650," ","integrate((B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(4 \, {\left(\frac{2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(B b^{3} + 4 \, B a b c - 2 \, A b^{2} c - 8 \, A a c^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{2 \, B a b^{2} + A b^{3} + 8 \, B a^{2} c - 12 \, A a b c}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((4*(2*(B*b*c^2 - 2*A*c^3)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(B*b^2*c - 2*A*b*c^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(B*b^3 + 4*B*a*b*c - 2*A*b^2*c - 8*A*a*c^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (2*B*a*b^2 + A*b^3 + 8*B*a^2*c - 12*A*a*b*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
975,1,333,0,0.254873," ","integrate((B*x+A)/x/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{{\left(3 \, A a^{5} b^{3} c^{2} + 16 \, B a^{7} c^{3} - 20 \, A a^{6} b c^{3}\right)} x}{a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}} + \frac{6 \, {\left(A a^{5} b^{4} c + 4 \, B a^{7} b c^{2} - 7 \, A a^{6} b^{2} c^{2} + 4 \, A a^{7} c^{3}\right)}}{a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}\right)} x + \frac{3 \, {\left(A a^{5} b^{5} + 2 \, B a^{7} b^{2} c - 6 \, A a^{6} b^{3} c + 8 \, B a^{8} c^{2}\right)}}{a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}\right)} x - \frac{B a^{7} b^{3} - 4 \, A a^{6} b^{4} - 12 \, B a^{8} b c + 28 \, A a^{7} b^{2} c - 32 \, A a^{8} c^{2}}{a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} + \frac{2 \, A \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}}"," ",0,"2/3*((((3*A*a^5*b^3*c^2 + 16*B*a^7*c^3 - 20*A*a^6*b*c^3)*x/(a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2) + 6*(A*a^5*b^4*c + 4*B*a^7*b*c^2 - 7*A*a^6*b^2*c^2 + 4*A*a^7*c^3)/(a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2))*x + 3*(A*a^5*b^5 + 2*B*a^7*b^2*c - 6*A*a^6*b^3*c + 8*B*a^8*c^2)/(a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2))*x - (B*a^7*b^3 - 4*A*a^6*b^4 - 12*B*a^8*b*c + 28*A*a^7*b^2*c - 32*A*a^8*c^2)/(a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2))/(c*x^2 + b*x + a)^(3/2) + 2*A*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^2)","A",0
976,1,483,0,0.267356," ","integrate((B*x+A)/x^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{{\left(3 \, B a^{9} b^{3} c^{2} - 6 \, A a^{8} b^{4} c^{2} - 20 \, B a^{10} b c^{3} + 38 \, A a^{9} b^{2} c^{3} - 40 \, A a^{10} c^{4}\right)} x}{a^{11} b^{4} - 8 \, a^{12} b^{2} c + 16 \, a^{13} c^{2}} + \frac{3 \, {\left(2 \, B a^{9} b^{4} c - 4 \, A a^{8} b^{5} c - 14 \, B a^{10} b^{2} c^{2} + 27 \, A a^{9} b^{3} c^{2} + 8 \, B a^{11} c^{3} - 36 \, A a^{10} b c^{3}\right)}}{a^{11} b^{4} - 8 \, a^{12} b^{2} c + 16 \, a^{13} c^{2}}\right)} x + \frac{3 \, {\left(B a^{9} b^{5} - 2 \, A a^{8} b^{6} - 6 \, B a^{10} b^{3} c + 12 \, A a^{9} b^{4} c - 8 \, A a^{10} b^{2} c^{2} - 16 \, A a^{11} c^{3}\right)}}{a^{11} b^{4} - 8 \, a^{12} b^{2} c + 16 \, a^{13} c^{2}}\right)} x + \frac{4 \, B a^{10} b^{4} - 7 \, A a^{9} b^{5} - 28 \, B a^{11} b^{2} c + 50 \, A a^{10} b^{3} c + 32 \, B a^{12} c^{2} - 80 \, A a^{11} b c^{2}}{a^{11} b^{4} - 8 \, a^{12} b^{2} c + 16 \, a^{13} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} + \frac{{\left(2 \, B a - 5 \, A b\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b + 2 \, A a \sqrt{c}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)} a^{3}}"," ",0,"2/3*((((3*B*a^9*b^3*c^2 - 6*A*a^8*b^4*c^2 - 20*B*a^10*b*c^3 + 38*A*a^9*b^2*c^3 - 40*A*a^10*c^4)*x/(a^11*b^4 - 8*a^12*b^2*c + 16*a^13*c^2) + 3*(2*B*a^9*b^4*c - 4*A*a^8*b^5*c - 14*B*a^10*b^2*c^2 + 27*A*a^9*b^3*c^2 + 8*B*a^11*c^3 - 36*A*a^10*b*c^3)/(a^11*b^4 - 8*a^12*b^2*c + 16*a^13*c^2))*x + 3*(B*a^9*b^5 - 2*A*a^8*b^6 - 6*B*a^10*b^3*c + 12*A*a^9*b^4*c - 8*A*a^10*b^2*c^2 - 16*A*a^11*c^3)/(a^11*b^4 - 8*a^12*b^2*c + 16*a^13*c^2))*x + (4*B*a^10*b^4 - 7*A*a^9*b^5 - 28*B*a^11*b^2*c + 50*A*a^10*b^3*c + 32*B*a^12*c^2 - 80*A*a^11*b*c^2)/(a^11*b^4 - 8*a^12*b^2*c + 16*a^13*c^2))/(c*x^2 + b*x + a)^(3/2) + (2*B*a - 5*A*b)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^3) + ((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b + 2*A*a*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)*a^3)","A",0
977,1,765,0,0.282626," ","integrate((B*x+A)/x^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(\frac{{\left(6 \, B a^{12} b^{4} c^{2} - 9 \, A a^{11} b^{5} c^{2} - 38 \, B a^{13} b^{2} c^{3} + 62 \, A a^{12} b^{3} c^{3} + 40 \, B a^{14} c^{4} - 96 \, A a^{13} b c^{4}\right)} x}{a^{15} b^{4} - 8 \, a^{16} b^{2} c + 16 \, a^{17} c^{2}} + \frac{3 \, {\left(4 \, B a^{12} b^{5} c - 6 \, A a^{11} b^{6} c - 27 \, B a^{13} b^{3} c^{2} + 44 \, A a^{12} b^{4} c^{2} + 36 \, B a^{14} b c^{3} - 80 \, A a^{13} b^{2} c^{3} + 16 \, A a^{14} c^{4}\right)}}{a^{15} b^{4} - 8 \, a^{16} b^{2} c + 16 \, a^{17} c^{2}}\right)} x + \frac{3 \, {\left(2 \, B a^{12} b^{6} - 3 \, A a^{11} b^{7} - 12 \, B a^{13} b^{4} c + 20 \, A a^{12} b^{5} c + 8 \, B a^{14} b^{2} c^{2} - 25 \, A a^{13} b^{3} c^{2} + 16 \, B a^{15} c^{3} - 20 \, A a^{14} b c^{3}\right)}}{a^{15} b^{4} - 8 \, a^{16} b^{2} c + 16 \, a^{17} c^{2}}\right)} x + \frac{7 \, B a^{13} b^{5} - 10 \, A a^{12} b^{6} - 50 \, B a^{14} b^{3} c + 78 \, A a^{13} b^{4} c + 80 \, B a^{15} b c^{2} - 162 \, A a^{14} b^{2} c^{2} + 56 \, A a^{15} c^{3}}{a^{15} b^{4} - 8 \, a^{16} b^{2} c + 16 \, a^{17} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} - \frac{5 \, {\left(4 \, B a b - 7 \, A b^{2} + 4 \, A a c\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{4}} + \frac{4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} \sqrt{c} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b \sqrt{c} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b + 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c - 8 \, B a^{3} \sqrt{c} + 24 \, A a^{2} b \sqrt{c}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{2} a^{4}}"," ",0,"-2/3*((((6*B*a^12*b^4*c^2 - 9*A*a^11*b^5*c^2 - 38*B*a^13*b^2*c^3 + 62*A*a^12*b^3*c^3 + 40*B*a^14*c^4 - 96*A*a^13*b*c^4)*x/(a^15*b^4 - 8*a^16*b^2*c + 16*a^17*c^2) + 3*(4*B*a^12*b^5*c - 6*A*a^11*b^6*c - 27*B*a^13*b^3*c^2 + 44*A*a^12*b^4*c^2 + 36*B*a^14*b*c^3 - 80*A*a^13*b^2*c^3 + 16*A*a^14*c^4)/(a^15*b^4 - 8*a^16*b^2*c + 16*a^17*c^2))*x + 3*(2*B*a^12*b^6 - 3*A*a^11*b^7 - 12*B*a^13*b^4*c + 20*A*a^12*b^5*c + 8*B*a^14*b^2*c^2 - 25*A*a^13*b^3*c^2 + 16*B*a^15*c^3 - 20*A*a^14*b*c^3)/(a^15*b^4 - 8*a^16*b^2*c + 16*a^17*c^2))*x + (7*B*a^13*b^5 - 10*A*a^12*b^6 - 50*B*a^14*b^3*c + 78*A*a^13*b^4*c + 80*B*a^15*b*c^2 - 162*A*a^14*b^2*c^2 + 56*A*a^15*c^3)/(a^15*b^4 - 8*a^16*b^2*c + 16*a^17*c^2))/(c*x^2 + b*x + a)^(3/2) - 5/4*(4*B*a*b - 7*A*b^2 + 4*A*a*c)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^4) + 1/4*(4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b - 11*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*sqrt(c) - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b*sqrt(c) - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b + 13*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c - 8*B*a^3*sqrt(c) + 24*A*a^2*b*sqrt(c))/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^2*a^4)","B",0
978,1,448,0,0.282311," ","integrate((e*x+d)/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(8 \, {\left(2 \, {\left(4 \, {\left(\frac{2 \, {\left(2 \, c^{5} d - b c^{4} e\right)} x}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}} + \frac{5 \, {\left(2 \, b c^{4} d - b^{2} c^{3} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(6 \, b^{2} c^{3} d + 8 \, a c^{4} d - 3 \, b^{3} c^{2} e - 4 \, a b c^{3} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(2 \, b^{3} c^{2} d + 24 \, a b c^{3} d - b^{4} c e - 12 \, a b^{2} c^{2} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{5 \, {\left(2 \, b^{4} c d - 48 \, a b^{2} c^{2} d - 96 \, a^{2} c^{3} d - b^{5} e + 24 \, a b^{3} c e + 48 \, a^{2} b c^{2} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{3 \, b^{5} d - 40 \, a b^{3} c d + 240 \, a^{2} b c^{2} d + 2 \, a b^{4} e - 48 \, a^{2} b^{2} c e - 96 \, a^{3} c^{2} e}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"-2/15*((8*(2*(4*(2*(2*c^5*d - b*c^4*e)*x/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3) + 5*(2*b*c^4*d - b^2*c^3*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(6*b^2*c^3*d + 8*a*c^4*d - 3*b^3*c^2*e - 4*a*b*c^3*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(2*b^3*c^2*d + 24*a*b*c^3*d - b^4*c*e - 12*a*b^2*c^2*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - 5*(2*b^4*c*d - 48*a*b^2*c^2*d - 96*a^2*c^3*d - b^5*e + 24*a*b^3*c*e + 48*a^2*b*c^2*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + (3*b^5*d - 40*a*b^3*c*d + 240*a^2*b*c^2*d + 2*a*b^4*e - 48*a^2*b^2*c*e - 96*a^3*c^2*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(c*x^2 + b*x + a)^(5/2)","B",0
979,1,788,0,0.320970," ","integrate((e*x+d)/(c*x^2+b*x+a)^(9/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(\frac{2 \, {\left(2 \, c^{7} d - b c^{6} e\right)} x}{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}} + \frac{7 \, {\left(2 \, b c^{6} d - b^{2} c^{5} e\right)}}{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)} x + \frac{7 \, {\left(10 \, b^{2} c^{5} d + 8 \, a c^{6} d - 5 \, b^{3} c^{4} e - 4 \, a b c^{5} e\right)}}{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)} x + \frac{35 \, {\left(2 \, b^{3} c^{4} d + 8 \, a b c^{5} d - b^{4} c^{3} e - 4 \, a b^{2} c^{4} e\right)}}{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)} x + \frac{35 \, {\left(2 \, b^{4} c^{3} d + 48 \, a b^{2} c^{4} d + 32 \, a^{2} c^{5} d - b^{5} c^{2} e - 24 \, a b^{3} c^{3} e - 16 \, a^{2} b c^{4} e\right)}}{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)} x - \frac{7 \, {\left(2 \, b^{5} c^{2} d - 80 \, a b^{3} c^{3} d - 480 \, a^{2} b c^{4} d - b^{6} c e + 40 \, a b^{4} c^{2} e + 240 \, a^{2} b^{2} c^{3} e\right)}}{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)} x + \frac{7 \, {\left(2 \, b^{6} c d - 40 \, a b^{4} c^{2} d + 480 \, a^{2} b^{2} c^{3} d + 640 \, a^{3} c^{4} d - b^{7} e + 20 \, a b^{5} c e - 240 \, a^{2} b^{3} c^{2} e - 320 \, a^{3} b c^{3} e\right)}}{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)} x - \frac{5 \, b^{7} d - 84 \, a b^{5} c d + 560 \, a^{2} b^{3} c^{2} d - 2240 \, a^{3} b c^{3} d + 2 \, a b^{6} e - 40 \, a^{2} b^{4} c e + 480 \, a^{3} b^{2} c^{2} e + 640 \, a^{4} c^{3} e}{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)}}{35 \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}}}"," ",0,"2/35*((4*(2*(8*(2*(4*(2*(2*c^7*d - b*c^6*e)*x/(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) + 7*(2*b*c^6*d - b^2*c^5*e)/(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))*x + 7*(10*b^2*c^5*d + 8*a*c^6*d - 5*b^3*c^4*e - 4*a*b*c^5*e)/(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))*x + 35*(2*b^3*c^4*d + 8*a*b*c^5*d - b^4*c^3*e - 4*a*b^2*c^4*e)/(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))*x + 35*(2*b^4*c^3*d + 48*a*b^2*c^4*d + 32*a^2*c^5*d - b^5*c^2*e - 24*a*b^3*c^3*e - 16*a^2*b*c^4*e)/(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))*x - 7*(2*b^5*c^2*d - 80*a*b^3*c^3*d - 480*a^2*b*c^4*d - b^6*c*e + 40*a*b^4*c^2*e + 240*a^2*b^2*c^3*e)/(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))*x + 7*(2*b^6*c*d - 40*a*b^4*c^2*d + 480*a^2*b^2*c^3*d + 640*a^3*c^4*d - b^7*e + 20*a*b^5*c*e - 240*a^2*b^3*c^2*e - 320*a^3*b*c^3*e)/(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))*x - (5*b^7*d - 84*a*b^5*c*d + 560*a^2*b^3*c^2*d - 2240*a^3*b*c^3*d + 2*a*b^6*e - 40*a^2*b^4*c*e + 480*a^3*b^2*c^2*e + 640*a^4*c^3*e)/(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))/(c*x^2 + b*x + a)^(7/2)","B",0
980,1,56,0,0.198300," ","integrate((1-x)/x/(x^2+3*x+1)^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x + \sqrt{x^{2} + 3 \, x + 1} + 1 \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} + 3 \, x + 1} - 1 \right|}\right) + \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} + 3 \, x + 1} - 3 \right|}\right)"," ",0,"-log(abs(-x + sqrt(x^2 + 3*x + 1) + 1)) + log(abs(-x + sqrt(x^2 + 3*x + 1) - 1)) + log(abs(-2*x + 2*sqrt(x^2 + 3*x + 1) - 3))","B",0
981,1,43,0,0.149617," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{15} \, B c x^{\frac{15}{2}} + \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{13} \, A c x^{\frac{13}{2}} + \frac{2}{11} \, B a x^{\frac{11}{2}} + \frac{2}{11} \, A b x^{\frac{11}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}}"," ",0,"2/15*B*c*x^(15/2) + 2/13*B*b*x^(13/2) + 2/13*A*c*x^(13/2) + 2/11*B*a*x^(11/2) + 2/11*A*b*x^(11/2) + 2/9*A*a*x^(9/2)","A",0
982,1,43,0,0.187665," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{13} \, B c x^{\frac{13}{2}} + \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{11} \, A c x^{\frac{11}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{9} \, A b x^{\frac{9}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}}"," ",0,"2/13*B*c*x^(13/2) + 2/11*B*b*x^(11/2) + 2/11*A*c*x^(11/2) + 2/9*B*a*x^(9/2) + 2/9*A*b*x^(9/2) + 2/7*A*a*x^(7/2)","A",0
983,1,43,0,0.151024," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{11} \, B c x^{\frac{11}{2}} + \frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{9} \, A c x^{\frac{9}{2}} + \frac{2}{7} \, B a x^{\frac{7}{2}} + \frac{2}{7} \, A b x^{\frac{7}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}}"," ",0,"2/11*B*c*x^(11/2) + 2/9*B*b*x^(9/2) + 2/9*A*c*x^(9/2) + 2/7*B*a*x^(7/2) + 2/7*A*b*x^(7/2) + 2/5*A*a*x^(5/2)","A",0
984,1,43,0,0.219277," ","integrate((B*x+A)*(c*x^2+b*x+a)*x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{7} \, A c x^{\frac{7}{2}} + \frac{2}{5} \, B a x^{\frac{5}{2}} + \frac{2}{5} \, A b x^{\frac{5}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}}"," ",0,"2/9*B*c*x^(9/2) + 2/7*B*b*x^(7/2) + 2/7*A*c*x^(7/2) + 2/5*B*a*x^(5/2) + 2/5*A*b*x^(5/2) + 2/3*A*a*x^(3/2)","A",0
985,1,43,0,0.155655," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(1/2),x, algorithm=""giac"")","\frac{2}{7} \, B c x^{\frac{7}{2}} + \frac{2}{5} \, B b x^{\frac{5}{2}} + \frac{2}{5} \, A c x^{\frac{5}{2}} + \frac{2}{3} \, B a x^{\frac{3}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}} + 2 \, A a \sqrt{x}"," ",0,"2/7*B*c*x^(7/2) + 2/5*B*b*x^(5/2) + 2/5*A*c*x^(5/2) + 2/3*B*a*x^(3/2) + 2/3*A*b*x^(3/2) + 2*A*a*sqrt(x)","A",0
986,1,43,0,0.150732," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, B c x^{\frac{5}{2}} + \frac{2}{3} \, B b x^{\frac{3}{2}} + \frac{2}{3} \, A c x^{\frac{3}{2}} + 2 \, B a \sqrt{x} + 2 \, A b \sqrt{x} - \frac{2 \, A a}{\sqrt{x}}"," ",0,"2/5*B*c*x^(5/2) + 2/3*B*b*x^(3/2) + 2/3*A*c*x^(3/2) + 2*B*a*sqrt(x) + 2*A*b*sqrt(x) - 2*A*a/sqrt(x)","A",0
987,1,41,0,0.152416," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, B c x^{\frac{3}{2}} + 2 \, B b \sqrt{x} + 2 \, A c \sqrt{x} - \frac{2 \, {\left(3 \, B a x + 3 \, A b x + A a\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*B*c*x^(3/2) + 2*B*b*sqrt(x) + 2*A*c*sqrt(x) - 2/3*(3*B*a*x + 3*A*b*x + A*a)/x^(3/2)","A",0
988,1,42,0,0.166376," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(7/2),x, algorithm=""giac"")","2 \, B c \sqrt{x} - \frac{2 \, {\left(15 \, B b x^{2} + 15 \, A c x^{2} + 5 \, B a x + 5 \, A b x + 3 \, A a\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2*B*c*sqrt(x) - 2/15*(15*B*b*x^2 + 15*A*c*x^2 + 5*B*a*x + 5*A*b*x + 3*A*a)/x^(5/2)","A",0
989,1,41,0,0.150275," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, B c x^{3} + 35 \, B b x^{2} + 35 \, A c x^{2} + 21 \, B a x + 21 \, A b x + 15 \, A a\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(105*B*c*x^3 + 35*B*b*x^2 + 35*A*c*x^2 + 21*B*a*x + 21*A*b*x + 15*A*a)/x^(7/2)","A",0
990,1,103,0,0.153484," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{19} \, B c^{2} x^{\frac{19}{2}} + \frac{4}{17} \, B b c x^{\frac{17}{2}} + \frac{2}{17} \, A c^{2} x^{\frac{17}{2}} + \frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{4}{15} \, B a c x^{\frac{15}{2}} + \frac{4}{15} \, A b c x^{\frac{15}{2}} + \frac{4}{13} \, B a b x^{\frac{13}{2}} + \frac{2}{13} \, A b^{2} x^{\frac{13}{2}} + \frac{4}{13} \, A a c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{4}{11} \, A a b x^{\frac{11}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}}"," ",0,"2/19*B*c^2*x^(19/2) + 4/17*B*b*c*x^(17/2) + 2/17*A*c^2*x^(17/2) + 2/15*B*b^2*x^(15/2) + 4/15*B*a*c*x^(15/2) + 4/15*A*b*c*x^(15/2) + 4/13*B*a*b*x^(13/2) + 2/13*A*b^2*x^(13/2) + 4/13*A*a*c*x^(13/2) + 2/11*B*a^2*x^(11/2) + 4/11*A*a*b*x^(11/2) + 2/9*A*a^2*x^(9/2)","A",0
991,1,103,0,0.163672," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{17} \, B c^{2} x^{\frac{17}{2}} + \frac{4}{15} \, B b c x^{\frac{15}{2}} + \frac{2}{15} \, A c^{2} x^{\frac{15}{2}} + \frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{4}{13} \, B a c x^{\frac{13}{2}} + \frac{4}{13} \, A b c x^{\frac{13}{2}} + \frac{4}{11} \, B a b x^{\frac{11}{2}} + \frac{2}{11} \, A b^{2} x^{\frac{11}{2}} + \frac{4}{11} \, A a c x^{\frac{11}{2}} + \frac{2}{9} \, B a^{2} x^{\frac{9}{2}} + \frac{4}{9} \, A a b x^{\frac{9}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}}"," ",0,"2/17*B*c^2*x^(17/2) + 4/15*B*b*c*x^(15/2) + 2/15*A*c^2*x^(15/2) + 2/13*B*b^2*x^(13/2) + 4/13*B*a*c*x^(13/2) + 4/13*A*b*c*x^(13/2) + 4/11*B*a*b*x^(11/2) + 2/11*A*b^2*x^(11/2) + 4/11*A*a*c*x^(11/2) + 2/9*B*a^2*x^(9/2) + 4/9*A*a*b*x^(9/2) + 2/7*A*a^2*x^(7/2)","A",0
992,1,103,0,0.157598," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{15} \, B c^{2} x^{\frac{15}{2}} + \frac{4}{13} \, B b c x^{\frac{13}{2}} + \frac{2}{13} \, A c^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B b^{2} x^{\frac{11}{2}} + \frac{4}{11} \, B a c x^{\frac{11}{2}} + \frac{4}{11} \, A b c x^{\frac{11}{2}} + \frac{4}{9} \, B a b x^{\frac{9}{2}} + \frac{2}{9} \, A b^{2} x^{\frac{9}{2}} + \frac{4}{9} \, A a c x^{\frac{9}{2}} + \frac{2}{7} \, B a^{2} x^{\frac{7}{2}} + \frac{4}{7} \, A a b x^{\frac{7}{2}} + \frac{2}{5} \, A a^{2} x^{\frac{5}{2}}"," ",0,"2/15*B*c^2*x^(15/2) + 4/13*B*b*c*x^(13/2) + 2/13*A*c^2*x^(13/2) + 2/11*B*b^2*x^(11/2) + 4/11*B*a*c*x^(11/2) + 4/11*A*b*c*x^(11/2) + 4/9*B*a*b*x^(9/2) + 2/9*A*b^2*x^(9/2) + 4/9*A*a*c*x^(9/2) + 2/7*B*a^2*x^(7/2) + 4/7*A*a*b*x^(7/2) + 2/5*A*a^2*x^(5/2)","A",0
993,1,103,0,0.158110," ","integrate((B*x+A)*(c*x^2+b*x+a)^2*x^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, B c^{2} x^{\frac{13}{2}} + \frac{4}{11} \, B b c x^{\frac{11}{2}} + \frac{2}{11} \, A c^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B b^{2} x^{\frac{9}{2}} + \frac{4}{9} \, B a c x^{\frac{9}{2}} + \frac{4}{9} \, A b c x^{\frac{9}{2}} + \frac{4}{7} \, B a b x^{\frac{7}{2}} + \frac{2}{7} \, A b^{2} x^{\frac{7}{2}} + \frac{4}{7} \, A a c x^{\frac{7}{2}} + \frac{2}{5} \, B a^{2} x^{\frac{5}{2}} + \frac{4}{5} \, A a b x^{\frac{5}{2}} + \frac{2}{3} \, A a^{2} x^{\frac{3}{2}}"," ",0,"2/13*B*c^2*x^(13/2) + 4/11*B*b*c*x^(11/2) + 2/11*A*c^2*x^(11/2) + 2/9*B*b^2*x^(9/2) + 4/9*B*a*c*x^(9/2) + 4/9*A*b*c*x^(9/2) + 4/7*B*a*b*x^(7/2) + 2/7*A*b^2*x^(7/2) + 4/7*A*a*c*x^(7/2) + 2/5*B*a^2*x^(5/2) + 4/5*A*a*b*x^(5/2) + 2/3*A*a^2*x^(3/2)","A",0
994,1,103,0,0.157006," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, B c^{2} x^{\frac{11}{2}} + \frac{4}{9} \, B b c x^{\frac{9}{2}} + \frac{2}{9} \, A c^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B b^{2} x^{\frac{7}{2}} + \frac{4}{7} \, B a c x^{\frac{7}{2}} + \frac{4}{7} \, A b c x^{\frac{7}{2}} + \frac{4}{5} \, B a b x^{\frac{5}{2}} + \frac{2}{5} \, A b^{2} x^{\frac{5}{2}} + \frac{4}{5} \, A a c x^{\frac{5}{2}} + \frac{2}{3} \, B a^{2} x^{\frac{3}{2}} + \frac{4}{3} \, A a b x^{\frac{3}{2}} + 2 \, A a^{2} \sqrt{x}"," ",0,"2/11*B*c^2*x^(11/2) + 4/9*B*b*c*x^(9/2) + 2/9*A*c^2*x^(9/2) + 2/7*B*b^2*x^(7/2) + 4/7*B*a*c*x^(7/2) + 4/7*A*b*c*x^(7/2) + 4/5*B*a*b*x^(5/2) + 2/5*A*b^2*x^(5/2) + 4/5*A*a*c*x^(5/2) + 2/3*B*a^2*x^(3/2) + 4/3*A*a*b*x^(3/2) + 2*A*a^2*sqrt(x)","A",0
995,1,103,0,0.159822," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{9} \, B c^{2} x^{\frac{9}{2}} + \frac{4}{7} \, B b c x^{\frac{7}{2}} + \frac{2}{7} \, A c^{2} x^{\frac{7}{2}} + \frac{2}{5} \, B b^{2} x^{\frac{5}{2}} + \frac{4}{5} \, B a c x^{\frac{5}{2}} + \frac{4}{5} \, A b c x^{\frac{5}{2}} + \frac{4}{3} \, B a b x^{\frac{3}{2}} + \frac{2}{3} \, A b^{2} x^{\frac{3}{2}} + \frac{4}{3} \, A a c x^{\frac{3}{2}} + 2 \, B a^{2} \sqrt{x} + 4 \, A a b \sqrt{x} - \frac{2 \, A a^{2}}{\sqrt{x}}"," ",0,"2/9*B*c^2*x^(9/2) + 4/7*B*b*c*x^(7/2) + 2/7*A*c^2*x^(7/2) + 2/5*B*b^2*x^(5/2) + 4/5*B*a*c*x^(5/2) + 4/5*A*b*c*x^(5/2) + 4/3*B*a*b*x^(3/2) + 2/3*A*b^2*x^(3/2) + 4/3*A*a*c*x^(3/2) + 2*B*a^2*sqrt(x) + 4*A*a*b*sqrt(x) - 2*A*a^2/sqrt(x)","A",0
996,1,101,0,0.167547," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, B c^{2} x^{\frac{7}{2}} + \frac{4}{5} \, B b c x^{\frac{5}{2}} + \frac{2}{5} \, A c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B b^{2} x^{\frac{3}{2}} + \frac{4}{3} \, B a c x^{\frac{3}{2}} + \frac{4}{3} \, A b c x^{\frac{3}{2}} + 4 \, B a b \sqrt{x} + 2 \, A b^{2} \sqrt{x} + 4 \, A a c \sqrt{x} - \frac{2 \, {\left(3 \, B a^{2} x + 6 \, A a b x + A a^{2}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/7*B*c^2*x^(7/2) + 4/5*B*b*c*x^(5/2) + 2/5*A*c^2*x^(5/2) + 2/3*B*b^2*x^(3/2) + 4/3*B*a*c*x^(3/2) + 4/3*A*b*c*x^(3/2) + 4*B*a*b*sqrt(x) + 2*A*b^2*sqrt(x) + 4*A*a*c*sqrt(x) - 2/3*(3*B*a^2*x + 6*A*a*b*x + A*a^2)/x^(3/2)","A",0
997,1,102,0,0.202691," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{5} \, B c^{2} x^{\frac{5}{2}} + \frac{4}{3} \, B b c x^{\frac{3}{2}} + \frac{2}{3} \, A c^{2} x^{\frac{3}{2}} + 2 \, B b^{2} \sqrt{x} + 4 \, B a c \sqrt{x} + 4 \, A b c \sqrt{x} - \frac{2 \, {\left(30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 30 \, A a c x^{2} + 5 \, B a^{2} x + 10 \, A a b x + 3 \, A a^{2}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/5*B*c^2*x^(5/2) + 4/3*B*b*c*x^(3/2) + 2/3*A*c^2*x^(3/2) + 2*B*b^2*sqrt(x) + 4*B*a*c*sqrt(x) + 4*A*b*c*sqrt(x) - 2/15*(30*B*a*b*x^2 + 15*A*b^2*x^2 + 30*A*a*c*x^2 + 5*B*a^2*x + 10*A*a*b*x + 3*A*a^2)/x^(5/2)","A",0
998,1,102,0,0.160546," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(9/2),x, algorithm=""giac"")","\frac{2}{3} \, B c^{2} x^{\frac{3}{2}} + 4 \, B b c \sqrt{x} + 2 \, A c^{2} \sqrt{x} - \frac{2 \, {\left(105 \, B b^{2} x^{3} + 210 \, B a c x^{3} + 210 \, A b c x^{3} + 70 \, B a b x^{2} + 35 \, A b^{2} x^{2} + 70 \, A a c x^{2} + 21 \, B a^{2} x + 42 \, A a b x + 15 \, A a^{2}\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"2/3*B*c^2*x^(3/2) + 4*B*b*c*sqrt(x) + 2*A*c^2*sqrt(x) - 2/105*(105*B*b^2*x^3 + 210*B*a*c*x^3 + 210*A*b*c*x^3 + 70*B*a*b*x^2 + 35*A*b^2*x^2 + 70*A*a*c*x^2 + 21*B*a^2*x + 42*A*a*b*x + 15*A*a^2)/x^(7/2)","A",0
999,1,193,0,0.226481," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{23} \, B c^{3} x^{\frac{23}{2}} + \frac{2}{7} \, B b c^{2} x^{\frac{21}{2}} + \frac{2}{21} \, A c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B b^{2} c x^{\frac{19}{2}} + \frac{6}{19} \, B a c^{2} x^{\frac{19}{2}} + \frac{6}{19} \, A b c^{2} x^{\frac{19}{2}} + \frac{2}{17} \, B b^{3} x^{\frac{17}{2}} + \frac{12}{17} \, B a b c x^{\frac{17}{2}} + \frac{6}{17} \, A b^{2} c x^{\frac{17}{2}} + \frac{6}{17} \, A a c^{2} x^{\frac{17}{2}} + \frac{2}{5} \, B a b^{2} x^{\frac{15}{2}} + \frac{2}{15} \, A b^{3} x^{\frac{15}{2}} + \frac{2}{5} \, B a^{2} c x^{\frac{15}{2}} + \frac{4}{5} \, A a b c x^{\frac{15}{2}} + \frac{6}{13} \, B a^{2} b x^{\frac{13}{2}} + \frac{6}{13} \, A a b^{2} x^{\frac{13}{2}} + \frac{6}{13} \, A a^{2} c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} + \frac{6}{11} \, A a^{2} b x^{\frac{11}{2}} + \frac{2}{9} \, A a^{3} x^{\frac{9}{2}}"," ",0,"2/23*B*c^3*x^(23/2) + 2/7*B*b*c^2*x^(21/2) + 2/21*A*c^3*x^(21/2) + 6/19*B*b^2*c*x^(19/2) + 6/19*B*a*c^2*x^(19/2) + 6/19*A*b*c^2*x^(19/2) + 2/17*B*b^3*x^(17/2) + 12/17*B*a*b*c*x^(17/2) + 6/17*A*b^2*c*x^(17/2) + 6/17*A*a*c^2*x^(17/2) + 2/5*B*a*b^2*x^(15/2) + 2/15*A*b^3*x^(15/2) + 2/5*B*a^2*c*x^(15/2) + 4/5*A*a*b*c*x^(15/2) + 6/13*B*a^2*b*x^(13/2) + 6/13*A*a*b^2*x^(13/2) + 6/13*A*a^2*c*x^(13/2) + 2/11*B*a^3*x^(11/2) + 6/11*A*a^2*b*x^(11/2) + 2/9*A*a^3*x^(9/2)","A",0
1000,1,193,0,0.204927," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{21} \, B c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B b c^{2} x^{\frac{19}{2}} + \frac{2}{19} \, A c^{3} x^{\frac{19}{2}} + \frac{6}{17} \, B b^{2} c x^{\frac{17}{2}} + \frac{6}{17} \, B a c^{2} x^{\frac{17}{2}} + \frac{6}{17} \, A b c^{2} x^{\frac{17}{2}} + \frac{2}{15} \, B b^{3} x^{\frac{15}{2}} + \frac{4}{5} \, B a b c x^{\frac{15}{2}} + \frac{2}{5} \, A b^{2} c x^{\frac{15}{2}} + \frac{2}{5} \, A a c^{2} x^{\frac{15}{2}} + \frac{6}{13} \, B a b^{2} x^{\frac{13}{2}} + \frac{2}{13} \, A b^{3} x^{\frac{13}{2}} + \frac{6}{13} \, B a^{2} c x^{\frac{13}{2}} + \frac{12}{13} \, A a b c x^{\frac{13}{2}} + \frac{6}{11} \, B a^{2} b x^{\frac{11}{2}} + \frac{6}{11} \, A a b^{2} x^{\frac{11}{2}} + \frac{6}{11} \, A a^{2} c x^{\frac{11}{2}} + \frac{2}{9} \, B a^{3} x^{\frac{9}{2}} + \frac{2}{3} \, A a^{2} b x^{\frac{9}{2}} + \frac{2}{7} \, A a^{3} x^{\frac{7}{2}}"," ",0,"2/21*B*c^3*x^(21/2) + 6/19*B*b*c^2*x^(19/2) + 2/19*A*c^3*x^(19/2) + 6/17*B*b^2*c*x^(17/2) + 6/17*B*a*c^2*x^(17/2) + 6/17*A*b*c^2*x^(17/2) + 2/15*B*b^3*x^(15/2) + 4/5*B*a*b*c*x^(15/2) + 2/5*A*b^2*c*x^(15/2) + 2/5*A*a*c^2*x^(15/2) + 6/13*B*a*b^2*x^(13/2) + 2/13*A*b^3*x^(13/2) + 6/13*B*a^2*c*x^(13/2) + 12/13*A*a*b*c*x^(13/2) + 6/11*B*a^2*b*x^(11/2) + 6/11*A*a*b^2*x^(11/2) + 6/11*A*a^2*c*x^(11/2) + 2/9*B*a^3*x^(9/2) + 2/3*A*a^2*b*x^(9/2) + 2/7*A*a^3*x^(7/2)","A",0
1001,1,193,0,0.184853," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{19} \, B c^{3} x^{\frac{19}{2}} + \frac{6}{17} \, B b c^{2} x^{\frac{17}{2}} + \frac{2}{17} \, A c^{3} x^{\frac{17}{2}} + \frac{2}{5} \, B b^{2} c x^{\frac{15}{2}} + \frac{2}{5} \, B a c^{2} x^{\frac{15}{2}} + \frac{2}{5} \, A b c^{2} x^{\frac{15}{2}} + \frac{2}{13} \, B b^{3} x^{\frac{13}{2}} + \frac{12}{13} \, B a b c x^{\frac{13}{2}} + \frac{6}{13} \, A b^{2} c x^{\frac{13}{2}} + \frac{6}{13} \, A a c^{2} x^{\frac{13}{2}} + \frac{6}{11} \, B a b^{2} x^{\frac{11}{2}} + \frac{2}{11} \, A b^{3} x^{\frac{11}{2}} + \frac{6}{11} \, B a^{2} c x^{\frac{11}{2}} + \frac{12}{11} \, A a b c x^{\frac{11}{2}} + \frac{2}{3} \, B a^{2} b x^{\frac{9}{2}} + \frac{2}{3} \, A a b^{2} x^{\frac{9}{2}} + \frac{2}{3} \, A a^{2} c x^{\frac{9}{2}} + \frac{2}{7} \, B a^{3} x^{\frac{7}{2}} + \frac{6}{7} \, A a^{2} b x^{\frac{7}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}}"," ",0,"2/19*B*c^3*x^(19/2) + 6/17*B*b*c^2*x^(17/2) + 2/17*A*c^3*x^(17/2) + 2/5*B*b^2*c*x^(15/2) + 2/5*B*a*c^2*x^(15/2) + 2/5*A*b*c^2*x^(15/2) + 2/13*B*b^3*x^(13/2) + 12/13*B*a*b*c*x^(13/2) + 6/13*A*b^2*c*x^(13/2) + 6/13*A*a*c^2*x^(13/2) + 6/11*B*a*b^2*x^(11/2) + 2/11*A*b^3*x^(11/2) + 6/11*B*a^2*c*x^(11/2) + 12/11*A*a*b*c*x^(11/2) + 2/3*B*a^2*b*x^(9/2) + 2/3*A*a*b^2*x^(9/2) + 2/3*A*a^2*c*x^(9/2) + 2/7*B*a^3*x^(7/2) + 6/7*A*a^2*b*x^(7/2) + 2/5*A*a^3*x^(5/2)","A",0
1002,1,193,0,0.162898," ","integrate((B*x+A)*(c*x^2+b*x+a)^3*x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, B c^{3} x^{\frac{17}{2}} + \frac{2}{5} \, B b c^{2} x^{\frac{15}{2}} + \frac{2}{15} \, A c^{3} x^{\frac{15}{2}} + \frac{6}{13} \, B b^{2} c x^{\frac{13}{2}} + \frac{6}{13} \, B a c^{2} x^{\frac{13}{2}} + \frac{6}{13} \, A b c^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B b^{3} x^{\frac{11}{2}} + \frac{12}{11} \, B a b c x^{\frac{11}{2}} + \frac{6}{11} \, A b^{2} c x^{\frac{11}{2}} + \frac{6}{11} \, A a c^{2} x^{\frac{11}{2}} + \frac{2}{3} \, B a b^{2} x^{\frac{9}{2}} + \frac{2}{9} \, A b^{3} x^{\frac{9}{2}} + \frac{2}{3} \, B a^{2} c x^{\frac{9}{2}} + \frac{4}{3} \, A a b c x^{\frac{9}{2}} + \frac{6}{7} \, B a^{2} b x^{\frac{7}{2}} + \frac{6}{7} \, A a b^{2} x^{\frac{7}{2}} + \frac{6}{7} \, A a^{2} c x^{\frac{7}{2}} + \frac{2}{5} \, B a^{3} x^{\frac{5}{2}} + \frac{6}{5} \, A a^{2} b x^{\frac{5}{2}} + \frac{2}{3} \, A a^{3} x^{\frac{3}{2}}"," ",0,"2/17*B*c^3*x^(17/2) + 2/5*B*b*c^2*x^(15/2) + 2/15*A*c^3*x^(15/2) + 6/13*B*b^2*c*x^(13/2) + 6/13*B*a*c^2*x^(13/2) + 6/13*A*b*c^2*x^(13/2) + 2/11*B*b^3*x^(11/2) + 12/11*B*a*b*c*x^(11/2) + 6/11*A*b^2*c*x^(11/2) + 6/11*A*a*c^2*x^(11/2) + 2/3*B*a*b^2*x^(9/2) + 2/9*A*b^3*x^(9/2) + 2/3*B*a^2*c*x^(9/2) + 4/3*A*a*b*c*x^(9/2) + 6/7*B*a^2*b*x^(7/2) + 6/7*A*a*b^2*x^(7/2) + 6/7*A*a^2*c*x^(7/2) + 2/5*B*a^3*x^(5/2) + 6/5*A*a^2*b*x^(5/2) + 2/3*A*a^3*x^(3/2)","A",0
1003,1,193,0,0.165392," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, B c^{3} x^{\frac{15}{2}} + \frac{6}{13} \, B b c^{2} x^{\frac{13}{2}} + \frac{2}{13} \, A c^{3} x^{\frac{13}{2}} + \frac{6}{11} \, B b^{2} c x^{\frac{11}{2}} + \frac{6}{11} \, B a c^{2} x^{\frac{11}{2}} + \frac{6}{11} \, A b c^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B b^{3} x^{\frac{9}{2}} + \frac{4}{3} \, B a b c x^{\frac{9}{2}} + \frac{2}{3} \, A b^{2} c x^{\frac{9}{2}} + \frac{2}{3} \, A a c^{2} x^{\frac{9}{2}} + \frac{6}{7} \, B a b^{2} x^{\frac{7}{2}} + \frac{2}{7} \, A b^{3} x^{\frac{7}{2}} + \frac{6}{7} \, B a^{2} c x^{\frac{7}{2}} + \frac{12}{7} \, A a b c x^{\frac{7}{2}} + \frac{6}{5} \, B a^{2} b x^{\frac{5}{2}} + \frac{6}{5} \, A a b^{2} x^{\frac{5}{2}} + \frac{6}{5} \, A a^{2} c x^{\frac{5}{2}} + \frac{2}{3} \, B a^{3} x^{\frac{3}{2}} + 2 \, A a^{2} b x^{\frac{3}{2}} + 2 \, A a^{3} \sqrt{x}"," ",0,"2/15*B*c^3*x^(15/2) + 6/13*B*b*c^2*x^(13/2) + 2/13*A*c^3*x^(13/2) + 6/11*B*b^2*c*x^(11/2) + 6/11*B*a*c^2*x^(11/2) + 6/11*A*b*c^2*x^(11/2) + 2/9*B*b^3*x^(9/2) + 4/3*B*a*b*c*x^(9/2) + 2/3*A*b^2*c*x^(9/2) + 2/3*A*a*c^2*x^(9/2) + 6/7*B*a*b^2*x^(7/2) + 2/7*A*b^3*x^(7/2) + 6/7*B*a^2*c*x^(7/2) + 12/7*A*a*b*c*x^(7/2) + 6/5*B*a^2*b*x^(5/2) + 6/5*A*a*b^2*x^(5/2) + 6/5*A*a^2*c*x^(5/2) + 2/3*B*a^3*x^(3/2) + 2*A*a^2*b*x^(3/2) + 2*A*a^3*sqrt(x)","A",0
1004,1,193,0,0.170482," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{13} \, B c^{3} x^{\frac{13}{2}} + \frac{6}{11} \, B b c^{2} x^{\frac{11}{2}} + \frac{2}{11} \, A c^{3} x^{\frac{11}{2}} + \frac{2}{3} \, B b^{2} c x^{\frac{9}{2}} + \frac{2}{3} \, B a c^{2} x^{\frac{9}{2}} + \frac{2}{3} \, A b c^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B b^{3} x^{\frac{7}{2}} + \frac{12}{7} \, B a b c x^{\frac{7}{2}} + \frac{6}{7} \, A b^{2} c x^{\frac{7}{2}} + \frac{6}{7} \, A a c^{2} x^{\frac{7}{2}} + \frac{6}{5} \, B a b^{2} x^{\frac{5}{2}} + \frac{2}{5} \, A b^{3} x^{\frac{5}{2}} + \frac{6}{5} \, B a^{2} c x^{\frac{5}{2}} + \frac{12}{5} \, A a b c x^{\frac{5}{2}} + 2 \, B a^{2} b x^{\frac{3}{2}} + 2 \, A a b^{2} x^{\frac{3}{2}} + 2 \, A a^{2} c x^{\frac{3}{2}} + 2 \, B a^{3} \sqrt{x} + 6 \, A a^{2} b \sqrt{x} - \frac{2 \, A a^{3}}{\sqrt{x}}"," ",0,"2/13*B*c^3*x^(13/2) + 6/11*B*b*c^2*x^(11/2) + 2/11*A*c^3*x^(11/2) + 2/3*B*b^2*c*x^(9/2) + 2/3*B*a*c^2*x^(9/2) + 2/3*A*b*c^2*x^(9/2) + 2/7*B*b^3*x^(7/2) + 12/7*B*a*b*c*x^(7/2) + 6/7*A*b^2*c*x^(7/2) + 6/7*A*a*c^2*x^(7/2) + 6/5*B*a*b^2*x^(5/2) + 2/5*A*b^3*x^(5/2) + 6/5*B*a^2*c*x^(5/2) + 12/5*A*a*b*c*x^(5/2) + 2*B*a^2*b*x^(3/2) + 2*A*a*b^2*x^(3/2) + 2*A*a^2*c*x^(3/2) + 2*B*a^3*sqrt(x) + 6*A*a^2*b*sqrt(x) - 2*A*a^3/sqrt(x)","A",0
1005,1,191,0,0.179163," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{11} \, B c^{3} x^{\frac{11}{2}} + \frac{2}{3} \, B b c^{2} x^{\frac{9}{2}} + \frac{2}{9} \, A c^{3} x^{\frac{9}{2}} + \frac{6}{7} \, B b^{2} c x^{\frac{7}{2}} + \frac{6}{7} \, B a c^{2} x^{\frac{7}{2}} + \frac{6}{7} \, A b c^{2} x^{\frac{7}{2}} + \frac{2}{5} \, B b^{3} x^{\frac{5}{2}} + \frac{12}{5} \, B a b c x^{\frac{5}{2}} + \frac{6}{5} \, A b^{2} c x^{\frac{5}{2}} + \frac{6}{5} \, A a c^{2} x^{\frac{5}{2}} + 2 \, B a b^{2} x^{\frac{3}{2}} + \frac{2}{3} \, A b^{3} x^{\frac{3}{2}} + 2 \, B a^{2} c x^{\frac{3}{2}} + 4 \, A a b c x^{\frac{3}{2}} + 6 \, B a^{2} b \sqrt{x} + 6 \, A a b^{2} \sqrt{x} + 6 \, A a^{2} c \sqrt{x} - \frac{2 \, {\left(3 \, B a^{3} x + 9 \, A a^{2} b x + A a^{3}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/11*B*c^3*x^(11/2) + 2/3*B*b*c^2*x^(9/2) + 2/9*A*c^3*x^(9/2) + 6/7*B*b^2*c*x^(7/2) + 6/7*B*a*c^2*x^(7/2) + 6/7*A*b*c^2*x^(7/2) + 2/5*B*b^3*x^(5/2) + 12/5*B*a*b*c*x^(5/2) + 6/5*A*b^2*c*x^(5/2) + 6/5*A*a*c^2*x^(5/2) + 2*B*a*b^2*x^(3/2) + 2/3*A*b^3*x^(3/2) + 2*B*a^2*c*x^(3/2) + 4*A*a*b*c*x^(3/2) + 6*B*a^2*b*sqrt(x) + 6*A*a*b^2*sqrt(x) + 6*A*a^2*c*sqrt(x) - 2/3*(3*B*a^3*x + 9*A*a^2*b*x + A*a^3)/x^(3/2)","A",0
1006,1,192,0,0.197682," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{9} \, B c^{3} x^{\frac{9}{2}} + \frac{6}{7} \, B b c^{2} x^{\frac{7}{2}} + \frac{2}{7} \, A c^{3} x^{\frac{7}{2}} + \frac{6}{5} \, B b^{2} c x^{\frac{5}{2}} + \frac{6}{5} \, B a c^{2} x^{\frac{5}{2}} + \frac{6}{5} \, A b c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B b^{3} x^{\frac{3}{2}} + 4 \, B a b c x^{\frac{3}{2}} + 2 \, A b^{2} c x^{\frac{3}{2}} + 2 \, A a c^{2} x^{\frac{3}{2}} + 6 \, B a b^{2} \sqrt{x} + 2 \, A b^{3} \sqrt{x} + 6 \, B a^{2} c \sqrt{x} + 12 \, A a b c \sqrt{x} - \frac{2 \, {\left(45 \, B a^{2} b x^{2} + 45 \, A a b^{2} x^{2} + 45 \, A a^{2} c x^{2} + 5 \, B a^{3} x + 15 \, A a^{2} b x + 3 \, A a^{3}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/9*B*c^3*x^(9/2) + 6/7*B*b*c^2*x^(7/2) + 2/7*A*c^3*x^(7/2) + 6/5*B*b^2*c*x^(5/2) + 6/5*B*a*c^2*x^(5/2) + 6/5*A*b*c^2*x^(5/2) + 2/3*B*b^3*x^(3/2) + 4*B*a*b*c*x^(3/2) + 2*A*b^2*c*x^(3/2) + 2*A*a*c^2*x^(3/2) + 6*B*a*b^2*sqrt(x) + 2*A*b^3*sqrt(x) + 6*B*a^2*c*sqrt(x) + 12*A*a*b*c*sqrt(x) - 2/15*(45*B*a^2*b*x^2 + 45*A*a*b^2*x^2 + 45*A*a^2*c*x^2 + 5*B*a^3*x + 15*A*a^2*b*x + 3*A*a^3)/x^(5/2)","A",0
1007,1,192,0,0.170525," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(9/2),x, algorithm=""giac"")","\frac{2}{7} \, B c^{3} x^{\frac{7}{2}} + \frac{6}{5} \, B b c^{2} x^{\frac{5}{2}} + \frac{2}{5} \, A c^{3} x^{\frac{5}{2}} + 2 \, B b^{2} c x^{\frac{3}{2}} + 2 \, B a c^{2} x^{\frac{3}{2}} + 2 \, A b c^{2} x^{\frac{3}{2}} + 2 \, B b^{3} \sqrt{x} + 12 \, B a b c \sqrt{x} + 6 \, A b^{2} c \sqrt{x} + 6 \, A a c^{2} \sqrt{x} - \frac{2 \, {\left(105 \, B a b^{2} x^{3} + 35 \, A b^{3} x^{3} + 105 \, B a^{2} c x^{3} + 210 \, A a b c x^{3} + 35 \, B a^{2} b x^{2} + 35 \, A a b^{2} x^{2} + 35 \, A a^{2} c x^{2} + 7 \, B a^{3} x + 21 \, A a^{2} b x + 5 \, A a^{3}\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"2/7*B*c^3*x^(7/2) + 6/5*B*b*c^2*x^(5/2) + 2/5*A*c^3*x^(5/2) + 2*B*b^2*c*x^(3/2) + 2*B*a*c^2*x^(3/2) + 2*A*b*c^2*x^(3/2) + 2*B*b^3*sqrt(x) + 12*B*a*b*c*sqrt(x) + 6*A*b^2*c*sqrt(x) + 6*A*a*c^2*sqrt(x) - 2/35*(105*B*a*b^2*x^3 + 35*A*b^3*x^3 + 105*B*a^2*c*x^3 + 210*A*a*b*c*x^3 + 35*B*a^2*b*x^2 + 35*A*a*b^2*x^2 + 35*A*a^2*c*x^2 + 7*B*a^3*x + 21*A*a^2*b*x + 5*A*a^3)/x^(7/2)","A",0
1008,1,192,0,0.168175," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(11/2),x, algorithm=""giac"")","\frac{2}{5} \, B c^{3} x^{\frac{5}{2}} + 2 \, B b c^{2} x^{\frac{3}{2}} + \frac{2}{3} \, A c^{3} x^{\frac{3}{2}} + 6 \, B b^{2} c \sqrt{x} + 6 \, B a c^{2} \sqrt{x} + 6 \, A b c^{2} \sqrt{x} - \frac{2 \, {\left(315 \, B b^{3} x^{4} + 1890 \, B a b c x^{4} + 945 \, A b^{2} c x^{4} + 945 \, A a c^{2} x^{4} + 315 \, B a b^{2} x^{3} + 105 \, A b^{3} x^{3} + 315 \, B a^{2} c x^{3} + 630 \, A a b c x^{3} + 189 \, B a^{2} b x^{2} + 189 \, A a b^{2} x^{2} + 189 \, A a^{2} c x^{2} + 45 \, B a^{3} x + 135 \, A a^{2} b x + 35 \, A a^{3}\right)}}{315 \, x^{\frac{9}{2}}}"," ",0,"2/5*B*c^3*x^(5/2) + 2*B*b*c^2*x^(3/2) + 2/3*A*c^3*x^(3/2) + 6*B*b^2*c*sqrt(x) + 6*B*a*c^2*sqrt(x) + 6*A*b*c^2*sqrt(x) - 2/315*(315*B*b^3*x^4 + 1890*B*a*b*c*x^4 + 945*A*b^2*c*x^4 + 945*A*a*c^2*x^4 + 315*B*a*b^2*x^3 + 105*A*b^3*x^3 + 315*B*a^2*c*x^3 + 630*A*a*b*c*x^3 + 189*B*a^2*b*x^2 + 189*A*a*b^2*x^2 + 189*A*a^2*c*x^2 + 45*B*a^3*x + 135*A*a^2*b*x + 35*A*a^3)/x^(9/2)","A",0
1009,1,5319,0,1.359269," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left({\left(2 \, b^{6} c^{3} - 18 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 32 \, a^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A c^{2} - {\left(2 \, b^{7} c^{2} - 20 \, a b^{5} c^{3} + 64 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, a b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 16 \, a^{2} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + 32 \, a^{3} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} A {\left| c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, a b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 18 \, a^{2} b^{4} c^{4} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 48 \, a^{3} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 32 \, a^{4} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} B {\left| c \right|} - {\left(2 \, b^{6} c^{5} - 14 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6}\right)} A + {\left(2 \, b^{7} c^{4} - 16 \, a b^{5} c^{5} + 36 \, a^{2} b^{3} c^{6} - 16 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b c^{5} + \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{4 \, {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} c^{2}} - \frac{{\left({\left(2 \, b^{6} c^{3} - 18 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 32 \, a^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A c^{2} - {\left(2 \, b^{7} c^{2} - 20 \, a b^{5} c^{3} + 64 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 2 \, a b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 16 \, a^{2} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 32 \, a^{3} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} A {\left| c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 2 \, a b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 18 \, a^{2} b^{4} c^{4} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 48 \, a^{3} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 32 \, a^{4} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} B {\left| c \right|} - {\left(2 \, b^{6} c^{5} - 14 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6}\right)} A + {\left(2 \, b^{7} c^{4} - 16 \, a b^{5} c^{5} + 36 \, a^{2} b^{3} c^{6} - 16 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b c^{5} - \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{4 \, {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} c^{2}} + \frac{2 \, {\left(3 \, B c^{4} x^{\frac{5}{2}} - 5 \, B b c^{3} x^{\frac{3}{2}} + 5 \, A c^{4} x^{\frac{3}{2}} + 15 \, B b^{2} c^{2} \sqrt{x} - 15 \, B a c^{3} \sqrt{x} - 15 \, A b c^{3} \sqrt{x}\right)}}{15 \, c^{5}}"," ",0,"1/4*((2*b^6*c^3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*A*c^2 - (2*b^7*c^2 - 20*a*b^5*c^3 + 64*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a^2*b*c^4)*B*c^2 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*a*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 16*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + 32*a^3*b*c^6 - 2*(b^2 - 4*a*c)*a*b^3*c^4 + 8*(b^2 - 4*a*c)*a^2*b*c^5)*A*abs(c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*a*b^6*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 18*a^2*b^4*c^4 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 32*a^4*c^6 - 2*(b^2 - 4*a*c)*a*b^4*c^3 + 10*(b^2 - 4*a*c)*a^2*b^2*c^4 - 8*(b^2 - 4*a*c)*a^3*c^5)*B*abs(c) - (2*b^6*c^5 - 14*a*b^4*c^6 + 24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 - 4*a*c)*a*b^2*c^6)*A + (2*b^7*c^4 - 16*a*b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b*c^5 + sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^7 - 4*a^2*c^8)*c^2) - 1/4*((2*b^6*c^3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*A*c^2 - (2*b^7*c^2 - 20*a*b^5*c^3 + 64*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a^2*b*c^4)*B*c^2 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 2*a*b^5*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 16*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 32*a^3*b*c^6 + 2*(b^2 - 4*a*c)*a*b^3*c^4 - 8*(b^2 - 4*a*c)*a^2*b*c^5)*A*abs(c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 2*a*b^6*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 18*a^2*b^4*c^4 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 32*a^4*c^6 + 2*(b^2 - 4*a*c)*a*b^4*c^3 - 10*(b^2 - 4*a*c)*a^2*b^2*c^4 + 8*(b^2 - 4*a*c)*a^3*c^5)*B*abs(c) - (2*b^6*c^5 - 14*a*b^4*c^6 + 24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 - 4*a*c)*a*b^2*c^6)*A + (2*b^7*c^4 - 16*a*b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b*c^5 - sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^7 - 4*a^2*c^8)*c^2) + 2/15*(3*B*c^4*x^(5/2) - 5*B*b*c^3*x^(3/2) + 5*A*c^4*x^(3/2) + 15*B*b^2*c^2*sqrt(x) - 15*B*a*c^3*sqrt(x) - 15*A*b*c^3*sqrt(x))/c^5","B",0
1010,1,4399,0,1.376354," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{{\left({\left(2 \, b^{5} c^{3} - 16 \, a b^{3} c^{4} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A c^{2} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 32 \, a^{3} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A {\left| c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 32 \, a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B {\left| c \right|} - {\left(2 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} A + {\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b c^{3} + \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{4 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} + \frac{{\left({\left(2 \, b^{5} c^{3} - 16 \, a b^{3} c^{4} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A c^{2} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 32 \, a^{3} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A {\left| c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 32 \, a^{3} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B {\left| c \right|} - {\left(2 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} A + {\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b c^{3} - \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{4 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} + \frac{2 \, {\left(B c^{2} x^{\frac{3}{2}} - 3 \, B b c \sqrt{x} + 3 \, A c^{2} \sqrt{x}\right)}}{3 \, c^{3}}"," ",0,"-1/4*((2*b^5*c^3 - 16*a*b^3*c^4 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*A*c^2 - (2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*B*c^2 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 2*a*b^4*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 16*a^2*b^2*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 32*a^3*c^6 - 2*(b^2 - 4*a*c)*a*b^2*c^4 + 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 32*a^3*b*c^5 - 2*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*B*abs(c) - (2*b^5*c^5 - 12*a*b^3*c^6 + 16*a^2*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 2*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*A + (2*b^6*c^4 - 14*a*b^4*c^5 + 24*a^2*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b*c^3 + sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 1/4*((2*b^5*c^3 - 16*a*b^3*c^4 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*A*c^2 - (2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*B*c^2 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 2*a*b^4*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 16*a^2*b^2*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 - 32*a^3*c^6 + 2*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 32*a^3*b*c^5 + 2*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*B*abs(c) - (2*b^5*c^5 - 12*a*b^3*c^6 + 16*a^2*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 2*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*A + (2*b^6*c^4 - 14*a*b^4*c^5 + 24*a^2*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b*c^3 - sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 2/3*(B*c^2*x^(3/2) - 3*B*b*c*sqrt(x) + 3*A*c^2*sqrt(x))/c^3","B",0
1011,1,3186,0,1.176797," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{c} + \frac{{\left({\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} A c^{2} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} B c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B {\left| c \right|} - {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} A + {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{4 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}} - \frac{{\left({\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} A c^{2} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} B c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B {\left| c \right|} - {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} A + {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{4 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}}"," ",0,"2*B*sqrt(x)/c + 1/4*((2*b^4*c^3 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*A*c^2 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*B*c^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 32*a^3*c^5 - 2*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*B*abs(c) - (2*b^4*c^5 - 8*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5)*A + (2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/4*((2*b^4*c^3 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*A*c^2 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*B*c^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 32*a^3*c^5 + 2*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*B*abs(c) - (2*b^4*c^5 - 8*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5)*A + (2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2)","B",0
1012,1,1404,0,0.952130," ","integrate((B*x+A)/(c*x^2+b*x+a)/x^(1/2),x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} A - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} A + 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"1/2*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 + 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*A - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/2*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*A + 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
1013,1,2809,0,1.231045," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{2 \, A}{a \sqrt{x}} - \frac{{\left({\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} A a^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} A {\left| a \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 16 \, a^{3} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 32 \, a^{4} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2}\right)} B {\left| a \right|} + {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} A - 2 \, {\left(2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a b + \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left({\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} A a^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} A {\left| a \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, a^{3} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, a^{4} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2}\right)} B {\left| a \right|} + {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} A - 2 \, {\left(2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a b - \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| a \right|} {\left| c \right|}}"," ",0,"-2*A/(a*sqrt(x)) - 1/4*((2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*A*a^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2)*A*abs(a) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*a^2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 16*a^3*b^2*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 32*a^4*c^3 + 2*(b^2 - 4*a*c)*a^2*b^2*c - 8*(b^2 - 4*a*c)*a^3*c^2)*B*abs(a) + (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*A - 2*(2*a^3*b^3*c^2 - 8*a^4*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a*b + sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(a)*abs(c)) + 1/4*((2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*A*a^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2)*A*abs(a) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*a^2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 16*a^3*b^2*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*a^4*c^3 - 2*(b^2 - 4*a*c)*a^2*b^2*c + 8*(b^2 - 4*a*c)*a^3*c^2)*B*abs(a) + (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*A - 2*(2*a^3*b^3*c^2 - 8*a^4*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a*b - sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(a)*abs(c))","B",0
1014,1,2874,0,1.289534," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 18 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 48 \, a^{2} b^{2} c^{3} - 14 \, a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 32 \, a^{3} c^{4} + 24 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} + 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} - 12 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{2} b + \sqrt{a^{4} b^{2} - 4 \, a^{5} c}}{a^{2} c}}}\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c \right|}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 18 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 48 \, a^{2} b^{2} c^{3} - 14 \, a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 32 \, a^{3} c^{4} + 24 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} + 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} - 12 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{2} b - \sqrt{a^{4} b^{2} - 4 \, a^{5} c}}{a^{2} c}}}\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c \right|}} - \frac{2 \, {\left(3 \, B a x - 3 \, A b x + A a\right)}}{3 \, a^{2} x^{\frac{3}{2}}}"," ",0,"1/2*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 2*b^6*c + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 18*a*b^4*c^2 + 2*b^5*c^2 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 48*a^2*b^2*c^3 - 14*a*b^3*c^3 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 32*a^3*c^4 + 24*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*(b^2 - 4*a*c)*b^4*c - 10*(b^2 - 4*a*c)*a*b^2*c^2 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3 + 6*(b^2 - 4*a*c)*a*b*c^3)*A - (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 16*a^2*b^3*c^2 + 2*a*b^4*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 - 12*a^2*b^2*c^3 + 16*a^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 4*(b^2 - 4*a*c)*a^2*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^2*b + sqrt(a^4*b^2 - 4*a^5*c))/(a^2*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c)) + 1/2*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 2*b^6*c + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 18*a*b^4*c^2 + 2*b^5*c^2 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 48*a^2*b^2*c^3 - 14*a*b^3*c^3 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 32*a^3*c^4 + 24*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^4*c + 10*(b^2 - 4*a*c)*a*b^2*c^2 - 2*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3 + 6*(b^2 - 4*a*c)*a*b*c^3)*A - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 16*a^2*b^3*c^2 + 2*a*b^4*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 12*a^2*b^2*c^3 + 16*a^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 4*(b^2 - 4*a*c)*a^2*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^2*b - sqrt(a^4*b^2 - 4*a^5*c))/(a^2*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c)) - 2/3*(3*B*a*x - 3*A*b*x + A*a)/(a^2*x^(3/2))","B",0
1015,1,5013,0,2.146583," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{{\left({\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} A a^{2} - {\left(2 \, a b^{5} c^{2} - 16 \, a^{2} b^{3} c^{3} + 32 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} B a^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 20 \, a^{2} b^{5} c^{2} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 64 \, a^{3} b^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, a^{4} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} A {\left| a \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, a^{2} b^{6} c + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 18 \, a^{3} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 48 \, a^{4} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 32 \, a^{5} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} B {\left| a \right|} + {\left(2 \, a^{2} b^{6} c^{2} - 14 \, a^{3} b^{4} c^{3} + 24 \, a^{4} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3}\right)} A - {\left(2 \, a^{3} b^{5} c^{2} - 12 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b + \sqrt{a^{6} b^{2} - 4 \, a^{7} c}}{a^{3} c}}}\right)}{4 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c - 2 \, a^{5} b^{3} c + 16 \, a^{7} c^{2} + 8 \, a^{6} b c^{2} + a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left({\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} A a^{2} - {\left(2 \, a b^{5} c^{2} - 16 \, a^{2} b^{3} c^{3} + 32 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} B a^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 20 \, a^{2} b^{5} c^{2} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 64 \, a^{3} b^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 64 \, a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} A {\left| a \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c + 2 \, a^{2} b^{6} c + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 18 \, a^{3} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 48 \, a^{4} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 32 \, a^{5} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} B {\left| a \right|} + {\left(2 \, a^{2} b^{6} c^{2} - 14 \, a^{3} b^{4} c^{3} + 24 \, a^{4} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3}\right)} A - {\left(2 \, a^{3} b^{5} c^{2} - 12 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b - \sqrt{a^{6} b^{2} - 4 \, a^{7} c}}{a^{3} c}}}\right)}{4 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c - 2 \, a^{5} b^{3} c + 16 \, a^{7} c^{2} + 8 \, a^{6} b c^{2} + a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} {\left| a \right|} {\left| c \right|}} + \frac{2 \, {\left(15 \, B a b x^{2} - 15 \, A b^{2} x^{2} + 15 \, A a c x^{2} - 5 \, B a^{2} x + 5 \, A a b x - 3 \, A a^{2}\right)}}{15 \, a^{3} x^{\frac{5}{2}}}"," ",0,"-1/4*((2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*A*a^2 - (2*a*b^5*c^2 - 16*a^2*b^3*c^3 + 32*a^3*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*b*c^3)*B*a^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*a*b^7*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 20*a^2*b^5*c^2 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 64*a^3*b^3*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*a^4*b*c^4 + 2*(b^2 - 4*a*c)*a*b^5*c - 12*(b^2 - 4*a*c)*a^2*b^3*c^2 + 16*(b^2 - 4*a*c)*a^3*b*c^3)*A*abs(a) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*a^2*b^6*c + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 18*a^3*b^4*c^2 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 48*a^4*b^2*c^3 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 32*a^5*c^4 + 2*(b^2 - 4*a*c)*a^2*b^4*c - 10*(b^2 - 4*a*c)*a^3*b^2*c^2 + 8*(b^2 - 4*a*c)*a^4*c^3)*B*abs(a) + (2*a^2*b^6*c^2 - 14*a^3*b^4*c^3 + 24*a^4*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^4*c^2 + 6*(b^2 - 4*a*c)*a^3*b^2*c^3)*A - (2*a^3*b^5*c^2 - 12*a^4*b^3*c^3 + 16*a^5*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 2*(b^2 - 4*a*c)*a^3*b^3*c^2 + 4*(b^2 - 4*a*c)*a^4*b*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b + sqrt(a^6*b^2 - 4*a^7*c))/(a^3*c)))/((a^5*b^4 - 8*a^6*b^2*c - 2*a^5*b^3*c + 16*a^7*c^2 + 8*a^6*b*c^2 + a^5*b^2*c^2 - 4*a^6*c^3)*abs(a)*abs(c)) + 1/4*((2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*A*a^2 - (2*a*b^5*c^2 - 16*a^2*b^3*c^3 + 32*a^3*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*b*c^3)*B*a^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 2*a*b^7*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 20*a^2*b^5*c^2 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 64*a^3*b^3*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 64*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a*b^5*c + 12*(b^2 - 4*a*c)*a^2*b^3*c^2 - 16*(b^2 - 4*a*c)*a^3*b*c^3)*A*abs(a) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c + 2*a^2*b^6*c + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 18*a^3*b^4*c^2 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 48*a^4*b^2*c^3 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 32*a^5*c^4 - 2*(b^2 - 4*a*c)*a^2*b^4*c + 10*(b^2 - 4*a*c)*a^3*b^2*c^2 - 8*(b^2 - 4*a*c)*a^4*c^3)*B*abs(a) + (2*a^2*b^6*c^2 - 14*a^3*b^4*c^3 + 24*a^4*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^4*c^2 + 6*(b^2 - 4*a*c)*a^3*b^2*c^3)*A - (2*a^3*b^5*c^2 - 12*a^4*b^3*c^3 + 16*a^5*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 2*(b^2 - 4*a*c)*a^3*b^3*c^2 + 4*(b^2 - 4*a*c)*a^4*b*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b - sqrt(a^6*b^2 - 4*a^7*c))/(a^3*c)))/((a^5*b^4 - 8*a^6*b^2*c - 2*a^5*b^3*c + 16*a^7*c^2 + 8*a^6*b*c^2 + a^5*b^2*c^2 - 4*a^6*c^3)*abs(a)*abs(c)) + 2/15*(15*B*a*b*x^2 - 15*A*b^2*x^2 + 15*A*a*c*x^2 - 5*B*a^2*x + 5*A*a*b*x - 3*A*a^2)/(a^3*x^(5/2))","B",0
1016,1,4086,0,1.862591," ","integrate((B*x+A)/x^(9/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 11 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 41 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 22 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 7 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 82 \, a^{2} b^{4} c^{3} - 18 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 112 \, a^{3} b^{2} c^{4} + 50 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 32 \, a^{4} c^{5} - 40 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 14 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 20 \, a^{2} b^{5} c^{2} + 2 \, a b^{6} c^{2} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 64 \, a^{3} b^{3} c^{3} - 16 \, a^{2} b^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, a^{4} b c^{4} + 36 \, a^{3} b^{2} c^{4} - 16 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{4} b + \sqrt{a^{8} b^{2} - 4 \, a^{9} c}}{a^{4} c}}}\right)}{2 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c - 2 \, a^{5} b^{3} c + 16 \, a^{7} c^{2} + 8 \, a^{6} b c^{2} + a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} {\left| c \right|}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 11 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 41 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 22 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 7 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 82 \, a^{2} b^{4} c^{3} + 18 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 112 \, a^{3} b^{2} c^{4} - 50 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 32 \, a^{4} c^{5} + 40 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 14 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 26 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 20 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 64 \, a^{3} b^{3} c^{3} + 16 \, a^{2} b^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 64 \, a^{4} b c^{4} - 36 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{4} b - \sqrt{a^{8} b^{2} - 4 \, a^{9} c}}{a^{4} c}}}\right)}{2 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c - 2 \, a^{5} b^{3} c + 16 \, a^{7} c^{2} + 8 \, a^{6} b c^{2} + a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} {\left| c \right|}} - \frac{2 \, {\left(105 \, B a b^{2} x^{3} - 105 \, A b^{3} x^{3} - 105 \, B a^{2} c x^{3} + 210 \, A a b c x^{3} - 35 \, B a^{2} b x^{2} + 35 \, A a b^{2} x^{2} - 35 \, A a^{2} c x^{2} + 21 \, B a^{3} x - 21 \, A a^{2} b x + 15 \, A a^{3}\right)}}{105 \, a^{4} x^{\frac{7}{2}}}"," ",0,"1/2*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8 - 11*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c - 2*b^8*c + 41*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 22*a*b^6*c^2 + 2*b^7*c^2 - 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 26*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 7*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 82*a^2*b^4*c^3 - 18*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 13*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 112*a^3*b^2*c^4 + 50*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 32*a^4*c^5 - 40*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 2*(b^2 - 4*a*c)*b^6*c - 14*(b^2 - 4*a*c)*a*b^4*c^2 - 2*(b^2 - 4*a*c)*b^5*c^2 + 26*(b^2 - 4*a*c)*a^2*b^2*c^3 + 10*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^3*c^4 - 10*(b^2 - 4*a*c)*a^2*b*c^4)*A - (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*a*b^7*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 20*a^2*b^5*c^2 + 2*a*b^6*c^2 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 64*a^3*b^3*c^3 - 16*a^2*b^4*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*a^4*b*c^4 + 36*a^3*b^2*c^4 - 16*a^4*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 2*(b^2 - 4*a*c)*a*b^5*c - 12*(b^2 - 4*a*c)*a^2*b^3*c^2 - 2*(b^2 - 4*a*c)*a*b^4*c^2 + 16*(b^2 - 4*a*c)*a^3*b*c^3 + 8*(b^2 - 4*a*c)*a^2*b^2*c^3 - 4*(b^2 - 4*a*c)*a^3*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^4*b + sqrt(a^8*b^2 - 4*a^9*c))/(a^4*c)))/((a^5*b^4 - 8*a^6*b^2*c - 2*a^5*b^3*c + 16*a^7*c^2 + 8*a^6*b*c^2 + a^5*b^2*c^2 - 4*a^6*c^3)*abs(c)) + 1/2*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8 - 11*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c + 2*b^8*c + 41*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 - 22*a*b^6*c^2 - 2*b^7*c^2 - 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 26*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 7*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 82*a^2*b^4*c^3 + 18*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 13*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 112*a^3*b^2*c^4 - 50*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 32*a^4*c^5 + 40*a^3*b*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^6*c + 14*(b^2 - 4*a*c)*a*b^4*c^2 + 2*(b^2 - 4*a*c)*b^5*c^2 - 26*(b^2 - 4*a*c)*a^2*b^2*c^3 - 10*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^3*c^4 + 10*(b^2 - 4*a*c)*a^2*b*c^4)*A - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 2*a*b^7*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 20*a^2*b^5*c^2 - 2*a*b^6*c^2 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 64*a^3*b^3*c^3 + 16*a^2*b^4*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 64*a^4*b*c^4 - 36*a^3*b^2*c^4 + 16*a^4*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 2*(b^2 - 4*a*c)*a*b^5*c + 12*(b^2 - 4*a*c)*a^2*b^3*c^2 + 2*(b^2 - 4*a*c)*a*b^4*c^2 - 16*(b^2 - 4*a*c)*a^3*b*c^3 - 8*(b^2 - 4*a*c)*a^2*b^2*c^3 + 4*(b^2 - 4*a*c)*a^3*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^4*b - sqrt(a^8*b^2 - 4*a^9*c))/(a^4*c)))/((a^5*b^4 - 8*a^6*b^2*c - 2*a^5*b^3*c + 16*a^7*c^2 + 8*a^6*b*c^2 + a^5*b^2*c^2 - 4*a^6*c^3)*abs(c)) - 2/105*(105*B*a*b^2*x^3 - 105*A*b^3*x^3 - 105*B*a^2*c*x^3 + 210*A*a*b*c*x^3 - 35*B*a^2*b*x^2 + 35*A*a*b^2*x^2 - 35*A*a^2*c*x^2 + 21*B*a^3*x - 21*A*a^2*b*x + 15*A*a^3)/(a^4*x^(7/2))","B",0
1017,1,5691,0,2.126602," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{c^{2}} + \frac{B b^{3} x^{\frac{3}{2}} - 3 \, B a b c x^{\frac{3}{2}} - A b^{2} c x^{\frac{3}{2}} + 2 \, A a c^{2} x^{\frac{3}{2}} + B a b^{2} \sqrt{x} - 2 \, B a^{2} c \sqrt{x} - A a b c \sqrt{x}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} {\left(c x^{2} + b x + a\right)}} + \frac{{\left({\left(2 \, b^{4} c^{3} - 20 \, a b^{2} c^{4} + 48 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} A - {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} B + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 2 \, a b^{5} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - 16 \, a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + 32 \, a^{3} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} A {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} - 320 \, a^{4} c^{7} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} B {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - {\left(2 \, b^{8} c^{7} - 32 \, a b^{6} c^{8} + 160 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} A + {\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} + \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{8 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{4} c^{3} - 20 \, a b^{2} c^{4} + 48 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} A - {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} B - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 2 \, a b^{5} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} + 16 \, a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 32 \, a^{3} b c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} A {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 320 \, a^{4} c^{7} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} B {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - {\left(2 \, b^{8} c^{7} - 32 \, a b^{6} c^{8} + 160 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} A + {\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} - \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{8 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}}"," ",0,"2*B*sqrt(x)/c^2 + (B*b^3*x^(3/2) - 3*B*a*b*c*x^(3/2) - A*b^2*c*x^(3/2) + 2*A*a*c^2*x^(3/2) + B*a*b^2*sqrt(x) - 2*B*a^2*c*sqrt(x) - A*a*b*c*sqrt(x))/((b^2*c^2 - 4*a*c^3)*(c*x^2 + b*x + a)) + 1/8*((2*b^4*c^3 - 20*a*b^2*c^4 + 48*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*A - (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2*B + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 16*a^2*b^3*c^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 32*a^3*b*c^7 - 2*(b^2 - 4*a*c)*a*b^3*c^5 + 8*(b^2 - 4*a*c)*a^2*b*c^6)*A*abs(-b^2*c^2 + 4*a*c^3) - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 - 320*a^4*c^7 - 6*(b^2 - 4*a*c)*a*b^4*c^4 + 44*(b^2 - 4*a*c)*a^2*b^2*c^5 - 80*(b^2 - 4*a*c)*a^3*c^6)*B*abs(-b^2*c^2 + 4*a*c^3) - (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2*b^2*c^9)*A + (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^3*c^2 - 4*a*b*c^3 + sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c)) - 1/8*((2*b^4*c^3 - 20*a*b^2*c^4 + 48*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*A - (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2*B - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 16*a^2*b^3*c^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 32*a^3*b*c^7 + 2*(b^2 - 4*a*c)*a*b^3*c^5 - 8*(b^2 - 4*a*c)*a^2*b*c^6)*A*abs(-b^2*c^2 + 4*a*c^3) + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 320*a^4*c^7 + 6*(b^2 - 4*a*c)*a*b^4*c^4 - 44*(b^2 - 4*a*c)*a^2*b^2*c^5 + 80*(b^2 - 4*a*c)*a^3*c^6)*B*abs(-b^2*c^2 + 4*a*c^3) - (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2*b^2*c^9)*A + (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^3*c^2 - 4*a*b*c^3 - sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c))","B",0
1018,1,4544,0,1.830553," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{B b^{2} x^{\frac{3}{2}} - 2 \, B a c x^{\frac{3}{2}} - A b c x^{\frac{3}{2}} + B a b \sqrt{x} - 2 \, A a c \sqrt{x}}{{\left(b^{2} c - 4 \, a c^{2}\right)} {\left(c x^{2} + b x + a\right)}} + \frac{{\left({\left(2 \, b^{3} c^{3} - 8 \, a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} A + {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} B - 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 32 \, a^{3} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A {\left| b^{2} c - 4 \, a c^{2} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 32 \, a^{3} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B {\left| b^{2} c - 4 \, a c^{2} \right|} - {\left(2 \, b^{7} c^{5} - 8 \, a b^{5} c^{6} - 32 \, a^{2} b^{3} c^{7} + 128 \, a^{3} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} A - {\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} + \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{8 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{3} - 8 \, a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} A + {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} B + 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 32 \, a^{3} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A {\left| b^{2} c - 4 \, a c^{2} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 32 \, a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B {\left| b^{2} c - 4 \, a c^{2} \right|} - {\left(2 \, b^{7} c^{5} - 8 \, a b^{5} c^{6} - 32 \, a^{2} b^{3} c^{7} + 128 \, a^{3} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} A - {\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} - \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{8 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}}"," ",0,"-(B*b^2*x^(3/2) - 2*B*a*c*x^(3/2) - A*b*c*x^(3/2) + B*a*b*sqrt(x) - 2*A*a*c*sqrt(x))/((b^2*c - 4*a*c^2)*(c*x^2 + b*x + a)) + 1/8*((2*b^3*c^3 - 8*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^3 - 2*(b^2 - 4*a*c)*b*c^3)*(b^2*c - 4*a*c^2)^2*A + (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2*B - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 2*a*b^4*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 16*a^2*b^2*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 - 32*a^3*c^6 + 2*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(b^2*c - 4*a*c^2) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 32*a^3*b*c^5 + 2*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*B*abs(b^2*c - 4*a*c^2) - (2*b^7*c^5 - 8*a*b^5*c^6 - 32*a^2*b^3*c^7 + 128*a^3*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 2*(b^2 - 4*a*c)*b^5*c^5 + 32*(b^2 - 4*a*c)*a^2*b*c^7)*A - (2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^3*c - 4*a*b*c^2 + sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c)) - 1/8*((2*b^3*c^3 - 8*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^3 - 2*(b^2 - 4*a*c)*b*c^3)*(b^2*c - 4*a*c^2)^2*A + (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2*B + 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 2*a*b^4*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 16*a^2*b^2*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 32*a^3*c^6 - 2*(b^2 - 4*a*c)*a*b^2*c^4 + 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(b^2*c - 4*a*c^2) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 32*a^3*b*c^5 - 2*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*B*abs(b^2*c - 4*a*c^2) - (2*b^7*c^5 - 8*a*b^5*c^6 - 32*a^2*b^3*c^7 + 128*a^3*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 2*(b^2 - 4*a*c)*b^5*c^5 + 32*(b^2 - 4*a*c)*a^2*b*c^7)*A - (2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^3*c - 4*a*b*c^2 - sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c))","B",0
1019,1,3781,0,1.597106," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{B b x^{\frac{3}{2}} - 2 \, A c x^{\frac{3}{2}} + 2 \, B a \sqrt{x} - A b \sqrt{x}}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} B - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 2 \, b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 16 \, a b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 32 \, a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A {\left| b^{2} - 4 \, a c \right|} + 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 32 \, a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} B {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} B + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 2 \, b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 16 \, a b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 32 \, a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 32 \, a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} B {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}}"," ",0,"(B*b*x^(3/2) - 2*A*c*x^(3/2) + 2*B*a*sqrt(x) - A*b*sqrt(x))/((c*x^2 + b*x + a)*(b^2 - 4*a*c)) - 1/8*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*B - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 16*a*b^3*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 32*a^2*b*c^4 + 2*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) + 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*a*b^4*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 16*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 32*a^3*c^4 + 2*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*B*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*B + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 16*a*b^3*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + 32*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*a*b^4*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 16*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 32*a^3*c^4 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*B*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c))","B",0
1020,1,4434,0,1.810901," ","integrate((B*x+A)/(c*x^2+b*x+a)^2/x^(1/2),x, algorithm=""giac"")","-\frac{2 \, B a c x^{\frac{3}{2}} - A b c x^{\frac{3}{2}} + B a b \sqrt{x} - A b^{2} \sqrt{x} + 2 \, A a c \sqrt{x}}{{\left(a b^{2} - 4 \, a^{2} c\right)} {\left(c x^{2} + b x + a\right)}} - \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} A - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} B - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 192 \, a^{4} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} A {\left| a b^{2} - 4 \, a^{2} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 16 \, a^{3} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, a^{4} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} B {\left| a b^{2} - 4 \, a^{2} c \right|} + {\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A + 4 \, {\left(2 \, a^{3} b^{6} c^{2} - 16 \, a^{4} b^{4} c^{3} + 32 \, a^{5} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{8 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} A - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} B - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 192 \, a^{4} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} A {\left| a b^{2} - 4 \, a^{2} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 16 \, a^{3} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 32 \, a^{4} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} B {\left| a b^{2} - 4 \, a^{2} c \right|} + {\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A + 4 \, {\left(2 \, a^{3} b^{6} c^{2} - 16 \, a^{4} b^{4} c^{3} + 32 \, a^{5} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{8 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}}"," ",0,"-(2*B*a*c*x^(3/2) - A*b*c*x^(3/2) + B*a*b*sqrt(x) - A*b^2*sqrt(x) + 2*A*a*c*sqrt(x))/((a*b^2 - 4*a^2*c)*(c*x^2 + b*x + a)) - 1/8*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2*A - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*(a*b^2 - 4*a^2*c)^2*B - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 192*a^4*c^4 + 2*(b^2 - 4*a*c)*a*b^4*c - 20*(b^2 - 4*a*c)*a^2*b^2*c^2 + 48*(b^2 - 4*a*c)*a^3*c^3)*A*abs(a*b^2 - 4*a^2*c) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*a^2*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 16*a^3*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*a^4*b*c^3 + 2*(b^2 - 4*a*c)*a^2*b^3*c - 8*(b^2 - 4*a*c)*a^3*b*c^2)*B*abs(a*b^2 - 4*a^2*c) + (2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4)*A + 4*(2*a^3*b^6*c^2 - 16*a^4*b^4*c^3 + 32*a^5*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*(b^2 - 4*a*c)*a^3*b^4*c^2 + 8*(b^2 - 4*a*c)*a^4*b^2*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/8*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2*A - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*(a*b^2 - 4*a^2*c)^2*B - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 192*a^4*c^4 - 2*(b^2 - 4*a*c)*a*b^4*c + 20*(b^2 - 4*a*c)*a^2*b^2*c^2 - 48*(b^2 - 4*a*c)*a^3*c^3)*A*abs(a*b^2 - 4*a^2*c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 2*a^2*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 16*a^3*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 32*a^4*b*c^3 - 2*(b^2 - 4*a*c)*a^2*b^3*c + 8*(b^2 - 4*a*c)*a^3*b*c^2)*B*abs(a*b^2 - 4*a^2*c) + (2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4)*A + 4*(2*a^3*b^6*c^2 - 16*a^4*b^4*c^3 + 32*a^5*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*(b^2 - 4*a*c)*a^3*b^4*c^2 + 8*(b^2 - 4*a*c)*a^4*b^2*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c))","B",0
1021,1,5405,0,2.214620," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{B a b c x^{2} - 3 \, A b^{2} c x^{2} + 10 \, A a c^{2} x^{2} + B a b^{2} x - 3 \, A b^{3} x - 2 \, B a^{2} c x + 11 \, A a b c x - 2 \, A a b^{2} + 8 \, A a^{2} c}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(c x^{\frac{5}{2}} + b x^{\frac{3}{2}} + a \sqrt{x}\right)}} - \frac{{\left({\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} A - {\left(2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} B + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 6 \, a^{2} b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 74 \, a^{3} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 304 \, a^{4} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 416 \, a^{5} b c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} A {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 2 \, a^{3} b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 28 \, a^{4} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 128 \, a^{5} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} + 192 \, a^{6} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{3}\right)} B {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + {\left(6 \, a^{4} b^{8} c^{2} - 80 \, a^{5} b^{6} c^{3} + 352 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4}\right)} A - {\left(2 \, a^{5} b^{7} c^{2} - 40 \, a^{6} b^{5} c^{3} + 224 \, a^{7} b^{3} c^{4} - 384 \, a^{8} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c + \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{8 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 48 \, a^{7} b^{2} c^{2} + 16 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} - 64 \, a^{8} c^{3} - 32 \, a^{7} b c^{3} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}} + \frac{{\left({\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} A - {\left(2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} B - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + 6 \, a^{2} b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 74 \, a^{3} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 304 \, a^{4} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 416 \, a^{5} b c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} A {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, a^{3} b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 28 \, a^{4} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 128 \, a^{5} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} - 192 \, a^{6} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{3}\right)} B {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + {\left(6 \, a^{4} b^{8} c^{2} - 80 \, a^{5} b^{6} c^{3} + 352 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4}\right)} A - {\left(2 \, a^{5} b^{7} c^{2} - 40 \, a^{6} b^{5} c^{3} + 224 \, a^{7} b^{3} c^{4} - 384 \, a^{8} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c - \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{8 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 48 \, a^{7} b^{2} c^{2} + 16 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} - 64 \, a^{8} c^{3} - 32 \, a^{7} b c^{3} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}}"," ",0,"(B*a*b*c*x^2 - 3*A*b^2*c*x^2 + 10*A*a*c^2*x^2 + B*a*b^2*x - 3*A*b^3*x - 2*B*a^2*c*x + 11*A*a*b*c*x - 2*A*a*b^2 + 8*A*a^2*c)/((a^2*b^2 - 4*a^3*c)*(c*x^(5/2) + b*x^(3/2) + a*sqrt(x))) - 1/8*((6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*(a^2*b^2 - 4*a^3*c)^2*A - (2*a*b^3*c^2 - 8*a^2*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a^2*b^2 - 4*a^3*c)^2*B + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 6*a^2*b^7*c + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 74*a^3*b^5*c^2 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 304*a^4*b^3*c^3 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + 416*a^5*b*c^4 + 6*(b^2 - 4*a*c)*a^2*b^5*c - 50*(b^2 - 4*a*c)*a^3*b^3*c^2 + 104*(b^2 - 4*a*c)*a^4*b*c^3)*A*abs(a^2*b^2 - 4*a^3*c) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 2*a^3*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 28*a^4*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 128*a^5*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^4 + 192*a^6*c^4 + 2*(b^2 - 4*a*c)*a^3*b^4*c - 20*(b^2 - 4*a*c)*a^4*b^2*c^2 + 48*(b^2 - 4*a*c)*a^5*c^3)*B*abs(a^2*b^2 - 4*a^3*c) + (6*a^4*b^8*c^2 - 80*a^5*b^6*c^3 + 352*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 6*(b^2 - 4*a*c)*a^4*b^6*c^2 + 56*(b^2 - 4*a*c)*a^5*b^4*c^3 - 128*(b^2 - 4*a*c)*a^6*b^2*c^4)*A - (2*a^5*b^7*c^2 - 40*a^6*b^5*c^3 + 224*a^7*b^3*c^4 - 384*a^8*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 2*(b^2 - 4*a*c)*a^5*b^5*c^2 + 32*(b^2 - 4*a*c)*a^6*b^3*c^3 - 96*(b^2 - 4*a*c)*a^7*b*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^2*b^3 - 4*a^3*b*c + sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6 - 12*a^6*b^4*c - 2*a^5*b^5*c + 48*a^7*b^2*c^2 + 16*a^6*b^3*c^2 + a^5*b^4*c^2 - 64*a^8*c^3 - 32*a^7*b*c^3 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*abs(a^2*b^2 - 4*a^3*c)*abs(c)) + 1/8*((6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*(a^2*b^2 - 4*a^3*c)^2*A - (2*a*b^3*c^2 - 8*a^2*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a^2*b^2 - 4*a^3*c)^2*B - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + 6*a^2*b^7*c + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 50*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - 74*a^3*b^5*c^2 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 25*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 304*a^4*b^3*c^3 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 416*a^5*b*c^4 - 6*(b^2 - 4*a*c)*a^2*b^5*c + 50*(b^2 - 4*a*c)*a^3*b^3*c^2 - 104*(b^2 - 4*a*c)*a^4*b*c^3)*A*abs(a^2*b^2 - 4*a^3*c) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*a^3*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - 28*a^4*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 128*a^5*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^4 - 192*a^6*c^4 - 2*(b^2 - 4*a*c)*a^3*b^4*c + 20*(b^2 - 4*a*c)*a^4*b^2*c^2 - 48*(b^2 - 4*a*c)*a^5*c^3)*B*abs(a^2*b^2 - 4*a^3*c) + (6*a^4*b^8*c^2 - 80*a^5*b^6*c^3 + 352*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 6*(b^2 - 4*a*c)*a^4*b^6*c^2 + 56*(b^2 - 4*a*c)*a^5*b^4*c^3 - 128*(b^2 - 4*a*c)*a^6*b^2*c^4)*A - (2*a^5*b^7*c^2 - 40*a^6*b^5*c^3 + 224*a^7*b^3*c^4 - 384*a^8*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 2*(b^2 - 4*a*c)*a^5*b^5*c^2 + 32*(b^2 - 4*a*c)*a^6*b^3*c^3 - 96*(b^2 - 4*a*c)*a^7*b*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^2*b^3 - 4*a^3*b*c - sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6 - 12*a^6*b^4*c - 2*a^5*b^5*c + 48*a^7*b^2*c^2 + 16*a^6*b^3*c^2 + a^5*b^4*c^2 - 64*a^8*c^3 - 32*a^7*b*c^3 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*abs(a^2*b^2 - 4*a^3*c)*abs(c))","B",0
1022,1,6335,0,2.561605," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{B a b^{2} c x^{\frac{3}{2}} - A b^{3} c x^{\frac{3}{2}} - 2 \, B a^{2} c^{2} x^{\frac{3}{2}} + 3 \, A a b c^{2} x^{\frac{3}{2}} + B a b^{3} \sqrt{x} - A b^{4} \sqrt{x} - 3 \, B a^{2} b c \sqrt{x} + 4 \, A a b^{2} c \sqrt{x} - 2 \, A a^{2} c^{2} \sqrt{x}}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(c x^{2} + b x + a\right)}} + \frac{{\left({\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} A - {\left(6 \, a b^{4} c^{2} - 44 \, a^{2} b^{2} c^{3} + 80 \, a^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} B + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c - 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} + 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} - 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} + 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} - 448 \, a^{7} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} + 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} A {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 6 \, a^{4} b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 74 \, a^{5} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 304 \, a^{6} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 416 \, a^{7} b c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{3}\right)} B {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + {\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} A - {\left(6 \, a^{7} b^{8} c^{2} - 80 \, a^{8} b^{6} c^{3} + 352 \, a^{9} b^{4} c^{4} - 512 \, a^{10} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{2} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c + \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{8 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} - \frac{{\left({\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} A - {\left(6 \, a b^{4} c^{2} - 44 \, a^{2} b^{2} c^{3} + 80 \, a^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} B - 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c + 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} - 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} + 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} - 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} + 448 \, a^{7} c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} - 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} A {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c + 6 \, a^{4} b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} - 74 \, a^{5} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} + 304 \, a^{6} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} - 416 \, a^{7} b c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{3}\right)} B {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + {\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} A - {\left(6 \, a^{7} b^{8} c^{2} - 80 \, a^{8} b^{6} c^{3} + 352 \, a^{9} b^{4} c^{4} - 512 \, a^{10} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{2} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c - \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{8 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} - \frac{2 \, {\left(3 \, B a x - 6 \, A b x + A a\right)}}{3 \, a^{3} x^{\frac{3}{2}}}"," ",0,"-(B*a*b^2*c*x^(3/2) - A*b^3*c*x^(3/2) - 2*B*a^2*c^2*x^(3/2) + 3*A*a*b*c^2*x^(3/2) + B*a*b^3*sqrt(x) - A*b^4*sqrt(x) - 3*B*a^2*b*c*sqrt(x) + 4*A*a*b^2*c*sqrt(x) - 2*A*a^2*c^2*sqrt(x))/((a^3*b^2 - 4*a^4*c)*(c*x^2 + b*x + a)) + 1/8*((10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*A - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3*b^2 - 4*a^4*c)^2*B + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c - 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 + 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 - 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 + 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^5 - 448*a^7*c^5 + 10*(b^2 - 4*a*c)*a^3*b^6*c - 88*(b^2 - 4*a*c)*a^4*b^4*c^2 + 220*(b^2 - 4*a*c)*a^5*b^2*c^3 - 112*(b^2 - 4*a*c)*a^6*c^4)*A*abs(a^3*b^2 - 4*a^4*c) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 74*a^5*b^5*c^2 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 304*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 416*a^7*b*c^4 + 6*(b^2 - 4*a*c)*a^4*b^5*c - 50*(b^2 - 4*a*c)*a^5*b^3*c^2 + 104*(b^2 - 4*a*c)*a^6*b*c^3)*B*abs(a^3*b^2 - 4*a^4*c) + (10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5)*A - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4 - 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2 - 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 - 128*(b^2 - 4*a*c)*a^9*b^2*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^3 - 4*a^4*b*c + sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) - 1/8*((10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*A - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3*b^2 - 4*a^4*c)^2*B - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c + 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 - 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 + 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 - 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^5 + 448*a^7*c^5 - 10*(b^2 - 4*a*c)*a^3*b^6*c + 88*(b^2 - 4*a*c)*a^4*b^4*c^2 - 220*(b^2 - 4*a*c)*a^5*b^2*c^3 + 112*(b^2 - 4*a*c)*a^6*c^4)*A*abs(a^3*b^2 - 4*a^4*c) + 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c + 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 - 74*a^5*b^5*c^2 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 + 304*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 - 416*a^7*b*c^4 - 6*(b^2 - 4*a*c)*a^4*b^5*c + 50*(b^2 - 4*a*c)*a^5*b^3*c^2 - 104*(b^2 - 4*a*c)*a^6*b*c^3)*B*abs(a^3*b^2 - 4*a^4*c) + (10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5)*A - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4 - 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2 - 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 - 128*(b^2 - 4*a*c)*a^9*b^2*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^3 - 4*a^4*b*c - sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) - 2/3*(3*B*a*x - 6*A*b*x + A*a)/(a^3*x^(3/2))","B",0
1023,1,3997,0,2.414743," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 2 \, b^{6} c^{2} - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 24 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 288 \, a^{2} b^{2} c^{4} + 112 \, a b^{3} c^{4} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 640 \, a^{3} c^{5} - 416 \, a^{2} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 160 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} - 104 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A + 3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 160 \, a^{2} b^{3} c^{3} + 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 256 \, a^{3} b c^{4} - 192 \, a^{2} b^{2} c^{4} + 448 \, a^{3} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} + \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{16 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 2 \, b^{6} c^{2} - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 24 \, a b^{4} c^{3} + 2 \, b^{5} c^{3} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 288 \, a^{2} b^{2} c^{4} - 112 \, a b^{3} c^{4} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 640 \, a^{3} c^{5} + 416 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 104 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A + 3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 32 \, a b^{5} c^{2} + 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 160 \, a^{2} b^{3} c^{3} - 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 256 \, a^{3} b c^{4} + 192 \, a^{2} b^{2} c^{4} - 448 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} - \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{16 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} - \frac{5 \, B b^{4} c x^{\frac{7}{2}} - 37 \, B a b^{2} c^{2} x^{\frac{7}{2}} - A b^{3} c^{2} x^{\frac{7}{2}} + 44 \, B a^{2} c^{3} x^{\frac{7}{2}} + 16 \, A a b c^{3} x^{\frac{7}{2}} + 3 \, B b^{5} x^{\frac{5}{2}} - 20 \, B a b^{3} c x^{\frac{5}{2}} + A b^{4} c x^{\frac{5}{2}} - 4 \, B a^{2} b c^{2} x^{\frac{5}{2}} + 5 \, A a b^{2} c^{2} x^{\frac{5}{2}} + 36 \, A a^{2} c^{3} x^{\frac{5}{2}} + 6 \, B a b^{4} x^{\frac{3}{2}} - 49 \, B a^{2} b^{2} c x^{\frac{3}{2}} + 2 \, A a b^{3} c x^{\frac{3}{2}} + 28 \, B a^{3} c^{2} x^{\frac{3}{2}} + 28 \, A a^{2} b c^{2} x^{\frac{3}{2}} + 3 \, B a^{2} b^{3} \sqrt{x} - 24 \, B a^{3} b c \sqrt{x} + A a^{2} b^{2} c \sqrt{x} + 20 \, A a^{3} c^{2} \sqrt{x}}{4 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"1/16*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 2*b^6*c^2 - 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 24*a*b^4*c^3 - 2*b^5*c^3 + 320*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 288*a^2*b^2*c^4 + 112*a*b^3*c^4 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 640*a^3*c^5 - 416*a^2*b*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 104*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + 2*(b^2 - 4*a*c)*b^4*c^2 + 32*(b^2 - 4*a*c)*a*b^2*c^3 + 2*(b^2 - 4*a*c)*b^3*c^3 - 160*(b^2 - 4*a*c)*a^2*c^4 - 104*(b^2 - 4*a*c)*a*b*c^4)*A + 3*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 2*b^7*c + 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*a*b^5*c^2 - 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 160*a^2*b^3*c^3 + 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 256*a^3*b*c^4 - 192*a^2*b^2*c^4 + 448*a^3*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 2*(b^2 - 4*a*c)*b^5*c - 24*(b^2 - 4*a*c)*a*b^3*c^2 + 2*(b^2 - 4*a*c)*b^4*c^2 + 64*(b^2 - 4*a*c)*a^2*b*c^3 - 20*(b^2 - 4*a*c)*a*b^2*c^3 + 112*(b^2 - 4*a*c)*a^2*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 + sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(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)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) + 1/16*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 2*b^6*c^2 - 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 24*a*b^4*c^3 + 2*b^5*c^3 + 320*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 288*a^2*b^2*c^4 - 112*a*b^3*c^4 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 640*a^3*c^5 + 416*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 104*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 - 32*(b^2 - 4*a*c)*a*b^2*c^3 - 2*(b^2 - 4*a*c)*b^3*c^3 + 160*(b^2 - 4*a*c)*a^2*c^4 + 104*(b^2 - 4*a*c)*a*b*c^4)*A + 3*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 2*b^7*c + 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 32*a*b^5*c^2 + 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 160*a^2*b^3*c^3 - 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 256*a^3*b*c^4 + 192*a^2*b^2*c^4 - 448*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^5*c + 24*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*b^4*c^2 - 64*(b^2 - 4*a*c)*a^2*b*c^3 + 20*(b^2 - 4*a*c)*a*b^2*c^3 - 112*(b^2 - 4*a*c)*a^2*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 - sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(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)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) - 1/4*(5*B*b^4*c*x^(7/2) - 37*B*a*b^2*c^2*x^(7/2) - A*b^3*c^2*x^(7/2) + 44*B*a^2*c^3*x^(7/2) + 16*A*a*b*c^3*x^(7/2) + 3*B*b^5*x^(5/2) - 20*B*a*b^3*c*x^(5/2) + A*b^4*c*x^(5/2) - 4*B*a^2*b*c^2*x^(5/2) + 5*A*a*b^2*c^2*x^(5/2) + 36*A*a^2*c^3*x^(5/2) + 6*B*a*b^4*x^(3/2) - 49*B*a^2*b^2*c*x^(3/2) + 2*A*a*b^3*c*x^(3/2) + 28*B*a^3*c^2*x^(3/2) + 28*A*a^2*b*c^2*x^(3/2) + 3*B*a^2*b^3*sqrt(x) - 24*B*a^3*b*c*sqrt(x) + A*a^2*b^2*c*sqrt(x) + 20*A*a^3*c^2*sqrt(x))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^2 + b*x + a)^2)","B",0
1024,1,7586,0,3.363731," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, {\left(2 \, b^{4} c^{3} - 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} A + {\left(2 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 128 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} B - 24 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 2 \, a b^{7} c^{4} + 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + 24 \, a^{2} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 96 \, a^{3} b^{3} c^{6} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} + 128 \, a^{4} b c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} A {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 2 \, a b^{8} c^{3} - 192 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 16 \, a^{2} b^{6} c^{4} + 896 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 288 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 384 \, a^{3} b^{4} c^{5} - 1280 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 640 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 1792 \, a^{4} b^{2} c^{6} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} + 2560 \, a^{5} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} + 640 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} B {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} - 3 \, {\left(2 \, b^{12} c^{5} - 8 \, a b^{10} c^{6} - 192 \, a^{2} b^{8} c^{7} + 1792 \, a^{3} b^{6} c^{8} - 5632 \, a^{4} b^{4} c^{9} + 6144 \, a^{5} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{5} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} + 2816 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{7} - 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{10} c^{5} + 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c^{7} - 1024 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{8} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{9}\right)} A - {\left(2 \, b^{13} c^{4} - 68 \, a b^{11} c^{5} + 688 \, a^{2} b^{9} c^{6} - 2688 \, a^{3} b^{7} c^{7} + 2048 \, a^{4} b^{5} c^{8} + 11264 \, a^{5} b^{3} c^{9} - 20480 \, a^{6} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{13} c^{2} + 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{11} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} - 344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{9} c^{4} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{5} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} + 30 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{9} c^{5} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{6} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} - 5632 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{7} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 10240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{8} + 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{11} c^{4} + 60 \, {\left(b^{2} - 4 \, a c\right)} a b^{9} c^{5} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{7} c^{6} + 896 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{7} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{8} - 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{9}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + \sqrt{{\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)}^{2} - 4 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{32 \, {\left(a b^{10} c^{3} - 20 \, a^{2} b^{8} c^{4} - 2 \, a b^{9} c^{4} + 160 \, a^{3} b^{6} c^{5} + 32 \, a^{2} b^{7} c^{5} + a b^{8} c^{5} - 640 \, a^{4} b^{4} c^{6} - 192 \, a^{3} b^{5} c^{6} - 16 \, a^{2} b^{6} c^{6} + 1280 \, a^{5} b^{2} c^{7} + 512 \, a^{4} b^{3} c^{7} + 96 \, a^{3} b^{4} c^{7} - 1024 \, a^{6} c^{8} - 512 \, a^{5} b c^{8} - 256 \, a^{4} b^{2} c^{8} + 256 \, a^{5} c^{9}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} {\left| c \right|}} - \frac{{\left(3 \, {\left(2 \, b^{4} c^{3} - 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} A + {\left(2 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 128 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} B + 24 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 2 \, a b^{7} c^{4} + 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} - 24 \, a^{2} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} + 96 \, a^{3} b^{3} c^{6} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} - 128 \, a^{4} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} A {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} + 2 \, a b^{8} c^{3} - 192 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 16 \, a^{2} b^{6} c^{4} + 896 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 288 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} - 384 \, a^{3} b^{4} c^{5} - 1280 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 640 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} + 1792 \, a^{4} b^{2} c^{6} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} - 2560 \, a^{5} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} + 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} - 640 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} B {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} - 3 \, {\left(2 \, b^{12} c^{5} - 8 \, a b^{10} c^{6} - 192 \, a^{2} b^{8} c^{7} + 1792 \, a^{3} b^{6} c^{8} - 5632 \, a^{4} b^{4} c^{9} + 6144 \, a^{5} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{5} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} + 2816 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{7} - 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{10} c^{5} + 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c^{7} - 1024 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{8} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{9}\right)} A - {\left(2 \, b^{13} c^{4} - 68 \, a b^{11} c^{5} + 688 \, a^{2} b^{9} c^{6} - 2688 \, a^{3} b^{7} c^{7} + 2048 \, a^{4} b^{5} c^{8} + 11264 \, a^{5} b^{3} c^{9} - 20480 \, a^{6} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{13} c^{2} + 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{11} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} - 344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{9} c^{4} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{5} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} + 30 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{9} c^{5} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{6} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} - 5632 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{7} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 10240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{8} + 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{11} c^{4} + 60 \, {\left(b^{2} - 4 \, a c\right)} a b^{9} c^{5} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{7} c^{6} + 896 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{7} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{8} - 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{9}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} - \sqrt{{\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)}^{2} - 4 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{32 \, {\left(a b^{10} c^{3} - 20 \, a^{2} b^{8} c^{4} - 2 \, a b^{9} c^{4} + 160 \, a^{3} b^{6} c^{5} + 32 \, a^{2} b^{7} c^{5} + a b^{8} c^{5} - 640 \, a^{4} b^{4} c^{6} - 192 \, a^{3} b^{5} c^{6} - 16 \, a^{2} b^{6} c^{6} + 1280 \, a^{5} b^{2} c^{7} + 512 \, a^{4} b^{3} c^{7} + 96 \, a^{3} b^{4} c^{7} - 1024 \, a^{6} c^{8} - 512 \, a^{5} b c^{8} - 256 \, a^{4} b^{2} c^{8} + 256 \, a^{5} c^{9}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} {\left| c \right|}} + \frac{B b^{3} c x^{\frac{7}{2}} - 16 \, B a b c^{2} x^{\frac{7}{2}} + 3 \, A b^{2} c^{2} x^{\frac{7}{2}} + 12 \, A a c^{3} x^{\frac{7}{2}} - B b^{4} x^{\frac{5}{2}} - 5 \, B a b^{2} c x^{\frac{5}{2}} + 5 \, A b^{3} c x^{\frac{5}{2}} - 36 \, B a^{2} c^{2} x^{\frac{5}{2}} + 16 \, A a b c^{2} x^{\frac{5}{2}} - 2 \, B a b^{3} x^{\frac{3}{2}} - 28 \, B a^{2} b c x^{\frac{3}{2}} + 19 \, A a b^{2} c x^{\frac{3}{2}} - 4 \, A a^{2} c^{2} x^{\frac{3}{2}} - B a^{2} b^{2} \sqrt{x} - 20 \, B a^{3} c \sqrt{x} + 12 \, A a^{2} b c \sqrt{x}}{4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"1/32*(3*(2*b^4*c^3 - 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 - 8*(b^2 - 4*a*c)*a*c^4)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*A + (2*b^5*c^2 - 40*a*b^3*c^3 + 128*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 32*(b^2 - 4*a*c)*a*b*c^3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*B - 24*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 2*a*b^7*c^4 + 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 + 24*a^2*b^5*c^5 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 - 96*a^3*b^3*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^7 + 128*a^4*b*c^7 + 2*(b^2 - 4*a*c)*a*b^5*c^4 - 16*(b^2 - 4*a*c)*a^2*b^3*c^5 + 32*(b^2 - 4*a*c)*a^3*b*c^6)*A*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 2*a*b^8*c^3 - 192*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 16*a^2*b^6*c^4 + 896*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 288*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + 384*a^3*b^4*c^5 - 1280*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 640*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 1792*a^4*b^2*c^6 + 320*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^7 + 2560*a^5*c^7 + 2*(b^2 - 4*a*c)*a*b^6*c^3 + 24*(b^2 - 4*a*c)*a^2*b^4*c^4 - 288*(b^2 - 4*a*c)*a^3*b^2*c^5 + 640*(b^2 - 4*a*c)*a^4*c^6)*B*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) - 3*(2*b^12*c^5 - 8*a*b^10*c^6 - 192*a^2*b^8*c^7 + 1792*a^3*b^6*c^8 - 5632*a^4*b^4*c^9 + 6144*a^5*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^12*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^10*c^5 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 + 2816*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^7 - 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^9 - 2*(b^2 - 4*a*c)*b^10*c^5 + 192*(b^2 - 4*a*c)*a^2*b^6*c^7 - 1024*(b^2 - 4*a*c)*a^3*b^4*c^8 + 1536*(b^2 - 4*a*c)*a^4*b^2*c^9)*A - (2*b^13*c^4 - 68*a*b^11*c^5 + 688*a^2*b^9*c^6 - 2688*a^3*b^7*c^7 + 2048*a^4*b^5*c^8 + 11264*a^5*b^3*c^9 - 20480*a^6*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^13*c^2 + 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^11*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^12*c^3 - 344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^9*c^4 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^5 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 + 30*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^9*c^5 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^6 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 - 5632*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^7 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 10240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^8 + 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^9 - 2*(b^2 - 4*a*c)*b^11*c^4 + 60*(b^2 - 4*a*c)*a*b^9*c^5 - 448*(b^2 - 4*a*c)*a^2*b^7*c^6 + 896*(b^2 - 4*a*c)*a^3*b^5*c^7 + 1536*(b^2 - 4*a*c)*a^4*b^3*c^8 - 5120*(b^2 - 4*a*c)*a^5*b*c^9)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)^2 - 4*(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)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/((a*b^10*c^3 - 20*a^2*b^8*c^4 - 2*a*b^9*c^4 + 160*a^3*b^6*c^5 + 32*a^2*b^7*c^5 + a*b^8*c^5 - 640*a^4*b^4*c^6 - 192*a^3*b^5*c^6 - 16*a^2*b^6*c^6 + 1280*a^5*b^2*c^7 + 512*a^4*b^3*c^7 + 96*a^3*b^4*c^7 - 1024*a^6*c^8 - 512*a^5*b*c^8 - 256*a^4*b^2*c^8 + 256*a^5*c^9)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*abs(c)) - 1/32*(3*(2*b^4*c^3 - 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 - 8*(b^2 - 4*a*c)*a*c^4)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*A + (2*b^5*c^2 - 40*a*b^3*c^3 + 128*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 32*(b^2 - 4*a*c)*a*b*c^3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*B + 24*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 + 2*a*b^7*c^4 + 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 - 24*a^2*b^5*c^5 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 + 96*a^3*b^3*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^7 - 128*a^4*b*c^7 - 2*(b^2 - 4*a*c)*a*b^5*c^4 + 16*(b^2 - 4*a*c)*a^2*b^3*c^5 - 32*(b^2 - 4*a*c)*a^3*b*c^6)*A*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 + 2*a*b^8*c^3 - 192*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 + 16*a^2*b^6*c^4 + 896*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 288*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 - 384*a^3*b^4*c^5 - 1280*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 640*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 + 1792*a^4*b^2*c^6 + 320*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^7 - 2560*a^5*c^7 - 2*(b^2 - 4*a*c)*a*b^6*c^3 - 24*(b^2 - 4*a*c)*a^2*b^4*c^4 + 288*(b^2 - 4*a*c)*a^3*b^2*c^5 - 640*(b^2 - 4*a*c)*a^4*c^6)*B*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) - 3*(2*b^12*c^5 - 8*a*b^10*c^6 - 192*a^2*b^8*c^7 + 1792*a^3*b^6*c^8 - 5632*a^4*b^4*c^9 + 6144*a^5*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^12*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^10*c^5 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 + 2816*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^7 - 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^9 - 2*(b^2 - 4*a*c)*b^10*c^5 + 192*(b^2 - 4*a*c)*a^2*b^6*c^7 - 1024*(b^2 - 4*a*c)*a^3*b^4*c^8 + 1536*(b^2 - 4*a*c)*a^4*b^2*c^9)*A - (2*b^13*c^4 - 68*a*b^11*c^5 + 688*a^2*b^9*c^6 - 2688*a^3*b^7*c^7 + 2048*a^4*b^5*c^8 + 11264*a^5*b^3*c^9 - 20480*a^6*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^13*c^2 + 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^11*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^12*c^3 - 344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^9*c^4 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^5 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 + 30*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^9*c^5 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^6 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 - 5632*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^7 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 10240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^8 + 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^9 - 2*(b^2 - 4*a*c)*b^11*c^4 + 60*(b^2 - 4*a*c)*a*b^9*c^5 - 448*(b^2 - 4*a*c)*a^2*b^7*c^6 + 896*(b^2 - 4*a*c)*a^3*b^5*c^7 + 1536*(b^2 - 4*a*c)*a^4*b^3*c^8 - 5120*(b^2 - 4*a*c)*a^5*b*c^9)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 - sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)^2 - 4*(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)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/((a*b^10*c^3 - 20*a^2*b^8*c^4 - 2*a*b^9*c^4 + 160*a^3*b^6*c^5 + 32*a^2*b^7*c^5 + a*b^8*c^5 - 640*a^4*b^4*c^6 - 192*a^3*b^5*c^6 - 16*a^2*b^6*c^6 + 1280*a^5*b^2*c^7 + 512*a^4*b^3*c^7 + 96*a^3*b^4*c^7 - 1024*a^6*c^8 - 512*a^5*b*c^8 - 256*a^4*b^2*c^8 + 256*a^5*c^9)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*abs(c)) + 1/4*(B*b^3*c*x^(7/2) - 16*B*a*b*c^2*x^(7/2) + 3*A*b^2*c^2*x^(7/2) + 12*A*a*c^3*x^(7/2) - B*b^4*x^(5/2) - 5*B*a*b^2*c*x^(5/2) + 5*A*b^3*c*x^(5/2) - 36*B*a^2*c^2*x^(5/2) + 16*A*a*b*c^2*x^(5/2) - 2*B*a*b^3*x^(3/2) - 28*B*a^2*b*c*x^(3/2) + 19*A*a*b^2*c*x^(3/2) - 4*A*a^2*c^2*x^(3/2) - B*a^2*b^2*sqrt(x) - 20*B*a^3*c*sqrt(x) + 12*A*a^2*b*c*sqrt(x))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^2 + b*x + a)^2)","B",0
1025,1,3170,0,2.334909," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 8 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{2} b^{2} c^{3} + 16 \, a b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 128 \, a^{3} c^{4} - 96 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A - 2 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 4 \, a b^{5} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 32 \, a^{2} b^{3} c^{2} + 6 \, a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 64 \, a^{3} b c^{3} - 16 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{16 \, {\left(a b^{8} - 16 \, a^{2} b^{6} c - 2 \, a b^{7} c + 96 \, a^{3} b^{4} c^{2} + 24 \, a^{2} b^{5} c^{2} + a b^{6} c^{2} - 256 \, a^{4} b^{2} c^{3} - 96 \, a^{3} b^{3} c^{3} - 12 \, a^{2} b^{4} c^{3} + 256 \, a^{5} c^{4} + 128 \, a^{4} b c^{4} + 48 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} {\left| c \right|}} + \frac{3 \, {\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 8 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{2} b^{2} c^{3} - 16 \, a b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 128 \, a^{3} c^{4} + 96 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A - 2 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 4 \, a b^{5} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 32 \, a^{2} b^{3} c^{2} - 6 \, a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 64 \, a^{3} b c^{3} + 16 \, a^{2} b^{2} c^{3} + 32 \, a^{3} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} - \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{16 \, {\left(a b^{8} - 16 \, a^{2} b^{6} c - 2 \, a b^{7} c + 96 \, a^{3} b^{4} c^{2} + 24 \, a^{2} b^{5} c^{2} + a b^{6} c^{2} - 256 \, a^{4} b^{2} c^{3} - 96 \, a^{3} b^{3} c^{3} - 12 \, a^{2} b^{4} c^{3} + 256 \, a^{5} c^{4} + 128 \, a^{4} b c^{4} + 48 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} {\left| c \right|}} + \frac{3 \, B b^{2} c x^{\frac{7}{2}} + 12 \, B a c^{2} x^{\frac{7}{2}} - 12 \, A b c^{2} x^{\frac{7}{2}} + 5 \, B b^{3} x^{\frac{5}{2}} + 16 \, B a b c x^{\frac{5}{2}} - 19 \, A b^{2} c x^{\frac{5}{2}} + 4 \, A a c^{2} x^{\frac{5}{2}} + 19 \, B a b^{2} x^{\frac{3}{2}} - 5 \, A b^{3} x^{\frac{3}{2}} - 4 \, B a^{2} c x^{\frac{3}{2}} - 16 \, A a b c x^{\frac{3}{2}} + 12 \, B a^{2} b \sqrt{x} - 3 \, A a b^{2} \sqrt{x} - 12 \, A a^{2} c \sqrt{x}}{4 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"3/16*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 2*b^6*c - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 8*a*b^4*c^2 + 2*b^5*c^2 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^2*b^2*c^3 + 16*a*b^3*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 128*a^3*c^4 - 96*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*(b^2 - 4*a*c)*b^4*c - 2*(b^2 - 4*a*c)*b^3*c^2 - 32*(b^2 - 4*a*c)*a^2*c^3 - 24*(b^2 - 4*a*c)*a*b*c^3)*A - 2*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 4*a*b^5*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 32*a^2*b^3*c^2 + 6*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 64*a^3*b*c^3 - 16*a^2*b^2*c^3 - 32*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 4*(b^2 - 4*a*c)*a*b^3*c - 16*(b^2 - 4*a*c)*a^2*b*c^2 - 6*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(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)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((a*b^8 - 16*a^2*b^6*c - 2*a*b^7*c + 96*a^3*b^4*c^2 + 24*a^2*b^5*c^2 + a*b^6*c^2 - 256*a^4*b^2*c^3 - 96*a^3*b^3*c^3 - 12*a^2*b^4*c^3 + 256*a^5*c^4 + 128*a^4*b*c^4 + 48*a^3*b^2*c^4 - 64*a^4*c^5)*abs(c)) + 3/16*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 2*b^6*c - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 8*a*b^4*c^2 - 2*b^5*c^2 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^2*b^2*c^3 - 16*a*b^3*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 128*a^3*c^4 + 96*a^2*b*c^4 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^4*c + 2*(b^2 - 4*a*c)*b^3*c^2 + 32*(b^2 - 4*a*c)*a^2*c^3 + 24*(b^2 - 4*a*c)*a*b*c^3)*A - 2*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 4*a*b^5*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 32*a^2*b^3*c^2 - 6*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 64*a^3*b*c^3 + 16*a^2*b^2*c^3 + 32*a^3*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 4*(b^2 - 4*a*c)*a*b^3*c + 16*(b^2 - 4*a*c)*a^2*b*c^2 + 6*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 - sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(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)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((a*b^8 - 16*a^2*b^6*c - 2*a*b^7*c + 96*a^3*b^4*c^2 + 24*a^2*b^5*c^2 + a*b^6*c^2 - 256*a^4*b^2*c^3 - 96*a^3*b^3*c^3 - 12*a^2*b^4*c^3 + 256*a^5*c^4 + 128*a^4*b*c^4 + 48*a^3*b^2*c^4 - 64*a^4*c^5)*abs(c)) + 1/4*(3*B*b^2*c*x^(7/2) + 12*B*a*c^2*x^(7/2) - 12*A*b*c^2*x^(7/2) + 5*B*b^3*x^(5/2) + 16*B*a*b*c*x^(5/2) - 19*A*b^2*c*x^(5/2) + 4*A*a*c^2*x^(5/2) + 19*B*a*b^2*x^(3/2) - 5*A*b^3*x^(3/2) - 4*B*a^2*c*x^(3/2) - 16*A*a*b*c*x^(3/2) + 12*B*a^2*b*sqrt(x) - 3*A*a*b^2*sqrt(x) - 12*A*a^2*c*sqrt(x))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","B",0
1026,1,7277,0,3.195128," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left({\left(2 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} - 160 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 40 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} A - 12 \, {\left(2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} B + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{9} - 28 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c - 2 \, a b^{9} c + 240 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} + 56 \, a^{2} b^{7} c^{2} - 832 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 288 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 480 \, a^{3} b^{5} c^{3} + 1024 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 512 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 1664 \, a^{4} b^{3} c^{4} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 2048 \, a^{5} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{7} c - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 512 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} + 6 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, a^{2} b^{8} c + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + 16 \, a^{3} b^{6} c^{2} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 256 \, a^{5} b^{2} c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 512 \, a^{6} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} B {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} + {\left(2 \, a^{2} b^{12} c^{2} - 136 \, a^{3} b^{10} c^{3} + 1856 \, a^{4} b^{8} c^{4} - 10496 \, a^{5} b^{6} c^{5} + 27136 \, a^{6} b^{4} c^{6} - 26624 \, a^{7} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{12} + 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{11} c - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{10} c^{2} + 5248 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{3} - 13568 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{4} + 13312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{10} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{8} c^{3} - 1344 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{4} + 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{6}\right)} A + 6 \, {\left(6 \, a^{3} b^{11} c^{2} - 88 \, a^{4} b^{9} c^{3} + 448 \, a^{5} b^{7} c^{4} - 768 \, a^{6} b^{5} c^{5} - 512 \, a^{7} b^{3} c^{6} + 2048 \, a^{8} b c^{7} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{3} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{4} + 512 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + \sqrt{{\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)}}}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}}}}\right)}{32 \, {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c - 2 \, a^{3} b^{9} c + 160 \, a^{5} b^{6} c^{2} + 32 \, a^{4} b^{7} c^{2} + a^{3} b^{8} c^{2} - 640 \, a^{6} b^{4} c^{3} - 192 \, a^{5} b^{5} c^{3} - 16 \, a^{4} b^{6} c^{3} + 1280 \, a^{7} b^{2} c^{4} + 512 \, a^{6} b^{3} c^{4} + 96 \, a^{5} b^{4} c^{4} - 1024 \, a^{8} c^{5} - 512 \, a^{7} b c^{5} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} - 160 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 40 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} A - 12 \, {\left(2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} B - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{9} - 28 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c + 2 \, a b^{9} c + 240 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} - 56 \, a^{2} b^{7} c^{2} - 832 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 288 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 480 \, a^{3} b^{5} c^{3} + 1024 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 512 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 1664 \, a^{4} b^{3} c^{4} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 2048 \, a^{5} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{7} c + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} + 512 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} - 6 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c + 2 \, a^{2} b^{8} c + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 16 \, a^{3} b^{6} c^{2} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 256 \, a^{5} b^{2} c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} - 512 \, a^{6} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} B {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} + {\left(2 \, a^{2} b^{12} c^{2} - 136 \, a^{3} b^{10} c^{3} + 1856 \, a^{4} b^{8} c^{4} - 10496 \, a^{5} b^{6} c^{5} + 27136 \, a^{6} b^{4} c^{6} - 26624 \, a^{7} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{12} + 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{11} c - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{10} c^{2} + 5248 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{3} - 13568 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{4} + 13312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{10} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{8} c^{3} - 1344 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{4} + 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{6}\right)} A + 6 \, {\left(6 \, a^{3} b^{11} c^{2} - 88 \, a^{4} b^{9} c^{3} + 448 \, a^{5} b^{7} c^{4} - 768 \, a^{6} b^{5} c^{5} - 512 \, a^{7} b^{3} c^{6} + 2048 \, a^{8} b c^{7} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{3} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{4} + 512 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} - \sqrt{{\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)}}}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}}}}\right)}{32 \, {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c - 2 \, a^{3} b^{9} c + 160 \, a^{5} b^{6} c^{2} + 32 \, a^{4} b^{7} c^{2} + a^{3} b^{8} c^{2} - 640 \, a^{6} b^{4} c^{3} - 192 \, a^{5} b^{5} c^{3} - 16 \, a^{4} b^{6} c^{3} + 1280 \, a^{7} b^{2} c^{4} + 512 \, a^{6} b^{3} c^{4} + 96 \, a^{5} b^{4} c^{4} - 1024 \, a^{8} c^{5} - 512 \, a^{7} b c^{5} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} {\left| c \right|}} - \frac{12 \, B a b c^{2} x^{\frac{7}{2}} - A b^{2} c^{2} x^{\frac{7}{2}} - 20 \, A a c^{3} x^{\frac{7}{2}} + 19 \, B a b^{2} c x^{\frac{5}{2}} - 2 \, A b^{3} c x^{\frac{5}{2}} - 4 \, B a^{2} c^{2} x^{\frac{5}{2}} - 28 \, A a b c^{2} x^{\frac{5}{2}} + 5 \, B a b^{3} x^{\frac{3}{2}} - A b^{4} x^{\frac{3}{2}} + 16 \, B a^{2} b c x^{\frac{3}{2}} - 5 \, A a b^{2} c x^{\frac{3}{2}} - 36 \, A a^{2} c^{2} x^{\frac{3}{2}} + 3 \, B a^{2} b^{2} \sqrt{x} + A a b^{3} \sqrt{x} + 12 \, B a^{3} c \sqrt{x} - 16 \, A a^{2} b c \sqrt{x}}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"1/32*((2*b^4*c^2 + 32*a*b^2*c^3 - 160*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 - 40*(b^2 - 4*a*c)*a*c^3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*A - 12*(2*a*b^3*c^2 - 8*a^2*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*B + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^9 - 28*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c - 2*a*b^9*c + 240*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 + 56*a^2*b^7*c^2 - 832*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 288*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 480*a^3*b^5*c^3 + 1024*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 512*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 1664*a^4*b^3*c^4 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 2048*a^5*b*c^5 + 2*(b^2 - 4*a*c)*a*b^7*c - 48*(b^2 - 4*a*c)*a^2*b^5*c^2 + 288*(b^2 - 4*a*c)*a^3*b^3*c^3 - 512*(b^2 - 4*a*c)*a^4*b*c^4)*A*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + 6*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*a^2*b^8*c + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 16*a^3*b^6*c^2 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 256*a^5*b^2*c^4 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 512*a^6*c^5 + 2*(b^2 - 4*a*c)*a^2*b^6*c - 8*(b^2 - 4*a*c)*a^3*b^4*c^2 - 32*(b^2 - 4*a*c)*a^4*b^2*c^3 + 128*(b^2 - 4*a*c)*a^5*c^4)*B*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + (2*a^2*b^12*c^2 - 136*a^3*b^10*c^3 + 1856*a^4*b^8*c^4 - 10496*a^5*b^6*c^5 + 27136*a^6*b^4*c^6 - 26624*a^7*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^12 + 68*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^11*c - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^10*c^2 + 5248*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^3 - 13568*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^4 + 13312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^6 - 2*(b^2 - 4*a*c)*a^2*b^10*c^2 + 128*(b^2 - 4*a*c)*a^3*b^8*c^3 - 1344*(b^2 - 4*a*c)*a^4*b^6*c^4 + 5120*(b^2 - 4*a*c)*a^5*b^4*c^5 - 6656*(b^2 - 4*a*c)*a^6*b^2*c^6)*A + 6*(6*a^3*b^11*c^2 - 88*a^4*b^9*c^3 + 448*a^5*b^7*c^4 - 768*a^6*b^5*c^5 - 512*a^7*b^3*c^6 + 2048*a^8*b*c^7 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^11 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 6*(b^2 - 4*a*c)*a^3*b^9*c^2 + 64*(b^2 - 4*a*c)*a^4*b^7*c^3 - 192*(b^2 - 4*a*c)*a^5*b^5*c^4 + 512*(b^2 - 4*a*c)*a^7*b*c^6)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)^2 - 4*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/((a^3*b^10 - 20*a^4*b^8*c - 2*a^3*b^9*c + 160*a^5*b^6*c^2 + 32*a^4*b^7*c^2 + a^3*b^8*c^2 - 640*a^6*b^4*c^3 - 192*a^5*b^5*c^3 - 16*a^4*b^6*c^3 + 1280*a^7*b^2*c^4 + 512*a^6*b^3*c^4 + 96*a^5*b^4*c^4 - 1024*a^8*c^5 - 512*a^7*b*c^5 - 256*a^6*b^2*c^5 + 256*a^7*c^6)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*abs(c)) - 1/32*((2*b^4*c^2 + 32*a*b^2*c^3 - 160*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 - 40*(b^2 - 4*a*c)*a*c^3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*A - 12*(2*a*b^3*c^2 - 8*a^2*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*B - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^9 - 28*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c + 2*a*b^9*c + 240*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 - 56*a^2*b^7*c^2 - 832*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 288*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 480*a^3*b^5*c^3 + 1024*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 512*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 1664*a^4*b^3*c^4 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 2048*a^5*b*c^5 - 2*(b^2 - 4*a*c)*a*b^7*c + 48*(b^2 - 4*a*c)*a^2*b^5*c^2 - 288*(b^2 - 4*a*c)*a^3*b^3*c^3 + 512*(b^2 - 4*a*c)*a^4*b*c^4)*A*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) - 6*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 2*a^2*b^8*c + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 16*a^3*b^6*c^2 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 256*a^5*b^2*c^4 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5 - 512*a^6*c^5 - 2*(b^2 - 4*a*c)*a^2*b^6*c + 8*(b^2 - 4*a*c)*a^3*b^4*c^2 + 32*(b^2 - 4*a*c)*a^4*b^2*c^3 - 128*(b^2 - 4*a*c)*a^5*c^4)*B*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + (2*a^2*b^12*c^2 - 136*a^3*b^10*c^3 + 1856*a^4*b^8*c^4 - 10496*a^5*b^6*c^5 + 27136*a^6*b^4*c^6 - 26624*a^7*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^12 + 68*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^11*c - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^10*c^2 + 5248*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^3 - 13568*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^4 + 13312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^6 - 2*(b^2 - 4*a*c)*a^2*b^10*c^2 + 128*(b^2 - 4*a*c)*a^3*b^8*c^3 - 1344*(b^2 - 4*a*c)*a^4*b^6*c^4 + 5120*(b^2 - 4*a*c)*a^5*b^4*c^5 - 6656*(b^2 - 4*a*c)*a^6*b^2*c^6)*A + 6*(6*a^3*b^11*c^2 - 88*a^4*b^9*c^3 + 448*a^5*b^7*c^4 - 768*a^6*b^5*c^5 - 512*a^7*b^3*c^6 + 2048*a^8*b*c^7 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^11 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 6*(b^2 - 4*a*c)*a^3*b^9*c^2 + 64*(b^2 - 4*a*c)*a^4*b^7*c^3 - 192*(b^2 - 4*a*c)*a^5*b^5*c^4 + 512*(b^2 - 4*a*c)*a^7*b*c^6)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 - sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)^2 - 4*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/((a^3*b^10 - 20*a^4*b^8*c - 2*a^3*b^9*c + 160*a^5*b^6*c^2 + 32*a^4*b^7*c^2 + a^3*b^8*c^2 - 640*a^6*b^4*c^3 - 192*a^5*b^5*c^3 - 16*a^4*b^6*c^3 + 1280*a^7*b^2*c^4 + 512*a^6*b^3*c^4 + 96*a^5*b^4*c^4 - 1024*a^8*c^5 - 512*a^7*b*c^5 - 256*a^6*b^2*c^5 + 256*a^7*c^6)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*abs(c)) - 1/4*(12*B*a*b*c^2*x^(7/2) - A*b^2*c^2*x^(7/2) - 20*A*a*c^3*x^(7/2) + 19*B*a*b^2*c*x^(5/2) - 2*A*b^3*c*x^(5/2) - 4*B*a^2*c^2*x^(5/2) - 28*A*a*b*c^2*x^(5/2) + 5*B*a*b^3*x^(3/2) - A*b^4*x^(3/2) + 16*B*a^2*b*c*x^(3/2) - 5*A*a*b^2*c*x^(3/2) - 36*A*a^2*c^2*x^(3/2) + 3*B*a^2*b^2*sqrt(x) + A*a*b^3*sqrt(x) + 12*B*a^3*c*sqrt(x) - 16*A*a^2*b*c*sqrt(x))/((a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(c*x^2 + b*x + a)^2)","B",0
1027,1,4621,0,2.464600," ","integrate((B*x+A)/(c*x^2+b*x+a)^3/x^(1/2),x, algorithm=""giac"")","\frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} - 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} + 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} - 352 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 48 \, a^{2} b^{5} c^{2} + 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 288 \, a^{3} b^{3} c^{3} - 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 512 \, a^{4} b c^{4} + 64 \, a^{3} b^{2} c^{4} + 320 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + \sqrt{{\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)}}}{a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}}}}\right)}{16 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c - 2 \, a^{3} b^{7} c + 96 \, a^{5} b^{4} c^{2} + 24 \, a^{4} b^{5} c^{2} + a^{3} b^{6} c^{2} - 256 \, a^{6} b^{2} c^{3} - 96 \, a^{5} b^{3} c^{3} - 12 \, a^{4} b^{4} c^{3} + 256 \, a^{7} c^{4} + 128 \, a^{6} b c^{4} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} {\left| c \right|}} + \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} - \sqrt{{\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)}}}{a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}}}}\right)}{16 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c - 2 \, a^{3} b^{7} c + 96 \, a^{5} b^{4} c^{2} + 24 \, a^{4} b^{5} c^{2} + a^{3} b^{6} c^{2} - 256 \, a^{6} b^{2} c^{3} - 96 \, a^{5} b^{3} c^{3} - 12 \, a^{4} b^{4} c^{3} + 256 \, a^{7} c^{4} + 128 \, a^{6} b c^{4} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} {\left| c \right|}} + \frac{B a b^{2} c^{2} x^{\frac{7}{2}} + 3 \, A b^{3} c^{2} x^{\frac{7}{2}} + 20 \, B a^{2} c^{3} x^{\frac{7}{2}} - 24 \, A a b c^{3} x^{\frac{7}{2}} + 2 \, B a b^{3} c x^{\frac{5}{2}} + 6 \, A b^{4} c x^{\frac{5}{2}} + 28 \, B a^{2} b c^{2} x^{\frac{5}{2}} - 49 \, A a b^{2} c^{2} x^{\frac{5}{2}} + 28 \, A a^{2} c^{3} x^{\frac{5}{2}} + B a b^{4} x^{\frac{3}{2}} + 3 \, A b^{5} x^{\frac{3}{2}} + 5 \, B a^{2} b^{2} c x^{\frac{3}{2}} - 20 \, A a b^{3} c x^{\frac{3}{2}} + 36 \, B a^{3} c^{2} x^{\frac{3}{2}} - 4 \, A a^{2} b c^{2} x^{\frac{3}{2}} - B a^{2} b^{3} \sqrt{x} + 5 \, A a b^{4} \sqrt{x} + 16 \, B a^{3} b c \sqrt{x} - 37 \, A a^{2} b^{2} c \sqrt{x} + 44 \, A a^{3} c^{2} \sqrt{x}}{4 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"1/16*(3*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8 - 17*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c - 2*b^8*c + 116*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 26*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 34*a*b^6*c^2 + 2*b^7*c^2 - 368*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 13*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 232*a^2*b^4*c^3 - 30*a*b^5*c^3 + 448*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 736*a^3*b^2*c^4 + 176*a^2*b^3*c^4 - 112*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 896*a^4*c^5 - 352*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 2*(b^2 - 4*a*c)*b^6*c - 26*(b^2 - 4*a*c)*a*b^4*c^2 - 2*(b^2 - 4*a*c)*b^5*c^2 + 128*(b^2 - 4*a*c)*a^2*b^2*c^3 + 22*(b^2 - 4*a*c)*a*b^3*c^3 - 224*(b^2 - 4*a*c)*a^3*c^4 - 88*(b^2 - 4*a*c)*a^2*b*c^4)*A + (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*a*b^7*c + 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 48*a^2*b^5*c^2 + 2*a*b^6*c^2 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 288*a^3*b^3*c^3 - 44*a^2*b^4*c^3 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 512*a^4*b*c^4 + 64*a^3*b^2*c^4 + 320*a^4*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 36*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 2*(b^2 - 4*a*c)*a*b^5*c - 40*(b^2 - 4*a*c)*a^2*b^3*c^2 - 2*(b^2 - 4*a*c)*a*b^4*c^2 + 128*(b^2 - 4*a*c)*a^3*b*c^3 + 36*(b^2 - 4*a*c)*a^2*b^2*c^3 + 80*(b^2 - 4*a*c)*a^3*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)^2 - 4*(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)))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/((a^3*b^8 - 16*a^4*b^6*c - 2*a^3*b^7*c + 96*a^5*b^4*c^2 + 24*a^4*b^5*c^2 + a^3*b^6*c^2 - 256*a^6*b^2*c^3 - 96*a^5*b^3*c^3 - 12*a^4*b^4*c^3 + 256*a^7*c^4 + 128*a^6*b*c^4 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*abs(c)) + 1/16*(3*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8 - 17*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c + 2*b^8*c + 116*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 26*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 - 34*a*b^6*c^2 - 2*b^7*c^2 - 368*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 13*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 232*a^2*b^4*c^3 + 30*a*b^5*c^3 + 448*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 224*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 736*a^3*b^2*c^4 - 176*a^2*b^3*c^4 - 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 896*a^4*c^5 + 352*a^3*b*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^6*c + 26*(b^2 - 4*a*c)*a*b^4*c^2 + 2*(b^2 - 4*a*c)*b^5*c^2 - 128*(b^2 - 4*a*c)*a^2*b^2*c^3 - 22*(b^2 - 4*a*c)*a*b^3*c^3 + 224*(b^2 - 4*a*c)*a^3*c^4 + 88*(b^2 - 4*a*c)*a^2*b*c^4)*A + (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 2*a*b^7*c + 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 48*a^2*b^5*c^2 - 2*a*b^6*c^2 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 288*a^3*b^3*c^3 + 44*a^2*b^4*c^3 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 512*a^4*b*c^4 - 64*a^3*b^2*c^4 - 320*a^4*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 - 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 36*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 2*(b^2 - 4*a*c)*a*b^5*c + 40*(b^2 - 4*a*c)*a^2*b^3*c^2 + 2*(b^2 - 4*a*c)*a*b^4*c^2 - 128*(b^2 - 4*a*c)*a^3*b*c^3 - 36*(b^2 - 4*a*c)*a^2*b^2*c^3 - 80*(b^2 - 4*a*c)*a^3*c^4)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 - sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)^2 - 4*(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)))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/((a^3*b^8 - 16*a^4*b^6*c - 2*a^3*b^7*c + 96*a^5*b^4*c^2 + 24*a^4*b^5*c^2 + a^3*b^6*c^2 - 256*a^6*b^2*c^3 - 96*a^5*b^3*c^3 - 12*a^4*b^4*c^3 + 256*a^7*c^4 + 128*a^6*b*c^4 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*abs(c)) + 1/4*(B*a*b^2*c^2*x^(7/2) + 3*A*b^3*c^2*x^(7/2) + 20*B*a^2*c^3*x^(7/2) - 24*A*a*b*c^3*x^(7/2) + 2*B*a*b^3*c*x^(5/2) + 6*A*b^4*c*x^(5/2) + 28*B*a^2*b*c^2*x^(5/2) - 49*A*a*b^2*c^2*x^(5/2) + 28*A*a^2*c^3*x^(5/2) + B*a*b^4*x^(3/2) + 3*A*b^5*x^(3/2) + 5*B*a^2*b^2*c*x^(3/2) - 20*A*a*b^3*c*x^(3/2) + 36*B*a^3*c^2*x^(3/2) - 4*A*a^2*b*c^2*x^(3/2) - B*a^2*b^3*sqrt(x) + 5*A*a*b^4*sqrt(x) + 16*B*a^3*b*c*sqrt(x) - 37*A*a^2*b^2*c*sqrt(x) + 44*A*a^3*c^2*sqrt(x))/((a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(c*x^2 + b*x + a)^2)","B",0
1028,1,9534,0,3.356821," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left({\left(10 \, b^{6} c^{2} - 114 \, a b^{4} c^{3} + 416 \, a^{2} b^{2} c^{4} - 480 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 57 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 37 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 120 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} A - {\left(2 \, a b^{5} c^{2} - 24 \, a^{2} b^{3} c^{3} + 64 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} B + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} - 102 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c - 10 \, a^{3} b^{11} c + 836 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + 164 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} + 204 \, a^{4} b^{9} c^{2} - 3440 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 1016 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 82 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} - 1672 \, a^{5} b^{7} c^{3} + 7104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 2816 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 508 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} + 6880 \, a^{6} b^{5} c^{4} - 5888 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 2944 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 1408 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} - 14208 \, a^{7} b^{3} c^{5} + 1472 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} + 11776 \, a^{8} b c^{6} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c - 164 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} + 1016 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} - 2816 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} + 2944 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} A {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{10} - 21 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{8} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 2 \, a^{4} b^{10} c + 184 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c^{2} + 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 42 \, a^{5} b^{8} c^{2} - 832 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c^{3} - 232 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 368 \, a^{6} b^{6} c^{3} + 1920 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{4} + 736 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 1664 \, a^{7} b^{4} c^{4} - 1792 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} c^{5} - 896 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 3840 \, a^{8} b^{2} c^{5} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{6} + 3584 \, a^{9} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{8} c - 34 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{6} c^{2} + 232 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{3} - 736 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{4} + 896 \, {\left(b^{2} - 4 \, a c\right)} a^{8} c^{5}\right)} B {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} + {\left(10 \, a^{6} b^{14} c^{2} - 254 \, a^{7} b^{12} c^{3} + 2712 \, a^{8} b^{10} c^{4} - 15552 \, a^{9} b^{8} c^{5} + 50432 \, a^{10} b^{6} c^{6} - 87552 \, a^{11} b^{4} c^{7} + 63488 \, a^{12} b^{2} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{14} + 127 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{13} c - 1356 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - 214 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{12} c^{2} + 7776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 1856 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} + 107 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{10} c^{3} - 25216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 8128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{8} c^{4} + 43776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 17920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} + 4064 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} c^{5} - 31744 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 15872 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} - 8960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c^{6} + 7936 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{7} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{12} c^{2} + 214 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{10} c^{3} - 1856 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{8} c^{4} + 8128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{6} c^{5} - 17920 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{4} c^{6} + 15872 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{2} c^{7}\right)} A - {\left(2 \, a^{7} b^{13} c^{2} - 52 \, a^{8} b^{11} c^{3} + 624 \, a^{9} b^{9} c^{4} - 4224 \, a^{10} b^{7} c^{5} + 16384 \, a^{11} b^{5} c^{6} - 33792 \, a^{12} b^{3} c^{7} + 28672 \, a^{13} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{13} + 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{11} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c - 312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{2} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} + 2112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{3} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} - 8192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{4} - 2432 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} + 16896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 1216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} - 14336 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b c^{6} - 7168 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} + 3584 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{11} c^{2} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{9} c^{3} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{7} c^{4} + 2432 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{5} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{3} c^{6} + 7168 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b c^{7}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + \sqrt{{\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right)}{32 \, {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c - 2 \, a^{7} b^{9} c + 160 \, a^{9} b^{6} c^{2} + 32 \, a^{8} b^{7} c^{2} + a^{7} b^{8} c^{2} - 640 \, a^{10} b^{4} c^{3} - 192 \, a^{9} b^{5} c^{3} - 16 \, a^{8} b^{6} c^{3} + 1280 \, a^{11} b^{2} c^{4} + 512 \, a^{10} b^{3} c^{4} + 96 \, a^{9} b^{4} c^{4} - 1024 \, a^{12} c^{5} - 512 \, a^{11} b c^{5} - 256 \, a^{10} b^{2} c^{5} + 256 \, a^{11} c^{6}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} {\left| c \right|}} + \frac{3 \, {\left({\left(10 \, b^{6} c^{2} - 114 \, a b^{4} c^{3} + 416 \, a^{2} b^{2} c^{4} - 480 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 57 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 37 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 120 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} A - {\left(2 \, a b^{5} c^{2} - 24 \, a^{2} b^{3} c^{3} + 64 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} B - 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} - 102 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 10 \, a^{3} b^{11} c + 836 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + 164 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - 204 \, a^{4} b^{9} c^{2} - 3440 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 1016 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 82 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 1672 \, a^{5} b^{7} c^{3} + 7104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 2816 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 508 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 6880 \, a^{6} b^{5} c^{4} - 5888 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 2944 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 1408 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 14208 \, a^{7} b^{3} c^{5} + 1472 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 11776 \, a^{8} b c^{6} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c + 164 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} - 1016 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} + 2816 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} - 2944 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} A {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{10} - 21 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{8} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c + 2 \, a^{4} b^{10} c + 184 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c^{2} + 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 42 \, a^{5} b^{8} c^{2} - 832 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c^{3} - 232 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 368 \, a^{6} b^{6} c^{3} + 1920 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{4} + 736 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 1664 \, a^{7} b^{4} c^{4} - 1792 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} c^{5} - 896 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 3840 \, a^{8} b^{2} c^{5} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{6} - 3584 \, a^{9} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{8} c + 34 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{6} c^{2} - 232 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{3} + 736 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{4} - 896 \, {\left(b^{2} - 4 \, a c\right)} a^{8} c^{5}\right)} B {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} + {\left(10 \, a^{6} b^{14} c^{2} - 254 \, a^{7} b^{12} c^{3} + 2712 \, a^{8} b^{10} c^{4} - 15552 \, a^{9} b^{8} c^{5} + 50432 \, a^{10} b^{6} c^{6} - 87552 \, a^{11} b^{4} c^{7} + 63488 \, a^{12} b^{2} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{14} + 127 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{13} c - 1356 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - 214 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{12} c^{2} + 7776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 1856 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} + 107 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{10} c^{3} - 25216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 8128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{8} c^{4} + 43776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 17920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} + 4064 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} c^{5} - 31744 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 15872 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} - 8960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c^{6} + 7936 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{7} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{12} c^{2} + 214 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{10} c^{3} - 1856 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{8} c^{4} + 8128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{6} c^{5} - 17920 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{4} c^{6} + 15872 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{2} c^{7}\right)} A - {\left(2 \, a^{7} b^{13} c^{2} - 52 \, a^{8} b^{11} c^{3} + 624 \, a^{9} b^{9} c^{4} - 4224 \, a^{10} b^{7} c^{5} + 16384 \, a^{11} b^{5} c^{6} - 33792 \, a^{12} b^{3} c^{7} + 28672 \, a^{13} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{13} + 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{11} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c - 312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{2} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} + 2112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{3} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} - 8192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{4} - 2432 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} + 16896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 1216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} - 14336 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b c^{6} - 7168 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} + 3584 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{11} c^{2} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{9} c^{3} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{7} c^{4} + 2432 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{5} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{3} c^{6} + 7168 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b c^{7}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} - \sqrt{{\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right)}{32 \, {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c - 2 \, a^{7} b^{9} c + 160 \, a^{9} b^{6} c^{2} + 32 \, a^{8} b^{7} c^{2} + a^{7} b^{8} c^{2} - 640 \, a^{10} b^{4} c^{3} - 192 \, a^{9} b^{5} c^{3} - 16 \, a^{8} b^{6} c^{3} + 1280 \, a^{11} b^{2} c^{4} + 512 \, a^{10} b^{3} c^{4} + 96 \, a^{9} b^{4} c^{4} - 1024 \, a^{12} c^{5} - 512 \, a^{11} b c^{5} - 256 \, a^{10} b^{2} c^{5} + 256 \, a^{11} c^{6}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} {\left| c \right|}} + \frac{3 \, B a b^{3} c^{2} x^{\frac{7}{2}} - 7 \, A b^{4} c^{2} x^{\frac{7}{2}} - 24 \, B a^{2} b c^{3} x^{\frac{7}{2}} + 47 \, A a b^{2} c^{3} x^{\frac{7}{2}} - 52 \, A a^{2} c^{4} x^{\frac{7}{2}} + 6 \, B a b^{4} c x^{\frac{5}{2}} - 14 \, A b^{5} c x^{\frac{5}{2}} - 49 \, B a^{2} b^{2} c^{2} x^{\frac{5}{2}} + 99 \, A a b^{3} c^{2} x^{\frac{5}{2}} + 28 \, B a^{3} c^{3} x^{\frac{5}{2}} - 136 \, A a^{2} b c^{3} x^{\frac{5}{2}} + 3 \, B a b^{5} x^{\frac{3}{2}} - 7 \, A b^{6} x^{\frac{3}{2}} - 20 \, B a^{2} b^{3} c x^{\frac{3}{2}} + 43 \, A a b^{4} c x^{\frac{3}{2}} - 4 \, B a^{3} b c^{2} x^{\frac{3}{2}} - 25 \, A a^{2} b^{2} c^{2} x^{\frac{3}{2}} - 68 \, A a^{3} c^{3} x^{\frac{3}{2}} + 5 \, B a^{2} b^{4} \sqrt{x} - 9 \, A a b^{5} \sqrt{x} - 37 \, B a^{3} b^{2} c \sqrt{x} + 66 \, A a^{2} b^{3} c \sqrt{x} + 44 \, B a^{4} c^{2} \sqrt{x} - 108 \, A a^{3} b c^{2} \sqrt{x}}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}} - \frac{2 \, A}{a^{3} \sqrt{x}}"," ",0,"-3/32*((10*b^6*c^2 - 114*a*b^4*c^3 + 416*a^2*b^2*c^4 - 480*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 57*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 37*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 74*(b^2 - 4*a*c)*a*b^2*c^3 - 120*(b^2 - 4*a*c)*a^2*c^4)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2*A - (2*a*b^5*c^2 - 24*a^2*b^3*c^3 + 64*a^3*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 + 16*(b^2 - 4*a*c)*a^2*b*c^3)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2*B + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^11 - 102*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c - 10*a^3*b^11*c + 836*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + 164*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 + 204*a^4*b^9*c^2 - 3440*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 1016*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 82*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 - 1672*a^5*b^7*c^3 + 7104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 2816*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 508*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 + 6880*a^6*b^5*c^4 - 5888*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 2944*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 1408*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 - 14208*a^7*b^3*c^5 + 1472*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 + 11776*a^8*b*c^6 + 10*(b^2 - 4*a*c)*a^3*b^9*c - 164*(b^2 - 4*a*c)*a^4*b^7*c^2 + 1016*(b^2 - 4*a*c)*a^5*b^5*c^3 - 2816*(b^2 - 4*a*c)*a^6*b^3*c^4 + 2944*(b^2 - 4*a*c)*a^7*b*c^5)*A*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^10 - 21*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^8*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 2*a^4*b^10*c + 184*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c^2 + 34*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 42*a^5*b^8*c^2 - 832*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c^3 - 232*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 17*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 368*a^6*b^6*c^3 + 1920*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^4 + 736*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 116*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 1664*a^7*b^4*c^4 - 1792*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*c^5 - 896*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 368*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 3840*a^8*b^2*c^5 + 448*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*c^6 + 3584*a^9*c^6 + 2*(b^2 - 4*a*c)*a^4*b^8*c - 34*(b^2 - 4*a*c)*a^5*b^6*c^2 + 232*(b^2 - 4*a*c)*a^6*b^4*c^3 - 736*(b^2 - 4*a*c)*a^7*b^2*c^4 + 896*(b^2 - 4*a*c)*a^8*c^5)*B*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2) + (10*a^6*b^14*c^2 - 254*a^7*b^12*c^3 + 2712*a^8*b^10*c^4 - 15552*a^9*b^8*c^5 + 50432*a^10*b^6*c^6 - 87552*a^11*b^4*c^7 + 63488*a^12*b^2*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^14 + 127*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^13*c - 1356*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - 214*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^12*c^2 + 7776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 1856*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 + 107*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^10*c^3 - 25216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 8128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^8*c^4 + 43776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 17920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 + 4064*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^6*c^5 - 31744*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 15872*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 - 8960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c^6 + 7936*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^7 - 10*(b^2 - 4*a*c)*a^6*b^12*c^2 + 214*(b^2 - 4*a*c)*a^7*b^10*c^3 - 1856*(b^2 - 4*a*c)*a^8*b^8*c^4 + 8128*(b^2 - 4*a*c)*a^9*b^6*c^5 - 17920*(b^2 - 4*a*c)*a^10*b^4*c^6 + 15872*(b^2 - 4*a*c)*a^11*b^2*c^7)*A - (2*a^7*b^13*c^2 - 52*a^8*b^11*c^3 + 624*a^9*b^9*c^4 - 4224*a^10*b^7*c^5 + 16384*a^11*b^5*c^6 - 33792*a^12*b^3*c^7 + 28672*a^13*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^13 + 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^11*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c - 312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^2 - 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 + 2112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^3 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 - 8192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^4 - 2432*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 + 16896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 1216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 - 14336*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b*c^6 - 7168*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 + 3584*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b*c^7 - 2*(b^2 - 4*a*c)*a^7*b^11*c^2 + 44*(b^2 - 4*a*c)*a^8*b^9*c^3 - 448*(b^2 - 4*a*c)*a^9*b^7*c^4 + 2432*(b^2 - 4*a*c)*a^10*b^5*c^5 - 6656*(b^2 - 4*a*c)*a^11*b^3*c^6 + 7168*(b^2 - 4*a*c)*a^12*b*c^7)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)^2 - 4*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/((a^7*b^10 - 20*a^8*b^8*c - 2*a^7*b^9*c + 160*a^9*b^6*c^2 + 32*a^8*b^7*c^2 + a^7*b^8*c^2 - 640*a^10*b^4*c^3 - 192*a^9*b^5*c^3 - 16*a^8*b^6*c^3 + 1280*a^11*b^2*c^4 + 512*a^10*b^3*c^4 + 96*a^9*b^4*c^4 - 1024*a^12*c^5 - 512*a^11*b*c^5 - 256*a^10*b^2*c^5 + 256*a^11*c^6)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*abs(c)) + 3/32*((10*b^6*c^2 - 114*a*b^4*c^3 + 416*a^2*b^2*c^4 - 480*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 57*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 37*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 74*(b^2 - 4*a*c)*a*b^2*c^3 - 120*(b^2 - 4*a*c)*a^2*c^4)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2*A - (2*a*b^5*c^2 - 24*a^2*b^3*c^3 + 64*a^3*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 + 16*(b^2 - 4*a*c)*a^2*b*c^3)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2*B - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^11 - 102*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 10*a^3*b^11*c + 836*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + 164*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - 204*a^4*b^9*c^2 - 3440*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 1016*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 82*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 1672*a^5*b^7*c^3 + 7104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 2816*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 508*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 6880*a^6*b^5*c^4 - 5888*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 2944*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 1408*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 14208*a^7*b^3*c^5 + 1472*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 11776*a^8*b*c^6 - 10*(b^2 - 4*a*c)*a^3*b^9*c + 164*(b^2 - 4*a*c)*a^4*b^7*c^2 - 1016*(b^2 - 4*a*c)*a^5*b^5*c^3 + 2816*(b^2 - 4*a*c)*a^6*b^3*c^4 - 2944*(b^2 - 4*a*c)*a^7*b*c^5)*A*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^10 - 21*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^8*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c + 2*a^4*b^10*c + 184*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c^2 + 34*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 42*a^5*b^8*c^2 - 832*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c^3 - 232*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 17*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 368*a^6*b^6*c^3 + 1920*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^4 + 736*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 116*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 1664*a^7*b^4*c^4 - 1792*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*c^5 - 896*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 368*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 3840*a^8*b^2*c^5 + 448*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*c^6 - 3584*a^9*c^6 - 2*(b^2 - 4*a*c)*a^4*b^8*c + 34*(b^2 - 4*a*c)*a^5*b^6*c^2 - 232*(b^2 - 4*a*c)*a^6*b^4*c^3 + 736*(b^2 - 4*a*c)*a^7*b^2*c^4 - 896*(b^2 - 4*a*c)*a^8*c^5)*B*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2) + (10*a^6*b^14*c^2 - 254*a^7*b^12*c^3 + 2712*a^8*b^10*c^4 - 15552*a^9*b^8*c^5 + 50432*a^10*b^6*c^6 - 87552*a^11*b^4*c^7 + 63488*a^12*b^2*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^14 + 127*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^13*c - 1356*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - 214*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^12*c^2 + 7776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 1856*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 + 107*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^10*c^3 - 25216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 8128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^8*c^4 + 43776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 17920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 + 4064*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^6*c^5 - 31744*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 15872*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 - 8960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c^6 + 7936*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^7 - 10*(b^2 - 4*a*c)*a^6*b^12*c^2 + 214*(b^2 - 4*a*c)*a^7*b^10*c^3 - 1856*(b^2 - 4*a*c)*a^8*b^8*c^4 + 8128*(b^2 - 4*a*c)*a^9*b^6*c^5 - 17920*(b^2 - 4*a*c)*a^10*b^4*c^6 + 15872*(b^2 - 4*a*c)*a^11*b^2*c^7)*A - (2*a^7*b^13*c^2 - 52*a^8*b^11*c^3 + 624*a^9*b^9*c^4 - 4224*a^10*b^7*c^5 + 16384*a^11*b^5*c^6 - 33792*a^12*b^3*c^7 + 28672*a^13*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^13 + 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^11*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c - 312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^2 - 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 + 2112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^3 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 - 8192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^4 - 2432*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 + 16896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 1216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 - 14336*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b*c^6 - 7168*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 + 3584*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b*c^7 - 2*(b^2 - 4*a*c)*a^7*b^11*c^2 + 44*(b^2 - 4*a*c)*a^8*b^9*c^3 - 448*(b^2 - 4*a*c)*a^9*b^7*c^4 + 2432*(b^2 - 4*a*c)*a^10*b^5*c^5 - 6656*(b^2 - 4*a*c)*a^11*b^3*c^6 + 7168*(b^2 - 4*a*c)*a^12*b*c^7)*B)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 - sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)^2 - 4*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/((a^7*b^10 - 20*a^8*b^8*c - 2*a^7*b^9*c + 160*a^9*b^6*c^2 + 32*a^8*b^7*c^2 + a^7*b^8*c^2 - 640*a^10*b^4*c^3 - 192*a^9*b^5*c^3 - 16*a^8*b^6*c^3 + 1280*a^11*b^2*c^4 + 512*a^10*b^3*c^4 + 96*a^9*b^4*c^4 - 1024*a^12*c^5 - 512*a^11*b*c^5 - 256*a^10*b^2*c^5 + 256*a^11*c^6)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*abs(c)) + 1/4*(3*B*a*b^3*c^2*x^(7/2) - 7*A*b^4*c^2*x^(7/2) - 24*B*a^2*b*c^3*x^(7/2) + 47*A*a*b^2*c^3*x^(7/2) - 52*A*a^2*c^4*x^(7/2) + 6*B*a*b^4*c*x^(5/2) - 14*A*b^5*c*x^(5/2) - 49*B*a^2*b^2*c^2*x^(5/2) + 99*A*a*b^3*c^2*x^(5/2) + 28*B*a^3*c^3*x^(5/2) - 136*A*a^2*b*c^3*x^(5/2) + 3*B*a*b^5*x^(3/2) - 7*A*b^6*x^(3/2) - 20*B*a^2*b^3*c*x^(3/2) + 43*A*a*b^4*c*x^(3/2) - 4*B*a^3*b*c^2*x^(3/2) - 25*A*a^2*b^2*c^2*x^(3/2) - 68*A*a^3*c^3*x^(3/2) + 5*B*a^2*b^4*sqrt(x) - 9*A*a*b^5*sqrt(x) - 37*B*a^3*b^2*c*sqrt(x) + 66*A*a^2*b^3*c*sqrt(x) + 44*B*a^4*c^2*sqrt(x) - 108*A*a^3*b*c^2*sqrt(x))/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(c*x^2 + b*x + a)^2) - 2*A/(a^3*sqrt(x))","B",0
1029,0,0,0,0.000000," ","integrate((B*x+A)*x^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{x}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(x), x)","F",0
1030,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{\sqrt{x}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(B*x + A)/sqrt(x), x)","F",0
1031,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(B*x + A)/x^(3/2), x)","F",0
1032,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(B*x + A)/x^(5/2), x)","F",0
1033,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(B*x + A)/x^(7/2), x)","F",0
1034,0,0,0,0.000000," ","integrate((2-5*x)*x^(7/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} x^{\frac{7}{2}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*x^(7/2), x)","F",0
1035,0,0,0,0.000000," ","integrate((2-5*x)*x^(5/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} x^{\frac{5}{2}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*x^(5/2), x)","F",0
1036,0,0,0,0.000000," ","integrate((2-5*x)*x^(3/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} x^{\frac{3}{2}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*x^(3/2), x)","F",0
1037,0,0,0,0.000000," ","integrate((2-5*x)*x^(1/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x), x)","F",0
1038,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(1/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{\sqrt{x}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/sqrt(x), x)","F",0
1039,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(3/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(3/2), x)","F",0
1040,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(5/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(5/2), x)","F",0
1041,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(7/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(7/2), x)","F",0
1042,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(9/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(9/2), x)","F",0
1043,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(11/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(11/2), x)","F",0
1044,0,0,0,0.000000," ","integrate((2-5*x)*x^(5/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)} x^{\frac{5}{2}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)*x^(5/2), x)","F",0
1045,0,0,0,0.000000," ","integrate((2-5*x)*x^(3/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)} x^{\frac{3}{2}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)*x^(3/2), x)","F",0
1046,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)*x^(1/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)} \sqrt{x}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)*sqrt(x), x)","F",0
1047,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{\sqrt{x}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/sqrt(x), x)","F",0
1048,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(3/2), x)","F",0
1049,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(5/2), x)","F",0
1050,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(7/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(7/2), x)","F",0
1051,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(9/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{x^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(9/2), x)","F",0
1052,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(11/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{x^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(11/2), x)","F",0
1053,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(13/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{x^{\frac{13}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(13/2), x)","F",0
1054,0,0,0,0.000000," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(15/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(5 \, x - 2\right)}}{x^{\frac{15}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(15/2), x)","F",0
1055,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x + a} \sqrt{e x}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x + a)*sqrt(e*x)), x)","F",0
1056,0,0,0,0.000000," ","integrate((2-5*x)*x^(7/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{7}{2}}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(7/2)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1057,0,0,0,0.000000," ","integrate((2-5*x)*x^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{5}{2}}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(5/2)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1058,0,0,0,0.000000," ","integrate((2-5*x)*x^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{3}{2}}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(3/2)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1059,0,0,0,0.000000," ","integrate((2-5*x)*x^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} \sqrt{x}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(-(5*x - 2)*sqrt(x)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1060,0,0,0,0.000000," ","integrate((2-5*x)/x^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}\,{d x}"," ",0,"integrate(-(5*x - 2)/(sqrt(3*x^2 + 5*x + 2)*sqrt(x)), x)","F",0
1061,0,0,0,0.000000," ","integrate((2-5*x)/x^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{\sqrt{3 \, x^{2} + 5 \, x + 2} x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/(sqrt(3*x^2 + 5*x + 2)*x^(3/2)), x)","F",0
1062,0,0,0,0.000000," ","integrate((2-5*x)/x^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{\sqrt{3 \, x^{2} + 5 \, x + 2} x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/(sqrt(3*x^2 + 5*x + 2)*x^(5/2)), x)","F",0
1063,0,0,0,0.000000," ","integrate((2-5*x)/x^(7/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{\sqrt{3 \, x^{2} + 5 \, x + 2} x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/(sqrt(3*x^2 + 5*x + 2)*x^(7/2)), x)","F",0
1064,0,0,0,0.000000," ","integrate((2-5*x)*x^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{7}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(7/2)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
1065,0,0,0,0.000000," ","integrate((2-5*x)*x^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{5}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(5/2)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
1066,0,0,0,0.000000," ","integrate((2-5*x)*x^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{3}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(3/2)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
1067,0,0,0,0.000000," ","integrate((2-5*x)*x^(1/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} \sqrt{x}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*sqrt(x)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
1068,0,0,0,0.000000," ","integrate((2-5*x)/(3*x^2+5*x+2)^(3/2)/x^(1/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} \sqrt{x}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(3/2)*sqrt(x)), x)","F",0
1069,0,0,0,0.000000," ","integrate((2-5*x)/x^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(3/2)*x^(3/2)), x)","F",0
1070,0,0,0,0.000000," ","integrate((2-5*x)/x^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(3/2)*x^(5/2)), x)","F",0
1071,0,0,0,0.000000," ","integrate((2-5*x)/x^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(3/2)*x^(7/2)), x)","F",0
1072,0,0,0,0.000000," ","integrate((2-5*x)*x^(13/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{13}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(13/2)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
1073,0,0,0,0.000000," ","integrate((2-5*x)*x^(11/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{11}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(11/2)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
1074,0,0,0,0.000000," ","integrate((2-5*x)*x^(9/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{9}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(9/2)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
1075,0,0,0,0.000000," ","integrate((2-5*x)*x^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{7}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(7/2)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
1076,0,0,0,0.000000," ","integrate((2-5*x)*x^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{5}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(5/2)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
1077,0,0,0,0.000000," ","integrate((2-5*x)*x^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} x^{\frac{3}{2}}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*x^(3/2)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
1078,0,0,0,0.000000," ","integrate((2-5*x)*x^(1/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(5 \, x - 2\right)} \sqrt{x}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)*sqrt(x)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
1079,0,0,0,0.000000," ","integrate((2-5*x)/(3*x^2+5*x+2)^(5/2)/x^(1/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} \sqrt{x}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(5/2)*sqrt(x)), x)","F",0
1080,0,0,0,0.000000," ","integrate((2-5*x)/x^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(5/2)*x^(3/2)), x)","F",0
1081,0,0,0,0.000000," ","integrate((2-5*x)/x^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(5/2)*x^(5/2)), x)","F",0
1082,0,0,0,0.000000," ","integrate((2-5*x)/x^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{5 \, x - 2}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(5*x - 2)/((3*x^2 + 5*x + 2)^(5/2)*x^(7/2)), x)","F",0
1083,1,2736,0,0.338267," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{B c^{3} m^{7} x^{8} x^{m} e^{m} + 3 \, B b c^{2} m^{7} x^{7} x^{m} e^{m} + A c^{3} m^{7} x^{7} x^{m} e^{m} + 28 \, B c^{3} m^{6} x^{8} x^{m} e^{m} + 3 \, B b^{2} c m^{7} x^{6} x^{m} e^{m} + 3 \, B a c^{2} m^{7} x^{6} x^{m} e^{m} + 3 \, A b c^{2} m^{7} x^{6} x^{m} e^{m} + 87 \, B b c^{2} m^{6} x^{7} x^{m} e^{m} + 29 \, A c^{3} m^{6} x^{7} x^{m} e^{m} + 322 \, B c^{3} m^{5} x^{8} x^{m} e^{m} + B b^{3} m^{7} x^{5} x^{m} e^{m} + 6 \, B a b c m^{7} x^{5} x^{m} e^{m} + 3 \, A b^{2} c m^{7} x^{5} x^{m} e^{m} + 3 \, A a c^{2} m^{7} x^{5} x^{m} e^{m} + 90 \, B b^{2} c m^{6} x^{6} x^{m} e^{m} + 90 \, B a c^{2} m^{6} x^{6} x^{m} e^{m} + 90 \, A b c^{2} m^{6} x^{6} x^{m} e^{m} + 1029 \, B b c^{2} m^{5} x^{7} x^{m} e^{m} + 343 \, A c^{3} m^{5} x^{7} x^{m} e^{m} + 1960 \, B c^{3} m^{4} x^{8} x^{m} e^{m} + 3 \, B a b^{2} m^{7} x^{4} x^{m} e^{m} + A b^{3} m^{7} x^{4} x^{m} e^{m} + 3 \, B a^{2} c m^{7} x^{4} x^{m} e^{m} + 6 \, A a b c m^{7} x^{4} x^{m} e^{m} + 31 \, B b^{3} m^{6} x^{5} x^{m} e^{m} + 186 \, B a b c m^{6} x^{5} x^{m} e^{m} + 93 \, A b^{2} c m^{6} x^{5} x^{m} e^{m} + 93 \, A a c^{2} m^{6} x^{5} x^{m} e^{m} + 1098 \, B b^{2} c m^{5} x^{6} x^{m} e^{m} + 1098 \, B a c^{2} m^{5} x^{6} x^{m} e^{m} + 1098 \, A b c^{2} m^{5} x^{6} x^{m} e^{m} + 6405 \, B b c^{2} m^{4} x^{7} x^{m} e^{m} + 2135 \, A c^{3} m^{4} x^{7} x^{m} e^{m} + 6769 \, B c^{3} m^{3} x^{8} x^{m} e^{m} + 3 \, B a^{2} b m^{7} x^{3} x^{m} e^{m} + 3 \, A a b^{2} m^{7} x^{3} x^{m} e^{m} + 3 \, A a^{2} c m^{7} x^{3} x^{m} e^{m} + 96 \, B a b^{2} m^{6} x^{4} x^{m} e^{m} + 32 \, A b^{3} m^{6} x^{4} x^{m} e^{m} + 96 \, B a^{2} c m^{6} x^{4} x^{m} e^{m} + 192 \, A a b c m^{6} x^{4} x^{m} e^{m} + 391 \, B b^{3} m^{5} x^{5} x^{m} e^{m} + 2346 \, B a b c m^{5} x^{5} x^{m} e^{m} + 1173 \, A b^{2} c m^{5} x^{5} x^{m} e^{m} + 1173 \, A a c^{2} m^{5} x^{5} x^{m} e^{m} + 7020 \, B b^{2} c m^{4} x^{6} x^{m} e^{m} + 7020 \, B a c^{2} m^{4} x^{6} x^{m} e^{m} + 7020 \, A b c^{2} m^{4} x^{6} x^{m} e^{m} + 22512 \, B b c^{2} m^{3} x^{7} x^{m} e^{m} + 7504 \, A c^{3} m^{3} x^{7} x^{m} e^{m} + 13132 \, B c^{3} m^{2} x^{8} x^{m} e^{m} + B a^{3} m^{7} x^{2} x^{m} e^{m} + 3 \, A a^{2} b m^{7} x^{2} x^{m} e^{m} + 99 \, B a^{2} b m^{6} x^{3} x^{m} e^{m} + 99 \, A a b^{2} m^{6} x^{3} x^{m} e^{m} + 99 \, A a^{2} c m^{6} x^{3} x^{m} e^{m} + 1254 \, B a b^{2} m^{5} x^{4} x^{m} e^{m} + 418 \, A b^{3} m^{5} x^{4} x^{m} e^{m} + 1254 \, B a^{2} c m^{5} x^{4} x^{m} e^{m} + 2508 \, A a b c m^{5} x^{4} x^{m} e^{m} + 2581 \, B b^{3} m^{4} x^{5} x^{m} e^{m} + 15486 \, B a b c m^{4} x^{5} x^{m} e^{m} + 7743 \, A b^{2} c m^{4} x^{5} x^{m} e^{m} + 7743 \, A a c^{2} m^{4} x^{5} x^{m} e^{m} + 25227 \, B b^{2} c m^{3} x^{6} x^{m} e^{m} + 25227 \, B a c^{2} m^{3} x^{6} x^{m} e^{m} + 25227 \, A b c^{2} m^{3} x^{6} x^{m} e^{m} + 44268 \, B b c^{2} m^{2} x^{7} x^{m} e^{m} + 14756 \, A c^{3} m^{2} x^{7} x^{m} e^{m} + 13068 \, B c^{3} m x^{8} x^{m} e^{m} + A a^{3} m^{7} x x^{m} e^{m} + 34 \, B a^{3} m^{6} x^{2} x^{m} e^{m} + 102 \, A a^{2} b m^{6} x^{2} x^{m} e^{m} + 1341 \, B a^{2} b m^{5} x^{3} x^{m} e^{m} + 1341 \, A a b^{2} m^{5} x^{3} x^{m} e^{m} + 1341 \, A a^{2} c m^{5} x^{3} x^{m} e^{m} + 8592 \, B a b^{2} m^{4} x^{4} x^{m} e^{m} + 2864 \, A b^{3} m^{4} x^{4} x^{m} e^{m} + 8592 \, B a^{2} c m^{4} x^{4} x^{m} e^{m} + 17184 \, A a b c m^{4} x^{4} x^{m} e^{m} + 9544 \, B b^{3} m^{3} x^{5} x^{m} e^{m} + 57264 \, B a b c m^{3} x^{5} x^{m} e^{m} + 28632 \, A b^{2} c m^{3} x^{5} x^{m} e^{m} + 28632 \, A a c^{2} m^{3} x^{5} x^{m} e^{m} + 50490 \, B b^{2} c m^{2} x^{6} x^{m} e^{m} + 50490 \, B a c^{2} m^{2} x^{6} x^{m} e^{m} + 50490 \, A b c^{2} m^{2} x^{6} x^{m} e^{m} + 44496 \, B b c^{2} m x^{7} x^{m} e^{m} + 14832 \, A c^{3} m x^{7} x^{m} e^{m} + 5040 \, B c^{3} x^{8} x^{m} e^{m} + 35 \, A a^{3} m^{6} x x^{m} e^{m} + 478 \, B a^{3} m^{5} x^{2} x^{m} e^{m} + 1434 \, A a^{2} b m^{5} x^{2} x^{m} e^{m} + 9585 \, B a^{2} b m^{4} x^{3} x^{m} e^{m} + 9585 \, A a b^{2} m^{4} x^{3} x^{m} e^{m} + 9585 \, A a^{2} c m^{4} x^{3} x^{m} e^{m} + 32979 \, B a b^{2} m^{3} x^{4} x^{m} e^{m} + 10993 \, A b^{3} m^{3} x^{4} x^{m} e^{m} + 32979 \, B a^{2} c m^{3} x^{4} x^{m} e^{m} + 65958 \, A a b c m^{3} x^{4} x^{m} e^{m} + 19564 \, B b^{3} m^{2} x^{5} x^{m} e^{m} + 117384 \, B a b c m^{2} x^{5} x^{m} e^{m} + 58692 \, A b^{2} c m^{2} x^{5} x^{m} e^{m} + 58692 \, A a c^{2} m^{2} x^{5} x^{m} e^{m} + 51432 \, B b^{2} c m x^{6} x^{m} e^{m} + 51432 \, B a c^{2} m x^{6} x^{m} e^{m} + 51432 \, A b c^{2} m x^{6} x^{m} e^{m} + 17280 \, B b c^{2} x^{7} x^{m} e^{m} + 5760 \, A c^{3} x^{7} x^{m} e^{m} + 511 \, A a^{3} m^{5} x x^{m} e^{m} + 3580 \, B a^{3} m^{4} x^{2} x^{m} e^{m} + 10740 \, A a^{2} b m^{4} x^{2} x^{m} e^{m} + 38592 \, B a^{2} b m^{3} x^{3} x^{m} e^{m} + 38592 \, A a b^{2} m^{3} x^{3} x^{m} e^{m} + 38592 \, A a^{2} c m^{3} x^{3} x^{m} e^{m} + 69936 \, B a b^{2} m^{2} x^{4} x^{m} e^{m} + 23312 \, A b^{3} m^{2} x^{4} x^{m} e^{m} + 69936 \, B a^{2} c m^{2} x^{4} x^{m} e^{m} + 139872 \, A a b c m^{2} x^{4} x^{m} e^{m} + 20304 \, B b^{3} m x^{5} x^{m} e^{m} + 121824 \, B a b c m x^{5} x^{m} e^{m} + 60912 \, A b^{2} c m x^{5} x^{m} e^{m} + 60912 \, A a c^{2} m x^{5} x^{m} e^{m} + 20160 \, B b^{2} c x^{6} x^{m} e^{m} + 20160 \, B a c^{2} x^{6} x^{m} e^{m} + 20160 \, A b c^{2} x^{6} x^{m} e^{m} + 4025 \, A a^{3} m^{4} x x^{m} e^{m} + 15289 \, B a^{3} m^{3} x^{2} x^{m} e^{m} + 45867 \, A a^{2} b m^{3} x^{2} x^{m} e^{m} + 86076 \, B a^{2} b m^{2} x^{3} x^{m} e^{m} + 86076 \, A a b^{2} m^{2} x^{3} x^{m} e^{m} + 86076 \, A a^{2} c m^{2} x^{3} x^{m} e^{m} + 74628 \, B a b^{2} m x^{4} x^{m} e^{m} + 24876 \, A b^{3} m x^{4} x^{m} e^{m} + 74628 \, B a^{2} c m x^{4} x^{m} e^{m} + 149256 \, A a b c m x^{4} x^{m} e^{m} + 8064 \, B b^{3} x^{5} x^{m} e^{m} + 48384 \, B a b c x^{5} x^{m} e^{m} + 24192 \, A b^{2} c x^{5} x^{m} e^{m} + 24192 \, A a c^{2} x^{5} x^{m} e^{m} + 18424 \, A a^{3} m^{3} x x^{m} e^{m} + 36706 \, B a^{3} m^{2} x^{2} x^{m} e^{m} + 110118 \, A a^{2} b m^{2} x^{2} x^{m} e^{m} + 96144 \, B a^{2} b m x^{3} x^{m} e^{m} + 96144 \, A a b^{2} m x^{3} x^{m} e^{m} + 96144 \, A a^{2} c m x^{3} x^{m} e^{m} + 30240 \, B a b^{2} x^{4} x^{m} e^{m} + 10080 \, A b^{3} x^{4} x^{m} e^{m} + 30240 \, B a^{2} c x^{4} x^{m} e^{m} + 60480 \, A a b c x^{4} x^{m} e^{m} + 48860 \, A a^{3} m^{2} x x^{m} e^{m} + 44712 \, B a^{3} m x^{2} x^{m} e^{m} + 134136 \, A a^{2} b m x^{2} x^{m} e^{m} + 40320 \, B a^{2} b x^{3} x^{m} e^{m} + 40320 \, A a b^{2} x^{3} x^{m} e^{m} + 40320 \, A a^{2} c x^{3} x^{m} e^{m} + 69264 \, A a^{3} m x x^{m} e^{m} + 20160 \, B a^{3} x^{2} x^{m} e^{m} + 60480 \, A a^{2} b x^{2} x^{m} e^{m} + 40320 \, A a^{3} x x^{m} e^{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*x^8*x^m*e^m + 3*B*b*c^2*m^7*x^7*x^m*e^m + A*c^3*m^7*x^7*x^m*e^m + 28*B*c^3*m^6*x^8*x^m*e^m + 3*B*b^2*c*m^7*x^6*x^m*e^m + 3*B*a*c^2*m^7*x^6*x^m*e^m + 3*A*b*c^2*m^7*x^6*x^m*e^m + 87*B*b*c^2*m^6*x^7*x^m*e^m + 29*A*c^3*m^6*x^7*x^m*e^m + 322*B*c^3*m^5*x^8*x^m*e^m + B*b^3*m^7*x^5*x^m*e^m + 6*B*a*b*c*m^7*x^5*x^m*e^m + 3*A*b^2*c*m^7*x^5*x^m*e^m + 3*A*a*c^2*m^7*x^5*x^m*e^m + 90*B*b^2*c*m^6*x^6*x^m*e^m + 90*B*a*c^2*m^6*x^6*x^m*e^m + 90*A*b*c^2*m^6*x^6*x^m*e^m + 1029*B*b*c^2*m^5*x^7*x^m*e^m + 343*A*c^3*m^5*x^7*x^m*e^m + 1960*B*c^3*m^4*x^8*x^m*e^m + 3*B*a*b^2*m^7*x^4*x^m*e^m + A*b^3*m^7*x^4*x^m*e^m + 3*B*a^2*c*m^7*x^4*x^m*e^m + 6*A*a*b*c*m^7*x^4*x^m*e^m + 31*B*b^3*m^6*x^5*x^m*e^m + 186*B*a*b*c*m^6*x^5*x^m*e^m + 93*A*b^2*c*m^6*x^5*x^m*e^m + 93*A*a*c^2*m^6*x^5*x^m*e^m + 1098*B*b^2*c*m^5*x^6*x^m*e^m + 1098*B*a*c^2*m^5*x^6*x^m*e^m + 1098*A*b*c^2*m^5*x^6*x^m*e^m + 6405*B*b*c^2*m^4*x^7*x^m*e^m + 2135*A*c^3*m^4*x^7*x^m*e^m + 6769*B*c^3*m^3*x^8*x^m*e^m + 3*B*a^2*b*m^7*x^3*x^m*e^m + 3*A*a*b^2*m^7*x^3*x^m*e^m + 3*A*a^2*c*m^7*x^3*x^m*e^m + 96*B*a*b^2*m^6*x^4*x^m*e^m + 32*A*b^3*m^6*x^4*x^m*e^m + 96*B*a^2*c*m^6*x^4*x^m*e^m + 192*A*a*b*c*m^6*x^4*x^m*e^m + 391*B*b^3*m^5*x^5*x^m*e^m + 2346*B*a*b*c*m^5*x^5*x^m*e^m + 1173*A*b^2*c*m^5*x^5*x^m*e^m + 1173*A*a*c^2*m^5*x^5*x^m*e^m + 7020*B*b^2*c*m^4*x^6*x^m*e^m + 7020*B*a*c^2*m^4*x^6*x^m*e^m + 7020*A*b*c^2*m^4*x^6*x^m*e^m + 22512*B*b*c^2*m^3*x^7*x^m*e^m + 7504*A*c^3*m^3*x^7*x^m*e^m + 13132*B*c^3*m^2*x^8*x^m*e^m + B*a^3*m^7*x^2*x^m*e^m + 3*A*a^2*b*m^7*x^2*x^m*e^m + 99*B*a^2*b*m^6*x^3*x^m*e^m + 99*A*a*b^2*m^6*x^3*x^m*e^m + 99*A*a^2*c*m^6*x^3*x^m*e^m + 1254*B*a*b^2*m^5*x^4*x^m*e^m + 418*A*b^3*m^5*x^4*x^m*e^m + 1254*B*a^2*c*m^5*x^4*x^m*e^m + 2508*A*a*b*c*m^5*x^4*x^m*e^m + 2581*B*b^3*m^4*x^5*x^m*e^m + 15486*B*a*b*c*m^4*x^5*x^m*e^m + 7743*A*b^2*c*m^4*x^5*x^m*e^m + 7743*A*a*c^2*m^4*x^5*x^m*e^m + 25227*B*b^2*c*m^3*x^6*x^m*e^m + 25227*B*a*c^2*m^3*x^6*x^m*e^m + 25227*A*b*c^2*m^3*x^6*x^m*e^m + 44268*B*b*c^2*m^2*x^7*x^m*e^m + 14756*A*c^3*m^2*x^7*x^m*e^m + 13068*B*c^3*m*x^8*x^m*e^m + A*a^3*m^7*x*x^m*e^m + 34*B*a^3*m^6*x^2*x^m*e^m + 102*A*a^2*b*m^6*x^2*x^m*e^m + 1341*B*a^2*b*m^5*x^3*x^m*e^m + 1341*A*a*b^2*m^5*x^3*x^m*e^m + 1341*A*a^2*c*m^5*x^3*x^m*e^m + 8592*B*a*b^2*m^4*x^4*x^m*e^m + 2864*A*b^3*m^4*x^4*x^m*e^m + 8592*B*a^2*c*m^4*x^4*x^m*e^m + 17184*A*a*b*c*m^4*x^4*x^m*e^m + 9544*B*b^3*m^3*x^5*x^m*e^m + 57264*B*a*b*c*m^3*x^5*x^m*e^m + 28632*A*b^2*c*m^3*x^5*x^m*e^m + 28632*A*a*c^2*m^3*x^5*x^m*e^m + 50490*B*b^2*c*m^2*x^6*x^m*e^m + 50490*B*a*c^2*m^2*x^6*x^m*e^m + 50490*A*b*c^2*m^2*x^6*x^m*e^m + 44496*B*b*c^2*m*x^7*x^m*e^m + 14832*A*c^3*m*x^7*x^m*e^m + 5040*B*c^3*x^8*x^m*e^m + 35*A*a^3*m^6*x*x^m*e^m + 478*B*a^3*m^5*x^2*x^m*e^m + 1434*A*a^2*b*m^5*x^2*x^m*e^m + 9585*B*a^2*b*m^4*x^3*x^m*e^m + 9585*A*a*b^2*m^4*x^3*x^m*e^m + 9585*A*a^2*c*m^4*x^3*x^m*e^m + 32979*B*a*b^2*m^3*x^4*x^m*e^m + 10993*A*b^3*m^3*x^4*x^m*e^m + 32979*B*a^2*c*m^3*x^4*x^m*e^m + 65958*A*a*b*c*m^3*x^4*x^m*e^m + 19564*B*b^3*m^2*x^5*x^m*e^m + 117384*B*a*b*c*m^2*x^5*x^m*e^m + 58692*A*b^2*c*m^2*x^5*x^m*e^m + 58692*A*a*c^2*m^2*x^5*x^m*e^m + 51432*B*b^2*c*m*x^6*x^m*e^m + 51432*B*a*c^2*m*x^6*x^m*e^m + 51432*A*b*c^2*m*x^6*x^m*e^m + 17280*B*b*c^2*x^7*x^m*e^m + 5760*A*c^3*x^7*x^m*e^m + 511*A*a^3*m^5*x*x^m*e^m + 3580*B*a^3*m^4*x^2*x^m*e^m + 10740*A*a^2*b*m^4*x^2*x^m*e^m + 38592*B*a^2*b*m^3*x^3*x^m*e^m + 38592*A*a*b^2*m^3*x^3*x^m*e^m + 38592*A*a^2*c*m^3*x^3*x^m*e^m + 69936*B*a*b^2*m^2*x^4*x^m*e^m + 23312*A*b^3*m^2*x^4*x^m*e^m + 69936*B*a^2*c*m^2*x^4*x^m*e^m + 139872*A*a*b*c*m^2*x^4*x^m*e^m + 20304*B*b^3*m*x^5*x^m*e^m + 121824*B*a*b*c*m*x^5*x^m*e^m + 60912*A*b^2*c*m*x^5*x^m*e^m + 60912*A*a*c^2*m*x^5*x^m*e^m + 20160*B*b^2*c*x^6*x^m*e^m + 20160*B*a*c^2*x^6*x^m*e^m + 20160*A*b*c^2*x^6*x^m*e^m + 4025*A*a^3*m^4*x*x^m*e^m + 15289*B*a^3*m^3*x^2*x^m*e^m + 45867*A*a^2*b*m^3*x^2*x^m*e^m + 86076*B*a^2*b*m^2*x^3*x^m*e^m + 86076*A*a*b^2*m^2*x^3*x^m*e^m + 86076*A*a^2*c*m^2*x^3*x^m*e^m + 74628*B*a*b^2*m*x^4*x^m*e^m + 24876*A*b^3*m*x^4*x^m*e^m + 74628*B*a^2*c*m*x^4*x^m*e^m + 149256*A*a*b*c*m*x^4*x^m*e^m + 8064*B*b^3*x^5*x^m*e^m + 48384*B*a*b*c*x^5*x^m*e^m + 24192*A*b^2*c*x^5*x^m*e^m + 24192*A*a*c^2*x^5*x^m*e^m + 18424*A*a^3*m^3*x*x^m*e^m + 36706*B*a^3*m^2*x^2*x^m*e^m + 110118*A*a^2*b*m^2*x^2*x^m*e^m + 96144*B*a^2*b*m*x^3*x^m*e^m + 96144*A*a*b^2*m*x^3*x^m*e^m + 96144*A*a^2*c*m*x^3*x^m*e^m + 30240*B*a*b^2*x^4*x^m*e^m + 10080*A*b^3*x^4*x^m*e^m + 30240*B*a^2*c*x^4*x^m*e^m + 60480*A*a*b*c*x^4*x^m*e^m + 48860*A*a^3*m^2*x*x^m*e^m + 44712*B*a^3*m*x^2*x^m*e^m + 134136*A*a^2*b*m*x^2*x^m*e^m + 40320*B*a^2*b*x^3*x^m*e^m + 40320*A*a*b^2*x^3*x^m*e^m + 40320*A*a^2*c*x^3*x^m*e^m + 69264*A*a^3*m*x*x^m*e^m + 20160*B*a^3*x^2*x^m*e^m + 60480*A*a^2*b*x^2*x^m*e^m + 40320*A*a^3*x*x^m*e^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
1084,1,1142,0,0.248531," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{B c^{2} m^{5} x^{6} x^{m} e^{m} + 2 \, B b c m^{5} x^{5} x^{m} e^{m} + A c^{2} m^{5} x^{5} x^{m} e^{m} + 15 \, B c^{2} m^{4} x^{6} x^{m} e^{m} + B b^{2} m^{5} x^{4} x^{m} e^{m} + 2 \, B a c m^{5} x^{4} x^{m} e^{m} + 2 \, A b c m^{5} x^{4} x^{m} e^{m} + 32 \, B b c m^{4} x^{5} x^{m} e^{m} + 16 \, A c^{2} m^{4} x^{5} x^{m} e^{m} + 85 \, B c^{2} m^{3} x^{6} x^{m} e^{m} + 2 \, B a b m^{5} x^{3} x^{m} e^{m} + A b^{2} m^{5} x^{3} x^{m} e^{m} + 2 \, A a c m^{5} x^{3} x^{m} e^{m} + 17 \, B b^{2} m^{4} x^{4} x^{m} e^{m} + 34 \, B a c m^{4} x^{4} x^{m} e^{m} + 34 \, A b c m^{4} x^{4} x^{m} e^{m} + 190 \, B b c m^{3} x^{5} x^{m} e^{m} + 95 \, A c^{2} m^{3} x^{5} x^{m} e^{m} + 225 \, B c^{2} m^{2} x^{6} x^{m} e^{m} + B a^{2} m^{5} x^{2} x^{m} e^{m} + 2 \, A a b m^{5} x^{2} x^{m} e^{m} + 36 \, B a b m^{4} x^{3} x^{m} e^{m} + 18 \, A b^{2} m^{4} x^{3} x^{m} e^{m} + 36 \, A a c m^{4} x^{3} x^{m} e^{m} + 107 \, B b^{2} m^{3} x^{4} x^{m} e^{m} + 214 \, B a c m^{3} x^{4} x^{m} e^{m} + 214 \, A b c m^{3} x^{4} x^{m} e^{m} + 520 \, B b c m^{2} x^{5} x^{m} e^{m} + 260 \, A c^{2} m^{2} x^{5} x^{m} e^{m} + 274 \, B c^{2} m x^{6} x^{m} e^{m} + A a^{2} m^{5} x x^{m} e^{m} + 19 \, B a^{2} m^{4} x^{2} x^{m} e^{m} + 38 \, A a b m^{4} x^{2} x^{m} e^{m} + 242 \, B a b m^{3} x^{3} x^{m} e^{m} + 121 \, A b^{2} m^{3} x^{3} x^{m} e^{m} + 242 \, A a c m^{3} x^{3} x^{m} e^{m} + 307 \, B b^{2} m^{2} x^{4} x^{m} e^{m} + 614 \, B a c m^{2} x^{4} x^{m} e^{m} + 614 \, A b c m^{2} x^{4} x^{m} e^{m} + 648 \, B b c m x^{5} x^{m} e^{m} + 324 \, A c^{2} m x^{5} x^{m} e^{m} + 120 \, B c^{2} x^{6} x^{m} e^{m} + 20 \, A a^{2} m^{4} x x^{m} e^{m} + 137 \, B a^{2} m^{3} x^{2} x^{m} e^{m} + 274 \, A a b m^{3} x^{2} x^{m} e^{m} + 744 \, B a b m^{2} x^{3} x^{m} e^{m} + 372 \, A b^{2} m^{2} x^{3} x^{m} e^{m} + 744 \, A a c m^{2} x^{3} x^{m} e^{m} + 396 \, B b^{2} m x^{4} x^{m} e^{m} + 792 \, B a c m x^{4} x^{m} e^{m} + 792 \, A b c m x^{4} x^{m} e^{m} + 288 \, B b c x^{5} x^{m} e^{m} + 144 \, A c^{2} x^{5} x^{m} e^{m} + 155 \, A a^{2} m^{3} x x^{m} e^{m} + 461 \, B a^{2} m^{2} x^{2} x^{m} e^{m} + 922 \, A a b m^{2} x^{2} x^{m} e^{m} + 1016 \, B a b m x^{3} x^{m} e^{m} + 508 \, A b^{2} m x^{3} x^{m} e^{m} + 1016 \, A a c m x^{3} x^{m} e^{m} + 180 \, B b^{2} x^{4} x^{m} e^{m} + 360 \, B a c x^{4} x^{m} e^{m} + 360 \, A b c x^{4} x^{m} e^{m} + 580 \, A a^{2} m^{2} x x^{m} e^{m} + 702 \, B a^{2} m x^{2} x^{m} e^{m} + 1404 \, A a b m x^{2} x^{m} e^{m} + 480 \, B a b x^{3} x^{m} e^{m} + 240 \, A b^{2} x^{3} x^{m} e^{m} + 480 \, A a c x^{3} x^{m} e^{m} + 1044 \, A a^{2} m x x^{m} e^{m} + 360 \, B a^{2} x^{2} x^{m} e^{m} + 720 \, A a b x^{2} x^{m} e^{m} + 720 \, A a^{2} x x^{m} e^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"(B*c^2*m^5*x^6*x^m*e^m + 2*B*b*c*m^5*x^5*x^m*e^m + A*c^2*m^5*x^5*x^m*e^m + 15*B*c^2*m^4*x^6*x^m*e^m + B*b^2*m^5*x^4*x^m*e^m + 2*B*a*c*m^5*x^4*x^m*e^m + 2*A*b*c*m^5*x^4*x^m*e^m + 32*B*b*c*m^4*x^5*x^m*e^m + 16*A*c^2*m^4*x^5*x^m*e^m + 85*B*c^2*m^3*x^6*x^m*e^m + 2*B*a*b*m^5*x^3*x^m*e^m + A*b^2*m^5*x^3*x^m*e^m + 2*A*a*c*m^5*x^3*x^m*e^m + 17*B*b^2*m^4*x^4*x^m*e^m + 34*B*a*c*m^4*x^4*x^m*e^m + 34*A*b*c*m^4*x^4*x^m*e^m + 190*B*b*c*m^3*x^5*x^m*e^m + 95*A*c^2*m^3*x^5*x^m*e^m + 225*B*c^2*m^2*x^6*x^m*e^m + B*a^2*m^5*x^2*x^m*e^m + 2*A*a*b*m^5*x^2*x^m*e^m + 36*B*a*b*m^4*x^3*x^m*e^m + 18*A*b^2*m^4*x^3*x^m*e^m + 36*A*a*c*m^4*x^3*x^m*e^m + 107*B*b^2*m^3*x^4*x^m*e^m + 214*B*a*c*m^3*x^4*x^m*e^m + 214*A*b*c*m^3*x^4*x^m*e^m + 520*B*b*c*m^2*x^5*x^m*e^m + 260*A*c^2*m^2*x^5*x^m*e^m + 274*B*c^2*m*x^6*x^m*e^m + A*a^2*m^5*x*x^m*e^m + 19*B*a^2*m^4*x^2*x^m*e^m + 38*A*a*b*m^4*x^2*x^m*e^m + 242*B*a*b*m^3*x^3*x^m*e^m + 121*A*b^2*m^3*x^3*x^m*e^m + 242*A*a*c*m^3*x^3*x^m*e^m + 307*B*b^2*m^2*x^4*x^m*e^m + 614*B*a*c*m^2*x^4*x^m*e^m + 614*A*b*c*m^2*x^4*x^m*e^m + 648*B*b*c*m*x^5*x^m*e^m + 324*A*c^2*m*x^5*x^m*e^m + 120*B*c^2*x^6*x^m*e^m + 20*A*a^2*m^4*x*x^m*e^m + 137*B*a^2*m^3*x^2*x^m*e^m + 274*A*a*b*m^3*x^2*x^m*e^m + 744*B*a*b*m^2*x^3*x^m*e^m + 372*A*b^2*m^2*x^3*x^m*e^m + 744*A*a*c*m^2*x^3*x^m*e^m + 396*B*b^2*m*x^4*x^m*e^m + 792*B*a*c*m*x^4*x^m*e^m + 792*A*b*c*m*x^4*x^m*e^m + 288*B*b*c*x^5*x^m*e^m + 144*A*c^2*x^5*x^m*e^m + 155*A*a^2*m^3*x*x^m*e^m + 461*B*a^2*m^2*x^2*x^m*e^m + 922*A*a*b*m^2*x^2*x^m*e^m + 1016*B*a*b*m*x^3*x^m*e^m + 508*A*b^2*m*x^3*x^m*e^m + 1016*A*a*c*m*x^3*x^m*e^m + 180*B*b^2*x^4*x^m*e^m + 360*B*a*c*x^4*x^m*e^m + 360*A*b*c*x^4*x^m*e^m + 580*A*a^2*m^2*x*x^m*e^m + 702*B*a^2*m*x^2*x^m*e^m + 1404*A*a*b*m*x^2*x^m*e^m + 480*B*a*b*x^3*x^m*e^m + 240*A*b^2*x^3*x^m*e^m + 480*A*a*c*x^3*x^m*e^m + 1044*A*a^2*m*x*x^m*e^m + 360*B*a^2*x^2*x^m*e^m + 720*A*a*b*x^2*x^m*e^m + 720*A*a^2*x*x^m*e^m)/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
1085,1,338,0,0.173464," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{B c m^{3} x^{4} x^{m} e^{m} + B b m^{3} x^{3} x^{m} e^{m} + A c m^{3} x^{3} x^{m} e^{m} + 6 \, B c m^{2} x^{4} x^{m} e^{m} + B a m^{3} x^{2} x^{m} e^{m} + A b m^{3} x^{2} x^{m} e^{m} + 7 \, B b m^{2} x^{3} x^{m} e^{m} + 7 \, A c m^{2} x^{3} x^{m} e^{m} + 11 \, B c m x^{4} x^{m} e^{m} + A a m^{3} x x^{m} e^{m} + 8 \, B a m^{2} x^{2} x^{m} e^{m} + 8 \, A b m^{2} x^{2} x^{m} e^{m} + 14 \, B b m x^{3} x^{m} e^{m} + 14 \, A c m x^{3} x^{m} e^{m} + 6 \, B c x^{4} x^{m} e^{m} + 9 \, A a m^{2} x x^{m} e^{m} + 19 \, B a m x^{2} x^{m} e^{m} + 19 \, A b m x^{2} x^{m} e^{m} + 8 \, B b x^{3} x^{m} e^{m} + 8 \, A c x^{3} x^{m} e^{m} + 26 \, A a m x x^{m} e^{m} + 12 \, B a x^{2} x^{m} e^{m} + 12 \, A b x^{2} x^{m} e^{m} + 24 \, A a x x^{m} e^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"(B*c*m^3*x^4*x^m*e^m + B*b*m^3*x^3*x^m*e^m + A*c*m^3*x^3*x^m*e^m + 6*B*c*m^2*x^4*x^m*e^m + B*a*m^3*x^2*x^m*e^m + A*b*m^3*x^2*x^m*e^m + 7*B*b*m^2*x^3*x^m*e^m + 7*A*c*m^2*x^3*x^m*e^m + 11*B*c*m*x^4*x^m*e^m + A*a*m^3*x*x^m*e^m + 8*B*a*m^2*x^2*x^m*e^m + 8*A*b*m^2*x^2*x^m*e^m + 14*B*b*m*x^3*x^m*e^m + 14*A*c*m*x^3*x^m*e^m + 6*B*c*x^4*x^m*e^m + 9*A*a*m^2*x*x^m*e^m + 19*B*a*m*x^2*x^m*e^m + 19*A*b*m*x^2*x^m*e^m + 8*B*b*x^3*x^m*e^m + 8*A*c*x^3*x^m*e^m + 26*A*a*m*x*x^m*e^m + 12*B*a*x^2*x^m*e^m + 12*A*b*x^2*x^m*e^m + 24*A*a*x*x^m*e^m)/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
1086,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + b*x + a), x)","F",0
1087,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{{\left(c x^{2} + b x + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + b*x + a)^2, x)","F",0
1088,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} {\left(B x + A\right)} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)*(B*x + A)*(e*x)^m, x)","F",0
1089,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(B x + A\right)} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(B*x + A)*(e*x)^m, x)","F",0
1090,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \left(e x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(B*x + A)*(e*x)^m, x)","F",0
1091,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/sqrt(c*x^2 + b*x + a), x)","F",0
1092,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + b*x + a)^(3/2), x)","F",0
1093,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \left(e x\right)^{m}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x)^m/(c*x^2 + b*x + a)^(5/2), x)","F",0
1094,0,0,0,0.000000," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p*(e*x)^m, x)","F",0
1095,0,0,0,0.000000," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p*x^3, x)","F",0
1096,0,0,0,0.000000," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p*x^2, x)","F",0
1097,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p} x\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p*x, x)","F",0
1098,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p, x)","F",0
1099,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^p/x,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p/x, x)","F",0
1100,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p/x^2, x)","F",0
1101,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p/x^3, x)","F",0
1102,1,847,0,0.182445," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} B c d m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} B b m^{3} x^{3} e^{4} + {\left(x e + d\right)}^{m} A c m^{3} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B c m^{2} x^{4} e^{4} + {\left(x e + d\right)}^{m} B b d m^{3} x^{2} e^{3} + {\left(x e + d\right)}^{m} A c d m^{3} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} B c d m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} B c d^{2} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} A b m^{3} x^{2} e^{4} + 7 \, {\left(x e + d\right)}^{m} B b m^{2} x^{3} e^{4} + 7 \, {\left(x e + d\right)}^{m} A c m^{2} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} B c m x^{4} e^{4} + {\left(x e + d\right)}^{m} A b d m^{3} x e^{3} + 5 \, {\left(x e + d\right)}^{m} B b d m^{2} x^{2} e^{3} + 5 \, {\left(x e + d\right)}^{m} A c d m^{2} x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} B c d m x^{3} e^{3} - 2 \, {\left(x e + d\right)}^{m} B b d^{2} m^{2} x e^{2} - 2 \, {\left(x e + d\right)}^{m} A c d^{2} m^{2} x e^{2} - 3 \, {\left(x e + d\right)}^{m} B c d^{2} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} B c d^{3} m x e + 8 \, {\left(x e + d\right)}^{m} A b m^{2} x^{2} e^{4} + 14 \, {\left(x e + d\right)}^{m} B b m x^{3} e^{4} + 14 \, {\left(x e + d\right)}^{m} A c m x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B c x^{4} e^{4} + 7 \, {\left(x e + d\right)}^{m} A b d m^{2} x e^{3} + 4 \, {\left(x e + d\right)}^{m} B b d m x^{2} e^{3} + 4 \, {\left(x e + d\right)}^{m} A c d m x^{2} e^{3} - {\left(x e + d\right)}^{m} A b d^{2} m^{2} e^{2} - 8 \, {\left(x e + d\right)}^{m} B b d^{2} m x e^{2} - 8 \, {\left(x e + d\right)}^{m} A c d^{2} m x e^{2} + 2 \, {\left(x e + d\right)}^{m} B b d^{3} m e + 2 \, {\left(x e + d\right)}^{m} A c d^{3} m e - 6 \, {\left(x e + d\right)}^{m} B c d^{4} + 19 \, {\left(x e + d\right)}^{m} A b m x^{2} e^{4} + 8 \, {\left(x e + d\right)}^{m} B b x^{3} e^{4} + 8 \, {\left(x e + d\right)}^{m} A c x^{3} e^{4} + 12 \, {\left(x e + d\right)}^{m} A b d m x e^{3} - 7 \, {\left(x e + d\right)}^{m} A b d^{2} m e^{2} + 8 \, {\left(x e + d\right)}^{m} B b d^{3} e + 8 \, {\left(x e + d\right)}^{m} A c d^{3} e + 12 \, {\left(x e + d\right)}^{m} A b x^{2} e^{4} - 12 \, {\left(x e + d\right)}^{m} A b d^{2} e^{2}}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"((x*e + d)^m*B*c*m^3*x^4*e^4 + (x*e + d)^m*B*c*d*m^3*x^3*e^3 + (x*e + d)^m*B*b*m^3*x^3*e^4 + (x*e + d)^m*A*c*m^3*x^3*e^4 + 6*(x*e + d)^m*B*c*m^2*x^4*e^4 + (x*e + d)^m*B*b*d*m^3*x^2*e^3 + (x*e + d)^m*A*c*d*m^3*x^2*e^3 + 3*(x*e + d)^m*B*c*d*m^2*x^3*e^3 - 3*(x*e + d)^m*B*c*d^2*m^2*x^2*e^2 + (x*e + d)^m*A*b*m^3*x^2*e^4 + 7*(x*e + d)^m*B*b*m^2*x^3*e^4 + 7*(x*e + d)^m*A*c*m^2*x^3*e^4 + 11*(x*e + d)^m*B*c*m*x^4*e^4 + (x*e + d)^m*A*b*d*m^3*x*e^3 + 5*(x*e + d)^m*B*b*d*m^2*x^2*e^3 + 5*(x*e + d)^m*A*c*d*m^2*x^2*e^3 + 2*(x*e + d)^m*B*c*d*m*x^3*e^3 - 2*(x*e + d)^m*B*b*d^2*m^2*x*e^2 - 2*(x*e + d)^m*A*c*d^2*m^2*x*e^2 - 3*(x*e + d)^m*B*c*d^2*m*x^2*e^2 + 6*(x*e + d)^m*B*c*d^3*m*x*e + 8*(x*e + d)^m*A*b*m^2*x^2*e^4 + 14*(x*e + d)^m*B*b*m*x^3*e^4 + 14*(x*e + d)^m*A*c*m*x^3*e^4 + 6*(x*e + d)^m*B*c*x^4*e^4 + 7*(x*e + d)^m*A*b*d*m^2*x*e^3 + 4*(x*e + d)^m*B*b*d*m*x^2*e^3 + 4*(x*e + d)^m*A*c*d*m*x^2*e^3 - (x*e + d)^m*A*b*d^2*m^2*e^2 - 8*(x*e + d)^m*B*b*d^2*m*x*e^2 - 8*(x*e + d)^m*A*c*d^2*m*x*e^2 + 2*(x*e + d)^m*B*b*d^3*m*e + 2*(x*e + d)^m*A*c*d^3*m*e - 6*(x*e + d)^m*B*c*d^4 + 19*(x*e + d)^m*A*b*m*x^2*e^4 + 8*(x*e + d)^m*B*b*x^3*e^4 + 8*(x*e + d)^m*A*c*x^3*e^4 + 12*(x*e + d)^m*A*b*d*m*x*e^3 - 7*(x*e + d)^m*A*b*d^2*m*e^2 + 8*(x*e + d)^m*B*b*d^3*e + 8*(x*e + d)^m*A*c*d^3*e + 12*(x*e + d)^m*A*b*x^2*e^4 - 12*(x*e + d)^m*A*b*d^2*e^2)/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
1103,1,210,0,0.167673," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{8} \, B c x^{8} e^{4} + \frac{4}{7} \, B c d x^{7} e^{3} + B c d^{2} x^{6} e^{2} + \frac{4}{5} \, B c d^{3} x^{5} e + \frac{1}{4} \, B c d^{4} x^{4} + \frac{1}{7} \, B b x^{7} e^{4} + \frac{1}{7} \, A c x^{7} e^{4} + \frac{2}{3} \, B b d x^{6} e^{3} + \frac{2}{3} \, A c d x^{6} e^{3} + \frac{6}{5} \, B b d^{2} x^{5} e^{2} + \frac{6}{5} \, A c d^{2} x^{5} e^{2} + B b d^{3} x^{4} e + A c d^{3} x^{4} e + \frac{1}{3} \, B b d^{4} x^{3} + \frac{1}{3} \, A c d^{4} x^{3} + \frac{1}{6} \, A b x^{6} e^{4} + \frac{4}{5} \, A b d x^{5} e^{3} + \frac{3}{2} \, A b d^{2} x^{4} e^{2} + \frac{4}{3} \, A b d^{3} x^{3} e + \frac{1}{2} \, A b d^{4} x^{2}"," ",0,"1/8*B*c*x^8*e^4 + 4/7*B*c*d*x^7*e^3 + B*c*d^2*x^6*e^2 + 4/5*B*c*d^3*x^5*e + 1/4*B*c*d^4*x^4 + 1/7*B*b*x^7*e^4 + 1/7*A*c*x^7*e^4 + 2/3*B*b*d*x^6*e^3 + 2/3*A*c*d*x^6*e^3 + 6/5*B*b*d^2*x^5*e^2 + 6/5*A*c*d^2*x^5*e^2 + B*b*d^3*x^4*e + A*c*d^3*x^4*e + 1/3*B*b*d^4*x^3 + 1/3*A*c*d^4*x^3 + 1/6*A*b*x^6*e^4 + 4/5*A*b*d*x^5*e^3 + 3/2*A*b*d^2*x^4*e^2 + 4/3*A*b*d^3*x^3*e + 1/2*A*b*d^4*x^2","A",0
1104,1,164,0,0.157290," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{7} \, B c x^{7} e^{3} + \frac{1}{2} \, B c d x^{6} e^{2} + \frac{3}{5} \, B c d^{2} x^{5} e + \frac{1}{4} \, B c d^{3} x^{4} + \frac{1}{6} \, B b x^{6} e^{3} + \frac{1}{6} \, A c x^{6} e^{3} + \frac{3}{5} \, B b d x^{5} e^{2} + \frac{3}{5} \, A c d x^{5} e^{2} + \frac{3}{4} \, B b d^{2} x^{4} e + \frac{3}{4} \, A c d^{2} x^{4} e + \frac{1}{3} \, B b d^{3} x^{3} + \frac{1}{3} \, A c d^{3} x^{3} + \frac{1}{5} \, A b x^{5} e^{3} + \frac{3}{4} \, A b d x^{4} e^{2} + A b d^{2} x^{3} e + \frac{1}{2} \, A b d^{3} x^{2}"," ",0,"1/7*B*c*x^7*e^3 + 1/2*B*c*d*x^6*e^2 + 3/5*B*c*d^2*x^5*e + 1/4*B*c*d^3*x^4 + 1/6*B*b*x^6*e^3 + 1/6*A*c*x^6*e^3 + 3/5*B*b*d*x^5*e^2 + 3/5*A*c*d*x^5*e^2 + 3/4*B*b*d^2*x^4*e + 3/4*A*c*d^2*x^4*e + 1/3*B*b*d^3*x^3 + 1/3*A*c*d^3*x^3 + 1/5*A*b*x^5*e^3 + 3/4*A*b*d*x^4*e^2 + A*b*d^2*x^3*e + 1/2*A*b*d^3*x^2","A",0
1105,1,117,0,0.161025," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{6} \, B c x^{6} e^{2} + \frac{2}{5} \, B c d x^{5} e + \frac{1}{4} \, B c d^{2} x^{4} + \frac{1}{5} \, B b x^{5} e^{2} + \frac{1}{5} \, A c x^{5} e^{2} + \frac{1}{2} \, B b d x^{4} e + \frac{1}{2} \, A c d x^{4} e + \frac{1}{3} \, B b d^{2} x^{3} + \frac{1}{3} \, A c d^{2} x^{3} + \frac{1}{4} \, A b x^{4} e^{2} + \frac{2}{3} \, A b d x^{3} e + \frac{1}{2} \, A b d^{2} x^{2}"," ",0,"1/6*B*c*x^6*e^2 + 2/5*B*c*d*x^5*e + 1/4*B*c*d^2*x^4 + 1/5*B*b*x^5*e^2 + 1/5*A*c*x^5*e^2 + 1/2*B*b*d*x^4*e + 1/2*A*c*d*x^4*e + 1/3*B*b*d^2*x^3 + 1/3*A*c*d^2*x^3 + 1/4*A*b*x^4*e^2 + 2/3*A*b*d*x^3*e + 1/2*A*b*d^2*x^2","A",0
1106,1,69,0,0.154001," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{5} \, B c x^{5} e + \frac{1}{4} \, B c d x^{4} + \frac{1}{4} \, B b x^{4} e + \frac{1}{4} \, A c x^{4} e + \frac{1}{3} \, B b d x^{3} + \frac{1}{3} \, A c d x^{3} + \frac{1}{3} \, A b x^{3} e + \frac{1}{2} \, A b d x^{2}"," ",0,"1/5*B*c*x^5*e + 1/4*B*c*d*x^4 + 1/4*B*b*x^4*e + 1/4*A*c*x^4*e + 1/3*B*b*d*x^3 + 1/3*A*c*d*x^3 + 1/3*A*b*x^3*e + 1/2*A*b*d*x^2","A",0
1107,1,29,0,0.147459," ","integrate((B*x+A)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{4} \, B c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, A b x^{2}"," ",0,"1/4*B*c*x^4 + 1/3*B*b*x^3 + 1/3*A*c*x^3 + 1/2*A*b*x^2","A",0
1108,1,117,0,0.162965," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d),x, algorithm=""giac"")","-{\left(B c d^{3} - B b d^{2} e - A c d^{2} e + A b d e^{2}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B c x^{3} e^{2} - 3 \, B c d x^{2} e + 6 \, B c d^{2} x + 3 \, B b x^{2} e^{2} + 3 \, A c x^{2} e^{2} - 6 \, B b d x e - 6 \, A c d x e + 6 \, A b x e^{2}\right)} e^{\left(-3\right)}"," ",0,"-(B*c*d^3 - B*b*d^2*e - A*c*d^2*e + A*b*d*e^2)*e^(-4)*log(abs(x*e + d)) + 1/6*(2*B*c*x^3*e^2 - 3*B*c*d*x^2*e + 6*B*c*d^2*x + 3*B*b*x^2*e^2 + 3*A*c*x^2*e^2 - 6*B*b*d*x*e - 6*A*c*d*x*e + 6*A*b*x*e^2)*e^(-3)","A",0
1109,1,167,0,0.160511," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(B c - \frac{2 \, {\left(3 \, B c d e - B b e^{2} - A c e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)} - {\left(3 \, B c d^{2} - 2 \, B b d e - 2 \, A c d e + A b e^{2}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c d^{3} e^{2}}{x e + d} - \frac{B b d^{2} e^{3}}{x e + d} - \frac{A c d^{2} e^{3}}{x e + d} + \frac{A b d e^{4}}{x e + d}\right)} e^{\left(-6\right)}"," ",0,"1/2*(B*c - 2*(3*B*c*d*e - B*b*e^2 - A*c*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4) - (3*B*c*d^2 - 2*B*b*d*e - 2*A*c*d*e + A*b*e^2)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c*d^3*e^2/(x*e + d) - B*b*d^2*e^3/(x*e + d) - A*c*d^2*e^3/(x*e + d) + A*b*d*e^4/(x*e + d))*e^(-6)","A",0
1110,1,113,0,0.157680," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^3,x, algorithm=""giac"")","B c x e^{\left(-3\right)} - {\left(3 \, B c d - B b e - A c e\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, B c d^{3} - 3 \, B b d^{2} e - 3 \, A c d^{2} e + A b d e^{2} + 2 \, {\left(3 \, B c d^{2} e - 2 \, B b d e^{2} - 2 \, A c d e^{2} + A b e^{3}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"B*c*x*e^(-3) - (3*B*c*d - B*b*e - A*c*e)*e^(-4)*log(abs(x*e + d)) - 1/2*(5*B*c*d^3 - 3*B*b*d^2*e - 3*A*c*d^2*e + A*b*d*e^2 + 2*(3*B*c*d^2*e - 2*B*b*d*e^2 - 2*A*c*d*e^2 + A*b*e^3)*x)*e^(-4)/(x*e + d)^2","A",0
1111,1,119,0,0.150945," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^4,x, algorithm=""giac"")","B c e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(6 \, {\left(3 \, B c d e - B b e^{2} - A c e^{2}\right)} x^{2} + 3 \, {\left(9 \, B c d^{2} - 2 \, B b d e - 2 \, A c d e - A b e^{2}\right)} x + {\left(11 \, B c d^{3} - 2 \, B b d^{2} e - 2 \, A c d^{2} e - A b d e^{2}\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"B*c*e^(-4)*log(abs(x*e + d)) + 1/6*(6*(3*B*c*d*e - B*b*e^2 - A*c*e^2)*x^2 + 3*(9*B*c*d^2 - 2*B*b*d*e - 2*A*c*d*e - A*b*e^2)*x + (11*B*c*d^3 - 2*B*b*d^2*e - 2*A*c*d^2*e - A*b*d*e^2)*e^(-1))*e^(-3)/(x*e + d)^3","A",0
1112,1,177,0,0.234637," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{12 \, B c e^{\left(-1\right)}}{x e + d} - \frac{18 \, B c d e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}} + \frac{12 \, B c d^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c d^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{6 \, B b}{{\left(x e + d\right)}^{2}} + \frac{6 \, A c}{{\left(x e + d\right)}^{2}} - \frac{8 \, B b d}{{\left(x e + d\right)}^{3}} - \frac{8 \, A c d}{{\left(x e + d\right)}^{3}} + \frac{3 \, B b d^{2}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A c d^{2}}{{\left(x e + d\right)}^{4}} + \frac{4 \, A b e}{{\left(x e + d\right)}^{3}} - \frac{3 \, A b d e}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-3\right)}"," ",0,"-1/12*(12*B*c*e^(-1)/(x*e + d) - 18*B*c*d*e^(-1)/(x*e + d)^2 + 12*B*c*d^2*e^(-1)/(x*e + d)^3 - 3*B*c*d^3*e^(-1)/(x*e + d)^4 + 6*B*b/(x*e + d)^2 + 6*A*c/(x*e + d)^2 - 8*B*b*d/(x*e + d)^3 - 8*A*c*d/(x*e + d)^3 + 3*B*b*d^2/(x*e + d)^4 + 3*A*c*d^2/(x*e + d)^4 + 4*A*b*e/(x*e + d)^3 - 3*A*b*d*e/(x*e + d)^4)*e^(-3)","A",0
1113,1,115,0,0.151086," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(30 \, B c x^{3} e^{3} + 30 \, B c d x^{2} e^{2} + 15 \, B c d^{2} x e + 3 \, B c d^{3} + 20 \, B b x^{2} e^{3} + 20 \, A c x^{2} e^{3} + 10 \, B b d x e^{2} + 10 \, A c d x e^{2} + 2 \, B b d^{2} e + 2 \, A c d^{2} e + 15 \, A b x e^{3} + 3 \, A b d e^{2}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/60*(30*B*c*x^3*e^3 + 30*B*c*d*x^2*e^2 + 15*B*c*d^2*x*e + 3*B*c*d^3 + 20*B*b*x^2*e^3 + 20*A*c*x^2*e^3 + 10*B*b*d*x*e^2 + 10*A*c*d*x*e^2 + 2*B*b*d^2*e + 2*A*c*d^2*e + 15*A*b*x*e^3 + 3*A*b*d*e^2)*e^(-4)/(x*e + d)^5","A",0
1114,1,2827,0,0.267687," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c^{2} m^{5} x^{6} e^{6} + {\left(x e + d\right)}^{m} B c^{2} d m^{5} x^{5} e^{5} + 2 \, {\left(x e + d\right)}^{m} B b c m^{5} x^{5} e^{6} + {\left(x e + d\right)}^{m} A c^{2} m^{5} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} B c^{2} m^{4} x^{6} e^{6} + 2 \, {\left(x e + d\right)}^{m} B b c d m^{5} x^{4} e^{5} + {\left(x e + d\right)}^{m} A c^{2} d m^{5} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} B c^{2} d m^{4} x^{5} e^{5} - 5 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{4} x^{4} e^{4} + {\left(x e + d\right)}^{m} B b^{2} m^{5} x^{4} e^{6} + 2 \, {\left(x e + d\right)}^{m} A b c m^{5} x^{4} e^{6} + 32 \, {\left(x e + d\right)}^{m} B b c m^{4} x^{5} e^{6} + 16 \, {\left(x e + d\right)}^{m} A c^{2} m^{4} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} B c^{2} m^{3} x^{6} e^{6} + {\left(x e + d\right)}^{m} B b^{2} d m^{5} x^{3} e^{5} + 2 \, {\left(x e + d\right)}^{m} A b c d m^{5} x^{3} e^{5} + 24 \, {\left(x e + d\right)}^{m} B b c d m^{4} x^{4} e^{5} + 12 \, {\left(x e + d\right)}^{m} A c^{2} d m^{4} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} B c^{2} d m^{3} x^{5} e^{5} - 8 \, {\left(x e + d\right)}^{m} B b c d^{2} m^{4} x^{3} e^{4} - 4 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{4} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{3} x^{4} e^{4} + 20 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} A b^{2} m^{5} x^{3} e^{6} + 17 \, {\left(x e + d\right)}^{m} B b^{2} m^{4} x^{4} e^{6} + 34 \, {\left(x e + d\right)}^{m} A b c m^{4} x^{4} e^{6} + 190 \, {\left(x e + d\right)}^{m} B b c m^{3} x^{5} e^{6} + 95 \, {\left(x e + d\right)}^{m} A c^{2} m^{3} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} B c^{2} m^{2} x^{6} e^{6} + {\left(x e + d\right)}^{m} A b^{2} d m^{5} x^{2} e^{5} + 14 \, {\left(x e + d\right)}^{m} B b^{2} d m^{4} x^{3} e^{5} + 28 \, {\left(x e + d\right)}^{m} A b c d m^{4} x^{3} e^{5} + 94 \, {\left(x e + d\right)}^{m} B b c d m^{3} x^{4} e^{5} + 47 \, {\left(x e + d\right)}^{m} A c^{2} d m^{3} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} B c^{2} d m^{2} x^{5} e^{5} - 3 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m^{4} x^{2} e^{4} - 6 \, {\left(x e + d\right)}^{m} A b c d^{2} m^{4} x^{2} e^{4} - 72 \, {\left(x e + d\right)}^{m} B b c d^{2} m^{3} x^{3} e^{4} - 36 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{3} x^{3} e^{4} - 55 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{2} x^{4} e^{4} + 24 \, {\left(x e + d\right)}^{m} B b c d^{3} m^{3} x^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m^{3} x^{2} e^{3} + 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m^{2} x^{3} e^{3} - 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{4} m^{2} x^{2} e^{2} + 18 \, {\left(x e + d\right)}^{m} A b^{2} m^{4} x^{3} e^{6} + 107 \, {\left(x e + d\right)}^{m} B b^{2} m^{3} x^{4} e^{6} + 214 \, {\left(x e + d\right)}^{m} A b c m^{3} x^{4} e^{6} + 520 \, {\left(x e + d\right)}^{m} B b c m^{2} x^{5} e^{6} + 260 \, {\left(x e + d\right)}^{m} A c^{2} m^{2} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} B c^{2} m x^{6} e^{6} + 16 \, {\left(x e + d\right)}^{m} A b^{2} d m^{4} x^{2} e^{5} + 65 \, {\left(x e + d\right)}^{m} B b^{2} d m^{3} x^{3} e^{5} + 130 \, {\left(x e + d\right)}^{m} A b c d m^{3} x^{3} e^{5} + 144 \, {\left(x e + d\right)}^{m} B b c d m^{2} x^{4} e^{5} + 72 \, {\left(x e + d\right)}^{m} A c^{2} d m^{2} x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} B c^{2} d m x^{5} e^{5} - 2 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m^{4} x e^{4} - 36 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m^{3} x^{2} e^{4} - 72 \, {\left(x e + d\right)}^{m} A b c d^{2} m^{3} x^{2} e^{4} - 160 \, {\left(x e + d\right)}^{m} B b c d^{2} m^{2} x^{3} e^{4} - 80 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{2} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m x^{4} e^{4} + 6 \, {\left(x e + d\right)}^{m} B b^{2} d^{3} m^{3} x e^{3} + 12 \, {\left(x e + d\right)}^{m} A b c d^{3} m^{3} x e^{3} + 168 \, {\left(x e + d\right)}^{m} B b c d^{3} m^{2} x^{2} e^{3} + 84 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m^{2} x^{2} e^{3} + 40 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m x^{3} e^{3} - 48 \, {\left(x e + d\right)}^{m} B b c d^{4} m^{2} x e^{2} - 24 \, {\left(x e + d\right)}^{m} A c^{2} d^{4} m^{2} x e^{2} - 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{4} m x^{2} e^{2} + 120 \, {\left(x e + d\right)}^{m} B c^{2} d^{5} m x e + 121 \, {\left(x e + d\right)}^{m} A b^{2} m^{3} x^{3} e^{6} + 307 \, {\left(x e + d\right)}^{m} B b^{2} m^{2} x^{4} e^{6} + 614 \, {\left(x e + d\right)}^{m} A b c m^{2} x^{4} e^{6} + 648 \, {\left(x e + d\right)}^{m} B b c m x^{5} e^{6} + 324 \, {\left(x e + d\right)}^{m} A c^{2} m x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} B c^{2} x^{6} e^{6} + 89 \, {\left(x e + d\right)}^{m} A b^{2} d m^{3} x^{2} e^{5} + 112 \, {\left(x e + d\right)}^{m} B b^{2} d m^{2} x^{3} e^{5} + 224 \, {\left(x e + d\right)}^{m} A b c d m^{2} x^{3} e^{5} + 72 \, {\left(x e + d\right)}^{m} B b c d m x^{4} e^{5} + 36 \, {\left(x e + d\right)}^{m} A c^{2} d m x^{4} e^{5} - 30 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m^{3} x e^{4} - 123 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m^{2} x^{2} e^{4} - 246 \, {\left(x e + d\right)}^{m} A b c d^{2} m^{2} x^{2} e^{4} - 96 \, {\left(x e + d\right)}^{m} B b c d^{2} m x^{3} e^{4} - 48 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m x^{3} e^{4} + 2 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} m^{3} e^{3} + 66 \, {\left(x e + d\right)}^{m} B b^{2} d^{3} m^{2} x e^{3} + 132 \, {\left(x e + d\right)}^{m} A b c d^{3} m^{2} x e^{3} + 144 \, {\left(x e + d\right)}^{m} B b c d^{3} m x^{2} e^{3} + 72 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m x^{2} e^{3} - 6 \, {\left(x e + d\right)}^{m} B b^{2} d^{4} m^{2} e^{2} - 12 \, {\left(x e + d\right)}^{m} A b c d^{4} m^{2} e^{2} - 288 \, {\left(x e + d\right)}^{m} B b c d^{4} m x e^{2} - 144 \, {\left(x e + d\right)}^{m} A c^{2} d^{4} m x e^{2} + 48 \, {\left(x e + d\right)}^{m} B b c d^{5} m e + 24 \, {\left(x e + d\right)}^{m} A c^{2} d^{5} m e - 120 \, {\left(x e + d\right)}^{m} B c^{2} d^{6} + 372 \, {\left(x e + d\right)}^{m} A b^{2} m^{2} x^{3} e^{6} + 396 \, {\left(x e + d\right)}^{m} B b^{2} m x^{4} e^{6} + 792 \, {\left(x e + d\right)}^{m} A b c m x^{4} e^{6} + 288 \, {\left(x e + d\right)}^{m} B b c x^{5} e^{6} + 144 \, {\left(x e + d\right)}^{m} A c^{2} x^{5} e^{6} + 194 \, {\left(x e + d\right)}^{m} A b^{2} d m^{2} x^{2} e^{5} + 60 \, {\left(x e + d\right)}^{m} B b^{2} d m x^{3} e^{5} + 120 \, {\left(x e + d\right)}^{m} A b c d m x^{3} e^{5} - 148 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m^{2} x e^{4} - 90 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} A b c d^{2} m x^{2} e^{4} + 30 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} m^{2} e^{3} + 180 \, {\left(x e + d\right)}^{m} B b^{2} d^{3} m x e^{3} + 360 \, {\left(x e + d\right)}^{m} A b c d^{3} m x e^{3} - 66 \, {\left(x e + d\right)}^{m} B b^{2} d^{4} m e^{2} - 132 \, {\left(x e + d\right)}^{m} A b c d^{4} m e^{2} + 288 \, {\left(x e + d\right)}^{m} B b c d^{5} e + 144 \, {\left(x e + d\right)}^{m} A c^{2} d^{5} e + 508 \, {\left(x e + d\right)}^{m} A b^{2} m x^{3} e^{6} + 180 \, {\left(x e + d\right)}^{m} B b^{2} x^{4} e^{6} + 360 \, {\left(x e + d\right)}^{m} A b c x^{4} e^{6} + 120 \, {\left(x e + d\right)}^{m} A b^{2} d m x^{2} e^{5} - 240 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m x e^{4} + 148 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} m e^{3} - 180 \, {\left(x e + d\right)}^{m} B b^{2} d^{4} e^{2} - 360 \, {\left(x e + d\right)}^{m} A b c d^{4} e^{2} + 240 \, {\left(x e + d\right)}^{m} A b^{2} x^{3} e^{6} + 240 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} e^{3}}{m^{6} e^{6} + 21 \, m^{5} e^{6} + 175 \, m^{4} e^{6} + 735 \, m^{3} e^{6} + 1624 \, m^{2} e^{6} + 1764 \, m e^{6} + 720 \, e^{6}}"," ",0,"((x*e + d)^m*B*c^2*m^5*x^6*e^6 + (x*e + d)^m*B*c^2*d*m^5*x^5*e^5 + 2*(x*e + d)^m*B*b*c*m^5*x^5*e^6 + (x*e + d)^m*A*c^2*m^5*x^5*e^6 + 15*(x*e + d)^m*B*c^2*m^4*x^6*e^6 + 2*(x*e + d)^m*B*b*c*d*m^5*x^4*e^5 + (x*e + d)^m*A*c^2*d*m^5*x^4*e^5 + 10*(x*e + d)^m*B*c^2*d*m^4*x^5*e^5 - 5*(x*e + d)^m*B*c^2*d^2*m^4*x^4*e^4 + (x*e + d)^m*B*b^2*m^5*x^4*e^6 + 2*(x*e + d)^m*A*b*c*m^5*x^4*e^6 + 32*(x*e + d)^m*B*b*c*m^4*x^5*e^6 + 16*(x*e + d)^m*A*c^2*m^4*x^5*e^6 + 85*(x*e + d)^m*B*c^2*m^3*x^6*e^6 + (x*e + d)^m*B*b^2*d*m^5*x^3*e^5 + 2*(x*e + d)^m*A*b*c*d*m^5*x^3*e^5 + 24*(x*e + d)^m*B*b*c*d*m^4*x^4*e^5 + 12*(x*e + d)^m*A*c^2*d*m^4*x^4*e^5 + 35*(x*e + d)^m*B*c^2*d*m^3*x^5*e^5 - 8*(x*e + d)^m*B*b*c*d^2*m^4*x^3*e^4 - 4*(x*e + d)^m*A*c^2*d^2*m^4*x^3*e^4 - 30*(x*e + d)^m*B*c^2*d^2*m^3*x^4*e^4 + 20*(x*e + d)^m*B*c^2*d^3*m^3*x^3*e^3 + (x*e + d)^m*A*b^2*m^5*x^3*e^6 + 17*(x*e + d)^m*B*b^2*m^4*x^4*e^6 + 34*(x*e + d)^m*A*b*c*m^4*x^4*e^6 + 190*(x*e + d)^m*B*b*c*m^3*x^5*e^6 + 95*(x*e + d)^m*A*c^2*m^3*x^5*e^6 + 225*(x*e + d)^m*B*c^2*m^2*x^6*e^6 + (x*e + d)^m*A*b^2*d*m^5*x^2*e^5 + 14*(x*e + d)^m*B*b^2*d*m^4*x^3*e^5 + 28*(x*e + d)^m*A*b*c*d*m^4*x^3*e^5 + 94*(x*e + d)^m*B*b*c*d*m^3*x^4*e^5 + 47*(x*e + d)^m*A*c^2*d*m^3*x^4*e^5 + 50*(x*e + d)^m*B*c^2*d*m^2*x^5*e^5 - 3*(x*e + d)^m*B*b^2*d^2*m^4*x^2*e^4 - 6*(x*e + d)^m*A*b*c*d^2*m^4*x^2*e^4 - 72*(x*e + d)^m*B*b*c*d^2*m^3*x^3*e^4 - 36*(x*e + d)^m*A*c^2*d^2*m^3*x^3*e^4 - 55*(x*e + d)^m*B*c^2*d^2*m^2*x^4*e^4 + 24*(x*e + d)^m*B*b*c*d^3*m^3*x^2*e^3 + 12*(x*e + d)^m*A*c^2*d^3*m^3*x^2*e^3 + 60*(x*e + d)^m*B*c^2*d^3*m^2*x^3*e^3 - 60*(x*e + d)^m*B*c^2*d^4*m^2*x^2*e^2 + 18*(x*e + d)^m*A*b^2*m^4*x^3*e^6 + 107*(x*e + d)^m*B*b^2*m^3*x^4*e^6 + 214*(x*e + d)^m*A*b*c*m^3*x^4*e^6 + 520*(x*e + d)^m*B*b*c*m^2*x^5*e^6 + 260*(x*e + d)^m*A*c^2*m^2*x^5*e^6 + 274*(x*e + d)^m*B*c^2*m*x^6*e^6 + 16*(x*e + d)^m*A*b^2*d*m^4*x^2*e^5 + 65*(x*e + d)^m*B*b^2*d*m^3*x^3*e^5 + 130*(x*e + d)^m*A*b*c*d*m^3*x^3*e^5 + 144*(x*e + d)^m*B*b*c*d*m^2*x^4*e^5 + 72*(x*e + d)^m*A*c^2*d*m^2*x^4*e^5 + 24*(x*e + d)^m*B*c^2*d*m*x^5*e^5 - 2*(x*e + d)^m*A*b^2*d^2*m^4*x*e^4 - 36*(x*e + d)^m*B*b^2*d^2*m^3*x^2*e^4 - 72*(x*e + d)^m*A*b*c*d^2*m^3*x^2*e^4 - 160*(x*e + d)^m*B*b*c*d^2*m^2*x^3*e^4 - 80*(x*e + d)^m*A*c^2*d^2*m^2*x^3*e^4 - 30*(x*e + d)^m*B*c^2*d^2*m*x^4*e^4 + 6*(x*e + d)^m*B*b^2*d^3*m^3*x*e^3 + 12*(x*e + d)^m*A*b*c*d^3*m^3*x*e^3 + 168*(x*e + d)^m*B*b*c*d^3*m^2*x^2*e^3 + 84*(x*e + d)^m*A*c^2*d^3*m^2*x^2*e^3 + 40*(x*e + d)^m*B*c^2*d^3*m*x^3*e^3 - 48*(x*e + d)^m*B*b*c*d^4*m^2*x*e^2 - 24*(x*e + d)^m*A*c^2*d^4*m^2*x*e^2 - 60*(x*e + d)^m*B*c^2*d^4*m*x^2*e^2 + 120*(x*e + d)^m*B*c^2*d^5*m*x*e + 121*(x*e + d)^m*A*b^2*m^3*x^3*e^6 + 307*(x*e + d)^m*B*b^2*m^2*x^4*e^6 + 614*(x*e + d)^m*A*b*c*m^2*x^4*e^6 + 648*(x*e + d)^m*B*b*c*m*x^5*e^6 + 324*(x*e + d)^m*A*c^2*m*x^5*e^6 + 120*(x*e + d)^m*B*c^2*x^6*e^6 + 89*(x*e + d)^m*A*b^2*d*m^3*x^2*e^5 + 112*(x*e + d)^m*B*b^2*d*m^2*x^3*e^5 + 224*(x*e + d)^m*A*b*c*d*m^2*x^3*e^5 + 72*(x*e + d)^m*B*b*c*d*m*x^4*e^5 + 36*(x*e + d)^m*A*c^2*d*m*x^4*e^5 - 30*(x*e + d)^m*A*b^2*d^2*m^3*x*e^4 - 123*(x*e + d)^m*B*b^2*d^2*m^2*x^2*e^4 - 246*(x*e + d)^m*A*b*c*d^2*m^2*x^2*e^4 - 96*(x*e + d)^m*B*b*c*d^2*m*x^3*e^4 - 48*(x*e + d)^m*A*c^2*d^2*m*x^3*e^4 + 2*(x*e + d)^m*A*b^2*d^3*m^3*e^3 + 66*(x*e + d)^m*B*b^2*d^3*m^2*x*e^3 + 132*(x*e + d)^m*A*b*c*d^3*m^2*x*e^3 + 144*(x*e + d)^m*B*b*c*d^3*m*x^2*e^3 + 72*(x*e + d)^m*A*c^2*d^3*m*x^2*e^3 - 6*(x*e + d)^m*B*b^2*d^4*m^2*e^2 - 12*(x*e + d)^m*A*b*c*d^4*m^2*e^2 - 288*(x*e + d)^m*B*b*c*d^4*m*x*e^2 - 144*(x*e + d)^m*A*c^2*d^4*m*x*e^2 + 48*(x*e + d)^m*B*b*c*d^5*m*e + 24*(x*e + d)^m*A*c^2*d^5*m*e - 120*(x*e + d)^m*B*c^2*d^6 + 372*(x*e + d)^m*A*b^2*m^2*x^3*e^6 + 396*(x*e + d)^m*B*b^2*m*x^4*e^6 + 792*(x*e + d)^m*A*b*c*m*x^4*e^6 + 288*(x*e + d)^m*B*b*c*x^5*e^6 + 144*(x*e + d)^m*A*c^2*x^5*e^6 + 194*(x*e + d)^m*A*b^2*d*m^2*x^2*e^5 + 60*(x*e + d)^m*B*b^2*d*m*x^3*e^5 + 120*(x*e + d)^m*A*b*c*d*m*x^3*e^5 - 148*(x*e + d)^m*A*b^2*d^2*m^2*x*e^4 - 90*(x*e + d)^m*B*b^2*d^2*m*x^2*e^4 - 180*(x*e + d)^m*A*b*c*d^2*m*x^2*e^4 + 30*(x*e + d)^m*A*b^2*d^3*m^2*e^3 + 180*(x*e + d)^m*B*b^2*d^3*m*x*e^3 + 360*(x*e + d)^m*A*b*c*d^3*m*x*e^3 - 66*(x*e + d)^m*B*b^2*d^4*m*e^2 - 132*(x*e + d)^m*A*b*c*d^4*m*e^2 + 288*(x*e + d)^m*B*b*c*d^5*e + 144*(x*e + d)^m*A*c^2*d^5*e + 508*(x*e + d)^m*A*b^2*m*x^3*e^6 + 180*(x*e + d)^m*B*b^2*x^4*e^6 + 360*(x*e + d)^m*A*b*c*x^4*e^6 + 120*(x*e + d)^m*A*b^2*d*m*x^2*e^5 - 240*(x*e + d)^m*A*b^2*d^2*m*x*e^4 + 148*(x*e + d)^m*A*b^2*d^3*m*e^3 - 180*(x*e + d)^m*B*b^2*d^4*e^2 - 360*(x*e + d)^m*A*b*c*d^4*e^2 + 240*(x*e + d)^m*A*b^2*x^3*e^6 + 240*(x*e + d)^m*A*b^2*d^3*e^3)/(m^6*e^6 + 21*m^5*e^6 + 175*m^4*e^6 + 735*m^3*e^6 + 1624*m^2*e^6 + 1764*m*e^6 + 720*e^6)","B",0
1115,1,285,0,0.155105," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{9} \, B c^{2} x^{9} e^{3} + \frac{3}{8} \, B c^{2} d x^{8} e^{2} + \frac{3}{7} \, B c^{2} d^{2} x^{7} e + \frac{1}{6} \, B c^{2} d^{3} x^{6} + \frac{1}{4} \, B b c x^{8} e^{3} + \frac{1}{8} \, A c^{2} x^{8} e^{3} + \frac{6}{7} \, B b c d x^{7} e^{2} + \frac{3}{7} \, A c^{2} d x^{7} e^{2} + B b c d^{2} x^{6} e + \frac{1}{2} \, A c^{2} d^{2} x^{6} e + \frac{2}{5} \, B b c d^{3} x^{5} + \frac{1}{5} \, A c^{2} d^{3} x^{5} + \frac{1}{7} \, B b^{2} x^{7} e^{3} + \frac{2}{7} \, A b c x^{7} e^{3} + \frac{1}{2} \, B b^{2} d x^{6} e^{2} + A b c d x^{6} e^{2} + \frac{3}{5} \, B b^{2} d^{2} x^{5} e + \frac{6}{5} \, A b c d^{2} x^{5} e + \frac{1}{4} \, B b^{2} d^{3} x^{4} + \frac{1}{2} \, A b c d^{3} x^{4} + \frac{1}{6} \, A b^{2} x^{6} e^{3} + \frac{3}{5} \, A b^{2} d x^{5} e^{2} + \frac{3}{4} \, A b^{2} d^{2} x^{4} e + \frac{1}{3} \, A b^{2} d^{3} x^{3}"," ",0,"1/9*B*c^2*x^9*e^3 + 3/8*B*c^2*d*x^8*e^2 + 3/7*B*c^2*d^2*x^7*e + 1/6*B*c^2*d^3*x^6 + 1/4*B*b*c*x^8*e^3 + 1/8*A*c^2*x^8*e^3 + 6/7*B*b*c*d*x^7*e^2 + 3/7*A*c^2*d*x^7*e^2 + B*b*c*d^2*x^6*e + 1/2*A*c^2*d^2*x^6*e + 2/5*B*b*c*d^3*x^5 + 1/5*A*c^2*d^3*x^5 + 1/7*B*b^2*x^7*e^3 + 2/7*A*b*c*x^7*e^3 + 1/2*B*b^2*d*x^6*e^2 + A*b*c*d*x^6*e^2 + 3/5*B*b^2*d^2*x^5*e + 6/5*A*b*c*d^2*x^5*e + 1/4*B*b^2*d^3*x^4 + 1/2*A*b*c*d^3*x^4 + 1/6*A*b^2*x^6*e^3 + 3/5*A*b^2*d*x^5*e^2 + 3/4*A*b^2*d^2*x^4*e + 1/3*A*b^2*d^3*x^3","A",0
1116,1,205,0,0.149546," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{8} \, B c^{2} x^{8} e^{2} + \frac{2}{7} \, B c^{2} d x^{7} e + \frac{1}{6} \, B c^{2} d^{2} x^{6} + \frac{2}{7} \, B b c x^{7} e^{2} + \frac{1}{7} \, A c^{2} x^{7} e^{2} + \frac{2}{3} \, B b c d x^{6} e + \frac{1}{3} \, A c^{2} d x^{6} e + \frac{2}{5} \, B b c d^{2} x^{5} + \frac{1}{5} \, A c^{2} d^{2} x^{5} + \frac{1}{6} \, B b^{2} x^{6} e^{2} + \frac{1}{3} \, A b c x^{6} e^{2} + \frac{2}{5} \, B b^{2} d x^{5} e + \frac{4}{5} \, A b c d x^{5} e + \frac{1}{4} \, B b^{2} d^{2} x^{4} + \frac{1}{2} \, A b c d^{2} x^{4} + \frac{1}{5} \, A b^{2} x^{5} e^{2} + \frac{1}{2} \, A b^{2} d x^{4} e + \frac{1}{3} \, A b^{2} d^{2} x^{3}"," ",0,"1/8*B*c^2*x^8*e^2 + 2/7*B*c^2*d*x^7*e + 1/6*B*c^2*d^2*x^6 + 2/7*B*b*c*x^7*e^2 + 1/7*A*c^2*x^7*e^2 + 2/3*B*b*c*d*x^6*e + 1/3*A*c^2*d*x^6*e + 2/5*B*b*c*d^2*x^5 + 1/5*A*c^2*d^2*x^5 + 1/6*B*b^2*x^6*e^2 + 1/3*A*b*c*x^6*e^2 + 2/5*B*b^2*d*x^5*e + 4/5*A*b*c*d*x^5*e + 1/4*B*b^2*d^2*x^4 + 1/2*A*b*c*d^2*x^4 + 1/5*A*b^2*x^5*e^2 + 1/2*A*b^2*d*x^4*e + 1/3*A*b^2*d^2*x^3","A",0
1117,1,123,0,0.154892," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{7} \, B c^{2} x^{7} e + \frac{1}{6} \, B c^{2} d x^{6} + \frac{1}{3} \, B b c x^{6} e + \frac{1}{6} \, A c^{2} x^{6} e + \frac{2}{5} \, B b c d x^{5} + \frac{1}{5} \, A c^{2} d x^{5} + \frac{1}{5} \, B b^{2} x^{5} e + \frac{2}{5} \, A b c x^{5} e + \frac{1}{4} \, B b^{2} d x^{4} + \frac{1}{2} \, A b c d x^{4} + \frac{1}{4} \, A b^{2} x^{4} e + \frac{1}{3} \, A b^{2} d x^{3}"," ",0,"1/7*B*c^2*x^7*e + 1/6*B*c^2*d*x^6 + 1/3*B*b*c*x^6*e + 1/6*A*c^2*x^6*e + 2/5*B*b*c*d*x^5 + 1/5*A*c^2*d*x^5 + 1/5*B*b^2*x^5*e + 2/5*A*b*c*x^5*e + 1/4*B*b^2*d*x^4 + 1/2*A*b*c*d*x^4 + 1/4*A*b^2*x^4*e + 1/3*A*b^2*d*x^3","A",0
1118,1,53,0,0.158824," ","integrate((B*x+A)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{2} x^{6} + \frac{2}{5} \, B b c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{4} \, B b^{2} x^{4} + \frac{1}{2} \, A b c x^{4} + \frac{1}{3} \, A b^{2} x^{3}"," ",0,"1/6*B*c^2*x^6 + 2/5*B*b*c*x^5 + 1/5*A*c^2*x^5 + 1/4*B*b^2*x^4 + 1/2*A*b*c*x^4 + 1/3*A*b^2*x^3","A",0
1119,1,322,0,0.155403," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d),x, algorithm=""giac"")","-{\left(B c^{2} d^{5} - 2 \, B b c d^{4} e - A c^{2} d^{4} e + B b^{2} d^{3} e^{2} + 2 \, A b c d^{3} e^{2} - A b^{2} d^{2} e^{3}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(12 \, B c^{2} x^{5} e^{4} - 15 \, B c^{2} d x^{4} e^{3} + 20 \, B c^{2} d^{2} x^{3} e^{2} - 30 \, B c^{2} d^{3} x^{2} e + 60 \, B c^{2} d^{4} x + 30 \, B b c x^{4} e^{4} + 15 \, A c^{2} x^{4} e^{4} - 40 \, B b c d x^{3} e^{3} - 20 \, A c^{2} d x^{3} e^{3} + 60 \, B b c d^{2} x^{2} e^{2} + 30 \, A c^{2} d^{2} x^{2} e^{2} - 120 \, B b c d^{3} x e - 60 \, A c^{2} d^{3} x e + 20 \, B b^{2} x^{3} e^{4} + 40 \, A b c x^{3} e^{4} - 30 \, B b^{2} d x^{2} e^{3} - 60 \, A b c d x^{2} e^{3} + 60 \, B b^{2} d^{2} x e^{2} + 120 \, A b c d^{2} x e^{2} + 30 \, A b^{2} x^{2} e^{4} - 60 \, A b^{2} d x e^{3}\right)} e^{\left(-5\right)}"," ",0,"-(B*c^2*d^5 - 2*B*b*c*d^4*e - A*c^2*d^4*e + B*b^2*d^3*e^2 + 2*A*b*c*d^3*e^2 - A*b^2*d^2*e^3)*e^(-6)*log(abs(x*e + d)) + 1/60*(12*B*c^2*x^5*e^4 - 15*B*c^2*d*x^4*e^3 + 20*B*c^2*d^2*x^3*e^2 - 30*B*c^2*d^3*x^2*e + 60*B*c^2*d^4*x + 30*B*b*c*x^4*e^4 + 15*A*c^2*x^4*e^4 - 40*B*b*c*d*x^3*e^3 - 20*A*c^2*d*x^3*e^3 + 60*B*b*c*d^2*x^2*e^2 + 30*A*c^2*d^2*x^2*e^2 - 120*B*b*c*d^3*x*e - 60*A*c^2*d^3*x*e + 20*B*b^2*x^3*e^4 + 40*A*b*c*x^3*e^4 - 30*B*b^2*d*x^2*e^3 - 60*A*b*c*d*x^2*e^3 + 60*B*b^2*d^2*x*e^2 + 120*A*b*c*d^2*x*e^2 + 30*A*b^2*x^2*e^4 - 60*A*b^2*d*x*e^3)*e^(-5)","B",0
1120,1,380,0,0.168843," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, B c^{2} - \frac{4 \, {\left(5 \, B c^{2} d e - 2 \, B b c e^{2} - A c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(10 \, B c^{2} d^{2} e^{2} - 8 \, B b c d e^{3} - 4 \, A c^{2} d e^{3} + B b^{2} e^{4} + 2 \, A b c e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{12 \, {\left(10 \, B c^{2} d^{3} e^{3} - 12 \, B b c d^{2} e^{4} - 6 \, A c^{2} d^{2} e^{4} + 3 \, B b^{2} d e^{5} + 6 \, A b c d e^{5} - A b^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{4} e^{\left(-6\right)} - {\left(5 \, B c^{2} d^{4} - 8 \, B b c d^{3} e - 4 \, A c^{2} d^{3} e + 3 \, B b^{2} d^{2} e^{2} + 6 \, A b c d^{2} e^{2} - 2 \, A b^{2} d e^{3}\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c^{2} d^{5} e^{4}}{x e + d} - \frac{2 \, B b c d^{4} e^{5}}{x e + d} - \frac{A c^{2} d^{4} e^{5}}{x e + d} + \frac{B b^{2} d^{3} e^{6}}{x e + d} + \frac{2 \, A b c d^{3} e^{6}}{x e + d} - \frac{A b^{2} d^{2} e^{7}}{x e + d}\right)} e^{\left(-10\right)}"," ",0,"1/12*(3*B*c^2 - 4*(5*B*c^2*d*e - 2*B*b*c*e^2 - A*c^2*e^2)*e^(-1)/(x*e + d) + 6*(10*B*c^2*d^2*e^2 - 8*B*b*c*d*e^3 - 4*A*c^2*d*e^3 + B*b^2*e^4 + 2*A*b*c*e^4)*e^(-2)/(x*e + d)^2 - 12*(10*B*c^2*d^3*e^3 - 12*B*b*c*d^2*e^4 - 6*A*c^2*d^2*e^4 + 3*B*b^2*d*e^5 + 6*A*b*c*d*e^5 - A*b^2*e^6)*e^(-3)/(x*e + d)^3)*(x*e + d)^4*e^(-6) - (5*B*c^2*d^4 - 8*B*b*c*d^3*e - 4*A*c^2*d^3*e + 3*B*b^2*d^2*e^2 + 6*A*b*c*d^2*e^2 - 2*A*b^2*d*e^3)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c^2*d^5*e^4/(x*e + d) - 2*B*b*c*d^4*e^5/(x*e + d) - A*c^2*d^4*e^5/(x*e + d) + B*b^2*d^3*e^6/(x*e + d) + 2*A*b*c*d^3*e^6/(x*e + d) - A*b^2*d^2*e^7/(x*e + d))*e^(-10)","B",0
1121,1,307,0,0.159348," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^3,x, algorithm=""giac"")","-{\left(10 \, B c^{2} d^{3} - 12 \, B b c d^{2} e - 6 \, A c^{2} d^{2} e + 3 \, B b^{2} d e^{2} + 6 \, A b c d e^{2} - A b^{2} e^{3}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B c^{2} x^{3} e^{6} - 9 \, B c^{2} d x^{2} e^{5} + 36 \, B c^{2} d^{2} x e^{4} + 6 \, B b c x^{2} e^{6} + 3 \, A c^{2} x^{2} e^{6} - 36 \, B b c d x e^{5} - 18 \, A c^{2} d x e^{5} + 6 \, B b^{2} x e^{6} + 12 \, A b c x e^{6}\right)} e^{\left(-9\right)} - \frac{{\left(9 \, B c^{2} d^{5} - 14 \, B b c d^{4} e - 7 \, A c^{2} d^{4} e + 5 \, B b^{2} d^{3} e^{2} + 10 \, A b c d^{3} e^{2} - 3 \, A b^{2} d^{2} e^{3} + 2 \, {\left(5 \, B c^{2} d^{4} e - 8 \, B b c d^{3} e^{2} - 4 \, A c^{2} d^{3} e^{2} + 3 \, B b^{2} d^{2} e^{3} + 6 \, A b c d^{2} e^{3} - 2 \, A b^{2} d e^{4}\right)} x\right)} e^{\left(-6\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-(10*B*c^2*d^3 - 12*B*b*c*d^2*e - 6*A*c^2*d^2*e + 3*B*b^2*d*e^2 + 6*A*b*c*d*e^2 - A*b^2*e^3)*e^(-6)*log(abs(x*e + d)) + 1/6*(2*B*c^2*x^3*e^6 - 9*B*c^2*d*x^2*e^5 + 36*B*c^2*d^2*x*e^4 + 6*B*b*c*x^2*e^6 + 3*A*c^2*x^2*e^6 - 36*B*b*c*d*x*e^5 - 18*A*c^2*d*x*e^5 + 6*B*b^2*x*e^6 + 12*A*b*c*x*e^6)*e^(-9) - 1/2*(9*B*c^2*d^5 - 14*B*b*c*d^4*e - 7*A*c^2*d^4*e + 5*B*b^2*d^3*e^2 + 10*A*b*c*d^3*e^2 - 3*A*b^2*d^2*e^3 + 2*(5*B*c^2*d^4*e - 8*B*b*c*d^3*e^2 - 4*A*c^2*d^3*e^2 + 3*B*b^2*d^2*e^3 + 6*A*b*c*d^2*e^3 - 2*A*b^2*d*e^4)*x)*e^(-6)/(x*e + d)^2","A",0
1122,1,299,0,0.157569," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^4,x, algorithm=""giac"")","{\left(10 \, B c^{2} d^{2} - 8 \, B b c d e - 4 \, A c^{2} d e + B b^{2} e^{2} + 2 \, A b c e^{2}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B c^{2} x^{2} e^{4} - 8 \, B c^{2} d x e^{3} + 4 \, B b c x e^{4} + 2 \, A c^{2} x e^{4}\right)} e^{\left(-8\right)} + \frac{{\left(47 \, B c^{2} d^{5} - 52 \, B b c d^{4} e - 26 \, A c^{2} d^{4} e + 11 \, B b^{2} d^{3} e^{2} + 22 \, A b c d^{3} e^{2} - 2 \, A b^{2} d^{2} e^{3} + 6 \, {\left(10 \, B c^{2} d^{3} e^{2} - 12 \, B b c d^{2} e^{3} - 6 \, A c^{2} d^{2} e^{3} + 3 \, B b^{2} d e^{4} + 6 \, A b c d e^{4} - A b^{2} e^{5}\right)} x^{2} + 3 \, {\left(35 \, B c^{2} d^{4} e - 40 \, B b c d^{3} e^{2} - 20 \, A c^{2} d^{3} e^{2} + 9 \, B b^{2} d^{2} e^{3} + 18 \, A b c d^{2} e^{3} - 2 \, A b^{2} d e^{4}\right)} x\right)} e^{\left(-6\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"(10*B*c^2*d^2 - 8*B*b*c*d*e - 4*A*c^2*d*e + B*b^2*e^2 + 2*A*b*c*e^2)*e^(-6)*log(abs(x*e + d)) + 1/2*(B*c^2*x^2*e^4 - 8*B*c^2*d*x*e^3 + 4*B*b*c*x*e^4 + 2*A*c^2*x*e^4)*e^(-8) + 1/6*(47*B*c^2*d^5 - 52*B*b*c*d^4*e - 26*A*c^2*d^4*e + 11*B*b^2*d^3*e^2 + 22*A*b*c*d^3*e^2 - 2*A*b^2*d^2*e^3 + 6*(10*B*c^2*d^3*e^2 - 12*B*b*c*d^2*e^3 - 6*A*c^2*d^2*e^3 + 3*B*b^2*d*e^4 + 6*A*b*c*d*e^4 - A*b^2*e^5)*x^2 + 3*(35*B*c^2*d^4*e - 40*B*b*c*d^3*e^2 - 20*A*c^2*d^3*e^2 + 9*B*b^2*d^2*e^3 + 18*A*b*c*d^2*e^3 - 2*A*b^2*d*e^4)*x)*e^(-6)/(x*e + d)^3","A",0
1123,1,474,0,0.177100," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^5,x, algorithm=""giac"")","{\left(x e + d\right)} B c^{2} e^{\left(-6\right)} + {\left(5 \, B c^{2} d - 2 \, B b c e - A c^{2} e\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{120 \, B c^{2} d^{2} e^{22}}{x e + d} - \frac{60 \, B c^{2} d^{3} e^{22}}{{\left(x e + d\right)}^{2}} + \frac{20 \, B c^{2} d^{4} e^{22}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c^{2} d^{5} e^{22}}{{\left(x e + d\right)}^{4}} - \frac{96 \, B b c d e^{23}}{x e + d} - \frac{48 \, A c^{2} d e^{23}}{x e + d} + \frac{72 \, B b c d^{2} e^{23}}{{\left(x e + d\right)}^{2}} + \frac{36 \, A c^{2} d^{2} e^{23}}{{\left(x e + d\right)}^{2}} - \frac{32 \, B b c d^{3} e^{23}}{{\left(x e + d\right)}^{3}} - \frac{16 \, A c^{2} d^{3} e^{23}}{{\left(x e + d\right)}^{3}} + \frac{6 \, B b c d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A c^{2} d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{12 \, B b^{2} e^{24}}{x e + d} + \frac{24 \, A b c e^{24}}{x e + d} - \frac{18 \, B b^{2} d e^{24}}{{\left(x e + d\right)}^{2}} - \frac{36 \, A b c d e^{24}}{{\left(x e + d\right)}^{2}} + \frac{12 \, B b^{2} d^{2} e^{24}}{{\left(x e + d\right)}^{3}} + \frac{24 \, A b c d^{2} e^{24}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B b^{2} d^{3} e^{24}}{{\left(x e + d\right)}^{4}} - \frac{6 \, A b c d^{3} e^{24}}{{\left(x e + d\right)}^{4}} + \frac{6 \, A b^{2} e^{25}}{{\left(x e + d\right)}^{2}} - \frac{8 \, A b^{2} d e^{25}}{{\left(x e + d\right)}^{3}} + \frac{3 \, A b^{2} d^{2} e^{25}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-28\right)}"," ",0,"(x*e + d)*B*c^2*e^(-6) + (5*B*c^2*d - 2*B*b*c*e - A*c^2*e)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(120*B*c^2*d^2*e^22/(x*e + d) - 60*B*c^2*d^3*e^22/(x*e + d)^2 + 20*B*c^2*d^4*e^22/(x*e + d)^3 - 3*B*c^2*d^5*e^22/(x*e + d)^4 - 96*B*b*c*d*e^23/(x*e + d) - 48*A*c^2*d*e^23/(x*e + d) + 72*B*b*c*d^2*e^23/(x*e + d)^2 + 36*A*c^2*d^2*e^23/(x*e + d)^2 - 32*B*b*c*d^3*e^23/(x*e + d)^3 - 16*A*c^2*d^3*e^23/(x*e + d)^3 + 6*B*b*c*d^4*e^23/(x*e + d)^4 + 3*A*c^2*d^4*e^23/(x*e + d)^4 + 12*B*b^2*e^24/(x*e + d) + 24*A*b*c*e^24/(x*e + d) - 18*B*b^2*d*e^24/(x*e + d)^2 - 36*A*b*c*d*e^24/(x*e + d)^2 + 12*B*b^2*d^2*e^24/(x*e + d)^3 + 24*A*b*c*d^2*e^24/(x*e + d)^3 - 3*B*b^2*d^3*e^24/(x*e + d)^4 - 6*A*b*c*d^3*e^24/(x*e + d)^4 + 6*A*b^2*e^25/(x*e + d)^2 - 8*A*b^2*d*e^25/(x*e + d)^3 + 3*A*b^2*d^2*e^25/(x*e + d)^4)*e^(-28)","B",0
1124,1,301,0,0.158143," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^6,x, algorithm=""giac"")","B c^{2} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(60 \, {\left(5 \, B c^{2} d e^{3} - 2 \, B b c e^{4} - A c^{2} e^{4}\right)} x^{4} + 30 \, {\left(30 \, B c^{2} d^{2} e^{2} - 8 \, B b c d e^{3} - 4 \, A c^{2} d e^{3} - B b^{2} e^{4} - 2 \, A b c e^{4}\right)} x^{3} + 10 \, {\left(110 \, B c^{2} d^{3} e - 24 \, B b c d^{2} e^{2} - 12 \, A c^{2} d^{2} e^{2} - 3 \, B b^{2} d e^{3} - 6 \, A b c d e^{3} - 2 \, A b^{2} e^{4}\right)} x^{2} + 5 \, {\left(125 \, B c^{2} d^{4} - 24 \, B b c d^{3} e - 12 \, A c^{2} d^{3} e - 3 \, B b^{2} d^{2} e^{2} - 6 \, A b c d^{2} e^{2} - 2 \, A b^{2} d e^{3}\right)} x + {\left(137 \, B c^{2} d^{5} - 24 \, B b c d^{4} e - 12 \, A c^{2} d^{4} e - 3 \, B b^{2} d^{3} e^{2} - 6 \, A b c d^{3} e^{2} - 2 \, A b^{2} d^{2} e^{3}\right)} e^{\left(-1\right)}\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"B*c^2*e^(-6)*log(abs(x*e + d)) + 1/60*(60*(5*B*c^2*d*e^3 - 2*B*b*c*e^4 - A*c^2*e^4)*x^4 + 30*(30*B*c^2*d^2*e^2 - 8*B*b*c*d*e^3 - 4*A*c^2*d*e^3 - B*b^2*e^4 - 2*A*b*c*e^4)*x^3 + 10*(110*B*c^2*d^3*e - 24*B*b*c*d^2*e^2 - 12*A*c^2*d^2*e^2 - 3*B*b^2*d*e^3 - 6*A*b*c*d*e^3 - 2*A*b^2*e^4)*x^2 + 5*(125*B*c^2*d^4 - 24*B*b*c*d^3*e - 12*A*c^2*d^3*e - 3*B*b^2*d^2*e^2 - 6*A*b*c*d^2*e^2 - 2*A*b^2*d*e^3)*x + (137*B*c^2*d^5 - 24*B*b*c*d^4*e - 12*A*c^2*d^4*e - 3*B*b^2*d^3*e^2 - 6*A*b*c*d^3*e^2 - 2*A*b^2*d^2*e^3)*e^(-1))*e^(-5)/(x*e + d)^5","A",0
1125,1,318,0,0.178760," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(60 \, B c^{2} x^{5} e^{5} + 150 \, B c^{2} d x^{4} e^{4} + 200 \, B c^{2} d^{2} x^{3} e^{3} + 150 \, B c^{2} d^{3} x^{2} e^{2} + 60 \, B c^{2} d^{4} x e + 10 \, B c^{2} d^{5} + 60 \, B b c x^{4} e^{5} + 30 \, A c^{2} x^{4} e^{5} + 80 \, B b c d x^{3} e^{4} + 40 \, A c^{2} d x^{3} e^{4} + 60 \, B b c d^{2} x^{2} e^{3} + 30 \, A c^{2} d^{2} x^{2} e^{3} + 24 \, B b c d^{3} x e^{2} + 12 \, A c^{2} d^{3} x e^{2} + 4 \, B b c d^{4} e + 2 \, A c^{2} d^{4} e + 20 \, B b^{2} x^{3} e^{5} + 40 \, A b c x^{3} e^{5} + 15 \, B b^{2} d x^{2} e^{4} + 30 \, A b c d x^{2} e^{4} + 6 \, B b^{2} d^{2} x e^{3} + 12 \, A b c d^{2} x e^{3} + B b^{2} d^{3} e^{2} + 2 \, A b c d^{3} e^{2} + 15 \, A b^{2} x^{2} e^{5} + 6 \, A b^{2} d x e^{4} + A b^{2} d^{2} e^{3}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(60*B*c^2*x^5*e^5 + 150*B*c^2*d*x^4*e^4 + 200*B*c^2*d^2*x^3*e^3 + 150*B*c^2*d^3*x^2*e^2 + 60*B*c^2*d^4*x*e + 10*B*c^2*d^5 + 60*B*b*c*x^4*e^5 + 30*A*c^2*x^4*e^5 + 80*B*b*c*d*x^3*e^4 + 40*A*c^2*d*x^3*e^4 + 60*B*b*c*d^2*x^2*e^3 + 30*A*c^2*d^2*x^2*e^3 + 24*B*b*c*d^3*x*e^2 + 12*A*c^2*d^3*x*e^2 + 4*B*b*c*d^4*e + 2*A*c^2*d^4*e + 20*B*b^2*x^3*e^5 + 40*A*b*c*x^3*e^5 + 15*B*b^2*d*x^2*e^4 + 30*A*b*c*d*x^2*e^4 + 6*B*b^2*d^2*x*e^3 + 12*A*b*c*d^2*x*e^3 + B*b^2*d^3*e^2 + 2*A*b*c*d^3*e^2 + 15*A*b^2*x^2*e^5 + 6*A*b^2*d*x*e^4 + A*b^2*d^2*e^3)*e^(-6)/(x*e + d)^6","A",0
1126,1,320,0,0.157493," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(210 \, B c^{2} x^{5} e^{5} + 350 \, B c^{2} d x^{4} e^{4} + 350 \, B c^{2} d^{2} x^{3} e^{3} + 210 \, B c^{2} d^{3} x^{2} e^{2} + 70 \, B c^{2} d^{4} x e + 10 \, B c^{2} d^{5} + 280 \, B b c x^{4} e^{5} + 140 \, A c^{2} x^{4} e^{5} + 280 \, B b c d x^{3} e^{4} + 140 \, A c^{2} d x^{3} e^{4} + 168 \, B b c d^{2} x^{2} e^{3} + 84 \, A c^{2} d^{2} x^{2} e^{3} + 56 \, B b c d^{3} x e^{2} + 28 \, A c^{2} d^{3} x e^{2} + 8 \, B b c d^{4} e + 4 \, A c^{2} d^{4} e + 105 \, B b^{2} x^{3} e^{5} + 210 \, A b c x^{3} e^{5} + 63 \, B b^{2} d x^{2} e^{4} + 126 \, A b c d x^{2} e^{4} + 21 \, B b^{2} d^{2} x e^{3} + 42 \, A b c d^{2} x e^{3} + 3 \, B b^{2} d^{3} e^{2} + 6 \, A b c d^{3} e^{2} + 84 \, A b^{2} x^{2} e^{5} + 28 \, A b^{2} d x e^{4} + 4 \, A b^{2} d^{2} e^{3}\right)} e^{\left(-6\right)}}{420 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/420*(210*B*c^2*x^5*e^5 + 350*B*c^2*d*x^4*e^4 + 350*B*c^2*d^2*x^3*e^3 + 210*B*c^2*d^3*x^2*e^2 + 70*B*c^2*d^4*x*e + 10*B*c^2*d^5 + 280*B*b*c*x^4*e^5 + 140*A*c^2*x^4*e^5 + 280*B*b*c*d*x^3*e^4 + 140*A*c^2*d*x^3*e^4 + 168*B*b*c*d^2*x^2*e^3 + 84*A*c^2*d^2*x^2*e^3 + 56*B*b*c*d^3*x*e^2 + 28*A*c^2*d^3*x*e^2 + 8*B*b*c*d^4*e + 4*A*c^2*d^4*e + 105*B*b^2*x^3*e^5 + 210*A*b*c*x^3*e^5 + 63*B*b^2*d*x^2*e^4 + 126*A*b*c*d*x^2*e^4 + 21*B*b^2*d^2*x*e^3 + 42*A*b*c*d^2*x*e^3 + 3*B*b^2*d^3*e^2 + 6*A*b*c*d^3*e^2 + 84*A*b^2*x^2*e^5 + 28*A*b^2*d*x*e^4 + 4*A*b^2*d^2*e^3)*e^(-6)/(x*e + d)^7","A",0
1127,1,6663,0,0.389883," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c^{3} m^{7} x^{8} e^{8} + {\left(x e + d\right)}^{m} B c^{3} d m^{7} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} B b c^{2} m^{7} x^{7} e^{8} + {\left(x e + d\right)}^{m} A c^{3} m^{7} x^{7} e^{8} + 28 \, {\left(x e + d\right)}^{m} B c^{3} m^{6} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{7} x^{6} e^{7} + {\left(x e + d\right)}^{m} A c^{3} d m^{7} x^{6} e^{7} + 21 \, {\left(x e + d\right)}^{m} B c^{3} d m^{6} x^{7} e^{7} - 7 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{6} x^{6} e^{6} + 3 \, {\left(x e + d\right)}^{m} B b^{2} c m^{7} x^{6} e^{8} + 3 \, {\left(x e + d\right)}^{m} A b c^{2} m^{7} x^{6} e^{8} + 87 \, {\left(x e + d\right)}^{m} B b c^{2} m^{6} x^{7} e^{8} + 29 \, {\left(x e + d\right)}^{m} A c^{3} m^{6} x^{7} e^{8} + 322 \, {\left(x e + d\right)}^{m} B c^{3} m^{5} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{7} x^{5} e^{7} + 3 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{7} x^{5} e^{7} + 69 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{6} x^{6} e^{7} + 23 \, {\left(x e + d\right)}^{m} A c^{3} d m^{6} x^{6} e^{7} + 175 \, {\left(x e + d\right)}^{m} B c^{3} d m^{5} x^{7} e^{7} - 18 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{6} x^{5} e^{6} - 6 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{6} x^{5} e^{6} - 105 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{5} x^{6} e^{6} + 42 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{5} x^{5} e^{5} + {\left(x e + d\right)}^{m} B b^{3} m^{7} x^{5} e^{8} + 3 \, {\left(x e + d\right)}^{m} A b^{2} c m^{7} x^{5} e^{8} + 90 \, {\left(x e + d\right)}^{m} B b^{2} c m^{6} x^{6} e^{8} + 90 \, {\left(x e + d\right)}^{m} A b c^{2} m^{6} x^{6} e^{8} + 1029 \, {\left(x e + d\right)}^{m} B b c^{2} m^{5} x^{7} e^{8} + 343 \, {\left(x e + d\right)}^{m} A c^{3} m^{5} x^{7} e^{8} + 1960 \, {\left(x e + d\right)}^{m} B c^{3} m^{4} x^{8} e^{8} + {\left(x e + d\right)}^{m} B b^{3} d m^{7} x^{4} e^{7} + 3 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{7} x^{4} e^{7} + 75 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{6} x^{5} e^{7} + 75 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{6} x^{5} e^{7} + 615 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{5} x^{6} e^{7} + 205 \, {\left(x e + d\right)}^{m} A c^{3} d m^{5} x^{6} e^{7} + 735 \, {\left(x e + d\right)}^{m} B c^{3} d m^{4} x^{7} e^{7} - 15 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{6} x^{4} e^{6} - 15 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{6} x^{4} e^{6} - 324 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{5} x^{5} e^{6} - 108 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{5} x^{5} e^{6} - 595 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{4} x^{6} e^{6} + 90 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{5} x^{4} e^{5} + 30 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{5} x^{4} e^{5} + 420 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{4} x^{5} e^{5} - 210 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{4} x^{4} e^{4} + {\left(x e + d\right)}^{m} A b^{3} m^{7} x^{4} e^{8} + 31 \, {\left(x e + d\right)}^{m} B b^{3} m^{6} x^{5} e^{8} + 93 \, {\left(x e + d\right)}^{m} A b^{2} c m^{6} x^{5} e^{8} + 1098 \, {\left(x e + d\right)}^{m} B b^{2} c m^{5} x^{6} e^{8} + 1098 \, {\left(x e + d\right)}^{m} A b c^{2} m^{5} x^{6} e^{8} + 6405 \, {\left(x e + d\right)}^{m} B b c^{2} m^{4} x^{7} e^{8} + 2135 \, {\left(x e + d\right)}^{m} A c^{3} m^{4} x^{7} e^{8} + 6769 \, {\left(x e + d\right)}^{m} B c^{3} m^{3} x^{8} e^{8} + {\left(x e + d\right)}^{m} A b^{3} d m^{7} x^{3} e^{7} + 27 \, {\left(x e + d\right)}^{m} B b^{3} d m^{6} x^{4} e^{7} + 81 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{6} x^{4} e^{7} + 723 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{5} x^{5} e^{7} + 723 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{5} x^{5} e^{7} + 2715 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{4} x^{6} e^{7} + 905 \, {\left(x e + d\right)}^{m} A c^{3} d m^{4} x^{6} e^{7} + 1624 \, {\left(x e + d\right)}^{m} B c^{3} d m^{3} x^{7} e^{7} - 4 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{6} x^{3} e^{6} - 12 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{6} x^{3} e^{6} - 315 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{5} x^{4} e^{6} - 315 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{5} x^{4} e^{6} - 2070 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{4} x^{5} e^{6} - 690 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{4} x^{5} e^{6} - 1575 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{3} x^{6} e^{6} + 60 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{5} x^{3} e^{5} + 60 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{5} x^{3} e^{5} + 1260 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{4} x^{4} e^{5} + 420 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{4} x^{4} e^{5} + 1470 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{3} x^{5} e^{5} - 360 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m^{4} x^{3} e^{4} - 120 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{4} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{3} x^{4} e^{4} + 840 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m^{3} x^{3} e^{3} + 32 \, {\left(x e + d\right)}^{m} A b^{3} m^{6} x^{4} e^{8} + 391 \, {\left(x e + d\right)}^{m} B b^{3} m^{5} x^{5} e^{8} + 1173 \, {\left(x e + d\right)}^{m} A b^{2} c m^{5} x^{5} e^{8} + 7020 \, {\left(x e + d\right)}^{m} B b^{2} c m^{4} x^{6} e^{8} + 7020 \, {\left(x e + d\right)}^{m} A b c^{2} m^{4} x^{6} e^{8} + 22512 \, {\left(x e + d\right)}^{m} B b c^{2} m^{3} x^{7} e^{8} + 7504 \, {\left(x e + d\right)}^{m} A c^{3} m^{3} x^{7} e^{8} + 13132 \, {\left(x e + d\right)}^{m} B c^{3} m^{2} x^{8} e^{8} + 29 \, {\left(x e + d\right)}^{m} A b^{3} d m^{6} x^{3} e^{7} + 283 \, {\left(x e + d\right)}^{m} B b^{3} d m^{5} x^{4} e^{7} + 849 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{5} x^{4} e^{7} + 3405 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{4} x^{5} e^{7} + 3405 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{4} x^{5} e^{7} + 6222 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{3} x^{6} e^{7} + 2074 \, {\left(x e + d\right)}^{m} A c^{3} d m^{3} x^{6} e^{7} + 1764 \, {\left(x e + d\right)}^{m} B c^{3} d m^{2} x^{7} e^{7} - 3 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{6} x^{2} e^{6} - 96 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{5} x^{3} e^{6} - 288 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{5} x^{3} e^{6} - 2355 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{4} x^{4} e^{6} - 2355 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{4} x^{4} e^{6} - 5940 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{3} x^{5} e^{6} - 1980 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{3} x^{5} e^{6} - 1918 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{2} x^{6} e^{6} + 12 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{5} x^{2} e^{5} + 36 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{5} x^{2} e^{5} + 1080 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{4} x^{3} e^{5} + 1080 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{4} x^{3} e^{5} + 5310 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{3} x^{4} e^{5} + 1770 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{3} x^{4} e^{5} + 2100 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{2} x^{5} e^{5} - 180 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m^{4} x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m^{4} x^{2} e^{4} - 3960 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m^{3} x^{3} e^{4} - 1320 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{3} x^{3} e^{4} - 2310 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{2} x^{4} e^{4} + 1080 \, {\left(x e + d\right)}^{m} B b c^{2} d^{5} m^{3} x^{2} e^{3} + 360 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m^{3} x^{2} e^{3} + 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m^{2} x^{3} e^{3} - 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{6} m^{2} x^{2} e^{2} + 418 \, {\left(x e + d\right)}^{m} A b^{3} m^{5} x^{4} e^{8} + 2581 \, {\left(x e + d\right)}^{m} B b^{3} m^{4} x^{5} e^{8} + 7743 \, {\left(x e + d\right)}^{m} A b^{2} c m^{4} x^{5} e^{8} + 25227 \, {\left(x e + d\right)}^{m} B b^{2} c m^{3} x^{6} e^{8} + 25227 \, {\left(x e + d\right)}^{m} A b c^{2} m^{3} x^{6} e^{8} + 44268 \, {\left(x e + d\right)}^{m} B b c^{2} m^{2} x^{7} e^{8} + 14756 \, {\left(x e + d\right)}^{m} A c^{3} m^{2} x^{7} e^{8} + 13068 \, {\left(x e + d\right)}^{m} B c^{3} m x^{8} e^{8} + 331 \, {\left(x e + d\right)}^{m} A b^{3} d m^{5} x^{3} e^{7} + 1449 \, {\left(x e + d\right)}^{m} B b^{3} d m^{4} x^{4} e^{7} + 4347 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{4} x^{4} e^{7} + 8202 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{3} x^{5} e^{7} + 8202 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{3} x^{5} e^{7} + 6936 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{2} x^{6} e^{7} + 2312 \, {\left(x e + d\right)}^{m} A c^{3} d m^{2} x^{6} e^{7} + 720 \, {\left(x e + d\right)}^{m} B c^{3} d m x^{7} e^{7} - 81 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{5} x^{2} e^{6} - 844 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{4} x^{3} e^{6} - 2532 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{4} x^{3} e^{6} - 7605 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{3} x^{4} e^{6} - 7605 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{3} x^{4} e^{6} - 7632 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{2} x^{5} e^{6} - 2544 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{2} x^{5} e^{6} - 840 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m x^{6} e^{6} + 6 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{5} x e^{5} + 264 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{4} x^{2} e^{5} + 792 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{4} x^{2} e^{5} + 6180 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{3} x^{3} e^{5} + 6180 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{3} x^{3} e^{5} + 8460 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{2} x^{4} e^{5} + 2820 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{2} x^{4} e^{5} + 1008 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m x^{5} e^{5} - 24 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m^{4} x e^{4} - 72 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m^{4} x e^{4} - 2880 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m^{3} x^{2} e^{4} - 2880 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m^{3} x^{2} e^{4} - 9360 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m^{2} x^{3} e^{4} - 3120 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{2} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m x^{4} e^{4} + 360 \, {\left(x e + d\right)}^{m} B b^{2} c d^{5} m^{3} x e^{3} + 360 \, {\left(x e + d\right)}^{m} A b c^{2} d^{5} m^{3} x e^{3} + 9720 \, {\left(x e + d\right)}^{m} B b c^{2} d^{5} m^{2} x^{2} e^{3} + 3240 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m^{2} x^{2} e^{3} + 1680 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m x^{3} e^{3} - 2160 \, {\left(x e + d\right)}^{m} B b c^{2} d^{6} m^{2} x e^{2} - 720 \, {\left(x e + d\right)}^{m} A c^{3} d^{6} m^{2} x e^{2} - 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{6} m x^{2} e^{2} + 5040 \, {\left(x e + d\right)}^{m} B c^{3} d^{7} m x e + 2864 \, {\left(x e + d\right)}^{m} A b^{3} m^{4} x^{4} e^{8} + 9544 \, {\left(x e + d\right)}^{m} B b^{3} m^{3} x^{5} e^{8} + 28632 \, {\left(x e + d\right)}^{m} A b^{2} c m^{3} x^{5} e^{8} + 50490 \, {\left(x e + d\right)}^{m} B b^{2} c m^{2} x^{6} e^{8} + 50490 \, {\left(x e + d\right)}^{m} A b c^{2} m^{2} x^{6} e^{8} + 44496 \, {\left(x e + d\right)}^{m} B b c^{2} m x^{7} e^{8} + 14832 \, {\left(x e + d\right)}^{m} A c^{3} m x^{7} e^{8} + 5040 \, {\left(x e + d\right)}^{m} B c^{3} x^{8} e^{8} + 1871 \, {\left(x e + d\right)}^{m} A b^{3} d m^{4} x^{3} e^{7} + 3748 \, {\left(x e + d\right)}^{m} B b^{3} d m^{3} x^{4} e^{7} + 11244 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{3} x^{4} e^{7} + 9480 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{2} x^{5} e^{7} + 9480 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{2} x^{5} e^{7} + 2880 \, {\left(x e + d\right)}^{m} B b c^{2} d m x^{6} e^{7} + 960 \, {\left(x e + d\right)}^{m} A c^{3} d m x^{6} e^{7} - 831 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{4} x^{2} e^{6} - 3264 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{3} x^{3} e^{6} - 9792 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{3} x^{3} e^{6} - 10590 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{2} x^{4} e^{6} - 10590 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{2} x^{4} e^{6} - 3456 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m x^{5} e^{6} - 1152 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m x^{5} e^{6} + 156 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{4} x e^{5} + 2004 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{3} x^{2} e^{5} + 6012 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{3} x^{2} e^{5} + 11880 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{2} x^{3} e^{5} + 11880 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{2} x^{3} e^{5} + 4320 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m x^{4} e^{5} + 1440 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m x^{4} e^{5} - 6 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m^{4} e^{4} - 504 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m^{3} x e^{4} - 1512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m^{3} x e^{4} - 12780 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m^{2} x^{2} e^{4} - 12780 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m^{2} x^{2} e^{4} - 5760 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m x^{3} e^{4} - 1920 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m x^{3} e^{4} + 24 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} m^{3} e^{3} + 72 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} m^{3} e^{3} + 5400 \, {\left(x e + d\right)}^{m} B b^{2} c d^{5} m^{2} x e^{3} + 5400 \, {\left(x e + d\right)}^{m} A b c^{2} d^{5} m^{2} x e^{3} + 8640 \, {\left(x e + d\right)}^{m} B b c^{2} d^{5} m x^{2} e^{3} + 2880 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m x^{2} e^{3} - 360 \, {\left(x e + d\right)}^{m} B b^{2} c d^{6} m^{2} e^{2} - 360 \, {\left(x e + d\right)}^{m} A b c^{2} d^{6} m^{2} e^{2} - 17280 \, {\left(x e + d\right)}^{m} B b c^{2} d^{6} m x e^{2} - 5760 \, {\left(x e + d\right)}^{m} A c^{3} d^{6} m x e^{2} + 2160 \, {\left(x e + d\right)}^{m} B b c^{2} d^{7} m e + 720 \, {\left(x e + d\right)}^{m} A c^{3} d^{7} m e - 5040 \, {\left(x e + d\right)}^{m} B c^{3} d^{8} + 10993 \, {\left(x e + d\right)}^{m} A b^{3} m^{3} x^{4} e^{8} + 19564 \, {\left(x e + d\right)}^{m} B b^{3} m^{2} x^{5} e^{8} + 58692 \, {\left(x e + d\right)}^{m} A b^{2} c m^{2} x^{5} e^{8} + 51432 \, {\left(x e + d\right)}^{m} B b^{2} c m x^{6} e^{8} + 51432 \, {\left(x e + d\right)}^{m} A b c^{2} m x^{6} e^{8} + 17280 \, {\left(x e + d\right)}^{m} B b c^{2} x^{7} e^{8} + 5760 \, {\left(x e + d\right)}^{m} A c^{3} x^{7} e^{8} + 5380 \, {\left(x e + d\right)}^{m} A b^{3} d m^{3} x^{3} e^{7} + 4572 \, {\left(x e + d\right)}^{m} B b^{3} d m^{2} x^{4} e^{7} + 13716 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{2} x^{4} e^{7} + 4032 \, {\left(x e + d\right)}^{m} B b^{2} c d m x^{5} e^{7} + 4032 \, {\left(x e + d\right)}^{m} A b c^{2} d m x^{5} e^{7} - 3951 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{3} x^{2} e^{6} - 5200 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{2} x^{3} e^{6} - 15600 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{2} x^{3} e^{6} - 5040 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m x^{4} e^{6} - 5040 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m x^{4} e^{6} + 1506 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{3} x e^{5} + 5784 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{2} x^{2} e^{5} + 17352 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{2} x^{2} e^{5} + 6720 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m x^{3} e^{5} + 6720 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m x^{3} e^{5} - 156 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m^{3} e^{4} - 3504 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m^{2} x e^{4} - 10512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m^{2} x e^{4} - 10080 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m x^{2} e^{4} - 10080 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m x^{2} e^{4} + 504 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} m^{2} e^{3} + 1512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} m^{2} e^{3} + 20160 \, {\left(x e + d\right)}^{m} B b^{2} c d^{5} m x e^{3} + 20160 \, {\left(x e + d\right)}^{m} A b c^{2} d^{5} m x e^{3} - 5400 \, {\left(x e + d\right)}^{m} B b^{2} c d^{6} m e^{2} - 5400 \, {\left(x e + d\right)}^{m} A b c^{2} d^{6} m e^{2} + 17280 \, {\left(x e + d\right)}^{m} B b c^{2} d^{7} e + 5760 \, {\left(x e + d\right)}^{m} A c^{3} d^{7} e + 23312 \, {\left(x e + d\right)}^{m} A b^{3} m^{2} x^{4} e^{8} + 20304 \, {\left(x e + d\right)}^{m} B b^{3} m x^{5} e^{8} + 60912 \, {\left(x e + d\right)}^{m} A b^{2} c m x^{5} e^{8} + 20160 \, {\left(x e + d\right)}^{m} B b^{2} c x^{6} e^{8} + 20160 \, {\left(x e + d\right)}^{m} A b c^{2} x^{6} e^{8} + 7172 \, {\left(x e + d\right)}^{m} A b^{3} d m^{2} x^{3} e^{7} + 2016 \, {\left(x e + d\right)}^{m} B b^{3} d m x^{4} e^{7} + 6048 \, {\left(x e + d\right)}^{m} A b^{2} c d m x^{4} e^{7} - 8238 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{2} x^{2} e^{6} - 2688 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m x^{3} e^{6} - 8064 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m x^{3} e^{6} + 6396 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{2} x e^{5} + 4032 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m x^{2} e^{5} + 12096 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m x^{2} e^{5} - 1506 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m^{2} e^{4} - 8064 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m x e^{4} - 24192 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m x e^{4} + 3504 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} m e^{3} + 10512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} m e^{3} - 20160 \, {\left(x e + d\right)}^{m} B b^{2} c d^{6} e^{2} - 20160 \, {\left(x e + d\right)}^{m} A b c^{2} d^{6} e^{2} + 24876 \, {\left(x e + d\right)}^{m} A b^{3} m x^{4} e^{8} + 8064 \, {\left(x e + d\right)}^{m} B b^{3} x^{5} e^{8} + 24192 \, {\left(x e + d\right)}^{m} A b^{2} c x^{5} e^{8} + 3360 \, {\left(x e + d\right)}^{m} A b^{3} d m x^{3} e^{7} - 5040 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m x^{2} e^{6} + 10080 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m x e^{5} - 6396 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m e^{4} + 8064 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} e^{3} + 24192 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} e^{3} + 10080 \, {\left(x e + d\right)}^{m} A b^{3} x^{4} e^{8} - 10080 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} e^{4}}{m^{8} e^{8} + 36 \, m^{7} e^{8} + 546 \, m^{6} e^{8} + 4536 \, m^{5} e^{8} + 22449 \, m^{4} e^{8} + 67284 \, m^{3} e^{8} + 118124 \, m^{2} e^{8} + 109584 \, m e^{8} + 40320 \, e^{8}}"," ",0,"((x*e + d)^m*B*c^3*m^7*x^8*e^8 + (x*e + d)^m*B*c^3*d*m^7*x^7*e^7 + 3*(x*e + d)^m*B*b*c^2*m^7*x^7*e^8 + (x*e + d)^m*A*c^3*m^7*x^7*e^8 + 28*(x*e + d)^m*B*c^3*m^6*x^8*e^8 + 3*(x*e + d)^m*B*b*c^2*d*m^7*x^6*e^7 + (x*e + d)^m*A*c^3*d*m^7*x^6*e^7 + 21*(x*e + d)^m*B*c^3*d*m^6*x^7*e^7 - 7*(x*e + d)^m*B*c^3*d^2*m^6*x^6*e^6 + 3*(x*e + d)^m*B*b^2*c*m^7*x^6*e^8 + 3*(x*e + d)^m*A*b*c^2*m^7*x^6*e^8 + 87*(x*e + d)^m*B*b*c^2*m^6*x^7*e^8 + 29*(x*e + d)^m*A*c^3*m^6*x^7*e^8 + 322*(x*e + d)^m*B*c^3*m^5*x^8*e^8 + 3*(x*e + d)^m*B*b^2*c*d*m^7*x^5*e^7 + 3*(x*e + d)^m*A*b*c^2*d*m^7*x^5*e^7 + 69*(x*e + d)^m*B*b*c^2*d*m^6*x^6*e^7 + 23*(x*e + d)^m*A*c^3*d*m^6*x^6*e^7 + 175*(x*e + d)^m*B*c^3*d*m^5*x^7*e^7 - 18*(x*e + d)^m*B*b*c^2*d^2*m^6*x^5*e^6 - 6*(x*e + d)^m*A*c^3*d^2*m^6*x^5*e^6 - 105*(x*e + d)^m*B*c^3*d^2*m^5*x^6*e^6 + 42*(x*e + d)^m*B*c^3*d^3*m^5*x^5*e^5 + (x*e + d)^m*B*b^3*m^7*x^5*e^8 + 3*(x*e + d)^m*A*b^2*c*m^7*x^5*e^8 + 90*(x*e + d)^m*B*b^2*c*m^6*x^6*e^8 + 90*(x*e + d)^m*A*b*c^2*m^6*x^6*e^8 + 1029*(x*e + d)^m*B*b*c^2*m^5*x^7*e^8 + 343*(x*e + d)^m*A*c^3*m^5*x^7*e^8 + 1960*(x*e + d)^m*B*c^3*m^4*x^8*e^8 + (x*e + d)^m*B*b^3*d*m^7*x^4*e^7 + 3*(x*e + d)^m*A*b^2*c*d*m^7*x^4*e^7 + 75*(x*e + d)^m*B*b^2*c*d*m^6*x^5*e^7 + 75*(x*e + d)^m*A*b*c^2*d*m^6*x^5*e^7 + 615*(x*e + d)^m*B*b*c^2*d*m^5*x^6*e^7 + 205*(x*e + d)^m*A*c^3*d*m^5*x^6*e^7 + 735*(x*e + d)^m*B*c^3*d*m^4*x^7*e^7 - 15*(x*e + d)^m*B*b^2*c*d^2*m^6*x^4*e^6 - 15*(x*e + d)^m*A*b*c^2*d^2*m^6*x^4*e^6 - 324*(x*e + d)^m*B*b*c^2*d^2*m^5*x^5*e^6 - 108*(x*e + d)^m*A*c^3*d^2*m^5*x^5*e^6 - 595*(x*e + d)^m*B*c^3*d^2*m^4*x^6*e^6 + 90*(x*e + d)^m*B*b*c^2*d^3*m^5*x^4*e^5 + 30*(x*e + d)^m*A*c^3*d^3*m^5*x^4*e^5 + 420*(x*e + d)^m*B*c^3*d^3*m^4*x^5*e^5 - 210*(x*e + d)^m*B*c^3*d^4*m^4*x^4*e^4 + (x*e + d)^m*A*b^3*m^7*x^4*e^8 + 31*(x*e + d)^m*B*b^3*m^6*x^5*e^8 + 93*(x*e + d)^m*A*b^2*c*m^6*x^5*e^8 + 1098*(x*e + d)^m*B*b^2*c*m^5*x^6*e^8 + 1098*(x*e + d)^m*A*b*c^2*m^5*x^6*e^8 + 6405*(x*e + d)^m*B*b*c^2*m^4*x^7*e^8 + 2135*(x*e + d)^m*A*c^3*m^4*x^7*e^8 + 6769*(x*e + d)^m*B*c^3*m^3*x^8*e^8 + (x*e + d)^m*A*b^3*d*m^7*x^3*e^7 + 27*(x*e + d)^m*B*b^3*d*m^6*x^4*e^7 + 81*(x*e + d)^m*A*b^2*c*d*m^6*x^4*e^7 + 723*(x*e + d)^m*B*b^2*c*d*m^5*x^5*e^7 + 723*(x*e + d)^m*A*b*c^2*d*m^5*x^5*e^7 + 2715*(x*e + d)^m*B*b*c^2*d*m^4*x^6*e^7 + 905*(x*e + d)^m*A*c^3*d*m^4*x^6*e^7 + 1624*(x*e + d)^m*B*c^3*d*m^3*x^7*e^7 - 4*(x*e + d)^m*B*b^3*d^2*m^6*x^3*e^6 - 12*(x*e + d)^m*A*b^2*c*d^2*m^6*x^3*e^6 - 315*(x*e + d)^m*B*b^2*c*d^2*m^5*x^4*e^6 - 315*(x*e + d)^m*A*b*c^2*d^2*m^5*x^4*e^6 - 2070*(x*e + d)^m*B*b*c^2*d^2*m^4*x^5*e^6 - 690*(x*e + d)^m*A*c^3*d^2*m^4*x^5*e^6 - 1575*(x*e + d)^m*B*c^3*d^2*m^3*x^6*e^6 + 60*(x*e + d)^m*B*b^2*c*d^3*m^5*x^3*e^5 + 60*(x*e + d)^m*A*b*c^2*d^3*m^5*x^3*e^5 + 1260*(x*e + d)^m*B*b*c^2*d^3*m^4*x^4*e^5 + 420*(x*e + d)^m*A*c^3*d^3*m^4*x^4*e^5 + 1470*(x*e + d)^m*B*c^3*d^3*m^3*x^5*e^5 - 360*(x*e + d)^m*B*b*c^2*d^4*m^4*x^3*e^4 - 120*(x*e + d)^m*A*c^3*d^4*m^4*x^3*e^4 - 1260*(x*e + d)^m*B*c^3*d^4*m^3*x^4*e^4 + 840*(x*e + d)^m*B*c^3*d^5*m^3*x^3*e^3 + 32*(x*e + d)^m*A*b^3*m^6*x^4*e^8 + 391*(x*e + d)^m*B*b^3*m^5*x^5*e^8 + 1173*(x*e + d)^m*A*b^2*c*m^5*x^5*e^8 + 7020*(x*e + d)^m*B*b^2*c*m^4*x^6*e^8 + 7020*(x*e + d)^m*A*b*c^2*m^4*x^6*e^8 + 22512*(x*e + d)^m*B*b*c^2*m^3*x^7*e^8 + 7504*(x*e + d)^m*A*c^3*m^3*x^7*e^8 + 13132*(x*e + d)^m*B*c^3*m^2*x^8*e^8 + 29*(x*e + d)^m*A*b^3*d*m^6*x^3*e^7 + 283*(x*e + d)^m*B*b^3*d*m^5*x^4*e^7 + 849*(x*e + d)^m*A*b^2*c*d*m^5*x^4*e^7 + 3405*(x*e + d)^m*B*b^2*c*d*m^4*x^5*e^7 + 3405*(x*e + d)^m*A*b*c^2*d*m^4*x^5*e^7 + 6222*(x*e + d)^m*B*b*c^2*d*m^3*x^6*e^7 + 2074*(x*e + d)^m*A*c^3*d*m^3*x^6*e^7 + 1764*(x*e + d)^m*B*c^3*d*m^2*x^7*e^7 - 3*(x*e + d)^m*A*b^3*d^2*m^6*x^2*e^6 - 96*(x*e + d)^m*B*b^3*d^2*m^5*x^3*e^6 - 288*(x*e + d)^m*A*b^2*c*d^2*m^5*x^3*e^6 - 2355*(x*e + d)^m*B*b^2*c*d^2*m^4*x^4*e^6 - 2355*(x*e + d)^m*A*b*c^2*d^2*m^4*x^4*e^6 - 5940*(x*e + d)^m*B*b*c^2*d^2*m^3*x^5*e^6 - 1980*(x*e + d)^m*A*c^3*d^2*m^3*x^5*e^6 - 1918*(x*e + d)^m*B*c^3*d^2*m^2*x^6*e^6 + 12*(x*e + d)^m*B*b^3*d^3*m^5*x^2*e^5 + 36*(x*e + d)^m*A*b^2*c*d^3*m^5*x^2*e^5 + 1080*(x*e + d)^m*B*b^2*c*d^3*m^4*x^3*e^5 + 1080*(x*e + d)^m*A*b*c^2*d^3*m^4*x^3*e^5 + 5310*(x*e + d)^m*B*b*c^2*d^3*m^3*x^4*e^5 + 1770*(x*e + d)^m*A*c^3*d^3*m^3*x^4*e^5 + 2100*(x*e + d)^m*B*c^3*d^3*m^2*x^5*e^5 - 180*(x*e + d)^m*B*b^2*c*d^4*m^4*x^2*e^4 - 180*(x*e + d)^m*A*b*c^2*d^4*m^4*x^2*e^4 - 3960*(x*e + d)^m*B*b*c^2*d^4*m^3*x^3*e^4 - 1320*(x*e + d)^m*A*c^3*d^4*m^3*x^3*e^4 - 2310*(x*e + d)^m*B*c^3*d^4*m^2*x^4*e^4 + 1080*(x*e + d)^m*B*b*c^2*d^5*m^3*x^2*e^3 + 360*(x*e + d)^m*A*c^3*d^5*m^3*x^2*e^3 + 2520*(x*e + d)^m*B*c^3*d^5*m^2*x^3*e^3 - 2520*(x*e + d)^m*B*c^3*d^6*m^2*x^2*e^2 + 418*(x*e + d)^m*A*b^3*m^5*x^4*e^8 + 2581*(x*e + d)^m*B*b^3*m^4*x^5*e^8 + 7743*(x*e + d)^m*A*b^2*c*m^4*x^5*e^8 + 25227*(x*e + d)^m*B*b^2*c*m^3*x^6*e^8 + 25227*(x*e + d)^m*A*b*c^2*m^3*x^6*e^8 + 44268*(x*e + d)^m*B*b*c^2*m^2*x^7*e^8 + 14756*(x*e + d)^m*A*c^3*m^2*x^7*e^8 + 13068*(x*e + d)^m*B*c^3*m*x^8*e^8 + 331*(x*e + d)^m*A*b^3*d*m^5*x^3*e^7 + 1449*(x*e + d)^m*B*b^3*d*m^4*x^4*e^7 + 4347*(x*e + d)^m*A*b^2*c*d*m^4*x^4*e^7 + 8202*(x*e + d)^m*B*b^2*c*d*m^3*x^5*e^7 + 8202*(x*e + d)^m*A*b*c^2*d*m^3*x^5*e^7 + 6936*(x*e + d)^m*B*b*c^2*d*m^2*x^6*e^7 + 2312*(x*e + d)^m*A*c^3*d*m^2*x^6*e^7 + 720*(x*e + d)^m*B*c^3*d*m*x^7*e^7 - 81*(x*e + d)^m*A*b^3*d^2*m^5*x^2*e^6 - 844*(x*e + d)^m*B*b^3*d^2*m^4*x^3*e^6 - 2532*(x*e + d)^m*A*b^2*c*d^2*m^4*x^3*e^6 - 7605*(x*e + d)^m*B*b^2*c*d^2*m^3*x^4*e^6 - 7605*(x*e + d)^m*A*b*c^2*d^2*m^3*x^4*e^6 - 7632*(x*e + d)^m*B*b*c^2*d^2*m^2*x^5*e^6 - 2544*(x*e + d)^m*A*c^3*d^2*m^2*x^5*e^6 - 840*(x*e + d)^m*B*c^3*d^2*m*x^6*e^6 + 6*(x*e + d)^m*A*b^3*d^3*m^5*x*e^5 + 264*(x*e + d)^m*B*b^3*d^3*m^4*x^2*e^5 + 792*(x*e + d)^m*A*b^2*c*d^3*m^4*x^2*e^5 + 6180*(x*e + d)^m*B*b^2*c*d^3*m^3*x^3*e^5 + 6180*(x*e + d)^m*A*b*c^2*d^3*m^3*x^3*e^5 + 8460*(x*e + d)^m*B*b*c^2*d^3*m^2*x^4*e^5 + 2820*(x*e + d)^m*A*c^3*d^3*m^2*x^4*e^5 + 1008*(x*e + d)^m*B*c^3*d^3*m*x^5*e^5 - 24*(x*e + d)^m*B*b^3*d^4*m^4*x*e^4 - 72*(x*e + d)^m*A*b^2*c*d^4*m^4*x*e^4 - 2880*(x*e + d)^m*B*b^2*c*d^4*m^3*x^2*e^4 - 2880*(x*e + d)^m*A*b*c^2*d^4*m^3*x^2*e^4 - 9360*(x*e + d)^m*B*b*c^2*d^4*m^2*x^3*e^4 - 3120*(x*e + d)^m*A*c^3*d^4*m^2*x^3*e^4 - 1260*(x*e + d)^m*B*c^3*d^4*m*x^4*e^4 + 360*(x*e + d)^m*B*b^2*c*d^5*m^3*x*e^3 + 360*(x*e + d)^m*A*b*c^2*d^5*m^3*x*e^3 + 9720*(x*e + d)^m*B*b*c^2*d^5*m^2*x^2*e^3 + 3240*(x*e + d)^m*A*c^3*d^5*m^2*x^2*e^3 + 1680*(x*e + d)^m*B*c^3*d^5*m*x^3*e^3 - 2160*(x*e + d)^m*B*b*c^2*d^6*m^2*x*e^2 - 720*(x*e + d)^m*A*c^3*d^6*m^2*x*e^2 - 2520*(x*e + d)^m*B*c^3*d^6*m*x^2*e^2 + 5040*(x*e + d)^m*B*c^3*d^7*m*x*e + 2864*(x*e + d)^m*A*b^3*m^4*x^4*e^8 + 9544*(x*e + d)^m*B*b^3*m^3*x^5*e^8 + 28632*(x*e + d)^m*A*b^2*c*m^3*x^5*e^8 + 50490*(x*e + d)^m*B*b^2*c*m^2*x^6*e^8 + 50490*(x*e + d)^m*A*b*c^2*m^2*x^6*e^8 + 44496*(x*e + d)^m*B*b*c^2*m*x^7*e^8 + 14832*(x*e + d)^m*A*c^3*m*x^7*e^8 + 5040*(x*e + d)^m*B*c^3*x^8*e^8 + 1871*(x*e + d)^m*A*b^3*d*m^4*x^3*e^7 + 3748*(x*e + d)^m*B*b^3*d*m^3*x^4*e^7 + 11244*(x*e + d)^m*A*b^2*c*d*m^3*x^4*e^7 + 9480*(x*e + d)^m*B*b^2*c*d*m^2*x^5*e^7 + 9480*(x*e + d)^m*A*b*c^2*d*m^2*x^5*e^7 + 2880*(x*e + d)^m*B*b*c^2*d*m*x^6*e^7 + 960*(x*e + d)^m*A*c^3*d*m*x^6*e^7 - 831*(x*e + d)^m*A*b^3*d^2*m^4*x^2*e^6 - 3264*(x*e + d)^m*B*b^3*d^2*m^3*x^3*e^6 - 9792*(x*e + d)^m*A*b^2*c*d^2*m^3*x^3*e^6 - 10590*(x*e + d)^m*B*b^2*c*d^2*m^2*x^4*e^6 - 10590*(x*e + d)^m*A*b*c^2*d^2*m^2*x^4*e^6 - 3456*(x*e + d)^m*B*b*c^2*d^2*m*x^5*e^6 - 1152*(x*e + d)^m*A*c^3*d^2*m*x^5*e^6 + 156*(x*e + d)^m*A*b^3*d^3*m^4*x*e^5 + 2004*(x*e + d)^m*B*b^3*d^3*m^3*x^2*e^5 + 6012*(x*e + d)^m*A*b^2*c*d^3*m^3*x^2*e^5 + 11880*(x*e + d)^m*B*b^2*c*d^3*m^2*x^3*e^5 + 11880*(x*e + d)^m*A*b*c^2*d^3*m^2*x^3*e^5 + 4320*(x*e + d)^m*B*b*c^2*d^3*m*x^4*e^5 + 1440*(x*e + d)^m*A*c^3*d^3*m*x^4*e^5 - 6*(x*e + d)^m*A*b^3*d^4*m^4*e^4 - 504*(x*e + d)^m*B*b^3*d^4*m^3*x*e^4 - 1512*(x*e + d)^m*A*b^2*c*d^4*m^3*x*e^4 - 12780*(x*e + d)^m*B*b^2*c*d^4*m^2*x^2*e^4 - 12780*(x*e + d)^m*A*b*c^2*d^4*m^2*x^2*e^4 - 5760*(x*e + d)^m*B*b*c^2*d^4*m*x^3*e^4 - 1920*(x*e + d)^m*A*c^3*d^4*m*x^3*e^4 + 24*(x*e + d)^m*B*b^3*d^5*m^3*e^3 + 72*(x*e + d)^m*A*b^2*c*d^5*m^3*e^3 + 5400*(x*e + d)^m*B*b^2*c*d^5*m^2*x*e^3 + 5400*(x*e + d)^m*A*b*c^2*d^5*m^2*x*e^3 + 8640*(x*e + d)^m*B*b*c^2*d^5*m*x^2*e^3 + 2880*(x*e + d)^m*A*c^3*d^5*m*x^2*e^3 - 360*(x*e + d)^m*B*b^2*c*d^6*m^2*e^2 - 360*(x*e + d)^m*A*b*c^2*d^6*m^2*e^2 - 17280*(x*e + d)^m*B*b*c^2*d^6*m*x*e^2 - 5760*(x*e + d)^m*A*c^3*d^6*m*x*e^2 + 2160*(x*e + d)^m*B*b*c^2*d^7*m*e + 720*(x*e + d)^m*A*c^3*d^7*m*e - 5040*(x*e + d)^m*B*c^3*d^8 + 10993*(x*e + d)^m*A*b^3*m^3*x^4*e^8 + 19564*(x*e + d)^m*B*b^3*m^2*x^5*e^8 + 58692*(x*e + d)^m*A*b^2*c*m^2*x^5*e^8 + 51432*(x*e + d)^m*B*b^2*c*m*x^6*e^8 + 51432*(x*e + d)^m*A*b*c^2*m*x^6*e^8 + 17280*(x*e + d)^m*B*b*c^2*x^7*e^8 + 5760*(x*e + d)^m*A*c^3*x^7*e^8 + 5380*(x*e + d)^m*A*b^3*d*m^3*x^3*e^7 + 4572*(x*e + d)^m*B*b^3*d*m^2*x^4*e^7 + 13716*(x*e + d)^m*A*b^2*c*d*m^2*x^4*e^7 + 4032*(x*e + d)^m*B*b^2*c*d*m*x^5*e^7 + 4032*(x*e + d)^m*A*b*c^2*d*m*x^5*e^7 - 3951*(x*e + d)^m*A*b^3*d^2*m^3*x^2*e^6 - 5200*(x*e + d)^m*B*b^3*d^2*m^2*x^3*e^6 - 15600*(x*e + d)^m*A*b^2*c*d^2*m^2*x^3*e^6 - 5040*(x*e + d)^m*B*b^2*c*d^2*m*x^4*e^6 - 5040*(x*e + d)^m*A*b*c^2*d^2*m*x^4*e^6 + 1506*(x*e + d)^m*A*b^3*d^3*m^3*x*e^5 + 5784*(x*e + d)^m*B*b^3*d^3*m^2*x^2*e^5 + 17352*(x*e + d)^m*A*b^2*c*d^3*m^2*x^2*e^5 + 6720*(x*e + d)^m*B*b^2*c*d^3*m*x^3*e^5 + 6720*(x*e + d)^m*A*b*c^2*d^3*m*x^3*e^5 - 156*(x*e + d)^m*A*b^3*d^4*m^3*e^4 - 3504*(x*e + d)^m*B*b^3*d^4*m^2*x*e^4 - 10512*(x*e + d)^m*A*b^2*c*d^4*m^2*x*e^4 - 10080*(x*e + d)^m*B*b^2*c*d^4*m*x^2*e^4 - 10080*(x*e + d)^m*A*b*c^2*d^4*m*x^2*e^4 + 504*(x*e + d)^m*B*b^3*d^5*m^2*e^3 + 1512*(x*e + d)^m*A*b^2*c*d^5*m^2*e^3 + 20160*(x*e + d)^m*B*b^2*c*d^5*m*x*e^3 + 20160*(x*e + d)^m*A*b*c^2*d^5*m*x*e^3 - 5400*(x*e + d)^m*B*b^2*c*d^6*m*e^2 - 5400*(x*e + d)^m*A*b*c^2*d^6*m*e^2 + 17280*(x*e + d)^m*B*b*c^2*d^7*e + 5760*(x*e + d)^m*A*c^3*d^7*e + 23312*(x*e + d)^m*A*b^3*m^2*x^4*e^8 + 20304*(x*e + d)^m*B*b^3*m*x^5*e^8 + 60912*(x*e + d)^m*A*b^2*c*m*x^5*e^8 + 20160*(x*e + d)^m*B*b^2*c*x^6*e^8 + 20160*(x*e + d)^m*A*b*c^2*x^6*e^8 + 7172*(x*e + d)^m*A*b^3*d*m^2*x^3*e^7 + 2016*(x*e + d)^m*B*b^3*d*m*x^4*e^7 + 6048*(x*e + d)^m*A*b^2*c*d*m*x^4*e^7 - 8238*(x*e + d)^m*A*b^3*d^2*m^2*x^2*e^6 - 2688*(x*e + d)^m*B*b^3*d^2*m*x^3*e^6 - 8064*(x*e + d)^m*A*b^2*c*d^2*m*x^3*e^6 + 6396*(x*e + d)^m*A*b^3*d^3*m^2*x*e^5 + 4032*(x*e + d)^m*B*b^3*d^3*m*x^2*e^5 + 12096*(x*e + d)^m*A*b^2*c*d^3*m*x^2*e^5 - 1506*(x*e + d)^m*A*b^3*d^4*m^2*e^4 - 8064*(x*e + d)^m*B*b^3*d^4*m*x*e^4 - 24192*(x*e + d)^m*A*b^2*c*d^4*m*x*e^4 + 3504*(x*e + d)^m*B*b^3*d^5*m*e^3 + 10512*(x*e + d)^m*A*b^2*c*d^5*m*e^3 - 20160*(x*e + d)^m*B*b^2*c*d^6*e^2 - 20160*(x*e + d)^m*A*b*c^2*d^6*e^2 + 24876*(x*e + d)^m*A*b^3*m*x^4*e^8 + 8064*(x*e + d)^m*B*b^3*x^5*e^8 + 24192*(x*e + d)^m*A*b^2*c*x^5*e^8 + 3360*(x*e + d)^m*A*b^3*d*m*x^3*e^7 - 5040*(x*e + d)^m*A*b^3*d^2*m*x^2*e^6 + 10080*(x*e + d)^m*A*b^3*d^3*m*x*e^5 - 6396*(x*e + d)^m*A*b^3*d^4*m*e^4 + 8064*(x*e + d)^m*B*b^3*d^5*e^3 + 24192*(x*e + d)^m*A*b^2*c*d^5*e^3 + 10080*(x*e + d)^m*A*b^3*x^4*e^8 - 10080*(x*e + d)^m*A*b^3*d^4*e^4)/(m^8*e^8 + 36*m^7*e^8 + 546*m^6*e^8 + 4536*m^5*e^8 + 22449*m^4*e^8 + 67284*m^3*e^8 + 118124*m^2*e^8 + 109584*m*e^8 + 40320*e^8)","B",0
1128,1,524,0,0.160393," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{12} \, B c^{3} x^{12} e^{4} + \frac{4}{11} \, B c^{3} d x^{11} e^{3} + \frac{3}{5} \, B c^{3} d^{2} x^{10} e^{2} + \frac{4}{9} \, B c^{3} d^{3} x^{9} e + \frac{1}{8} \, B c^{3} d^{4} x^{8} + \frac{3}{11} \, B b c^{2} x^{11} e^{4} + \frac{1}{11} \, A c^{3} x^{11} e^{4} + \frac{6}{5} \, B b c^{2} d x^{10} e^{3} + \frac{2}{5} \, A c^{3} d x^{10} e^{3} + 2 \, B b c^{2} d^{2} x^{9} e^{2} + \frac{2}{3} \, A c^{3} d^{2} x^{9} e^{2} + \frac{3}{2} \, B b c^{2} d^{3} x^{8} e + \frac{1}{2} \, A c^{3} d^{3} x^{8} e + \frac{3}{7} \, B b c^{2} d^{4} x^{7} + \frac{1}{7} \, A c^{3} d^{4} x^{7} + \frac{3}{10} \, B b^{2} c x^{10} e^{4} + \frac{3}{10} \, A b c^{2} x^{10} e^{4} + \frac{4}{3} \, B b^{2} c d x^{9} e^{3} + \frac{4}{3} \, A b c^{2} d x^{9} e^{3} + \frac{9}{4} \, B b^{2} c d^{2} x^{8} e^{2} + \frac{9}{4} \, A b c^{2} d^{2} x^{8} e^{2} + \frac{12}{7} \, B b^{2} c d^{3} x^{7} e + \frac{12}{7} \, A b c^{2} d^{3} x^{7} e + \frac{1}{2} \, B b^{2} c d^{4} x^{6} + \frac{1}{2} \, A b c^{2} d^{4} x^{6} + \frac{1}{9} \, B b^{3} x^{9} e^{4} + \frac{1}{3} \, A b^{2} c x^{9} e^{4} + \frac{1}{2} \, B b^{3} d x^{8} e^{3} + \frac{3}{2} \, A b^{2} c d x^{8} e^{3} + \frac{6}{7} \, B b^{3} d^{2} x^{7} e^{2} + \frac{18}{7} \, A b^{2} c d^{2} x^{7} e^{2} + \frac{2}{3} \, B b^{3} d^{3} x^{6} e + 2 \, A b^{2} c d^{3} x^{6} e + \frac{1}{5} \, B b^{3} d^{4} x^{5} + \frac{3}{5} \, A b^{2} c d^{4} x^{5} + \frac{1}{8} \, A b^{3} x^{8} e^{4} + \frac{4}{7} \, A b^{3} d x^{7} e^{3} + A b^{3} d^{2} x^{6} e^{2} + \frac{4}{5} \, A b^{3} d^{3} x^{5} e + \frac{1}{4} \, A b^{3} d^{4} x^{4}"," ",0,"1/12*B*c^3*x^12*e^4 + 4/11*B*c^3*d*x^11*e^3 + 3/5*B*c^3*d^2*x^10*e^2 + 4/9*B*c^3*d^3*x^9*e + 1/8*B*c^3*d^4*x^8 + 3/11*B*b*c^2*x^11*e^4 + 1/11*A*c^3*x^11*e^4 + 6/5*B*b*c^2*d*x^10*e^3 + 2/5*A*c^3*d*x^10*e^3 + 2*B*b*c^2*d^2*x^9*e^2 + 2/3*A*c^3*d^2*x^9*e^2 + 3/2*B*b*c^2*d^3*x^8*e + 1/2*A*c^3*d^3*x^8*e + 3/7*B*b*c^2*d^4*x^7 + 1/7*A*c^3*d^4*x^7 + 3/10*B*b^2*c*x^10*e^4 + 3/10*A*b*c^2*x^10*e^4 + 4/3*B*b^2*c*d*x^9*e^3 + 4/3*A*b*c^2*d*x^9*e^3 + 9/4*B*b^2*c*d^2*x^8*e^2 + 9/4*A*b*c^2*d^2*x^8*e^2 + 12/7*B*b^2*c*d^3*x^7*e + 12/7*A*b*c^2*d^3*x^7*e + 1/2*B*b^2*c*d^4*x^6 + 1/2*A*b*c^2*d^4*x^6 + 1/9*B*b^3*x^9*e^4 + 1/3*A*b^2*c*x^9*e^4 + 1/2*B*b^3*d*x^8*e^3 + 3/2*A*b^2*c*d*x^8*e^3 + 6/7*B*b^3*d^2*x^7*e^2 + 18/7*A*b^2*c*d^2*x^7*e^2 + 2/3*B*b^3*d^3*x^6*e + 2*A*b^2*c*d^3*x^6*e + 1/5*B*b^3*d^4*x^5 + 3/5*A*b^2*c*d^4*x^5 + 1/8*A*b^3*x^8*e^4 + 4/7*A*b^3*d*x^7*e^3 + A*b^3*d^2*x^6*e^2 + 4/5*A*b^3*d^3*x^5*e + 1/4*A*b^3*d^4*x^4","A",0
1129,1,408,0,0.200088," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{11} \, B c^{3} x^{11} e^{3} + \frac{3}{10} \, B c^{3} d x^{10} e^{2} + \frac{1}{3} \, B c^{3} d^{2} x^{9} e + \frac{1}{8} \, B c^{3} d^{3} x^{8} + \frac{3}{10} \, B b c^{2} x^{10} e^{3} + \frac{1}{10} \, A c^{3} x^{10} e^{3} + B b c^{2} d x^{9} e^{2} + \frac{1}{3} \, A c^{3} d x^{9} e^{2} + \frac{9}{8} \, B b c^{2} d^{2} x^{8} e + \frac{3}{8} \, A c^{3} d^{2} x^{8} e + \frac{3}{7} \, B b c^{2} d^{3} x^{7} + \frac{1}{7} \, A c^{3} d^{3} x^{7} + \frac{1}{3} \, B b^{2} c x^{9} e^{3} + \frac{1}{3} \, A b c^{2} x^{9} e^{3} + \frac{9}{8} \, B b^{2} c d x^{8} e^{2} + \frac{9}{8} \, A b c^{2} d x^{8} e^{2} + \frac{9}{7} \, B b^{2} c d^{2} x^{7} e + \frac{9}{7} \, A b c^{2} d^{2} x^{7} e + \frac{1}{2} \, B b^{2} c d^{3} x^{6} + \frac{1}{2} \, A b c^{2} d^{3} x^{6} + \frac{1}{8} \, B b^{3} x^{8} e^{3} + \frac{3}{8} \, A b^{2} c x^{8} e^{3} + \frac{3}{7} \, B b^{3} d x^{7} e^{2} + \frac{9}{7} \, A b^{2} c d x^{7} e^{2} + \frac{1}{2} \, B b^{3} d^{2} x^{6} e + \frac{3}{2} \, A b^{2} c d^{2} x^{6} e + \frac{1}{5} \, B b^{3} d^{3} x^{5} + \frac{3}{5} \, A b^{2} c d^{3} x^{5} + \frac{1}{7} \, A b^{3} x^{7} e^{3} + \frac{1}{2} \, A b^{3} d x^{6} e^{2} + \frac{3}{5} \, A b^{3} d^{2} x^{5} e + \frac{1}{4} \, A b^{3} d^{3} x^{4}"," ",0,"1/11*B*c^3*x^11*e^3 + 3/10*B*c^3*d*x^10*e^2 + 1/3*B*c^3*d^2*x^9*e + 1/8*B*c^3*d^3*x^8 + 3/10*B*b*c^2*x^10*e^3 + 1/10*A*c^3*x^10*e^3 + B*b*c^2*d*x^9*e^2 + 1/3*A*c^3*d*x^9*e^2 + 9/8*B*b*c^2*d^2*x^8*e + 3/8*A*c^3*d^2*x^8*e + 3/7*B*b*c^2*d^3*x^7 + 1/7*A*c^3*d^3*x^7 + 1/3*B*b^2*c*x^9*e^3 + 1/3*A*b*c^2*x^9*e^3 + 9/8*B*b^2*c*d*x^8*e^2 + 9/8*A*b*c^2*d*x^8*e^2 + 9/7*B*b^2*c*d^2*x^7*e + 9/7*A*b*c^2*d^2*x^7*e + 1/2*B*b^2*c*d^3*x^6 + 1/2*A*b*c^2*d^3*x^6 + 1/8*B*b^3*x^8*e^3 + 3/8*A*b^2*c*x^8*e^3 + 3/7*B*b^3*d*x^7*e^2 + 9/7*A*b^2*c*d*x^7*e^2 + 1/2*B*b^3*d^2*x^6*e + 3/2*A*b^2*c*d^2*x^6*e + 1/5*B*b^3*d^3*x^5 + 3/5*A*b^2*c*d^3*x^5 + 1/7*A*b^3*x^7*e^3 + 1/2*A*b^3*d*x^6*e^2 + 3/5*A*b^3*d^2*x^5*e + 1/4*A*b^3*d^3*x^4","A",0
1130,1,292,0,0.176383," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{10} \, B c^{3} x^{10} e^{2} + \frac{2}{9} \, B c^{3} d x^{9} e + \frac{1}{8} \, B c^{3} d^{2} x^{8} + \frac{1}{3} \, B b c^{2} x^{9} e^{2} + \frac{1}{9} \, A c^{3} x^{9} e^{2} + \frac{3}{4} \, B b c^{2} d x^{8} e + \frac{1}{4} \, A c^{3} d x^{8} e + \frac{3}{7} \, B b c^{2} d^{2} x^{7} + \frac{1}{7} \, A c^{3} d^{2} x^{7} + \frac{3}{8} \, B b^{2} c x^{8} e^{2} + \frac{3}{8} \, A b c^{2} x^{8} e^{2} + \frac{6}{7} \, B b^{2} c d x^{7} e + \frac{6}{7} \, A b c^{2} d x^{7} e + \frac{1}{2} \, B b^{2} c d^{2} x^{6} + \frac{1}{2} \, A b c^{2} d^{2} x^{6} + \frac{1}{7} \, B b^{3} x^{7} e^{2} + \frac{3}{7} \, A b^{2} c x^{7} e^{2} + \frac{1}{3} \, B b^{3} d x^{6} e + A b^{2} c d x^{6} e + \frac{1}{5} \, B b^{3} d^{2} x^{5} + \frac{3}{5} \, A b^{2} c d^{2} x^{5} + \frac{1}{6} \, A b^{3} x^{6} e^{2} + \frac{2}{5} \, A b^{3} d x^{5} e + \frac{1}{4} \, A b^{3} d^{2} x^{4}"," ",0,"1/10*B*c^3*x^10*e^2 + 2/9*B*c^3*d*x^9*e + 1/8*B*c^3*d^2*x^8 + 1/3*B*b*c^2*x^9*e^2 + 1/9*A*c^3*x^9*e^2 + 3/4*B*b*c^2*d*x^8*e + 1/4*A*c^3*d*x^8*e + 3/7*B*b*c^2*d^2*x^7 + 1/7*A*c^3*d^2*x^7 + 3/8*B*b^2*c*x^8*e^2 + 3/8*A*b*c^2*x^8*e^2 + 6/7*B*b^2*c*d*x^7*e + 6/7*A*b*c^2*d*x^7*e + 1/2*B*b^2*c*d^2*x^6 + 1/2*A*b*c^2*d^2*x^6 + 1/7*B*b^3*x^7*e^2 + 3/7*A*b^2*c*x^7*e^2 + 1/3*B*b^3*d*x^6*e + A*b^2*c*d*x^6*e + 1/5*B*b^3*d^2*x^5 + 3/5*A*b^2*c*d^2*x^5 + 1/6*A*b^3*x^6*e^2 + 2/5*A*b^3*d*x^5*e + 1/4*A*b^3*d^2*x^4","A",0
1131,1,177,0,0.190299," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{9} \, B c^{3} x^{9} e + \frac{1}{8} \, B c^{3} d x^{8} + \frac{3}{8} \, B b c^{2} x^{8} e + \frac{1}{8} \, A c^{3} x^{8} e + \frac{3}{7} \, B b c^{2} d x^{7} + \frac{1}{7} \, A c^{3} d x^{7} + \frac{3}{7} \, B b^{2} c x^{7} e + \frac{3}{7} \, A b c^{2} x^{7} e + \frac{1}{2} \, B b^{2} c d x^{6} + \frac{1}{2} \, A b c^{2} d x^{6} + \frac{1}{6} \, B b^{3} x^{6} e + \frac{1}{2} \, A b^{2} c x^{6} e + \frac{1}{5} \, B b^{3} d x^{5} + \frac{3}{5} \, A b^{2} c d x^{5} + \frac{1}{5} \, A b^{3} x^{5} e + \frac{1}{4} \, A b^{3} d x^{4}"," ",0,"1/9*B*c^3*x^9*e + 1/8*B*c^3*d*x^8 + 3/8*B*b*c^2*x^8*e + 1/8*A*c^3*x^8*e + 3/7*B*b*c^2*d*x^7 + 1/7*A*c^3*d*x^7 + 3/7*B*b^2*c*x^7*e + 3/7*A*b*c^2*x^7*e + 1/2*B*b^2*c*d*x^6 + 1/2*A*b*c^2*d*x^6 + 1/6*B*b^3*x^6*e + 1/2*A*b^2*c*x^6*e + 1/5*B*b^3*d*x^5 + 3/5*A*b^2*c*d*x^5 + 1/5*A*b^3*x^5*e + 1/4*A*b^3*d*x^4","A",0
1132,1,77,0,0.150237," ","integrate((B*x+A)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{8} \, B c^{3} x^{8} + \frac{3}{7} \, B b c^{2} x^{7} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{2} \, B b^{2} c x^{6} + \frac{1}{2} \, A b c^{2} x^{6} + \frac{1}{5} \, B b^{3} x^{5} + \frac{3}{5} \, A b^{2} c x^{5} + \frac{1}{4} \, A b^{3} x^{4}"," ",0,"1/8*B*c^3*x^8 + 3/7*B*b*c^2*x^7 + 1/7*A*c^3*x^7 + 1/2*B*b^2*c*x^6 + 1/2*A*b*c^2*x^6 + 1/5*B*b^3*x^5 + 3/5*A*b^2*c*x^5 + 1/4*A*b^3*x^4","A",0
1133,1,629,0,0.182737," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d),x, algorithm=""giac"")","-{\left(B c^{3} d^{7} - 3 \, B b c^{2} d^{6} e - A c^{3} d^{6} e + 3 \, B b^{2} c d^{5} e^{2} + 3 \, A b c^{2} d^{5} e^{2} - B b^{3} d^{4} e^{3} - 3 \, A b^{2} c d^{4} e^{3} + A b^{3} d^{3} e^{4}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{420} \, {\left(60 \, B c^{3} x^{7} e^{6} - 70 \, B c^{3} d x^{6} e^{5} + 84 \, B c^{3} d^{2} x^{5} e^{4} - 105 \, B c^{3} d^{3} x^{4} e^{3} + 140 \, B c^{3} d^{4} x^{3} e^{2} - 210 \, B c^{3} d^{5} x^{2} e + 420 \, B c^{3} d^{6} x + 210 \, B b c^{2} x^{6} e^{6} + 70 \, A c^{3} x^{6} e^{6} - 252 \, B b c^{2} d x^{5} e^{5} - 84 \, A c^{3} d x^{5} e^{5} + 315 \, B b c^{2} d^{2} x^{4} e^{4} + 105 \, A c^{3} d^{2} x^{4} e^{4} - 420 \, B b c^{2} d^{3} x^{3} e^{3} - 140 \, A c^{3} d^{3} x^{3} e^{3} + 630 \, B b c^{2} d^{4} x^{2} e^{2} + 210 \, A c^{3} d^{4} x^{2} e^{2} - 1260 \, B b c^{2} d^{5} x e - 420 \, A c^{3} d^{5} x e + 252 \, B b^{2} c x^{5} e^{6} + 252 \, A b c^{2} x^{5} e^{6} - 315 \, B b^{2} c d x^{4} e^{5} - 315 \, A b c^{2} d x^{4} e^{5} + 420 \, B b^{2} c d^{2} x^{3} e^{4} + 420 \, A b c^{2} d^{2} x^{3} e^{4} - 630 \, B b^{2} c d^{3} x^{2} e^{3} - 630 \, A b c^{2} d^{3} x^{2} e^{3} + 1260 \, B b^{2} c d^{4} x e^{2} + 1260 \, A b c^{2} d^{4} x e^{2} + 105 \, B b^{3} x^{4} e^{6} + 315 \, A b^{2} c x^{4} e^{6} - 140 \, B b^{3} d x^{3} e^{5} - 420 \, A b^{2} c d x^{3} e^{5} + 210 \, B b^{3} d^{2} x^{2} e^{4} + 630 \, A b^{2} c d^{2} x^{2} e^{4} - 420 \, B b^{3} d^{3} x e^{3} - 1260 \, A b^{2} c d^{3} x e^{3} + 140 \, A b^{3} x^{3} e^{6} - 210 \, A b^{3} d x^{2} e^{5} + 420 \, A b^{3} d^{2} x e^{4}\right)} e^{\left(-7\right)}"," ",0,"-(B*c^3*d^7 - 3*B*b*c^2*d^6*e - A*c^3*d^6*e + 3*B*b^2*c*d^5*e^2 + 3*A*b*c^2*d^5*e^2 - B*b^3*d^4*e^3 - 3*A*b^2*c*d^4*e^3 + A*b^3*d^3*e^4)*e^(-8)*log(abs(x*e + d)) + 1/420*(60*B*c^3*x^7*e^6 - 70*B*c^3*d*x^6*e^5 + 84*B*c^3*d^2*x^5*e^4 - 105*B*c^3*d^3*x^4*e^3 + 140*B*c^3*d^4*x^3*e^2 - 210*B*c^3*d^5*x^2*e + 420*B*c^3*d^6*x + 210*B*b*c^2*x^6*e^6 + 70*A*c^3*x^6*e^6 - 252*B*b*c^2*d*x^5*e^5 - 84*A*c^3*d*x^5*e^5 + 315*B*b*c^2*d^2*x^4*e^4 + 105*A*c^3*d^2*x^4*e^4 - 420*B*b*c^2*d^3*x^3*e^3 - 140*A*c^3*d^3*x^3*e^3 + 630*B*b*c^2*d^4*x^2*e^2 + 210*A*c^3*d^4*x^2*e^2 - 1260*B*b*c^2*d^5*x*e - 420*A*c^3*d^5*x*e + 252*B*b^2*c*x^5*e^6 + 252*A*b*c^2*x^5*e^6 - 315*B*b^2*c*d*x^4*e^5 - 315*A*b*c^2*d*x^4*e^5 + 420*B*b^2*c*d^2*x^3*e^4 + 420*A*b*c^2*d^2*x^3*e^4 - 630*B*b^2*c*d^3*x^2*e^3 - 630*A*b*c^2*d^3*x^2*e^3 + 1260*B*b^2*c*d^4*x*e^2 + 1260*A*b*c^2*d^4*x*e^2 + 105*B*b^3*x^4*e^6 + 315*A*b^2*c*x^4*e^6 - 140*B*b^3*d*x^3*e^5 - 420*A*b^2*c*d*x^3*e^5 + 210*B*b^3*d^2*x^2*e^4 + 630*A*b^2*c*d^2*x^2*e^4 - 420*B*b^3*d^3*x*e^3 - 1260*A*b^2*c*d^3*x*e^3 + 140*A*b^3*x^3*e^6 - 210*A*b^3*d*x^2*e^5 + 420*A*b^3*d^2*x*e^4)*e^(-7)","B",0
1134,1,673,0,0.197810," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{60} \, {\left(10 \, B c^{3} - \frac{12 \, {\left(7 \, B c^{3} d e - 3 \, B b c^{2} e^{2} - A c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{45 \, {\left(7 \, B c^{3} d^{2} e^{2} - 6 \, B b c^{2} d e^{3} - 2 \, A c^{3} d e^{3} + B b^{2} c e^{4} + A b c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{20 \, {\left(35 \, B c^{3} d^{3} e^{3} - 45 \, B b c^{2} d^{2} e^{4} - 15 \, A c^{3} d^{2} e^{4} + 15 \, B b^{2} c d e^{5} + 15 \, A b c^{2} d e^{5} - B b^{3} e^{6} - 3 \, A b^{2} c e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{30 \, {\left(35 \, B c^{3} d^{4} e^{4} - 60 \, B b c^{2} d^{3} e^{5} - 20 \, A c^{3} d^{3} e^{5} + 30 \, B b^{2} c d^{2} e^{6} + 30 \, A b c^{2} d^{2} e^{6} - 4 \, B b^{3} d e^{7} - 12 \, A b^{2} c d e^{7} + A b^{3} e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{180 \, {\left(7 \, B c^{3} d^{5} e^{5} - 15 \, B b c^{2} d^{4} e^{6} - 5 \, A c^{3} d^{4} e^{6} + 10 \, B b^{2} c d^{3} e^{7} + 10 \, A b c^{2} d^{3} e^{7} - 2 \, B b^{3} d^{2} e^{8} - 6 \, A b^{2} c d^{2} e^{8} + A b^{3} d e^{9}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}}\right)} {\left(x e + d\right)}^{6} e^{\left(-8\right)} - {\left(7 \, B c^{3} d^{6} - 18 \, B b c^{2} d^{5} e - 6 \, A c^{3} d^{5} e + 15 \, B b^{2} c d^{4} e^{2} + 15 \, A b c^{2} d^{4} e^{2} - 4 \, B b^{3} d^{3} e^{3} - 12 \, A b^{2} c d^{3} e^{3} + 3 \, A b^{3} d^{2} e^{4}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c^{3} d^{7} e^{6}}{x e + d} - \frac{3 \, B b c^{2} d^{6} e^{7}}{x e + d} - \frac{A c^{3} d^{6} e^{7}}{x e + d} + \frac{3 \, B b^{2} c d^{5} e^{8}}{x e + d} + \frac{3 \, A b c^{2} d^{5} e^{8}}{x e + d} - \frac{B b^{3} d^{4} e^{9}}{x e + d} - \frac{3 \, A b^{2} c d^{4} e^{9}}{x e + d} + \frac{A b^{3} d^{3} e^{10}}{x e + d}\right)} e^{\left(-14\right)}"," ",0,"1/60*(10*B*c^3 - 12*(7*B*c^3*d*e - 3*B*b*c^2*e^2 - A*c^3*e^2)*e^(-1)/(x*e + d) + 45*(7*B*c^3*d^2*e^2 - 6*B*b*c^2*d*e^3 - 2*A*c^3*d*e^3 + B*b^2*c*e^4 + A*b*c^2*e^4)*e^(-2)/(x*e + d)^2 - 20*(35*B*c^3*d^3*e^3 - 45*B*b*c^2*d^2*e^4 - 15*A*c^3*d^2*e^4 + 15*B*b^2*c*d*e^5 + 15*A*b*c^2*d*e^5 - B*b^3*e^6 - 3*A*b^2*c*e^6)*e^(-3)/(x*e + d)^3 + 30*(35*B*c^3*d^4*e^4 - 60*B*b*c^2*d^3*e^5 - 20*A*c^3*d^3*e^5 + 30*B*b^2*c*d^2*e^6 + 30*A*b*c^2*d^2*e^6 - 4*B*b^3*d*e^7 - 12*A*b^2*c*d*e^7 + A*b^3*e^8)*e^(-4)/(x*e + d)^4 - 180*(7*B*c^3*d^5*e^5 - 15*B*b*c^2*d^4*e^6 - 5*A*c^3*d^4*e^6 + 10*B*b^2*c*d^3*e^7 + 10*A*b*c^2*d^3*e^7 - 2*B*b^3*d^2*e^8 - 6*A*b^2*c*d^2*e^8 + A*b^3*d*e^9)*e^(-5)/(x*e + d)^5)*(x*e + d)^6*e^(-8) - (7*B*c^3*d^6 - 18*B*b*c^2*d^5*e - 6*A*c^3*d^5*e + 15*B*b^2*c*d^4*e^2 + 15*A*b*c^2*d^4*e^2 - 4*B*b^3*d^3*e^3 - 12*A*b^2*c*d^3*e^3 + 3*A*b^3*d^2*e^4)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c^3*d^7*e^6/(x*e + d) - 3*B*b*c^2*d^6*e^7/(x*e + d) - A*c^3*d^6*e^7/(x*e + d) + 3*B*b^2*c*d^5*e^8/(x*e + d) + 3*A*b*c^2*d^5*e^8/(x*e + d) - B*b^3*d^4*e^9/(x*e + d) - 3*A*b^2*c*d^4*e^9/(x*e + d) + A*b^3*d^3*e^10/(x*e + d))*e^(-14)","B",0
1135,1,599,0,0.185784," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d)^3,x, algorithm=""giac"")","-3 \, {\left(7 \, B c^{3} d^{5} - 15 \, B b c^{2} d^{4} e - 5 \, A c^{3} d^{4} e + 10 \, B b^{2} c d^{3} e^{2} + 10 \, A b c^{2} d^{3} e^{2} - 2 \, B b^{3} d^{2} e^{3} - 6 \, A b^{2} c d^{2} e^{3} + A b^{3} d e^{4}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{20} \, {\left(4 \, B c^{3} x^{5} e^{12} - 15 \, B c^{3} d x^{4} e^{11} + 40 \, B c^{3} d^{2} x^{3} e^{10} - 100 \, B c^{3} d^{3} x^{2} e^{9} + 300 \, B c^{3} d^{4} x e^{8} + 15 \, B b c^{2} x^{4} e^{12} + 5 \, A c^{3} x^{4} e^{12} - 60 \, B b c^{2} d x^{3} e^{11} - 20 \, A c^{3} d x^{3} e^{11} + 180 \, B b c^{2} d^{2} x^{2} e^{10} + 60 \, A c^{3} d^{2} x^{2} e^{10} - 600 \, B b c^{2} d^{3} x e^{9} - 200 \, A c^{3} d^{3} x e^{9} + 20 \, B b^{2} c x^{3} e^{12} + 20 \, A b c^{2} x^{3} e^{12} - 90 \, B b^{2} c d x^{2} e^{11} - 90 \, A b c^{2} d x^{2} e^{11} + 360 \, B b^{2} c d^{2} x e^{10} + 360 \, A b c^{2} d^{2} x e^{10} + 10 \, B b^{3} x^{2} e^{12} + 30 \, A b^{2} c x^{2} e^{12} - 60 \, B b^{3} d x e^{11} - 180 \, A b^{2} c d x e^{11} + 20 \, A b^{3} x e^{12}\right)} e^{\left(-15\right)} - \frac{{\left(13 \, B c^{3} d^{7} - 33 \, B b c^{2} d^{6} e - 11 \, A c^{3} d^{6} e + 27 \, B b^{2} c d^{5} e^{2} + 27 \, A b c^{2} d^{5} e^{2} - 7 \, B b^{3} d^{4} e^{3} - 21 \, A b^{2} c d^{4} e^{3} + 5 \, A b^{3} d^{3} e^{4} + 2 \, {\left(7 \, B c^{3} d^{6} e - 18 \, B b c^{2} d^{5} e^{2} - 6 \, A c^{3} d^{5} e^{2} + 15 \, B b^{2} c d^{4} e^{3} + 15 \, A b c^{2} d^{4} e^{3} - 4 \, B b^{3} d^{3} e^{4} - 12 \, A b^{2} c d^{3} e^{4} + 3 \, A b^{3} d^{2} e^{5}\right)} x\right)} e^{\left(-8\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-3*(7*B*c^3*d^5 - 15*B*b*c^2*d^4*e - 5*A*c^3*d^4*e + 10*B*b^2*c*d^3*e^2 + 10*A*b*c^2*d^3*e^2 - 2*B*b^3*d^2*e^3 - 6*A*b^2*c*d^2*e^3 + A*b^3*d*e^4)*e^(-8)*log(abs(x*e + d)) + 1/20*(4*B*c^3*x^5*e^12 - 15*B*c^3*d*x^4*e^11 + 40*B*c^3*d^2*x^3*e^10 - 100*B*c^3*d^3*x^2*e^9 + 300*B*c^3*d^4*x*e^8 + 15*B*b*c^2*x^4*e^12 + 5*A*c^3*x^4*e^12 - 60*B*b*c^2*d*x^3*e^11 - 20*A*c^3*d*x^3*e^11 + 180*B*b*c^2*d^2*x^2*e^10 + 60*A*c^3*d^2*x^2*e^10 - 600*B*b*c^2*d^3*x*e^9 - 200*A*c^3*d^3*x*e^9 + 20*B*b^2*c*x^3*e^12 + 20*A*b*c^2*x^3*e^12 - 90*B*b^2*c*d*x^2*e^11 - 90*A*b*c^2*d*x^2*e^11 + 360*B*b^2*c*d^2*x*e^10 + 360*A*b*c^2*d^2*x*e^10 + 10*B*b^3*x^2*e^12 + 30*A*b^2*c*x^2*e^12 - 60*B*b^3*d*x*e^11 - 180*A*b^2*c*d*x*e^11 + 20*A*b^3*x*e^12)*e^(-15) - 1/2*(13*B*c^3*d^7 - 33*B*b*c^2*d^6*e - 11*A*c^3*d^6*e + 27*B*b^2*c*d^5*e^2 + 27*A*b*c^2*d^5*e^2 - 7*B*b^3*d^4*e^3 - 21*A*b^2*c*d^4*e^3 + 5*A*b^3*d^3*e^4 + 2*(7*B*c^3*d^6*e - 18*B*b*c^2*d^5*e^2 - 6*A*c^3*d^5*e^2 + 15*B*b^2*c*d^4*e^3 + 15*A*b*c^2*d^4*e^3 - 4*B*b^3*d^3*e^4 - 12*A*b^2*c*d^3*e^4 + 3*A*b^3*d^2*e^5)*x)*e^(-8)/(x*e + d)^2","A",0
1136,1,581,0,0.164607," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d)^4,x, algorithm=""giac"")","{\left(35 \, B c^{3} d^{4} - 60 \, B b c^{2} d^{3} e - 20 \, A c^{3} d^{3} e + 30 \, B b^{2} c d^{2} e^{2} + 30 \, A b c^{2} d^{2} e^{2} - 4 \, B b^{3} d e^{3} - 12 \, A b^{2} c d e^{3} + A b^{3} e^{4}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, B c^{3} x^{4} e^{12} - 16 \, B c^{3} d x^{3} e^{11} + 60 \, B c^{3} d^{2} x^{2} e^{10} - 240 \, B c^{3} d^{3} x e^{9} + 12 \, B b c^{2} x^{3} e^{12} + 4 \, A c^{3} x^{3} e^{12} - 72 \, B b c^{2} d x^{2} e^{11} - 24 \, A c^{3} d x^{2} e^{11} + 360 \, B b c^{2} d^{2} x e^{10} + 120 \, A c^{3} d^{2} x e^{10} + 18 \, B b^{2} c x^{2} e^{12} + 18 \, A b c^{2} x^{2} e^{12} - 144 \, B b^{2} c d x e^{11} - 144 \, A b c^{2} d x e^{11} + 12 \, B b^{3} x e^{12} + 36 \, A b^{2} c x e^{12}\right)} e^{\left(-16\right)} + \frac{{\left(107 \, B c^{3} d^{7} - 222 \, B b c^{2} d^{6} e - 74 \, A c^{3} d^{6} e + 141 \, B b^{2} c d^{5} e^{2} + 141 \, A b c^{2} d^{5} e^{2} - 26 \, B b^{3} d^{4} e^{3} - 78 \, A b^{2} c d^{4} e^{3} + 11 \, A b^{3} d^{3} e^{4} + 18 \, {\left(7 \, B c^{3} d^{5} e^{2} - 15 \, B b c^{2} d^{4} e^{3} - 5 \, A c^{3} d^{4} e^{3} + 10 \, B b^{2} c d^{3} e^{4} + 10 \, A b c^{2} d^{3} e^{4} - 2 \, B b^{3} d^{2} e^{5} - 6 \, A b^{2} c d^{2} e^{5} + A b^{3} d e^{6}\right)} x^{2} + 3 \, {\left(77 \, B c^{3} d^{6} e - 162 \, B b c^{2} d^{5} e^{2} - 54 \, A c^{3} d^{5} e^{2} + 105 \, B b^{2} c d^{4} e^{3} + 105 \, A b c^{2} d^{4} e^{3} - 20 \, B b^{3} d^{3} e^{4} - 60 \, A b^{2} c d^{3} e^{4} + 9 \, A b^{3} d^{2} e^{5}\right)} x\right)} e^{\left(-8\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"(35*B*c^3*d^4 - 60*B*b*c^2*d^3*e - 20*A*c^3*d^3*e + 30*B*b^2*c*d^2*e^2 + 30*A*b*c^2*d^2*e^2 - 4*B*b^3*d*e^3 - 12*A*b^2*c*d*e^3 + A*b^3*e^4)*e^(-8)*log(abs(x*e + d)) + 1/12*(3*B*c^3*x^4*e^12 - 16*B*c^3*d*x^3*e^11 + 60*B*c^3*d^2*x^2*e^10 - 240*B*c^3*d^3*x*e^9 + 12*B*b*c^2*x^3*e^12 + 4*A*c^3*x^3*e^12 - 72*B*b*c^2*d*x^2*e^11 - 24*A*c^3*d*x^2*e^11 + 360*B*b*c^2*d^2*x*e^10 + 120*A*c^3*d^2*x*e^10 + 18*B*b^2*c*x^2*e^12 + 18*A*b*c^2*x^2*e^12 - 144*B*b^2*c*d*x*e^11 - 144*A*b*c^2*d*x*e^11 + 12*B*b^3*x*e^12 + 36*A*b^2*c*x*e^12)*e^(-16) + 1/6*(107*B*c^3*d^7 - 222*B*b*c^2*d^6*e - 74*A*c^3*d^6*e + 141*B*b^2*c*d^5*e^2 + 141*A*b*c^2*d^5*e^2 - 26*B*b^3*d^4*e^3 - 78*A*b^2*c*d^4*e^3 + 11*A*b^3*d^3*e^4 + 18*(7*B*c^3*d^5*e^2 - 15*B*b*c^2*d^4*e^3 - 5*A*c^3*d^4*e^3 + 10*B*b^2*c*d^3*e^4 + 10*A*b*c^2*d^3*e^4 - 2*B*b^3*d^2*e^5 - 6*A*b^2*c*d^2*e^5 + A*b^3*d*e^6)*x^2 + 3*(77*B*c^3*d^6*e - 162*B*b*c^2*d^5*e^2 - 54*A*c^3*d^5*e^2 + 105*B*b^2*c*d^4*e^3 + 105*A*b*c^2*d^4*e^3 - 20*B*b^3*d^3*e^4 - 60*A*b^2*c*d^3*e^4 + 9*A*b^3*d^2*e^5)*x)*e^(-8)/(x*e + d)^3","A",0
1137,1,330,0,0.156086," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x),x, algorithm=""giac"")","\frac{A d^{4} \log\left({\left| x \right|}\right)}{b} + \frac{3 \, B c^{3} x^{4} e^{4} + 16 \, B c^{3} d x^{3} e^{3} + 36 \, B c^{3} d^{2} x^{2} e^{2} + 48 \, B c^{3} d^{3} x e - 4 \, B b c^{2} x^{3} e^{4} + 4 \, A c^{3} x^{3} e^{4} - 24 \, B b c^{2} d x^{2} e^{3} + 24 \, A c^{3} d x^{2} e^{3} - 72 \, B b c^{2} d^{2} x e^{2} + 72 \, A c^{3} d^{2} x e^{2} + 6 \, B b^{2} c x^{2} e^{4} - 6 \, A b c^{2} x^{2} e^{4} + 48 \, B b^{2} c d x e^{3} - 48 \, A b c^{2} d x e^{3} - 12 \, B b^{3} x e^{4} + 12 \, A b^{2} c x e^{4}}{12 \, c^{4}} + \frac{{\left(B b c^{4} d^{4} - A c^{5} d^{4} - 4 \, B b^{2} c^{3} d^{3} e + 4 \, A b c^{4} d^{3} e + 6 \, B b^{3} c^{2} d^{2} e^{2} - 6 \, A b^{2} c^{3} d^{2} e^{2} - 4 \, B b^{4} c d e^{3} + 4 \, A b^{3} c^{2} d e^{3} + B b^{5} e^{4} - A b^{4} c e^{4}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{5}}"," ",0,"A*d^4*log(abs(x))/b + 1/12*(3*B*c^3*x^4*e^4 + 16*B*c^3*d*x^3*e^3 + 36*B*c^3*d^2*x^2*e^2 + 48*B*c^3*d^3*x*e - 4*B*b*c^2*x^3*e^4 + 4*A*c^3*x^3*e^4 - 24*B*b*c^2*d*x^2*e^3 + 24*A*c^3*d*x^2*e^3 - 72*B*b*c^2*d^2*x*e^2 + 72*A*c^3*d^2*x*e^2 + 6*B*b^2*c*x^2*e^4 - 6*A*b*c^2*x^2*e^4 + 48*B*b^2*c*d*x*e^3 - 48*A*b*c^2*d*x*e^3 - 12*B*b^3*x*e^4 + 12*A*b^2*c*x*e^4)/c^4 + (B*b*c^4*d^4 - A*c^5*d^4 - 4*B*b^2*c^3*d^3*e + 4*A*b*c^4*d^3*e + 6*B*b^3*c^2*d^2*e^2 - 6*A*b^2*c^3*d^2*e^2 - 4*B*b^4*c*d*e^3 + 4*A*b^3*c^2*d*e^3 + B*b^5*e^4 - A*b^4*c*e^4)*log(abs(c*x + b))/(b*c^5)","A",0
1138,1,207,0,0.152257," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x),x, algorithm=""giac"")","\frac{A d^{3} \log\left({\left| x \right|}\right)}{b} + \frac{2 \, B c^{2} x^{3} e^{3} + 9 \, B c^{2} d x^{2} e^{2} + 18 \, B c^{2} d^{2} x e - 3 \, B b c x^{2} e^{3} + 3 \, A c^{2} x^{2} e^{3} - 18 \, B b c d x e^{2} + 18 \, A c^{2} d x e^{2} + 6 \, B b^{2} x e^{3} - 6 \, A b c x e^{3}}{6 \, c^{3}} + \frac{{\left(B b c^{3} d^{3} - A c^{4} d^{3} - 3 \, B b^{2} c^{2} d^{2} e + 3 \, A b c^{3} d^{2} e + 3 \, B b^{3} c d e^{2} - 3 \, A b^{2} c^{2} d e^{2} - B b^{4} e^{3} + A b^{3} c e^{3}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{4}}"," ",0,"A*d^3*log(abs(x))/b + 1/6*(2*B*c^2*x^3*e^3 + 9*B*c^2*d*x^2*e^2 + 18*B*c^2*d^2*x*e - 3*B*b*c*x^2*e^3 + 3*A*c^2*x^2*e^3 - 18*B*b*c*d*x*e^2 + 18*A*c^2*d*x*e^2 + 6*B*b^2*x*e^3 - 6*A*b*c*x*e^3)/c^3 + (B*b*c^3*d^3 - A*c^4*d^3 - 3*B*b^2*c^2*d^2*e + 3*A*b*c^3*d^2*e + 3*B*b^3*c*d*e^2 - 3*A*b^2*c^2*d*e^2 - B*b^4*e^3 + A*b^3*c*e^3)*log(abs(c*x + b))/(b*c^4)","A",0
1139,1,117,0,0.151043," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x),x, algorithm=""giac"")","\frac{A d^{2} \log\left({\left| x \right|}\right)}{b} + \frac{B c x^{2} e^{2} + 4 \, B c d x e - 2 \, B b x e^{2} + 2 \, A c x e^{2}}{2 \, c^{2}} + \frac{{\left(B b c^{2} d^{2} - A c^{3} d^{2} - 2 \, B b^{2} c d e + 2 \, A b c^{2} d e + B b^{3} e^{2} - A b^{2} c e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{3}}"," ",0,"A*d^2*log(abs(x))/b + 1/2*(B*c*x^2*e^2 + 4*B*c*d*x*e - 2*B*b*x*e^2 + 2*A*c*x*e^2)/c^2 + (B*b*c^2*d^2 - A*c^3*d^2 - 2*B*b^2*c*d*e + 2*A*b*c^2*d*e + B*b^3*e^2 - A*b^2*c*e^2)*log(abs(c*x + b))/(b*c^3)","A",0
1140,1,59,0,0.145687," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{B x e}{c} + \frac{A d \log\left({\left| x \right|}\right)}{b} + \frac{{\left(B b c d - A c^{2} d - B b^{2} e + A b c e\right)} \log\left({\left| c x + b \right|}\right)}{b c^{2}}"," ",0,"B*x*e/c + A*d*log(abs(x))/b + (B*b*c*d - A*c^2*d - B*b^2*e + A*b*c*e)*log(abs(c*x + b))/(b*c^2)","A",0
1141,1,31,0,0.180043," ","integrate((B*x+A)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{A \log\left({\left| x \right|}\right)}{b} + \frac{{\left(B b - A c\right)} \log\left({\left| c x + b \right|}\right)}{b c}"," ",0,"A*log(abs(x))/b + (B*b - A*c)*log(abs(c*x + b))/(b*c)","A",0
1142,1,85,0,0.159575," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{{\left(B b c - A c^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{2} d - b^{2} c e} - \frac{{\left(B d e - A e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{c d^{2} e - b d e^{2}} + \frac{A \log\left({\left| x \right|}\right)}{b d}"," ",0,"(B*b*c - A*c^2)*log(abs(c*x + b))/(b*c^2*d - b^2*c*e) - (B*d*e - A*e^2)*log(abs(x*e + d))/(c*d^2*e - b*d*e^2) + A*log(abs(x))/(b*d)","A",0
1143,1,323,0,0.237929," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{{\left(B b c d^{2} e^{2} - 2 \, A c^{2} d^{2} e^{2} + 2 \, A b c d e^{3} - A b^{2} e^{4}\right)} e^{\left(-2\right)} \log\left(\frac{{\left| 2 \, c d e - \frac{2 \, c d^{2} e}{x e + d} - b e^{2} + \frac{2 \, b d e^{2}}{x e + d} - {\left| b \right|} e^{2} \right|}}{{\left| 2 \, c d e - \frac{2 \, c d^{2} e}{x e + d} - b e^{2} + \frac{2 \, b d e^{2}}{x e + d} + {\left| b \right|} e^{2} \right|}}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} {\left| b \right|}} + \frac{{\left(B c d^{2} - 2 \, A c d e + A b e^{2}\right)} \log\left({\left| c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} \right|}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)}} + \frac{\frac{B d e^{2}}{x e + d} - \frac{A e^{3}}{x e + d}}{c d^{2} e^{2} - b d e^{3}}"," ",0,"-1/2*(B*b*c*d^2*e^2 - 2*A*c^2*d^2*e^2 + 2*A*b*c*d*e^3 - A*b^2*e^4)*e^(-2)*log(abs(2*c*d*e - 2*c*d^2*e/(x*e + d) - b*e^2 + 2*b*d*e^2/(x*e + d) - abs(b)*e^2)/abs(2*c*d*e - 2*c*d^2*e/(x*e + d) - b*e^2 + 2*b*d*e^2/(x*e + d) + abs(b)*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*abs(b)) + 1/2*(B*c*d^2 - 2*A*c*d*e + A*b*e^2)*log(abs(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2))/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2) + (B*d*e^2/(x*e + d) - A*e^3/(x*e + d))/(c*d^2*e^2 - b*d*e^3)","B",0
1144,1,308,0,0.159729," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x),x, algorithm=""giac"")","\frac{{\left(B b c^{3} - A c^{4}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{4} d^{3} - 3 \, b^{2} c^{3} d^{2} e + 3 \, b^{3} c^{2} d e^{2} - b^{4} c e^{3}} - \frac{{\left(B c^{2} d^{3} e - 3 \, A c^{2} d^{2} e^{2} + 3 \, A b c d e^{3} - A b^{2} e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4}} + \frac{A \log\left({\left| x \right|}\right)}{b d^{3}} + \frac{3 \, B c^{2} d^{5} - 4 \, B b c d^{4} e - 5 \, A c^{2} d^{4} e + B b^{2} d^{3} e^{2} + 8 \, A b c d^{3} e^{2} - 3 \, A b^{2} d^{2} e^{3} + 2 \, {\left(B c^{2} d^{4} e - B b c d^{3} e^{2} - 2 \, A c^{2} d^{3} e^{2} + 3 \, A b c d^{2} e^{3} - A b^{2} d e^{4}\right)} x}{2 \, {\left(c d - b e\right)}^{3} {\left(x e + d\right)}^{2} d^{3}}"," ",0,"(B*b*c^3 - A*c^4)*log(abs(c*x + b))/(b*c^4*d^3 - 3*b^2*c^3*d^2*e + 3*b^3*c^2*d*e^2 - b^4*c*e^3) - (B*c^2*d^3*e - 3*A*c^2*d^2*e^2 + 3*A*b*c*d*e^3 - A*b^2*e^4)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4) + A*log(abs(x))/(b*d^3) + 1/2*(3*B*c^2*d^5 - 4*B*b*c*d^4*e - 5*A*c^2*d^4*e + B*b^2*d^3*e^2 + 8*A*b*c*d^3*e^2 - 3*A*b^2*d^2*e^3 + 2*(B*c^2*d^4*e - B*b*c*d^3*e^2 - 2*A*c^2*d^3*e^2 + 3*A*b*c*d^2*e^3 - A*b^2*d*e^4)*x)/((c*d - b*e)^3*(x*e + d)^2*d^3)","A",0
1145,1,475,0,0.168603," ","integrate((B*x+A)/(e*x+d)^4/(c*x^2+b*x),x, algorithm=""giac"")","\frac{{\left(B b c^{4} - A c^{5}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{5} d^{4} - 4 \, b^{2} c^{4} d^{3} e + 6 \, b^{3} c^{3} d^{2} e^{2} - 4 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}} - \frac{{\left(B c^{3} d^{4} e - 4 \, A c^{3} d^{3} e^{2} + 6 \, A b c^{2} d^{2} e^{3} - 4 \, A b^{2} c d e^{4} + A b^{3} e^{5}\right)} \log\left({\left| x e + d \right|}\right)}{c^{4} d^{8} e - 4 \, b c^{3} d^{7} e^{2} + 6 \, b^{2} c^{2} d^{6} e^{3} - 4 \, b^{3} c d^{5} e^{4} + b^{4} d^{4} e^{5}} + \frac{A \log\left({\left| x \right|}\right)}{b d^{4}} + \frac{11 \, B c^{3} d^{7} - 18 \, B b c^{2} d^{6} e - 26 \, A c^{3} d^{6} e + 9 \, B b^{2} c d^{5} e^{2} + 57 \, A b c^{2} d^{5} e^{2} - 2 \, B b^{3} d^{4} e^{3} - 42 \, A b^{2} c d^{4} e^{3} + 11 \, A b^{3} d^{3} e^{4} + 6 \, {\left(B c^{3} d^{5} e^{2} - B b c^{2} d^{4} e^{3} - 3 \, A c^{3} d^{4} e^{3} + 6 \, A b c^{2} d^{3} e^{4} - 4 \, A b^{2} c d^{2} e^{5} + A b^{3} d e^{6}\right)} x^{2} + 3 \, {\left(5 \, B c^{3} d^{6} e - 6 \, B b c^{2} d^{5} e^{2} - 14 \, A c^{3} d^{5} e^{2} + B b^{2} c d^{4} e^{3} + 29 \, A b c^{2} d^{4} e^{3} - 20 \, A b^{2} c d^{3} e^{4} + 5 \, A b^{3} d^{2} e^{5}\right)} x}{6 \, {\left(c d - b e\right)}^{4} {\left(x e + d\right)}^{3} d^{4}}"," ",0,"(B*b*c^4 - A*c^5)*log(abs(c*x + b))/(b*c^5*d^4 - 4*b^2*c^4*d^3*e + 6*b^3*c^3*d^2*e^2 - 4*b^4*c^2*d*e^3 + b^5*c*e^4) - (B*c^3*d^4*e - 4*A*c^3*d^3*e^2 + 6*A*b*c^2*d^2*e^3 - 4*A*b^2*c*d*e^4 + A*b^3*e^5)*log(abs(x*e + d))/(c^4*d^8*e - 4*b*c^3*d^7*e^2 + 6*b^2*c^2*d^6*e^3 - 4*b^3*c*d^5*e^4 + b^4*d^4*e^5) + A*log(abs(x))/(b*d^4) + 1/6*(11*B*c^3*d^7 - 18*B*b*c^2*d^6*e - 26*A*c^3*d^6*e + 9*B*b^2*c*d^5*e^2 + 57*A*b*c^2*d^5*e^2 - 2*B*b^3*d^4*e^3 - 42*A*b^2*c*d^4*e^3 + 11*A*b^3*d^3*e^4 + 6*(B*c^3*d^5*e^2 - B*b*c^2*d^4*e^3 - 3*A*c^3*d^4*e^3 + 6*A*b*c^2*d^3*e^4 - 4*A*b^2*c*d^2*e^5 + A*b^3*d*e^6)*x^2 + 3*(5*B*c^3*d^6*e - 6*B*b*c^2*d^5*e^2 - 14*A*c^3*d^5*e^2 + B*b^2*c*d^4*e^3 + 29*A*b*c^2*d^4*e^3 - 20*A*b^2*c*d^3*e^4 + 5*A*b^3*d^2*e^5)*x)/((c*d - b*e)^4*(x*e + d)^3*d^4)","A",0
1146,1,315,0,0.155101," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(B b d^{4} - 2 \, A c d^{4} + 4 \, A b d^{3} e\right)} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{B c^{2} x^{2} e^{4} + 8 \, B c^{2} d x e^{3} - 4 \, B b c x e^{4} + 2 \, A c^{2} x e^{4}}{2 \, c^{4}} - \frac{{\left(B b c^{4} d^{4} - 2 \, A c^{5} d^{4} + 4 \, A b c^{4} d^{3} e - 6 \, B b^{3} c^{2} d^{2} e^{2} + 8 \, B b^{4} c d e^{3} - 4 \, A b^{3} c^{2} d e^{3} - 3 \, B b^{5} e^{4} + 2 \, A b^{4} c e^{4}\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{4}} - \frac{A b c^{4} d^{4} - {\left(B b c^{4} d^{4} - 2 \, A c^{5} d^{4} - 4 \, B b^{2} c^{3} d^{3} e + 4 \, A b c^{4} d^{3} e + 6 \, B b^{3} c^{2} d^{2} e^{2} - 6 \, A b^{2} c^{3} d^{2} e^{2} - 4 \, B b^{4} c d e^{3} + 4 \, A b^{3} c^{2} d e^{3} + B b^{5} e^{4} - A b^{4} c e^{4}\right)} x}{{\left(c x + b\right)} b^{2} c^{4} x}"," ",0,"(B*b*d^4 - 2*A*c*d^4 + 4*A*b*d^3*e)*log(abs(x))/b^3 + 1/2*(B*c^2*x^2*e^4 + 8*B*c^2*d*x*e^3 - 4*B*b*c*x*e^4 + 2*A*c^2*x*e^4)/c^4 - (B*b*c^4*d^4 - 2*A*c^5*d^4 + 4*A*b*c^4*d^3*e - 6*B*b^3*c^2*d^2*e^2 + 8*B*b^4*c*d*e^3 - 4*A*b^3*c^2*d*e^3 - 3*B*b^5*e^4 + 2*A*b^4*c*e^4)*log(abs(c*x + b))/(b^3*c^4) - (A*b*c^4*d^4 - (B*b*c^4*d^4 - 2*A*c^5*d^4 - 4*B*b^2*c^3*d^3*e + 4*A*b*c^4*d^3*e + 6*B*b^3*c^2*d^2*e^2 - 6*A*b^2*c^3*d^2*e^2 - 4*B*b^4*c*d*e^3 + 4*A*b^3*c^2*d*e^3 + B*b^5*e^4 - A*b^4*c*e^4)*x)/((c*x + b)*b^2*c^4*x)","B",0
1147,1,229,0,0.189232," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{B x e^{3}}{c^{2}} + \frac{{\left(B b d^{3} - 2 \, A c d^{3} + 3 \, A b d^{2} e\right)} \log\left({\left| x \right|}\right)}{b^{3}} - \frac{{\left(B b c^{3} d^{3} - 2 \, A c^{4} d^{3} + 3 \, A b c^{3} d^{2} e - 3 \, B b^{3} c d e^{2} + 2 \, B b^{4} e^{3} - A b^{3} c e^{3}\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{3}} - \frac{A b c^{2} d^{3} - \frac{{\left(B b c^{3} d^{3} - 2 \, A c^{4} d^{3} - 3 \, B b^{2} c^{2} d^{2} e + 3 \, A b c^{3} d^{2} e + 3 \, B b^{3} c d e^{2} - 3 \, A b^{2} c^{2} d e^{2} - B b^{4} e^{3} + A b^{3} c e^{3}\right)} x}{c}}{{\left(c x + b\right)} b^{2} c^{2} x}"," ",0,"B*x*e^3/c^2 + (B*b*d^3 - 2*A*c*d^3 + 3*A*b*d^2*e)*log(abs(x))/b^3 - (B*b*c^3*d^3 - 2*A*c^4*d^3 + 3*A*b*c^3*d^2*e - 3*B*b^3*c*d*e^2 + 2*B*b^4*e^3 - A*b^3*c*e^3)*log(abs(c*x + b))/(b^3*c^3) - (A*b*c^2*d^3 - (B*b*c^3*d^3 - 2*A*c^4*d^3 - 3*B*b^2*c^2*d^2*e + 3*A*b*c^3*d^2*e + 3*B*b^3*c*d*e^2 - 3*A*b^2*c^2*d*e^2 - B*b^4*e^3 + A*b^3*c*e^3)*x/c)/((c*x + b)*b^2*c^2*x)","A",0
1148,1,167,0,0.154749," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(B b d^{2} - 2 \, A c d^{2} + 2 \, A b d e\right)} \log\left({\left| x \right|}\right)}{b^{3}} - \frac{{\left(B b c^{2} d^{2} - 2 \, A c^{3} d^{2} + 2 \, A b c^{2} d e - B b^{3} e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{2}} - \frac{A b c^{2} d^{2} - {\left(B b c^{2} d^{2} - 2 \, A c^{3} d^{2} - 2 \, B b^{2} c d e + 2 \, A b c^{2} d e + B b^{3} e^{2} - A b^{2} c e^{2}\right)} x}{{\left(c x + b\right)} b^{2} c^{2} x}"," ",0,"(B*b*d^2 - 2*A*c*d^2 + 2*A*b*d*e)*log(abs(x))/b^3 - (B*b*c^2*d^2 - 2*A*c^3*d^2 + 2*A*b*c^2*d*e - B*b^3*e^2)*log(abs(c*x + b))/(b^3*c^2) - (A*b*c^2*d^2 - (B*b*c^2*d^2 - 2*A*c^3*d^2 - 2*B*b^2*c*d*e + 2*A*b*c^2*d*e + B*b^3*e^2 - A*b^2*c*e^2)*x)/((c*x + b)*b^2*c^2*x)","A",0
1149,1,112,0,0.155519," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(B b d - 2 \, A c d + A b e\right)} \log\left({\left| x \right|}\right)}{b^{3}} - \frac{{\left(B b c d - 2 \, A c^{2} d + A b c e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c} + \frac{B b c d x - 2 \, A c^{2} d x - B b^{2} x e + A b c x e - A b c d}{{\left(c x^{2} + b x\right)} b^{2} c}"," ",0,"(B*b*d - 2*A*c*d + A*b*e)*log(abs(x))/b^3 - (B*b*c*d - 2*A*c^2*d + A*b*c*e)*log(abs(c*x + b))/(b^3*c) + (B*b*c*d*x - 2*A*c^2*d*x - B*b^2*x*e + A*b*c*x*e - A*b*c*d)/((c*x^2 + b*x)*b^2*c)","A",0
1150,1,71,0,0.159975," ","integrate((B*x+A)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(B b - 2 \, A c\right)} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{B b x - 2 \, A c x - A b}{{\left(c x^{2} + b x\right)} b^{2}} - \frac{{\left(B b c - 2 \, A c^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c}"," ",0,"(B*b - 2*A*c)*log(abs(x))/b^3 + (B*b*x - 2*A*c*x - A*b)/((c*x^2 + b*x)*b^2) - (B*b*c - 2*A*c^2)*log(abs(c*x + b))/(b^3*c)","A",0
1151,1,268,0,0.162534," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(B b c^{3} d - 2 \, A c^{4} d - 2 \, B b^{2} c^{2} e + 3 \, A b c^{3} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{3} d^{2} - 2 \, b^{4} c^{2} d e + b^{5} c e^{2}} - \frac{{\left(B d e^{3} - A e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}} + \frac{{\left(B b d - 2 \, A c d - A b e\right)} \log\left({\left| x \right|}\right)}{b^{3} d^{2}} - \frac{A b c^{2} d^{3} - 2 \, A b^{2} c d^{2} e + A b^{3} d e^{2} - {\left(B b c^{2} d^{3} - 2 \, A c^{3} d^{3} - B b^{2} c d^{2} e + 3 \, A b c^{2} d^{2} e - A b^{2} c d e^{2}\right)} x}{{\left(c d - b e\right)}^{2} {\left(c x + b\right)} b^{2} d^{2} x}"," ",0,"-(B*b*c^3*d - 2*A*c^4*d - 2*B*b^2*c^2*e + 3*A*b*c^3*e)*log(abs(c*x + b))/(b^3*c^3*d^2 - 2*b^4*c^2*d*e + b^5*c*e^2) - (B*d*e^3 - A*e^4)*log(abs(x*e + d))/(c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3) + (B*b*d - 2*A*c*d - A*b*e)*log(abs(x))/(b^3*d^2) - (A*b*c^2*d^3 - 2*A*b^2*c*d^2*e + A*b^3*d*e^2 - (B*b*c^2*d^3 - 2*A*c^3*d^3 - B*b^2*c*d^2*e + 3*A*b*c^2*d^2*e - A*b^2*c*d*e^2)*x)/((c*d - b*e)^2*(c*x + b)*b^2*d^2*x)","A",0
1152,1,670,0,0.282142," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(2 \, B b c^{3} d^{4} e^{2} - 4 \, A c^{4} d^{4} e^{2} - 6 \, B b^{2} c^{2} d^{3} e^{3} + 8 \, A b c^{3} d^{3} e^{3} + 3 \, B b^{3} c d^{2} e^{4} - B b^{4} d e^{5} - 4 \, A b^{3} c d e^{5} + 2 \, A b^{4} e^{6}\right)} e^{\left(-2\right)} \log\left(\frac{{\left| 2 \, c d e - \frac{2 \, c d^{2} e}{x e + d} - b e^{2} + \frac{2 \, b d e^{2}}{x e + d} - {\left| b \right|} e^{2} \right|}}{{\left| 2 \, c d e - \frac{2 \, c d^{2} e}{x e + d} - b e^{2} + \frac{2 \, b d e^{2}}{x e + d} + {\left| b \right|} e^{2} \right|}}\right)}{2 \, {\left(b^{2} c^{3} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - b^{5} d^{3} e^{3}\right)} {\left| b \right|}} + \frac{{\left(3 \, B c d^{2} e^{2} - B b d e^{3} - 4 \, A c d e^{3} + 2 \, A b e^{4}\right)} \log\left({\left| c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} \right|}\right)}{2 \, {\left(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}\right)}} + \frac{\frac{B d e^{6}}{x e + d} - \frac{A e^{7}}{x e + d}}{c^{2} d^{4} e^{4} - 2 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6}} + \frac{\frac{B b c^{3} d^{3} e - 2 \, A c^{4} d^{3} e + 3 \, A b c^{3} d^{2} e^{2} - 3 \, A b^{2} c^{2} d e^{3} + A b^{3} c e^{4}}{c d^{2} - b d e} - \frac{{\left(B b c^{3} d^{4} e^{2} - 2 \, A c^{4} d^{4} e^{2} + 4 \, A b c^{3} d^{3} e^{3} - 6 \, A b^{2} c^{2} d^{2} e^{4} + 4 \, A b^{3} c d e^{5} - A b^{4} e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} - b d e\right)} {\left(x e + d\right)}}}{{\left(c d - b e\right)}^{2} b^{2} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}\right)} d^{2}}"," ",0,"1/2*(2*B*b*c^3*d^4*e^2 - 4*A*c^4*d^4*e^2 - 6*B*b^2*c^2*d^3*e^3 + 8*A*b*c^3*d^3*e^3 + 3*B*b^3*c*d^2*e^4 - B*b^4*d*e^5 - 4*A*b^3*c*d*e^5 + 2*A*b^4*e^6)*e^(-2)*log(abs(2*c*d*e - 2*c*d^2*e/(x*e + d) - b*e^2 + 2*b*d*e^2/(x*e + d) - abs(b)*e^2)/abs(2*c*d*e - 2*c*d^2*e/(x*e + d) - b*e^2 + 2*b*d*e^2/(x*e + d) + abs(b)*e^2))/((b^2*c^3*d^6 - 3*b^3*c^2*d^5*e + 3*b^4*c*d^4*e^2 - b^5*d^3*e^3)*abs(b)) + 1/2*(3*B*c*d^2*e^2 - B*b*d*e^3 - 4*A*c*d*e^3 + 2*A*b*e^4)*log(abs(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2))/(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) + (B*d*e^6/(x*e + d) - A*e^7/(x*e + d))/(c^2*d^4*e^4 - 2*b*c*d^3*e^5 + b^2*d^2*e^6) + ((B*b*c^3*d^3*e - 2*A*c^4*d^3*e + 3*A*b*c^3*d^2*e^2 - 3*A*b^2*c^2*d*e^3 + A*b^3*c*e^4)/(c*d^2 - b*d*e) - (B*b*c^3*d^4*e^2 - 2*A*c^4*d^4*e^2 + 4*A*b*c^3*d^3*e^3 - 6*A*b^2*c^2*d^2*e^4 + 4*A*b^3*c*d*e^5 - A*b^4*e^6)*e^(-1)/((c*d^2 - b*d*e)*(x*e + d)))/((c*d - b*e)^2*b^2*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)*d^2)","B",0
1153,1,745,0,0.203819," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(B b c^{5} d - 2 \, A c^{6} d - 4 \, B b^{2} c^{4} e + 5 \, A b c^{5} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{5} d^{4} - 4 \, b^{4} c^{4} d^{3} e + 6 \, b^{5} c^{3} d^{2} e^{2} - 4 \, b^{6} c^{2} d e^{3} + b^{7} c e^{4}} - \frac{{\left(6 \, B c^{2} d^{3} e^{3} - 4 \, B b c d^{2} e^{4} - 10 \, A c^{2} d^{2} e^{4} + B b^{2} d e^{5} + 10 \, A b c d e^{5} - 3 \, A b^{2} e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{4} d^{8} e - 4 \, b c^{3} d^{7} e^{2} + 6 \, b^{2} c^{2} d^{6} e^{3} - 4 \, b^{3} c d^{5} e^{4} + b^{4} d^{4} e^{5}} + \frac{{\left(B b d - 2 \, A c d - 3 \, A b e\right)} \log\left({\left| x \right|}\right)}{b^{3} d^{4}} - \frac{2 \, A b c^{4} d^{7} - 8 \, A b^{2} c^{3} d^{6} e + 12 \, A b^{3} c^{2} d^{5} e^{2} - 8 \, A b^{4} c d^{4} e^{3} + 2 \, A b^{5} d^{3} e^{4} - 2 \, {\left(B b c^{4} d^{5} e^{2} - 2 \, A c^{5} d^{5} e^{2} + 2 \, B b^{2} c^{3} d^{4} e^{3} + 5 \, A b c^{4} d^{4} e^{3} - 4 \, B b^{3} c^{2} d^{3} e^{4} - 10 \, A b^{2} c^{3} d^{3} e^{4} + B b^{4} c d^{2} e^{5} + 10 \, A b^{3} c^{2} d^{2} e^{5} - 3 \, A b^{4} c d e^{6}\right)} x^{3} - {\left(4 \, B b c^{4} d^{6} e - 8 \, A c^{5} d^{6} e + 3 \, B b^{2} c^{3} d^{5} e^{2} + 18 \, A b c^{4} d^{5} e^{2} - 4 \, B b^{3} c^{2} d^{4} e^{3} - 25 \, A b^{2} c^{3} d^{4} e^{3} - 5 \, B b^{4} c d^{3} e^{4} + 10 \, A b^{3} c^{2} d^{3} e^{4} + 2 \, B b^{5} d^{2} e^{5} + 11 \, A b^{4} c d^{2} e^{5} - 6 \, A b^{5} d e^{6}\right)} x^{2} - {\left(2 \, B b c^{4} d^{7} - 4 \, A c^{5} d^{7} - 2 \, B b^{2} c^{3} d^{6} e + 6 \, A b c^{4} d^{6} e + 7 \, B b^{3} c^{2} d^{5} e^{2} + 4 \, A b^{2} c^{3} d^{5} e^{2} - 10 \, B b^{4} c d^{4} e^{3} - 25 \, A b^{3} c^{2} d^{4} e^{3} + 3 \, B b^{5} d^{3} e^{4} + 28 \, A b^{4} c d^{3} e^{4} - 9 \, A b^{5} d^{2} e^{5}\right)} x}{2 \, {\left(c d - b e\right)}^{4} {\left(c x + b\right)} {\left(x e + d\right)}^{2} b^{2} d^{4} x}"," ",0,"-(B*b*c^5*d - 2*A*c^6*d - 4*B*b^2*c^4*e + 5*A*b*c^5*e)*log(abs(c*x + b))/(b^3*c^5*d^4 - 4*b^4*c^4*d^3*e + 6*b^5*c^3*d^2*e^2 - 4*b^6*c^2*d*e^3 + b^7*c*e^4) - (6*B*c^2*d^3*e^3 - 4*B*b*c*d^2*e^4 - 10*A*c^2*d^2*e^4 + B*b^2*d*e^5 + 10*A*b*c*d*e^5 - 3*A*b^2*e^6)*log(abs(x*e + d))/(c^4*d^8*e - 4*b*c^3*d^7*e^2 + 6*b^2*c^2*d^6*e^3 - 4*b^3*c*d^5*e^4 + b^4*d^4*e^5) + (B*b*d - 2*A*c*d - 3*A*b*e)*log(abs(x))/(b^3*d^4) - 1/2*(2*A*b*c^4*d^7 - 8*A*b^2*c^3*d^6*e + 12*A*b^3*c^2*d^5*e^2 - 8*A*b^4*c*d^4*e^3 + 2*A*b^5*d^3*e^4 - 2*(B*b*c^4*d^5*e^2 - 2*A*c^5*d^5*e^2 + 2*B*b^2*c^3*d^4*e^3 + 5*A*b*c^4*d^4*e^3 - 4*B*b^3*c^2*d^3*e^4 - 10*A*b^2*c^3*d^3*e^4 + B*b^4*c*d^2*e^5 + 10*A*b^3*c^2*d^2*e^5 - 3*A*b^4*c*d*e^6)*x^3 - (4*B*b*c^4*d^6*e - 8*A*c^5*d^6*e + 3*B*b^2*c^3*d^5*e^2 + 18*A*b*c^4*d^5*e^2 - 4*B*b^3*c^2*d^4*e^3 - 25*A*b^2*c^3*d^4*e^3 - 5*B*b^4*c*d^3*e^4 + 10*A*b^3*c^2*d^3*e^4 + 2*B*b^5*d^2*e^5 + 11*A*b^4*c*d^2*e^5 - 6*A*b^5*d*e^6)*x^2 - (2*B*b*c^4*d^7 - 4*A*c^5*d^7 - 2*B*b^2*c^3*d^6*e + 6*A*b*c^4*d^6*e + 7*B*b^3*c^2*d^5*e^2 + 4*A*b^2*c^3*d^5*e^2 - 10*B*b^4*c*d^4*e^3 - 25*A*b^3*c^2*d^4*e^3 + 3*B*b^5*d^3*e^4 + 28*A*b^4*c*d^3*e^4 - 9*A*b^5*d^2*e^5)*x)/((c*d - b*e)^4*(c*x + b)*(x*e + d)^2*b^2*d^4*x)","B",0
1154,1,511,0,0.161273," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{B x e^{5}}{c^{3}} - \frac{{\left(3 \, B b c d^{5} - 6 \, A c^{2} d^{5} - 5 \, B b^{2} d^{4} e + 15 \, A b c d^{4} e - 10 \, A b^{2} d^{3} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{{\left(3 \, B b c^{5} d^{5} - 6 \, A c^{6} d^{5} - 5 \, B b^{2} c^{4} d^{4} e + 15 \, A b c^{5} d^{4} e - 10 \, A b^{2} c^{4} d^{3} e^{2} + 5 \, B b^{5} c d e^{4} - 3 \, B b^{6} e^{5} + A b^{5} c e^{5}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c^{4}} - \frac{A b^{3} c^{4} d^{5} + 2 \, {\left(3 \, B b c^{6} d^{5} - 6 \, A c^{7} d^{5} - 5 \, B b^{2} c^{5} d^{4} e + 15 \, A b c^{6} d^{4} e - 10 \, A b^{2} c^{5} d^{3} e^{2} + 10 \, B b^{4} c^{3} d^{2} e^{3} - 10 \, B b^{5} c^{2} d e^{4} + 5 \, A b^{4} c^{3} d e^{4} + 3 \, B b^{6} c e^{5} - 2 \, A b^{5} c^{2} e^{5}\right)} x^{3} + {\left(9 \, B b^{2} c^{5} d^{5} - 18 \, A b c^{6} d^{5} - 15 \, B b^{3} c^{4} d^{4} e + 45 \, A b^{2} c^{5} d^{4} e + 10 \, B b^{4} c^{3} d^{3} e^{2} - 30 \, A b^{3} c^{4} d^{3} e^{2} + 10 \, B b^{5} c^{2} d^{2} e^{3} + 10 \, A b^{4} c^{3} d^{2} e^{3} - 15 \, B b^{6} c d e^{4} + 5 \, A b^{5} c^{2} d e^{4} + 5 \, B b^{7} e^{5} - 3 \, A b^{6} c e^{5}\right)} x^{2} + 2 \, {\left(B b^{3} c^{4} d^{5} - 2 \, A b^{2} c^{5} d^{5} + 5 \, A b^{3} c^{4} d^{4} e\right)} x}{2 \, {\left(c x + b\right)}^{2} b^{4} c^{4} x^{2}}"," ",0,"B*x*e^5/c^3 - (3*B*b*c*d^5 - 6*A*c^2*d^5 - 5*B*b^2*d^4*e + 15*A*b*c*d^4*e - 10*A*b^2*d^3*e^2)*log(abs(x))/b^5 + (3*B*b*c^5*d^5 - 6*A*c^6*d^5 - 5*B*b^2*c^4*d^4*e + 15*A*b*c^5*d^4*e - 10*A*b^2*c^4*d^3*e^2 + 5*B*b^5*c*d*e^4 - 3*B*b^6*e^5 + A*b^5*c*e^5)*log(abs(c*x + b))/(b^5*c^4) - 1/2*(A*b^3*c^4*d^5 + 2*(3*B*b*c^6*d^5 - 6*A*c^7*d^5 - 5*B*b^2*c^5*d^4*e + 15*A*b*c^6*d^4*e - 10*A*b^2*c^5*d^3*e^2 + 10*B*b^4*c^3*d^2*e^3 - 10*B*b^5*c^2*d*e^4 + 5*A*b^4*c^3*d*e^4 + 3*B*b^6*c*e^5 - 2*A*b^5*c^2*e^5)*x^3 + (9*B*b^2*c^5*d^5 - 18*A*b*c^6*d^5 - 15*B*b^3*c^4*d^4*e + 45*A*b^2*c^5*d^4*e + 10*B*b^4*c^3*d^3*e^2 - 30*A*b^3*c^4*d^3*e^2 + 10*B*b^5*c^2*d^2*e^3 + 10*A*b^4*c^3*d^2*e^3 - 15*B*b^6*c*d*e^4 + 5*A*b^5*c^2*d*e^4 + 5*B*b^7*e^5 - 3*A*b^6*c*e^5)*x^2 + 2*(B*b^3*c^4*d^5 - 2*A*b^2*c^5*d^5 + 5*A*b^3*c^4*d^4*e)*x)/((c*x + b)^2*b^4*c^4*x^2)","B",0
1155,1,428,0,0.162850," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, B b c d^{4} - 6 \, A c^{2} d^{4} - 4 \, B b^{2} d^{3} e + 12 \, A b c d^{3} e - 6 \, A b^{2} d^{2} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{{\left(3 \, B b c^{4} d^{4} - 6 \, A c^{5} d^{4} - 4 \, B b^{2} c^{3} d^{3} e + 12 \, A b c^{4} d^{3} e - 6 \, A b^{2} c^{3} d^{2} e^{2} + B b^{5} e^{4}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c^{3}} - \frac{A b^{3} c^{3} d^{4} + 2 \, {\left(3 \, B b c^{5} d^{4} - 6 \, A c^{6} d^{4} - 4 \, B b^{2} c^{4} d^{3} e + 12 \, A b c^{5} d^{3} e - 6 \, A b^{2} c^{4} d^{2} e^{2} + 4 \, B b^{4} c^{2} d e^{3} - 2 \, B b^{5} c e^{4} + A b^{4} c^{2} e^{4}\right)} x^{3} + {\left(9 \, B b^{2} c^{4} d^{4} - 18 \, A b c^{5} d^{4} - 12 \, B b^{3} c^{3} d^{3} e + 36 \, A b^{2} c^{4} d^{3} e + 6 \, B b^{4} c^{2} d^{2} e^{2} - 18 \, A b^{3} c^{3} d^{2} e^{2} + 4 \, B b^{5} c d e^{3} + 4 \, A b^{4} c^{2} d e^{3} - 3 \, B b^{6} e^{4} + A b^{5} c e^{4}\right)} x^{2} + 2 \, {\left(B b^{3} c^{3} d^{4} - 2 \, A b^{2} c^{4} d^{4} + 4 \, A b^{3} c^{3} d^{3} e\right)} x}{2 \, {\left(c x + b\right)}^{2} b^{4} c^{3} x^{2}}"," ",0,"-(3*B*b*c*d^4 - 6*A*c^2*d^4 - 4*B*b^2*d^3*e + 12*A*b*c*d^3*e - 6*A*b^2*d^2*e^2)*log(abs(x))/b^5 + (3*B*b*c^4*d^4 - 6*A*c^5*d^4 - 4*B*b^2*c^3*d^3*e + 12*A*b*c^4*d^3*e - 6*A*b^2*c^3*d^2*e^2 + B*b^5*e^4)*log(abs(c*x + b))/(b^5*c^3) - 1/2*(A*b^3*c^3*d^4 + 2*(3*B*b*c^5*d^4 - 6*A*c^6*d^4 - 4*B*b^2*c^4*d^3*e + 12*A*b*c^5*d^3*e - 6*A*b^2*c^4*d^2*e^2 + 4*B*b^4*c^2*d*e^3 - 2*B*b^5*c*e^4 + A*b^4*c^2*e^4)*x^3 + (9*B*b^2*c^4*d^4 - 18*A*b*c^5*d^4 - 12*B*b^3*c^3*d^3*e + 36*A*b^2*c^4*d^3*e + 6*B*b^4*c^2*d^2*e^2 - 18*A*b^3*c^3*d^2*e^2 + 4*B*b^5*c*d*e^3 + 4*A*b^4*c^2*d*e^3 - 3*B*b^6*e^4 + A*b^5*c*e^4)*x^2 + 2*(B*b^3*c^3*d^4 - 2*A*b^2*c^4*d^4 + 4*A*b^3*c^3*d^3*e)*x)/((c*x + b)^2*b^4*c^3*x^2)","A",0
1156,1,391,0,0.176224," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(B b c d^{3} - 2 \, A c^{2} d^{3} - B b^{2} d^{2} e + 3 \, A b c d^{2} e - A b^{2} d e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{3 \, {\left(B b c^{2} d^{3} - 2 \, A c^{3} d^{3} - B b^{2} c d^{2} e + 3 \, A b c^{2} d^{2} e - A b^{2} c d e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} - \frac{6 \, B b c^{4} d^{3} x^{3} - 12 \, A c^{5} d^{3} x^{3} - 6 \, B b^{2} c^{3} d^{2} x^{3} e + 18 \, A b c^{4} d^{2} x^{3} e + 9 \, B b^{2} c^{3} d^{3} x^{2} - 18 \, A b c^{4} d^{3} x^{2} - 6 \, A b^{2} c^{3} d x^{3} e^{2} - 9 \, B b^{3} c^{2} d^{2} x^{2} e + 27 \, A b^{2} c^{3} d^{2} x^{2} e + 2 \, B b^{3} c^{2} d^{3} x - 4 \, A b^{2} c^{3} d^{3} x + 2 \, B b^{4} c x^{3} e^{3} + 3 \, B b^{4} c d x^{2} e^{2} - 9 \, A b^{3} c^{2} d x^{2} e^{2} + 6 \, A b^{3} c^{2} d^{2} x e + A b^{3} c^{2} d^{3} + B b^{5} x^{2} e^{3} + A b^{4} c x^{2} e^{3}}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4} c^{2}}"," ",0,"-3*(B*b*c*d^3 - 2*A*c^2*d^3 - B*b^2*d^2*e + 3*A*b*c*d^2*e - A*b^2*d*e^2)*log(abs(x))/b^5 + 3*(B*b*c^2*d^3 - 2*A*c^3*d^3 - B*b^2*c*d^2*e + 3*A*b*c^2*d^2*e - A*b^2*c*d*e^2)*log(abs(c*x + b))/(b^5*c) - 1/2*(6*B*b*c^4*d^3*x^3 - 12*A*c^5*d^3*x^3 - 6*B*b^2*c^3*d^2*x^3*e + 18*A*b*c^4*d^2*x^3*e + 9*B*b^2*c^3*d^3*x^2 - 18*A*b*c^4*d^3*x^2 - 6*A*b^2*c^3*d*x^3*e^2 - 9*B*b^3*c^2*d^2*x^2*e + 27*A*b^2*c^3*d^2*x^2*e + 2*B*b^3*c^2*d^3*x - 4*A*b^2*c^3*d^3*x + 2*B*b^4*c*x^3*e^3 + 3*B*b^4*c*d*x^2*e^2 - 9*A*b^3*c^2*d*x^2*e^2 + 6*A*b^3*c^2*d^2*x*e + A*b^3*c^2*d^3 + B*b^5*x^2*e^3 + A*b^4*c*x^2*e^3)/((c*x^2 + b*x)^2*b^4*c^2)","B",0
1157,1,324,0,0.193141," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, B b c d^{2} - 6 \, A c^{2} d^{2} - 2 \, B b^{2} d e + 6 \, A b c d e - A b^{2} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{{\left(3 \, B b c^{2} d^{2} - 6 \, A c^{3} d^{2} - 2 \, B b^{2} c d e + 6 \, A b c^{2} d e - A b^{2} c e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} - \frac{6 \, B b c^{3} d^{2} x^{3} - 12 \, A c^{4} d^{2} x^{3} - 4 \, B b^{2} c^{2} d x^{3} e + 12 \, A b c^{3} d x^{3} e + 9 \, B b^{2} c^{2} d^{2} x^{2} - 18 \, A b c^{3} d^{2} x^{2} - 2 \, A b^{2} c^{2} x^{3} e^{2} - 6 \, B b^{3} c d x^{2} e + 18 \, A b^{2} c^{2} d x^{2} e + 2 \, B b^{3} c d^{2} x - 4 \, A b^{2} c^{2} d^{2} x + B b^{4} x^{2} e^{2} - 3 \, A b^{3} c x^{2} e^{2} + 4 \, A b^{3} c d x e + A b^{3} c d^{2}}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4} c}"," ",0,"-(3*B*b*c*d^2 - 6*A*c^2*d^2 - 2*B*b^2*d*e + 6*A*b*c*d*e - A*b^2*e^2)*log(abs(x))/b^5 + (3*B*b*c^2*d^2 - 6*A*c^3*d^2 - 2*B*b^2*c*d*e + 6*A*b*c^2*d*e - A*b^2*c*e^2)*log(abs(c*x + b))/(b^5*c) - 1/2*(6*B*b*c^3*d^2*x^3 - 12*A*c^4*d^2*x^3 - 4*B*b^2*c^2*d*x^3*e + 12*A*b*c^3*d*x^3*e + 9*B*b^2*c^2*d^2*x^2 - 18*A*b*c^3*d^2*x^2 - 2*A*b^2*c^2*x^3*e^2 - 6*B*b^3*c*d*x^2*e + 18*A*b^2*c^2*d*x^2*e + 2*B*b^3*c*d^2*x - 4*A*b^2*c^2*d^2*x + B*b^4*x^2*e^2 - 3*A*b^3*c*x^2*e^2 + 4*A*b^3*c*d*x*e + A*b^3*c*d^2)/((c*x^2 + b*x)^2*b^4*c)","A",0
1158,1,225,0,0.157100," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, B b c d - 6 \, A c^{2} d - B b^{2} e + 3 \, A b c e\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{{\left(3 \, B b c^{2} d - 6 \, A c^{3} d - B b^{2} c e + 3 \, A b c^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} - \frac{6 \, B b c^{2} d x^{3} - 12 \, A c^{3} d x^{3} - 2 \, B b^{2} c x^{3} e + 6 \, A b c^{2} x^{3} e + 9 \, B b^{2} c d x^{2} - 18 \, A b c^{2} d x^{2} - 3 \, B b^{3} x^{2} e + 9 \, A b^{2} c x^{2} e + 2 \, B b^{3} d x - 4 \, A b^{2} c d x + 2 \, A b^{3} x e + A b^{3} d}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4}}"," ",0,"-(3*B*b*c*d - 6*A*c^2*d - B*b^2*e + 3*A*b*c*e)*log(abs(x))/b^5 + (3*B*b*c^2*d - 6*A*c^3*d - B*b^2*c*e + 3*A*b*c^2*e)*log(abs(c*x + b))/(b^5*c) - 1/2*(6*B*b*c^2*d*x^3 - 12*A*c^3*d*x^3 - 2*B*b^2*c*x^3*e + 6*A*b*c^2*x^3*e + 9*B*b^2*c*d*x^2 - 18*A*b*c^2*d*x^2 - 3*B*b^3*x^2*e + 9*A*b^2*c*x^2*e + 2*B*b^3*d*x - 4*A*b^2*c*d*x + 2*A*b^3*x*e + A*b^3*d)/((c*x^2 + b*x)^2*b^4)","A",0
1159,1,124,0,0.153972," ","integrate((B*x+A)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(B b c - 2 \, A c^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{3 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} - \frac{6 \, B b c^{2} x^{3} - 12 \, A c^{3} x^{3} + 9 \, B b^{2} c x^{2} - 18 \, A b c^{2} x^{2} + 2 \, B b^{3} x - 4 \, A b^{2} c x + A b^{3}}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4}}"," ",0,"-3*(B*b*c - 2*A*c^2)*log(abs(x))/b^5 + 3*(B*b*c^2 - 2*A*c^3)*log(abs(c*x + b))/(b^5*c) - 1/2*(6*B*b*c^2*x^3 - 12*A*c^3*x^3 + 9*B*b^2*c*x^2 - 18*A*b*c^2*x^2 + 2*B*b^3*x - 4*A*b^2*c*x + A*b^3)/((c*x^2 + b*x)^2*b^4)","A",0
1160,1,649,0,0.242074," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(3 \, B b c^{5} d^{2} - 6 \, A c^{6} d^{2} - 8 \, B b^{2} c^{4} d e + 15 \, A b c^{5} d e + 6 \, B b^{3} c^{3} e^{2} - 10 \, A b^{2} c^{4} e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c^{4} d^{3} - 3 \, b^{6} c^{3} d^{2} e + 3 \, b^{7} c^{2} d e^{2} - b^{8} c e^{3}} - \frac{{\left(B d e^{5} - A e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4}} - \frac{{\left(3 \, B b c d^{2} - 6 \, A c^{2} d^{2} + B b^{2} d e - 3 \, A b c d e - A b^{2} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5} d^{3}} - \frac{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} + 2 \, {\left(3 \, B b c^{5} d^{5} - 6 \, A c^{6} d^{5} - 8 \, B b^{2} c^{4} d^{4} e + 15 \, A b c^{5} d^{4} e + 6 \, B b^{3} c^{3} d^{3} e^{2} - 10 \, A b^{2} c^{4} d^{3} e^{2} - B b^{4} c^{2} d^{2} e^{3} + A b^{4} c^{2} d e^{4}\right)} x^{3} + {\left(9 \, B b^{2} c^{4} d^{5} - 18 \, A b c^{5} d^{5} - 24 \, B b^{3} c^{3} d^{4} e + 45 \, A b^{2} c^{4} d^{4} e + 19 \, B b^{4} c^{2} d^{3} e^{2} - 30 \, A b^{3} c^{3} d^{3} e^{2} - 4 \, B b^{5} c d^{2} e^{3} - A b^{4} c^{2} d^{2} e^{3} + 4 \, A b^{5} c d e^{4}\right)} x^{2} + 2 \, {\left(B b^{3} c^{3} d^{5} - 2 \, A b^{2} c^{4} d^{5} - 3 \, B b^{4} c^{2} d^{4} e + 5 \, A b^{3} c^{3} d^{4} e + 3 \, B b^{5} c d^{3} e^{2} - 3 \, A b^{4} c^{2} d^{3} e^{2} - B b^{6} d^{2} e^{3} - A b^{5} c d^{2} e^{3} + A b^{6} d e^{4}\right)} x}{2 \, {\left(c d - b e\right)}^{3} {\left(c x + b\right)}^{2} b^{4} d^{3} x^{2}}"," ",0,"(3*B*b*c^5*d^2 - 6*A*c^6*d^2 - 8*B*b^2*c^4*d*e + 15*A*b*c^5*d*e + 6*B*b^3*c^3*e^2 - 10*A*b^2*c^4*e^2)*log(abs(c*x + b))/(b^5*c^4*d^3 - 3*b^6*c^3*d^2*e + 3*b^7*c^2*d*e^2 - b^8*c*e^3) - (B*d*e^5 - A*e^6)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4) - (3*B*b*c*d^2 - 6*A*c^2*d^2 + B*b^2*d*e - 3*A*b*c*d*e - A*b^2*e^2)*log(abs(x))/(b^5*d^3) - 1/2*(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 + 2*(3*B*b*c^5*d^5 - 6*A*c^6*d^5 - 8*B*b^2*c^4*d^4*e + 15*A*b*c^5*d^4*e + 6*B*b^3*c^3*d^3*e^2 - 10*A*b^2*c^4*d^3*e^2 - B*b^4*c^2*d^2*e^3 + A*b^4*c^2*d*e^4)*x^3 + (9*B*b^2*c^4*d^5 - 18*A*b*c^5*d^5 - 24*B*b^3*c^3*d^4*e + 45*A*b^2*c^4*d^4*e + 19*B*b^4*c^2*d^3*e^2 - 30*A*b^3*c^3*d^3*e^2 - 4*B*b^5*c*d^2*e^3 - A*b^4*c^2*d^2*e^3 + 4*A*b^5*c*d*e^4)*x^2 + 2*(B*b^3*c^3*d^5 - 2*A*b^2*c^4*d^5 - 3*B*b^4*c^2*d^4*e + 5*A*b^3*c^3*d^4*e + 3*B*b^5*c*d^3*e^2 - 3*A*b^4*c^2*d^3*e^2 - B*b^6*d^2*e^3 - A*b^5*c*d^2*e^3 + A*b^6*d*e^4)*x)/((c*d - b*e)^3*(c*x + b)^2*b^4*d^3*x^2)","B",0
1161,1,1292,0,0.365362," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(6 \, B b c^{5} d^{6} e^{2} - 12 \, A c^{6} d^{6} e^{2} - 20 \, B b^{2} c^{4} d^{5} e^{3} + 36 \, A b c^{5} d^{5} e^{3} + 20 \, B b^{3} c^{3} d^{4} e^{4} - 30 \, A b^{2} c^{4} d^{4} e^{4} - 5 \, B b^{5} c d^{2} e^{6} + 2 \, B b^{6} d e^{7} + 6 \, A b^{5} c d e^{7} - 3 \, A b^{6} e^{8}\right)} e^{\left(-2\right)} \log\left(\frac{{\left| 2 \, c d e - \frac{2 \, c d^{2} e}{x e + d} - b e^{2} + \frac{2 \, b d e^{2}}{x e + d} - {\left| b \right|} e^{2} \right|}}{{\left| 2 \, c d e - \frac{2 \, c d^{2} e}{x e + d} - b e^{2} + \frac{2 \, b d e^{2}}{x e + d} + {\left| b \right|} e^{2} \right|}}\right)}{2 \, {\left(b^{4} c^{4} d^{8} - 4 \, b^{5} c^{3} d^{7} e + 6 \, b^{6} c^{2} d^{6} e^{2} - 4 \, b^{7} c d^{5} e^{3} + b^{8} d^{4} e^{4}\right)} {\left| b \right|}} + \frac{{\left(5 \, B c d^{2} e^{4} - 2 \, B b d e^{5} - 6 \, A c d e^{5} + 3 \, A b e^{6}\right)} \log\left({\left| c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} \right|}\right)}{2 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)}} + \frac{\frac{B d e^{10}}{x e + d} - \frac{A e^{11}}{x e + d}}{c^{3} d^{6} e^{6} - 3 \, b c^{2} d^{5} e^{7} + 3 \, b^{2} c d^{4} e^{8} - b^{3} d^{3} e^{9}} - \frac{6 \, B b c^{6} d^{5} e - 12 \, A c^{7} d^{5} e - 17 \, B b^{2} c^{5} d^{4} e^{2} + 30 \, A b c^{6} d^{4} e^{2} + 12 \, B b^{3} c^{4} d^{3} e^{3} - 16 \, A b^{2} c^{5} d^{3} e^{3} - 8 \, B b^{4} c^{3} d^{2} e^{4} - 6 \, A b^{3} c^{4} d^{2} e^{4} + 2 \, B b^{5} c^{2} d e^{5} + 14 \, A b^{4} c^{3} d e^{5} - 5 \, A b^{5} c^{2} e^{6} - \frac{2 \, {\left(9 \, B b c^{6} d^{6} e^{2} - 18 \, A c^{7} d^{6} e^{2} - 30 \, B b^{2} c^{5} d^{5} e^{3} + 54 \, A b c^{6} d^{5} e^{3} + 31 \, B b^{3} c^{4} d^{4} e^{4} - 47 \, A b^{2} c^{5} d^{4} e^{4} - 24 \, B b^{4} c^{3} d^{3} e^{5} + 4 \, A b^{3} c^{4} d^{3} e^{5} + 11 \, B b^{5} c^{2} d^{2} e^{6} + 29 \, A b^{4} c^{3} d^{2} e^{6} - 2 \, B b^{6} c d e^{7} - 22 \, A b^{5} c^{2} d e^{7} + 5 \, A b^{6} c e^{8}\right)} e^{\left(-1\right)}}{x e + d} + \frac{{\left(18 \, B b c^{6} d^{7} e^{3} - 36 \, A c^{7} d^{7} e^{3} - 69 \, B b^{2} c^{5} d^{6} e^{4} + 126 \, A b c^{6} d^{6} e^{4} + 90 \, B b^{3} c^{4} d^{5} e^{5} - 144 \, A b^{2} c^{5} d^{5} e^{5} - 80 \, B b^{4} c^{3} d^{4} e^{6} + 45 \, A b^{3} c^{4} d^{4} e^{6} + 50 \, B b^{5} c^{2} d^{3} e^{7} + 70 \, A b^{4} c^{3} d^{3} e^{7} - 16 \, B b^{6} c d^{2} e^{8} - 87 \, A b^{5} c^{2} d^{2} e^{8} + 2 \, B b^{7} d e^{9} + 36 \, A b^{6} c d e^{9} - 5 \, A b^{7} e^{10}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{2 \, {\left(3 \, B b c^{6} d^{8} e^{4} - 6 \, A c^{7} d^{8} e^{4} - 13 \, B b^{2} c^{5} d^{7} e^{5} + 24 \, A b c^{6} d^{7} e^{5} + 20 \, B b^{3} c^{4} d^{6} e^{6} - 33 \, A b^{2} c^{5} d^{6} e^{6} - 20 \, B b^{4} c^{3} d^{5} e^{7} + 15 \, A b^{3} c^{4} d^{5} e^{7} + 15 \, B b^{5} c^{2} d^{4} e^{8} + 15 \, A b^{4} c^{3} d^{4} e^{8} - 6 \, B b^{6} c d^{3} e^{9} - 27 \, A b^{5} c^{2} d^{3} e^{9} + B b^{7} d^{2} e^{10} + 15 \, A b^{6} c d^{2} e^{10} - 3 \, A b^{7} d e^{11}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{2 \, {\left(c d - b e\right)}^{4} b^{4} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}\right)}^{2} d^{4}}"," ",0,"-1/2*(6*B*b*c^5*d^6*e^2 - 12*A*c^6*d^6*e^2 - 20*B*b^2*c^4*d^5*e^3 + 36*A*b*c^5*d^5*e^3 + 20*B*b^3*c^3*d^4*e^4 - 30*A*b^2*c^4*d^4*e^4 - 5*B*b^5*c*d^2*e^6 + 2*B*b^6*d*e^7 + 6*A*b^5*c*d*e^7 - 3*A*b^6*e^8)*e^(-2)*log(abs(2*c*d*e - 2*c*d^2*e/(x*e + d) - b*e^2 + 2*b*d*e^2/(x*e + d) - abs(b)*e^2)/abs(2*c*d*e - 2*c*d^2*e/(x*e + d) - b*e^2 + 2*b*d*e^2/(x*e + d) + abs(b)*e^2))/((b^4*c^4*d^8 - 4*b^5*c^3*d^7*e + 6*b^6*c^2*d^6*e^2 - 4*b^7*c*d^5*e^3 + b^8*d^4*e^4)*abs(b)) + 1/2*(5*B*c*d^2*e^4 - 2*B*b*d*e^5 - 6*A*c*d*e^5 + 3*A*b*e^6)*log(abs(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2))/(c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4) + (B*d*e^10/(x*e + d) - A*e^11/(x*e + d))/(c^3*d^6*e^6 - 3*b*c^2*d^5*e^7 + 3*b^2*c*d^4*e^8 - b^3*d^3*e^9) - 1/2*(6*B*b*c^6*d^5*e - 12*A*c^7*d^5*e - 17*B*b^2*c^5*d^4*e^2 + 30*A*b*c^6*d^4*e^2 + 12*B*b^3*c^4*d^3*e^3 - 16*A*b^2*c^5*d^3*e^3 - 8*B*b^4*c^3*d^2*e^4 - 6*A*b^3*c^4*d^2*e^4 + 2*B*b^5*c^2*d*e^5 + 14*A*b^4*c^3*d*e^5 - 5*A*b^5*c^2*e^6 - 2*(9*B*b*c^6*d^6*e^2 - 18*A*c^7*d^6*e^2 - 30*B*b^2*c^5*d^5*e^3 + 54*A*b*c^6*d^5*e^3 + 31*B*b^3*c^4*d^4*e^4 - 47*A*b^2*c^5*d^4*e^4 - 24*B*b^4*c^3*d^3*e^5 + 4*A*b^3*c^4*d^3*e^5 + 11*B*b^5*c^2*d^2*e^6 + 29*A*b^4*c^3*d^2*e^6 - 2*B*b^6*c*d*e^7 - 22*A*b^5*c^2*d*e^7 + 5*A*b^6*c*e^8)*e^(-1)/(x*e + d) + (18*B*b*c^6*d^7*e^3 - 36*A*c^7*d^7*e^3 - 69*B*b^2*c^5*d^6*e^4 + 126*A*b*c^6*d^6*e^4 + 90*B*b^3*c^4*d^5*e^5 - 144*A*b^2*c^5*d^5*e^5 - 80*B*b^4*c^3*d^4*e^6 + 45*A*b^3*c^4*d^4*e^6 + 50*B*b^5*c^2*d^3*e^7 + 70*A*b^4*c^3*d^3*e^7 - 16*B*b^6*c*d^2*e^8 - 87*A*b^5*c^2*d^2*e^8 + 2*B*b^7*d*e^9 + 36*A*b^6*c*d*e^9 - 5*A*b^7*e^10)*e^(-2)/(x*e + d)^2 - 2*(3*B*b*c^6*d^8*e^4 - 6*A*c^7*d^8*e^4 - 13*B*b^2*c^5*d^7*e^5 + 24*A*b*c^6*d^7*e^5 + 20*B*b^3*c^4*d^6*e^6 - 33*A*b^2*c^5*d^6*e^6 - 20*B*b^4*c^3*d^5*e^7 + 15*A*b^3*c^4*d^5*e^7 + 15*B*b^5*c^2*d^4*e^8 + 15*A*b^4*c^3*d^4*e^8 - 6*B*b^6*c*d^3*e^9 - 27*A*b^5*c^2*d^3*e^9 + B*b^7*d^2*e^10 + 15*A*b^6*c*d^2*e^10 - 3*A*b^7*d*e^11)*e^(-3)/(x*e + d)^3)/((c*d - b*e)^4*b^4*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)^2*d^4)","B",0
1162,1,521,0,0.232265," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B x e^{3} + \frac{36 \, B c^{5} d e^{2} + B b c^{4} e^{3} + 12 \, A c^{5} e^{3}}{c^{5}}\right)} x + \frac{3 \, {\left(120 \, B c^{5} d^{2} e + 12 \, B b c^{4} d e^{2} + 120 \, A c^{5} d e^{2} - 3 \, B b^{2} c^{3} e^{3} + 4 \, A b c^{4} e^{3}\right)}}{c^{5}}\right)} x + \frac{320 \, B c^{5} d^{3} + 120 \, B b c^{4} d^{2} e + 960 \, A c^{5} d^{2} e - 84 \, B b^{2} c^{3} d e^{2} + 120 \, A b c^{4} d e^{2} + 21 \, B b^{3} c^{2} e^{3} - 28 \, A b^{2} c^{3} e^{3}}{c^{5}}\right)} x + \frac{5 \, {\left(64 \, B b c^{4} d^{3} + 384 \, A c^{5} d^{3} - 120 \, B b^{2} c^{3} d^{2} e + 192 \, A b c^{4} d^{2} e + 84 \, B b^{3} c^{2} d e^{2} - 120 \, A b^{2} c^{3} d e^{2} - 21 \, B b^{4} c e^{3} + 28 \, A b^{3} c^{2} e^{3}\right)}}{c^{5}}\right)} x - \frac{15 \, {\left(64 \, B b^{2} c^{3} d^{3} - 128 \, A b c^{4} d^{3} - 120 \, B b^{3} c^{2} d^{2} e + 192 \, A b^{2} c^{3} d^{2} e + 84 \, B b^{4} c d e^{2} - 120 \, A b^{3} c^{2} d e^{2} - 21 \, B b^{5} e^{3} + 28 \, A b^{4} c e^{3}\right)}}{c^{5}}\right)} - \frac{{\left(64 \, B b^{3} c^{3} d^{3} - 128 \, A b^{2} c^{4} d^{3} - 120 \, B b^{4} c^{2} d^{2} e + 192 \, A b^{3} c^{3} d^{2} e + 84 \, B b^{5} c d e^{2} - 120 \, A b^{4} c^{2} d e^{2} - 21 \, B b^{6} e^{3} + 28 \, A b^{5} c e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{11}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*B*x*e^3 + (36*B*c^5*d*e^2 + B*b*c^4*e^3 + 12*A*c^5*e^3)/c^5)*x + 3*(120*B*c^5*d^2*e + 12*B*b*c^4*d*e^2 + 120*A*c^5*d*e^2 - 3*B*b^2*c^3*e^3 + 4*A*b*c^4*e^3)/c^5)*x + (320*B*c^5*d^3 + 120*B*b*c^4*d^2*e + 960*A*c^5*d^2*e - 84*B*b^2*c^3*d*e^2 + 120*A*b*c^4*d*e^2 + 21*B*b^3*c^2*e^3 - 28*A*b^2*c^3*e^3)/c^5)*x + 5*(64*B*b*c^4*d^3 + 384*A*c^5*d^3 - 120*B*b^2*c^3*d^2*e + 192*A*b*c^4*d^2*e + 84*B*b^3*c^2*d*e^2 - 120*A*b^2*c^3*d*e^2 - 21*B*b^4*c*e^3 + 28*A*b^3*c^2*e^3)/c^5)*x - 15*(64*B*b^2*c^3*d^3 - 128*A*b*c^4*d^3 - 120*B*b^3*c^2*d^2*e + 192*A*b^2*c^3*d^2*e + 84*B*b^4*c*d*e^2 - 120*A*b^3*c^2*d*e^2 - 21*B*b^5*e^3 + 28*A*b^4*c*e^3)/c^5) - 1/1024*(64*B*b^3*c^3*d^3 - 128*A*b^2*c^4*d^3 - 120*B*b^4*c^2*d^2*e + 192*A*b^3*c^3*d^2*e + 84*B*b^5*c*d*e^2 - 120*A*b^4*c^2*d*e^2 - 21*B*b^6*e^3 + 28*A*b^5*c*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
1163,1,349,0,0.215734," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, B x e^{2} + \frac{20 \, B c^{4} d e + B b c^{3} e^{2} + 10 \, A c^{4} e^{2}}{c^{4}}\right)} x + \frac{80 \, B c^{4} d^{2} + 20 \, B b c^{3} d e + 160 \, A c^{4} d e - 7 \, B b^{2} c^{2} e^{2} + 10 \, A b c^{3} e^{2}}{c^{4}}\right)} x + \frac{5 \, {\left(16 \, B b c^{3} d^{2} + 96 \, A c^{4} d^{2} - 20 \, B b^{2} c^{2} d e + 32 \, A b c^{3} d e + 7 \, B b^{3} c e^{2} - 10 \, A b^{2} c^{2} e^{2}\right)}}{c^{4}}\right)} x - \frac{15 \, {\left(16 \, B b^{2} c^{2} d^{2} - 32 \, A b c^{3} d^{2} - 20 \, B b^{3} c d e + 32 \, A b^{2} c^{2} d e + 7 \, B b^{4} e^{2} - 10 \, A b^{3} c e^{2}\right)}}{c^{4}}\right)} - \frac{{\left(16 \, B b^{3} c^{2} d^{2} - 32 \, A b^{2} c^{3} d^{2} - 20 \, B b^{4} c d e + 32 \, A b^{3} c^{2} d e + 7 \, B b^{5} e^{2} - 10 \, A b^{4} c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x)*(2*(4*(6*(8*B*x*e^2 + (20*B*c^4*d*e + B*b*c^3*e^2 + 10*A*c^4*e^2)/c^4)*x + (80*B*c^4*d^2 + 20*B*b*c^3*d*e + 160*A*c^4*d*e - 7*B*b^2*c^2*e^2 + 10*A*b*c^3*e^2)/c^4)*x + 5*(16*B*b*c^3*d^2 + 96*A*c^4*d^2 - 20*B*b^2*c^2*d*e + 32*A*b*c^3*d*e + 7*B*b^3*c*e^2 - 10*A*b^2*c^2*e^2)/c^4)*x - 15*(16*B*b^2*c^2*d^2 - 32*A*b*c^3*d^2 - 20*B*b^3*c*d*e + 32*A*b^2*c^2*d*e + 7*B*b^4*e^2 - 10*A*b^3*c*e^2)/c^4) - 1/256*(16*B*b^3*c^2*d^2 - 32*A*b^2*c^3*d^2 - 20*B*b^4*c*d*e + 32*A*b^3*c^2*d*e + 7*B*b^5*e^2 - 10*A*b^4*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
1164,1,205,0,0.231658," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, B x e + \frac{8 \, B c^{3} d + B b c^{2} e + 8 \, A c^{3} e}{c^{3}}\right)} x + \frac{8 \, B b c^{2} d + 48 \, A c^{3} d - 5 \, B b^{2} c e + 8 \, A b c^{2} e}{c^{3}}\right)} x - \frac{3 \, {\left(8 \, B b^{2} c d - 16 \, A b c^{2} d - 5 \, B b^{3} e + 8 \, A b^{2} c e\right)}}{c^{3}}\right)} - \frac{{\left(8 \, B b^{3} c d - 16 \, A b^{2} c^{2} d - 5 \, B b^{4} e + 8 \, A b^{3} c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*B*x*e + (8*B*c^3*d + B*b*c^2*e + 8*A*c^3*e)/c^3)*x + (8*B*b*c^2*d + 48*A*c^3*d - 5*B*b^2*c*e + 8*A*b*c^2*e)/c^3)*x - 3*(8*B*b^2*c*d - 16*A*b*c^2*d - 5*B*b^3*e + 8*A*b^2*c*e)/c^3) - 1/128*(8*B*b^3*c*d - 16*A*b^2*c^2*d - 5*B*b^4*e + 8*A*b^3*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
1165,1,102,0,0.270756," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, B x + \frac{B b c + 6 \, A c^{2}}{c^{2}}\right)} x - \frac{3 \, {\left(B b^{2} - 2 \, A b c\right)}}{c^{2}}\right)} - \frac{{\left(B b^{3} - 2 \, A b^{2} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*(4*B*x + (B*b*c + 6*A*c^2)/c^2)*x - 3*(B*b^2 - 2*A*b*c)/c^2) - 1/16*(B*b^3 - 2*A*b^2*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
1166,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1167,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,1,819,0,0.397498," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","-B \sqrt{c} e^{\left(-3\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b \right|}\right) - \frac{{\left(8 \, B c^{2} d^{3} - 12 \, B b c d^{2} e + 3 \, B b^{2} d e^{2} + A b^{2} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{4 \, {\left(c d^{2} e^{3} - b d e^{4}\right)} \sqrt{-c d^{2} + b d e}} - \frac{16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{\frac{5}{2}} d^{3} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B c^{3} d^{4} - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{2} d^{3} e - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A c^{3} d^{3} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b c^{\frac{5}{2}} d^{4} - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c^{\frac{3}{2}} d^{2} e^{2} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{\frac{5}{2}} d^{2} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c^{\frac{3}{2}} d^{3} e - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b c^{\frac{5}{2}} d^{3} e + 6 \, B b^{2} c^{2} d^{4} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c d^{2} e^{2} - 5 \, B b^{3} c d^{3} e - 2 \, A b^{2} c^{2} d^{3} e + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} \sqrt{c} d e^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{\frac{3}{2}} d e^{3} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} \sqrt{c} d^{2} e^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{\frac{3}{2}} d^{2} e^{2} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c d e^{3} + A b^{3} c d^{2} e^{2} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} \sqrt{c} e^{4} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} \sqrt{c} d e^{3}}{4 \, {\left(c^{\frac{3}{2}} d^{2} e^{3} - b \sqrt{c} d e^{4}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"-B*sqrt(c)*e^(-3)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b)) - 1/4*(8*B*c^2*d^3 - 12*B*b*c*d^2*e + 3*B*b^2*d*e^2 + A*b^2*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c*d^2*e^3 - b*d*e^4)*sqrt(-c*d^2 + b*d*e)) - 1/4*(16*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^(5/2)*d^3*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*c^3*d^4 - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^2*d^3*e - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*c^3*d^3*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b*c^(5/2)*d^4 - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c^(3/2)*d^2*e^2 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^(5/2)*d^2*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c^(3/2)*d^3*e - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b*c^(5/2)*d^3*e + 6*B*b^2*c^2*d^4 - (sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c*d^2*e^2 - 5*B*b^3*c*d^3*e - 2*A*b^2*c^2*d^3*e + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*sqrt(c)*d*e^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^(3/2)*d*e^3 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*sqrt(c)*d^2*e^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^(3/2)*d^2*e^2 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c*d*e^3 + A*b^3*c*d^2*e^2 - (sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*sqrt(c)*e^4 + (sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*sqrt(c)*d*e^3)/((c^(3/2)*d^2*e^3 - b*sqrt(c)*d*e^4)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2)","B",0
1169,1,1555,0,0.343692," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","\frac{{\left(B b^{3} d - 2 \, A b^{2} c d + A b^{3} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{8 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e}} + \frac{96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B c^{\frac{7}{2}} d^{5} e + 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{4} d^{6} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B c^{3} d^{4} e^{2} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c^{3} d^{5} e + 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{4} d^{5} e + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{\frac{7}{2}} d^{6} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c^{\frac{5}{2}} d^{4} e^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A c^{\frac{7}{2}} d^{4} e^{2} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c^{\frac{5}{2}} d^{5} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{\frac{7}{2}} d^{5} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c^{3} d^{6} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{2} d^{3} e^{3} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c^{2} d^{4} e^{2} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{3} d^{4} e^{2} - 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} c^{2} d^{5} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{3} d^{5} e + 8 \, B b^{3} c^{\frac{5}{2}} d^{6} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{\frac{5}{2}} d^{3} e^{3} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c^{\frac{3}{2}} d^{4} e^{2} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{\frac{5}{2}} d^{4} e^{2} - 14 \, B b^{4} c^{\frac{3}{2}} d^{5} e + 4 \, A b^{3} c^{\frac{5}{2}} d^{5} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c d^{2} e^{4} + 58 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c d^{3} e^{3} - 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{2} d^{3} e^{3} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} c d^{4} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c^{2} d^{4} e^{2} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} \sqrt{c} d^{2} e^{4} + 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{\frac{3}{2}} d^{2} e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} \sqrt{c} d^{3} e^{3} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c^{\frac{3}{2}} d^{3} e^{3} + 3 \, B b^{5} \sqrt{c} d^{4} e^{2} - 4 \, A b^{4} c^{\frac{3}{2}} d^{4} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} d e^{5} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c d e^{5} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} d^{2} e^{4} + 74 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c d^{2} e^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{5} d^{3} e^{3} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} c d^{3} e^{3} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} \sqrt{c} d e^{5} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} \sqrt{c} d^{2} e^{4} + 3 \, A b^{5} \sqrt{c} d^{3} e^{3} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} e^{6} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} d e^{5} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} d^{2} e^{4}}{24 \, {\left(c^{2} d^{4} e^{3} - 2 \, b c d^{3} e^{4} + b^{2} d^{2} e^{5}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{3}}"," ",0,"1/8*(B*b^3*d - 2*A*b^2*c*d + A*b^3*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*sqrt(-c*d^2 + b*d*e)) + 1/24*(96*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*c^(7/2)*d^5*e + 64*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^4*d^6 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*c^3*d^4*e^2 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c^3*d^5*e + 32*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^4*d^5*e + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^(7/2)*d^6 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c^(5/2)*d^4*e^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*c^(7/2)*d^4*e^2 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c^(5/2)*d^5*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^(7/2)*d^5*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c^3*d^6 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^2*d^3*e^3 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c^2*d^4*e^2 + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^3*d^4*e^2 - 84*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*c^2*d^5*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^3*d^5*e + 8*B*b^3*c^(5/2)*d^6 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^(5/2)*d^3*e^3 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c^(3/2)*d^4*e^2 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^(5/2)*d^4*e^2 - 14*B*b^4*c^(3/2)*d^5*e + 4*A*b^3*c^(5/2)*d^5*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c*d^2*e^4 + 58*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c*d^3*e^3 - 84*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^2*d^3*e^3 + 18*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*c*d^4*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c^2*d^4*e^2 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*sqrt(c)*d^2*e^4 + 78*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^(3/2)*d^2*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*sqrt(c)*d^3*e^3 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c^(3/2)*d^3*e^3 + 3*B*b^5*sqrt(c)*d^4*e^2 - 4*A*b^4*c^(3/2)*d^4*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*d*e^5 + 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c*d*e^5 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*d^2*e^4 + 74*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c*d^2*e^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^5*d^3*e^3 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*c*d^3*e^3 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*sqrt(c)*d*e^5 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*sqrt(c)*d^2*e^4 + 3*A*b^5*sqrt(c)*d^3*e^3 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*e^6 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*d*e^5 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*d^2*e^4)/((c^2*d^4*e^3 - 2*b*c*d^3*e^4 + b^2*d^2*e^5)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^3)","B",0
1170,1,1720,0,1.368123," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{384} \, {\left(2 \, \sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} {\left(\frac{2 \, {\left(\frac{4 \, {\left(\frac{10 \, B c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 29 \, B b c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, A c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 28 \, B b^{2} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, A b c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 9 \, B b^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 4 \, A b^{2} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + A b^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{14} - 3 \, b c^{2} d^{5} e^{15} + 3 \, b^{2} c d^{4} e^{16} - b^{3} d^{3} e^{17}} - \frac{6 \, {\left(B c^{3} d^{7} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, B b c^{2} d^{6} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A c^{3} d^{6} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, B b^{2} c d^{5} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, A b c^{2} d^{5} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - B b^{3} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, A b^{2} c d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + A b^{3} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(c^{3} d^{6} e^{14} - 3 \, b c^{2} d^{5} e^{15} + 3 \, b^{2} c d^{4} e^{16} - b^{3} d^{3} e^{17}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{8 \, B c^{3} d^{5} e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, B b c^{2} d^{4} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 8 \, A c^{3} d^{4} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 19 \, B b^{2} c d^{3} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A b c^{2} d^{3} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, B b^{3} d^{2} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 13 \, A b^{2} c d^{2} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, A b^{3} d e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{14} - 3 \, b c^{2} d^{5} e^{15} + 3 \, b^{2} c d^{4} e^{16} - b^{3} d^{3} e^{17}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{16 \, B c^{3} d^{4} e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 40 \, B b c^{2} d^{3} e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, A c^{3} d^{3} e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 18 \, B b^{2} c d^{2} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, A b c^{2} d^{2} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 9 \, B b^{3} d e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 38 \, A b^{2} c d e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 15 \, A b^{3} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{14} - 3 \, b c^{2} d^{5} e^{15} + 3 \, b^{2} c d^{4} e^{16} - b^{3} d^{3} e^{17}}\right)} + \frac{{\left(32 \, \sqrt{c d^{2} - b d e} B c^{\frac{7}{2}} d^{4} - 80 \, \sqrt{c d^{2} - b d e} B b c^{\frac{5}{2}} d^{3} e + 32 \, \sqrt{c d^{2} - b d e} A c^{\frac{7}{2}} d^{3} e - 24 \, B b^{3} c d^{2} e^{3} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 48 \, A b^{2} c^{2} d^{2} e^{3} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 36 \, \sqrt{c d^{2} - b d e} B b^{2} c^{\frac{3}{2}} d^{2} e^{2} - 48 \, \sqrt{c d^{2} - b d e} A b c^{\frac{5}{2}} d^{2} e^{2} + 9 \, B b^{4} d e^{4} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 48 \, A b^{3} c d e^{4} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 18 \, \sqrt{c d^{2} - b d e} B b^{3} \sqrt{c} d e^{3} + 76 \, \sqrt{c d^{2} - b d e} A b^{2} c^{\frac{3}{2}} d e^{3} + 15 \, A b^{4} e^{5} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 30 \, \sqrt{c d^{2} - b d e} A b^{3} \sqrt{c} e^{4}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e} c^{3} d^{6} e^{5} - 3 \, \sqrt{c d^{2} - b d e} b c^{2} d^{5} e^{6} + 3 \, \sqrt{c d^{2} - b d e} b^{2} c d^{4} e^{7} - \sqrt{c d^{2} - b d e} b^{3} d^{3} e^{8}} + \frac{3 \, {\left(8 \, B b^{3} c d^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A b^{2} c^{2} d^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, B b^{4} d e \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, A b^{3} c d e \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, A b^{4} e^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\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)} \sqrt{c d^{2} - b d e}}\right)} e^{2}"," ",0,"-1/384*(2*sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)*(2*(4*((10*B*c^3*d^6*e^11*sgn(1/(x*e + d)) - 29*B*b*c^2*d^5*e^12*sgn(1/(x*e + d)) - 2*A*c^3*d^5*e^12*sgn(1/(x*e + d)) + 28*B*b^2*c*d^4*e^13*sgn(1/(x*e + d)) + 5*A*b*c^2*d^4*e^13*sgn(1/(x*e + d)) - 9*B*b^3*d^3*e^14*sgn(1/(x*e + d)) - 4*A*b^2*c*d^3*e^14*sgn(1/(x*e + d)) + A*b^3*d^2*e^15*sgn(1/(x*e + d)))/(c^3*d^6*e^14 - 3*b*c^2*d^5*e^15 + 3*b^2*c*d^4*e^16 - b^3*d^3*e^17) - 6*(B*c^3*d^7*e^12*sgn(1/(x*e + d)) - 3*B*b*c^2*d^6*e^13*sgn(1/(x*e + d)) - A*c^3*d^6*e^13*sgn(1/(x*e + d)) + 3*B*b^2*c*d^5*e^14*sgn(1/(x*e + d)) + 3*A*b*c^2*d^5*e^14*sgn(1/(x*e + d)) - B*b^3*d^4*e^15*sgn(1/(x*e + d)) - 3*A*b^2*c*d^4*e^15*sgn(1/(x*e + d)) + A*b^3*d^3*e^16*sgn(1/(x*e + d)))*e^(-1)/((c^3*d^6*e^14 - 3*b*c^2*d^5*e^15 + 3*b^2*c*d^4*e^16 - b^3*d^3*e^17)*(x*e + d)))*e^(-1)/(x*e + d) - (8*B*c^3*d^5*e^10*sgn(1/(x*e + d)) - 24*B*b*c^2*d^4*e^11*sgn(1/(x*e + d)) + 8*A*c^3*d^4*e^11*sgn(1/(x*e + d)) + 19*B*b^2*c*d^3*e^12*sgn(1/(x*e + d)) - 16*A*b*c^2*d^3*e^12*sgn(1/(x*e + d)) - 3*B*b^3*d^2*e^13*sgn(1/(x*e + d)) + 13*A*b^2*c*d^2*e^13*sgn(1/(x*e + d)) - 5*A*b^3*d*e^14*sgn(1/(x*e + d)))/(c^3*d^6*e^14 - 3*b*c^2*d^5*e^15 + 3*b^2*c*d^4*e^16 - b^3*d^3*e^17))*e^(-1)/(x*e + d) - (16*B*c^3*d^4*e^9*sgn(1/(x*e + d)) - 40*B*b*c^2*d^3*e^10*sgn(1/(x*e + d)) + 16*A*c^3*d^3*e^10*sgn(1/(x*e + d)) + 18*B*b^2*c*d^2*e^11*sgn(1/(x*e + d)) - 24*A*b*c^2*d^2*e^11*sgn(1/(x*e + d)) - 9*B*b^3*d*e^12*sgn(1/(x*e + d)) + 38*A*b^2*c*d*e^12*sgn(1/(x*e + d)) - 15*A*b^3*e^13*sgn(1/(x*e + d)))/(c^3*d^6*e^14 - 3*b*c^2*d^5*e^15 + 3*b^2*c*d^4*e^16 - b^3*d^3*e^17)) + (32*sqrt(c*d^2 - b*d*e)*B*c^(7/2)*d^4 - 80*sqrt(c*d^2 - b*d*e)*B*b*c^(5/2)*d^3*e + 32*sqrt(c*d^2 - b*d*e)*A*c^(7/2)*d^3*e - 24*B*b^3*c*d^2*e^3*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 48*A*b^2*c^2*d^2*e^3*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 36*sqrt(c*d^2 - b*d*e)*B*b^2*c^(3/2)*d^2*e^2 - 48*sqrt(c*d^2 - b*d*e)*A*b*c^(5/2)*d^2*e^2 + 9*B*b^4*d*e^4*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 48*A*b^3*c*d*e^4*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 18*sqrt(c*d^2 - b*d*e)*B*b^3*sqrt(c)*d*e^3 + 76*sqrt(c*d^2 - b*d*e)*A*b^2*c^(3/2)*d*e^3 + 15*A*b^4*e^5*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 30*sqrt(c*d^2 - b*d*e)*A*b^3*sqrt(c)*e^4)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*c^3*d^6*e^5 - 3*sqrt(c*d^2 - b*d*e)*b*c^2*d^5*e^6 + 3*sqrt(c*d^2 - b*d*e)*b^2*c*d^4*e^7 - sqrt(c*d^2 - b*d*e)*b^3*d^3*e^8) + 3*(8*B*b^3*c*d^2*sgn(1/(x*e + d)) - 16*A*b^2*c^2*d^2*sgn(1/(x*e + d)) - 3*B*b^4*d*e*sgn(1/(x*e + d)) + 16*A*b^3*c*d*e*sgn(1/(x*e + d)) - 5*A*b^4*e^2*sgn(1/(x*e + d)))*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((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)*sqrt(c*d^2 - b*d*e)))*e^2","B",0
1171,1,4102,0,0.543936," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","\frac{{\left(16 \, B b^{3} c^{2} d^{3} - 32 \, A b^{2} c^{3} d^{3} - 12 \, B b^{4} c d^{2} e + 48 \, A b^{3} c^{2} d^{2} e + 3 \, B b^{5} d e^{2} - 30 \, A b^{4} c d e^{2} + 7 \, A b^{5} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{128 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} \sqrt{-c d^{2} + b d e}} + \frac{5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B c^{\frac{13}{2}} d^{9} e + 2048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B c^{7} d^{10} + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B c^{6} d^{8} e^{2} + 3584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{6} d^{9} e + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{7} d^{9} e + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c^{\frac{13}{2}} d^{10} - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b c^{\frac{11}{2}} d^{8} e^{2} + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A c^{\frac{13}{2}} d^{8} e^{2} - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c^{\frac{11}{2}} d^{9} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{\frac{13}{2}} d^{9} e + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c^{6} d^{10} - 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b c^{5} d^{7} e^{3} - 24832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{5} d^{8} e^{2} + 9216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{6} d^{8} e^{2} - 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c^{5} d^{9} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{6} d^{9} e + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c^{\frac{11}{2}} d^{10} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{2} c^{\frac{9}{2}} d^{7} e^{3} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b c^{\frac{11}{2}} d^{7} e^{3} - 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c^{\frac{9}{2}} d^{8} e^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{\frac{11}{2}} d^{8} e^{2} - 8000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} c^{\frac{9}{2}} d^{9} e + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c^{\frac{11}{2}} d^{9} e + 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} c^{5} d^{10} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{2} c^{4} d^{6} e^{4} + 13760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} c^{4} d^{7} e^{3} - 50048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{5} d^{7} e^{3} + 3200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} c^{4} d^{8} e^{2} - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{5} d^{8} e^{2} - 2080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{5} c^{4} d^{9} e + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} c^{5} d^{9} e + 64 \, B b^{5} c^{\frac{9}{2}} d^{10} + 36320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{3} c^{\frac{7}{2}} d^{6} e^{4} + 70720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{2} c^{\frac{9}{2}} d^{6} e^{4} + 15520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{4} c^{\frac{7}{2}} d^{7} e^{3} - 17600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c^{\frac{9}{2}} d^{7} e^{3} + 4720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{5} c^{\frac{7}{2}} d^{8} e^{2} - 7200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c^{\frac{9}{2}} d^{8} e^{2} - 208 \, B b^{6} c^{\frac{7}{2}} d^{9} e + 96 \, A b^{5} c^{\frac{9}{2}} d^{9} e - 28000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{3} c^{3} d^{5} e^{5} + 15040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{2} c^{4} d^{5} e^{5} + 2000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{4} c^{3} d^{6} e^{4} + 129280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} c^{4} d^{6} e^{4} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{5} c^{3} d^{7} e^{3} + 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} c^{4} d^{7} e^{3} + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{6} c^{3} d^{8} e^{2} - 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} c^{4} d^{8} e^{2} - 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{3} c^{\frac{5}{2}} d^{4} e^{6} + 4320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{2} c^{\frac{7}{2}} d^{4} e^{6} - 39560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{4} c^{\frac{5}{2}} d^{5} e^{5} - 52000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{3} c^{\frac{7}{2}} d^{5} e^{5} - 14360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{5} c^{\frac{5}{2}} d^{6} e^{4} + 81920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{4} c^{\frac{7}{2}} d^{6} e^{4} - 3120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{6} c^{\frac{5}{2}} d^{7} e^{3} + 13760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{5} c^{\frac{7}{2}} d^{7} e^{3} + 144 \, B b^{7} c^{\frac{5}{2}} d^{8} e^{2} - 192 \, A b^{6} c^{\frac{7}{2}} d^{8} e^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{3} c^{2} d^{3} e^{7} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{2} c^{3} d^{3} e^{7} + 9640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{4} c^{2} d^{4} e^{6} - 20320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{3} c^{3} d^{4} e^{6} - 17284 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{5} c^{2} d^{5} e^{5} - 120680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{4} c^{3} d^{5} e^{5} - 6920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{6} c^{2} d^{6} e^{4} + 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{5} c^{3} d^{6} e^{4} - 1260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{7} c^{2} d^{7} e^{3} + 4280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{6} c^{3} d^{7} e^{3} + 1620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{4} c^{\frac{3}{2}} d^{3} e^{7} - 6480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{3} c^{\frac{5}{2}} d^{3} e^{7} + 15090 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{5} c^{\frac{3}{2}} d^{4} e^{6} + 7260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{4} c^{\frac{5}{2}} d^{4} e^{6} + 330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{6} c^{\frac{3}{2}} d^{5} e^{5} - 85780 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{5} c^{\frac{5}{2}} d^{5} e^{5} - 570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{7} c^{\frac{3}{2}} d^{6} e^{4} - 6340 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{6} c^{\frac{5}{2}} d^{6} e^{4} - 150 \, B b^{8} c^{\frac{3}{2}} d^{7} e^{3} + 476 \, A b^{7} c^{\frac{5}{2}} d^{7} e^{3} + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{4} c d^{2} e^{8} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{3} c^{2} d^{2} e^{8} - 570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{5} c d^{3} e^{7} + 10740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{4} c^{2} d^{3} e^{7} + 7878 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{6} c d^{4} e^{6} + 47944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{5} c^{2} d^{4} e^{6} + 2370 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{7} c d^{5} e^{5} - 25220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{6} c^{2} d^{5} e^{5} + 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{8} c d^{6} e^{4} - 3080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{7} c^{2} d^{6} e^{4} - 405 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{5} \sqrt{c} d^{2} e^{8} + 4050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{4} c^{\frac{3}{2}} d^{2} e^{8} - 1470 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{6} \sqrt{c} d^{3} e^{7} + 9310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{5} c^{\frac{3}{2}} d^{3} e^{7} + 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{7} \sqrt{c} d^{4} e^{6} + 35330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{6} c^{\frac{3}{2}} d^{4} e^{6} + 630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{8} \sqrt{c} d^{5} e^{5} - 1750 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{7} c^{\frac{3}{2}} d^{5} e^{5} + 45 \, B b^{9} \sqrt{c} d^{6} e^{4} - 380 \, A b^{8} c^{\frac{3}{2}} d^{6} e^{4} - 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{5} d e^{9} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{4} c d e^{9} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{6} d^{2} e^{8} - 1190 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{5} c d^{2} e^{8} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{7} d^{3} e^{7} - 4658 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{6} c d^{3} e^{7} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{8} d^{4} e^{6} + 10510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{7} c d^{4} e^{6} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{9} d^{5} e^{5} + 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{8} c d^{5} e^{5} - 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{5} \sqrt{c} d e^{9} - 3430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{6} \sqrt{c} d^{2} e^{8} - 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{7} \sqrt{c} d^{3} e^{7} + 1470 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{8} \sqrt{c} d^{4} e^{6} + 105 \, A b^{9} \sqrt{c} d^{5} e^{5} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{5} e^{10} - 490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{6} d e^{9} - 896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{7} d^{2} e^{8} - 790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{8} d^{3} e^{7} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{9} d^{4} e^{6}}{1920 \, {\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)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{5}}"," ",0,"1/128*(16*B*b^3*c^2*d^3 - 32*A*b^2*c^3*d^3 - 12*B*b^4*c*d^2*e + 48*A*b^3*c^2*d^2*e + 3*B*b^5*d*e^2 - 30*A*b^4*c*d*e^2 + 7*A*b^5*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*sqrt(-c*d^2 + b*d*e)) + 1/1920*(5120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*c^(13/2)*d^9*e + 2048*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*c^7*d^10 + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*c^6*d^8*e^2 + 3584*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^6*d^9*e + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^7*d^9*e + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c^(13/2)*d^10 - 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b*c^(11/2)*d^8*e^2 + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*c^(13/2)*d^8*e^2 - 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c^(11/2)*d^9*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^(13/2)*d^9*e + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c^6*d^10 - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b*c^5*d^7*e^3 - 24832*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^5*d^8*e^2 + 9216*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^6*d^8*e^2 - 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c^5*d^9*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^6*d^9*e + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c^(11/2)*d^10 - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^2*c^(9/2)*d^7*e^3 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b*c^(11/2)*d^7*e^3 - 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c^(9/2)*d^8*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^(11/2)*d^8*e^2 - 8000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*c^(9/2)*d^9*e + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c^(11/2)*d^9*e + 640*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*c^5*d^10 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^2*c^4*d^6*e^4 + 13760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*c^4*d^7*e^3 - 50048*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^5*d^7*e^3 + 3200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*c^4*d^8*e^2 - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^5*d^8*e^2 - 2080*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^5*c^4*d^9*e + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*c^5*d^9*e + 64*B*b^5*c^(9/2)*d^10 + 36320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^3*c^(7/2)*d^6*e^4 + 70720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^2*c^(9/2)*d^6*e^4 + 15520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^4*c^(7/2)*d^7*e^3 - 17600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c^(9/2)*d^7*e^3 + 4720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^5*c^(7/2)*d^8*e^2 - 7200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c^(9/2)*d^8*e^2 - 208*B*b^6*c^(7/2)*d^9*e + 96*A*b^5*c^(9/2)*d^9*e - 28000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^3*c^3*d^5*e^5 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^2*c^4*d^5*e^5 + 2000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^4*c^3*d^6*e^4 + 129280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*c^4*d^6*e^4 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^5*c^3*d^7*e^3 + 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*c^4*d^7*e^3 + 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^6*c^3*d^8*e^2 - 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*c^4*d^8*e^2 - 2160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^3*c^(5/2)*d^4*e^6 + 4320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^2*c^(7/2)*d^4*e^6 - 39560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^4*c^(5/2)*d^5*e^5 - 52000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^3*c^(7/2)*d^5*e^5 - 14360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^5*c^(5/2)*d^6*e^4 + 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^4*c^(7/2)*d^6*e^4 - 3120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^6*c^(5/2)*d^7*e^3 + 13760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^5*c^(7/2)*d^7*e^3 + 144*B*b^7*c^(5/2)*d^8*e^2 - 192*A*b^6*c^(7/2)*d^8*e^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^3*c^2*d^3*e^7 + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^2*c^3*d^3*e^7 + 9640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^4*c^2*d^4*e^6 - 20320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^3*c^3*d^4*e^6 - 17284*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^5*c^2*d^5*e^5 - 120680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^4*c^3*d^5*e^5 - 6920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^6*c^2*d^6*e^4 + 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^5*c^3*d^6*e^4 - 1260*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^7*c^2*d^7*e^3 + 4280*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^6*c^3*d^7*e^3 + 1620*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^4*c^(3/2)*d^3*e^7 - 6480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^3*c^(5/2)*d^3*e^7 + 15090*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^5*c^(3/2)*d^4*e^6 + 7260*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^4*c^(5/2)*d^4*e^6 + 330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^6*c^(3/2)*d^5*e^5 - 85780*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^5*c^(5/2)*d^5*e^5 - 570*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^7*c^(3/2)*d^6*e^4 - 6340*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^6*c^(5/2)*d^6*e^4 - 150*B*b^8*c^(3/2)*d^7*e^3 + 476*A*b^7*c^(5/2)*d^7*e^3 + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^4*c*d^2*e^8 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^3*c^2*d^2*e^8 - 570*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^5*c*d^3*e^7 + 10740*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^4*c^2*d^3*e^7 + 7878*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^6*c*d^4*e^6 + 47944*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^5*c^2*d^4*e^6 + 2370*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^7*c*d^5*e^5 - 25220*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^6*c^2*d^5*e^5 + 270*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^8*c*d^6*e^4 - 3080*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^7*c^2*d^6*e^4 - 405*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^5*sqrt(c)*d^2*e^8 + 4050*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^4*c^(3/2)*d^2*e^8 - 1470*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^6*sqrt(c)*d^3*e^7 + 9310*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^5*c^(3/2)*d^3*e^7 + 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^7*sqrt(c)*d^4*e^6 + 35330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^6*c^(3/2)*d^4*e^6 + 630*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^8*sqrt(c)*d^5*e^5 - 1750*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^7*c^(3/2)*d^5*e^5 + 45*B*b^9*sqrt(c)*d^6*e^4 - 380*A*b^8*c^(3/2)*d^6*e^4 - 45*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^5*d*e^9 + 450*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^4*c*d*e^9 - 210*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^6*d^2*e^8 - 1190*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^5*c*d^2*e^8 - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^7*d^3*e^7 - 4658*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^6*c*d^3*e^7 + 210*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^8*d^4*e^6 + 10510*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^7*c*d^4*e^6 + 45*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^9*d^5*e^5 + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^8*c*d^5*e^5 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^5*sqrt(c)*d*e^9 - 3430*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^6*sqrt(c)*d^2*e^8 - 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^7*sqrt(c)*d^3*e^7 + 1470*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^8*sqrt(c)*d^4*e^6 + 105*A*b^9*sqrt(c)*d^5*e^5 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^5*e^10 - 490*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^6*d*e^9 - 896*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^7*d^2*e^8 - 790*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^8*d^3*e^7 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^9*d^4*e^6)/((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)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^5)","B",0
1172,1,518,0,0.249158," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{107520} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, B c x e^{2} + \frac{28 \, B c^{7} d e + 15 \, B b c^{6} e^{2} + 14 \, A c^{7} e^{2}}{c^{6}}\right)} x + \frac{168 \, B c^{7} d^{2} + 364 \, B b c^{6} d e + 336 \, A c^{7} d e + 3 \, B b^{2} c^{5} e^{2} + 182 \, A b c^{6} e^{2}}{c^{6}}\right)} x + \frac{3 \, {\left(616 \, B b c^{6} d^{2} + 560 \, A c^{7} d^{2} + 28 \, B b^{2} c^{5} d e + 1232 \, A b c^{6} d e - 9 \, B b^{3} c^{4} e^{2} + 14 \, A b^{2} c^{5} e^{2}\right)}}{c^{6}}\right)} x + \frac{7 \, {\left(24 \, B b^{2} c^{5} d^{2} + 720 \, A b c^{6} d^{2} - 28 \, B b^{3} c^{4} d e + 48 \, A b^{2} c^{5} d e + 9 \, B b^{4} c^{3} e^{2} - 14 \, A b^{3} c^{4} e^{2}\right)}}{c^{6}}\right)} x - \frac{35 \, {\left(24 \, B b^{3} c^{4} d^{2} - 48 \, A b^{2} c^{5} d^{2} - 28 \, B b^{4} c^{3} d e + 48 \, A b^{3} c^{4} d e + 9 \, B b^{5} c^{2} e^{2} - 14 \, A b^{4} c^{3} e^{2}\right)}}{c^{6}}\right)} x + \frac{105 \, {\left(24 \, B b^{4} c^{3} d^{2} - 48 \, A b^{3} c^{4} d^{2} - 28 \, B b^{5} c^{2} d e + 48 \, A b^{4} c^{3} d e + 9 \, B b^{6} c e^{2} - 14 \, A b^{5} c^{2} e^{2}\right)}}{c^{6}}\right)} + \frac{{\left(24 \, B b^{5} c^{2} d^{2} - 48 \, A b^{4} c^{3} d^{2} - 28 \, B b^{6} c d e + 48 \, A b^{5} c^{2} d e + 9 \, B b^{7} e^{2} - 14 \, A b^{6} c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{11}{2}}}"," ",0,"1/107520*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*(12*B*c*x*e^2 + (28*B*c^7*d*e + 15*B*b*c^6*e^2 + 14*A*c^7*e^2)/c^6)*x + (168*B*c^7*d^2 + 364*B*b*c^6*d*e + 336*A*c^7*d*e + 3*B*b^2*c^5*e^2 + 182*A*b*c^6*e^2)/c^6)*x + 3*(616*B*b*c^6*d^2 + 560*A*c^7*d^2 + 28*B*b^2*c^5*d*e + 1232*A*b*c^6*d*e - 9*B*b^3*c^4*e^2 + 14*A*b^2*c^5*e^2)/c^6)*x + 7*(24*B*b^2*c^5*d^2 + 720*A*b*c^6*d^2 - 28*B*b^3*c^4*d*e + 48*A*b^2*c^5*d*e + 9*B*b^4*c^3*e^2 - 14*A*b^3*c^4*e^2)/c^6)*x - 35*(24*B*b^3*c^4*d^2 - 48*A*b^2*c^5*d^2 - 28*B*b^4*c^3*d*e + 48*A*b^3*c^4*d*e + 9*B*b^5*c^2*e^2 - 14*A*b^4*c^3*e^2)/c^6)*x + 105*(24*B*b^4*c^3*d^2 - 48*A*b^3*c^4*d^2 - 28*B*b^5*c^2*d*e + 48*A*b^4*c^3*d*e + 9*B*b^6*c*e^2 - 14*A*b^5*c^2*e^2)/c^6) + 1/2048*(24*B*b^5*c^2*d^2 - 48*A*b^4*c^3*d^2 - 28*B*b^6*c*d*e + 48*A*b^5*c^2*d*e + 9*B*b^7*e^2 - 14*A*b^6*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
1173,1,317,0,0.238729," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B c x e + \frac{12 \, B c^{6} d + 13 \, B b c^{5} e + 12 \, A c^{6} e}{c^{5}}\right)} x + \frac{3 \, {\left(44 \, B b c^{5} d + 40 \, A c^{6} d + B b^{2} c^{4} e + 44 \, A b c^{5} e\right)}}{c^{5}}\right)} x + \frac{12 \, B b^{2} c^{4} d + 360 \, A b c^{5} d - 7 \, B b^{3} c^{3} e + 12 \, A b^{2} c^{4} e}{c^{5}}\right)} x - \frac{5 \, {\left(12 \, B b^{3} c^{3} d - 24 \, A b^{2} c^{4} d - 7 \, B b^{4} c^{2} e + 12 \, A b^{3} c^{3} e\right)}}{c^{5}}\right)} x + \frac{15 \, {\left(12 \, B b^{4} c^{2} d - 24 \, A b^{3} c^{3} d - 7 \, B b^{5} c e + 12 \, A b^{4} c^{2} e\right)}}{c^{5}}\right)} + \frac{{\left(12 \, B b^{5} c d - 24 \, A b^{4} c^{2} d - 7 \, B b^{6} e + 12 \, A b^{5} c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*B*c*x*e + (12*B*c^6*d + 13*B*b*c^5*e + 12*A*c^6*e)/c^5)*x + 3*(44*B*b*c^5*d + 40*A*c^6*d + B*b^2*c^4*e + 44*A*b*c^5*e)/c^5)*x + (12*B*b^2*c^4*d + 360*A*b*c^5*d - 7*B*b^3*c^3*e + 12*A*b^2*c^4*e)/c^5)*x - 5*(12*B*b^3*c^3*d - 24*A*b^2*c^4*d - 7*B*b^4*c^2*e + 12*A*b^3*c^3*e)/c^5)*x + 15*(12*B*b^4*c^2*d - 24*A*b^3*c^3*d - 7*B*b^5*c*e + 12*A*b^4*c^2*e)/c^5) + 1/1024*(12*B*b^5*c*d - 24*A*b^4*c^2*d - 7*B*b^6*e + 12*A*b^5*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
1174,1,162,0,0.217857," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{640} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, B c x + \frac{11 \, B b c^{4} + 10 \, A c^{5}}{c^{4}}\right)} x + \frac{B b^{2} c^{3} + 30 \, A b c^{4}}{c^{4}}\right)} x - \frac{5 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)}}{c^{4}}\right)} x + \frac{15 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)}}{c^{4}}\right)} + \frac{3 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/640*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*B*c*x + (11*B*b*c^4 + 10*A*c^5)/c^4)*x + (B*b^2*c^3 + 30*A*b*c^4)/c^4)*x - 5*(B*b^3*c^2 - 2*A*b^2*c^3)/c^4)*x + 15*(B*b^4*c - 2*A*b^3*c^2)/c^4) + 3/256*(B*b^5 - 2*A*b^4*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
1175,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1176,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1177,1,936,0,0.521799," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, B c^{2} d^{3} - 20 \, B b c d^{2} e - 8 \, A c^{2} d^{2} e + 5 \, B b^{2} d e^{2} + 8 \, A b c d e^{2} - A b^{2} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right) e^{\left(-5\right)}}{4 \, \sqrt{-c d^{2} + b d e}} - \frac{3 \, {\left(16 \, B c^{2} d^{2} - 12 \, B b c d e - 8 \, A c^{2} d e + B b^{2} e^{2} + 4 \, A b c e^{2}\right)} e^{\left(-5\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b \right|}\right)}{8 \, \sqrt{c}} + \frac{1}{4} \, {\left(2 \, B c x e^{\left(-3\right)} - \frac{{\left(12 \, B c^{2} d e^{8} - 5 \, B b c e^{9} - 4 \, A c^{2} e^{9}\right)} e^{\left(-12\right)}}{c}\right)} \sqrt{c x^{2} + b x} - \frac{{\left(32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{\frac{5}{2}} d^{3} e + 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B c^{3} d^{4} - 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{2} d^{3} e - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A c^{3} d^{3} e + 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b c^{\frac{5}{2}} d^{4} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c^{\frac{3}{2}} d^{2} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{\frac{5}{2}} d^{2} e^{2} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c^{\frac{3}{2}} d^{3} e - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b c^{\frac{5}{2}} d^{3} e + 14 \, B b^{2} c^{2} d^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c d^{2} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{2} d^{2} e^{2} - 9 \, B b^{3} c d^{3} e - 10 \, A b^{2} c^{2} d^{3} e + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} \sqrt{c} d e^{3} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{\frac{3}{2}} d e^{3} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} \sqrt{c} d^{2} e^{2} + 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{\frac{3}{2}} d^{2} e^{2} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c d e^{3} + 5 \, A b^{3} c d^{2} e^{2} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} \sqrt{c} e^{4} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} \sqrt{c} d e^{3}\right)} e^{\left(-5\right)}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2} \sqrt{c}}"," ",0,"-3/4*(16*B*c^2*d^3 - 20*B*b*c*d^2*e - 8*A*c^2*d^2*e + 5*B*b^2*d*e^2 + 8*A*b*c*d*e^2 - A*b^2*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))*e^(-5)/sqrt(-c*d^2 + b*d*e) - 3/8*(16*B*c^2*d^2 - 12*B*b*c*d*e - 8*A*c^2*d*e + B*b^2*e^2 + 4*A*b*c*e^2)*e^(-5)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b))/sqrt(c) + 1/4*(2*B*c*x*e^(-3) - (12*B*c^2*d*e^8 - 5*B*b*c*e^9 - 4*A*c^2*e^9)*e^(-12)/c)*sqrt(c*x^2 + b*x) - 1/4*(32*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^(5/2)*d^3*e + 56*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*c^3*d^4 - 44*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^2*d^3*e - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*c^3*d^3*e + 56*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b*c^(5/2)*d^4 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c^(3/2)*d^2*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^(5/2)*d^2*e^2 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c^(3/2)*d^3*e - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b*c^(5/2)*d^3*e + 14*B*b^2*c^2*d^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c*d^2*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^2*d^2*e^2 - 9*B*b^3*c*d^3*e - 10*A*b^2*c^2*d^3*e + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*sqrt(c)*d*e^3 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^(3/2)*d*e^3 + 7*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*sqrt(c)*d^2*e^2 + 28*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^(3/2)*d^2*e^2 + (sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c*d*e^3 + 5*A*b^3*c*d^2*e^2 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*sqrt(c)*e^4 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*sqrt(c)*d*e^3)*e^(-5)/(((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2*sqrt(c))","B",0
1178,1,1788,0,0.667474," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","\sqrt{c x^{2} + b x} B c e^{\left(-4\right)} + \frac{{\left(8 \, B c^{2} d - 3 \, B b c e - 2 \, A c^{2} e\right)} e^{\left(-5\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b \right|}\right)}{2 \, \sqrt{c}} + \frac{{\left(64 \, B c^{3} d^{4} - 120 \, B b c^{2} d^{3} e - 16 \, A c^{3} d^{3} e + 60 \, B b^{2} c d^{2} e^{2} + 24 \, A b c^{2} d^{2} e^{2} - 5 \, B b^{3} d e^{3} - 6 \, A b^{2} c d e^{3} - A b^{3} e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{8 \, {\left(c d^{2} e^{5} - b d e^{6}\right)} \sqrt{-c d^{2} + b d e}} + \frac{960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B c^{4} d^{5} e + 832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{\frac{9}{2}} d^{6} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B c^{\frac{7}{2}} d^{4} e^{2} - 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c^{\frac{7}{2}} d^{5} e - 352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{\frac{9}{2}} d^{5} e + 1248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{4} d^{6} - 1464 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c^{3} d^{4} e^{2} - 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A c^{4} d^{4} e^{2} - 1656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c^{3} d^{5} e - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{4} d^{5} e + 624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c^{\frac{7}{2}} d^{6} - 504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{\frac{5}{2}} d^{3} e^{3} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{\frac{7}{2}} d^{3} e^{3} - 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c^{\frac{5}{2}} d^{4} e^{2} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{\frac{7}{2}} d^{4} e^{2} - 876 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} c^{\frac{5}{2}} d^{5} e - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{\frac{7}{2}} d^{5} e + 104 \, B b^{3} c^{3} d^{6} + 540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c^{2} d^{3} e^{3} + 504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{3} d^{3} e^{3} + 414 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c^{2} d^{4} e^{2} + 516 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{3} d^{4} e^{2} - 134 \, B b^{4} c^{2} d^{5} e - 44 \, A b^{3} c^{3} d^{5} e + 252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{\frac{3}{2}} d^{2} e^{4} + 216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{\frac{5}{2}} d^{2} e^{4} + 478 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c^{\frac{3}{2}} d^{3} e^{3} + 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{\frac{5}{2}} d^{3} e^{3} + 282 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} c^{\frac{3}{2}} d^{4} e^{2} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c^{\frac{5}{2}} d^{4} e^{2} - 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c d^{2} e^{4} - 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{2} d^{2} e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} c d^{3} e^{3} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c^{2} d^{3} e^{3} + 33 \, B b^{5} c d^{4} e^{2} + 44 \, A b^{4} c^{2} d^{4} e^{2} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} \sqrt{c} d e^{5} - 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{\frac{3}{2}} d e^{5} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} \sqrt{c} d^{2} e^{4} - 106 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{\frac{3}{2}} d^{2} e^{4} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{5} \sqrt{c} d^{3} e^{3} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} c^{\frac{3}{2}} d^{3} e^{3} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c d e^{5} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c d^{2} e^{4} - 3 \, A b^{5} c d^{3} e^{3} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} \sqrt{c} e^{6} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} \sqrt{c} d e^{5} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} \sqrt{c} d^{2} e^{4}}{24 \, {\left(c^{\frac{3}{2}} d^{2} e^{5} - b \sqrt{c} d e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{3}}"," ",0,"sqrt(c*x^2 + b*x)*B*c*e^(-4) + 1/2*(8*B*c^2*d - 3*B*b*c*e - 2*A*c^2*e)*e^(-5)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b))/sqrt(c) + 1/8*(64*B*c^3*d^4 - 120*B*b*c^2*d^3*e - 16*A*c^3*d^3*e + 60*B*b^2*c*d^2*e^2 + 24*A*b*c^2*d^2*e^2 - 5*B*b^3*d*e^3 - 6*A*b^2*c*d*e^3 - A*b^3*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c*d^2*e^5 - b*d*e^6)*sqrt(-c*d^2 + b*d*e)) + 1/24*(960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*c^4*d^5*e + 832*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^(9/2)*d^6 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*c^(7/2)*d^4*e^2 - 400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c^(7/2)*d^5*e - 352*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^(9/2)*d^5*e + 1248*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^4*d^6 - 1464*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c^3*d^4*e^2 - 432*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*c^4*d^4*e^2 - 1656*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c^3*d^5*e - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^4*d^5*e + 624*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c^(7/2)*d^6 - 504*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^(5/2)*d^3*e^3 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^(7/2)*d^3*e^3 - 840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c^(5/2)*d^4*e^2 + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^(7/2)*d^4*e^2 - 876*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*c^(5/2)*d^5*e - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^(7/2)*d^5*e + 104*B*b^3*c^3*d^6 + 540*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c^2*d^3*e^3 + 504*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^3*d^3*e^3 + 414*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c^2*d^4*e^2 + 516*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^3*d^4*e^2 - 134*B*b^4*c^2*d^5*e - 44*A*b^3*c^3*d^5*e + 252*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^(3/2)*d^2*e^4 + 216*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^(5/2)*d^2*e^4 + 478*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c^(3/2)*d^3*e^3 + 420*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^(5/2)*d^3*e^3 + 282*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*c^(3/2)*d^4*e^2 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c^(5/2)*d^4*e^2 - 21*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c*d^2*e^4 - 54*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^2*d^2*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*c*d^3*e^3 + 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c^2*d^3*e^3 + 33*B*b^5*c*d^4*e^2 + 44*A*b^4*c^2*d^4*e^2 - 33*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*sqrt(c)*d*e^5 - 78*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^(3/2)*d*e^5 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*sqrt(c)*d^2*e^4 - 106*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^(3/2)*d^2*e^4 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^5*sqrt(c)*d^3*e^3 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*c^(3/2)*d^3*e^3 - 33*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c*d*e^5 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c*d^2*e^4 - 3*A*b^5*c*d^3*e^3 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*sqrt(c)*e^6 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*sqrt(c)*d*e^5 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*sqrt(c)*d^2*e^4)/((c^(3/2)*d^2*e^5 - b*sqrt(c)*d*e^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^3)","B",0
1179,1,1255,0,1.190892," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{192} \, {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} {\left(\frac{2 \, {\left(\frac{4 \, {\left(\frac{26 \, B c^{4} d^{8} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 95 \, B b c^{3} d^{7} e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 18 \, A c^{4} d^{7} e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 129 \, B b^{2} c^{2} d^{6} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 63 \, A b c^{3} d^{6} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 77 \, B b^{3} c d^{5} e^{26} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 81 \, A b^{2} c^{2} d^{5} e^{26} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 17 \, B b^{4} d^{4} e^{27} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 45 \, A b^{3} c d^{4} e^{27} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 9 \, A b^{4} d^{3} e^{28} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{28} - 3 \, b c^{2} d^{5} e^{29} + 3 \, b^{2} c d^{4} e^{30} - b^{3} d^{3} e^{31}} - \frac{6 \, {\left(B c^{4} d^{9} e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 4 \, B b c^{3} d^{8} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A c^{4} d^{8} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 6 \, B b^{2} c^{2} d^{7} e^{26} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 4 \, A b c^{3} d^{7} e^{26} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 4 \, B b^{3} c d^{6} e^{27} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 6 \, A b^{2} c^{2} d^{6} e^{27} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + B b^{4} d^{5} e^{28} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 4 \, A b^{3} c d^{5} e^{28} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A b^{4} d^{4} e^{29} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(c^{3} d^{6} e^{28} - 3 \, b c^{2} d^{5} e^{29} + 3 \, b^{2} c d^{4} e^{30} - b^{3} d^{3} e^{31}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{184 \, B c^{4} d^{7} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 608 \, B b c^{3} d^{6} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 72 \, A c^{4} d^{6} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 723 \, B b^{2} c^{2} d^{5} e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 216 \, A b c^{3} d^{5} e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 358 \, B b^{3} c d^{4} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 219 \, A b^{2} c^{2} d^{4} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 59 \, B b^{4} d^{3} e^{26} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 78 \, A b^{3} c d^{3} e^{26} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, A b^{4} d^{2} e^{27} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{28} - 3 \, b c^{2} d^{5} e^{29} + 3 \, b^{2} c d^{4} e^{30} - b^{3} d^{3} e^{31}}\right)} e^{\left(-1\right)}}{x e + d} + \frac{400 \, B c^{4} d^{6} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 1176 \, B b c^{3} d^{5} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, A c^{4} d^{5} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 1158 \, B b^{2} c^{2} d^{4} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 120 \, A b c^{3} d^{4} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 397 \, B b^{3} c d^{3} e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 78 \, A b^{2} c^{2} d^{3} e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 15 \, B b^{4} d^{2} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, A b^{3} c d^{2} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 9 \, A b^{4} d e^{26} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{28} - 3 \, b c^{2} d^{5} e^{29} + 3 \, b^{2} c d^{4} e^{30} - b^{3} d^{3} e^{31}}\right)} - \frac{{\left(400 \, B c^{\frac{7}{2}} d^{4} - 776 \, B b c^{\frac{5}{2}} d^{3} e - 48 \, A c^{\frac{7}{2}} d^{3} e + 382 \, B b^{2} c^{\frac{3}{2}} d^{2} e^{2} + 72 \, A b c^{\frac{5}{2}} d^{2} e^{2} - 15 \, B b^{3} \sqrt{c} d e^{3} - 6 \, A b^{2} c^{\frac{3}{2}} d e^{3} - 9 \, A b^{3} \sqrt{c} e^{4}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{2} d^{4} e^{7} - 2 \, b c d^{3} e^{8} + b^{2} d^{2} e^{9}}\right)} e^{2}"," ",0,"-1/192*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)*(2*(4*((26*B*c^4*d^8*e^23*sgn(1/(x*e + d)) - 95*B*b*c^3*d^7*e^24*sgn(1/(x*e + d)) - 18*A*c^4*d^7*e^24*sgn(1/(x*e + d)) + 129*B*b^2*c^2*d^6*e^25*sgn(1/(x*e + d)) + 63*A*b*c^3*d^6*e^25*sgn(1/(x*e + d)) - 77*B*b^3*c*d^5*e^26*sgn(1/(x*e + d)) - 81*A*b^2*c^2*d^5*e^26*sgn(1/(x*e + d)) + 17*B*b^4*d^4*e^27*sgn(1/(x*e + d)) + 45*A*b^3*c*d^4*e^27*sgn(1/(x*e + d)) - 9*A*b^4*d^3*e^28*sgn(1/(x*e + d)))/(c^3*d^6*e^28 - 3*b*c^2*d^5*e^29 + 3*b^2*c*d^4*e^30 - b^3*d^3*e^31) - 6*(B*c^4*d^9*e^24*sgn(1/(x*e + d)) - 4*B*b*c^3*d^8*e^25*sgn(1/(x*e + d)) - A*c^4*d^8*e^25*sgn(1/(x*e + d)) + 6*B*b^2*c^2*d^7*e^26*sgn(1/(x*e + d)) + 4*A*b*c^3*d^7*e^26*sgn(1/(x*e + d)) - 4*B*b^3*c*d^6*e^27*sgn(1/(x*e + d)) - 6*A*b^2*c^2*d^6*e^27*sgn(1/(x*e + d)) + B*b^4*d^5*e^28*sgn(1/(x*e + d)) + 4*A*b^3*c*d^5*e^28*sgn(1/(x*e + d)) - A*b^4*d^4*e^29*sgn(1/(x*e + d)))*e^(-1)/((c^3*d^6*e^28 - 3*b*c^2*d^5*e^29 + 3*b^2*c*d^4*e^30 - b^3*d^3*e^31)*(x*e + d)))*e^(-1)/(x*e + d) - (184*B*c^4*d^7*e^22*sgn(1/(x*e + d)) - 608*B*b*c^3*d^6*e^23*sgn(1/(x*e + d)) - 72*A*c^4*d^6*e^23*sgn(1/(x*e + d)) + 723*B*b^2*c^2*d^5*e^24*sgn(1/(x*e + d)) + 216*A*b*c^3*d^5*e^24*sgn(1/(x*e + d)) - 358*B*b^3*c*d^4*e^25*sgn(1/(x*e + d)) - 219*A*b^2*c^2*d^4*e^25*sgn(1/(x*e + d)) + 59*B*b^4*d^3*e^26*sgn(1/(x*e + d)) + 78*A*b^3*c*d^3*e^26*sgn(1/(x*e + d)) - 3*A*b^4*d^2*e^27*sgn(1/(x*e + d)))/(c^3*d^6*e^28 - 3*b*c^2*d^5*e^29 + 3*b^2*c*d^4*e^30 - b^3*d^3*e^31))*e^(-1)/(x*e + d) + (400*B*c^4*d^6*e^21*sgn(1/(x*e + d)) - 1176*B*b*c^3*d^5*e^22*sgn(1/(x*e + d)) - 48*A*c^4*d^5*e^22*sgn(1/(x*e + d)) + 1158*B*b^2*c^2*d^4*e^23*sgn(1/(x*e + d)) + 120*A*b*c^3*d^4*e^23*sgn(1/(x*e + d)) - 397*B*b^3*c*d^3*e^24*sgn(1/(x*e + d)) - 78*A*b^2*c^2*d^3*e^24*sgn(1/(x*e + d)) + 15*B*b^4*d^2*e^25*sgn(1/(x*e + d)) - 3*A*b^3*c*d^2*e^25*sgn(1/(x*e + d)) + 9*A*b^4*d*e^26*sgn(1/(x*e + d)))/(c^3*d^6*e^28 - 3*b*c^2*d^5*e^29 + 3*b^2*c*d^4*e^30 - b^3*d^3*e^31)) - (400*B*c^(7/2)*d^4 - 776*B*b*c^(5/2)*d^3*e - 48*A*c^(7/2)*d^3*e + 382*B*b^2*c^(3/2)*d^2*e^2 + 72*A*b*c^(5/2)*d^2*e^2 - 15*B*b^3*sqrt(c)*d*e^3 - 6*A*b^2*c^(3/2)*d*e^3 - 9*A*b^3*sqrt(c)*e^4)*sgn(1/(x*e + d))/(c^2*d^4*e^7 - 2*b*c*d^3*e^8 + b^2*d^2*e^9))*e^2","B",0
1180,1,4214,0,0.704500," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{3 \, {\left(B b^{5} d - 2 \, A b^{4} c d + A b^{5} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{128 \, {\left(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}\right)} \sqrt{-c d^{2} + b d e}} + \frac{10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B c^{\frac{13}{2}} d^{9} e + 4096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B c^{7} d^{10} + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B c^{6} d^{8} e^{2} + 9728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{6} d^{9} e + 1024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{7} d^{9} e + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c^{\frac{13}{2}} d^{10} + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B c^{\frac{11}{2}} d^{7} e^{3} - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b c^{\frac{11}{2}} d^{8} e^{2} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A c^{\frac{13}{2}} d^{8} e^{2} - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c^{\frac{11}{2}} d^{9} e + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{\frac{13}{2}} d^{9} e + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c^{6} d^{10} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B c^{5} d^{6} e^{4} - 21760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b c^{5} d^{7} e^{3} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A c^{6} d^{7} e^{3} - 38144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{5} d^{8} e^{2} + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{6} d^{8} e^{2} - 21760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c^{5} d^{9} e + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{6} d^{9} e + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c^{\frac{11}{2}} d^{10} - 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b c^{\frac{9}{2}} d^{6} e^{4} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A c^{\frac{11}{2}} d^{6} e^{4} - 19200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{2} c^{\frac{9}{2}} d^{7} e^{3} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b c^{\frac{11}{2}} d^{7} e^{3} - 19200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c^{\frac{9}{2}} d^{8} e^{2} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{\frac{11}{2}} d^{8} e^{2} - 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} c^{\frac{9}{2}} d^{9} e + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c^{\frac{11}{2}} d^{9} e + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} c^{5} d^{10} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b c^{4} d^{5} e^{5} + 6400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{2} c^{4} d^{6} e^{4} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b c^{5} d^{6} e^{4} + 19200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} c^{4} d^{7} e^{3} - 7936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{5} d^{7} e^{3} + 6400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} c^{4} d^{8} e^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{5} d^{8} e^{2} - 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{5} c^{4} d^{9} e + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} c^{5} d^{9} e + 128 \, B b^{5} c^{\frac{9}{2}} d^{10} + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{2} c^{\frac{7}{2}} d^{5} e^{5} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b c^{\frac{9}{2}} d^{5} e^{5} + 25600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{3} c^{\frac{7}{2}} d^{6} e^{4} - 6400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{2} c^{\frac{9}{2}} d^{6} e^{4} + 25600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{4} c^{\frac{7}{2}} d^{7} e^{3} - 6400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c^{\frac{9}{2}} d^{7} e^{3} + 8240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{5} c^{\frac{7}{2}} d^{8} e^{2} - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c^{\frac{9}{2}} d^{8} e^{2} - 336 \, B b^{6} c^{\frac{7}{2}} d^{9} e + 32 \, A b^{5} c^{\frac{9}{2}} d^{9} e + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{2} c^{3} d^{4} e^{6} + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{3} c^{3} d^{5} e^{5} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{2} c^{4} d^{5} e^{5} + 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{4} c^{3} d^{6} e^{4} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} c^{4} d^{6} e^{4} + 9120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{5} c^{3} d^{7} e^{3} - 1600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} c^{4} d^{7} e^{3} + 2480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{6} c^{3} d^{8} e^{2} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} c^{4} d^{8} e^{2} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{3} c^{\frac{5}{2}} d^{4} e^{6} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{2} c^{\frac{7}{2}} d^{4} e^{6} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{3} c^{\frac{7}{2}} d^{5} e^{5} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{5} c^{\frac{5}{2}} d^{6} e^{4} + 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{4} c^{\frac{7}{2}} d^{6} e^{4} + 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{6} c^{\frac{5}{2}} d^{7} e^{3} + 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{5} c^{\frac{7}{2}} d^{7} e^{3} + 248 \, B b^{7} c^{\frac{5}{2}} d^{8} e^{2} - 64 \, A b^{6} c^{\frac{7}{2}} d^{8} e^{2} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{3} c^{2} d^{3} e^{7} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{4} c^{2} d^{4} e^{6} + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{3} c^{3} d^{4} e^{6} - 3548 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{5} c^{2} d^{5} e^{5} + 4280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{4} c^{3} d^{5} e^{5} - 1600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{6} c^{2} d^{6} e^{4} + 2080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{5} c^{3} d^{6} e^{4} - 100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{7} c^{2} d^{7} e^{3} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{6} c^{3} d^{7} e^{3} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{4} c^{\frac{3}{2}} d^{3} e^{7} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{3} c^{\frac{5}{2}} d^{3} e^{7} - 3070 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{5} c^{\frac{3}{2}} d^{4} e^{6} + 7420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{4} c^{\frac{5}{2}} d^{4} e^{6} - 2670 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{6} c^{\frac{3}{2}} d^{5} e^{5} + 2860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{5} c^{\frac{5}{2}} d^{5} e^{5} - 650 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{7} c^{\frac{3}{2}} d^{6} e^{4} + 860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{6} c^{\frac{5}{2}} d^{6} e^{4} - 10 \, B b^{8} c^{\frac{3}{2}} d^{7} e^{3} + 12 \, A b^{7} c^{\frac{5}{2}} d^{7} e^{3} - 2090 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{5} c d^{3} e^{7} - 4780 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{4} c^{2} d^{3} e^{7} - 2114 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{6} c d^{4} e^{6} + 1448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{5} c^{2} d^{4} e^{6} - 1070 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{7} c d^{5} e^{5} + 540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{6} c^{2} d^{5} e^{5} - 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{8} c d^{6} e^{4} + 200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{7} c^{2} d^{6} e^{4} + 135 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{5} \sqrt{c} d^{2} e^{8} - 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{4} c^{\frac{3}{2}} d^{2} e^{8} - 790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{6} \sqrt{c} d^{3} e^{7} - 5330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{5} c^{\frac{3}{2}} d^{3} e^{7} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{7} \sqrt{c} d^{4} e^{6} - 1390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{6} c^{\frac{3}{2}} d^{4} e^{6} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{8} \sqrt{c} d^{5} e^{5} - 230 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{7} c^{\frac{3}{2}} d^{5} e^{5} - 15 \, B b^{9} \sqrt{c} d^{6} e^{4} + 20 \, A b^{8} c^{\frac{3}{2}} d^{6} e^{4} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{5} d e^{9} - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{4} c d e^{9} + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{6} d^{2} e^{8} + 330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{5} c d^{2} e^{8} - 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{7} d^{3} e^{7} - 2626 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{6} c d^{3} e^{7} - 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{8} d^{4} e^{6} - 930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{7} c d^{4} e^{6} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{9} d^{5} e^{5} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{8} c d^{5} e^{5} + 135 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{5} \sqrt{c} d e^{9} + 490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{6} \sqrt{c} d^{2} e^{8} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{7} \sqrt{c} d^{3} e^{7} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{8} \sqrt{c} d^{4} e^{6} - 15 \, A b^{9} \sqrt{c} d^{5} e^{5} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{5} e^{10} + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{6} d e^{9} + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{7} d^{2} e^{8} - 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{8} d^{3} e^{7} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{9} d^{4} e^{6}}{640 \, {\left(c^{3} d^{6} e^{5} - 3 \, b c^{2} d^{5} e^{6} + 3 \, b^{2} c d^{4} e^{7} - b^{3} d^{3} e^{8}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{5}}"," ",0,"-3/128*(B*b^5*d - 2*A*b^4*c*d + A*b^5*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((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)*sqrt(-c*d^2 + b*d*e)) + 1/640*(10240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*c^(13/2)*d^9*e + 4096*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*c^7*d^10 + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*c^6*d^8*e^2 + 9728*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^6*d^9*e + 1024*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^7*d^9*e + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c^(13/2)*d^10 + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*c^(11/2)*d^7*e^3 - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b*c^(11/2)*d^8*e^2 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*c^(13/2)*d^8*e^2 - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c^(11/2)*d^9*e + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^(13/2)*d^9*e + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c^6*d^10 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*c^5*d^6*e^4 - 21760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b*c^5*d^7*e^3 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*c^6*d^7*e^3 - 38144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^5*d^8*e^2 + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^6*d^8*e^2 - 21760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c^5*d^9*e + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^6*d^9*e + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c^(11/2)*d^10 - 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b*c^(9/2)*d^6*e^4 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*c^(11/2)*d^6*e^4 - 19200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^2*c^(9/2)*d^7*e^3 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b*c^(11/2)*d^7*e^3 - 19200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c^(9/2)*d^8*e^2 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^(11/2)*d^8*e^2 - 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*c^(9/2)*d^9*e + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c^(11/2)*d^9*e + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*c^5*d^10 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b*c^4*d^5*e^5 + 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^2*c^4*d^6*e^4 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b*c^5*d^6*e^4 + 19200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*c^4*d^7*e^3 - 7936*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^5*d^7*e^3 + 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*c^4*d^8*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^5*d^8*e^2 - 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^5*c^4*d^9*e + 320*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*c^5*d^9*e + 128*B*b^5*c^(9/2)*d^10 + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^2*c^(7/2)*d^5*e^5 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b*c^(9/2)*d^5*e^5 + 25600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^3*c^(7/2)*d^6*e^4 - 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^2*c^(9/2)*d^6*e^4 + 25600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^4*c^(7/2)*d^7*e^3 - 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c^(9/2)*d^7*e^3 + 8240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^5*c^(7/2)*d^8*e^2 - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c^(9/2)*d^8*e^2 - 336*B*b^6*c^(7/2)*d^9*e + 32*A*b^5*c^(9/2)*d^9*e + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^2*c^3*d^4*e^6 + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^3*c^3*d^5*e^5 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^2*c^4*d^5*e^5 + 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^4*c^3*d^6*e^4 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*c^4*d^6*e^4 + 9120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^5*c^3*d^7*e^3 - 1600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*c^4*d^7*e^3 + 2480*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^6*c^3*d^8*e^2 - 640*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*c^4*d^8*e^2 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^3*c^(5/2)*d^4*e^6 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^2*c^(7/2)*d^4*e^6 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^3*c^(7/2)*d^5*e^5 + 80*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^5*c^(5/2)*d^6*e^4 + 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^4*c^(7/2)*d^6*e^4 + 840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^6*c^(5/2)*d^7*e^3 + 160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^5*c^(7/2)*d^7*e^3 + 248*B*b^7*c^(5/2)*d^8*e^2 - 64*A*b^6*c^(7/2)*d^8*e^2 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^3*c^2*d^3*e^7 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^4*c^2*d^4*e^6 + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^3*c^3*d^4*e^6 - 3548*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^5*c^2*d^5*e^5 + 4280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^4*c^3*d^5*e^5 - 1600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^6*c^2*d^6*e^4 + 2080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^5*c^3*d^6*e^4 - 100*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^7*c^2*d^7*e^3 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^6*c^3*d^7*e^3 - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^4*c^(3/2)*d^3*e^7 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^3*c^(5/2)*d^3*e^7 - 3070*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^5*c^(3/2)*d^4*e^6 + 7420*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^4*c^(5/2)*d^4*e^6 - 2670*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^6*c^(3/2)*d^5*e^5 + 2860*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^5*c^(5/2)*d^5*e^5 - 650*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^7*c^(3/2)*d^6*e^4 + 860*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^6*c^(5/2)*d^6*e^4 - 10*B*b^8*c^(3/2)*d^7*e^3 + 12*A*b^7*c^(5/2)*d^7*e^3 - 2090*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^5*c*d^3*e^7 - 4780*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^4*c^2*d^3*e^7 - 2114*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^6*c*d^4*e^6 + 1448*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^5*c^2*d^4*e^6 - 1070*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^7*c*d^5*e^5 + 540*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^6*c^2*d^5*e^5 - 150*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^8*c*d^6*e^4 + 200*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^7*c^2*d^6*e^4 + 135*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^5*sqrt(c)*d^2*e^8 - 270*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^4*c^(3/2)*d^2*e^8 - 790*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^6*sqrt(c)*d^3*e^7 - 5330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^5*c^(3/2)*d^3*e^7 - 640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^7*sqrt(c)*d^4*e^6 - 1390*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^6*c^(3/2)*d^4*e^6 - 210*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^8*sqrt(c)*d^5*e^5 - 230*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^7*c^(3/2)*d^5*e^5 - 15*B*b^9*sqrt(c)*d^6*e^4 + 20*A*b^8*c^(3/2)*d^6*e^4 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^5*d*e^9 - 30*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^4*c*d*e^9 + 70*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^6*d^2*e^8 + 330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^5*c*d^2*e^8 - 128*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^7*d^3*e^7 - 2626*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^6*c*d^3*e^7 - 70*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^8*d^4*e^6 - 930*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^7*c*d^4*e^6 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^9*d^5*e^5 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^8*c*d^5*e^5 + 135*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^5*sqrt(c)*d*e^9 + 490*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^6*sqrt(c)*d^2*e^8 - 640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^7*sqrt(c)*d^3*e^7 - 210*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^8*sqrt(c)*d^4*e^6 - 15*A*b^9*sqrt(c)*d^5*e^5 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^5*e^10 + 70*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^6*d*e^9 + 128*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^7*d^2*e^8 - 70*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^8*d^3*e^7 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^9*d^4*e^6)/((c^3*d^6*e^5 - 3*b*c^2*d^5*e^6 + 3*b^2*c*d^4*e^7 - b^3*d^3*e^8)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^5)","B",0
1181,1,5748,0,0.810864," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(12 \, B b^{5} c d^{2} - 24 \, A b^{4} c^{2} d^{2} - 5 \, B b^{6} d e + 24 \, A b^{5} c d e - 7 \, A b^{6} e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{512 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} \sqrt{-c d^{2} + b d e}} + \frac{49152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B c^{8} d^{11} e + 16384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B c^{\frac{17}{2}} d^{12} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B c^{\frac{15}{2}} d^{10} e^{2} + 69632 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b c^{\frac{15}{2}} d^{11} e + 8192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A c^{\frac{17}{2}} d^{11} e + 49152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{8} d^{12} + 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B c^{7} d^{9} e^{3} - 36864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b c^{7} d^{10} e^{2} + 24576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A c^{8} d^{10} e^{2} - 36864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{7} d^{11} e + 24576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{8} d^{11} e + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c^{\frac{15}{2}} d^{12} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B c^{\frac{13}{2}} d^{8} e^{4} - 138240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b c^{\frac{13}{2}} d^{9} e^{3} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A c^{\frac{15}{2}} d^{9} e^{3} - 254976 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{2} c^{\frac{13}{2}} d^{10} e^{2} + 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b c^{\frac{15}{2}} d^{10} e^{2} - 138240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c^{\frac{13}{2}} d^{11} e + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{\frac{15}{2}} d^{11} e + 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c^{7} d^{12} - 117760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b c^{6} d^{8} e^{4} + 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A c^{7} d^{8} e^{4} - 211968 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{2} c^{6} d^{9} e^{3} - 211968 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} c^{6} d^{10} e^{2} - 117760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} c^{6} d^{11} e + 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{7} d^{11} e + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} c^{\frac{13}{2}} d^{12} - 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b c^{\frac{11}{2}} d^{7} e^{5} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b c^{\frac{13}{2}} d^{8} e^{4} + 92160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{3} c^{\frac{11}{2}} d^{9} e^{3} - 101376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{2} c^{\frac{13}{2}} d^{9} e^{3} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c^{\frac{13}{2}} d^{10} e^{2} - 48384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{5} c^{\frac{11}{2}} d^{11} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c^{\frac{13}{2}} d^{11} e + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{5} c^{6} d^{12} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{2} c^{5} d^{7} e^{5} - 81920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b c^{6} d^{7} e^{5} + 276480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{3} c^{5} d^{8} e^{4} - 119808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{2} c^{6} d^{8} e^{4} + 276480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{4} c^{5} d^{9} e^{3} - 119808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} c^{6} d^{9} e^{3} + 80640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{5} c^{5} d^{10} e^{2} - 43520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} c^{6} d^{10} e^{2} - 9984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{6} c^{5} d^{11} e + 1536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} c^{6} d^{11} e + 256 \, B b^{6} c^{\frac{11}{2}} d^{12} + 92160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{2} c^{\frac{9}{2}} d^{6} e^{6} + 153600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{3} c^{\frac{9}{2}} d^{7} e^{5} - 122880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{2} c^{\frac{11}{2}} d^{7} e^{5} + 230400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{4} c^{\frac{9}{2}} d^{8} e^{4} - 55296 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{3} c^{\frac{11}{2}} d^{8} e^{4} + 164160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{5} c^{\frac{9}{2}} d^{9} e^{3} - 51840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{4} c^{\frac{11}{2}} d^{9} e^{3} + 43968 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{6} c^{\frac{9}{2}} d^{10} e^{2} - 18432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{5} c^{\frac{11}{2}} d^{10} e^{2} - 832 \, B b^{7} c^{\frac{9}{2}} d^{11} e + 128 \, A b^{6} c^{\frac{11}{2}} d^{11} e + 112640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{3} c^{4} d^{6} e^{6} + 122880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{2} c^{5} d^{6} e^{6} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{4} c^{4} d^{7} e^{5} - 12288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{3} c^{5} d^{7} e^{5} + 34560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{5} c^{4} d^{8} e^{4} + 41472 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{4} c^{5} d^{8} e^{4} + 36160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{6} c^{4} d^{9} e^{3} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{5} c^{5} d^{9} e^{3} + 9792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{7} c^{4} d^{10} e^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{6} c^{5} d^{10} e^{2} - 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{3} c^{\frac{7}{2}} d^{5} e^{7} + 337920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{3} c^{\frac{9}{2}} d^{6} e^{6} - 84192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{5} c^{\frac{7}{2}} d^{7} e^{5} + 100800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{4} c^{\frac{9}{2}} d^{7} e^{5} - 38160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{6} c^{\frac{7}{2}} d^{8} e^{4} + 60480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{5} c^{\frac{9}{2}} d^{8} e^{4} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{7} c^{\frac{7}{2}} d^{9} e^{3} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{6} c^{\frac{9}{2}} d^{9} e^{3} + 816 \, B b^{8} c^{\frac{7}{2}} d^{10} e^{2} - 320 \, A b^{7} c^{\frac{9}{2}} d^{10} e^{2} - 143360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{4} c^{3} d^{5} e^{7} - 81920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{3} c^{4} d^{5} e^{7} - 85536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{5} c^{3} d^{6} e^{6} + 336960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{4} c^{4} d^{6} e^{6} - 82656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{6} c^{3} d^{7} e^{5} + 87360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{5} c^{4} d^{7} e^{5} - 25600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{7} c^{3} d^{8} e^{4} + 33920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{6} c^{4} d^{8} e^{4} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{8} c^{3} d^{9} e^{3} + 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{7} c^{4} d^{9} e^{3} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{4} c^{\frac{5}{2}} d^{4} e^{8} - 117720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{5} c^{\frac{5}{2}} d^{5} e^{7} - 317520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{4} c^{\frac{7}{2}} d^{5} e^{7} - 58936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{6} c^{\frac{5}{2}} d^{6} e^{6} + 95424 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{5} c^{\frac{7}{2}} d^{6} e^{6} - 34920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{7} c^{\frac{5}{2}} d^{7} e^{5} + 15120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{6} c^{\frac{7}{2}} d^{7} e^{5} - 8280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{8} c^{\frac{5}{2}} d^{8} e^{4} + 11136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{7} c^{\frac{7}{2}} d^{8} e^{4} - 80 \, B b^{9} c^{\frac{5}{2}} d^{9} e^{3} + 96 \, A b^{8} c^{\frac{7}{2}} d^{9} e^{3} + 54960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{5} c^{2} d^{4} e^{8} + 2720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{4} c^{3} d^{4} e^{8} - 18408 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{6} c^{2} d^{5} e^{7} - 419328 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{5} c^{3} d^{5} e^{7} - 1128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{7} c^{2} d^{6} e^{6} - 71808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{6} c^{3} d^{6} e^{6} - 4680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{8} c^{2} d^{7} e^{5} - 18080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{7} c^{3} d^{7} e^{5} - 1560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{9} c^{2} d^{8} e^{4} + 2112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{8} c^{3} d^{8} e^{4} + 1980 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{5} c^{\frac{3}{2}} d^{3} e^{9} - 3960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{4} c^{\frac{5}{2}} d^{3} e^{9} + 62070 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{6} c^{\frac{3}{2}} d^{4} e^{8} + 99480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{5} c^{\frac{5}{2}} d^{4} e^{8} + 29608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{7} c^{\frac{3}{2}} d^{5} e^{7} - 242840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{6} c^{\frac{5}{2}} d^{5} e^{7} + 15420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{8} c^{\frac{3}{2}} d^{6} e^{6} - 64440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{7} c^{\frac{5}{2}} d^{6} e^{6} + 1740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{9} c^{\frac{3}{2}} d^{7} e^{5} - 12384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{8} c^{\frac{5}{2}} d^{7} e^{5} - 130 \, B b^{10} c^{\frac{3}{2}} d^{8} e^{4} + 176 \, A b^{9} c^{\frac{5}{2}} d^{8} e^{4} + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{5} c d^{2} e^{10} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{4} c^{2} d^{2} e^{10} - 2680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{6} c d^{3} e^{9} + 15720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{5} c^{2} d^{3} e^{9} + 32064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{7} c d^{4} e^{8} + 170520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{6} c^{2} d^{4} e^{8} + 19944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{8} c d^{5} e^{7} - 47400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{7} c^{2} d^{5} e^{7} + 7180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{9} c d^{6} e^{6} - 16320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{8} c^{2} d^{6} e^{6} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{10} c d^{7} e^{5} - 3120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{9} c^{2} d^{7} e^{5} - 825 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{6} \sqrt{c} d^{2} e^{10} + 3960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{5} c^{\frac{3}{2}} d^{2} e^{10} - 3825 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{7} \sqrt{c} d^{3} e^{9} + 6390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{6} c^{\frac{3}{2}} d^{3} e^{9} + 8430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{8} \sqrt{c} d^{4} e^{8} + 115328 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{7} c^{\frac{3}{2}} d^{4} e^{8} + 4950 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{9} \sqrt{c} d^{5} e^{7} + 14460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{8} c^{\frac{3}{2}} d^{5} e^{7} + 1275 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{10} \sqrt{c} d^{6} e^{6} + 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{9} c^{\frac{3}{2}} d^{6} e^{6} + 75 \, B b^{11} \sqrt{c} d^{7} e^{5} - 290 \, A b^{10} c^{\frac{3}{2}} d^{7} e^{5} - 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{6} d e^{11} + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{5} c d e^{11} - 425 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{7} d^{2} e^{10} - 3140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{6} c d^{2} e^{10} - 990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{8} d^{3} e^{9} - 13896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{7} c d^{3} e^{9} + 990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{9} d^{4} e^{8} + 38784 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{8} c d^{4} e^{8} + 425 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{10} d^{5} e^{7} + 9440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{9} c d^{5} e^{7} + 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{11} d^{6} e^{6} + 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{10} c d^{6} e^{6} - 1155 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{6} \sqrt{c} d e^{11} - 5355 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{7} \sqrt{c} d^{2} e^{10} - 9702 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{8} \sqrt{c} d^{3} e^{9} + 6930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{9} \sqrt{c} d^{4} e^{8} + 1785 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{10} \sqrt{c} d^{5} e^{7} + 105 \, A b^{11} \sqrt{c} d^{6} e^{6} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{6} e^{12} - 595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{7} d e^{11} - 1386 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{8} d^{2} e^{10} - 1686 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{9} d^{3} e^{9} + 595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{10} d^{4} e^{8} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{11} d^{5} e^{7}}{7680 \, {\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)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{6}}"," ",0,"-1/512*(12*B*b^5*c*d^2 - 24*A*b^4*c^2*d^2 - 5*B*b^6*d*e + 24*A*b^5*c*d*e - 7*A*b^6*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*sqrt(-c*d^2 + b*d*e)) + 1/7680*(49152*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*c^8*d^11*e + 16384*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*c^(17/2)*d^12 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*c^(15/2)*d^10*e^2 + 69632*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b*c^(15/2)*d^11*e + 8192*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*c^(17/2)*d^11*e + 49152*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^8*d^12 + 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*c^7*d^9*e^3 - 36864*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b*c^7*d^10*e^2 + 24576*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*c^8*d^10*e^2 - 36864*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^7*d^11*e + 24576*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^8*d^11*e + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c^(15/2)*d^12 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*c^(13/2)*d^8*e^4 - 138240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b*c^(13/2)*d^9*e^3 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*c^(15/2)*d^9*e^3 - 254976*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^2*c^(13/2)*d^10*e^2 + 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b*c^(15/2)*d^10*e^2 - 138240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c^(13/2)*d^11*e + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^(15/2)*d^11*e + 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c^7*d^12 - 117760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b*c^6*d^8*e^4 + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*c^7*d^8*e^4 - 211968*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^2*c^6*d^9*e^3 - 211968*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*c^6*d^10*e^2 - 117760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*c^6*d^11*e + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^7*d^11*e + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*c^(13/2)*d^12 - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b*c^(11/2)*d^7*e^5 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b*c^(13/2)*d^8*e^4 + 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^3*c^(11/2)*d^9*e^3 - 101376*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^2*c^(13/2)*d^9*e^3 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c^(13/2)*d^10*e^2 - 48384*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^5*c^(11/2)*d^11*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c^(13/2)*d^11*e + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^5*c^6*d^12 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^2*c^5*d^7*e^5 - 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b*c^6*d^7*e^5 + 276480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^3*c^5*d^8*e^4 - 119808*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^2*c^6*d^8*e^4 + 276480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^4*c^5*d^9*e^3 - 119808*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*c^6*d^9*e^3 + 80640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^5*c^5*d^10*e^2 - 43520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*c^6*d^10*e^2 - 9984*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^6*c^5*d^11*e + 1536*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*c^6*d^11*e + 256*B*b^6*c^(11/2)*d^12 + 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^2*c^(9/2)*d^6*e^6 + 153600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^3*c^(9/2)*d^7*e^5 - 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^2*c^(11/2)*d^7*e^5 + 230400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^4*c^(9/2)*d^8*e^4 - 55296*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^3*c^(11/2)*d^8*e^4 + 164160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^5*c^(9/2)*d^9*e^3 - 51840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^4*c^(11/2)*d^9*e^3 + 43968*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^6*c^(9/2)*d^10*e^2 - 18432*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^5*c^(11/2)*d^10*e^2 - 832*B*b^7*c^(9/2)*d^11*e + 128*A*b^6*c^(11/2)*d^11*e + 112640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^3*c^4*d^6*e^6 + 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^2*c^5*d^6*e^6 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^4*c^4*d^7*e^5 - 12288*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^3*c^5*d^7*e^5 + 34560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^5*c^4*d^8*e^4 + 41472*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^4*c^5*d^8*e^4 + 36160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^6*c^4*d^9*e^3 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^5*c^5*d^9*e^3 + 9792*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^7*c^4*d^10*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^6*c^5*d^10*e^2 - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^3*c^(7/2)*d^5*e^7 + 337920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^3*c^(9/2)*d^6*e^6 - 84192*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^5*c^(7/2)*d^7*e^5 + 100800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^4*c^(9/2)*d^7*e^5 - 38160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^6*c^(7/2)*d^8*e^4 + 60480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^5*c^(9/2)*d^8*e^4 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^7*c^(7/2)*d^9*e^3 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^6*c^(9/2)*d^9*e^3 + 816*B*b^8*c^(7/2)*d^10*e^2 - 320*A*b^7*c^(9/2)*d^10*e^2 - 143360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^4*c^3*d^5*e^7 - 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^3*c^4*d^5*e^7 - 85536*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^5*c^3*d^6*e^6 + 336960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^4*c^4*d^6*e^6 - 82656*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^6*c^3*d^7*e^5 + 87360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^5*c^4*d^7*e^5 - 25600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^7*c^3*d^8*e^4 + 33920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^6*c^4*d^8*e^4 - 960*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^8*c^3*d^9*e^3 + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^7*c^4*d^9*e^3 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^4*c^(5/2)*d^4*e^8 - 117720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^5*c^(5/2)*d^5*e^7 - 317520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^4*c^(7/2)*d^5*e^7 - 58936*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^6*c^(5/2)*d^6*e^6 + 95424*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^5*c^(7/2)*d^6*e^6 - 34920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^7*c^(5/2)*d^7*e^5 + 15120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^6*c^(7/2)*d^7*e^5 - 8280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^8*c^(5/2)*d^8*e^4 + 11136*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^7*c^(7/2)*d^8*e^4 - 80*B*b^9*c^(5/2)*d^9*e^3 + 96*A*b^8*c^(7/2)*d^9*e^3 + 54960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^5*c^2*d^4*e^8 + 2720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^4*c^3*d^4*e^8 - 18408*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^6*c^2*d^5*e^7 - 419328*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^5*c^3*d^5*e^7 - 1128*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^7*c^2*d^6*e^6 - 71808*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^6*c^3*d^6*e^6 - 4680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^8*c^2*d^7*e^5 - 18080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^7*c^3*d^7*e^5 - 1560*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^9*c^2*d^8*e^4 + 2112*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^8*c^3*d^8*e^4 + 1980*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^5*c^(3/2)*d^3*e^9 - 3960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^4*c^(5/2)*d^3*e^9 + 62070*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^6*c^(3/2)*d^4*e^8 + 99480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^5*c^(5/2)*d^4*e^8 + 29608*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^7*c^(3/2)*d^5*e^7 - 242840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^6*c^(5/2)*d^5*e^7 + 15420*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^8*c^(3/2)*d^6*e^6 - 64440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^7*c^(5/2)*d^6*e^6 + 1740*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^9*c^(3/2)*d^7*e^5 - 12384*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^8*c^(5/2)*d^7*e^5 - 130*B*b^10*c^(3/2)*d^8*e^4 + 176*A*b^9*c^(5/2)*d^8*e^4 + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^5*c*d^2*e^10 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^4*c^2*d^2*e^10 - 2680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^6*c*d^3*e^9 + 15720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^5*c^2*d^3*e^9 + 32064*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^7*c*d^4*e^8 + 170520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^6*c^2*d^4*e^8 + 19944*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^8*c*d^5*e^7 - 47400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^7*c^2*d^5*e^7 + 7180*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^9*c*d^6*e^6 - 16320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^8*c^2*d^6*e^6 + 720*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^10*c*d^7*e^5 - 3120*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^9*c^2*d^7*e^5 - 825*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^6*sqrt(c)*d^2*e^10 + 3960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^5*c^(3/2)*d^2*e^10 - 3825*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^7*sqrt(c)*d^3*e^9 + 6390*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^6*c^(3/2)*d^3*e^9 + 8430*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^8*sqrt(c)*d^4*e^8 + 115328*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^7*c^(3/2)*d^4*e^8 + 4950*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^9*sqrt(c)*d^5*e^7 + 14460*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^8*c^(3/2)*d^5*e^7 + 1275*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^10*sqrt(c)*d^6*e^6 + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^9*c^(3/2)*d^6*e^6 + 75*B*b^11*sqrt(c)*d^7*e^5 - 290*A*b^10*c^(3/2)*d^7*e^5 - 75*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^6*d*e^11 + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^5*c*d*e^11 - 425*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^7*d^2*e^10 - 3140*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^6*c*d^2*e^10 - 990*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^8*d^3*e^9 - 13896*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^7*c*d^3*e^9 + 990*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^9*d^4*e^8 + 38784*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^8*c*d^4*e^8 + 425*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^10*d^5*e^7 + 9440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^9*c*d^5*e^7 + 75*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^11*d^6*e^6 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^10*c*d^6*e^6 - 1155*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^6*sqrt(c)*d*e^11 - 5355*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^7*sqrt(c)*d^2*e^10 - 9702*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^8*sqrt(c)*d^3*e^9 + 6930*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^9*sqrt(c)*d^4*e^8 + 1785*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^10*sqrt(c)*d^5*e^7 + 105*A*b^11*sqrt(c)*d^6*e^6 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^6*e^12 - 595*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^7*d*e^11 - 1386*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^8*d^2*e^10 - 1686*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^9*d^3*e^9 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^10*d^4*e^8 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^11*d^5*e^7)/((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)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^6)","B",0
1182,1,7914,0,0.981451," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(24 \, B b^{5} c^{2} d^{3} - 48 \, A b^{4} c^{3} d^{3} - 20 \, B b^{6} c d^{2} e + 72 \, A b^{5} c^{2} d^{2} e + 5 \, B b^{7} d e^{2} - 42 \, A b^{6} c d e^{2} + 9 \, A b^{7} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{1024 \, {\left(c^{5} d^{10} - 5 \, b c^{4} d^{9} e + 10 \, b^{2} c^{3} d^{8} e^{2} - 10 \, b^{3} c^{2} d^{7} e^{3} + 5 \, b^{4} c d^{6} e^{4} - b^{5} d^{5} e^{5}\right)} \sqrt{-c d^{2} + b d e}} + \frac{458752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B c^{\frac{19}{2}} d^{13} e + 131072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B c^{10} d^{14} + 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B c^{9} d^{12} e^{2} + 868352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b c^{9} d^{13} e + 98304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A c^{10} d^{13} e + 458752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b c^{\frac{19}{2}} d^{14} + 573440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B c^{\frac{17}{2}} d^{11} e^{3} - 57344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b c^{\frac{17}{2}} d^{12} e^{2} + 344064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A c^{\frac{19}{2}} d^{12} e^{2} - 57344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{2} c^{\frac{17}{2}} d^{13} e + 344064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b c^{\frac{19}{2}} d^{13} e + 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{9} d^{14} + 286720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B c^{8} d^{10} e^{4} - 1519616 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b c^{8} d^{11} e^{3} + 516096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A c^{9} d^{11} e^{3} - 2990080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{2} c^{8} d^{12} e^{2} + 737280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b c^{9} d^{12} e^{2} - 1519616 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} c^{8} d^{13} e + 516096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{9} d^{13} e + 573440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c^{\frac{17}{2}} d^{14} - 1792000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b c^{\frac{15}{2}} d^{10} e^{4} + 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A c^{\frac{17}{2}} d^{10} e^{4} - 3627008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{2} c^{\frac{15}{2}} d^{11} e^{3} + 258048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b c^{\frac{17}{2}} d^{11} e^{3} - 3627008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{3} c^{\frac{15}{2}} d^{12} e^{2} + 258048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{2} c^{\frac{17}{2}} d^{12} e^{2} - 1792000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{4} c^{\frac{15}{2}} d^{13} e + 430080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c^{\frac{17}{2}} d^{13} e + 286720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} c^{8} d^{14} - 1433600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b c^{7} d^{9} e^{5} - 960512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{2} c^{7} d^{10} e^{4} - 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b c^{8} d^{10} e^{4} + 55296 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{3} c^{7} d^{11} e^{3} - 1683456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{2} c^{8} d^{11} e^{3} - 960512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{4} c^{7} d^{12} e^{2} - 688128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} c^{8} d^{12} e^{2} - 1025024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{5} c^{7} d^{13} e + 215040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} c^{8} d^{13} e + 86016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{5} c^{\frac{15}{2}} d^{14} + 358400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{2} c^{\frac{13}{2}} d^{9} e^{5} - 2150400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b c^{\frac{15}{2}} d^{9} e^{5} + 4515840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{3} c^{\frac{13}{2}} d^{10} e^{4} - 2795520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{2} c^{\frac{15}{2}} d^{10} e^{4} + 4515840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{4} c^{\frac{13}{2}} d^{11} e^{3} - 2795520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{3} c^{\frac{15}{2}} d^{11} e^{3} + 1078784 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{5} c^{\frac{13}{2}} d^{12} e^{2} - 967680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{4} c^{\frac{15}{2}} d^{12} e^{2} - 326144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{6} c^{\frac{13}{2}} d^{13} e + 64512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{5} c^{\frac{15}{2}} d^{13} e + 14336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{6} c^{7} d^{14} + 2867200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{2} c^{6} d^{8} e^{6} + 3512320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{3} c^{6} d^{9} e^{5} - 4300800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{2} c^{7} d^{9} e^{5} + 5806080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{4} c^{6} d^{10} e^{4} - 2119680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{3} c^{7} d^{10} e^{4} + 4076800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{5} c^{6} d^{11} e^{3} - 1774080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{4} c^{7} d^{11} e^{3} + 1028608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{6} c^{6} d^{12} e^{2} - 580608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{5} c^{7} d^{12} e^{2} - 55552 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{7} c^{6} d^{13} e + 10752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{6} c^{7} d^{13} e + 1024 \, B b^{7} c^{\frac{13}{2}} d^{14} + 5017600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{3} c^{\frac{11}{2}} d^{8} e^{6} + 4300800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{2} c^{\frac{13}{2}} d^{8} e^{6} + 1720320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{4} c^{\frac{11}{2}} d^{9} e^{5} - 1935360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{3} c^{\frac{13}{2}} d^{9} e^{5} + 1975680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{5} c^{\frac{11}{2}} d^{10} e^{4} + 564480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{4} c^{\frac{13}{2}} d^{10} e^{4} + 1511552 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{6} c^{\frac{11}{2}} d^{11} e^{3} - 413952 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{5} c^{\frac{13}{2}} d^{11} e^{3} + 380800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{7} c^{\frac{11}{2}} d^{12} e^{2} - 188160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{6} c^{\frac{13}{2}} d^{12} e^{2} - 3968 \, B b^{8} c^{\frac{11}{2}} d^{13} e + 768 \, A b^{7} c^{\frac{13}{2}} d^{13} e - 2867200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{3} c^{5} d^{7} e^{7} + 1863680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{4} c^{5} d^{8} e^{6} + 13762560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{3} c^{6} d^{8} e^{6} - 2088576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{5} c^{5} d^{9} e^{5} + 2327808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{4} c^{6} d^{9} e^{5} - 815360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{6} c^{5} d^{10} e^{4} + 1881600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{5} c^{6} d^{10} e^{4} + 184576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{7} c^{5} d^{11} e^{3} + 75264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{6} c^{6} d^{11} e^{3} + 68096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{8} c^{5} d^{12} e^{2} - 32256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{7} c^{6} d^{12} e^{2} - 7884800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{4} c^{\frac{9}{2}} d^{7} e^{7} - 4300800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{3} c^{\frac{11}{2}} d^{7} e^{7} - 2283456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{5} c^{\frac{9}{2}} d^{8} e^{6} + 16695168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{4} c^{\frac{11}{2}} d^{8} e^{6} - 2968896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{6} c^{\frac{9}{2}} d^{9} e^{5} + 3067008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{5} c^{\frac{11}{2}} d^{9} e^{5} - 1017856 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{7} c^{\frac{9}{2}} d^{10} e^{4} + 1430016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{6} c^{\frac{11}{2}} d^{10} e^{4} - 33152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{8} c^{\frac{9}{2}} d^{11} e^{3} + 64512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{7} c^{\frac{11}{2}} d^{11} e^{3} + 4864 \, B b^{9} c^{\frac{9}{2}} d^{12} e^{2} - 2304 \, A b^{8} c^{\frac{11}{2}} d^{12} e^{2} + 1433600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{4} c^{4} d^{6} e^{8} - 7790944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{5} c^{4} d^{7} e^{7} - 18193728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{4} c^{5} d^{7} e^{7} - 2131136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{6} c^{4} d^{8} e^{6} + 7469952 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{5} c^{5} d^{8} e^{6} - 1485344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{7} c^{4} d^{9} e^{5} + 716352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{6} c^{5} d^{9} e^{5} - 459200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{8} c^{4} d^{10} e^{4} + 618240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{7} c^{5} d^{10} e^{4} - 11200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{9} c^{4} d^{11} e^{3} + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{8} c^{5} d^{11} e^{3} + 5338480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{5} c^{\frac{7}{2}} d^{6} e^{8} + 1078560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{4} c^{\frac{9}{2}} d^{6} e^{8} - 2001328 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{6} c^{\frac{7}{2}} d^{7} e^{7} - 28144032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{5} c^{\frac{9}{2}} d^{7} e^{7} + 333872 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{7} c^{\frac{7}{2}} d^{8} e^{6} - 2198112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{6} c^{\frac{9}{2}} d^{8} e^{6} - 160720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{8} c^{\frac{7}{2}} d^{9} e^{5} - 971040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{7} c^{\frac{9}{2}} d^{9} e^{5} - 123200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{9} c^{\frac{7}{2}} d^{10} e^{4} + 168000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{8} c^{\frac{9}{2}} d^{10} e^{4} - 800 \, B b^{10} c^{\frac{7}{2}} d^{11} e^{3} + 960 \, A b^{9} c^{\frac{9}{2}} d^{11} e^{3} - 106960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{5} c^{3} d^{5} e^{9} - 359520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{4} c^{4} d^{5} e^{9} + 6953408 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{6} c^{3} d^{6} e^{8} + 10063872 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{5} c^{4} d^{6} e^{8} + 1909360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{7} c^{3} d^{7} e^{7} - 20156640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{6} c^{4} d^{7} e^{7} + 1255408 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{8} c^{3} d^{8} e^{6} - 3698688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{7} c^{4} d^{8} e^{6} + 192640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{9} c^{3} d^{9} e^{5} - 913920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{8} c^{4} d^{9} e^{5} - 19600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{10} c^{3} d^{10} e^{4} + 26880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{9} c^{4} d^{10} e^{4} + 32760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} B b^{5} c^{\frac{5}{2}} d^{4} e^{10} - 65520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} A b^{4} c^{\frac{7}{2}} d^{4} e^{10} - 1337000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{6} c^{\frac{5}{2}} d^{5} e^{9} + 808080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{5} c^{\frac{7}{2}} d^{5} e^{9} + 3935624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{7} c^{\frac{5}{2}} d^{6} e^{8} + 19619376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{6} c^{\frac{7}{2}} d^{6} e^{8} + 1520624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{8} c^{\frac{5}{2}} d^{7} e^{7} - 5499984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{7} c^{\frac{7}{2}} d^{7} e^{7} + 673400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{9} c^{\frac{5}{2}} d^{8} e^{6} - 1233120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{8} c^{\frac{7}{2}} d^{8} e^{6} + 104440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{10} c^{\frac{5}{2}} d^{9} e^{5} - 351456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{9} c^{\frac{7}{2}} d^{9} e^{5} - 1400 \, B b^{11} c^{\frac{5}{2}} d^{10} e^{4} + 1920 \, A b^{10} c^{\frac{7}{2}} d^{10} e^{4} + 2520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13} B b^{5} c^{2} d^{3} e^{11} - 5040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13} A b^{4} c^{3} d^{3} e^{11} - 133000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{6} c^{2} d^{4} e^{10} + 505680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{5} c^{3} d^{4} e^{10} - 2213764 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{7} c^{2} d^{5} e^{9} - 1120056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{6} c^{3} d^{5} e^{9} + 595552 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{8} c^{2} d^{6} e^{8} + 16718928 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{7} c^{3} d^{6} e^{8} + 229936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{9} c^{2} d^{7} e^{7} + 1320144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{8} c^{3} d^{7} e^{7} + 133000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{10} c^{2} d^{8} e^{6} + 122304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{9} c^{3} d^{8} e^{6} + 21980 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{11} c^{2} d^{9} e^{5} - 66696 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{10} c^{3} d^{9} e^{5} - 27300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} B b^{6} c^{\frac{3}{2}} d^{3} e^{11} + 98280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} A b^{5} c^{\frac{5}{2}} d^{3} e^{11} - 42350 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{7} c^{\frac{3}{2}} d^{4} e^{10} - 383460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{6} c^{\frac{5}{2}} d^{4} e^{10} - 1534330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{8} c^{\frac{3}{2}} d^{5} e^{9} - 5388180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{7} c^{\frac{5}{2}} d^{5} e^{9} - 422380 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{9} c^{\frac{3}{2}} d^{6} e^{8} + 7011480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{8} c^{\frac{5}{2}} d^{6} e^{8} - 141400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{10} c^{\frac{3}{2}} d^{7} e^{7} + 1334256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{9} c^{\frac{5}{2}} d^{7} e^{7} - 4550 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{11} c^{\frac{3}{2}} d^{8} e^{6} + 183372 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{10} c^{\frac{5}{2}} d^{8} e^{6} + 1750 \, B b^{12} c^{\frac{3}{2}} d^{9} e^{5} - 5124 \, A b^{11} c^{\frac{5}{2}} d^{9} e^{5} - 2100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13} B b^{6} c d^{2} e^{12} + 7560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13} A b^{5} c^{2} d^{2} e^{12} + 23450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{7} c d^{3} e^{11} - 264180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{6} c^{2} d^{3} e^{11} + 133070 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{8} c d^{4} e^{10} - 960960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{7} c^{2} d^{4} e^{10} - 549660 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{9} c d^{5} e^{9} - 5471640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{8} c^{2} d^{5} e^{9} - 243320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{10} c d^{6} e^{8} + 1126440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{9} c^{2} d^{6} e^{8} - 67550 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{11} c d^{7} e^{7} + 317100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{10} c^{2} d^{7} e^{7} - 5250 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{12} c d^{8} e^{6} + 45360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{11} c^{2} d^{8} e^{6} + 6825 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} B b^{7} \sqrt{c} d^{2} e^{12} - 57330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} A b^{6} c^{\frac{3}{2}} d^{2} e^{12} + 38500 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} B b^{8} \sqrt{c} d^{3} e^{11} - 122430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{7} c^{\frac{3}{2}} d^{3} e^{11} + 89145 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} B b^{9} \sqrt{c} d^{4} e^{10} - 30240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{8} c^{\frac{3}{2}} d^{4} e^{10} - 107520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} B b^{10} \sqrt{c} d^{5} e^{9} - 2566620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{9} c^{\frac{3}{2}} d^{5} e^{9} - 49525 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{11} \sqrt{c} d^{6} e^{8} - 195090 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{10} c^{\frac{3}{2}} d^{6} e^{8} - 10500 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{12} \sqrt{c} d^{7} e^{7} + 4410 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{11} c^{\frac{3}{2}} d^{7} e^{7} - 525 \, B b^{13} \sqrt{c} d^{8} e^{6} + 3780 \, A b^{12} c^{\frac{3}{2}} d^{8} e^{6} + 525 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13} B b^{7} d e^{13} - 4410 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13} A b^{6} c d e^{13} + 3500 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} B b^{8} d^{2} e^{12} + 38010 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{7} c d^{2} e^{12} + 9905 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} B b^{9} d^{3} e^{11} + 227640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{8} c d^{3} e^{11} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} B b^{10} d^{4} e^{10} + 429876 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{9} c d^{4} e^{10} - 9905 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{11} d^{5} e^{9} - 641130 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{10} c d^{5} e^{9} - 3500 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{12} d^{6} e^{8} - 117390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{11} c d^{6} e^{8} - 525 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{13} d^{7} e^{7} - 8820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{12} c d^{7} e^{7} + 12285 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{12} A b^{7} \sqrt{c} d e^{13} + 69300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{10} A b^{8} \sqrt{c} d^{2} e^{12} + 160461 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} A b^{9} \sqrt{c} d^{3} e^{11} + 193536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} A b^{10} \sqrt{c} d^{4} e^{10} - 89145 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{11} \sqrt{c} d^{5} e^{9} - 18900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{12} \sqrt{c} d^{6} e^{8} - 945 \, A b^{13} \sqrt{c} d^{7} e^{7} + 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13} A b^{7} e^{14} + 6300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11} A b^{8} d e^{13} + 17829 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} A b^{9} d^{2} e^{12} + 27648 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} A b^{10} d^{3} e^{11} + 25179 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{11} d^{4} e^{10} - 6300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{12} d^{5} e^{9} - 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{13} d^{6} e^{8}}{107520 \, {\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)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{7}}"," ",0,"-1/1024*(24*B*b^5*c^2*d^3 - 48*A*b^4*c^3*d^3 - 20*B*b^6*c*d^2*e + 72*A*b^5*c^2*d^2*e + 5*B*b^7*d*e^2 - 42*A*b^6*c*d*e^2 + 9*A*b^7*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^5*d^10 - 5*b*c^4*d^9*e + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 + 5*b^4*c*d^6*e^4 - b^5*d^5*e^5)*sqrt(-c*d^2 + b*d*e)) + 1/107520*(458752*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*c^(19/2)*d^13*e + 131072*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*c^10*d^14 + 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*c^9*d^12*e^2 + 868352*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b*c^9*d^13*e + 98304*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*c^10*d^13*e + 458752*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b*c^(19/2)*d^14 + 573440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*c^(17/2)*d^11*e^3 - 57344*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b*c^(17/2)*d^12*e^2 + 344064*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*c^(19/2)*d^12*e^2 - 57344*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^2*c^(17/2)*d^13*e + 344064*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b*c^(19/2)*d^13*e + 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^9*d^14 + 286720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*c^8*d^10*e^4 - 1519616*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b*c^8*d^11*e^3 + 516096*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*c^9*d^11*e^3 - 2990080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^2*c^8*d^12*e^2 + 737280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b*c^9*d^12*e^2 - 1519616*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*c^8*d^13*e + 516096*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^9*d^13*e + 573440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c^(17/2)*d^14 - 1792000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b*c^(15/2)*d^10*e^4 + 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*c^(17/2)*d^10*e^4 - 3627008*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^2*c^(15/2)*d^11*e^3 + 258048*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b*c^(17/2)*d^11*e^3 - 3627008*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^3*c^(15/2)*d^12*e^2 + 258048*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^2*c^(17/2)*d^12*e^2 - 1792000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^4*c^(15/2)*d^13*e + 430080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c^(17/2)*d^13*e + 286720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*c^8*d^14 - 1433600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b*c^7*d^9*e^5 - 960512*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^2*c^7*d^10*e^4 - 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b*c^8*d^10*e^4 + 55296*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^3*c^7*d^11*e^3 - 1683456*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^2*c^8*d^11*e^3 - 960512*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^4*c^7*d^12*e^2 - 688128*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*c^8*d^12*e^2 - 1025024*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^5*c^7*d^13*e + 215040*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*c^8*d^13*e + 86016*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^5*c^(15/2)*d^14 + 358400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^2*c^(13/2)*d^9*e^5 - 2150400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b*c^(15/2)*d^9*e^5 + 4515840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^3*c^(13/2)*d^10*e^4 - 2795520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^2*c^(15/2)*d^10*e^4 + 4515840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^4*c^(13/2)*d^11*e^3 - 2795520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^3*c^(15/2)*d^11*e^3 + 1078784*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^5*c^(13/2)*d^12*e^2 - 967680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^4*c^(15/2)*d^12*e^2 - 326144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^6*c^(13/2)*d^13*e + 64512*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^5*c^(15/2)*d^13*e + 14336*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^6*c^7*d^14 + 2867200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^2*c^6*d^8*e^6 + 3512320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^3*c^6*d^9*e^5 - 4300800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^2*c^7*d^9*e^5 + 5806080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^4*c^6*d^10*e^4 - 2119680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^3*c^7*d^10*e^4 + 4076800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^5*c^6*d^11*e^3 - 1774080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^4*c^7*d^11*e^3 + 1028608*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^6*c^6*d^12*e^2 - 580608*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^5*c^7*d^12*e^2 - 55552*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^7*c^6*d^13*e + 10752*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^6*c^7*d^13*e + 1024*B*b^7*c^(13/2)*d^14 + 5017600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^3*c^(11/2)*d^8*e^6 + 4300800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^2*c^(13/2)*d^8*e^6 + 1720320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^4*c^(11/2)*d^9*e^5 - 1935360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^3*c^(13/2)*d^9*e^5 + 1975680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^5*c^(11/2)*d^10*e^4 + 564480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^4*c^(13/2)*d^10*e^4 + 1511552*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^6*c^(11/2)*d^11*e^3 - 413952*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^5*c^(13/2)*d^11*e^3 + 380800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^7*c^(11/2)*d^12*e^2 - 188160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^6*c^(13/2)*d^12*e^2 - 3968*B*b^8*c^(11/2)*d^13*e + 768*A*b^7*c^(13/2)*d^13*e - 2867200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^3*c^5*d^7*e^7 + 1863680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^4*c^5*d^8*e^6 + 13762560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^3*c^6*d^8*e^6 - 2088576*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^5*c^5*d^9*e^5 + 2327808*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^4*c^6*d^9*e^5 - 815360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^6*c^5*d^10*e^4 + 1881600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^5*c^6*d^10*e^4 + 184576*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^7*c^5*d^11*e^3 + 75264*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^6*c^6*d^11*e^3 + 68096*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^8*c^5*d^12*e^2 - 32256*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^7*c^6*d^12*e^2 - 7884800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^4*c^(9/2)*d^7*e^7 - 4300800*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^3*c^(11/2)*d^7*e^7 - 2283456*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^5*c^(9/2)*d^8*e^6 + 16695168*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^4*c^(11/2)*d^8*e^6 - 2968896*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^6*c^(9/2)*d^9*e^5 + 3067008*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^5*c^(11/2)*d^9*e^5 - 1017856*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^7*c^(9/2)*d^10*e^4 + 1430016*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^6*c^(11/2)*d^10*e^4 - 33152*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^8*c^(9/2)*d^11*e^3 + 64512*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^7*c^(11/2)*d^11*e^3 + 4864*B*b^9*c^(9/2)*d^12*e^2 - 2304*A*b^8*c^(11/2)*d^12*e^2 + 1433600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^4*c^4*d^6*e^8 - 7790944*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^5*c^4*d^7*e^7 - 18193728*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^4*c^5*d^7*e^7 - 2131136*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^6*c^4*d^8*e^6 + 7469952*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^5*c^5*d^8*e^6 - 1485344*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^7*c^4*d^9*e^5 + 716352*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^6*c^5*d^9*e^5 - 459200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^8*c^4*d^10*e^4 + 618240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^7*c^5*d^10*e^4 - 11200*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^9*c^4*d^11*e^3 + 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^8*c^5*d^11*e^3 + 5338480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^5*c^(7/2)*d^6*e^8 + 1078560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^4*c^(9/2)*d^6*e^8 - 2001328*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^6*c^(7/2)*d^7*e^7 - 28144032*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^5*c^(9/2)*d^7*e^7 + 333872*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^7*c^(7/2)*d^8*e^6 - 2198112*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^6*c^(9/2)*d^8*e^6 - 160720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^8*c^(7/2)*d^9*e^5 - 971040*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^7*c^(9/2)*d^9*e^5 - 123200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^9*c^(7/2)*d^10*e^4 + 168000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^8*c^(9/2)*d^10*e^4 - 800*B*b^10*c^(7/2)*d^11*e^3 + 960*A*b^9*c^(9/2)*d^11*e^3 - 106960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^5*c^3*d^5*e^9 - 359520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^4*c^4*d^5*e^9 + 6953408*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^6*c^3*d^6*e^8 + 10063872*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^5*c^4*d^6*e^8 + 1909360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^7*c^3*d^7*e^7 - 20156640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^6*c^4*d^7*e^7 + 1255408*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^8*c^3*d^8*e^6 - 3698688*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^7*c^4*d^8*e^6 + 192640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^9*c^3*d^9*e^5 - 913920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^8*c^4*d^9*e^5 - 19600*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^10*c^3*d^10*e^4 + 26880*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^9*c^4*d^10*e^4 + 32760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*B*b^5*c^(5/2)*d^4*e^10 - 65520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*A*b^4*c^(7/2)*d^4*e^10 - 1337000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^6*c^(5/2)*d^5*e^9 + 808080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^5*c^(7/2)*d^5*e^9 + 3935624*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^7*c^(5/2)*d^6*e^8 + 19619376*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^6*c^(7/2)*d^6*e^8 + 1520624*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^8*c^(5/2)*d^7*e^7 - 5499984*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^7*c^(7/2)*d^7*e^7 + 673400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^9*c^(5/2)*d^8*e^6 - 1233120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^8*c^(7/2)*d^8*e^6 + 104440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^10*c^(5/2)*d^9*e^5 - 351456*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^9*c^(7/2)*d^9*e^5 - 1400*B*b^11*c^(5/2)*d^10*e^4 + 1920*A*b^10*c^(7/2)*d^10*e^4 + 2520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^13*B*b^5*c^2*d^3*e^11 - 5040*(sqrt(c)*x - sqrt(c*x^2 + b*x))^13*A*b^4*c^3*d^3*e^11 - 133000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^6*c^2*d^4*e^10 + 505680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^5*c^3*d^4*e^10 - 2213764*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^7*c^2*d^5*e^9 - 1120056*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^6*c^3*d^5*e^9 + 595552*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^8*c^2*d^6*e^8 + 16718928*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^7*c^3*d^6*e^8 + 229936*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^9*c^2*d^7*e^7 + 1320144*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^8*c^3*d^7*e^7 + 133000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^10*c^2*d^8*e^6 + 122304*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^9*c^3*d^8*e^6 + 21980*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^11*c^2*d^9*e^5 - 66696*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^10*c^3*d^9*e^5 - 27300*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*B*b^6*c^(3/2)*d^3*e^11 + 98280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*A*b^5*c^(5/2)*d^3*e^11 - 42350*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^7*c^(3/2)*d^4*e^10 - 383460*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^6*c^(5/2)*d^4*e^10 - 1534330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^8*c^(3/2)*d^5*e^9 - 5388180*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^7*c^(5/2)*d^5*e^9 - 422380*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^9*c^(3/2)*d^6*e^8 + 7011480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^8*c^(5/2)*d^6*e^8 - 141400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^10*c^(3/2)*d^7*e^7 + 1334256*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^9*c^(5/2)*d^7*e^7 - 4550*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^11*c^(3/2)*d^8*e^6 + 183372*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^10*c^(5/2)*d^8*e^6 + 1750*B*b^12*c^(3/2)*d^9*e^5 - 5124*A*b^11*c^(5/2)*d^9*e^5 - 2100*(sqrt(c)*x - sqrt(c*x^2 + b*x))^13*B*b^6*c*d^2*e^12 + 7560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^13*A*b^5*c^2*d^2*e^12 + 23450*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^7*c*d^3*e^11 - 264180*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^6*c^2*d^3*e^11 + 133070*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^8*c*d^4*e^10 - 960960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^7*c^2*d^4*e^10 - 549660*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^9*c*d^5*e^9 - 5471640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^8*c^2*d^5*e^9 - 243320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^10*c*d^6*e^8 + 1126440*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^9*c^2*d^6*e^8 - 67550*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^11*c*d^7*e^7 + 317100*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^10*c^2*d^7*e^7 - 5250*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^12*c*d^8*e^6 + 45360*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^11*c^2*d^8*e^6 + 6825*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*B*b^7*sqrt(c)*d^2*e^12 - 57330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*A*b^6*c^(3/2)*d^2*e^12 + 38500*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*B*b^8*sqrt(c)*d^3*e^11 - 122430*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^7*c^(3/2)*d^3*e^11 + 89145*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*B*b^9*sqrt(c)*d^4*e^10 - 30240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^8*c^(3/2)*d^4*e^10 - 107520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*B*b^10*sqrt(c)*d^5*e^9 - 2566620*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^9*c^(3/2)*d^5*e^9 - 49525*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^11*sqrt(c)*d^6*e^8 - 195090*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^10*c^(3/2)*d^6*e^8 - 10500*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^12*sqrt(c)*d^7*e^7 + 4410*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^11*c^(3/2)*d^7*e^7 - 525*B*b^13*sqrt(c)*d^8*e^6 + 3780*A*b^12*c^(3/2)*d^8*e^6 + 525*(sqrt(c)*x - sqrt(c*x^2 + b*x))^13*B*b^7*d*e^13 - 4410*(sqrt(c)*x - sqrt(c*x^2 + b*x))^13*A*b^6*c*d*e^13 + 3500*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*B*b^8*d^2*e^12 + 38010*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^7*c*d^2*e^12 + 9905*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*B*b^9*d^3*e^11 + 227640*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^8*c*d^3*e^11 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*B*b^10*d^4*e^10 + 429876*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^9*c*d^4*e^10 - 9905*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^11*d^5*e^9 - 641130*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^10*c*d^5*e^9 - 3500*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^12*d^6*e^8 - 117390*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^11*c*d^6*e^8 - 525*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^13*d^7*e^7 - 8820*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^12*c*d^7*e^7 + 12285*(sqrt(c)*x - sqrt(c*x^2 + b*x))^12*A*b^7*sqrt(c)*d*e^13 + 69300*(sqrt(c)*x - sqrt(c*x^2 + b*x))^10*A*b^8*sqrt(c)*d^2*e^12 + 160461*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*A*b^9*sqrt(c)*d^3*e^11 + 193536*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*A*b^10*sqrt(c)*d^4*e^10 - 89145*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^11*sqrt(c)*d^5*e^9 - 18900*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^12*sqrt(c)*d^6*e^8 - 945*A*b^13*sqrt(c)*d^7*e^7 + 945*(sqrt(c)*x - sqrt(c*x^2 + b*x))^13*A*b^7*e^14 + 6300*(sqrt(c)*x - sqrt(c*x^2 + b*x))^11*A*b^8*d*e^13 + 17829*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*A*b^9*d^2*e^12 + 27648*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*A*b^10*d^3*e^11 + 25179*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^11*d^4*e^10 - 6300*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^12*d^5*e^9 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^13*d^6*e^8)/((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)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^7)","B",0
1183,1,681,0,0.304014," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{2064384} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, B c^{2} x e^{2} + \frac{36 \, B c^{10} d e + 37 \, B b c^{9} e^{2} + 18 \, A c^{10} e^{2}}{c^{8}}\right)} x + \frac{3 \, {\left(96 \, B c^{10} d^{2} + 396 \, B b c^{9} d e + 192 \, A c^{10} d e + 103 \, B b^{2} c^{8} e^{2} + 198 \, A b c^{9} e^{2}\right)}}{c^{8}}\right)} x + \frac{2784 \, B b c^{9} d^{2} + 1344 \, A c^{10} d^{2} + 2916 \, B b^{2} c^{8} d e + 5568 \, A b c^{9} d e + 5 \, B b^{3} c^{7} e^{2} + 1458 \, A b^{2} c^{8} e^{2}}{c^{8}}\right)} x + \frac{3552 \, B b^{2} c^{8} d^{2} + 6720 \, A b c^{9} d^{2} + 36 \, B b^{3} c^{7} d e + 7104 \, A b^{2} c^{8} d e - 11 \, B b^{4} c^{6} e^{2} + 18 \, A b^{3} c^{7} e^{2}}{c^{8}}\right)} x + \frac{9 \, {\left(32 \, B b^{3} c^{7} d^{2} + 4032 \, A b^{2} c^{8} d^{2} - 36 \, B b^{4} c^{6} d e + 64 \, A b^{3} c^{7} d e + 11 \, B b^{5} c^{5} e^{2} - 18 \, A b^{4} c^{6} e^{2}\right)}}{c^{8}}\right)} x - \frac{21 \, {\left(32 \, B b^{4} c^{6} d^{2} - 64 \, A b^{3} c^{7} d^{2} - 36 \, B b^{5} c^{5} d e + 64 \, A b^{4} c^{6} d e + 11 \, B b^{6} c^{4} e^{2} - 18 \, A b^{5} c^{5} e^{2}\right)}}{c^{8}}\right)} x + \frac{105 \, {\left(32 \, B b^{5} c^{5} d^{2} - 64 \, A b^{4} c^{6} d^{2} - 36 \, B b^{6} c^{4} d e + 64 \, A b^{5} c^{5} d e + 11 \, B b^{7} c^{3} e^{2} - 18 \, A b^{6} c^{4} e^{2}\right)}}{c^{8}}\right)} x - \frac{315 \, {\left(32 \, B b^{6} c^{4} d^{2} - 64 \, A b^{5} c^{5} d^{2} - 36 \, B b^{7} c^{3} d e + 64 \, A b^{6} c^{4} d e + 11 \, B b^{8} c^{2} e^{2} - 18 \, A b^{7} c^{3} e^{2}\right)}}{c^{8}}\right)} - \frac{5 \, {\left(32 \, B b^{7} c^{2} d^{2} - 64 \, A b^{6} c^{3} d^{2} - 36 \, B b^{8} c d e + 64 \, A b^{7} c^{2} d e + 11 \, B b^{9} e^{2} - 18 \, A b^{8} c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{65536 \, c^{\frac{13}{2}}}"," ",0,"1/2064384*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(4*(14*(16*B*c^2*x*e^2 + (36*B*c^10*d*e + 37*B*b*c^9*e^2 + 18*A*c^10*e^2)/c^8)*x + 3*(96*B*c^10*d^2 + 396*B*b*c^9*d*e + 192*A*c^10*d*e + 103*B*b^2*c^8*e^2 + 198*A*b*c^9*e^2)/c^8)*x + (2784*B*b*c^9*d^2 + 1344*A*c^10*d^2 + 2916*B*b^2*c^8*d*e + 5568*A*b*c^9*d*e + 5*B*b^3*c^7*e^2 + 1458*A*b^2*c^8*e^2)/c^8)*x + (3552*B*b^2*c^8*d^2 + 6720*A*b*c^9*d^2 + 36*B*b^3*c^7*d*e + 7104*A*b^2*c^8*d*e - 11*B*b^4*c^6*e^2 + 18*A*b^3*c^7*e^2)/c^8)*x + 9*(32*B*b^3*c^7*d^2 + 4032*A*b^2*c^8*d^2 - 36*B*b^4*c^6*d*e + 64*A*b^3*c^7*d*e + 11*B*b^5*c^5*e^2 - 18*A*b^4*c^6*e^2)/c^8)*x - 21*(32*B*b^4*c^6*d^2 - 64*A*b^3*c^7*d^2 - 36*B*b^5*c^5*d*e + 64*A*b^4*c^6*d*e + 11*B*b^6*c^4*e^2 - 18*A*b^5*c^5*e^2)/c^8)*x + 105*(32*B*b^5*c^5*d^2 - 64*A*b^4*c^6*d^2 - 36*B*b^6*c^4*d*e + 64*A*b^5*c^5*d*e + 11*B*b^7*c^3*e^2 - 18*A*b^6*c^4*e^2)/c^8)*x - 315*(32*B*b^6*c^4*d^2 - 64*A*b^5*c^5*d^2 - 36*B*b^7*c^3*d*e + 64*A*b^6*c^4*d*e + 11*B*b^8*c^2*e^2 - 18*A*b^7*c^3*e^2)/c^8) - 5/65536*(32*B*b^7*c^2*d^2 - 64*A*b^6*c^3*d^2 - 36*B*b^8*c*d*e + 64*A*b^7*c^2*d*e + 11*B*b^9*e^2 - 18*A*b^8*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(13/2)","A",0
1184,1,425,0,0.270488," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{344064} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, B c^{2} x e + \frac{16 \, B c^{9} d + 33 \, B b c^{8} e + 16 \, A c^{9} e}{c^{7}}\right)} x + \frac{464 \, B b c^{8} d + 224 \, A c^{9} d + 243 \, B b^{2} c^{7} e + 464 \, A b c^{8} e}{c^{7}}\right)} x + \frac{592 \, B b^{2} c^{7} d + 1120 \, A b c^{8} d + 3 \, B b^{3} c^{6} e + 592 \, A b^{2} c^{7} e}{c^{7}}\right)} x + \frac{3 \, {\left(16 \, B b^{3} c^{6} d + 2016 \, A b^{2} c^{7} d - 9 \, B b^{4} c^{5} e + 16 \, A b^{3} c^{6} e\right)}}{c^{7}}\right)} x - \frac{7 \, {\left(16 \, B b^{4} c^{5} d - 32 \, A b^{3} c^{6} d - 9 \, B b^{5} c^{4} e + 16 \, A b^{4} c^{5} e\right)}}{c^{7}}\right)} x + \frac{35 \, {\left(16 \, B b^{5} c^{4} d - 32 \, A b^{4} c^{5} d - 9 \, B b^{6} c^{3} e + 16 \, A b^{5} c^{4} e\right)}}{c^{7}}\right)} x - \frac{105 \, {\left(16 \, B b^{6} c^{3} d - 32 \, A b^{5} c^{4} d - 9 \, B b^{7} c^{2} e + 16 \, A b^{6} c^{3} e\right)}}{c^{7}}\right)} - \frac{5 \, {\left(16 \, B b^{7} c d - 32 \, A b^{6} c^{2} d - 9 \, B b^{8} e + 16 \, A b^{7} c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{11}{2}}}"," ",0,"1/344064*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(12*(14*B*c^2*x*e + (16*B*c^9*d + 33*B*b*c^8*e + 16*A*c^9*e)/c^7)*x + (464*B*b*c^8*d + 224*A*c^9*d + 243*B*b^2*c^7*e + 464*A*b*c^8*e)/c^7)*x + (592*B*b^2*c^7*d + 1120*A*b*c^8*d + 3*B*b^3*c^6*e + 592*A*b^2*c^7*e)/c^7)*x + 3*(16*B*b^3*c^6*d + 2016*A*b^2*c^7*d - 9*B*b^4*c^5*e + 16*A*b^3*c^6*e)/c^7)*x - 7*(16*B*b^4*c^5*d - 32*A*b^3*c^6*d - 9*B*b^5*c^4*e + 16*A*b^4*c^5*e)/c^7)*x + 35*(16*B*b^5*c^4*d - 32*A*b^4*c^5*d - 9*B*b^6*c^3*e + 16*A*b^5*c^4*e)/c^7)*x - 105*(16*B*b^6*c^3*d - 32*A*b^5*c^4*d - 9*B*b^7*c^2*e + 16*A*b^6*c^3*e)/c^7) - 5/32768*(16*B*b^7*c*d - 32*A*b^6*c^2*d - 9*B*b^8*e + 16*A*b^7*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
1185,1,221,0,0.255514," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{21504} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, B c^{2} x + \frac{29 \, B b c^{7} + 14 \, A c^{8}}{c^{6}}\right)} x + \frac{37 \, B b^{2} c^{6} + 70 \, A b c^{7}}{c^{6}}\right)} x + \frac{3 \, {\left(B b^{3} c^{5} + 126 \, A b^{2} c^{6}\right)}}{c^{6}}\right)} x - \frac{7 \, {\left(B b^{4} c^{4} - 2 \, A b^{3} c^{5}\right)}}{c^{6}}\right)} x + \frac{35 \, {\left(B b^{5} c^{3} - 2 \, A b^{4} c^{4}\right)}}{c^{6}}\right)} x - \frac{105 \, {\left(B b^{6} c^{2} - 2 \, A b^{5} c^{3}\right)}}{c^{6}}\right)} - \frac{5 \, {\left(B b^{7} - 2 \, A b^{6} c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{9}{2}}}"," ",0,"1/21504*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(12*B*c^2*x + (29*B*b*c^7 + 14*A*c^8)/c^6)*x + (37*B*b^2*c^6 + 70*A*b*c^7)/c^6)*x + 3*(B*b^3*c^5 + 126*A*b^2*c^6)/c^6)*x - 7*(B*b^4*c^4 - 2*A*b^3*c^5)/c^6)*x + 35*(B*b^5*c^3 - 2*A*b^4*c^4)/c^6)*x - 105*(B*b^6*c^2 - 2*A*b^5*c^3)/c^6) - 5/2048*(B*b^7 - 2*A*b^6*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
1186,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1187,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1188,1,1425,0,0.629699," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(24 \, B c^{3} d^{5} - 52 \, B b c^{2} d^{4} e - 16 \, A c^{3} d^{4} e + 35 \, B b^{2} c d^{3} e^{2} + 32 \, A b c^{2} d^{3} e^{2} - 7 \, B b^{3} d^{2} e^{3} - 19 \, A b^{2} c d^{2} e^{3} + 3 \, A b^{3} d e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right) e^{\left(-7\right)}}{4 \, \sqrt{-c d^{2} + b d e}} + \frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, B c^{2} x e^{\left(-3\right)} - \frac{{\left(24 \, B c^{5} d e^{21} - 17 \, B b c^{4} e^{22} - 8 \, A c^{5} e^{22}\right)} e^{\left(-25\right)}}{c^{3}}\right)} x + \frac{{\left(288 \, B c^{5} d^{2} e^{20} - 312 \, B b c^{4} d e^{21} - 144 \, A c^{5} d e^{21} + 59 \, B b^{2} c^{3} e^{22} + 104 \, A b c^{4} e^{22}\right)} e^{\left(-25\right)}}{c^{3}}\right)} x - \frac{3 \, {\left(640 \, B c^{5} d^{3} e^{19} - 864 \, B b c^{4} d^{2} e^{20} - 384 \, A c^{5} d^{2} e^{20} + 264 \, B b^{2} c^{3} d e^{21} + 432 \, A b c^{4} d e^{21} - 5 \, B b^{3} c^{2} e^{22} - 88 \, A b^{2} c^{3} e^{22}\right)} e^{\left(-25\right)}}{c^{3}}\right)} - \frac{5 \, {\left(384 \, B c^{4} d^{4} - 640 \, B b c^{3} d^{3} e - 256 \, A c^{4} d^{3} e + 288 \, B b^{2} c^{2} d^{2} e^{2} + 384 \, A b c^{3} d^{2} e^{2} - 24 \, B b^{3} c d e^{3} - 144 \, A b^{2} c^{2} d e^{3} - B b^{4} e^{4} + 8 \, A b^{3} c e^{4}\right)} e^{\left(-7\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b \right|}\right)}{128 \, c^{\frac{3}{2}}} - \frac{{\left(48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{\frac{7}{2}} d^{5} e + 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B c^{4} d^{6} - 156 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{3} d^{5} e - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A c^{4} d^{5} e + 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b c^{\frac{7}{2}} d^{6} - 100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c^{\frac{5}{2}} d^{4} e^{2} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{\frac{7}{2}} d^{4} e^{2} - 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c^{\frac{5}{2}} d^{5} e - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b c^{\frac{7}{2}} d^{5} e + 22 \, B b^{2} c^{3} d^{6} + 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c^{2} d^{4} e^{2} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{3} d^{4} e^{2} - 35 \, B b^{3} c^{2} d^{5} e - 18 \, A b^{2} c^{3} d^{5} e + 65 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c^{\frac{3}{2}} d^{3} e^{3} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{\frac{5}{2}} d^{3} e^{3} + 83 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} c^{\frac{3}{2}} d^{4} e^{2} + 124 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{\frac{5}{2}} d^{4} e^{2} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c d^{3} e^{3} - 51 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{2} d^{3} e^{3} + 13 \, B b^{4} c d^{4} e^{2} + 27 \, A b^{3} c^{2} d^{4} e^{2} - 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} \sqrt{c} d^{2} e^{4} - 49 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{\frac{3}{2}} d^{2} e^{4} - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} \sqrt{c} d^{3} e^{3} - 59 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c^{\frac{3}{2}} d^{3} e^{3} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c d^{2} e^{4} - 9 \, A b^{4} c d^{3} e^{3} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} \sqrt{c} d e^{5} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} \sqrt{c} d^{2} e^{4}\right)} e^{\left(-7\right)}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2} \sqrt{c}}"," ",0,"-5/4*(24*B*c^3*d^5 - 52*B*b*c^2*d^4*e - 16*A*c^3*d^4*e + 35*B*b^2*c*d^3*e^2 + 32*A*b*c^2*d^3*e^2 - 7*B*b^3*d^2*e^3 - 19*A*b^2*c*d^2*e^3 + 3*A*b^3*d*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))*e^(-7)/sqrt(-c*d^2 + b*d*e) + 1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*B*c^2*x*e^(-3) - (24*B*c^5*d*e^21 - 17*B*b*c^4*e^22 - 8*A*c^5*e^22)*e^(-25)/c^3)*x + (288*B*c^5*d^2*e^20 - 312*B*b*c^4*d*e^21 - 144*A*c^5*d*e^21 + 59*B*b^2*c^3*e^22 + 104*A*b*c^4*e^22)*e^(-25)/c^3)*x - 3*(640*B*c^5*d^3*e^19 - 864*B*b*c^4*d^2*e^20 - 384*A*c^5*d^2*e^20 + 264*B*b^2*c^3*d*e^21 + 432*A*b*c^4*d*e^21 - 5*B*b^3*c^2*e^22 - 88*A*b^2*c^3*e^22)*e^(-25)/c^3) - 5/128*(384*B*c^4*d^4 - 640*B*b*c^3*d^3*e - 256*A*c^4*d^3*e + 288*B*b^2*c^2*d^2*e^2 + 384*A*b*c^3*d^2*e^2 - 24*B*b^3*c*d*e^3 - 144*A*b^2*c^2*d*e^3 - B*b^4*e^4 + 8*A*b^3*c*e^4)*e^(-7)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b))/c^(3/2) - 1/4*(48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^(7/2)*d^5*e + 88*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*c^4*d^6 - 156*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^3*d^5*e - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*c^4*d^5*e + 88*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b*c^(7/2)*d^6 - 100*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c^(5/2)*d^4*e^2 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^(7/2)*d^4*e^2 - 160*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c^(5/2)*d^5*e - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b*c^(7/2)*d^5*e + 22*B*b^2*c^3*d^6 + 75*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c^2*d^4*e^2 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^3*d^4*e^2 - 35*B*b^3*c^2*d^5*e - 18*A*b^2*c^3*d^5*e + 65*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c^(3/2)*d^3*e^3 + 80*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^(5/2)*d^3*e^3 + 83*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*c^(3/2)*d^4*e^2 + 124*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^(5/2)*d^4*e^2 - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c*d^3*e^3 - 51*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^2*d^3*e^3 + 13*B*b^4*c*d^4*e^2 + 27*A*b^3*c^2*d^4*e^2 - 13*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*sqrt(c)*d^2*e^4 - 49*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^(3/2)*d^2*e^4 - 11*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*sqrt(c)*d^3*e^3 - 59*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c^(3/2)*d^3*e^3 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c*d^2*e^4 - 9*A*b^4*c*d^3*e^3 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*sqrt(c)*d*e^5 + 7*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*sqrt(c)*d^2*e^4)*e^(-7)/(((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2*sqrt(c))","B",0
1189,1,1907,0,0.800907," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","\frac{5 \, {\left(64 \, B c^{3} d^{4} - 112 \, B b c^{2} d^{3} e - 32 \, A c^{3} d^{3} e + 56 \, B b^{2} c d^{2} e^{2} + 48 \, A b c^{2} d^{2} e^{2} - 7 \, B b^{3} d e^{3} - 18 \, A b^{2} c d e^{3} + A b^{3} e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right) e^{\left(-7\right)}}{8 \, \sqrt{-c d^{2} + b d e}} + \frac{5 \, {\left(64 \, B c^{3} d^{3} - 80 \, B b c^{2} d^{2} e - 32 \, A c^{3} d^{2} e + 24 \, B b^{2} c d e^{2} + 32 \, A b c^{2} d e^{2} - B b^{3} e^{3} - 6 \, A b^{2} c e^{3}\right)} e^{\left(-7\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b \right|}\right)}{16 \, \sqrt{c}} + \frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, B c^{2} x e^{\left(-4\right)} - \frac{{\left(24 \, B c^{4} d e^{17} - 13 \, B b c^{3} e^{18} - 6 \, A c^{4} e^{18}\right)} e^{\left(-22\right)}}{c^{2}}\right)} x + \frac{3 \, {\left(80 \, B c^{4} d^{2} e^{16} - 72 \, B b c^{3} d e^{17} - 32 \, A c^{4} d e^{17} + 11 \, B b^{2} c^{2} e^{18} + 18 \, A b c^{3} e^{18}\right)} e^{\left(-22\right)}}{c^{2}}\right)} + \frac{{\left(2592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B c^{4} d^{5} e + 2368 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{\frac{9}{2}} d^{6} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B c^{\frac{7}{2}} d^{4} e^{2} - 1168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c^{\frac{7}{2}} d^{5} e - 1504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{\frac{9}{2}} d^{5} e + 3552 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{4} d^{6} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c^{3} d^{4} e^{2} - 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A c^{4} d^{4} e^{2} - 4512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c^{3} d^{5} e - 2256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{4} d^{5} e + 1776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c^{\frac{7}{2}} d^{6} - 1200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{\frac{5}{2}} d^{3} e^{3} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{\frac{7}{2}} d^{3} e^{3} - 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c^{\frac{5}{2}} d^{4} e^{2} + 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{\frac{7}{2}} d^{4} e^{2} - 2340 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} c^{\frac{5}{2}} d^{5} e - 1128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{\frac{7}{2}} d^{5} e + 296 \, B b^{3} c^{3} d^{6} + 1560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c^{2} d^{3} e^{3} + 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{3} d^{3} e^{3} + 1314 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c^{2} d^{4} e^{2} + 2412 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{3} d^{4} e^{2} - 350 \, B b^{4} c^{2} d^{5} e - 188 \, A b^{3} c^{3} d^{5} e + 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c^{\frac{3}{2}} d^{2} e^{4} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{\frac{5}{2}} d^{2} e^{4} + 1186 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c^{\frac{3}{2}} d^{3} e^{3} + 1308 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{\frac{5}{2}} d^{3} e^{3} + 786 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} c^{\frac{3}{2}} d^{4} e^{2} + 1272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c^{\frac{5}{2}} d^{4} e^{2} - 147 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} c d^{2} e^{4} - 666 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{2} d^{2} e^{4} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} c d^{3} e^{3} - 462 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c^{2} d^{3} e^{3} + 87 \, B b^{5} c d^{4} e^{2} + 188 \, A b^{4} c^{2} d^{4} e^{2} - 87 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} \sqrt{c} d e^{5} - 306 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c^{\frac{3}{2}} d e^{5} - 136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} \sqrt{c} d^{2} e^{4} - 574 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c^{\frac{3}{2}} d^{2} e^{4} - 57 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{5} \sqrt{c} d^{3} e^{3} - 324 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} c^{\frac{3}{2}} d^{3} e^{3} + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} c d e^{5} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} c d^{2} e^{4} - 33 \, A b^{5} c d^{3} e^{3} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} \sqrt{c} e^{6} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} \sqrt{c} d e^{5} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} \sqrt{c} d^{2} e^{4}\right)} e^{\left(-7\right)}}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{3} \sqrt{c}}"," ",0,"5/8*(64*B*c^3*d^4 - 112*B*b*c^2*d^3*e - 32*A*c^3*d^3*e + 56*B*b^2*c*d^2*e^2 + 48*A*b*c^2*d^2*e^2 - 7*B*b^3*d*e^3 - 18*A*b^2*c*d*e^3 + A*b^3*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))*e^(-7)/sqrt(-c*d^2 + b*d*e) + 5/16*(64*B*c^3*d^3 - 80*B*b*c^2*d^2*e - 32*A*c^3*d^2*e + 24*B*b^2*c*d*e^2 + 32*A*b*c^2*d*e^2 - B*b^3*e^3 - 6*A*b^2*c*e^3)*e^(-7)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b))/sqrt(c) + 1/24*sqrt(c*x^2 + b*x)*(2*(4*B*c^2*x*e^(-4) - (24*B*c^4*d*e^17 - 13*B*b*c^3*e^18 - 6*A*c^4*e^18)*e^(-22)/c^2)*x + 3*(80*B*c^4*d^2*e^16 - 72*B*b*c^3*d*e^17 - 32*A*c^4*d*e^17 + 11*B*b^2*c^2*e^18 + 18*A*b*c^3*e^18)*e^(-22)/c^2) + 1/24*(2592*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*c^4*d^5*e + 2368*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^(9/2)*d^6 + 720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*c^(7/2)*d^4*e^2 - 1168*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c^(7/2)*d^5*e - 1504*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^(9/2)*d^5*e + 3552*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^4*d^6 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c^3*d^4*e^2 - 1680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*c^4*d^4*e^2 - 4512*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c^3*d^5*e - 2256*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^4*d^5*e + 1776*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c^(7/2)*d^6 - 1200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^(5/2)*d^3*e^3 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^(7/2)*d^3*e^3 - 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c^(5/2)*d^4*e^2 + 400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^(7/2)*d^4*e^2 - 2340*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*c^(5/2)*d^5*e - 1128*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^(7/2)*d^5*e + 296*B*b^3*c^3*d^6 + 1560*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c^2*d^3*e^3 + 2160*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^3*d^3*e^3 + 1314*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c^2*d^4*e^2 + 2412*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^3*d^4*e^2 - 350*B*b^4*c^2*d^5*e - 188*A*b^3*c^3*d^5*e + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c^(3/2)*d^2*e^4 + 720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^(5/2)*d^2*e^4 + 1186*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c^(3/2)*d^3*e^3 + 1308*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^(5/2)*d^3*e^3 + 786*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*c^(3/2)*d^4*e^2 + 1272*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c^(5/2)*d^4*e^2 - 147*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*c*d^2*e^4 - 666*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^2*d^2*e^4 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*c*d^3*e^3 - 462*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c^2*d^3*e^3 + 87*B*b^5*c*d^4*e^2 + 188*A*b^4*c^2*d^4*e^2 - 87*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*sqrt(c)*d*e^5 - 306*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c^(3/2)*d*e^5 - 136*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*sqrt(c)*d^2*e^4 - 574*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c^(3/2)*d^2*e^4 - 57*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^5*sqrt(c)*d^3*e^3 - 324*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*c^(3/2)*d^3*e^3 + 21*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*c*d*e^5 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*c*d^2*e^4 - 33*A*b^5*c*d^3*e^3 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*sqrt(c)*e^6 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*sqrt(c)*d*e^5 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*sqrt(c)*d^2*e^4)*e^(-7)/(((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^3*sqrt(c))","B",0
1190,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1191,1,311,0,0.328826," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(\frac{6 \, B x e^{3}}{c} + \frac{24 \, B c^{3} d e^{2} - 7 \, B b c^{2} e^{3} + 8 \, A c^{3} e^{3}}{c^{4}}\right)} x + \frac{144 \, B c^{3} d^{2} e - 120 \, B b c^{2} d e^{2} + 144 \, A c^{3} d e^{2} + 35 \, B b^{2} c e^{3} - 40 \, A b c^{2} e^{3}}{c^{4}}\right)} x + \frac{3 \, {\left(64 \, B c^{3} d^{3} - 144 \, B b c^{2} d^{2} e + 192 \, A c^{3} d^{2} e + 120 \, B b^{2} c d e^{2} - 144 \, A b c^{2} d e^{2} - 35 \, B b^{3} e^{3} + 40 \, A b^{2} c e^{3}\right)}}{c^{4}}\right)} + \frac{{\left(64 \, B b c^{3} d^{3} - 128 \, A c^{4} d^{3} - 144 \, B b^{2} c^{2} d^{2} e + 192 \, A b c^{3} d^{2} e + 120 \, B b^{3} c d e^{2} - 144 \, A b^{2} c^{2} d e^{2} - 35 \, B b^{4} e^{3} + 40 \, A b^{3} c e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*B*x*e^3/c + (24*B*c^3*d*e^2 - 7*B*b*c^2*e^3 + 8*A*c^3*e^3)/c^4)*x + (144*B*c^3*d^2*e - 120*B*b*c^2*d*e^2 + 144*A*c^3*d*e^2 + 35*B*b^2*c*e^3 - 40*A*b*c^2*e^3)/c^4)*x + 3*(64*B*c^3*d^3 - 144*B*b*c^2*d^2*e + 192*A*c^3*d^2*e + 120*B*b^2*c*d*e^2 - 144*A*b*c^2*d*e^2 - 35*B*b^3*e^3 + 40*A*b^2*c*e^3)/c^4) + 1/128*(64*B*b*c^3*d^3 - 128*A*c^4*d^3 - 144*B*b^2*c^2*d^2*e + 192*A*b*c^3*d^2*e + 120*B*b^3*c*d*e^2 - 144*A*b^2*c^2*d*e^2 - 35*B*b^4*e^3 + 40*A*b^3*c*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
1192,1,196,0,0.281745," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(\frac{4 \, B x e^{2}}{c} + \frac{12 \, B c^{2} d e - 5 \, B b c e^{2} + 6 \, A c^{2} e^{2}}{c^{3}}\right)} x + \frac{3 \, {\left(8 \, B c^{2} d^{2} - 12 \, B b c d e + 16 \, A c^{2} d e + 5 \, B b^{2} e^{2} - 6 \, A b c e^{2}\right)}}{c^{3}}\right)} + \frac{{\left(8 \, B b c^{2} d^{2} - 16 \, A c^{3} d^{2} - 12 \, B b^{2} c d e + 16 \, A b c^{2} d e + 5 \, B b^{3} e^{2} - 6 \, A b^{2} c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*(4*B*x*e^2/c + (12*B*c^2*d*e - 5*B*b*c*e^2 + 6*A*c^2*e^2)/c^3)*x + 3*(8*B*c^2*d^2 - 12*B*b*c*d*e + 16*A*c^2*d*e + 5*B*b^2*e^2 - 6*A*b*c*e^2)/c^3) + 1/16*(8*B*b*c^2*d^2 - 16*A*c^3*d^2 - 12*B*b^2*c*d*e + 16*A*b*c^2*d*e + 5*B*b^3*e^2 - 6*A*b^2*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
1193,1,110,0,0.280643," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(\frac{2 \, B x e}{c} + \frac{4 \, B c d - 3 \, B b e + 4 \, A c e}{c^{2}}\right)} + \frac{{\left(4 \, B b c d - 8 \, A c^{2} d - 3 \, B b^{2} e + 4 \, A b c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*B*x*e/c + (4*B*c*d - 3*B*b*e + 4*A*c*e)/c^2) + 1/8*(4*B*b*c*d - 8*A*c^2*d - 3*B*b^2*e + 4*A*b*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
1194,1,60,0,0.267488," ","integrate((B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x} B}{c} + \frac{{\left(B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"sqrt(c*x^2 + b*x)*B/c + 1/2*(B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
1195,-2,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1196,1,509,0,1.096123," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{{\left(B b d e^{2} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 2 \, A c d e^{2} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 2 \, \sqrt{c d^{2} - b d e} B \sqrt{c} d e + A b e^{3} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 2 \, \sqrt{c d^{2} - b d e} A \sqrt{c} e^{2}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e} c d^{2} - \sqrt{c d^{2} - b d e} b d e} - \frac{2 \, {\left(B d e \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A e^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} \sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}}}{c d^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b d e \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}} - \frac{{\left(B b d e^{3} - 2 \, A c d e^{3} + A b e^{4}\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c d^{2} e - b d e^{2}\right)} \sqrt{c d^{2} - b d e} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"-1/2*((B*b*d*e^2*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 2*A*c*d*e^2*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 2*sqrt(c*d^2 - b*d*e)*B*sqrt(c)*d*e + A*b*e^3*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 2*sqrt(c*d^2 - b*d*e)*A*sqrt(c)*e^2)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*c*d^2 - sqrt(c*d^2 - b*d*e)*b*d*e) - 2*(B*d*e*sgn(1/(x*e + d)) - A*e^2*sgn(1/(x*e + d)))*sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)/(c*d^2*sgn(1/(x*e + d))^2 - b*d*e*sgn(1/(x*e + d))^2) - (B*b*d*e^3 - 2*A*c*d*e^3 + A*b*e^4)*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((c*d^2*e - b*d*e^2)*sqrt(c*d^2 - b*d*e)*sgn(1/(x*e + d))))*e^(-2)","B",0
1197,1,769,0,0.310400," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, B b c d^{2} - 8 \, A c^{2} d^{2} - B b^{2} d e + 8 \, A b c d e - 3 \, A b^{2} e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e}} + \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B c^{\frac{5}{2}} d^{4} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{\frac{3}{2}} d^{3} e - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A c^{\frac{5}{2}} d^{3} e + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b c^{2} d^{4} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c d^{2} e^{2} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{2} d^{2} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b c^{2} d^{3} e + 2 \, B b^{2} c^{\frac{3}{2}} d^{4} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} \sqrt{c} d^{2} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{\frac{3}{2}} d^{2} e^{2} + B b^{3} \sqrt{c} d^{3} e - 6 \, A b^{2} c^{\frac{3}{2}} d^{3} e - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} d e^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c d e^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} d^{2} e^{2} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c d^{2} e^{2} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} \sqrt{c} d e^{3} + 3 \, A b^{3} \sqrt{c} d^{2} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} e^{4} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} d e^{3}}{4 \, {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"-1/4*(4*B*b*c*d^2 - 8*A*c^2*d^2 - B*b^2*d*e + 8*A*b*c*d*e - 3*A*b^2*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*sqrt(-c*d^2 + b*d*e)) + 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*c^(5/2)*d^4 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^(3/2)*d^3*e - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*c^(5/2)*d^3*e + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b*c^2*d^4 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c*d^2*e^2 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^2*d^2*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b*c^2*d^3*e + 2*B*b^2*c^(3/2)*d^4 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*sqrt(c)*d^2*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^(3/2)*d^2*e^2 + B*b^3*sqrt(c)*d^3*e - 6*A*b^2*c^(3/2)*d^3*e - (sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*d*e^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c*d*e^3 + (sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*d^2*e^2 + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c*d^2*e^2 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*sqrt(c)*d*e^3 + 3*A*b^3*sqrt(c)*d^2*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*e^4 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*d*e^3)/((c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2)","B",0
1198,1,1667,0,0.385121," ","integrate((B*x+A)/(e*x+d)^4/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{{\left(8 \, B b c^{2} d^{3} - 16 \, A c^{3} d^{3} - 4 \, B b^{2} c d^{2} e + 24 \, A b c^{2} d^{2} e + B b^{3} d e^{2} - 18 \, A b^{2} c d e^{2} + 5 \, A b^{3} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{8 \, {\left(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}\right)} \sqrt{-c d^{2} + b d e}} + \frac{64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{4} d^{6} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c^{3} d^{5} e - 352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{4} d^{5} e + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{\frac{7}{2}} d^{6} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b c^{\frac{5}{2}} d^{4} e^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A c^{\frac{7}{2}} d^{4} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} c^{\frac{5}{2}} d^{5} e - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{\frac{7}{2}} d^{5} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c^{3} d^{6} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b c^{2} d^{3} e^{3} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A c^{3} d^{3} e^{3} + 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} c^{2} d^{4} e^{2} + 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c^{3} d^{4} e^{2} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} c^{2} d^{5} e - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c^{3} d^{5} e + 8 \, B b^{3} c^{\frac{5}{2}} d^{6} - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{2} c^{\frac{3}{2}} d^{3} e^{3} + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b c^{\frac{5}{2}} d^{3} e^{3} + 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{3} c^{\frac{3}{2}} d^{4} e^{2} + 756 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} c^{\frac{5}{2}} d^{4} e^{2} + 10 \, B b^{4} c^{\frac{3}{2}} d^{5} e - 44 \, A b^{3} c^{\frac{5}{2}} d^{5} e - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{2} c d^{2} e^{4} + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b c^{2} d^{2} e^{4} - 74 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{3} c d^{3} e^{3} - 204 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} c^{2} d^{3} e^{3} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{4} c d^{4} e^{2} + 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} c^{2} d^{4} e^{2} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} B b^{3} \sqrt{c} d^{2} e^{4} - 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{2} c^{\frac{3}{2}} d^{2} e^{4} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{4} \sqrt{c} d^{3} e^{3} - 498 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{3} c^{\frac{3}{2}} d^{3} e^{3} - 3 \, B b^{5} \sqrt{c} d^{4} e^{2} + 44 \, A b^{4} c^{\frac{3}{2}} d^{4} e^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} B b^{3} d e^{5} - 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{2} c d e^{5} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{4} d^{2} e^{4} - 34 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{3} c d^{2} e^{4} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{5} d^{3} e^{3} - 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{4} c d^{3} e^{3} + 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} A b^{3} \sqrt{c} d e^{5} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{4} \sqrt{c} d^{2} e^{4} - 15 \, A b^{5} \sqrt{c} d^{3} e^{3} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} A b^{3} e^{6} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{4} d e^{5} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{5} d^{2} e^{4}}{24 \, {\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{3}}"," ",0,"-1/8*(8*B*b*c^2*d^3 - 16*A*c^3*d^3 - 4*B*b^2*c*d^2*e + 24*A*b*c^2*d^2*e + B*b^3*d*e^2 - 18*A*b^2*c*d*e^2 + 5*A*b^3*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((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)*sqrt(-c*d^2 + b*d*e)) + 1/24*(64*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^4*d^6 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c^3*d^5*e - 352*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^4*d^5*e + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^(7/2)*d^6 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b*c^(5/2)*d^4*e^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*c^(7/2)*d^4*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*c^(5/2)*d^5*e - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^(7/2)*d^5*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c^3*d^6 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b*c^2*d^3*e^3 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*c^3*d^3*e^3 + 168*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*c^2*d^4*e^2 + 400*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c^3*d^4*e^2 + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*c^2*d^5*e - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c^3*d^5*e + 8*B*b^3*c^(5/2)*d^6 - 60*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^2*c^(3/2)*d^3*e^3 + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b*c^(5/2)*d^3*e^3 + 54*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^3*c^(3/2)*d^4*e^2 + 756*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*c^(5/2)*d^4*e^2 + 10*B*b^4*c^(3/2)*d^5*e - 44*A*b^3*c^(5/2)*d^5*e - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^2*c*d^2*e^4 + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b*c^2*d^2*e^4 - 74*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^3*c*d^3*e^3 - 204*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*c^2*d^3*e^3 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^4*c*d^4*e^2 + 336*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*c^2*d^4*e^2 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*B*b^3*sqrt(c)*d^2*e^4 - 270*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^2*c^(3/2)*d^2*e^4 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^4*sqrt(c)*d^3*e^3 - 498*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^3*c^(3/2)*d^3*e^3 - 3*B*b^5*sqrt(c)*d^4*e^2 + 44*A*b^4*c^(3/2)*d^4*e^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*B*b^3*d*e^5 - 54*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^2*c*d*e^5 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^4*d^2*e^4 - 34*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^3*c*d^2*e^4 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^5*d^3*e^3 - 180*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^4*c*d^3*e^3 + 75*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*A*b^3*sqrt(c)*d*e^5 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^4*sqrt(c)*d^2*e^4 - 15*A*b^5*sqrt(c)*d^3*e^3 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*A*b^3*e^6 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^4*d*e^5 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^5*d^2*e^4)/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^3)","B",0
1199,1,251,0,0.314353," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{\frac{8 \, A d^{3}}{b} - {\left({\left(\frac{2 \, B x e^{3}}{c} + \frac{12 \, B b^{2} c^{2} d e^{2} - 5 \, B b^{3} c e^{3} + 4 \, A b^{2} c^{2} e^{3}}{b^{2} c^{3}}\right)} x + \frac{8 \, B b c^{3} d^{3} - 16 \, A c^{4} d^{3} - 24 \, B b^{2} c^{2} d^{2} e + 24 \, A b c^{3} d^{2} e + 36 \, B b^{3} c d e^{2} - 24 \, A b^{2} c^{2} d e^{2} - 15 \, B b^{4} e^{3} + 12 \, A b^{3} c e^{3}}{b^{2} c^{3}}\right)} x}{4 \, \sqrt{c x^{2} + b x}} - \frac{3 \, {\left(8 \, B c^{2} d^{2} e - 12 \, B b c d e^{2} + 8 \, A c^{2} d e^{2} + 5 \, B b^{2} e^{3} - 4 \, A b c e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{7}{2}}}"," ",0,"-1/4*(8*A*d^3/b - ((2*B*x*e^3/c + (12*B*b^2*c^2*d*e^2 - 5*B*b^3*c*e^3 + 4*A*b^2*c^2*e^3)/(b^2*c^3))*x + (8*B*b*c^3*d^3 - 16*A*c^4*d^3 - 24*B*b^2*c^2*d^2*e + 24*A*b*c^3*d^2*e + 36*B*b^3*c*d*e^2 - 24*A*b^2*c^2*d*e^2 - 15*B*b^4*e^3 + 12*A*b^3*c*e^3)/(b^2*c^3))*x)/sqrt(c*x^2 + b*x) - 3/8*(8*B*c^2*d^2*e - 12*B*b*c*d*e^2 + 8*A*c^2*d*e^2 + 5*B*b^2*e^3 - 4*A*b*c*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
1200,1,155,0,0.318137," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, A d^{2}}{b} - {\left(\frac{B x e^{2}}{c} + \frac{2 \, B b c^{2} d^{2} - 4 \, A c^{3} d^{2} - 4 \, B b^{2} c d e + 4 \, A b c^{2} d e + 3 \, B b^{3} e^{2} - 2 \, A b^{2} c e^{2}}{b^{2} c^{2}}\right)} x}{\sqrt{c x^{2} + b x}} - \frac{{\left(4 \, B c d e - 3 \, B b e^{2} + 2 \, A c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"-(2*A*d^2/b - (B*x*e^2/c + (2*B*b*c^2*d^2 - 4*A*c^3*d^2 - 4*B*b^2*c*d*e + 4*A*b*c^2*d*e + 3*B*b^3*e^2 - 2*A*b^2*c*e^2)/(b^2*c^2))*x)/sqrt(c*x^2 + b*x) - 1/2*(4*B*c*d*e - 3*B*b*e^2 + 2*A*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
1201,1,95,0,0.304974," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{B e \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}} - \frac{2 \, {\left(\frac{A d}{b} - \frac{{\left(B b c d - 2 \, A c^{2} d - B b^{2} e + A b c e\right)} x}{b^{2} c}\right)}}{\sqrt{c x^{2} + b x}}"," ",0,"-B*e*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2) - 2*(A*d/b - (B*b*c*d - 2*A*c^2*d - B*b^2*e + A*b*c*e)*x/(b^2*c))/sqrt(c*x^2 + b*x)","A",0
1202,1,33,0,0.280999," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{A}{b} - \frac{{\left(B b - 2 \, A c\right)} x}{b^{2}}\right)}}{\sqrt{c x^{2} + b x}}"," ",0,"-2*(A/b - (B*b - 2*A*c)*x/b^2)/sqrt(c*x^2 + b*x)","A",0
1203,1,187,0,0.278832," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B b c d^{2} - 2 \, A c^{2} d^{2} + A b c d e\right)} x}{b^{2} c d^{3} - b^{3} d^{2} e} - \frac{A b c d^{2} - A b^{2} d e}{b^{2} c d^{3} - b^{3} d^{2} e}\right)}}{\sqrt{c x^{2} + b x}} + \frac{2 \, {\left(B d e - A e^{2}\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{{\left(c d^{2} - b d e\right)} \sqrt{-c d^{2} + b d e}}"," ",0,"2*((B*b*c*d^2 - 2*A*c^2*d^2 + A*b*c*d*e)*x/(b^2*c*d^3 - b^3*d^2*e) - (A*b*c*d^2 - A*b^2*d*e)/(b^2*c*d^3 - b^3*d^2*e))/sqrt(c*x^2 + b*x) + 2*(B*d*e - A*e^2)*arctan(((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c*d^2 - b*d*e)*sqrt(-c*d^2 + b*d*e))","A",0
1204,1,1181,0,1.617573," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{{\left(4 \, B b^{2} c d^{2} e^{3} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 4 \, \sqrt{c d^{2} - b d e} B b c^{\frac{3}{2}} d^{2} e^{2} - 8 \, \sqrt{c d^{2} - b d e} A c^{\frac{5}{2}} d^{2} e^{2} - B b^{3} d e^{4} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 6 \, A b^{2} c d e^{4} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 2 \, \sqrt{c d^{2} - b d e} B b^{2} \sqrt{c} d e^{3} + 8 \, \sqrt{c d^{2} - b d e} A b c^{\frac{3}{2}} d e^{3} + 3 \, A b^{3} e^{5} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 6 \, \sqrt{c d^{2} - b d e} A b^{2} \sqrt{c} e^{4}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e} b^{2} c^{2} d^{4} - 2 \, \sqrt{c d^{2} - b d e} b^{3} c d^{3} e + \sqrt{c d^{2} - b d e} b^{4} d^{2} e^{2}} + \frac{2 \, {\left(\frac{{\left(\frac{2 \, B b c^{2} d^{3} e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 4 \, A c^{3} d^{3} e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, B b^{2} c d^{2} e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 6 \, A b c^{2} d^{2} e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - B b^{3} d e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, A b^{2} c d e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, A b^{3} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{b^{2} c^{2} d^{4} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 2 \, b^{3} c d^{3} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + b^{4} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}} - \frac{{\left(B b^{2} c d^{3} e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - B b^{3} d^{2} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A b^{2} c d^{2} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + A b^{3} d e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(b^{2} c^{2} d^{4} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 2 \, b^{3} c d^{3} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + b^{4} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{2 \, B b c^{2} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 4 \, A c^{3} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + B b^{2} c d e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 4 \, A b c^{2} d e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, A b^{2} c e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{b^{2} c^{2} d^{4} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 2 \, b^{3} c d^{3} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + b^{4} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)}}{\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}}} - \frac{{\left(4 \, B c d^{2} e^{4} - B b d e^{5} - 6 \, A c d e^{5} + 3 \, A b e^{6}\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} \sqrt{c d^{2} - b d e} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"-1/2*((4*B*b^2*c*d^2*e^3*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 4*sqrt(c*d^2 - b*d*e)*B*b*c^(3/2)*d^2*e^2 - 8*sqrt(c*d^2 - b*d*e)*A*c^(5/2)*d^2*e^2 - B*b^3*d*e^4*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 6*A*b^2*c*d*e^4*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 2*sqrt(c*d^2 - b*d*e)*B*b^2*sqrt(c)*d*e^3 + 8*sqrt(c*d^2 - b*d*e)*A*b*c^(3/2)*d*e^3 + 3*A*b^3*e^5*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 6*sqrt(c*d^2 - b*d*e)*A*b^2*sqrt(c)*e^4)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*b^2*c^2*d^4 - 2*sqrt(c*d^2 - b*d*e)*b^3*c*d^3*e + sqrt(c*d^2 - b*d*e)*b^4*d^2*e^2) + 2*(((2*B*b*c^2*d^3*e^8*sgn(1/(x*e + d)) - 4*A*c^3*d^3*e^8*sgn(1/(x*e + d)) + 2*B*b^2*c*d^2*e^9*sgn(1/(x*e + d)) + 6*A*b*c^2*d^2*e^9*sgn(1/(x*e + d)) - B*b^3*d*e^10*sgn(1/(x*e + d)) - 8*A*b^2*c*d*e^10*sgn(1/(x*e + d)) + 3*A*b^3*e^11*sgn(1/(x*e + d)))/(b^2*c^2*d^4*e^5*sgn(1/(x*e + d))^2 - 2*b^3*c*d^3*e^6*sgn(1/(x*e + d))^2 + b^4*d^2*e^7*sgn(1/(x*e + d))^2) - (B*b^2*c*d^3*e^10*sgn(1/(x*e + d)) - B*b^3*d^2*e^11*sgn(1/(x*e + d)) - A*b^2*c*d^2*e^11*sgn(1/(x*e + d)) + A*b^3*d*e^12*sgn(1/(x*e + d)))*e^(-1)/((b^2*c^2*d^4*e^5*sgn(1/(x*e + d))^2 - 2*b^3*c*d^3*e^6*sgn(1/(x*e + d))^2 + b^4*d^2*e^7*sgn(1/(x*e + d))^2)*(x*e + d)))*e^(-1)/(x*e + d) - (2*B*b*c^2*d^2*e^7*sgn(1/(x*e + d)) - 4*A*c^3*d^2*e^7*sgn(1/(x*e + d)) + B*b^2*c*d*e^8*sgn(1/(x*e + d)) + 4*A*b*c^2*d*e^8*sgn(1/(x*e + d)) - 3*A*b^2*c*e^9*sgn(1/(x*e + d)))/(b^2*c^2*d^4*e^5*sgn(1/(x*e + d))^2 - 2*b^3*c*d^3*e^6*sgn(1/(x*e + d))^2 + b^4*d^2*e^7*sgn(1/(x*e + d))^2))/sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) - (4*B*c*d^2*e^4 - B*b*d*e^5 - 6*A*c*d*e^5 + 3*A*b*e^6)*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3)*sqrt(c*d^2 - b*d*e)*sgn(1/(x*e + d))))*e^(-2)","B",0
1205,1,1095,0,0.390924," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B b c^{3} d^{6} - 2 \, A c^{4} d^{6} + 3 \, A b c^{3} d^{5} e - 3 \, A b^{2} c^{2} d^{4} e^{2} + A b^{3} c d^{3} e^{3}\right)} x}{b^{2} c^{3} d^{9} - 3 \, b^{3} c^{2} d^{8} e + 3 \, b^{4} c d^{7} e^{2} - b^{5} d^{6} e^{3}} - \frac{A b c^{3} d^{6} - 3 \, A b^{2} c^{2} d^{5} e + 3 \, A b^{3} c d^{4} e^{2} - A b^{4} d^{3} e^{3}}{b^{2} c^{3} d^{9} - 3 \, b^{3} c^{2} d^{8} e + 3 \, b^{4} c d^{7} e^{2} - b^{5} d^{6} e^{3}}\right)}}{\sqrt{c x^{2} + b x}} - \frac{3 \, {\left(8 \, B c^{2} d^{3} e - 4 \, B b c d^{2} e^{2} - 16 \, A c^{2} d^{2} e^{2} + B b^{2} d e^{3} + 16 \, A b c d e^{3} - 5 \, A b^{2} e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{4 \, {\left(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}\right)} \sqrt{-c d^{2} + b d e}} + \frac{40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B c^{\frac{5}{2}} d^{4} e + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B c^{2} d^{3} e^{2} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b c^{2} d^{4} e - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b c^{\frac{3}{2}} d^{3} e^{2} - 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A c^{\frac{5}{2}} d^{3} e^{2} + 10 \, B b^{2} c^{\frac{3}{2}} d^{4} e - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b c d^{2} e^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A c^{2} d^{2} e^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{2} c d^{3} e^{2} - 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b c^{2} d^{3} e^{2} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} B b^{2} \sqrt{c} d^{2} e^{3} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b c^{\frac{3}{2}} d^{2} e^{3} - 3 \, B b^{3} \sqrt{c} d^{3} e^{2} - 14 \, A b^{2} c^{\frac{3}{2}} d^{3} e^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} B b^{2} d e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b c d e^{4} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} B b^{3} d^{2} e^{3} + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{2} c d^{2} e^{3} - 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} A b^{2} \sqrt{c} d e^{4} + 7 \, A b^{3} \sqrt{c} d^{2} e^{3} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} A b^{2} e^{5} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} A b^{3} d e^{4}}{4 \, {\left(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}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"2*((B*b*c^3*d^6 - 2*A*c^4*d^6 + 3*A*b*c^3*d^5*e - 3*A*b^2*c^2*d^4*e^2 + A*b^3*c*d^3*e^3)*x/(b^2*c^3*d^9 - 3*b^3*c^2*d^8*e + 3*b^4*c*d^7*e^2 - b^5*d^6*e^3) - (A*b*c^3*d^6 - 3*A*b^2*c^2*d^5*e + 3*A*b^3*c*d^4*e^2 - A*b^4*d^3*e^3)/(b^2*c^3*d^9 - 3*b^3*c^2*d^8*e + 3*b^4*c*d^7*e^2 - b^5*d^6*e^3))/sqrt(c*x^2 + b*x) - 3/4*(8*B*c^2*d^3*e - 4*B*b*c*d^2*e^2 - 16*A*c^2*d^2*e^2 + B*b^2*d*e^3 + 16*A*b*c*d*e^3 - 5*A*b^2*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((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)*sqrt(-c*d^2 + b*d*e)) + 1/4*(40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*c^(5/2)*d^4*e + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*c^2*d^3*e^2 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b*c^2*d^4*e - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b*c^(3/2)*d^3*e^2 - 56*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*c^(5/2)*d^3*e^2 + 10*B*b^2*c^(3/2)*d^4*e - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b*c*d^2*e^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*c^2*d^2*e^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^2*c*d^3*e^2 - 56*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b*c^2*d^3*e^2 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*B*b^2*sqrt(c)*d^2*e^3 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b*c^(3/2)*d^2*e^3 - 3*B*b^3*sqrt(c)*d^3*e^2 - 14*A*b^2*c^(3/2)*d^3*e^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*B*b^2*d*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b*c*d*e^4 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))*B*b^3*d^2*e^3 + 44*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^2*c*d^2*e^3 - 13*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*A*b^2*sqrt(c)*d*e^4 + 7*A*b^3*sqrt(c)*d^2*e^3 - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*A*b^2*e^5 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))*A*b^3*d*e^4)/((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)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2)","B",0
1206,1,370,0,0.299088," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{\frac{2 \, A d^{4}}{b} - {\left({\left({\left(\frac{3 \, B x e^{4}}{c} - \frac{4 \, {\left(4 \, B b c^{5} d^{4} - 8 \, A c^{6} d^{4} - 4 \, B b^{2} c^{4} d^{3} e + 16 \, A b c^{5} d^{3} e - 3 \, B b^{3} c^{3} d^{2} e^{2} - 6 \, A b^{2} c^{4} d^{2} e^{2} + 8 \, B b^{4} c^{2} d e^{3} - 2 \, A b^{3} c^{3} d e^{3} - 5 \, B b^{5} c e^{4} + 2 \, A b^{4} c^{2} e^{4}\right)}}{b^{4} c^{3}}\right)} x - \frac{3 \, {\left(8 \, B b^{2} c^{4} d^{4} - 16 \, A b c^{5} d^{4} - 8 \, B b^{3} c^{3} d^{3} e + 32 \, A b^{2} c^{4} d^{3} e - 12 \, A b^{3} c^{3} d^{2} e^{2} + 8 \, B b^{5} c d e^{3} - 5 \, B b^{6} e^{4} + 2 \, A b^{5} c e^{4}\right)}}{b^{4} c^{3}}\right)} x - \frac{6 \, {\left(B b^{3} c^{3} d^{4} - 2 \, A b^{2} c^{4} d^{4} + 4 \, A b^{3} c^{3} d^{3} e\right)}}{b^{4} c^{3}}\right)} x}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}} - \frac{{\left(8 \, B c d e^{3} - 5 \, B b e^{4} + 2 \, A c e^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{7}{2}}}"," ",0,"-1/3*(2*A*d^4/b - (((3*B*x*e^4/c - 4*(4*B*b*c^5*d^4 - 8*A*c^6*d^4 - 4*B*b^2*c^4*d^3*e + 16*A*b*c^5*d^3*e - 3*B*b^3*c^3*d^2*e^2 - 6*A*b^2*c^4*d^2*e^2 + 8*B*b^4*c^2*d*e^3 - 2*A*b^3*c^3*d*e^3 - 5*B*b^5*c*e^4 + 2*A*b^4*c^2*e^4)/(b^4*c^3))*x - 3*(8*B*b^2*c^4*d^4 - 16*A*b*c^5*d^4 - 8*B*b^3*c^3*d^3*e + 32*A*b^2*c^4*d^3*e - 12*A*b^3*c^3*d^2*e^2 + 8*B*b^5*c*d*e^3 - 5*B*b^6*e^4 + 2*A*b^5*c*e^4)/(b^4*c^3))*x - 6*(B*b^3*c^3*d^4 - 2*A*b^2*c^4*d^4 + 4*A*b^3*c^3*d^3*e)/(b^4*c^3))*x)/(c*x^2 + b*x)^(3/2) - 1/2*(8*B*c*d*e^3 - 5*B*b*e^4 + 2*A*c*e^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
1207,1,289,0,0.308189," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{B e^{3} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}} - \frac{2 \, {\left(\frac{A d^{3}}{b} + {\left(x {\left(\frac{{\left(8 \, B b c^{4} d^{3} - 16 \, A c^{5} d^{3} - 6 \, B b^{2} c^{3} d^{2} e + 24 \, A b c^{4} d^{2} e - 3 \, B b^{3} c^{2} d e^{2} - 6 \, A b^{2} c^{3} d e^{2} + 4 \, B b^{4} c e^{3} - A b^{3} c^{2} e^{3}\right)} x}{b^{4} c^{2}} + \frac{3 \, {\left(4 \, B b^{2} c^{3} d^{3} - 8 \, A b c^{4} d^{3} - 3 \, B b^{3} c^{2} d^{2} e + 12 \, A b^{2} c^{3} d^{2} e - 3 \, A b^{3} c^{2} d e^{2} + B b^{5} e^{3}\right)}}{b^{4} c^{2}}\right)} + \frac{3 \, {\left(B b^{3} c^{2} d^{3} - 2 \, A b^{2} c^{3} d^{3} + 3 \, A b^{3} c^{2} d^{2} e\right)}}{b^{4} c^{2}}\right)} x\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"-B*e^3*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2) - 2/3*(A*d^3/b + (x*((8*B*b*c^4*d^3 - 16*A*c^5*d^3 - 6*B*b^2*c^3*d^2*e + 24*A*b*c^4*d^2*e - 3*B*b^3*c^2*d*e^2 - 6*A*b^2*c^3*d*e^2 + 4*B*b^4*c*e^3 - A*b^3*c^2*e^3)*x/(b^4*c^2) + 3*(4*B*b^2*c^3*d^3 - 8*A*b*c^4*d^3 - 3*B*b^3*c^2*d^2*e + 12*A*b^2*c^3*d^2*e - 3*A*b^3*c^2*d*e^2 + B*b^5*e^3)/(b^4*c^2)) + 3*(B*b^3*c^2*d^3 - 2*A*b^2*c^3*d^3 + 3*A*b^3*c^2*d^2*e)/(b^4*c^2))*x)/(c*x^2 + b*x)^(3/2)","A",0
1208,1,176,0,0.293332," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{A d^{2}}{b} + {\left(x {\left(\frac{{\left(8 \, B b c^{2} d^{2} - 16 \, A c^{3} d^{2} - 4 \, B b^{2} c d e + 16 \, A b c^{2} d e - B b^{3} e^{2} - 2 \, A b^{2} c e^{2}\right)} x}{b^{4}} + \frac{3 \, {\left(4 \, B b^{2} c d^{2} - 8 \, A b c^{2} d^{2} - 2 \, B b^{3} d e + 8 \, A b^{2} c d e - A b^{3} e^{2}\right)}}{b^{4}}\right)} + \frac{3 \, {\left(B b^{3} d^{2} - 2 \, A b^{2} c d^{2} + 2 \, A b^{3} d e\right)}}{b^{4}}\right)} x\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"-2/3*(A*d^2/b + (x*((8*B*b*c^2*d^2 - 16*A*c^3*d^2 - 4*B*b^2*c*d*e + 16*A*b*c^2*d*e - B*b^3*e^2 - 2*A*b^2*c*e^2)*x/b^4 + 3*(4*B*b^2*c*d^2 - 8*A*b*c^2*d^2 - 2*B*b^3*d*e + 8*A*b^2*c*d*e - A*b^3*e^2)/b^4) + 3*(B*b^3*d^2 - 2*A*b^2*c*d^2 + 2*A*b^3*d*e)/b^4)*x)/(c*x^2 + b*x)^(3/2)","B",0
1209,1,132,0,0.297088," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(x {\left(\frac{2 \, {\left(4 \, B b c^{2} d - 8 \, A c^{3} d - B b^{2} c e + 4 \, A b c^{2} e\right)} x}{b^{4}} + \frac{3 \, {\left(4 \, B b^{2} c d - 8 \, A b c^{2} d - B b^{3} e + 4 \, A b^{2} c e\right)}}{b^{4}}\right)} + \frac{3 \, {\left(B b^{3} d - 2 \, A b^{2} c d + A b^{3} e\right)}}{b^{4}}\right)} x + \frac{A d}{b}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((x*(2*(4*B*b*c^2*d - 8*A*c^3*d - B*b^2*c*e + 4*A*b*c^2*e)*x/b^4 + 3*(4*B*b^2*c*d - 8*A*b*c^2*d - B*b^3*e + 4*A*b^2*c*e)/b^4) + 3*(B*b^3*d - 2*A*b^2*c*d + A*b^3*e)/b^4)*x + A*d/b)/(c*x^2 + b*x)^(3/2)","A",0
1210,1,82,0,0.236359," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(4 \, x {\left(\frac{2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x}{b^{4}} + \frac{3 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)}}{b^{4}}\right)} + \frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)}}{b^{4}}\right)} x + \frac{A}{b}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((4*x*(2*(B*b*c^2 - 2*A*c^3)*x/b^4 + 3*(B*b^2*c - 2*A*b*c^2)/b^4) + 3*(B*b^3 - 2*A*b^2*c)/b^4)*x + A/b)/(c*x^2 + b*x)^(3/2)","A",0
1211,1,853,0,0.275052," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(B d e^{3} - A e^{4}\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e}} - \frac{2 \, {\left({\left({\left(\frac{{\left(8 \, B b c^{6} d^{10} - 16 \, A c^{7} d^{10} - 30 \, B b^{2} c^{5} d^{9} e + 56 \, A b c^{6} d^{9} e + 39 \, B b^{3} c^{4} d^{8} e^{2} - 66 \, A b^{2} c^{5} d^{8} e^{2} - 20 \, B b^{4} c^{3} d^{7} e^{3} + 25 \, A b^{3} c^{4} d^{7} e^{3} + 3 \, B b^{5} c^{2} d^{6} e^{4} + 4 \, A b^{4} c^{3} d^{6} e^{4} - 3 \, A b^{5} c^{2} d^{5} e^{5}\right)} x}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}} + \frac{3 \, {\left(4 \, B b^{2} c^{5} d^{10} - 8 \, A b c^{6} d^{10} - 15 \, B b^{3} c^{4} d^{9} e + 28 \, A b^{2} c^{5} d^{9} e + 20 \, B b^{4} c^{3} d^{8} e^{2} - 33 \, A b^{3} c^{4} d^{8} e^{2} - 11 \, B b^{5} c^{2} d^{7} e^{3} + 12 \, A b^{4} c^{3} d^{7} e^{3} + 2 \, B b^{6} c d^{6} e^{4} + 3 \, A b^{5} c^{2} d^{6} e^{4} - 2 \, A b^{6} c d^{5} e^{5}\right)}}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}}\right)} x + \frac{3 \, {\left(B b^{3} c^{4} d^{10} - 2 \, A b^{2} c^{5} d^{10} - 4 \, B b^{4} c^{3} d^{9} e + 7 \, A b^{3} c^{4} d^{9} e + 6 \, B b^{5} c^{2} d^{8} e^{2} - 8 \, A b^{4} c^{3} d^{8} e^{2} - 4 \, B b^{6} c d^{7} e^{3} + 2 \, A b^{5} c^{2} d^{7} e^{3} + B b^{7} d^{6} e^{4} + 2 \, A b^{6} c d^{6} e^{4} - A b^{7} d^{5} e^{5}\right)}}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}}\right)} x + \frac{A b^{3} c^{4} d^{10} - 4 \, A b^{4} c^{3} d^{9} e + 6 \, A b^{5} c^{2} d^{8} e^{2} - 4 \, A b^{6} c d^{7} e^{3} + A b^{7} d^{6} e^{4}}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"2*(B*d*e^3 - A*e^4)*arctan(((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*sqrt(-c*d^2 + b*d*e)) - 2/3*((((8*B*b*c^6*d^10 - 16*A*c^7*d^10 - 30*B*b^2*c^5*d^9*e + 56*A*b*c^6*d^9*e + 39*B*b^3*c^4*d^8*e^2 - 66*A*b^2*c^5*d^8*e^2 - 20*B*b^4*c^3*d^7*e^3 + 25*A*b^3*c^4*d^7*e^3 + 3*B*b^5*c^2*d^6*e^4 + 4*A*b^4*c^3*d^6*e^4 - 3*A*b^5*c^2*d^5*e^5)*x/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4) + 3*(4*B*b^2*c^5*d^10 - 8*A*b*c^6*d^10 - 15*B*b^3*c^4*d^9*e + 28*A*b^2*c^5*d^9*e + 20*B*b^4*c^3*d^8*e^2 - 33*A*b^3*c^4*d^8*e^2 - 11*B*b^5*c^2*d^7*e^3 + 12*A*b^4*c^3*d^7*e^3 + 2*B*b^6*c*d^6*e^4 + 3*A*b^5*c^2*d^6*e^4 - 2*A*b^6*c*d^5*e^5)/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4))*x + 3*(B*b^3*c^4*d^10 - 2*A*b^2*c^5*d^10 - 4*B*b^4*c^3*d^9*e + 7*A*b^3*c^4*d^9*e + 6*B*b^5*c^2*d^8*e^2 - 8*A*b^4*c^3*d^8*e^2 - 4*B*b^6*c*d^7*e^3 + 2*A*b^5*c^2*d^7*e^3 + B*b^7*d^6*e^4 + 2*A*b^6*c*d^6*e^4 - A*b^7*d^5*e^5)/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4))*x + (A*b^3*c^4*d^10 - 4*A*b^4*c^3*d^9*e + 6*A*b^5*c^2*d^8*e^2 - 4*A*b^6*c*d^7*e^3 + A*b^7*d^6*e^4)/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4))/(c*x^2 + b*x)^(3/2)","B",0
1212,1,2413,0,2.299005," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{{\left(32 \, \sqrt{c d^{2} - b d e} B b c^{4} d^{4} e^{2} - 64 \, \sqrt{c d^{2} - b d e} A c^{5} d^{4} e^{2} - 80 \, \sqrt{c d^{2} - b d e} B b^{2} c^{3} d^{3} e^{3} + 128 \, \sqrt{c d^{2} - b d e} A b c^{4} d^{3} e^{3} - 24 \, B b^{4} c^{\frac{3}{2}} d^{2} e^{5} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 36 \, \sqrt{c d^{2} - b d e} B b^{3} c^{2} d^{2} e^{4} - 24 \, \sqrt{c d^{2} - b d e} A b^{2} c^{3} d^{2} e^{4} + 9 \, B b^{5} \sqrt{c} d e^{6} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 30 \, A b^{4} c^{\frac{3}{2}} d e^{6} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 18 \, \sqrt{c d^{2} - b d e} B b^{4} c d e^{5} - 40 \, \sqrt{c d^{2} - b d e} A b^{3} c^{2} d e^{5} - 15 \, A b^{5} \sqrt{c} e^{7} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 30 \, \sqrt{c d^{2} - b d e} A b^{4} c e^{6}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e} b^{4} c^{\frac{7}{2}} d^{6} - 3 \, \sqrt{c d^{2} - b d e} b^{5} c^{\frac{5}{2}} d^{5} e + 3 \, \sqrt{c d^{2} - b d e} b^{6} c^{\frac{3}{2}} d^{4} e^{2} - \sqrt{c d^{2} - b d e} b^{7} \sqrt{c} d^{3} e^{3}} + \frac{2 \, {\left(\frac{{\left(\frac{{\left(\frac{{\left(\frac{4 \, {\left(4 \, B b c^{5} d^{7} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, A c^{6} d^{7} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, B b^{2} c^{4} d^{6} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 28 \, A b c^{5} d^{6} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 21 \, B b^{3} c^{3} d^{5} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 30 \, A b^{2} c^{4} d^{5} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 18 \, B b^{4} c^{2} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, A b^{3} c^{3} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 12 \, B b^{5} c d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 18 \, A b^{4} c^{2} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, B b^{6} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 18 \, A b^{5} c d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, A b^{6} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}} + \frac{3 \, {\left(B b^{4} c^{2} d^{5} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, B b^{5} c d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A b^{4} c^{2} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + B b^{6} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, A b^{5} c d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A b^{6} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{3 \, {\left(16 \, B b c^{5} d^{6} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, A c^{6} d^{6} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 56 \, B b^{2} c^{4} d^{5} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 96 \, A b c^{5} d^{5} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 60 \, B b^{3} c^{3} d^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 80 \, A b^{2} c^{4} d^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 42 \, B b^{4} c^{2} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 20 \, B b^{5} c d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 46 \, A b^{4} c^{2} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, B b^{6} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 30 \, A b^{5} c d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, A b^{6} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(8 \, B b c^{5} d^{5} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A c^{6} d^{5} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, B b^{2} c^{4} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 40 \, A b c^{5} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 19 \, B b^{3} c^{3} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 22 \, A b^{2} c^{4} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 11 \, B b^{4} c^{2} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 7 \, A b^{3} c^{3} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, B b^{5} c d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 15 \, A b^{4} c^{2} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, A b^{5} c e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{16 \, B b c^{5} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, A c^{6} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 40 \, B b^{2} c^{4} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 64 \, A b c^{5} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 18 \, B b^{3} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 12 \, A b^{2} c^{4} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 9 \, B b^{4} c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 20 \, A b^{3} c^{3} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 15 \, A b^{4} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)}}{{\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}\right)}^{\frac{3}{2}}} + \frac{3 \, {\left(8 \, B c d^{2} e^{6} - 3 \, B b d e^{7} - 10 \, A c d e^{7} + 5 \, A b e^{8}\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4}\right)} \sqrt{c d^{2} - b d e} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"1/6*((32*sqrt(c*d^2 - b*d*e)*B*b*c^4*d^4*e^2 - 64*sqrt(c*d^2 - b*d*e)*A*c^5*d^4*e^2 - 80*sqrt(c*d^2 - b*d*e)*B*b^2*c^3*d^3*e^3 + 128*sqrt(c*d^2 - b*d*e)*A*b*c^4*d^3*e^3 - 24*B*b^4*c^(3/2)*d^2*e^5*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 36*sqrt(c*d^2 - b*d*e)*B*b^3*c^2*d^2*e^4 - 24*sqrt(c*d^2 - b*d*e)*A*b^2*c^3*d^2*e^4 + 9*B*b^5*sqrt(c)*d*e^6*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 30*A*b^4*c^(3/2)*d*e^6*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 18*sqrt(c*d^2 - b*d*e)*B*b^4*c*d*e^5 - 40*sqrt(c*d^2 - b*d*e)*A*b^3*c^2*d*e^5 - 15*A*b^5*sqrt(c)*e^7*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 30*sqrt(c*d^2 - b*d*e)*A*b^4*c*e^6)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*b^4*c^(7/2)*d^6 - 3*sqrt(c*d^2 - b*d*e)*b^5*c^(5/2)*d^5*e + 3*sqrt(c*d^2 - b*d*e)*b^6*c^(3/2)*d^4*e^2 - sqrt(c*d^2 - b*d*e)*b^7*sqrt(c)*d^3*e^3) + 2*((((4*(4*B*b*c^5*d^7*e^16*sgn(1/(x*e + d)) - 8*A*c^6*d^7*e^16*sgn(1/(x*e + d)) - 16*B*b^2*c^4*d^6*e^17*sgn(1/(x*e + d)) + 28*A*b*c^5*d^6*e^17*sgn(1/(x*e + d)) + 21*B*b^3*c^3*d^5*e^18*sgn(1/(x*e + d)) - 30*A*b^2*c^4*d^5*e^18*sgn(1/(x*e + d)) - 18*B*b^4*c^2*d^4*e^19*sgn(1/(x*e + d)) + 5*A*b^3*c^3*d^4*e^19*sgn(1/(x*e + d)) + 12*B*b^5*c*d^3*e^20*sgn(1/(x*e + d)) + 18*A*b^4*c^2*d^3*e^20*sgn(1/(x*e + d)) - 3*B*b^6*d^2*e^21*sgn(1/(x*e + d)) - 18*A*b^5*c*d^2*e^21*sgn(1/(x*e + d)) + 5*A*b^6*d*e^22*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2) + 3*(B*b^4*c^2*d^5*e^20*sgn(1/(x*e + d)) - 2*B*b^5*c*d^4*e^21*sgn(1/(x*e + d)) - A*b^4*c^2*d^4*e^21*sgn(1/(x*e + d)) + B*b^6*d^3*e^22*sgn(1/(x*e + d)) + 2*A*b^5*c*d^3*e^22*sgn(1/(x*e + d)) - A*b^6*d^2*e^23*sgn(1/(x*e + d)))*e^(-1)/((b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2)*(x*e + d)))*e^(-1)/(x*e + d) - 3*(16*B*b*c^5*d^6*e^15*sgn(1/(x*e + d)) - 32*A*c^6*d^6*e^15*sgn(1/(x*e + d)) - 56*B*b^2*c^4*d^5*e^16*sgn(1/(x*e + d)) + 96*A*b*c^5*d^5*e^16*sgn(1/(x*e + d)) + 60*B*b^3*c^3*d^4*e^17*sgn(1/(x*e + d)) - 80*A*b^2*c^4*d^4*e^17*sgn(1/(x*e + d)) - 42*B*b^4*c^2*d^3*e^18*sgn(1/(x*e + d)) + 20*B*b^5*c*d^2*e^19*sgn(1/(x*e + d)) + 46*A*b^4*c^2*d^2*e^19*sgn(1/(x*e + d)) - 3*B*b^6*d*e^20*sgn(1/(x*e + d)) - 30*A*b^5*c*d*e^20*sgn(1/(x*e + d)) + 5*A*b^6*e^21*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2))*e^(-1)/(x*e + d) + 6*(8*B*b*c^5*d^5*e^14*sgn(1/(x*e + d)) - 16*A*c^6*d^5*e^14*sgn(1/(x*e + d)) - 24*B*b^2*c^4*d^4*e^15*sgn(1/(x*e + d)) + 40*A*b*c^5*d^4*e^15*sgn(1/(x*e + d)) + 19*B*b^3*c^3*d^3*e^16*sgn(1/(x*e + d)) - 22*A*b^2*c^4*d^3*e^16*sgn(1/(x*e + d)) - 11*B*b^4*c^2*d^2*e^17*sgn(1/(x*e + d)) - 7*A*b^3*c^3*d^2*e^17*sgn(1/(x*e + d)) + 3*B*b^5*c*d*e^18*sgn(1/(x*e + d)) + 15*A*b^4*c^2*d*e^18*sgn(1/(x*e + d)) - 5*A*b^5*c*e^19*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2))*e^(-1)/(x*e + d) - (16*B*b*c^5*d^4*e^13*sgn(1/(x*e + d)) - 32*A*c^6*d^4*e^13*sgn(1/(x*e + d)) - 40*B*b^2*c^4*d^3*e^14*sgn(1/(x*e + d)) + 64*A*b*c^5*d^3*e^14*sgn(1/(x*e + d)) + 18*B*b^3*c^3*d^2*e^15*sgn(1/(x*e + d)) - 12*A*b^2*c^4*d^2*e^15*sgn(1/(x*e + d)) - 9*B*b^4*c^2*d*e^16*sgn(1/(x*e + d)) - 20*A*b^3*c^3*d*e^16*sgn(1/(x*e + d)) + 15*A*b^4*c^2*e^17*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2))/(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)^(3/2) + 3*(8*B*c*d^2*e^6 - 3*B*b*d*e^7 - 10*A*c*d*e^7 + 5*A*b*e^8)*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4)*sqrt(c*d^2 - b*d*e)*sgn(1/(x*e + d))))*e^(-2)","B",0
1213,1,1383,0,0.242103," ","integrate((B*x+A)*(e*x+d)^(7/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d^{4} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d^{4} e^{\left(-2\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c d^{4} e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c d^{4} e^{\left(-3\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b d^{3} e^{\left(-1\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b d^{3} e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A c d^{3} e^{\left(-2\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B c d^{3} e^{\left(-3\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b d^{2} e^{\left(-1\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b d^{2} e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c d^{2} e^{\left(-2\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c d^{2} e^{\left(-3\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b d e^{\left(-1\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b d e^{\left(-2\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A c d e^{\left(-2\right)} + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B c d e^{\left(-3\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b e^{\left(-1\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b e^{\left(-2\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A c e^{\left(-2\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B c e^{\left(-3\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d^4*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d^4*e^(-2) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*d^4*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*d^4*e^(-3) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*d^3*e^(-1) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*d^3*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*c*d^3*e^(-2) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*c*d^3*e^(-3) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*d^2*e^(-1) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*d^2*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c*d^2*e^(-2) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c*d^2*e^(-3) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*d*e^(-1) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*d*e^(-2) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*c*d*e^(-2) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*c*d*e^(-3) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b*e^(-1) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b*e^(-2) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*c*e^(-2) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*c*e^(-3))*e^(-1)","B",0
1214,1,999,0,0.214822," ","integrate((B*x+A)*(e*x+d)^(5/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d^{3} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d^{3} e^{\left(-2\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c d^{3} e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c d^{3} e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b d^{2} e^{\left(-1\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b d^{2} e^{\left(-2\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A c d^{2} e^{\left(-2\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B c d^{2} e^{\left(-3\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b d e^{\left(-1\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b d e^{\left(-2\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c d e^{\left(-2\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c d e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b e^{\left(-1\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b e^{\left(-2\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A c e^{\left(-2\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B c e^{\left(-3\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d^3*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d^3*e^(-2) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*d^3*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*d^3*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*d^2*e^(-1) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*d^2*e^(-2) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*c*d^2*e^(-2) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*c*d^2*e^(-3) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*d*e^(-1) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*d*e^(-2) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c*d*e^(-2) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c*d*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*e^(-1) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*e^(-2) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*c*e^(-2) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*c*e^(-3))*e^(-1)","B",0
1215,1,667,0,0.190429," ","integrate((B*x+A)*(e*x+d)^(3/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d^{2} e^{\left(-1\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d^{2} e^{\left(-2\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c d^{2} e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c d^{2} e^{\left(-3\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b d e^{\left(-1\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b d e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A c d e^{\left(-2\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B c d e^{\left(-3\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b e^{\left(-1\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b e^{\left(-2\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c e^{\left(-2\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c e^{\left(-3\right)}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d^2*e^(-1) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d^2*e^(-2) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*d^2*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*d^2*e^(-3) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*d*e^(-1) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*d*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*c*d*e^(-2) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*c*d*e^(-3) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*e^(-1) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*e^(-2) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c*e^(-2) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c*e^(-3))*e^(-1)","B",0
1216,1,386,0,0.171661," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d e^{\left(-1\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d e^{\left(-2\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c d e^{\left(-2\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c d e^{\left(-3\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b e^{\left(-1\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b e^{\left(-2\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A c e^{\left(-2\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B c e^{\left(-3\right)}\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d*e^(-1) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d*e^(-2) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*d*e^(-2) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*d*e^(-3) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*e^(-1) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*e^(-2) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*c*e^(-2) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*c*e^(-3))*e^(-1)","B",0
1217,1,167,0,0.179348," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b e^{\left(-1\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b e^{\left(-2\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c e^{\left(-2\right)} + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c e^{\left(-3\right)}\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*e^(-1) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*e^(-2) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*e^(-2) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*e^(-3))*e^(-1)","A",0
1218,1,167,0,0.180231," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c e^{16} - 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B c d e^{16} + 45 \, \sqrt{x e + d} B c d^{2} e^{16} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} B b e^{17} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c e^{17} - 30 \, \sqrt{x e + d} B b d e^{17} - 30 \, \sqrt{x e + d} A c d e^{17} + 15 \, \sqrt{x e + d} A b e^{18}\right)} e^{\left(-20\right)} + \frac{2 \, {\left(B c d^{3} - B b d^{2} e - A c d^{2} e + A b d e^{2}\right)} e^{\left(-4\right)}}{\sqrt{x e + d}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*c*e^16 - 15*(x*e + d)^(3/2)*B*c*d*e^16 + 45*sqrt(x*e + d)*B*c*d^2*e^16 + 5*(x*e + d)^(3/2)*B*b*e^17 + 5*(x*e + d)^(3/2)*A*c*e^17 - 30*sqrt(x*e + d)*B*b*d*e^17 - 30*sqrt(x*e + d)*A*c*d*e^17 + 15*sqrt(x*e + d)*A*b*e^18)*e^(-20) + 2*(B*c*d^3 - B*b*d^2*e - A*c*d^2*e + A*b*d*e^2)*e^(-4)/sqrt(x*e + d)","A",0
1219,1,156,0,0.179938," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B c e^{8} - 9 \, \sqrt{x e + d} B c d e^{8} + 3 \, \sqrt{x e + d} B b e^{9} + 3 \, \sqrt{x e + d} A c e^{9}\right)} e^{\left(-12\right)} - \frac{2 \, {\left(9 \, {\left(x e + d\right)} B c d^{2} - B c d^{3} - 6 \, {\left(x e + d\right)} B b d e - 6 \, {\left(x e + d\right)} A c d e + B b d^{2} e + A c d^{2} e + 3 \, {\left(x e + d\right)} A b e^{2} - A b d e^{2}\right)} e^{\left(-4\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*B*c*e^8 - 9*sqrt(x*e + d)*B*c*d*e^8 + 3*sqrt(x*e + d)*B*b*e^9 + 3*sqrt(x*e + d)*A*c*e^9)*e^(-12) - 2/3*(9*(x*e + d)*B*c*d^2 - B*c*d^3 - 6*(x*e + d)*B*b*d*e - 6*(x*e + d)*A*c*d*e + B*b*d^2*e + A*c*d^2*e + 3*(x*e + d)*A*b*e^2 - A*b*d*e^2)*e^(-4)/(x*e + d)^(3/2)","A",0
1220,1,152,0,0.188727," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(7/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} B c e^{\left(-4\right)} + \frac{2 \, {\left(45 \, {\left(x e + d\right)}^{2} B c d - 15 \, {\left(x e + d\right)} B c d^{2} + 3 \, B c d^{3} - 15 \, {\left(x e + d\right)}^{2} B b e - 15 \, {\left(x e + d\right)}^{2} A c e + 10 \, {\left(x e + d\right)} B b d e + 10 \, {\left(x e + d\right)} A c d e - 3 \, B b d^{2} e - 3 \, A c d^{2} e - 5 \, {\left(x e + d\right)} A b e^{2} + 3 \, A b d e^{2}\right)} e^{\left(-4\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2*sqrt(x*e + d)*B*c*e^(-4) + 2/15*(45*(x*e + d)^2*B*c*d - 15*(x*e + d)*B*c*d^2 + 3*B*c*d^3 - 15*(x*e + d)^2*B*b*e - 15*(x*e + d)^2*A*c*e + 10*(x*e + d)*B*b*d*e + 10*(x*e + d)*A*c*d*e - 3*B*b*d^2*e - 3*A*c*d^2*e - 5*(x*e + d)*A*b*e^2 + 3*A*b*d*e^2)*e^(-4)/(x*e + d)^(5/2)","A",0
1221,1,2710,0,0.339841," ","integrate((B*x+A)*(e*x+d)^(7/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d^{4} e^{\left(-2\right)} + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d^{4} e^{\left(-3\right)} + 831402 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b c d^{4} e^{\left(-3\right)} + 92378 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b c d^{4} e^{\left(-4\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c^{2} d^{4} e^{\left(-4\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c^{2} d^{4} e^{\left(-5\right)} + 1662804 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} d^{3} e^{\left(-2\right)} + 184756 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} d^{3} e^{\left(-3\right)} + 369512 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b c d^{3} e^{\left(-3\right)} + 167960 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b c d^{3} e^{\left(-4\right)} + 83980 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A c^{2} d^{3} e^{\left(-4\right)} + 19380 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B c^{2} d^{3} e^{\left(-5\right)} + 277134 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{2} d^{2} e^{\left(-2\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{2} d^{2} e^{\left(-3\right)} + 251940 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b c d^{2} e^{\left(-3\right)} + 58140 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b c d^{2} e^{\left(-4\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A c^{2} d^{2} e^{\left(-4\right)} + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B c^{2} d^{2} e^{\left(-5\right)} + 83980 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{2} d e^{\left(-2\right)} + 19380 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{2} d e^{\left(-3\right)} + 38760 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b c d e^{\left(-3\right)} + 18088 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b c d e^{\left(-4\right)} + 9044 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A c^{2} d e^{\left(-4\right)} + 532 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B c^{2} d e^{\left(-5\right)} + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{2} e^{\left(-2\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{2} e^{\left(-3\right)} + 4522 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b c e^{\left(-3\right)} + 266 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b c e^{\left(-4\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A c^{2} e^{\left(-4\right)} + 63 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B c^{2} e^{\left(-5\right)}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d^4*e^(-2) + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d^4*e^(-3) + 831402*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*c*d^4*e^(-3) + 92378*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*c*d^4*e^(-4) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c^2*d^4*e^(-4) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c^2*d^4*e^(-5) + 1662804*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*d^3*e^(-2) + 184756*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*d^3*e^(-3) + 369512*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*c*d^3*e^(-3) + 167960*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*c*d^3*e^(-4) + 83980*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*c^2*d^3*e^(-4) + 19380*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*c^2*d^3*e^(-5) + 277134*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^2*d^2*e^(-2) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^2*d^2*e^(-3) + 251940*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b*c*d^2*e^(-3) + 58140*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b*c*d^2*e^(-4) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*c^2*d^2*e^(-4) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*c^2*d^2*e^(-5) + 83980*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^2*d*e^(-2) + 19380*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^2*d*e^(-3) + 38760*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b*c*d*e^(-3) + 18088*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b*c*d*e^(-4) + 9044*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*c^2*d*e^(-4) + 532*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*c^2*d*e^(-5) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^2*e^(-2) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^2*e^(-3) + 4522*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b*c*e^(-3) + 266*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b*c*e^(-4) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*c^2*e^(-4) + 63*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*c^2*e^(-5))*e^(-1)","B",0
1222,1,2007,0,0.286666," ","integrate((B*x+A)*(e*x+d)^(5/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d^{3} e^{\left(-2\right)} + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d^{3} e^{\left(-3\right)} + 43758 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b c d^{3} e^{\left(-3\right)} + 4862 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b c d^{3} e^{\left(-4\right)} + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c^{2} d^{3} e^{\left(-4\right)} + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c^{2} d^{3} e^{\left(-5\right)} + 65637 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} d^{2} e^{\left(-2\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} d^{2} e^{\left(-3\right)} + 14586 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b c d^{2} e^{\left(-3\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b c d^{2} e^{\left(-4\right)} + 3315 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A c^{2} d^{2} e^{\left(-4\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B c^{2} d^{2} e^{\left(-5\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{2} d e^{\left(-2\right)} + 3315 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{2} d e^{\left(-3\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b c d e^{\left(-3\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b c d e^{\left(-4\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A c^{2} d e^{\left(-4\right)} + 357 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B c^{2} d e^{\left(-5\right)} + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{2} e^{\left(-2\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{2} e^{\left(-3\right)} + 510 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b c e^{\left(-3\right)} + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b c e^{\left(-4\right)} + 119 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A c^{2} e^{\left(-4\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B c^{2} e^{\left(-5\right)}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d^3*e^(-2) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d^3*e^(-3) + 43758*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*c*d^3*e^(-3) + 4862*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*c*d^3*e^(-4) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c^2*d^3*e^(-4) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c^2*d^3*e^(-5) + 65637*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*d^2*e^(-2) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*d^2*e^(-3) + 14586*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*c*d^2*e^(-3) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*c*d^2*e^(-4) + 3315*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*c^2*d^2*e^(-4) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*c^2*d^2*e^(-5) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^2*d*e^(-2) + 3315*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^2*d*e^(-3) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b*c*d*e^(-3) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b*c*d*e^(-4) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*c^2*d*e^(-4) + 357*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*c^2*d*e^(-5) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^2*e^(-2) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^2*e^(-3) + 510*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b*c*e^(-3) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b*c*e^(-4) + 119*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*c^2*e^(-4) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*c^2*e^(-5))*e^(-1)","B",0
1223,1,1382,0,0.239024," ","integrate((B*x+A)*(e*x+d)^(3/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d^{2} e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d^{2} e^{\left(-3\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b c d^{2} e^{\left(-3\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b c d^{2} e^{\left(-4\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c^{2} d^{2} e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c^{2} d^{2} e^{\left(-5\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} d e^{\left(-2\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} d e^{\left(-3\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b c d e^{\left(-3\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b c d e^{\left(-4\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A c^{2} d e^{\left(-4\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B c^{2} d e^{\left(-5\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{2} e^{\left(-2\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{2} e^{\left(-3\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b c e^{\left(-3\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b c e^{\left(-4\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A c^{2} e^{\left(-4\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B c^{2} e^{\left(-5\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d^2*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d^2*e^(-3) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*c*d^2*e^(-3) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*c*d^2*e^(-4) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c^2*d^2*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c^2*d^2*e^(-5) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*d*e^(-2) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*d*e^(-3) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*c*d*e^(-3) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*c*d*e^(-4) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*c^2*d*e^(-4) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*c^2*d*e^(-5) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^2*e^(-2) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^2*e^(-3) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b*c*e^(-3) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b*c*e^(-4) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*c^2*e^(-4) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*c^2*e^(-5))*e^(-1)","B",0
1224,1,835,0,0.208270," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d e^{\left(-3\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b c d e^{\left(-3\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b c d e^{\left(-4\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c^{2} d e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c^{2} d e^{\left(-5\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} e^{\left(-2\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} e^{\left(-3\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b c e^{\left(-3\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b c e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A c^{2} e^{\left(-4\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B c^{2} e^{\left(-5\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d*e^(-3) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*c*d*e^(-3) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*c*d*e^(-4) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c^2*d*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c^2*d*e^(-5) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*e^(-2) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*e^(-3) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*c*e^(-3) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*c*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*c^2*e^(-4) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*c^2*e^(-5))*e^(-1)","B",0
1225,1,378,0,0.185850," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} e^{\left(-3\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b c e^{\left(-3\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b c e^{\left(-4\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c^{2} e^{\left(-4\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c^{2} e^{\left(-5\right)}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*e^(-3) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*c*e^(-3) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*c*e^(-4) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c^2*e^(-4) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c^2*e^(-5))*e^(-1)","A",0
1226,1,441,0,0.560993," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} B c^{2} e^{48} - 225 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{2} d e^{48} + 630 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{2} d^{2} e^{48} - 1050 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{2} d^{3} e^{48} + 1575 \, \sqrt{x e + d} B c^{2} d^{4} e^{48} + 90 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c e^{49} + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{2} e^{49} - 504 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c d e^{49} - 252 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{2} d e^{49} + 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c d^{2} e^{49} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d^{2} e^{49} - 2520 \, \sqrt{x e + d} B b c d^{3} e^{49} - 1260 \, \sqrt{x e + d} A c^{2} d^{3} e^{49} + 63 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} e^{50} + 126 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c e^{50} - 315 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} d e^{50} - 630 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c d e^{50} + 945 \, \sqrt{x e + d} B b^{2} d^{2} e^{50} + 1890 \, \sqrt{x e + d} A b c d^{2} e^{50} + 105 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} e^{51} - 630 \, \sqrt{x e + d} A b^{2} d e^{51}\right)} e^{\left(-54\right)} + \frac{2 \, {\left(B c^{2} d^{5} - 2 \, B b c d^{4} e - A c^{2} d^{4} e + B b^{2} d^{3} e^{2} + 2 \, A b c d^{3} e^{2} - A b^{2} d^{2} e^{3}\right)} e^{\left(-6\right)}}{\sqrt{x e + d}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*B*c^2*e^48 - 225*(x*e + d)^(7/2)*B*c^2*d*e^48 + 630*(x*e + d)^(5/2)*B*c^2*d^2*e^48 - 1050*(x*e + d)^(3/2)*B*c^2*d^3*e^48 + 1575*sqrt(x*e + d)*B*c^2*d^4*e^48 + 90*(x*e + d)^(7/2)*B*b*c*e^49 + 45*(x*e + d)^(7/2)*A*c^2*e^49 - 504*(x*e + d)^(5/2)*B*b*c*d*e^49 - 252*(x*e + d)^(5/2)*A*c^2*d*e^49 + 1260*(x*e + d)^(3/2)*B*b*c*d^2*e^49 + 630*(x*e + d)^(3/2)*A*c^2*d^2*e^49 - 2520*sqrt(x*e + d)*B*b*c*d^3*e^49 - 1260*sqrt(x*e + d)*A*c^2*d^3*e^49 + 63*(x*e + d)^(5/2)*B*b^2*e^50 + 126*(x*e + d)^(5/2)*A*b*c*e^50 - 315*(x*e + d)^(3/2)*B*b^2*d*e^50 - 630*(x*e + d)^(3/2)*A*b*c*d*e^50 + 945*sqrt(x*e + d)*B*b^2*d^2*e^50 + 1890*sqrt(x*e + d)*A*b*c*d^2*e^50 + 105*(x*e + d)^(3/2)*A*b^2*e^51 - 630*sqrt(x*e + d)*A*b^2*d*e^51)*e^(-54) + 2*(B*c^2*d^5 - 2*B*b*c*d^4*e - A*c^2*d^4*e + B*b^2*d^3*e^2 + 2*A*b*c*d^3*e^2 - A*b^2*d^2*e^3)*e^(-6)/sqrt(x*e + d)","A",0
1227,1,427,0,0.261977," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{2} e^{36} - 105 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{2} d e^{36} + 350 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{2} d^{2} e^{36} - 1050 \, \sqrt{x e + d} B c^{2} d^{3} e^{36} + 42 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c e^{37} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{2} e^{37} - 280 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c d e^{37} - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d e^{37} + 1260 \, \sqrt{x e + d} B b c d^{2} e^{37} + 630 \, \sqrt{x e + d} A c^{2} d^{2} e^{37} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} e^{38} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c e^{38} - 315 \, \sqrt{x e + d} B b^{2} d e^{38} - 630 \, \sqrt{x e + d} A b c d e^{38} + 105 \, \sqrt{x e + d} A b^{2} e^{39}\right)} e^{\left(-42\right)} - \frac{2 \, {\left(15 \, {\left(x e + d\right)} B c^{2} d^{4} - B c^{2} d^{5} - 24 \, {\left(x e + d\right)} B b c d^{3} e - 12 \, {\left(x e + d\right)} A c^{2} d^{3} e + 2 \, B b c d^{4} e + A c^{2} d^{4} e + 9 \, {\left(x e + d\right)} B b^{2} d^{2} e^{2} + 18 \, {\left(x e + d\right)} A b c d^{2} e^{2} - B b^{2} d^{3} e^{2} - 2 \, A b c d^{3} e^{2} - 6 \, {\left(x e + d\right)} A b^{2} d e^{3} + A b^{2} d^{2} e^{3}\right)} e^{\left(-6\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/105*(15*(x*e + d)^(7/2)*B*c^2*e^36 - 105*(x*e + d)^(5/2)*B*c^2*d*e^36 + 350*(x*e + d)^(3/2)*B*c^2*d^2*e^36 - 1050*sqrt(x*e + d)*B*c^2*d^3*e^36 + 42*(x*e + d)^(5/2)*B*b*c*e^37 + 21*(x*e + d)^(5/2)*A*c^2*e^37 - 280*(x*e + d)^(3/2)*B*b*c*d*e^37 - 140*(x*e + d)^(3/2)*A*c^2*d*e^37 + 1260*sqrt(x*e + d)*B*b*c*d^2*e^37 + 630*sqrt(x*e + d)*A*c^2*d^2*e^37 + 35*(x*e + d)^(3/2)*B*b^2*e^38 + 70*(x*e + d)^(3/2)*A*b*c*e^38 - 315*sqrt(x*e + d)*B*b^2*d*e^38 - 630*sqrt(x*e + d)*A*b*c*d*e^38 + 105*sqrt(x*e + d)*A*b^2*e^39)*e^(-42) - 2/3*(15*(x*e + d)*B*c^2*d^4 - B*c^2*d^5 - 24*(x*e + d)*B*b*c*d^3*e - 12*(x*e + d)*A*c^2*d^3*e + 2*B*b*c*d^4*e + A*c^2*d^4*e + 9*(x*e + d)*B*b^2*d^2*e^2 + 18*(x*e + d)*A*b*c*d^2*e^2 - B*b^2*d^3*e^2 - 2*A*b*c*d^3*e^2 - 6*(x*e + d)*A*b^2*d*e^3 + A*b^2*d^2*e^3)*e^(-6)/(x*e + d)^(3/2)","A",0
1228,1,427,0,0.233626," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{2} e^{24} - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{2} d e^{24} + 150 \, \sqrt{x e + d} B c^{2} d^{2} e^{24} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c e^{25} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} e^{25} - 120 \, \sqrt{x e + d} B b c d e^{25} - 60 \, \sqrt{x e + d} A c^{2} d e^{25} + 15 \, \sqrt{x e + d} B b^{2} e^{26} + 30 \, \sqrt{x e + d} A b c e^{26}\right)} e^{\left(-30\right)} + \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} B c^{2} d^{3} - 25 \, {\left(x e + d\right)} B c^{2} d^{4} + 3 \, B c^{2} d^{5} - 180 \, {\left(x e + d\right)}^{2} B b c d^{2} e - 90 \, {\left(x e + d\right)}^{2} A c^{2} d^{2} e + 40 \, {\left(x e + d\right)} B b c d^{3} e + 20 \, {\left(x e + d\right)} A c^{2} d^{3} e - 6 \, B b c d^{4} e - 3 \, A c^{2} d^{4} e + 45 \, {\left(x e + d\right)}^{2} B b^{2} d e^{2} + 90 \, {\left(x e + d\right)}^{2} A b c d e^{2} - 15 \, {\left(x e + d\right)} B b^{2} d^{2} e^{2} - 30 \, {\left(x e + d\right)} A b c d^{2} e^{2} + 3 \, B b^{2} d^{3} e^{2} + 6 \, A b c d^{3} e^{2} - 15 \, {\left(x e + d\right)}^{2} A b^{2} e^{3} + 10 \, {\left(x e + d\right)} A b^{2} d e^{3} - 3 \, A b^{2} d^{2} e^{3}\right)} e^{\left(-6\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*c^2*e^24 - 25*(x*e + d)^(3/2)*B*c^2*d*e^24 + 150*sqrt(x*e + d)*B*c^2*d^2*e^24 + 10*(x*e + d)^(3/2)*B*b*c*e^25 + 5*(x*e + d)^(3/2)*A*c^2*e^25 - 120*sqrt(x*e + d)*B*b*c*d*e^25 - 60*sqrt(x*e + d)*A*c^2*d*e^25 + 15*sqrt(x*e + d)*B*b^2*e^26 + 30*sqrt(x*e + d)*A*b*c*e^26)*e^(-30) + 2/15*(150*(x*e + d)^2*B*c^2*d^3 - 25*(x*e + d)*B*c^2*d^4 + 3*B*c^2*d^5 - 180*(x*e + d)^2*B*b*c*d^2*e - 90*(x*e + d)^2*A*c^2*d^2*e + 40*(x*e + d)*B*b*c*d^3*e + 20*(x*e + d)*A*c^2*d^3*e - 6*B*b*c*d^4*e - 3*A*c^2*d^4*e + 45*(x*e + d)^2*B*b^2*d*e^2 + 90*(x*e + d)^2*A*b*c*d*e^2 - 15*(x*e + d)*B*b^2*d^2*e^2 - 30*(x*e + d)*A*b*c*d^2*e^2 + 3*B*b^2*d^3*e^2 + 6*A*b*c*d^3*e^2 - 15*(x*e + d)^2*A*b^2*e^3 + 10*(x*e + d)*A*b^2*d*e^3 - 3*A*b^2*d^2*e^3)*e^(-6)/(x*e + d)^(5/2)","A",0
1229,1,476,0,0.296984," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, A d^{4} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}} + \frac{2 \, {\left(B b c^{4} d^{4} - A c^{5} d^{4} - 4 \, B b^{2} c^{3} d^{3} e + 4 \, A b c^{4} d^{3} e + 6 \, B b^{3} c^{2} d^{2} e^{2} - 6 \, A b^{2} c^{3} d^{2} e^{2} - 4 \, B b^{4} c d e^{3} + 4 \, A b^{3} c^{2} d e^{3} + B b^{5} e^{4} - A b^{4} c e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b c^{4}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{6} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{6} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{6} d^{2} + 105 \, \sqrt{x e + d} B c^{6} d^{3} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{5} e + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{6} e - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{5} d e + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{6} d e - 315 \, \sqrt{x e + d} B b c^{5} d^{2} e + 315 \, \sqrt{x e + d} A c^{6} d^{2} e + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{4} e^{2} - 35 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{5} e^{2} + 315 \, \sqrt{x e + d} B b^{2} c^{4} d e^{2} - 315 \, \sqrt{x e + d} A b c^{5} d e^{2} - 105 \, \sqrt{x e + d} B b^{3} c^{3} e^{3} + 105 \, \sqrt{x e + d} A b^{2} c^{4} e^{3}\right)}}{105 \, c^{7}}"," ",0,"2*A*d^4*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)) + 2*(B*b*c^4*d^4 - A*c^5*d^4 - 4*B*b^2*c^3*d^3*e + 4*A*b*c^4*d^3*e + 6*B*b^3*c^2*d^2*e^2 - 6*A*b^2*c^3*d^2*e^2 - 4*B*b^4*c*d*e^3 + 4*A*b^3*c^2*d*e^3 + B*b^5*e^4 - A*b^4*c*e^4)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b*c^4) + 2/105*(15*(x*e + d)^(7/2)*B*c^6 + 21*(x*e + d)^(5/2)*B*c^6*d + 35*(x*e + d)^(3/2)*B*c^6*d^2 + 105*sqrt(x*e + d)*B*c^6*d^3 - 21*(x*e + d)^(5/2)*B*b*c^5*e + 21*(x*e + d)^(5/2)*A*c^6*e - 70*(x*e + d)^(3/2)*B*b*c^5*d*e + 70*(x*e + d)^(3/2)*A*c^6*d*e - 315*sqrt(x*e + d)*B*b*c^5*d^2*e + 315*sqrt(x*e + d)*A*c^6*d^2*e + 35*(x*e + d)^(3/2)*B*b^2*c^4*e^2 - 35*(x*e + d)^(3/2)*A*b*c^5*e^2 + 315*sqrt(x*e + d)*B*b^2*c^4*d*e^2 - 315*sqrt(x*e + d)*A*b*c^5*d*e^2 - 105*sqrt(x*e + d)*B*b^3*c^3*e^3 + 105*sqrt(x*e + d)*A*b^2*c^4*e^3)/c^7","B",0
1230,1,316,0,0.238565," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, A d^{3} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}} + \frac{2 \, {\left(B b c^{3} d^{3} - A c^{4} d^{3} - 3 \, B b^{2} c^{2} d^{2} e + 3 \, A b c^{3} d^{2} e + 3 \, B b^{3} c d e^{2} - 3 \, A b^{2} c^{2} d e^{2} - B b^{4} e^{3} + A b^{3} c e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b c^{3}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{4} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{4} d + 15 \, \sqrt{x e + d} B c^{4} d^{2} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{3} e + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{4} e - 30 \, \sqrt{x e + d} B b c^{3} d e + 30 \, \sqrt{x e + d} A c^{4} d e + 15 \, \sqrt{x e + d} B b^{2} c^{2} e^{2} - 15 \, \sqrt{x e + d} A b c^{3} e^{2}\right)}}{15 \, c^{5}}"," ",0,"2*A*d^3*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)) + 2*(B*b*c^3*d^3 - A*c^4*d^3 - 3*B*b^2*c^2*d^2*e + 3*A*b*c^3*d^2*e + 3*B*b^3*c*d*e^2 - 3*A*b^2*c^2*d*e^2 - B*b^4*e^3 + A*b^3*c*e^3)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b*c^3) + 2/15*(3*(x*e + d)^(5/2)*B*c^4 + 5*(x*e + d)^(3/2)*B*c^4*d + 15*sqrt(x*e + d)*B*c^4*d^2 - 5*(x*e + d)^(3/2)*B*b*c^3*e + 5*(x*e + d)^(3/2)*A*c^4*e - 30*sqrt(x*e + d)*B*b*c^3*d*e + 30*sqrt(x*e + d)*A*c^4*d*e + 15*sqrt(x*e + d)*B*b^2*c^2*e^2 - 15*sqrt(x*e + d)*A*b*c^3*e^2)/c^5","B",0
1231,1,197,0,0.185739," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, A d^{2} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}} + \frac{2 \, {\left(B b c^{2} d^{2} - A c^{3} d^{2} - 2 \, B b^{2} c d e + 2 \, A b c^{2} d e + B b^{3} e^{2} - A b^{2} c e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b c^{2}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B c^{2} + 3 \, \sqrt{x e + d} B c^{2} d - 3 \, \sqrt{x e + d} B b c e + 3 \, \sqrt{x e + d} A c^{2} e\right)}}{3 \, c^{3}}"," ",0,"2*A*d^2*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)) + 2*(B*b*c^2*d^2 - A*c^3*d^2 - 2*B*b^2*c*d*e + 2*A*b*c^2*d*e + B*b^3*e^2 - A*b^2*c*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b*c^2) + 2/3*((x*e + d)^(3/2)*B*c^2 + 3*sqrt(x*e + d)*B*c^2*d - 3*sqrt(x*e + d)*B*b*c*e + 3*sqrt(x*e + d)*A*c^2*e)/c^3","A",0
1232,1,116,0,0.204159," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, A d \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}} + \frac{2 \, \sqrt{x e + d} B}{c} + \frac{2 \, {\left(B b c d - A c^{2} d - B b^{2} e + A b c e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b c}"," ",0,"2*A*d*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)) + 2*sqrt(x*e + d)*B/c + 2*(B*b*c*d - A*c^2*d - B*b^2*e + A*b*c*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b*c)","A",0
1233,1,79,0,0.193635," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b - A c\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b} + \frac{2 \, A \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}}"," ",0,"2*(B*b - A*c)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b) + 2*A*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d))","A",0
1234,1,129,0,0.224655," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b c - A c^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b c d - b^{2} e\right)} \sqrt{-c^{2} d + b c e}} + \frac{2 \, {\left(B d - A e\right)}}{{\left(c d^{2} - b d e\right)} \sqrt{x e + d}} + \frac{2 \, A \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d} d}"," ",0,"2*(B*b*c - A*c^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b*c*d - b^2*e)*sqrt(-c^2*d + b*c*e)) + 2*(B*d - A*e)/((c*d^2 - b*d*e)*sqrt(x*e + d)) + 2*A*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)*d)","A",0
1235,1,217,0,0.219135," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b c^{2} - A c^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} \sqrt{-c^{2} d + b c e}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)} B c d^{2} + B c d^{3} - 6 \, {\left(x e + d\right)} A c d e - B b d^{2} e - A c d^{2} e + 3 \, {\left(x e + d\right)} A b e^{2} + A b d e^{2}\right)}}{3 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{2 \, A \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d} d^{2}}"," ",0,"2*(B*b*c^2 - A*c^3)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*sqrt(-c^2*d + b*c*e)) + 2/3*(3*(x*e + d)*B*c*d^2 + B*c*d^3 - 6*(x*e + d)*A*c*d*e - B*b*d^2*e - A*c*d^2*e + 3*(x*e + d)*A*b*e^2 + A*b*d*e^2)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*(x*e + d)^(3/2)) + 2*A*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)*d^2)","A",0
1236,1,386,0,0.233661," ","integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b c^{3} - A c^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + 3 \, b^{3} c d e^{2} - b^{4} e^{3}\right)} \sqrt{-c^{2} d + b c e}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} B c^{2} d^{3} + 5 \, {\left(x e + d\right)} B c^{2} d^{4} + 3 \, B c^{2} d^{5} - 45 \, {\left(x e + d\right)}^{2} A c^{2} d^{2} e - 5 \, {\left(x e + d\right)} B b c d^{3} e - 10 \, {\left(x e + d\right)} A c^{2} d^{3} e - 6 \, B b c d^{4} e - 3 \, A c^{2} d^{4} e + 45 \, {\left(x e + d\right)}^{2} A b c d e^{2} + 15 \, {\left(x e + d\right)} A b c d^{2} e^{2} + 3 \, B b^{2} d^{3} e^{2} + 6 \, A b c d^{3} e^{2} - 15 \, {\left(x e + d\right)}^{2} A b^{2} e^{3} - 5 \, {\left(x e + d\right)} A b^{2} d e^{3} - 3 \, A b^{2} d^{2} e^{3}\right)}}{15 \, {\left(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}\right)} {\left(x e + d\right)}^{\frac{5}{2}}} + \frac{2 \, A \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d} d^{3}}"," ",0,"2*(B*b*c^3 - A*c^4)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b*c^3*d^3 - 3*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 - b^4*e^3)*sqrt(-c^2*d + b*c*e)) + 2/15*(15*(x*e + d)^2*B*c^2*d^3 + 5*(x*e + d)*B*c^2*d^4 + 3*B*c^2*d^5 - 45*(x*e + d)^2*A*c^2*d^2*e - 5*(x*e + d)*B*b*c*d^3*e - 10*(x*e + d)*A*c^2*d^3*e - 6*B*b*c*d^4*e - 3*A*c^2*d^4*e + 45*(x*e + d)^2*A*b*c*d*e^2 + 15*(x*e + d)*A*b*c*d^2*e^2 + 3*B*b^2*d^3*e^2 + 6*A*b*c*d^3*e^2 - 15*(x*e + d)^2*A*b^2*e^3 - 5*(x*e + d)*A*b^2*d*e^3 - 3*A*b^2*d^2*e^3)/((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)*(x*e + d)^(5/2)) + 2*A*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)*d^3)","A",0
1237,1,615,0,0.277982," ","integrate((B*x+A)/(e*x+d)^(9/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, {\left(B b c^{4} - A c^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b c^{4} d^{4} - 4 \, b^{2} c^{3} d^{3} e + 6 \, b^{3} c^{2} d^{2} e^{2} - 4 \, b^{4} c d e^{3} + b^{5} e^{4}\right)} \sqrt{-c^{2} d + b c e}} + \frac{2 \, {\left(105 \, {\left(x e + d\right)}^{3} B c^{3} d^{4} + 35 \, {\left(x e + d\right)}^{2} B c^{3} d^{5} + 21 \, {\left(x e + d\right)} B c^{3} d^{6} + 15 \, B c^{3} d^{7} - 420 \, {\left(x e + d\right)}^{3} A c^{3} d^{3} e - 35 \, {\left(x e + d\right)}^{2} B b c^{2} d^{4} e - 105 \, {\left(x e + d\right)}^{2} A c^{3} d^{4} e - 42 \, {\left(x e + d\right)} B b c^{2} d^{5} e - 42 \, {\left(x e + d\right)} A c^{3} d^{5} e - 45 \, B b c^{2} d^{6} e - 15 \, A c^{3} d^{6} e + 630 \, {\left(x e + d\right)}^{3} A b c^{2} d^{2} e^{2} + 210 \, {\left(x e + d\right)}^{2} A b c^{2} d^{3} e^{2} + 21 \, {\left(x e + d\right)} B b^{2} c d^{4} e^{2} + 105 \, {\left(x e + d\right)} A b c^{2} d^{4} e^{2} + 45 \, B b^{2} c d^{5} e^{2} + 45 \, A b c^{2} d^{5} e^{2} - 420 \, {\left(x e + d\right)}^{3} A b^{2} c d e^{3} - 140 \, {\left(x e + d\right)}^{2} A b^{2} c d^{2} e^{3} - 84 \, {\left(x e + d\right)} A b^{2} c d^{3} e^{3} - 15 \, B b^{3} d^{4} e^{3} - 45 \, A b^{2} c d^{4} e^{3} + 105 \, {\left(x e + d\right)}^{3} A b^{3} e^{4} + 35 \, {\left(x e + d\right)}^{2} A b^{3} d e^{4} + 21 \, {\left(x e + d\right)} A b^{3} d^{2} e^{4} + 15 \, A b^{3} d^{3} e^{4}\right)}}{105 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} {\left(x e + d\right)}^{\frac{7}{2}}} + \frac{2 \, A \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d} d^{4}}"," ",0,"2*(B*b*c^4 - A*c^5)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b*c^4*d^4 - 4*b^2*c^3*d^3*e + 6*b^3*c^2*d^2*e^2 - 4*b^4*c*d*e^3 + b^5*e^4)*sqrt(-c^2*d + b*c*e)) + 2/105*(105*(x*e + d)^3*B*c^3*d^4 + 35*(x*e + d)^2*B*c^3*d^5 + 21*(x*e + d)*B*c^3*d^6 + 15*B*c^3*d^7 - 420*(x*e + d)^3*A*c^3*d^3*e - 35*(x*e + d)^2*B*b*c^2*d^4*e - 105*(x*e + d)^2*A*c^3*d^4*e - 42*(x*e + d)*B*b*c^2*d^5*e - 42*(x*e + d)*A*c^3*d^5*e - 45*B*b*c^2*d^6*e - 15*A*c^3*d^6*e + 630*(x*e + d)^3*A*b*c^2*d^2*e^2 + 210*(x*e + d)^2*A*b*c^2*d^3*e^2 + 21*(x*e + d)*B*b^2*c*d^4*e^2 + 105*(x*e + d)*A*b*c^2*d^4*e^2 + 45*B*b^2*c*d^5*e^2 + 45*A*b*c^2*d^5*e^2 - 420*(x*e + d)^3*A*b^2*c*d*e^3 - 140*(x*e + d)^2*A*b^2*c*d^2*e^3 - 84*(x*e + d)*A*b^2*c*d^3*e^3 - 15*B*b^3*d^4*e^3 - 45*A*b^2*c*d^4*e^3 + 105*(x*e + d)^3*A*b^3*e^4 + 35*(x*e + d)^2*A*b^3*d*e^4 + 21*(x*e + d)*A*b^3*d^2*e^4 + 15*A*b^3*d^3*e^4)/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*(x*e + d)^(7/2)) + 2*A*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)*d^4)","B",0
1238,1,846,0,0.314358," ","integrate((B*x+A)*(e*x+d)^(9/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(2 \, B b d^{5} - 4 \, A c d^{5} + 9 \, A b d^{4} e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} - \frac{{\left(2 \, B b c^{5} d^{5} - 4 \, A c^{6} d^{5} - B b^{2} c^{4} d^{4} e + 11 \, A b c^{5} d^{4} e - 16 \, B b^{3} c^{3} d^{3} e^{2} - 4 \, A b^{2} c^{4} d^{3} e^{2} + 34 \, B b^{4} c^{2} d^{2} e^{3} - 14 \, A b^{3} c^{3} d^{2} e^{3} - 26 \, B b^{5} c d e^{4} + 16 \, A b^{4} c^{2} d e^{4} + 7 \, B b^{6} e^{5} - 5 \, A b^{5} c e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3} c^{4}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b c^{4} d^{4} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{5} d^{4} e - \sqrt{x e + d} B b c^{4} d^{5} e + 2 \, \sqrt{x e + d} A c^{5} d^{5} e - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{3} d^{3} e^{2} + 4 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{4} d^{3} e^{2} + 4 \, \sqrt{x e + d} B b^{2} c^{3} d^{4} e^{2} - 5 \, \sqrt{x e + d} A b c^{4} d^{4} e^{2} + 6 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c^{2} d^{2} e^{3} - 6 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{3} d^{2} e^{3} - 6 \, \sqrt{x e + d} B b^{3} c^{2} d^{3} e^{3} + 6 \, \sqrt{x e + d} A b^{2} c^{3} d^{3} e^{3} - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} c d e^{4} + 4 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c^{2} d e^{4} + 4 \, \sqrt{x e + d} B b^{4} c d^{2} e^{4} - 4 \, \sqrt{x e + d} A b^{3} c^{2} d^{2} e^{4} + {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} e^{5} - {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} c e^{5} - \sqrt{x e + d} B b^{5} d e^{5} + \sqrt{x e + d} A b^{4} c d e^{5}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2} c^{4}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{8} e^{2} + 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{8} d e^{2} + 90 \, \sqrt{x e + d} B c^{8} d^{2} e^{2} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{7} e^{3} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{8} e^{3} - 120 \, \sqrt{x e + d} B b c^{7} d e^{3} + 60 \, \sqrt{x e + d} A c^{8} d e^{3} + 45 \, \sqrt{x e + d} B b^{2} c^{6} e^{4} - 30 \, \sqrt{x e + d} A b c^{7} e^{4}\right)}}{15 \, c^{10}}"," ",0,"(2*B*b*d^5 - 4*A*c*d^5 + 9*A*b*d^4*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) - (2*B*b*c^5*d^5 - 4*A*c^6*d^5 - B*b^2*c^4*d^4*e + 11*A*b*c^5*d^4*e - 16*B*b^3*c^3*d^3*e^2 - 4*A*b^2*c^4*d^3*e^2 + 34*B*b^4*c^2*d^2*e^3 - 14*A*b^3*c^3*d^2*e^3 - 26*B*b^5*c*d*e^4 + 16*A*b^4*c^2*d*e^4 + 7*B*b^6*e^5 - 5*A*b^5*c*e^5)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3*c^4) + ((x*e + d)^(3/2)*B*b*c^4*d^4*e - 2*(x*e + d)^(3/2)*A*c^5*d^4*e - sqrt(x*e + d)*B*b*c^4*d^5*e + 2*sqrt(x*e + d)*A*c^5*d^5*e - 4*(x*e + d)^(3/2)*B*b^2*c^3*d^3*e^2 + 4*(x*e + d)^(3/2)*A*b*c^4*d^3*e^2 + 4*sqrt(x*e + d)*B*b^2*c^3*d^4*e^2 - 5*sqrt(x*e + d)*A*b*c^4*d^4*e^2 + 6*(x*e + d)^(3/2)*B*b^3*c^2*d^2*e^3 - 6*(x*e + d)^(3/2)*A*b^2*c^3*d^2*e^3 - 6*sqrt(x*e + d)*B*b^3*c^2*d^3*e^3 + 6*sqrt(x*e + d)*A*b^2*c^3*d^3*e^3 - 4*(x*e + d)^(3/2)*B*b^4*c*d*e^4 + 4*(x*e + d)^(3/2)*A*b^3*c^2*d*e^4 + 4*sqrt(x*e + d)*B*b^4*c*d^2*e^4 - 4*sqrt(x*e + d)*A*b^3*c^2*d^2*e^4 + (x*e + d)^(3/2)*B*b^5*e^5 - (x*e + d)^(3/2)*A*b^4*c*e^5 - sqrt(x*e + d)*B*b^5*d*e^5 + sqrt(x*e + d)*A*b^4*c*d*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2*c^4) + 2/15*(3*(x*e + d)^(5/2)*B*c^8*e^2 + 15*(x*e + d)^(3/2)*B*c^8*d*e^2 + 90*sqrt(x*e + d)*B*c^8*d^2*e^2 - 10*(x*e + d)^(3/2)*B*b*c^7*e^3 + 5*(x*e + d)^(3/2)*A*c^8*e^3 - 120*sqrt(x*e + d)*B*b*c^7*d*e^3 + 60*sqrt(x*e + d)*A*c^8*d*e^3 + 45*sqrt(x*e + d)*B*b^2*c^6*e^4 - 30*sqrt(x*e + d)*A*b*c^7*e^4)/c^10","B",0
1239,1,639,0,0.305459," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(2 \, B b d^{4} - 4 \, A c d^{4} + 7 \, A b d^{3} e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} - \frac{{\left(2 \, B b c^{4} d^{4} - 4 \, A c^{5} d^{4} - B b^{2} c^{3} d^{3} e + 9 \, A b c^{4} d^{3} e - 9 \, B b^{3} c^{2} d^{2} e^{2} - 3 \, A b^{2} c^{3} d^{2} e^{2} + 13 \, B b^{4} c d e^{3} - 5 \, A b^{3} c^{2} d e^{3} - 5 \, B b^{5} e^{4} + 3 \, A b^{4} c e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3} c^{3}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B c^{4} e^{2} + 9 \, \sqrt{x e + d} B c^{4} d e^{2} - 6 \, \sqrt{x e + d} B b c^{3} e^{3} + 3 \, \sqrt{x e + d} A c^{4} e^{3}\right)}}{3 \, c^{6}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b c^{3} d^{3} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{4} d^{3} e - \sqrt{x e + d} B b c^{3} d^{4} e + 2 \, \sqrt{x e + d} A c^{4} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{2} d^{2} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{3} d^{2} e^{2} + 3 \, \sqrt{x e + d} B b^{2} c^{2} d^{3} e^{2} - 4 \, \sqrt{x e + d} A b c^{3} d^{3} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c d e^{3} - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{2} d e^{3} - 3 \, \sqrt{x e + d} B b^{3} c d^{2} e^{3} + 3 \, \sqrt{x e + d} A b^{2} c^{2} d^{2} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} e^{4} + {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c e^{4} + \sqrt{x e + d} B b^{4} d e^{4} - \sqrt{x e + d} A b^{3} c d e^{4}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2} c^{3}}"," ",0,"(2*B*b*d^4 - 4*A*c*d^4 + 7*A*b*d^3*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) - (2*B*b*c^4*d^4 - 4*A*c^5*d^4 - B*b^2*c^3*d^3*e + 9*A*b*c^4*d^3*e - 9*B*b^3*c^2*d^2*e^2 - 3*A*b^2*c^3*d^2*e^2 + 13*B*b^4*c*d*e^3 - 5*A*b^3*c^2*d*e^3 - 5*B*b^5*e^4 + 3*A*b^4*c*e^4)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3*c^3) + 2/3*((x*e + d)^(3/2)*B*c^4*e^2 + 9*sqrt(x*e + d)*B*c^4*d*e^2 - 6*sqrt(x*e + d)*B*b*c^3*e^3 + 3*sqrt(x*e + d)*A*c^4*e^3)/c^6 + ((x*e + d)^(3/2)*B*b*c^3*d^3*e - 2*(x*e + d)^(3/2)*A*c^4*d^3*e - sqrt(x*e + d)*B*b*c^3*d^4*e + 2*sqrt(x*e + d)*A*c^4*d^4*e - 3*(x*e + d)^(3/2)*B*b^2*c^2*d^2*e^2 + 3*(x*e + d)^(3/2)*A*b*c^3*d^2*e^2 + 3*sqrt(x*e + d)*B*b^2*c^2*d^3*e^2 - 4*sqrt(x*e + d)*A*b*c^3*d^3*e^2 + 3*(x*e + d)^(3/2)*B*b^3*c*d*e^3 - 3*(x*e + d)^(3/2)*A*b^2*c^2*d*e^3 - 3*sqrt(x*e + d)*B*b^3*c*d^2*e^3 + 3*sqrt(x*e + d)*A*b^2*c^2*d^2*e^3 - (x*e + d)^(3/2)*B*b^4*e^4 + (x*e + d)^(3/2)*A*b^3*c*e^4 + sqrt(x*e + d)*B*b^4*d*e^4 - sqrt(x*e + d)*A*b^3*c*d*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2*c^3)","B",0
1240,1,468,0,0.237327," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e^{2}}{c^{2}} + \frac{{\left(2 \, B b d^{3} - 4 \, A c d^{3} + 5 \, A b d^{2} e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} - \frac{{\left(2 \, B b c^{3} d^{3} - 4 \, A c^{4} d^{3} - B b^{2} c^{2} d^{2} e + 7 \, A b c^{3} d^{2} e - 4 \, B b^{3} c d e^{2} - 2 \, A b^{2} c^{2} d e^{2} + 3 \, B b^{4} e^{3} - A b^{3} c e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3} c^{2}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b c^{2} d^{2} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d^{2} e - \sqrt{x e + d} B b c^{2} d^{3} e + 2 \, \sqrt{x e + d} A c^{3} d^{3} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c d e^{2} + 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{2} d e^{2} + 2 \, \sqrt{x e + d} B b^{2} c d^{2} e^{2} - 3 \, \sqrt{x e + d} A b c^{2} d^{2} e^{2} + {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c e^{3} - \sqrt{x e + d} B b^{3} d e^{3} + \sqrt{x e + d} A b^{2} c d e^{3}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2} c^{2}}"," ",0,"2*sqrt(x*e + d)*B*e^2/c^2 + (2*B*b*d^3 - 4*A*c*d^3 + 5*A*b*d^2*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) - (2*B*b*c^3*d^3 - 4*A*c^4*d^3 - B*b^2*c^2*d^2*e + 7*A*b*c^3*d^2*e - 4*B*b^3*c*d*e^2 - 2*A*b^2*c^2*d*e^2 + 3*B*b^4*e^3 - A*b^3*c*e^3)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3*c^2) + ((x*e + d)^(3/2)*B*b*c^2*d^2*e - 2*(x*e + d)^(3/2)*A*c^3*d^2*e - sqrt(x*e + d)*B*b*c^2*d^3*e + 2*sqrt(x*e + d)*A*c^3*d^3*e - 2*(x*e + d)^(3/2)*B*b^2*c*d*e^2 + 2*(x*e + d)^(3/2)*A*b*c^2*d*e^2 + 2*sqrt(x*e + d)*B*b^2*c*d^2*e^2 - 3*sqrt(x*e + d)*A*b*c^2*d^2*e^2 + (x*e + d)^(3/2)*B*b^3*e^3 - (x*e + d)^(3/2)*A*b^2*c*e^3 - sqrt(x*e + d)*B*b^3*d*e^3 + sqrt(x*e + d)*A*b^2*c*d*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2*c^2)","B",0
1241,1,334,0,0.212554," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(2 \, B b d^{2} - 4 \, A c d^{2} + 3 \, A b d e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} - \frac{{\left(2 \, B b c^{2} d^{2} - 4 \, A c^{3} d^{2} - B b^{2} c d e + 5 \, A b c^{2} d e - B b^{3} e^{2} - A b^{2} c e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3} c} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b c d e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d e - \sqrt{x e + d} B b c d^{2} e + 2 \, \sqrt{x e + d} A c^{2} d^{2} e - {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} e^{2} + {\left(x e + d\right)}^{\frac{3}{2}} A b c e^{2} + \sqrt{x e + d} B b^{2} d e^{2} - 2 \, \sqrt{x e + d} A b c d e^{2}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2} c}"," ",0,"(2*B*b*d^2 - 4*A*c*d^2 + 3*A*b*d*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) - (2*B*b*c^2*d^2 - 4*A*c^3*d^2 - B*b^2*c*d*e + 5*A*b*c^2*d*e - B*b^3*e^2 - A*b^2*c*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3*c) + ((x*e + d)^(3/2)*B*b*c*d*e - 2*(x*e + d)^(3/2)*A*c^2*d*e - sqrt(x*e + d)*B*b*c*d^2*e + 2*sqrt(x*e + d)*A*c^2*d^2*e - (x*e + d)^(3/2)*B*b^2*e^2 + (x*e + d)^(3/2)*A*b*c*e^2 + sqrt(x*e + d)*B*b^2*d*e^2 - 2*sqrt(x*e + d)*A*b*c*d*e^2)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2*c)","B",0
1242,1,234,0,0.220743," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B b c d - 4 \, A c^{2} d - B b^{2} e + 3 \, A b c e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3}} + \frac{{\left(2 \, B b d - 4 \, A c d + A b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c e - \sqrt{x e + d} B b d e + 2 \, \sqrt{x e + d} A c d e - \sqrt{x e + d} A b e^{2}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2}}"," ",0,"-(2*B*b*c*d - 4*A*c^2*d - B*b^2*e + 3*A*b*c*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3) + (2*B*b*d - 4*A*c*d + A*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) + ((x*e + d)^(3/2)*B*b*e - 2*(x*e + d)^(3/2)*A*c*e - sqrt(x*e + d)*B*b*d*e + 2*sqrt(x*e + d)*A*c*d*e - sqrt(x*e + d)*A*b*e^2)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2)","A",0
1243,1,315,0,0.237312," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B b c^{2} d - 4 \, A c^{3} d - 3 \, B b^{2} c e + 5 \, A b c^{2} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c d - b^{4} e\right)} \sqrt{-c^{2} d + b c e}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b c d e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d e - \sqrt{x e + d} B b c d^{2} e + 2 \, \sqrt{x e + d} A c^{2} d^{2} e + {\left(x e + d\right)}^{\frac{3}{2}} A b c e^{2} - 2 \, \sqrt{x e + d} A b c d e^{2} + \sqrt{x e + d} A b^{2} e^{3}}{{\left(b^{2} c d^{2} - b^{3} d e\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}} + \frac{{\left(2 \, B b d - 4 \, A c d - A b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d}"," ",0,"-(2*B*b*c^2*d - 4*A*c^3*d - 3*B*b^2*c*e + 5*A*b*c^2*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c*d - b^4*e)*sqrt(-c^2*d + b*c*e)) + ((x*e + d)^(3/2)*B*b*c*d*e - 2*(x*e + d)^(3/2)*A*c^2*d*e - sqrt(x*e + d)*B*b*c*d^2*e + 2*sqrt(x*e + d)*A*c^2*d^2*e + (x*e + d)^(3/2)*A*b*c*e^2 - 2*sqrt(x*e + d)*A*b*c*d*e^2 + sqrt(x*e + d)*A*b^2*e^3)/((b^2*c*d^2 - b^3*d*e)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)) + (2*B*b*d - 4*A*c*d - A*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d)","A",0
1244,1,500,0,0.256657," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B b c^{3} d - 4 \, A c^{4} d - 5 \, B b^{2} c^{2} e + 7 \, A b c^{3} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c^{2} d^{2} - 2 \, b^{4} c d e + b^{5} e^{2}\right)} \sqrt{-c^{2} d + b c e}} + \frac{{\left(x e + d\right)}^{2} B b c^{2} d^{2} e - 2 \, {\left(x e + d\right)}^{2} A c^{3} d^{2} e - {\left(x e + d\right)} B b c^{2} d^{3} e + 2 \, {\left(x e + d\right)} A c^{3} d^{3} e + 2 \, {\left(x e + d\right)}^{2} B b^{2} c d e^{2} + 2 \, {\left(x e + d\right)}^{2} A b c^{2} d e^{2} - 4 \, {\left(x e + d\right)} B b^{2} c d^{2} e^{2} - 3 \, {\left(x e + d\right)} A b c^{2} d^{2} e^{2} + 2 \, B b^{2} c d^{3} e^{2} - 3 \, {\left(x e + d\right)}^{2} A b^{2} c e^{3} + 2 \, {\left(x e + d\right)} B b^{3} d e^{3} + 7 \, {\left(x e + d\right)} A b^{2} c d e^{3} - 2 \, B b^{3} d^{2} e^{3} - 2 \, A b^{2} c d^{2} e^{3} - 3 \, {\left(x e + d\right)} A b^{3} e^{4} + 2 \, A b^{3} d e^{4}}{{\left(b^{2} c^{2} d^{4} - 2 \, b^{3} c d^{3} e + b^{4} d^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{\frac{5}{2}} c - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d + \sqrt{x e + d} c d^{2} + {\left(x e + d\right)}^{\frac{3}{2}} b e - \sqrt{x e + d} b d e\right)}} + \frac{{\left(2 \, B b d - 4 \, A c d - 3 \, A b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d^{2}}"," ",0,"-(2*B*b*c^3*d - 4*A*c^4*d - 5*B*b^2*c^2*e + 7*A*b*c^3*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c^2*d^2 - 2*b^4*c*d*e + b^5*e^2)*sqrt(-c^2*d + b*c*e)) + ((x*e + d)^2*B*b*c^2*d^2*e - 2*(x*e + d)^2*A*c^3*d^2*e - (x*e + d)*B*b*c^2*d^3*e + 2*(x*e + d)*A*c^3*d^3*e + 2*(x*e + d)^2*B*b^2*c*d*e^2 + 2*(x*e + d)^2*A*b*c^2*d*e^2 - 4*(x*e + d)*B*b^2*c*d^2*e^2 - 3*(x*e + d)*A*b*c^2*d^2*e^2 + 2*B*b^2*c*d^3*e^2 - 3*(x*e + d)^2*A*b^2*c*e^3 + 2*(x*e + d)*B*b^3*d*e^3 + 7*(x*e + d)*A*b^2*c*d*e^3 - 2*B*b^3*d^2*e^3 - 2*A*b^2*c*d^2*e^3 - 3*(x*e + d)*A*b^3*e^4 + 2*A*b^3*d*e^4)/((b^2*c^2*d^4 - 2*b^3*c*d^3*e + b^4*d^2*e^2)*((x*e + d)^(5/2)*c - 2*(x*e + d)^(3/2)*c*d + sqrt(x*e + d)*c*d^2 + (x*e + d)^(3/2)*b*e - sqrt(x*e + d)*b*d*e)) + (2*B*b*d - 4*A*c*d - 3*A*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d^2)","B",0
1245,1,603,0,0.318798," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B b c^{4} d - 4 \, A c^{5} d - 7 \, B b^{2} c^{3} e + 9 \, A b c^{4} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c^{3} d^{3} - 3 \, b^{4} c^{2} d^{2} e + 3 \, b^{5} c d e^{2} - b^{6} e^{3}\right)} \sqrt{-c^{2} d + b c e}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b c^{3} d^{3} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{4} d^{3} e - \sqrt{x e + d} B b c^{3} d^{4} e + 2 \, \sqrt{x e + d} A c^{4} d^{4} e + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{3} d^{2} e^{2} - 4 \, \sqrt{x e + d} A b c^{3} d^{3} e^{2} - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{2} d e^{3} + 6 \, \sqrt{x e + d} A b^{2} c^{2} d^{2} e^{3} + {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c e^{4} - 4 \, \sqrt{x e + d} A b^{3} c d e^{4} + \sqrt{x e + d} A b^{4} e^{5}}{{\left(b^{2} c^{3} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - b^{5} d^{3} e^{3}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}} + \frac{2 \, {\left(9 \, {\left(x e + d\right)} B c d^{2} e^{2} + B c d^{3} e^{2} - 3 \, {\left(x e + d\right)} B b d e^{3} - 12 \, {\left(x e + d\right)} A c d e^{3} - B b d^{2} e^{3} - A c d^{2} e^{3} + 6 \, {\left(x e + d\right)} A b e^{4} + A b d e^{4}\right)}}{3 \, {\left(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}\right)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{{\left(2 \, B b d - 4 \, A c d - 5 \, A b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d^{3}}"," ",0,"-(2*B*b*c^4*d - 4*A*c^5*d - 7*B*b^2*c^3*e + 9*A*b*c^4*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c^3*d^3 - 3*b^4*c^2*d^2*e + 3*b^5*c*d*e^2 - b^6*e^3)*sqrt(-c^2*d + b*c*e)) + ((x*e + d)^(3/2)*B*b*c^3*d^3*e - 2*(x*e + d)^(3/2)*A*c^4*d^3*e - sqrt(x*e + d)*B*b*c^3*d^4*e + 2*sqrt(x*e + d)*A*c^4*d^4*e + 3*(x*e + d)^(3/2)*A*b*c^3*d^2*e^2 - 4*sqrt(x*e + d)*A*b*c^3*d^3*e^2 - 3*(x*e + d)^(3/2)*A*b^2*c^2*d*e^3 + 6*sqrt(x*e + d)*A*b^2*c^2*d^2*e^3 + (x*e + d)^(3/2)*A*b^3*c*e^4 - 4*sqrt(x*e + d)*A*b^3*c*d*e^4 + sqrt(x*e + d)*A*b^4*e^5)/((b^2*c^3*d^6 - 3*b^3*c^2*d^5*e + 3*b^4*c*d^4*e^2 - b^5*d^3*e^3)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)) + 2/3*(9*(x*e + d)*B*c*d^2*e^2 + B*c*d^3*e^2 - 3*(x*e + d)*B*b*d*e^3 - 12*(x*e + d)*A*c*d*e^3 - B*b*d^2*e^3 - A*c*d^2*e^3 + 6*(x*e + d)*A*b*e^4 + A*b*d*e^4)/((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)*(x*e + d)^(3/2)) + (2*B*b*d - 4*A*c*d - 5*A*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d^3)","A",0
1246,1,867,0,0.489733," ","integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B b c^{5} d - 4 \, A c^{6} d - 9 \, B b^{2} c^{4} e + 11 \, A b c^{5} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c^{4} d^{4} - 4 \, b^{4} c^{3} d^{3} e + 6 \, b^{5} c^{2} d^{2} e^{2} - 4 \, b^{6} c d e^{3} + b^{7} e^{4}\right)} \sqrt{-c^{2} d + b c e}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} B b c^{4} d^{4} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{5} d^{4} e - \sqrt{x e + d} B b c^{4} d^{5} e + 2 \, \sqrt{x e + d} A c^{5} d^{5} e + 4 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{4} d^{3} e^{2} - 5 \, \sqrt{x e + d} A b c^{4} d^{4} e^{2} - 6 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{3} d^{2} e^{3} + 10 \, \sqrt{x e + d} A b^{2} c^{3} d^{3} e^{3} + 4 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c^{2} d e^{4} - 10 \, \sqrt{x e + d} A b^{3} c^{2} d^{2} e^{4} - {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} c e^{5} + 5 \, \sqrt{x e + d} A b^{4} c d e^{5} - \sqrt{x e + d} A b^{5} e^{6}}{{\left(b^{2} c^{4} d^{8} - 4 \, b^{3} c^{3} d^{7} e + 6 \, b^{4} c^{2} d^{6} e^{2} - 4 \, b^{5} c d^{5} e^{3} + b^{6} d^{4} e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}} + \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} B c^{2} d^{3} e^{2} + 15 \, {\left(x e + d\right)} B c^{2} d^{4} e^{2} + 3 \, B c^{2} d^{5} e^{2} - 60 \, {\left(x e + d\right)}^{2} B b c d^{2} e^{3} - 150 \, {\left(x e + d\right)}^{2} A c^{2} d^{2} e^{3} - 20 \, {\left(x e + d\right)} B b c d^{3} e^{3} - 20 \, {\left(x e + d\right)} A c^{2} d^{3} e^{3} - 6 \, B b c d^{4} e^{3} - 3 \, A c^{2} d^{4} e^{3} + 15 \, {\left(x e + d\right)}^{2} B b^{2} d e^{4} + 150 \, {\left(x e + d\right)}^{2} A b c d e^{4} + 5 \, {\left(x e + d\right)} B b^{2} d^{2} e^{4} + 30 \, {\left(x e + d\right)} A b c d^{2} e^{4} + 3 \, B b^{2} d^{3} e^{4} + 6 \, A b c d^{3} e^{4} - 45 \, {\left(x e + d\right)}^{2} A b^{2} e^{5} - 10 \, {\left(x e + d\right)} A b^{2} d e^{5} - 3 \, A b^{2} d^{2} e^{5}\right)}}{15 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} {\left(x e + d\right)}^{\frac{5}{2}}} + \frac{{\left(2 \, B b d - 4 \, A c d - 7 \, A b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d^{4}}"," ",0,"-(2*B*b*c^5*d - 4*A*c^6*d - 9*B*b^2*c^4*e + 11*A*b*c^5*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c^4*d^4 - 4*b^4*c^3*d^3*e + 6*b^5*c^2*d^2*e^2 - 4*b^6*c*d*e^3 + b^7*e^4)*sqrt(-c^2*d + b*c*e)) + ((x*e + d)^(3/2)*B*b*c^4*d^4*e - 2*(x*e + d)^(3/2)*A*c^5*d^4*e - sqrt(x*e + d)*B*b*c^4*d^5*e + 2*sqrt(x*e + d)*A*c^5*d^5*e + 4*(x*e + d)^(3/2)*A*b*c^4*d^3*e^2 - 5*sqrt(x*e + d)*A*b*c^4*d^4*e^2 - 6*(x*e + d)^(3/2)*A*b^2*c^3*d^2*e^3 + 10*sqrt(x*e + d)*A*b^2*c^3*d^3*e^3 + 4*(x*e + d)^(3/2)*A*b^3*c^2*d*e^4 - 10*sqrt(x*e + d)*A*b^3*c^2*d^2*e^4 - (x*e + d)^(3/2)*A*b^4*c*e^5 + 5*sqrt(x*e + d)*A*b^4*c*d*e^5 - sqrt(x*e + d)*A*b^5*e^6)/((b^2*c^4*d^8 - 4*b^3*c^3*d^7*e + 6*b^4*c^2*d^6*e^2 - 4*b^5*c*d^5*e^3 + b^6*d^4*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)) + 2/15*(90*(x*e + d)^2*B*c^2*d^3*e^2 + 15*(x*e + d)*B*c^2*d^4*e^2 + 3*B*c^2*d^5*e^2 - 60*(x*e + d)^2*B*b*c*d^2*e^3 - 150*(x*e + d)^2*A*c^2*d^2*e^3 - 20*(x*e + d)*B*b*c*d^3*e^3 - 20*(x*e + d)*A*c^2*d^3*e^3 - 6*B*b*c*d^4*e^3 - 3*A*c^2*d^4*e^3 + 15*(x*e + d)^2*B*b^2*d*e^4 + 150*(x*e + d)^2*A*b*c*d*e^4 + 5*(x*e + d)*B*b^2*d^2*e^4 + 30*(x*e + d)*A*b*c*d^2*e^4 + 3*B*b^2*d^3*e^4 + 6*A*b*c*d^3*e^4 - 45*(x*e + d)^2*A*b^2*e^5 - 10*(x*e + d)*A*b^2*d*e^5 - 3*A*b^2*d^2*e^5)/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*(x*e + d)^(5/2)) + (2*B*b*d - 4*A*c*d - 7*A*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d^4)","B",0
1247,1,1245,0,0.362658," ","integrate((B*x+A)*(e*x+d)^(9/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e^{4}}{c^{3}} - \frac{3 \, {\left(8 \, B b c d^{5} - 16 \, A c^{2} d^{5} - 12 \, B b^{2} d^{4} e + 36 \, A b c d^{4} e - 21 \, A b^{2} d^{3} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} + \frac{3 \, {\left(8 \, B b c^{5} d^{5} - 16 \, A c^{6} d^{5} - 16 \, B b^{2} c^{4} d^{4} e + 44 \, A b c^{5} d^{4} e + 5 \, B b^{3} c^{3} d^{3} e^{2} - 37 \, A b^{2} c^{4} d^{3} e^{2} + B b^{4} c^{2} d^{2} e^{3} + 7 \, A b^{3} c^{3} d^{2} e^{3} + 7 \, B b^{5} c d e^{4} + A b^{4} c^{2} d e^{4} - 5 \, B b^{6} e^{5} + A b^{5} c e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5} c^{3}} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{5} d^{4} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{6} d^{4} e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{5} d^{5} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{6} d^{5} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{5} d^{6} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{6} d^{6} e - 12 \, \sqrt{x e + d} B b c^{5} d^{7} e + 24 \, \sqrt{x e + d} A c^{6} d^{7} e - 15 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c^{4} d^{3} e^{2} + 48 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{5} d^{3} e^{2} + 63 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c^{4} d^{4} e^{2} - 180 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{5} d^{4} e^{2} - 81 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{4} d^{5} e^{2} + 216 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{5} d^{5} e^{2} + 33 \, \sqrt{x e + d} B b^{2} c^{4} d^{6} e^{2} - 84 \, \sqrt{x e + d} A b c^{5} d^{6} e^{2} - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{3} c^{3} d^{2} e^{3} - 21 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{2} c^{4} d^{2} e^{3} - 14 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} c^{3} d^{3} e^{3} + 136 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c^{4} d^{3} e^{3} + 41 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c^{3} d^{4} e^{3} - 217 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{4} d^{4} e^{3} - 24 \, \sqrt{x e + d} B b^{3} c^{3} d^{5} e^{3} + 102 \, \sqrt{x e + d} A b^{2} c^{4} d^{5} e^{3} + 19 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} c^{2} d e^{4} - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{3} c^{3} d e^{4} - 48 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} c^{2} d^{2} e^{4} - 24 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} c^{3} d^{2} e^{4} + 39 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} c^{2} d^{3} e^{4} + 74 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c^{3} d^{3} e^{4} - 10 \, \sqrt{x e + d} B b^{4} c^{2} d^{4} e^{4} - 45 \, \sqrt{x e + d} A b^{3} c^{3} d^{4} e^{4} - 9 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} c e^{5} + 5 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} c^{2} e^{5} + 38 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} c d e^{5} - 10 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} c^{2} d e^{5} - 49 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} c d^{2} e^{5} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} c^{2} d^{2} e^{5} + 20 \, \sqrt{x e + d} B b^{5} c d^{3} e^{5} - 7 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} e^{6} + 3 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} c e^{6} + 14 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d e^{6} - 6 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} c d e^{6} - 7 \, \sqrt{x e + d} B b^{6} d^{2} e^{6} + 3 \, \sqrt{x e + d} A b^{5} c d^{2} e^{6}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4} c^{3}}"," ",0,"2*sqrt(x*e + d)*B*e^4/c^3 - 3/4*(8*B*b*c*d^5 - 16*A*c^2*d^5 - 12*B*b^2*d^4*e + 36*A*b*c*d^4*e - 21*A*b^2*d^3*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) + 3/4*(8*B*b*c^5*d^5 - 16*A*c^6*d^5 - 16*B*b^2*c^4*d^4*e + 44*A*b*c^5*d^4*e + 5*B*b^3*c^3*d^3*e^2 - 37*A*b^2*c^4*d^3*e^2 + B*b^4*c^2*d^2*e^3 + 7*A*b^3*c^3*d^2*e^3 + 7*B*b^5*c*d*e^4 + A*b^4*c^2*d*e^4 - 5*B*b^6*e^5 + A*b^5*c*e^5)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5*c^3) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^5*d^4*e - 24*(x*e + d)^(7/2)*A*c^6*d^4*e - 36*(x*e + d)^(5/2)*B*b*c^5*d^5*e + 72*(x*e + d)^(5/2)*A*c^6*d^5*e + 36*(x*e + d)^(3/2)*B*b*c^5*d^6*e - 72*(x*e + d)^(3/2)*A*c^6*d^6*e - 12*sqrt(x*e + d)*B*b*c^5*d^7*e + 24*sqrt(x*e + d)*A*c^6*d^7*e - 15*(x*e + d)^(7/2)*B*b^2*c^4*d^3*e^2 + 48*(x*e + d)^(7/2)*A*b*c^5*d^3*e^2 + 63*(x*e + d)^(5/2)*B*b^2*c^4*d^4*e^2 - 180*(x*e + d)^(5/2)*A*b*c^5*d^4*e^2 - 81*(x*e + d)^(3/2)*B*b^2*c^4*d^5*e^2 + 216*(x*e + d)^(3/2)*A*b*c^5*d^5*e^2 + 33*sqrt(x*e + d)*B*b^2*c^4*d^6*e^2 - 84*sqrt(x*e + d)*A*b*c^5*d^6*e^2 - 3*(x*e + d)^(7/2)*B*b^3*c^3*d^2*e^3 - 21*(x*e + d)^(7/2)*A*b^2*c^4*d^2*e^3 - 14*(x*e + d)^(5/2)*B*b^3*c^3*d^3*e^3 + 136*(x*e + d)^(5/2)*A*b^2*c^4*d^3*e^3 + 41*(x*e + d)^(3/2)*B*b^3*c^3*d^4*e^3 - 217*(x*e + d)^(3/2)*A*b^2*c^4*d^4*e^3 - 24*sqrt(x*e + d)*B*b^3*c^3*d^5*e^3 + 102*sqrt(x*e + d)*A*b^2*c^4*d^5*e^3 + 19*(x*e + d)^(7/2)*B*b^4*c^2*d*e^4 - 3*(x*e + d)^(7/2)*A*b^3*c^3*d*e^4 - 48*(x*e + d)^(5/2)*B*b^4*c^2*d^2*e^4 - 24*(x*e + d)^(5/2)*A*b^3*c^3*d^2*e^4 + 39*(x*e + d)^(3/2)*B*b^4*c^2*d^3*e^4 + 74*(x*e + d)^(3/2)*A*b^3*c^3*d^3*e^4 - 10*sqrt(x*e + d)*B*b^4*c^2*d^4*e^4 - 45*sqrt(x*e + d)*A*b^3*c^3*d^4*e^4 - 9*(x*e + d)^(7/2)*B*b^5*c*e^5 + 5*(x*e + d)^(7/2)*A*b^4*c^2*e^5 + 38*(x*e + d)^(5/2)*B*b^5*c*d*e^5 - 10*(x*e + d)^(5/2)*A*b^4*c^2*d*e^5 - 49*(x*e + d)^(3/2)*B*b^5*c*d^2*e^5 + 5*(x*e + d)^(3/2)*A*b^4*c^2*d^2*e^5 + 20*sqrt(x*e + d)*B*b^5*c*d^3*e^5 - 7*(x*e + d)^(5/2)*B*b^6*e^6 + 3*(x*e + d)^(5/2)*A*b^5*c*e^6 + 14*(x*e + d)^(3/2)*B*b^6*d*e^6 - 6*(x*e + d)^(3/2)*A*b^5*c*d*e^6 - 7*sqrt(x*e + d)*B*b^6*d^2*e^6 + 3*sqrt(x*e + d)*A*b^5*c*d^2*e^6)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4*c^3)","B",0
1248,1,1047,0,0.341223," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(24 \, B b c d^{4} - 48 \, A c^{2} d^{4} - 28 \, B b^{2} d^{3} e + 84 \, A b c d^{3} e - 35 \, A b^{2} d^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} + \frac{{\left(24 \, B b c^{4} d^{4} - 48 \, A c^{5} d^{4} - 40 \, B b^{2} c^{3} d^{3} e + 108 \, A b c^{4} d^{3} e + 11 \, B b^{3} c^{2} d^{2} e^{2} - 71 \, A b^{2} c^{3} d^{2} e^{2} + 2 \, B b^{4} c d e^{3} + 10 \, A b^{3} c^{2} d e^{3} + 3 \, B b^{5} e^{4} + A b^{4} c e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5} c^{2}} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{4} d^{3} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{5} d^{3} e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{4} d^{4} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{5} d^{4} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{4} d^{5} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{5} d^{5} e - 12 \, \sqrt{x e + d} B b c^{4} d^{6} e + 24 \, \sqrt{x e + d} A c^{5} d^{6} e - 11 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c^{3} d^{2} e^{2} + 36 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{4} d^{2} e^{2} + 51 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c^{3} d^{3} e^{2} - 144 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{4} d^{3} e^{2} - 69 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{3} d^{4} e^{2} + 180 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{4} d^{4} e^{2} + 29 \, \sqrt{x e + d} B b^{2} c^{3} d^{5} e^{2} - 72 \, \sqrt{x e + d} A b c^{4} d^{5} e^{2} - 2 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{3} c^{2} d e^{3} - 10 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{2} c^{3} d e^{3} - 11 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} c^{2} d^{2} e^{3} + 85 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c^{3} d^{2} e^{3} + 32 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c^{2} d^{3} e^{3} - 148 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{3} d^{3} e^{3} - 19 \, \sqrt{x e + d} B b^{3} c^{2} d^{4} e^{3} + 73 \, \sqrt{x e + d} A b^{2} c^{3} d^{4} e^{3} + 5 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} c e^{4} - {\left(x e + d\right)}^{\frac{7}{2}} A b^{3} c^{2} e^{4} - 11 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} c d e^{4} - 13 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} c^{2} d e^{4} + 7 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} c d^{2} e^{4} + 42 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c^{2} d^{2} e^{4} - \sqrt{x e + d} B b^{4} c d^{3} e^{4} - 26 \, \sqrt{x e + d} A b^{3} c^{2} d^{3} e^{4} + 3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} e^{5} + {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} c e^{5} - 6 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d e^{5} - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} c d e^{5} + 3 \, \sqrt{x e + d} B b^{5} d^{2} e^{5} + \sqrt{x e + d} A b^{4} c d^{2} e^{5}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4} c^{2}}"," ",0,"-1/4*(24*B*b*c*d^4 - 48*A*c^2*d^4 - 28*B*b^2*d^3*e + 84*A*b*c*d^3*e - 35*A*b^2*d^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) + 1/4*(24*B*b*c^4*d^4 - 48*A*c^5*d^4 - 40*B*b^2*c^3*d^3*e + 108*A*b*c^4*d^3*e + 11*B*b^3*c^2*d^2*e^2 - 71*A*b^2*c^3*d^2*e^2 + 2*B*b^4*c*d*e^3 + 10*A*b^3*c^2*d*e^3 + 3*B*b^5*e^4 + A*b^4*c*e^4)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5*c^2) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^4*d^3*e - 24*(x*e + d)^(7/2)*A*c^5*d^3*e - 36*(x*e + d)^(5/2)*B*b*c^4*d^4*e + 72*(x*e + d)^(5/2)*A*c^5*d^4*e + 36*(x*e + d)^(3/2)*B*b*c^4*d^5*e - 72*(x*e + d)^(3/2)*A*c^5*d^5*e - 12*sqrt(x*e + d)*B*b*c^4*d^6*e + 24*sqrt(x*e + d)*A*c^5*d^6*e - 11*(x*e + d)^(7/2)*B*b^2*c^3*d^2*e^2 + 36*(x*e + d)^(7/2)*A*b*c^4*d^2*e^2 + 51*(x*e + d)^(5/2)*B*b^2*c^3*d^3*e^2 - 144*(x*e + d)^(5/2)*A*b*c^4*d^3*e^2 - 69*(x*e + d)^(3/2)*B*b^2*c^3*d^4*e^2 + 180*(x*e + d)^(3/2)*A*b*c^4*d^4*e^2 + 29*sqrt(x*e + d)*B*b^2*c^3*d^5*e^2 - 72*sqrt(x*e + d)*A*b*c^4*d^5*e^2 - 2*(x*e + d)^(7/2)*B*b^3*c^2*d*e^3 - 10*(x*e + d)^(7/2)*A*b^2*c^3*d*e^3 - 11*(x*e + d)^(5/2)*B*b^3*c^2*d^2*e^3 + 85*(x*e + d)^(5/2)*A*b^2*c^3*d^2*e^3 + 32*(x*e + d)^(3/2)*B*b^3*c^2*d^3*e^3 - 148*(x*e + d)^(3/2)*A*b^2*c^3*d^3*e^3 - 19*sqrt(x*e + d)*B*b^3*c^2*d^4*e^3 + 73*sqrt(x*e + d)*A*b^2*c^3*d^4*e^3 + 5*(x*e + d)^(7/2)*B*b^4*c*e^4 - (x*e + d)^(7/2)*A*b^3*c^2*e^4 - 11*(x*e + d)^(5/2)*B*b^4*c*d*e^4 - 13*(x*e + d)^(5/2)*A*b^3*c^2*d*e^4 + 7*(x*e + d)^(3/2)*B*b^4*c*d^2*e^4 + 42*(x*e + d)^(3/2)*A*b^3*c^2*d^2*e^4 - sqrt(x*e + d)*B*b^4*c*d^3*e^4 - 26*sqrt(x*e + d)*A*b^3*c^2*d^3*e^4 + 3*(x*e + d)^(5/2)*B*b^5*e^5 + (x*e + d)^(5/2)*A*b^4*c*e^5 - 6*(x*e + d)^(3/2)*B*b^5*d*e^5 - 2*(x*e + d)^(3/2)*A*b^4*c*d*e^5 + 3*sqrt(x*e + d)*B*b^5*d^2*e^5 + sqrt(x*e + d)*A*b^4*c*d^2*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4*c^2)","B",0
1249,1,841,0,0.340055," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(24 \, B b c d^{3} - 48 \, A c^{2} d^{3} - 20 \, B b^{2} d^{2} e + 60 \, A b c d^{2} e - 15 \, A b^{2} d e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} + \frac{{\left(24 \, B b c^{3} d^{3} - 48 \, A c^{4} d^{3} - 32 \, B b^{2} c^{2} d^{2} e + 84 \, A b c^{3} d^{2} e + 7 \, B b^{3} c d e^{2} - 39 \, A b^{2} c^{2} d e^{2} + B b^{4} e^{3} + 3 \, A b^{3} c e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5} c} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{3} d^{2} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{4} d^{2} e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{3} d^{3} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{4} d^{3} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{3} d^{4} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{4} d^{4} e - 12 \, \sqrt{x e + d} B b c^{3} d^{5} e + 24 \, \sqrt{x e + d} A c^{4} d^{5} e - 7 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c^{2} d e^{2} + 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{3} d e^{2} + 39 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c^{2} d^{2} e^{2} - 108 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{3} d^{2} e^{2} - 57 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{2} d^{3} e^{2} + 144 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{3} d^{3} e^{2} + 25 \, \sqrt{x e + d} B b^{2} c^{2} d^{4} e^{2} - 60 \, \sqrt{x e + d} A b c^{3} d^{4} e^{2} - {\left(x e + d\right)}^{\frac{7}{2}} B b^{3} c e^{3} - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{2} c^{2} e^{3} - 8 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} c d e^{3} + 46 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c^{2} d e^{3} + 23 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c d^{2} e^{3} - 91 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{2} d^{2} e^{3} - 14 \, \sqrt{x e + d} B b^{3} c d^{3} e^{3} + 48 \, \sqrt{x e + d} A b^{2} c^{2} d^{3} e^{3} + {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} e^{4} - 5 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} c e^{4} - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d e^{4} + 19 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c d e^{4} + \sqrt{x e + d} B b^{4} d^{2} e^{4} - 12 \, \sqrt{x e + d} A b^{3} c d^{2} e^{4}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4} c}"," ",0,"-1/4*(24*B*b*c*d^3 - 48*A*c^2*d^3 - 20*B*b^2*d^2*e + 60*A*b*c*d^2*e - 15*A*b^2*d*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) + 1/4*(24*B*b*c^3*d^3 - 48*A*c^4*d^3 - 32*B*b^2*c^2*d^2*e + 84*A*b*c^3*d^2*e + 7*B*b^3*c*d*e^2 - 39*A*b^2*c^2*d*e^2 + B*b^4*e^3 + 3*A*b^3*c*e^3)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5*c) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^3*d^2*e - 24*(x*e + d)^(7/2)*A*c^4*d^2*e - 36*(x*e + d)^(5/2)*B*b*c^3*d^3*e + 72*(x*e + d)^(5/2)*A*c^4*d^3*e + 36*(x*e + d)^(3/2)*B*b*c^3*d^4*e - 72*(x*e + d)^(3/2)*A*c^4*d^4*e - 12*sqrt(x*e + d)*B*b*c^3*d^5*e + 24*sqrt(x*e + d)*A*c^4*d^5*e - 7*(x*e + d)^(7/2)*B*b^2*c^2*d*e^2 + 24*(x*e + d)^(7/2)*A*b*c^3*d*e^2 + 39*(x*e + d)^(5/2)*B*b^2*c^2*d^2*e^2 - 108*(x*e + d)^(5/2)*A*b*c^3*d^2*e^2 - 57*(x*e + d)^(3/2)*B*b^2*c^2*d^3*e^2 + 144*(x*e + d)^(3/2)*A*b*c^3*d^3*e^2 + 25*sqrt(x*e + d)*B*b^2*c^2*d^4*e^2 - 60*sqrt(x*e + d)*A*b*c^3*d^4*e^2 - (x*e + d)^(7/2)*B*b^3*c*e^3 - 3*(x*e + d)^(7/2)*A*b^2*c^2*e^3 - 8*(x*e + d)^(5/2)*B*b^3*c*d*e^3 + 46*(x*e + d)^(5/2)*A*b^2*c^2*d*e^3 + 23*(x*e + d)^(3/2)*B*b^3*c*d^2*e^3 - 91*(x*e + d)^(3/2)*A*b^2*c^2*d^2*e^3 - 14*sqrt(x*e + d)*B*b^3*c*d^3*e^3 + 48*sqrt(x*e + d)*A*b^2*c^2*d^3*e^3 + (x*e + d)^(5/2)*B*b^4*e^4 - 5*(x*e + d)^(5/2)*A*b^3*c*e^4 - 2*(x*e + d)^(3/2)*B*b^4*d*e^4 + 19*(x*e + d)^(3/2)*A*b^3*c*d*e^4 + sqrt(x*e + d)*B*b^4*d^2*e^4 - 12*sqrt(x*e + d)*A*b^3*c*d^2*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4*c)","B",0
1250,1,661,0,0.278984," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(8 \, B b c^{2} d^{2} - 16 \, A c^{3} d^{2} - 8 \, B b^{2} c d e + 20 \, A b c^{2} d e + B b^{3} e^{2} - 5 \, A b^{2} c e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5}} - \frac{3 \, {\left(8 \, B b c d^{2} - 16 \, A c^{2} d^{2} - 4 \, B b^{2} d e + 12 \, A b c d e - A b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{2} d e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{3} d e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{2} d^{2} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{3} d^{2} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{2} d^{3} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d^{3} e - 12 \, \sqrt{x e + d} B b c^{2} d^{4} e + 24 \, \sqrt{x e + d} A c^{3} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c e^{2} + 12 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{2} e^{2} + 27 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c d e^{2} - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{2} d e^{2} - 45 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c d^{2} e^{2} + 108 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{2} d^{2} e^{2} + 21 \, \sqrt{x e + d} B b^{2} c d^{3} e^{2} - 48 \, \sqrt{x e + d} A b c^{2} d^{3} e^{2} - 5 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} e^{3} + 19 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c e^{3} + 14 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d e^{3} - 46 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c d e^{3} - 9 \, \sqrt{x e + d} B b^{3} d^{2} e^{3} + 27 \, \sqrt{x e + d} A b^{2} c d^{2} e^{3} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} e^{4} - 3 \, \sqrt{x e + d} A b^{3} d e^{4}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4}}"," ",0,"3/4*(8*B*b*c^2*d^2 - 16*A*c^3*d^2 - 8*B*b^2*c*d*e + 20*A*b*c^2*d*e + B*b^3*e^2 - 5*A*b^2*c*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5) - 3/4*(8*B*b*c*d^2 - 16*A*c^2*d^2 - 4*B*b^2*d*e + 12*A*b*c*d*e - A*b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^2*d*e - 24*(x*e + d)^(7/2)*A*c^3*d*e - 36*(x*e + d)^(5/2)*B*b*c^2*d^2*e + 72*(x*e + d)^(5/2)*A*c^3*d^2*e + 36*(x*e + d)^(3/2)*B*b*c^2*d^3*e - 72*(x*e + d)^(3/2)*A*c^3*d^3*e - 12*sqrt(x*e + d)*B*b*c^2*d^4*e + 24*sqrt(x*e + d)*A*c^3*d^4*e - 3*(x*e + d)^(7/2)*B*b^2*c*e^2 + 12*(x*e + d)^(7/2)*A*b*c^2*e^2 + 27*(x*e + d)^(5/2)*B*b^2*c*d*e^2 - 72*(x*e + d)^(5/2)*A*b*c^2*d*e^2 - 45*(x*e + d)^(3/2)*B*b^2*c*d^2*e^2 + 108*(x*e + d)^(3/2)*A*b*c^2*d^2*e^2 + 21*sqrt(x*e + d)*B*b^2*c*d^3*e^2 - 48*sqrt(x*e + d)*A*b*c^2*d^3*e^2 - 5*(x*e + d)^(5/2)*B*b^3*e^3 + 19*(x*e + d)^(5/2)*A*b^2*c*e^3 + 14*(x*e + d)^(3/2)*B*b^3*d*e^3 - 46*(x*e + d)^(3/2)*A*b^2*c*d*e^3 - 9*sqrt(x*e + d)*B*b^3*d^2*e^3 + 27*sqrt(x*e + d)*A*b^2*c*d^2*e^3 + 5*(x*e + d)^(3/2)*A*b^3*e^4 - 3*sqrt(x*e + d)*A*b^3*d*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4)","B",0
1251,1,841,0,0.286461," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(24 \, B b c^{3} d^{2} - 48 \, A c^{4} d^{2} - 40 \, B b^{2} c^{2} d e + 84 \, A b c^{3} d e + 15 \, B b^{3} c e^{2} - 35 \, A b^{2} c^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c d - b^{6} e\right)} \sqrt{-c^{2} d + b c e}} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{3} d^{2} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{4} d^{2} e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{3} d^{3} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{4} d^{3} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{3} d^{4} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{4} d^{4} e - 12 \, \sqrt{x e + d} B b c^{3} d^{5} e + 24 \, \sqrt{x e + d} A c^{4} d^{5} e - 11 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c^{2} d e^{2} + 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{3} d e^{2} + 51 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c^{2} d^{2} e^{2} - 108 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{3} d^{2} e^{2} - 69 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{2} d^{3} e^{2} + 144 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{3} d^{3} e^{2} + 29 \, \sqrt{x e + d} B b^{2} c^{2} d^{4} e^{2} - 60 \, \sqrt{x e + d} A b c^{3} d^{4} e^{2} - {\left(x e + d\right)}^{\frac{7}{2}} A b^{2} c^{2} e^{3} - 17 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} c d e^{3} + 40 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c^{2} d e^{3} + 38 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c d^{2} e^{3} - 85 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{2} d^{2} e^{3} - 21 \, \sqrt{x e + d} B b^{3} c d^{3} e^{3} + 46 \, \sqrt{x e + d} A b^{2} c^{2} d^{3} e^{3} - 2 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} c e^{4} - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d e^{4} + 13 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c d e^{4} + 4 \, \sqrt{x e + d} B b^{4} d^{2} e^{4} - 9 \, \sqrt{x e + d} A b^{3} c d^{2} e^{4} - {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} e^{5} - \sqrt{x e + d} A b^{4} d e^{5}}{4 \, {\left(b^{4} c d^{2} - b^{5} d e\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} - \frac{{\left(24 \, B b c d^{2} - 48 \, A c^{2} d^{2} - 4 \, B b^{2} d e + 12 \, A b c d e + A b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d}"," ",0,"1/4*(24*B*b*c^3*d^2 - 48*A*c^4*d^2 - 40*B*b^2*c^2*d*e + 84*A*b*c^3*d*e + 15*B*b^3*c*e^2 - 35*A*b^2*c^2*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c*d - b^6*e)*sqrt(-c^2*d + b*c*e)) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^3*d^2*e - 24*(x*e + d)^(7/2)*A*c^4*d^2*e - 36*(x*e + d)^(5/2)*B*b*c^3*d^3*e + 72*(x*e + d)^(5/2)*A*c^4*d^3*e + 36*(x*e + d)^(3/2)*B*b*c^3*d^4*e - 72*(x*e + d)^(3/2)*A*c^4*d^4*e - 12*sqrt(x*e + d)*B*b*c^3*d^5*e + 24*sqrt(x*e + d)*A*c^4*d^5*e - 11*(x*e + d)^(7/2)*B*b^2*c^2*d*e^2 + 24*(x*e + d)^(7/2)*A*b*c^3*d*e^2 + 51*(x*e + d)^(5/2)*B*b^2*c^2*d^2*e^2 - 108*(x*e + d)^(5/2)*A*b*c^3*d^2*e^2 - 69*(x*e + d)^(3/2)*B*b^2*c^2*d^3*e^2 + 144*(x*e + d)^(3/2)*A*b*c^3*d^3*e^2 + 29*sqrt(x*e + d)*B*b^2*c^2*d^4*e^2 - 60*sqrt(x*e + d)*A*b*c^3*d^4*e^2 - (x*e + d)^(7/2)*A*b^2*c^2*e^3 - 17*(x*e + d)^(5/2)*B*b^3*c*d*e^3 + 40*(x*e + d)^(5/2)*A*b^2*c^2*d*e^3 + 38*(x*e + d)^(3/2)*B*b^3*c*d^2*e^3 - 85*(x*e + d)^(3/2)*A*b^2*c^2*d^2*e^3 - 21*sqrt(x*e + d)*B*b^3*c*d^3*e^3 + 46*sqrt(x*e + d)*A*b^2*c^2*d^3*e^3 - 2*(x*e + d)^(5/2)*A*b^3*c*e^4 - 4*(x*e + d)^(3/2)*B*b^4*d*e^4 + 13*(x*e + d)^(3/2)*A*b^3*c*d*e^4 + 4*sqrt(x*e + d)*B*b^4*d^2*e^4 - 9*sqrt(x*e + d)*A*b^3*c*d^2*e^4 - (x*e + d)^(3/2)*A*b^4*e^5 - sqrt(x*e + d)*A*b^4*d*e^5)/((b^4*c*d^2 - b^5*d*e)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) - 1/4*(24*B*b*c*d^2 - 48*A*c^2*d^2 - 4*B*b^2*d*e + 12*A*b*c*d*e + A*b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d)","B",0
1252,1,1046,0,0.308879," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(24 \, B b c^{4} d^{2} - 48 \, A c^{5} d^{2} - 56 \, B b^{2} c^{3} d e + 108 \, A b c^{4} d e + 35 \, B b^{3} c^{2} e^{2} - 63 \, A b^{2} c^{3} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c^{2} d^{2} - 2 \, b^{6} c d e + b^{7} e^{2}\right)} \sqrt{-c^{2} d + b c e}} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{4} d^{3} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{5} d^{3} e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{4} d^{4} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{5} d^{4} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{4} d^{5} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{5} d^{5} e - 12 \, \sqrt{x e + d} B b c^{4} d^{6} e + 24 \, \sqrt{x e + d} A c^{5} d^{6} e - 19 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c^{3} d^{2} e^{2} + 36 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{4} d^{2} e^{2} + 75 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c^{3} d^{3} e^{2} - 144 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{4} d^{3} e^{2} - 93 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{3} d^{4} e^{2} + 180 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{4} d^{4} e^{2} + 37 \, \sqrt{x e + d} B b^{2} c^{3} d^{5} e^{2} - 72 \, \sqrt{x e + d} A b c^{4} d^{5} e^{2} + 4 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{3} c^{2} d e^{3} - 6 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{2} c^{3} d e^{3} - 41 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} c^{2} d^{2} e^{3} + 73 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c^{3} d^{2} e^{3} + 74 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c^{2} d^{3} e^{3} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{3} d^{3} e^{3} - 37 \, \sqrt{x e + d} B b^{3} c^{2} d^{4} e^{3} + 69 \, \sqrt{x e + d} A b^{2} c^{3} d^{4} e^{3} - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{3} c^{2} e^{4} + 8 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} c d e^{4} - {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} c^{2} d e^{4} - 24 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} c d^{2} e^{4} + 24 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c^{2} d^{2} e^{4} + 16 \, \sqrt{x e + d} B b^{4} c d^{3} e^{4} - 18 \, \sqrt{x e + d} A b^{3} c^{2} d^{3} e^{4} - 6 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} c e^{5} + 4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d e^{5} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} c d e^{5} - 4 \, \sqrt{x e + d} B b^{5} d^{2} e^{5} - 8 \, \sqrt{x e + d} A b^{4} c d^{2} e^{5} - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} e^{6} + 5 \, \sqrt{x e + d} A b^{5} d e^{6}}{4 \, {\left(b^{4} c^{2} d^{4} - 2 \, b^{5} c d^{3} e + b^{6} d^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} - \frac{{\left(24 \, B b c d^{2} - 48 \, A c^{2} d^{2} + 4 \, B b^{2} d e - 12 \, A b c d e - 3 \, A b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d^{2}}"," ",0,"1/4*(24*B*b*c^4*d^2 - 48*A*c^5*d^2 - 56*B*b^2*c^3*d*e + 108*A*b*c^4*d*e + 35*B*b^3*c^2*e^2 - 63*A*b^2*c^3*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c^2*d^2 - 2*b^6*c*d*e + b^7*e^2)*sqrt(-c^2*d + b*c*e)) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^4*d^3*e - 24*(x*e + d)^(7/2)*A*c^5*d^3*e - 36*(x*e + d)^(5/2)*B*b*c^4*d^4*e + 72*(x*e + d)^(5/2)*A*c^5*d^4*e + 36*(x*e + d)^(3/2)*B*b*c^4*d^5*e - 72*(x*e + d)^(3/2)*A*c^5*d^5*e - 12*sqrt(x*e + d)*B*b*c^4*d^6*e + 24*sqrt(x*e + d)*A*c^5*d^6*e - 19*(x*e + d)^(7/2)*B*b^2*c^3*d^2*e^2 + 36*(x*e + d)^(7/2)*A*b*c^4*d^2*e^2 + 75*(x*e + d)^(5/2)*B*b^2*c^3*d^3*e^2 - 144*(x*e + d)^(5/2)*A*b*c^4*d^3*e^2 - 93*(x*e + d)^(3/2)*B*b^2*c^3*d^4*e^2 + 180*(x*e + d)^(3/2)*A*b*c^4*d^4*e^2 + 37*sqrt(x*e + d)*B*b^2*c^3*d^5*e^2 - 72*sqrt(x*e + d)*A*b*c^4*d^5*e^2 + 4*(x*e + d)^(7/2)*B*b^3*c^2*d*e^3 - 6*(x*e + d)^(7/2)*A*b^2*c^3*d*e^3 - 41*(x*e + d)^(5/2)*B*b^3*c^2*d^2*e^3 + 73*(x*e + d)^(5/2)*A*b^2*c^3*d^2*e^3 + 74*(x*e + d)^(3/2)*B*b^3*c^2*d^3*e^3 - 136*(x*e + d)^(3/2)*A*b^2*c^3*d^3*e^3 - 37*sqrt(x*e + d)*B*b^3*c^2*d^4*e^3 + 69*sqrt(x*e + d)*A*b^2*c^3*d^4*e^3 - 3*(x*e + d)^(7/2)*A*b^3*c^2*e^4 + 8*(x*e + d)^(5/2)*B*b^4*c*d*e^4 - (x*e + d)^(5/2)*A*b^3*c^2*d*e^4 - 24*(x*e + d)^(3/2)*B*b^4*c*d^2*e^4 + 24*(x*e + d)^(3/2)*A*b^3*c^2*d^2*e^4 + 16*sqrt(x*e + d)*B*b^4*c*d^3*e^4 - 18*sqrt(x*e + d)*A*b^3*c^2*d^3*e^4 - 6*(x*e + d)^(5/2)*A*b^4*c*e^5 + 4*(x*e + d)^(3/2)*B*b^5*d*e^5 + 10*(x*e + d)^(3/2)*A*b^4*c*d*e^5 - 4*sqrt(x*e + d)*B*b^5*d^2*e^5 - 8*sqrt(x*e + d)*A*b^4*c*d^2*e^5 - 3*(x*e + d)^(3/2)*A*b^5*e^6 + 5*sqrt(x*e + d)*A*b^5*d*e^6)/((b^4*c^2*d^4 - 2*b^5*c*d^3*e + b^6*d^2*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) - 1/4*(24*B*b*c*d^2 - 48*A*c^2*d^2 + 4*B*b^2*d*e - 12*A*b*c*d*e - 3*A*b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d^2)","B",0
1253,1,1313,0,0.410666," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(8 \, B b c^{5} d^{2} - 16 \, A c^{6} d^{2} - 24 \, B b^{2} c^{4} d e + 44 \, A b c^{5} d e + 21 \, B b^{3} c^{3} e^{2} - 33 \, A b^{2} c^{4} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c^{3} d^{3} - 3 \, b^{6} c^{2} d^{2} e + 3 \, b^{7} c d e^{2} - b^{8} e^{3}\right)} \sqrt{-c^{2} d + b c e}} + \frac{2 \, {\left(B d e^{4} - A e^{5}\right)}}{{\left(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}\right)} \sqrt{x e + d}} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{5} d^{4} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{6} d^{4} e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{5} d^{5} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{6} d^{5} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{5} d^{6} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{6} d^{6} e - 12 \, \sqrt{x e + d} B b c^{5} d^{7} e + 24 \, \sqrt{x e + d} A c^{6} d^{7} e - 27 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c^{4} d^{3} e^{2} + 48 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{5} d^{3} e^{2} + 99 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c^{4} d^{4} e^{2} - 180 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{5} d^{4} e^{2} - 117 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{4} d^{5} e^{2} + 216 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{5} d^{5} e^{2} + 45 \, \sqrt{x e + d} B b^{2} c^{4} d^{6} e^{2} - 84 \, \sqrt{x e + d} A b c^{5} d^{6} e^{2} + 12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{3} c^{3} d^{2} e^{3} - 15 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{2} c^{4} d^{2} e^{3} - 77 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} c^{3} d^{3} e^{3} + 118 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c^{4} d^{3} e^{3} + 122 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c^{3} d^{4} e^{3} - 199 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{4} d^{4} e^{3} - 57 \, \sqrt{x e + d} B b^{3} c^{3} d^{5} e^{3} + 96 \, \sqrt{x e + d} A b^{2} c^{4} d^{5} e^{3} - 4 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} c^{2} d e^{4} - 9 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{3} c^{3} d e^{4} + 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} c^{2} d^{2} e^{4} + 3 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} c^{3} d^{2} e^{4} - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} c^{2} d^{3} e^{4} + 38 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c^{3} d^{3} e^{4} + 40 \, \sqrt{x e + d} B b^{4} c^{2} d^{4} e^{4} - 30 \, \sqrt{x e + d} A b^{3} c^{3} d^{4} e^{4} + 7 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} c^{2} e^{5} - 8 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} c d e^{5} - 41 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} c^{2} d e^{5} + 28 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} c d^{2} e^{5} + 58 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} c^{2} d^{2} e^{5} - 20 \, \sqrt{x e + d} B b^{5} c d^{3} e^{5} - 30 \, \sqrt{x e + d} A b^{4} c^{2} d^{3} e^{5} + 14 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} c e^{6} - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d e^{6} - 41 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} c d e^{6} + 4 \, \sqrt{x e + d} B b^{6} d^{2} e^{6} + 33 \, \sqrt{x e + d} A b^{5} c d^{2} e^{6} + 7 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} e^{7} - 9 \, \sqrt{x e + d} A b^{6} d e^{7}}{4 \, {\left(b^{4} c^{3} d^{6} - 3 \, b^{5} c^{2} d^{5} e + 3 \, b^{6} c d^{4} e^{2} - b^{7} d^{3} e^{3}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} - \frac{3 \, {\left(8 \, B b c d^{2} - 16 \, A c^{2} d^{2} + 4 \, B b^{2} d e - 12 \, A b c d e - 5 \, A b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d^{3}}"," ",0,"3/4*(8*B*b*c^5*d^2 - 16*A*c^6*d^2 - 24*B*b^2*c^4*d*e + 44*A*b*c^5*d*e + 21*B*b^3*c^3*e^2 - 33*A*b^2*c^4*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c^3*d^3 - 3*b^6*c^2*d^2*e + 3*b^7*c*d*e^2 - b^8*e^3)*sqrt(-c^2*d + b*c*e)) + 2*(B*d*e^4 - A*e^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)*sqrt(x*e + d)) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^5*d^4*e - 24*(x*e + d)^(7/2)*A*c^6*d^4*e - 36*(x*e + d)^(5/2)*B*b*c^5*d^5*e + 72*(x*e + d)^(5/2)*A*c^6*d^5*e + 36*(x*e + d)^(3/2)*B*b*c^5*d^6*e - 72*(x*e + d)^(3/2)*A*c^6*d^6*e - 12*sqrt(x*e + d)*B*b*c^5*d^7*e + 24*sqrt(x*e + d)*A*c^6*d^7*e - 27*(x*e + d)^(7/2)*B*b^2*c^4*d^3*e^2 + 48*(x*e + d)^(7/2)*A*b*c^5*d^3*e^2 + 99*(x*e + d)^(5/2)*B*b^2*c^4*d^4*e^2 - 180*(x*e + d)^(5/2)*A*b*c^5*d^4*e^2 - 117*(x*e + d)^(3/2)*B*b^2*c^4*d^5*e^2 + 216*(x*e + d)^(3/2)*A*b*c^5*d^5*e^2 + 45*sqrt(x*e + d)*B*b^2*c^4*d^6*e^2 - 84*sqrt(x*e + d)*A*b*c^5*d^6*e^2 + 12*(x*e + d)^(7/2)*B*b^3*c^3*d^2*e^3 - 15*(x*e + d)^(7/2)*A*b^2*c^4*d^2*e^3 - 77*(x*e + d)^(5/2)*B*b^3*c^3*d^3*e^3 + 118*(x*e + d)^(5/2)*A*b^2*c^4*d^3*e^3 + 122*(x*e + d)^(3/2)*B*b^3*c^3*d^4*e^3 - 199*(x*e + d)^(3/2)*A*b^2*c^4*d^4*e^3 - 57*sqrt(x*e + d)*B*b^3*c^3*d^5*e^3 + 96*sqrt(x*e + d)*A*b^2*c^4*d^5*e^3 - 4*(x*e + d)^(7/2)*B*b^4*c^2*d*e^4 - 9*(x*e + d)^(7/2)*A*b^3*c^3*d*e^4 + 36*(x*e + d)^(5/2)*B*b^4*c^2*d^2*e^4 + 3*(x*e + d)^(5/2)*A*b^3*c^3*d^2*e^4 - 72*(x*e + d)^(3/2)*B*b^4*c^2*d^3*e^4 + 38*(x*e + d)^(3/2)*A*b^3*c^3*d^3*e^4 + 40*sqrt(x*e + d)*B*b^4*c^2*d^4*e^4 - 30*sqrt(x*e + d)*A*b^3*c^3*d^4*e^4 + 7*(x*e + d)^(7/2)*A*b^4*c^2*e^5 - 8*(x*e + d)^(5/2)*B*b^5*c*d*e^5 - 41*(x*e + d)^(5/2)*A*b^4*c^2*d*e^5 + 28*(x*e + d)^(3/2)*B*b^5*c*d^2*e^5 + 58*(x*e + d)^(3/2)*A*b^4*c^2*d^2*e^5 - 20*sqrt(x*e + d)*B*b^5*c*d^3*e^5 - 30*sqrt(x*e + d)*A*b^4*c^2*d^3*e^5 + 14*(x*e + d)^(5/2)*A*b^5*c*e^6 - 4*(x*e + d)^(3/2)*B*b^6*d*e^6 - 41*(x*e + d)^(3/2)*A*b^5*c*d*e^6 + 4*sqrt(x*e + d)*B*b^6*d^2*e^6 + 33*sqrt(x*e + d)*A*b^5*c*d^2*e^6 + 7*(x*e + d)^(3/2)*A*b^6*e^7 - 9*sqrt(x*e + d)*A*b^6*d*e^7)/((b^4*c^3*d^6 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 - b^7*d^3*e^3)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) - 3/4*(8*B*b*c*d^2 - 16*A*c^2*d^2 + 4*B*b^2*d*e - 12*A*b*c*d*e - 5*A*b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d^3)","B",0
1254,1,1600,0,1.094695," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(24 \, B b c^{6} d^{2} - 48 \, A c^{7} d^{2} - 88 \, B b^{2} c^{5} d e + 156 \, A b c^{6} d e + 99 \, B b^{3} c^{4} e^{2} - 143 \, A b^{2} c^{5} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c^{4} d^{4} - 4 \, b^{6} c^{3} d^{3} e + 6 \, b^{7} c^{2} d^{2} e^{2} - 4 \, b^{8} c d e^{3} + b^{9} e^{4}\right)} \sqrt{-c^{2} d + b c e}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)} B c d^{2} e^{4} + B c d^{3} e^{4} - 6 \, {\left(x e + d\right)} B b d e^{5} - 18 \, {\left(x e + d\right)} A c d e^{5} - B b d^{2} e^{5} - A c d^{2} e^{5} + 9 \, {\left(x e + d\right)} A b e^{6} + A b d e^{6}\right)}}{3 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} {\left(x e + d\right)}^{\frac{3}{2}}} - \frac{12 \, {\left(x e + d\right)}^{\frac{7}{2}} B b c^{6} d^{5} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{7} d^{5} e - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} B b c^{6} d^{6} e + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{7} d^{6} e + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} B b c^{6} d^{7} e - 72 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{7} d^{7} e - 12 \, \sqrt{x e + d} B b c^{6} d^{8} e + 24 \, \sqrt{x e + d} A c^{7} d^{8} e - 35 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{2} c^{5} d^{4} e^{2} + 60 \, {\left(x e + d\right)}^{\frac{7}{2}} A b c^{6} d^{4} e^{2} + 123 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} c^{5} d^{5} e^{2} - 216 \, {\left(x e + d\right)}^{\frac{5}{2}} A b c^{6} d^{5} e^{2} - 141 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} c^{5} d^{6} e^{2} + 252 \, {\left(x e + d\right)}^{\frac{3}{2}} A b c^{6} d^{6} e^{2} + 53 \, \sqrt{x e + d} B b^{2} c^{5} d^{7} e^{2} - 96 \, \sqrt{x e + d} A b c^{6} d^{7} e^{2} + 24 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{3} c^{4} d^{3} e^{3} - 28 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{2} c^{5} d^{3} e^{3} - 125 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} c^{4} d^{4} e^{3} + 175 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{2} c^{5} d^{4} e^{3} + 182 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} c^{4} d^{5} e^{3} - 274 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} c^{5} d^{5} e^{3} - 81 \, \sqrt{x e + d} B b^{3} c^{4} d^{6} e^{3} + 127 \, \sqrt{x e + d} A b^{2} c^{5} d^{6} e^{3} - 16 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} c^{3} d^{2} e^{4} - 18 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{3} c^{4} d^{2} e^{4} + 96 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} c^{3} d^{3} e^{4} + 10 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} c^{4} d^{3} e^{4} - 160 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} c^{3} d^{4} e^{4} + 55 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} c^{4} d^{4} e^{4} + 80 \, \sqrt{x e + d} B b^{4} c^{3} d^{5} e^{4} - 45 \, \sqrt{x e + d} A b^{3} c^{4} d^{5} e^{4} + 4 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} c^{2} d e^{5} + 32 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} c^{3} d e^{5} - 44 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} c^{2} d^{2} e^{5} - 140 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} c^{3} d^{2} e^{5} + 100 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} c^{2} d^{3} e^{5} + 180 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} c^{3} d^{3} e^{5} - 60 \, \sqrt{x e + d} B b^{5} c^{2} d^{4} e^{5} - 80 \, \sqrt{x e + d} A b^{4} c^{3} d^{4} e^{5} - 11 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} c^{2} e^{6} + 8 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} c d e^{6} + 99 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} c^{2} d e^{6} - 32 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} c d^{2} e^{6} - 199 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} c^{2} d^{2} e^{6} + 24 \, \sqrt{x e + d} B b^{6} c d^{3} e^{6} + 123 \, \sqrt{x e + d} A b^{5} c^{2} d^{3} e^{6} - 22 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} c e^{7} + 4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{7} d e^{7} + 80 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} c d e^{7} - 4 \, \sqrt{x e + d} B b^{7} d^{2} e^{7} - 66 \, \sqrt{x e + d} A b^{6} c d^{2} e^{7} - 11 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{7} e^{8} + 13 \, \sqrt{x e + d} A b^{7} d e^{8}}{4 \, {\left(b^{4} c^{4} d^{8} - 4 \, b^{5} c^{3} d^{7} e + 6 \, b^{6} c^{2} d^{6} e^{2} - 4 \, b^{7} c d^{5} e^{3} + b^{8} d^{4} e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} - \frac{{\left(24 \, B b c d^{2} - 48 \, A c^{2} d^{2} + 20 \, B b^{2} d e - 60 \, A b c d e - 35 \, A b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d^{4}}"," ",0,"1/4*(24*B*b*c^6*d^2 - 48*A*c^7*d^2 - 88*B*b^2*c^5*d*e + 156*A*b*c^6*d*e + 99*B*b^3*c^4*e^2 - 143*A*b^2*c^5*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c^4*d^4 - 4*b^6*c^3*d^3*e + 6*b^7*c^2*d^2*e^2 - 4*b^8*c*d*e^3 + b^9*e^4)*sqrt(-c^2*d + b*c*e)) + 2/3*(15*(x*e + d)*B*c*d^2*e^4 + B*c*d^3*e^4 - 6*(x*e + d)*B*b*d*e^5 - 18*(x*e + d)*A*c*d*e^5 - B*b*d^2*e^5 - A*c*d^2*e^5 + 9*(x*e + d)*A*b*e^6 + A*b*d*e^6)/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*(x*e + d)^(3/2)) - 1/4*(12*(x*e + d)^(7/2)*B*b*c^6*d^5*e - 24*(x*e + d)^(7/2)*A*c^7*d^5*e - 36*(x*e + d)^(5/2)*B*b*c^6*d^6*e + 72*(x*e + d)^(5/2)*A*c^7*d^6*e + 36*(x*e + d)^(3/2)*B*b*c^6*d^7*e - 72*(x*e + d)^(3/2)*A*c^7*d^7*e - 12*sqrt(x*e + d)*B*b*c^6*d^8*e + 24*sqrt(x*e + d)*A*c^7*d^8*e - 35*(x*e + d)^(7/2)*B*b^2*c^5*d^4*e^2 + 60*(x*e + d)^(7/2)*A*b*c^6*d^4*e^2 + 123*(x*e + d)^(5/2)*B*b^2*c^5*d^5*e^2 - 216*(x*e + d)^(5/2)*A*b*c^6*d^5*e^2 - 141*(x*e + d)^(3/2)*B*b^2*c^5*d^6*e^2 + 252*(x*e + d)^(3/2)*A*b*c^6*d^6*e^2 + 53*sqrt(x*e + d)*B*b^2*c^5*d^7*e^2 - 96*sqrt(x*e + d)*A*b*c^6*d^7*e^2 + 24*(x*e + d)^(7/2)*B*b^3*c^4*d^3*e^3 - 28*(x*e + d)^(7/2)*A*b^2*c^5*d^3*e^3 - 125*(x*e + d)^(5/2)*B*b^3*c^4*d^4*e^3 + 175*(x*e + d)^(5/2)*A*b^2*c^5*d^4*e^3 + 182*(x*e + d)^(3/2)*B*b^3*c^4*d^5*e^3 - 274*(x*e + d)^(3/2)*A*b^2*c^5*d^5*e^3 - 81*sqrt(x*e + d)*B*b^3*c^4*d^6*e^3 + 127*sqrt(x*e + d)*A*b^2*c^5*d^6*e^3 - 16*(x*e + d)^(7/2)*B*b^4*c^3*d^2*e^4 - 18*(x*e + d)^(7/2)*A*b^3*c^4*d^2*e^4 + 96*(x*e + d)^(5/2)*B*b^4*c^3*d^3*e^4 + 10*(x*e + d)^(5/2)*A*b^3*c^4*d^3*e^4 - 160*(x*e + d)^(3/2)*B*b^4*c^3*d^4*e^4 + 55*(x*e + d)^(3/2)*A*b^3*c^4*d^4*e^4 + 80*sqrt(x*e + d)*B*b^4*c^3*d^5*e^4 - 45*sqrt(x*e + d)*A*b^3*c^4*d^5*e^4 + 4*(x*e + d)^(7/2)*B*b^5*c^2*d*e^5 + 32*(x*e + d)^(7/2)*A*b^4*c^3*d*e^5 - 44*(x*e + d)^(5/2)*B*b^5*c^2*d^2*e^5 - 140*(x*e + d)^(5/2)*A*b^4*c^3*d^2*e^5 + 100*(x*e + d)^(3/2)*B*b^5*c^2*d^3*e^5 + 180*(x*e + d)^(3/2)*A*b^4*c^3*d^3*e^5 - 60*sqrt(x*e + d)*B*b^5*c^2*d^4*e^5 - 80*sqrt(x*e + d)*A*b^4*c^3*d^4*e^5 - 11*(x*e + d)^(7/2)*A*b^5*c^2*e^6 + 8*(x*e + d)^(5/2)*B*b^6*c*d*e^6 + 99*(x*e + d)^(5/2)*A*b^5*c^2*d*e^6 - 32*(x*e + d)^(3/2)*B*b^6*c*d^2*e^6 - 199*(x*e + d)^(3/2)*A*b^5*c^2*d^2*e^6 + 24*sqrt(x*e + d)*B*b^6*c*d^3*e^6 + 123*sqrt(x*e + d)*A*b^5*c^2*d^3*e^6 - 22*(x*e + d)^(5/2)*A*b^6*c*e^7 + 4*(x*e + d)^(3/2)*B*b^7*d*e^7 + 80*(x*e + d)^(3/2)*A*b^6*c*d*e^7 - 4*sqrt(x*e + d)*B*b^7*d^2*e^7 - 66*sqrt(x*e + d)*A*b^6*c*d^2*e^7 - 11*(x*e + d)^(3/2)*A*b^7*e^8 + 13*sqrt(x*e + d)*A*b^7*d*e^8)/((b^4*c^4*d^8 - 4*b^5*c^3*d^7*e + 6*b^6*c^2*d^6*e^2 - 4*b^7*c*d^5*e^3 + b^8*d^4*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) - 1/4*(24*B*b*c*d^2 - 48*A*c^2*d^2 + 20*B*b^2*d*e - 60*A*b*c*d*e - 35*A*b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d^4)","B",0
1255,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d), x)","F",0
1256,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*(B*x + A)/sqrt(e*x + d), x)","F",0
1257,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*(B*x + A)/(e*x + d)^(3/2), x)","F",0
1258,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]Evaluation time: 1.83Unable to transpose Error: Bad Argument Value","F(-2)",0
1259,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*(B*x + A)/(e*x + d)^(7/2), x)","F",0
1260,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*(B*x + A)/sqrt(e*x + d), x)","F",0
1261,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*(B*x + A)/(e*x + d)^(3/2), x)","F",0
1262,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*(B*x + A)/(e*x + d)^(5/2), x)","F",0
1263,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*(B*x + A)/(e*x + d)^(7/2), x)","F",0
1264,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{5}{2}}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(5/2)/sqrt(c*x^2 + b*x), x)","F",0
1265,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(3/2)/sqrt(c*x^2 + b*x), x)","F",0
1266,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
1267,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x)*sqrt(e*x + d)), x)","F",0
1268,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x)*(e*x + d)^(3/2)), x)","F",0
1269,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x)*(e*x + d)^(5/2)), x)","F",0
1270,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x)*(e*x + d)^(7/2)), x)","F",0
1271,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(7/2)/(c*x^2 + b*x)^(3/2), x)","F",0
1272,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(5/2)/(c*x^2 + b*x)^(3/2), x)","F",0
1273,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(3/2)/(c*x^2 + b*x)^(3/2), x)","F",0
1274,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x + d}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x + d)/(c*x^2 + b*x)^(3/2), x)","F",0
1275,0,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(3/2)*sqrt(e*x + d)), x)","F",0
1276,-2,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 1.38Unable to transpose Error: Bad Argument Value","F(-2)",0
1277,-2,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 4.34Unable to transpose Error: Bad Argument Value","F(-2)",0
1278,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(7/2)/(c*x^2 + b*x)^(5/2), x)","F",0
1279,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(5/2)/(c*x^2 + b*x)^(5/2), x)","F",0
1280,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(3/2)/(c*x^2 + b*x)^(5/2), x)","F",0
1281,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x + d}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x + d)/(c*x^2 + b*x)^(5/2), x)","F",0
1282,0,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x)^(5/2)*sqrt(e*x + d)), x)","F",0
1283,-2,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 3.62Unable to transpose Error: Bad Argument Value","F(-2)",0
1284,1,256,0,0.155943," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{9} \, B c x^{9} e^{5} + \frac{5}{8} \, B c d x^{8} e^{4} + \frac{10}{7} \, B c d^{2} x^{7} e^{3} + \frac{5}{3} \, B c d^{3} x^{6} e^{2} + B c d^{4} x^{5} e + \frac{1}{4} \, B c d^{5} x^{4} + \frac{1}{8} \, A c x^{8} e^{5} + \frac{5}{7} \, A c d x^{7} e^{4} + \frac{5}{3} \, A c d^{2} x^{6} e^{3} + 2 \, A c d^{3} x^{5} e^{2} + \frac{5}{4} \, A c d^{4} x^{4} e + \frac{1}{3} \, A c d^{5} x^{3} + \frac{1}{7} \, B a x^{7} e^{5} + \frac{5}{6} \, B a d x^{6} e^{4} + 2 \, B a d^{2} x^{5} e^{3} + \frac{5}{2} \, B a d^{3} x^{4} e^{2} + \frac{5}{3} \, B a d^{4} x^{3} e + \frac{1}{2} \, B a d^{5} x^{2} + \frac{1}{6} \, A a x^{6} e^{5} + A a d x^{5} e^{4} + \frac{5}{2} \, A a d^{2} x^{4} e^{3} + \frac{10}{3} \, A a d^{3} x^{3} e^{2} + \frac{5}{2} \, A a d^{4} x^{2} e + A a d^{5} x"," ",0,"1/9*B*c*x^9*e^5 + 5/8*B*c*d*x^8*e^4 + 10/7*B*c*d^2*x^7*e^3 + 5/3*B*c*d^3*x^6*e^2 + B*c*d^4*x^5*e + 1/4*B*c*d^5*x^4 + 1/8*A*c*x^8*e^5 + 5/7*A*c*d*x^7*e^4 + 5/3*A*c*d^2*x^6*e^3 + 2*A*c*d^3*x^5*e^2 + 5/4*A*c*d^4*x^4*e + 1/3*A*c*d^5*x^3 + 1/7*B*a*x^7*e^5 + 5/6*B*a*d*x^6*e^4 + 2*B*a*d^2*x^5*e^3 + 5/2*B*a*d^3*x^4*e^2 + 5/3*B*a*d^4*x^3*e + 1/2*B*a*d^5*x^2 + 1/6*A*a*x^6*e^5 + A*a*d*x^5*e^4 + 5/2*A*a*d^2*x^4*e^3 + 10/3*A*a*d^3*x^3*e^2 + 5/2*A*a*d^4*x^2*e + A*a*d^5*x","B",0
1285,1,207,0,0.154997," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{8} \, B c x^{8} e^{4} + \frac{4}{7} \, B c d x^{7} e^{3} + B c d^{2} x^{6} e^{2} + \frac{4}{5} \, B c d^{3} x^{5} e + \frac{1}{4} \, B c d^{4} x^{4} + \frac{1}{7} \, A c x^{7} e^{4} + \frac{2}{3} \, A c d x^{6} e^{3} + \frac{6}{5} \, A c d^{2} x^{5} e^{2} + A c d^{3} x^{4} e + \frac{1}{3} \, A c d^{4} x^{3} + \frac{1}{6} \, B a x^{6} e^{4} + \frac{4}{5} \, B a d x^{5} e^{3} + \frac{3}{2} \, B a d^{2} x^{4} e^{2} + \frac{4}{3} \, B a d^{3} x^{3} e + \frac{1}{2} \, B a d^{4} x^{2} + \frac{1}{5} \, A a x^{5} e^{4} + A a d x^{4} e^{3} + 2 \, A a d^{2} x^{3} e^{2} + 2 \, A a d^{3} x^{2} e + A a d^{4} x"," ",0,"1/8*B*c*x^8*e^4 + 4/7*B*c*d*x^7*e^3 + B*c*d^2*x^6*e^2 + 4/5*B*c*d^3*x^5*e + 1/4*B*c*d^4*x^4 + 1/7*A*c*x^7*e^4 + 2/3*A*c*d*x^6*e^3 + 6/5*A*c*d^2*x^5*e^2 + A*c*d^3*x^4*e + 1/3*A*c*d^4*x^3 + 1/6*B*a*x^6*e^4 + 4/5*B*a*d*x^5*e^3 + 3/2*B*a*d^2*x^4*e^2 + 4/3*B*a*d^3*x^3*e + 1/2*B*a*d^4*x^2 + 1/5*A*a*x^5*e^4 + A*a*d*x^4*e^3 + 2*A*a*d^2*x^3*e^2 + 2*A*a*d^3*x^2*e + A*a*d^4*x","B",0
1286,1,160,0,0.149398," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{7} \, B c x^{7} e^{3} + \frac{1}{2} \, B c d x^{6} e^{2} + \frac{3}{5} \, B c d^{2} x^{5} e + \frac{1}{4} \, B c d^{3} x^{4} + \frac{1}{6} \, A c x^{6} e^{3} + \frac{3}{5} \, A c d x^{5} e^{2} + \frac{3}{4} \, A c d^{2} x^{4} e + \frac{1}{3} \, A c d^{3} x^{3} + \frac{1}{5} \, B a x^{5} e^{3} + \frac{3}{4} \, B a d x^{4} e^{2} + B a d^{2} x^{3} e + \frac{1}{2} \, B a d^{3} x^{2} + \frac{1}{4} \, A a x^{4} e^{3} + A a d x^{3} e^{2} + \frac{3}{2} \, A a d^{2} x^{2} e + A a d^{3} x"," ",0,"1/7*B*c*x^7*e^3 + 1/2*B*c*d*x^6*e^2 + 3/5*B*c*d^2*x^5*e + 1/4*B*c*d^3*x^4 + 1/6*A*c*x^6*e^3 + 3/5*A*c*d*x^5*e^2 + 3/4*A*c*d^2*x^4*e + 1/3*A*c*d^3*x^3 + 1/5*B*a*x^5*e^3 + 3/4*B*a*d*x^4*e^2 + B*a*d^2*x^3*e + 1/2*B*a*d^3*x^2 + 1/4*A*a*x^4*e^3 + A*a*d*x^3*e^2 + 3/2*A*a*d^2*x^2*e + A*a*d^3*x","A",0
1287,1,113,0,0.160096," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{6} \, B c x^{6} e^{2} + \frac{2}{5} \, B c d x^{5} e + \frac{1}{4} \, B c d^{2} x^{4} + \frac{1}{5} \, A c x^{5} e^{2} + \frac{1}{2} \, A c d x^{4} e + \frac{1}{3} \, A c d^{2} x^{3} + \frac{1}{4} \, B a x^{4} e^{2} + \frac{2}{3} \, B a d x^{3} e + \frac{1}{2} \, B a d^{2} x^{2} + \frac{1}{3} \, A a x^{3} e^{2} + A a d x^{2} e + A a d^{2} x"," ",0,"1/6*B*c*x^6*e^2 + 2/5*B*c*d*x^5*e + 1/4*B*c*d^2*x^4 + 1/5*A*c*x^5*e^2 + 1/2*A*c*d*x^4*e + 1/3*A*c*d^2*x^3 + 1/4*B*a*x^4*e^2 + 2/3*B*a*d*x^3*e + 1/2*B*a*d^2*x^2 + 1/3*A*a*x^3*e^2 + A*a*d*x^2*e + A*a*d^2*x","A",0
1288,1,66,0,0.155494," ","integrate((B*x+A)*(e*x+d)*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{5} \, B c x^{5} e + \frac{1}{4} \, B c d x^{4} + \frac{1}{4} \, A c x^{4} e + \frac{1}{3} \, A c d x^{3} + \frac{1}{3} \, B a x^{3} e + \frac{1}{2} \, B a d x^{2} + \frac{1}{2} \, A a x^{2} e + A a d x"," ",0,"1/5*B*c*x^5*e + 1/4*B*c*d*x^4 + 1/4*A*c*x^4*e + 1/3*A*c*d*x^3 + 1/3*B*a*x^3*e + 1/2*B*a*d*x^2 + 1/2*A*a*x^2*e + A*a*d*x","A",0
1289,1,26,0,0.151217," ","integrate((B*x+A)*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{4} \, B c x^{4} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + A a x"," ",0,"1/4*B*c*x^4 + 1/3*A*c*x^3 + 1/2*B*a*x^2 + A*a*x","A",0
1290,1,97,0,0.149339," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d),x, algorithm=""giac"")","-{\left(B c d^{3} - A c d^{2} e + B a d e^{2} - A a e^{3}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B c x^{3} e^{2} - 3 \, B c d x^{2} e + 6 \, B c d^{2} x + 3 \, A c x^{2} e^{2} - 6 \, A c d x e + 6 \, B a x e^{2}\right)} e^{\left(-3\right)}"," ",0,"-(B*c*d^3 - A*c*d^2*e + B*a*d*e^2 - A*a*e^3)*e^(-4)*log(abs(x*e + d)) + 1/6*(2*B*c*x^3*e^2 - 3*B*c*d*x^2*e + 6*B*c*d^2*x + 3*A*c*x^2*e^2 - 6*A*c*d*x*e + 6*B*a*x*e^2)*e^(-3)","A",0
1291,1,151,0,0.156492," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(B c - \frac{2 \, {\left(3 \, B c d e - A c e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)} - {\left(3 \, B c d^{2} - 2 \, A c d e + B a e^{2}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c d^{3} e^{2}}{x e + d} - \frac{A c d^{2} e^{3}}{x e + d} + \frac{B a d e^{4}}{x e + d} - \frac{A a e^{5}}{x e + d}\right)} e^{\left(-6\right)}"," ",0,"1/2*(B*c - 2*(3*B*c*d*e - A*c*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4) - (3*B*c*d^2 - 2*A*c*d*e + B*a*e^2)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c*d^3*e^2/(x*e + d) - A*c*d^2*e^3/(x*e + d) + B*a*d*e^4/(x*e + d) - A*a*e^5/(x*e + d))*e^(-6)","A",0
1292,1,96,0,0.149904," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^3,x, algorithm=""giac"")","B c x e^{\left(-3\right)} - {\left(3 \, B c d - A c e\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, B c d^{3} - 3 \, A c d^{2} e + B a d e^{2} + A a e^{3} + 2 \, {\left(3 \, B c d^{2} e - 2 \, A c d e^{2} + B a e^{3}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"B*c*x*e^(-3) - (3*B*c*d - A*c*e)*e^(-4)*log(abs(x*e + d)) - 1/2*(5*B*c*d^3 - 3*A*c*d^2*e + B*a*d*e^2 + A*a*e^3 + 2*(3*B*c*d^2*e - 2*A*c*d*e^2 + B*a*e^3)*x)*e^(-4)/(x*e + d)^2","A",0
1293,1,103,0,0.158322," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^4,x, algorithm=""giac"")","B c e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(6 \, {\left(3 \, B c d e - A c e^{2}\right)} x^{2} + 3 \, {\left(9 \, B c d^{2} - 2 \, A c d e - B a e^{2}\right)} x + {\left(11 \, B c d^{3} - 2 \, A c d^{2} e - B a d e^{2} - 2 \, A a e^{3}\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"B*c*e^(-4)*log(abs(x*e + d)) + 1/6*(6*(3*B*c*d*e - A*c*e^2)*x^2 + 3*(9*B*c*d^2 - 2*A*c*d*e - B*a*e^2)*x + (11*B*c*d^3 - 2*A*c*d^2*e - B*a*d*e^2 - 2*A*a*e^3)*e^(-1))*e^(-3)/(x*e + d)^3","A",0
1294,1,151,0,0.158745," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{12 \, B c e^{\left(-1\right)}}{x e + d} - \frac{18 \, B c d e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}} + \frac{12 \, B c d^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c d^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{6 \, A c}{{\left(x e + d\right)}^{2}} - \frac{8 \, A c d}{{\left(x e + d\right)}^{3}} + \frac{3 \, A c d^{2}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a e}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a d e}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a e^{2}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-3\right)}"," ",0,"-1/12*(12*B*c*e^(-1)/(x*e + d) - 18*B*c*d*e^(-1)/(x*e + d)^2 + 12*B*c*d^2*e^(-1)/(x*e + d)^3 - 3*B*c*d^3*e^(-1)/(x*e + d)^4 + 6*A*c/(x*e + d)^2 - 8*A*c*d/(x*e + d)^3 + 3*A*c*d^2/(x*e + d)^4 + 4*B*a*e/(x*e + d)^3 - 3*B*a*d*e/(x*e + d)^4 + 3*A*a*e^2/(x*e + d)^4)*e^(-3)","A",0
1295,1,95,0,0.178484," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(30 \, B c x^{3} e^{3} + 30 \, B c d x^{2} e^{2} + 15 \, B c d^{2} x e + 3 \, B c d^{3} + 20 \, A c x^{2} e^{3} + 10 \, A c d x e^{2} + 2 \, A c d^{2} e + 15 \, B a x e^{3} + 3 \, B a d e^{2} + 12 \, A a e^{3}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/60*(30*B*c*x^3*e^3 + 30*B*c*d*x^2*e^2 + 15*B*c*d^2*x*e + 3*B*c*d^3 + 20*A*c*x^2*e^3 + 10*A*c*d*x*e^2 + 2*A*c*d^2*e + 15*B*a*x*e^3 + 3*B*a*d*e^2 + 12*A*a*e^3)*e^(-4)/(x*e + d)^5","A",0
1296,1,93,0,0.172367," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(20 \, B c x^{3} e^{3} + 15 \, B c d x^{2} e^{2} + 6 \, B c d^{2} x e + B c d^{3} + 15 \, A c x^{2} e^{3} + 6 \, A c d x e^{2} + A c d^{2} e + 12 \, B a x e^{3} + 2 \, B a d e^{2} + 10 \, A a e^{3}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(20*B*c*x^3*e^3 + 15*B*c*d*x^2*e^2 + 6*B*c*d^2*x*e + B*c*d^3 + 15*A*c*x^2*e^3 + 6*A*c*d*x*e^2 + A*c*d^2*e + 12*B*a*x*e^3 + 2*B*a*d*e^2 + 10*A*a*e^3)*e^(-4)/(x*e + d)^6","A",0
1297,1,447,0,0.186327," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, B c^{2} x^{11} e^{5} + \frac{1}{2} \, B c^{2} d x^{10} e^{4} + \frac{10}{9} \, B c^{2} d^{2} x^{9} e^{3} + \frac{5}{4} \, B c^{2} d^{3} x^{8} e^{2} + \frac{5}{7} \, B c^{2} d^{4} x^{7} e + \frac{1}{6} \, B c^{2} d^{5} x^{6} + \frac{1}{10} \, A c^{2} x^{10} e^{5} + \frac{5}{9} \, A c^{2} d x^{9} e^{4} + \frac{5}{4} \, A c^{2} d^{2} x^{8} e^{3} + \frac{10}{7} \, A c^{2} d^{3} x^{7} e^{2} + \frac{5}{6} \, A c^{2} d^{4} x^{6} e + \frac{1}{5} \, A c^{2} d^{5} x^{5} + \frac{2}{9} \, B a c x^{9} e^{5} + \frac{5}{4} \, B a c d x^{8} e^{4} + \frac{20}{7} \, B a c d^{2} x^{7} e^{3} + \frac{10}{3} \, B a c d^{3} x^{6} e^{2} + 2 \, B a c d^{4} x^{5} e + \frac{1}{2} \, B a c d^{5} x^{4} + \frac{1}{4} \, A a c x^{8} e^{5} + \frac{10}{7} \, A a c d x^{7} e^{4} + \frac{10}{3} \, A a c d^{2} x^{6} e^{3} + 4 \, A a c d^{3} x^{5} e^{2} + \frac{5}{2} \, A a c d^{4} x^{4} e + \frac{2}{3} \, A a c d^{5} x^{3} + \frac{1}{7} \, B a^{2} x^{7} e^{5} + \frac{5}{6} \, B a^{2} d x^{6} e^{4} + 2 \, B a^{2} d^{2} x^{5} e^{3} + \frac{5}{2} \, B a^{2} d^{3} x^{4} e^{2} + \frac{5}{3} \, B a^{2} d^{4} x^{3} e + \frac{1}{2} \, B a^{2} d^{5} x^{2} + \frac{1}{6} \, A a^{2} x^{6} e^{5} + A a^{2} d x^{5} e^{4} + \frac{5}{2} \, A a^{2} d^{2} x^{4} e^{3} + \frac{10}{3} \, A a^{2} d^{3} x^{3} e^{2} + \frac{5}{2} \, A a^{2} d^{4} x^{2} e + A a^{2} d^{5} x"," ",0,"1/11*B*c^2*x^11*e^5 + 1/2*B*c^2*d*x^10*e^4 + 10/9*B*c^2*d^2*x^9*e^3 + 5/4*B*c^2*d^3*x^8*e^2 + 5/7*B*c^2*d^4*x^7*e + 1/6*B*c^2*d^5*x^6 + 1/10*A*c^2*x^10*e^5 + 5/9*A*c^2*d*x^9*e^4 + 5/4*A*c^2*d^2*x^8*e^3 + 10/7*A*c^2*d^3*x^7*e^2 + 5/6*A*c^2*d^4*x^6*e + 1/5*A*c^2*d^5*x^5 + 2/9*B*a*c*x^9*e^5 + 5/4*B*a*c*d*x^8*e^4 + 20/7*B*a*c*d^2*x^7*e^3 + 10/3*B*a*c*d^3*x^6*e^2 + 2*B*a*c*d^4*x^5*e + 1/2*B*a*c*d^5*x^4 + 1/4*A*a*c*x^8*e^5 + 10/7*A*a*c*d*x^7*e^4 + 10/3*A*a*c*d^2*x^6*e^3 + 4*A*a*c*d^3*x^5*e^2 + 5/2*A*a*c*d^4*x^4*e + 2/3*A*a*c*d^5*x^3 + 1/7*B*a^2*x^7*e^5 + 5/6*B*a^2*d*x^6*e^4 + 2*B*a^2*d^2*x^5*e^3 + 5/2*B*a^2*d^3*x^4*e^2 + 5/3*B*a^2*d^4*x^3*e + 1/2*B*a^2*d^5*x^2 + 1/6*A*a^2*x^6*e^5 + A*a^2*d*x^5*e^4 + 5/2*A*a^2*d^2*x^4*e^3 + 10/3*A*a^2*d^3*x^3*e^2 + 5/2*A*a^2*d^4*x^2*e + A*a^2*d^5*x","B",0
1298,1,365,0,0.193925," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{10} \, B c^{2} x^{10} e^{4} + \frac{4}{9} \, B c^{2} d x^{9} e^{3} + \frac{3}{4} \, B c^{2} d^{2} x^{8} e^{2} + \frac{4}{7} \, B c^{2} d^{3} x^{7} e + \frac{1}{6} \, B c^{2} d^{4} x^{6} + \frac{1}{9} \, A c^{2} x^{9} e^{4} + \frac{1}{2} \, A c^{2} d x^{8} e^{3} + \frac{6}{7} \, A c^{2} d^{2} x^{7} e^{2} + \frac{2}{3} \, A c^{2} d^{3} x^{6} e + \frac{1}{5} \, A c^{2} d^{4} x^{5} + \frac{1}{4} \, B a c x^{8} e^{4} + \frac{8}{7} \, B a c d x^{7} e^{3} + 2 \, B a c d^{2} x^{6} e^{2} + \frac{8}{5} \, B a c d^{3} x^{5} e + \frac{1}{2} \, B a c d^{4} x^{4} + \frac{2}{7} \, A a c x^{7} e^{4} + \frac{4}{3} \, A a c d x^{6} e^{3} + \frac{12}{5} \, A a c d^{2} x^{5} e^{2} + 2 \, A a c d^{3} x^{4} e + \frac{2}{3} \, A a c d^{4} x^{3} + \frac{1}{6} \, B a^{2} x^{6} e^{4} + \frac{4}{5} \, B a^{2} d x^{5} e^{3} + \frac{3}{2} \, B a^{2} d^{2} x^{4} e^{2} + \frac{4}{3} \, B a^{2} d^{3} x^{3} e + \frac{1}{2} \, B a^{2} d^{4} x^{2} + \frac{1}{5} \, A a^{2} x^{5} e^{4} + A a^{2} d x^{4} e^{3} + 2 \, A a^{2} d^{2} x^{3} e^{2} + 2 \, A a^{2} d^{3} x^{2} e + A a^{2} d^{4} x"," ",0,"1/10*B*c^2*x^10*e^4 + 4/9*B*c^2*d*x^9*e^3 + 3/4*B*c^2*d^2*x^8*e^2 + 4/7*B*c^2*d^3*x^7*e + 1/6*B*c^2*d^4*x^6 + 1/9*A*c^2*x^9*e^4 + 1/2*A*c^2*d*x^8*e^3 + 6/7*A*c^2*d^2*x^7*e^2 + 2/3*A*c^2*d^3*x^6*e + 1/5*A*c^2*d^4*x^5 + 1/4*B*a*c*x^8*e^4 + 8/7*B*a*c*d*x^7*e^3 + 2*B*a*c*d^2*x^6*e^2 + 8/5*B*a*c*d^3*x^5*e + 1/2*B*a*c*d^4*x^4 + 2/7*A*a*c*x^7*e^4 + 4/3*A*a*c*d*x^6*e^3 + 12/5*A*a*c*d^2*x^5*e^2 + 2*A*a*c*d^3*x^4*e + 2/3*A*a*c*d^4*x^3 + 1/6*B*a^2*x^6*e^4 + 4/5*B*a^2*d*x^5*e^3 + 3/2*B*a^2*d^2*x^4*e^2 + 4/3*B*a^2*d^3*x^3*e + 1/2*B*a^2*d^4*x^2 + 1/5*A*a^2*x^5*e^4 + A*a^2*d*x^4*e^3 + 2*A*a^2*d^2*x^3*e^2 + 2*A*a^2*d^3*x^2*e + A*a^2*d^4*x","A",0
1299,1,281,0,0.188543," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, B c^{2} x^{9} e^{3} + \frac{3}{8} \, B c^{2} d x^{8} e^{2} + \frac{3}{7} \, B c^{2} d^{2} x^{7} e + \frac{1}{6} \, B c^{2} d^{3} x^{6} + \frac{1}{8} \, A c^{2} x^{8} e^{3} + \frac{3}{7} \, A c^{2} d x^{7} e^{2} + \frac{1}{2} \, A c^{2} d^{2} x^{6} e + \frac{1}{5} \, A c^{2} d^{3} x^{5} + \frac{2}{7} \, B a c x^{7} e^{3} + B a c d x^{6} e^{2} + \frac{6}{5} \, B a c d^{2} x^{5} e + \frac{1}{2} \, B a c d^{3} x^{4} + \frac{1}{3} \, A a c x^{6} e^{3} + \frac{6}{5} \, A a c d x^{5} e^{2} + \frac{3}{2} \, A a c d^{2} x^{4} e + \frac{2}{3} \, A a c d^{3} x^{3} + \frac{1}{5} \, B a^{2} x^{5} e^{3} + \frac{3}{4} \, B a^{2} d x^{4} e^{2} + B a^{2} d^{2} x^{3} e + \frac{1}{2} \, B a^{2} d^{3} x^{2} + \frac{1}{4} \, A a^{2} x^{4} e^{3} + A a^{2} d x^{3} e^{2} + \frac{3}{2} \, A a^{2} d^{2} x^{2} e + A a^{2} d^{3} x"," ",0,"1/9*B*c^2*x^9*e^3 + 3/8*B*c^2*d*x^8*e^2 + 3/7*B*c^2*d^2*x^7*e + 1/6*B*c^2*d^3*x^6 + 1/8*A*c^2*x^8*e^3 + 3/7*A*c^2*d*x^7*e^2 + 1/2*A*c^2*d^2*x^6*e + 1/5*A*c^2*d^3*x^5 + 2/7*B*a*c*x^7*e^3 + B*a*c*d*x^6*e^2 + 6/5*B*a*c*d^2*x^5*e + 1/2*B*a*c*d^3*x^4 + 1/3*A*a*c*x^6*e^3 + 6/5*A*a*c*d*x^5*e^2 + 3/2*A*a*c*d^2*x^4*e + 2/3*A*a*c*d^3*x^3 + 1/5*B*a^2*x^5*e^3 + 3/4*B*a^2*d*x^4*e^2 + B*a^2*d^2*x^3*e + 1/2*B*a^2*d^3*x^2 + 1/4*A*a^2*x^4*e^3 + A*a^2*d*x^3*e^2 + 3/2*A*a^2*d^2*x^2*e + A*a^2*d^3*x","A",0
1300,1,200,0,0.164433," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, B c^{2} x^{8} e^{2} + \frac{2}{7} \, B c^{2} d x^{7} e + \frac{1}{6} \, B c^{2} d^{2} x^{6} + \frac{1}{7} \, A c^{2} x^{7} e^{2} + \frac{1}{3} \, A c^{2} d x^{6} e + \frac{1}{5} \, A c^{2} d^{2} x^{5} + \frac{1}{3} \, B a c x^{6} e^{2} + \frac{4}{5} \, B a c d x^{5} e + \frac{1}{2} \, B a c d^{2} x^{4} + \frac{2}{5} \, A a c x^{5} e^{2} + A a c d x^{4} e + \frac{2}{3} \, A a c d^{2} x^{3} + \frac{1}{4} \, B a^{2} x^{4} e^{2} + \frac{2}{3} \, B a^{2} d x^{3} e + \frac{1}{2} \, B a^{2} d^{2} x^{2} + \frac{1}{3} \, A a^{2} x^{3} e^{2} + A a^{2} d x^{2} e + A a^{2} d^{2} x"," ",0,"1/8*B*c^2*x^8*e^2 + 2/7*B*c^2*d*x^7*e + 1/6*B*c^2*d^2*x^6 + 1/7*A*c^2*x^7*e^2 + 1/3*A*c^2*d*x^6*e + 1/5*A*c^2*d^2*x^5 + 1/3*B*a*c*x^6*e^2 + 4/5*B*a*c*d*x^5*e + 1/2*B*a*c*d^2*x^4 + 2/5*A*a*c*x^5*e^2 + A*a*c*d*x^4*e + 2/3*A*a*c*d^2*x^3 + 1/4*B*a^2*x^4*e^2 + 2/3*B*a^2*d*x^3*e + 1/2*B*a^2*d^2*x^2 + 1/3*A*a^2*x^3*e^2 + A*a^2*d*x^2*e + A*a^2*d^2*x","A",0
1301,1,120,0,0.161328," ","integrate((B*x+A)*(e*x+d)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{7} \, B c^{2} x^{7} e + \frac{1}{6} \, B c^{2} d x^{6} + \frac{1}{6} \, A c^{2} x^{6} e + \frac{1}{5} \, A c^{2} d x^{5} + \frac{2}{5} \, B a c x^{5} e + \frac{1}{2} \, B a c d x^{4} + \frac{1}{2} \, A a c x^{4} e + \frac{2}{3} \, A a c d x^{3} + \frac{1}{3} \, B a^{2} x^{3} e + \frac{1}{2} \, B a^{2} d x^{2} + \frac{1}{2} \, A a^{2} x^{2} e + A a^{2} d x"," ",0,"1/7*B*c^2*x^7*e + 1/6*B*c^2*d*x^6 + 1/6*A*c^2*x^6*e + 1/5*A*c^2*d*x^5 + 2/5*B*a*c*x^5*e + 1/2*B*a*c*d*x^4 + 1/2*A*a*c*x^4*e + 2/3*A*a*c*d*x^3 + 1/3*B*a^2*x^3*e + 1/2*B*a^2*d*x^2 + 1/2*A*a^2*x^2*e + A*a^2*d*x","A",0
1302,1,50,0,0.150364," ","integrate((B*x+A)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{2} x^{6} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{2} \, B a c x^{4} + \frac{2}{3} \, A a c x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a^{2} x"," ",0,"1/6*B*c^2*x^6 + 1/5*A*c^2*x^5 + 1/2*B*a*c*x^4 + 2/3*A*a*c*x^3 + 1/2*B*a^2*x^2 + A*a^2*x","A",0
1303,1,244,0,0.163762," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d),x, algorithm=""giac"")","-{\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)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(12 \, B c^{2} x^{5} e^{4} - 15 \, B c^{2} d x^{4} e^{3} + 20 \, B c^{2} d^{2} x^{3} e^{2} - 30 \, B c^{2} d^{3} x^{2} e + 60 \, B c^{2} d^{4} x + 15 \, A c^{2} x^{4} e^{4} - 20 \, A c^{2} d x^{3} e^{3} + 30 \, A c^{2} d^{2} x^{2} e^{2} - 60 \, A c^{2} d^{3} x e + 40 \, B a c x^{3} e^{4} - 60 \, B a c d x^{2} e^{3} + 120 \, B a c d^{2} x e^{2} + 60 \, A a c x^{2} e^{4} - 120 \, A a c d x e^{3} + 60 \, B a^{2} x e^{4}\right)} e^{\left(-5\right)}"," ",0,"-(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)*e^(-6)*log(abs(x*e + d)) + 1/60*(12*B*c^2*x^5*e^4 - 15*B*c^2*d*x^4*e^3 + 20*B*c^2*d^2*x^3*e^2 - 30*B*c^2*d^3*x^2*e + 60*B*c^2*d^4*x + 15*A*c^2*x^4*e^4 - 20*A*c^2*d*x^3*e^3 + 30*A*c^2*d^2*x^2*e^2 - 60*A*c^2*d^3*x*e + 40*B*a*c*x^3*e^4 - 60*B*a*c*d*x^2*e^3 + 120*B*a*c*d^2*x*e^2 + 60*A*a*c*x^2*e^4 - 120*A*a*c*d*x*e^3 + 60*B*a^2*x*e^4)*e^(-5)","A",0
1304,1,317,0,0.229744," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, B c^{2} - \frac{4 \, {\left(5 \, B c^{2} d e - A c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{12 \, {\left(5 \, B c^{2} d^{2} e^{2} - 2 \, A c^{2} d e^{3} + B a c e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{24 \, {\left(5 \, B c^{2} d^{3} e^{3} - 3 \, A c^{2} d^{2} e^{4} + 3 \, B a c d e^{5} - A a c e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{4} e^{\left(-6\right)} - {\left(5 \, B c^{2} d^{4} - 4 \, A c^{2} d^{3} e + 6 \, B a c d^{2} e^{2} - 4 \, A a c d e^{3} + B a^{2} e^{4}\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c^{2} d^{5} e^{4}}{x e + d} - \frac{A c^{2} d^{4} e^{5}}{x e + d} + \frac{2 \, B a c d^{3} e^{6}}{x e + d} - \frac{2 \, A a c d^{2} e^{7}}{x e + d} + \frac{B a^{2} d e^{8}}{x e + d} - \frac{A a^{2} e^{9}}{x e + d}\right)} e^{\left(-10\right)}"," ",0,"1/12*(3*B*c^2 - 4*(5*B*c^2*d*e - A*c^2*e^2)*e^(-1)/(x*e + d) + 12*(5*B*c^2*d^2*e^2 - 2*A*c^2*d*e^3 + B*a*c*e^4)*e^(-2)/(x*e + d)^2 - 24*(5*B*c^2*d^3*e^3 - 3*A*c^2*d^2*e^4 + 3*B*a*c*d*e^5 - A*a*c*e^6)*e^(-3)/(x*e + d)^3)*(x*e + d)^4*e^(-6) - (5*B*c^2*d^4 - 4*A*c^2*d^3*e + 6*B*a*c*d^2*e^2 - 4*A*a*c*d*e^3 + B*a^2*e^4)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c^2*d^5*e^4/(x*e + d) - A*c^2*d^4*e^5/(x*e + d) + 2*B*a*c*d^3*e^6/(x*e + d) - 2*A*a*c*d^2*e^7/(x*e + d) + B*a^2*d*e^8/(x*e + d) - A*a^2*e^9/(x*e + d))*e^(-10)","A",0
1305,1,237,0,0.187217," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^3,x, algorithm=""giac"")","-2 \, {\left(5 \, B c^{2} d^{3} - 3 \, A c^{2} d^{2} e + 3 \, B a c d e^{2} - A a c e^{3}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B c^{2} x^{3} e^{6} - 9 \, B c^{2} d x^{2} e^{5} + 36 \, B c^{2} d^{2} x e^{4} + 3 \, A c^{2} x^{2} e^{6} - 18 \, A c^{2} d x e^{5} + 12 \, B a c x e^{6}\right)} e^{\left(-9\right)} - \frac{{\left(9 \, B c^{2} d^{5} - 7 \, A c^{2} d^{4} e + 10 \, 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(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)} e^{\left(-6\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-2*(5*B*c^2*d^3 - 3*A*c^2*d^2*e + 3*B*a*c*d*e^2 - A*a*c*e^3)*e^(-6)*log(abs(x*e + d)) + 1/6*(2*B*c^2*x^3*e^6 - 9*B*c^2*d*x^2*e^5 + 36*B*c^2*d^2*x*e^4 + 3*A*c^2*x^2*e^6 - 18*A*c^2*d*x*e^5 + 12*B*a*c*x*e^6)*e^(-9) - 1/2*(9*B*c^2*d^5 - 7*A*c^2*d^4*e + 10*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*(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)*e^(-6)/(x*e + d)^2","A",0
1306,1,237,0,0.154058," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^4,x, algorithm=""giac"")","2 \, {\left(5 \, B c^{2} d^{2} - 2 \, A c^{2} d e + B a c e^{2}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B c^{2} x^{2} e^{4} - 8 \, B c^{2} d x e^{3} + 2 \, A c^{2} x e^{4}\right)} e^{\left(-8\right)} + \frac{{\left(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} + 12 \, {\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} + 3 \, {\left(35 \, B c^{2} d^{4} e - 20 \, 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\right)} e^{\left(-6\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"2*(5*B*c^2*d^2 - 2*A*c^2*d*e + B*a*c*e^2)*e^(-6)*log(abs(x*e + d)) + 1/2*(B*c^2*x^2*e^4 - 8*B*c^2*d*x*e^3 + 2*A*c^2*x*e^4)*e^(-8) + 1/6*(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 + 12*(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 + 3*(35*B*c^2*d^4*e - 20*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)*e^(-6)/(x*e + d)^3","A",0
1307,1,372,0,0.174538," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^5,x, algorithm=""giac"")","{\left(x e + d\right)} B c^{2} e^{\left(-6\right)} + {\left(5 \, B c^{2} d - A c^{2} e\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{120 \, B c^{2} d^{2} e^{22}}{x e + d} - \frac{60 \, B c^{2} d^{3} e^{22}}{{\left(x e + d\right)}^{2}} + \frac{20 \, B c^{2} d^{4} e^{22}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c^{2} d^{5} e^{22}}{{\left(x e + d\right)}^{4}} - \frac{48 \, A c^{2} d e^{23}}{x e + d} + \frac{36 \, A c^{2} d^{2} e^{23}}{{\left(x e + d\right)}^{2}} - \frac{16 \, A c^{2} d^{3} e^{23}}{{\left(x e + d\right)}^{3}} + \frac{3 \, A c^{2} d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{24 \, B a c e^{24}}{x e + d} - \frac{36 \, B a c d e^{24}}{{\left(x e + d\right)}^{2}} + \frac{24 \, B a c d^{2} e^{24}}{{\left(x e + d\right)}^{3}} - \frac{6 \, B a c d^{3} e^{24}}{{\left(x e + d\right)}^{4}} + \frac{12 \, A a c e^{25}}{{\left(x e + d\right)}^{2}} - \frac{16 \, A a c d e^{25}}{{\left(x e + d\right)}^{3}} + \frac{6 \, A a c d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a^{2} e^{26}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a^{2} d e^{26}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a^{2} e^{27}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-28\right)}"," ",0,"(x*e + d)*B*c^2*e^(-6) + (5*B*c^2*d - A*c^2*e)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(120*B*c^2*d^2*e^22/(x*e + d) - 60*B*c^2*d^3*e^22/(x*e + d)^2 + 20*B*c^2*d^4*e^22/(x*e + d)^3 - 3*B*c^2*d^5*e^22/(x*e + d)^4 - 48*A*c^2*d*e^23/(x*e + d) + 36*A*c^2*d^2*e^23/(x*e + d)^2 - 16*A*c^2*d^3*e^23/(x*e + d)^3 + 3*A*c^2*d^4*e^23/(x*e + d)^4 + 24*B*a*c*e^24/(x*e + d) - 36*B*a*c*d*e^24/(x*e + d)^2 + 24*B*a*c*d^2*e^24/(x*e + d)^3 - 6*B*a*c*d^3*e^24/(x*e + d)^4 + 12*A*a*c*e^25/(x*e + d)^2 - 16*A*a*c*d*e^25/(x*e + d)^3 + 6*A*a*c*d^2*e^25/(x*e + d)^4 + 4*B*a^2*e^26/(x*e + d)^3 - 3*B*a^2*d*e^26/(x*e + d)^4 + 3*A*a^2*e^27/(x*e + d)^4)*e^(-28)","B",0
1308,1,239,0,0.204177," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^6,x, algorithm=""giac"")","B c^{2} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(60 \, {\left(5 \, B c^{2} d e^{3} - A c^{2} e^{4}\right)} x^{4} + 60 \, {\left(15 \, B c^{2} d^{2} e^{2} - 2 \, A c^{2} d e^{3} - B a c e^{4}\right)} x^{3} + 20 \, {\left(55 \, B c^{2} d^{3} e - 6 \, A c^{2} d^{2} e^{2} - 3 \, B a c d e^{3} - 2 \, A a c e^{4}\right)} x^{2} + 5 \, {\left(125 \, B c^{2} d^{4} - 12 \, A c^{2} d^{3} e - 6 \, B a c d^{2} e^{2} - 4 \, A a c d e^{3} - 3 \, B a^{2} e^{4}\right)} x + {\left(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}\right)} e^{\left(-1\right)}\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"B*c^2*e^(-6)*log(abs(x*e + d)) + 1/60*(60*(5*B*c^2*d*e^3 - A*c^2*e^4)*x^4 + 60*(15*B*c^2*d^2*e^2 - 2*A*c^2*d*e^3 - B*a*c*e^4)*x^3 + 20*(55*B*c^2*d^3*e - 6*A*c^2*d^2*e^2 - 3*B*a*c*d*e^3 - 2*A*a*c*e^4)*x^2 + 5*(125*B*c^2*d^4 - 12*A*c^2*d^3*e - 6*B*a*c*d^2*e^2 - 4*A*a*c*d*e^3 - 3*B*a^2*e^4)*x + (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)*e^(-1))*e^(-5)/(x*e + d)^5","A",0
1309,1,238,0,0.174784," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(30 \, B c^{2} x^{5} e^{5} + 75 \, B c^{2} d x^{4} e^{4} + 100 \, B c^{2} d^{2} x^{3} e^{3} + 75 \, B c^{2} d^{3} x^{2} e^{2} + 30 \, B c^{2} d^{4} x e + 5 \, B c^{2} d^{5} + 15 \, A c^{2} x^{4} e^{5} + 20 \, A c^{2} d x^{3} e^{4} + 15 \, A c^{2} d^{2} x^{2} e^{3} + 6 \, A c^{2} d^{3} x e^{2} + A c^{2} d^{4} e + 20 \, B a c x^{3} e^{5} + 15 \, B a c d x^{2} e^{4} + 6 \, B a c d^{2} x e^{3} + B a c d^{3} e^{2} + 15 \, A a c x^{2} e^{5} + 6 \, A a c d x e^{4} + A a c d^{2} e^{3} + 6 \, B a^{2} x e^{5} + B a^{2} d e^{4} + 5 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{30 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/30*(30*B*c^2*x^5*e^5 + 75*B*c^2*d*x^4*e^4 + 100*B*c^2*d^2*x^3*e^3 + 75*B*c^2*d^3*x^2*e^2 + 30*B*c^2*d^4*x*e + 5*B*c^2*d^5 + 15*A*c^2*x^4*e^5 + 20*A*c^2*d*x^3*e^4 + 15*A*c^2*d^2*x^2*e^3 + 6*A*c^2*d^3*x*e^2 + A*c^2*d^4*e + 20*B*a*c*x^3*e^5 + 15*B*a*c*d*x^2*e^4 + 6*B*a*c*d^2*x*e^3 + B*a*c*d^3*e^2 + 15*A*a*c*x^2*e^5 + 6*A*a*c*d*x*e^4 + A*a*c*d^2*e^3 + 6*B*a^2*x*e^5 + B*a^2*d*e^4 + 5*A*a^2*e^5)*e^(-6)/(x*e + d)^6","A",0
1310,1,242,0,0.175889," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(105 \, B c^{2} x^{5} e^{5} + 175 \, B c^{2} d x^{4} e^{4} + 175 \, B c^{2} d^{2} x^{3} e^{3} + 105 \, B c^{2} d^{3} x^{2} e^{2} + 35 \, B c^{2} d^{4} x e + 5 \, B c^{2} d^{5} + 70 \, A c^{2} x^{4} e^{5} + 70 \, A c^{2} d x^{3} e^{4} + 42 \, A c^{2} d^{2} x^{2} e^{3} + 14 \, A c^{2} d^{3} x e^{2} + 2 \, A c^{2} d^{4} e + 105 \, B a c x^{3} e^{5} + 63 \, B a c d x^{2} e^{4} + 21 \, B a c d^{2} x e^{3} + 3 \, B a c d^{3} e^{2} + 84 \, A a c x^{2} e^{5} + 28 \, A a c d x e^{4} + 4 \, A a c d^{2} e^{3} + 35 \, B a^{2} x e^{5} + 5 \, B a^{2} d e^{4} + 30 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{210 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/210*(105*B*c^2*x^5*e^5 + 175*B*c^2*d*x^4*e^4 + 175*B*c^2*d^2*x^3*e^3 + 105*B*c^2*d^3*x^2*e^2 + 35*B*c^2*d^4*x*e + 5*B*c^2*d^5 + 70*A*c^2*x^4*e^5 + 70*A*c^2*d*x^3*e^4 + 42*A*c^2*d^2*x^2*e^3 + 14*A*c^2*d^3*x*e^2 + 2*A*c^2*d^4*e + 105*B*a*c*x^3*e^5 + 63*B*a*c*d*x^2*e^4 + 21*B*a*c*d^2*x*e^3 + 3*B*a*c*d^3*e^2 + 84*A*a*c*x^2*e^5 + 28*A*a*c*d*x*e^4 + 4*A*a*c*d^2*e^3 + 35*B*a^2*x*e^5 + 5*B*a^2*d*e^4 + 30*A*a^2*e^5)*e^(-6)/(x*e + d)^7","A",0
1311,1,242,0,0.187644," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(280 \, B c^{2} x^{5} e^{5} + 350 \, B c^{2} d x^{4} e^{4} + 280 \, B c^{2} d^{2} x^{3} e^{3} + 140 \, B c^{2} d^{3} x^{2} e^{2} + 40 \, B c^{2} d^{4} x e + 5 \, B c^{2} d^{5} + 210 \, A c^{2} x^{4} e^{5} + 168 \, A c^{2} d x^{3} e^{4} + 84 \, A c^{2} d^{2} x^{2} e^{3} + 24 \, A c^{2} d^{3} x e^{2} + 3 \, A c^{2} d^{4} e + 336 \, B a c x^{3} e^{5} + 168 \, B a c d x^{2} e^{4} + 48 \, B a c d^{2} x e^{3} + 6 \, B a c d^{3} e^{2} + 280 \, A a c x^{2} e^{5} + 80 \, A a c d x e^{4} + 10 \, A a c d^{2} e^{3} + 120 \, B a^{2} x e^{5} + 15 \, B a^{2} d e^{4} + 105 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{840 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/840*(280*B*c^2*x^5*e^5 + 350*B*c^2*d*x^4*e^4 + 280*B*c^2*d^2*x^3*e^3 + 140*B*c^2*d^3*x^2*e^2 + 40*B*c^2*d^4*x*e + 5*B*c^2*d^5 + 210*A*c^2*x^4*e^5 + 168*A*c^2*d*x^3*e^4 + 84*A*c^2*d^2*x^2*e^3 + 24*A*c^2*d^3*x*e^2 + 3*A*c^2*d^4*e + 336*B*a*c*x^3*e^5 + 168*B*a*c*d*x^2*e^4 + 48*B*a*c*d^2*x*e^3 + 6*B*a*c*d^3*e^2 + 280*A*a*c*x^2*e^5 + 80*A*a*c*d*x*e^4 + 10*A*a*c*d^2*e^3 + 120*B*a^2*x*e^5 + 15*B*a^2*d*e^4 + 105*A*a^2*e^5)*e^(-6)/(x*e + d)^8","A",0
1312,1,242,0,0.193889," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(630 \, B c^{2} x^{5} e^{5} + 630 \, B c^{2} d x^{4} e^{4} + 420 \, B c^{2} d^{2} x^{3} e^{3} + 180 \, B c^{2} d^{3} x^{2} e^{2} + 45 \, B c^{2} d^{4} x e + 5 \, B c^{2} d^{5} + 504 \, A c^{2} x^{4} e^{5} + 336 \, A c^{2} d x^{3} e^{4} + 144 \, A c^{2} d^{2} x^{2} e^{3} + 36 \, A c^{2} d^{3} x e^{2} + 4 \, A c^{2} d^{4} e + 840 \, B a c x^{3} e^{5} + 360 \, B a c d x^{2} e^{4} + 90 \, B a c d^{2} x e^{3} + 10 \, B a c d^{3} e^{2} + 720 \, A a c x^{2} e^{5} + 180 \, A a c d x e^{4} + 20 \, A a c d^{2} e^{3} + 315 \, B a^{2} x e^{5} + 35 \, B a^{2} d e^{4} + 280 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{2520 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/2520*(630*B*c^2*x^5*e^5 + 630*B*c^2*d*x^4*e^4 + 420*B*c^2*d^2*x^3*e^3 + 180*B*c^2*d^3*x^2*e^2 + 45*B*c^2*d^4*x*e + 5*B*c^2*d^5 + 504*A*c^2*x^4*e^5 + 336*A*c^2*d*x^3*e^4 + 144*A*c^2*d^2*x^2*e^3 + 36*A*c^2*d^3*x*e^2 + 4*A*c^2*d^4*e + 840*B*a*c*x^3*e^5 + 360*B*a*c*d*x^2*e^4 + 90*B*a*c*d^2*x*e^3 + 10*B*a*c*d^3*e^2 + 720*A*a*c*x^2*e^5 + 180*A*a*c*d*x*e^4 + 20*A*a*c*d^2*e^3 + 315*B*a^2*x*e^5 + 35*B*a^2*d*e^4 + 280*A*a^2*e^5)*e^(-6)/(x*e + d)^9","A",0
1313,1,634,0,0.191726," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{13} \, B c^{3} x^{13} e^{5} + \frac{5}{12} \, B c^{3} d x^{12} e^{4} + \frac{10}{11} \, B c^{3} d^{2} x^{11} e^{3} + B c^{3} d^{3} x^{10} e^{2} + \frac{5}{9} \, B c^{3} d^{4} x^{9} e + \frac{1}{8} \, B c^{3} d^{5} x^{8} + \frac{1}{12} \, A c^{3} x^{12} e^{5} + \frac{5}{11} \, A c^{3} d x^{11} e^{4} + A c^{3} d^{2} x^{10} e^{3} + \frac{10}{9} \, A c^{3} d^{3} x^{9} e^{2} + \frac{5}{8} \, A c^{3} d^{4} x^{8} e + \frac{1}{7} \, A c^{3} d^{5} x^{7} + \frac{3}{11} \, B a c^{2} x^{11} e^{5} + \frac{3}{2} \, B a c^{2} d x^{10} e^{4} + \frac{10}{3} \, B a c^{2} d^{2} x^{9} e^{3} + \frac{15}{4} \, B a c^{2} d^{3} x^{8} e^{2} + \frac{15}{7} \, B a c^{2} d^{4} x^{7} e + \frac{1}{2} \, B a c^{2} d^{5} x^{6} + \frac{3}{10} \, A a c^{2} x^{10} e^{5} + \frac{5}{3} \, A a c^{2} d x^{9} e^{4} + \frac{15}{4} \, A a c^{2} d^{2} x^{8} e^{3} + \frac{30}{7} \, A a c^{2} d^{3} x^{7} e^{2} + \frac{5}{2} \, A a c^{2} d^{4} x^{6} e + \frac{3}{5} \, A a c^{2} d^{5} x^{5} + \frac{1}{3} \, B a^{2} c x^{9} e^{5} + \frac{15}{8} \, B a^{2} c d x^{8} e^{4} + \frac{30}{7} \, B a^{2} c d^{2} x^{7} e^{3} + 5 \, B a^{2} c d^{3} x^{6} e^{2} + 3 \, B a^{2} c d^{4} x^{5} e + \frac{3}{4} \, B a^{2} c d^{5} x^{4} + \frac{3}{8} \, A a^{2} c x^{8} e^{5} + \frac{15}{7} \, A a^{2} c d x^{7} e^{4} + 5 \, A a^{2} c d^{2} x^{6} e^{3} + 6 \, A a^{2} c d^{3} x^{5} e^{2} + \frac{15}{4} \, A a^{2} c d^{4} x^{4} e + A a^{2} c d^{5} x^{3} + \frac{1}{7} \, B a^{3} x^{7} e^{5} + \frac{5}{6} \, B a^{3} d x^{6} e^{4} + 2 \, B a^{3} d^{2} x^{5} e^{3} + \frac{5}{2} \, B a^{3} d^{3} x^{4} e^{2} + \frac{5}{3} \, B a^{3} d^{4} x^{3} e + \frac{1}{2} \, B a^{3} d^{5} x^{2} + \frac{1}{6} \, A a^{3} x^{6} e^{5} + A a^{3} d x^{5} e^{4} + \frac{5}{2} \, A a^{3} d^{2} x^{4} e^{3} + \frac{10}{3} \, A a^{3} d^{3} x^{3} e^{2} + \frac{5}{2} \, A a^{3} d^{4} x^{2} e + A a^{3} d^{5} x"," ",0,"1/13*B*c^3*x^13*e^5 + 5/12*B*c^3*d*x^12*e^4 + 10/11*B*c^3*d^2*x^11*e^3 + B*c^3*d^3*x^10*e^2 + 5/9*B*c^3*d^4*x^9*e + 1/8*B*c^3*d^5*x^8 + 1/12*A*c^3*x^12*e^5 + 5/11*A*c^3*d*x^11*e^4 + A*c^3*d^2*x^10*e^3 + 10/9*A*c^3*d^3*x^9*e^2 + 5/8*A*c^3*d^4*x^8*e + 1/7*A*c^3*d^5*x^7 + 3/11*B*a*c^2*x^11*e^5 + 3/2*B*a*c^2*d*x^10*e^4 + 10/3*B*a*c^2*d^2*x^9*e^3 + 15/4*B*a*c^2*d^3*x^8*e^2 + 15/7*B*a*c^2*d^4*x^7*e + 1/2*B*a*c^2*d^5*x^6 + 3/10*A*a*c^2*x^10*e^5 + 5/3*A*a*c^2*d*x^9*e^4 + 15/4*A*a*c^2*d^2*x^8*e^3 + 30/7*A*a*c^2*d^3*x^7*e^2 + 5/2*A*a*c^2*d^4*x^6*e + 3/5*A*a*c^2*d^5*x^5 + 1/3*B*a^2*c*x^9*e^5 + 15/8*B*a^2*c*d*x^8*e^4 + 30/7*B*a^2*c*d^2*x^7*e^3 + 5*B*a^2*c*d^3*x^6*e^2 + 3*B*a^2*c*d^4*x^5*e + 3/4*B*a^2*c*d^5*x^4 + 3/8*A*a^2*c*x^8*e^5 + 15/7*A*a^2*c*d*x^7*e^4 + 5*A*a^2*c*d^2*x^6*e^3 + 6*A*a^2*c*d^3*x^5*e^2 + 15/4*A*a^2*c*d^4*x^4*e + A*a^2*c*d^5*x^3 + 1/7*B*a^3*x^7*e^5 + 5/6*B*a^3*d*x^6*e^4 + 2*B*a^3*d^2*x^5*e^3 + 5/2*B*a^3*d^3*x^4*e^2 + 5/3*B*a^3*d^4*x^3*e + 1/2*B*a^3*d^5*x^2 + 1/6*A*a^3*x^6*e^5 + A*a^3*d*x^5*e^4 + 5/2*A*a^3*d^2*x^4*e^3 + 10/3*A*a^3*d^3*x^3*e^2 + 5/2*A*a^3*d^4*x^2*e + A*a^3*d^5*x","A",0
1314,1,520,0,0.205828," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{12} \, B c^{3} x^{12} e^{4} + \frac{4}{11} \, B c^{3} d x^{11} e^{3} + \frac{3}{5} \, B c^{3} d^{2} x^{10} e^{2} + \frac{4}{9} \, B c^{3} d^{3} x^{9} e + \frac{1}{8} \, B c^{3} d^{4} x^{8} + \frac{1}{11} \, A c^{3} x^{11} e^{4} + \frac{2}{5} \, A c^{3} d x^{10} e^{3} + \frac{2}{3} \, A c^{3} d^{2} x^{9} e^{2} + \frac{1}{2} \, A c^{3} d^{3} x^{8} e + \frac{1}{7} \, A c^{3} d^{4} x^{7} + \frac{3}{10} \, B a c^{2} x^{10} e^{4} + \frac{4}{3} \, B a c^{2} d x^{9} e^{3} + \frac{9}{4} \, B a c^{2} d^{2} x^{8} e^{2} + \frac{12}{7} \, B a c^{2} d^{3} x^{7} e + \frac{1}{2} \, B a c^{2} d^{4} x^{6} + \frac{1}{3} \, A a c^{2} x^{9} e^{4} + \frac{3}{2} \, A a c^{2} d x^{8} e^{3} + \frac{18}{7} \, A a c^{2} d^{2} x^{7} e^{2} + 2 \, A a c^{2} d^{3} x^{6} e + \frac{3}{5} \, A a c^{2} d^{4} x^{5} + \frac{3}{8} \, B a^{2} c x^{8} e^{4} + \frac{12}{7} \, B a^{2} c d x^{7} e^{3} + 3 \, B a^{2} c d^{2} x^{6} e^{2} + \frac{12}{5} \, B a^{2} c d^{3} x^{5} e + \frac{3}{4} \, B a^{2} c d^{4} x^{4} + \frac{3}{7} \, A a^{2} c x^{7} e^{4} + 2 \, A a^{2} c d x^{6} e^{3} + \frac{18}{5} \, A a^{2} c d^{2} x^{5} e^{2} + 3 \, A a^{2} c d^{3} x^{4} e + A a^{2} c d^{4} x^{3} + \frac{1}{6} \, B a^{3} x^{6} e^{4} + \frac{4}{5} \, B a^{3} d x^{5} e^{3} + \frac{3}{2} \, B a^{3} d^{2} x^{4} e^{2} + \frac{4}{3} \, B a^{3} d^{3} x^{3} e + \frac{1}{2} \, B a^{3} d^{4} x^{2} + \frac{1}{5} \, A a^{3} x^{5} e^{4} + A a^{3} d x^{4} e^{3} + 2 \, A a^{3} d^{2} x^{3} e^{2} + 2 \, A a^{3} d^{3} x^{2} e + A a^{3} d^{4} x"," ",0,"1/12*B*c^3*x^12*e^4 + 4/11*B*c^3*d*x^11*e^3 + 3/5*B*c^3*d^2*x^10*e^2 + 4/9*B*c^3*d^3*x^9*e + 1/8*B*c^3*d^4*x^8 + 1/11*A*c^3*x^11*e^4 + 2/5*A*c^3*d*x^10*e^3 + 2/3*A*c^3*d^2*x^9*e^2 + 1/2*A*c^3*d^3*x^8*e + 1/7*A*c^3*d^4*x^7 + 3/10*B*a*c^2*x^10*e^4 + 4/3*B*a*c^2*d*x^9*e^3 + 9/4*B*a*c^2*d^2*x^8*e^2 + 12/7*B*a*c^2*d^3*x^7*e + 1/2*B*a*c^2*d^4*x^6 + 1/3*A*a*c^2*x^9*e^4 + 3/2*A*a*c^2*d*x^8*e^3 + 18/7*A*a*c^2*d^2*x^7*e^2 + 2*A*a*c^2*d^3*x^6*e + 3/5*A*a*c^2*d^4*x^5 + 3/8*B*a^2*c*x^8*e^4 + 12/7*B*a^2*c*d*x^7*e^3 + 3*B*a^2*c*d^2*x^6*e^2 + 12/5*B*a^2*c*d^3*x^5*e + 3/4*B*a^2*c*d^4*x^4 + 3/7*A*a^2*c*x^7*e^4 + 2*A*a^2*c*d*x^6*e^3 + 18/5*A*a^2*c*d^2*x^5*e^2 + 3*A*a^2*c*d^3*x^4*e + A*a^2*c*d^4*x^3 + 1/6*B*a^3*x^6*e^4 + 4/5*B*a^3*d*x^5*e^3 + 3/2*B*a^3*d^2*x^4*e^2 + 4/3*B*a^3*d^3*x^3*e + 1/2*B*a^3*d^4*x^2 + 1/5*A*a^3*x^5*e^4 + A*a^3*d*x^4*e^3 + 2*A*a^3*d^2*x^3*e^2 + 2*A*a^3*d^3*x^2*e + A*a^3*d^4*x","A",0
1315,1,403,0,0.184355," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{11} \, B c^{3} x^{11} e^{3} + \frac{3}{10} \, B c^{3} d x^{10} e^{2} + \frac{1}{3} \, B c^{3} d^{2} x^{9} e + \frac{1}{8} \, B c^{3} d^{3} x^{8} + \frac{1}{10} \, A c^{3} x^{10} e^{3} + \frac{1}{3} \, A c^{3} d x^{9} e^{2} + \frac{3}{8} \, A c^{3} d^{2} x^{8} e + \frac{1}{7} \, A c^{3} d^{3} x^{7} + \frac{1}{3} \, B a c^{2} x^{9} e^{3} + \frac{9}{8} \, B a c^{2} d x^{8} e^{2} + \frac{9}{7} \, B a c^{2} d^{2} x^{7} e + \frac{1}{2} \, B a c^{2} d^{3} x^{6} + \frac{3}{8} \, A a c^{2} x^{8} e^{3} + \frac{9}{7} \, A a c^{2} d x^{7} e^{2} + \frac{3}{2} \, A a c^{2} d^{2} x^{6} e + \frac{3}{5} \, A a c^{2} d^{3} x^{5} + \frac{3}{7} \, B a^{2} c x^{7} e^{3} + \frac{3}{2} \, B a^{2} c d x^{6} e^{2} + \frac{9}{5} \, B a^{2} c d^{2} x^{5} e + \frac{3}{4} \, B a^{2} c d^{3} x^{4} + \frac{1}{2} \, A a^{2} c x^{6} e^{3} + \frac{9}{5} \, A a^{2} c d x^{5} e^{2} + \frac{9}{4} \, A a^{2} c d^{2} x^{4} e + A a^{2} c d^{3} x^{3} + \frac{1}{5} \, B a^{3} x^{5} e^{3} + \frac{3}{4} \, B a^{3} d x^{4} e^{2} + B a^{3} d^{2} x^{3} e + \frac{1}{2} \, B a^{3} d^{3} x^{2} + \frac{1}{4} \, A a^{3} x^{4} e^{3} + A a^{3} d x^{3} e^{2} + \frac{3}{2} \, A a^{3} d^{2} x^{2} e + A a^{3} d^{3} x"," ",0,"1/11*B*c^3*x^11*e^3 + 3/10*B*c^3*d*x^10*e^2 + 1/3*B*c^3*d^2*x^9*e + 1/8*B*c^3*d^3*x^8 + 1/10*A*c^3*x^10*e^3 + 1/3*A*c^3*d*x^9*e^2 + 3/8*A*c^3*d^2*x^8*e + 1/7*A*c^3*d^3*x^7 + 1/3*B*a*c^2*x^9*e^3 + 9/8*B*a*c^2*d*x^8*e^2 + 9/7*B*a*c^2*d^2*x^7*e + 1/2*B*a*c^2*d^3*x^6 + 3/8*A*a*c^2*x^8*e^3 + 9/7*A*a*c^2*d*x^7*e^2 + 3/2*A*a*c^2*d^2*x^6*e + 3/5*A*a*c^2*d^3*x^5 + 3/7*B*a^2*c*x^7*e^3 + 3/2*B*a^2*c*d*x^6*e^2 + 9/5*B*a^2*c*d^2*x^5*e + 3/4*B*a^2*c*d^3*x^4 + 1/2*A*a^2*c*x^6*e^3 + 9/5*A*a^2*c*d*x^5*e^2 + 9/4*A*a^2*c*d^2*x^4*e + A*a^2*c*d^3*x^3 + 1/5*B*a^3*x^5*e^3 + 3/4*B*a^3*d*x^4*e^2 + B*a^3*d^2*x^3*e + 1/2*B*a^3*d^3*x^2 + 1/4*A*a^3*x^4*e^3 + A*a^3*d*x^3*e^2 + 3/2*A*a^3*d^2*x^2*e + A*a^3*d^3*x","A",0
1316,1,287,0,0.154080," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{10} \, B c^{3} x^{10} e^{2} + \frac{2}{9} \, B c^{3} d x^{9} e + \frac{1}{8} \, B c^{3} d^{2} x^{8} + \frac{1}{9} \, A c^{3} x^{9} e^{2} + \frac{1}{4} \, A c^{3} d x^{8} e + \frac{1}{7} \, A c^{3} d^{2} x^{7} + \frac{3}{8} \, B a c^{2} x^{8} e^{2} + \frac{6}{7} \, B a c^{2} d x^{7} e + \frac{1}{2} \, B a c^{2} d^{2} x^{6} + \frac{3}{7} \, A a c^{2} x^{7} e^{2} + A a c^{2} d x^{6} e + \frac{3}{5} \, A a c^{2} d^{2} x^{5} + \frac{1}{2} \, B a^{2} c x^{6} e^{2} + \frac{6}{5} \, B a^{2} c d x^{5} e + \frac{3}{4} \, B a^{2} c d^{2} x^{4} + \frac{3}{5} \, A a^{2} c x^{5} e^{2} + \frac{3}{2} \, A a^{2} c d x^{4} e + A a^{2} c d^{2} x^{3} + \frac{1}{4} \, B a^{3} x^{4} e^{2} + \frac{2}{3} \, B a^{3} d x^{3} e + \frac{1}{2} \, B a^{3} d^{2} x^{2} + \frac{1}{3} \, A a^{3} x^{3} e^{2} + A a^{3} d x^{2} e + A a^{3} d^{2} x"," ",0,"1/10*B*c^3*x^10*e^2 + 2/9*B*c^3*d*x^9*e + 1/8*B*c^3*d^2*x^8 + 1/9*A*c^3*x^9*e^2 + 1/4*A*c^3*d*x^8*e + 1/7*A*c^3*d^2*x^7 + 3/8*B*a*c^2*x^8*e^2 + 6/7*B*a*c^2*d*x^7*e + 1/2*B*a*c^2*d^2*x^6 + 3/7*A*a*c^2*x^7*e^2 + A*a*c^2*d*x^6*e + 3/5*A*a*c^2*d^2*x^5 + 1/2*B*a^2*c*x^6*e^2 + 6/5*B*a^2*c*d*x^5*e + 3/4*B*a^2*c*d^2*x^4 + 3/5*A*a^2*c*x^5*e^2 + 3/2*A*a^2*c*d*x^4*e + A*a^2*c*d^2*x^3 + 1/4*B*a^3*x^4*e^2 + 2/3*B*a^3*d*x^3*e + 1/2*B*a^3*d^2*x^2 + 1/3*A*a^3*x^3*e^2 + A*a^3*d*x^2*e + A*a^3*d^2*x","A",0
1317,1,173,0,0.170031," ","integrate((B*x+A)*(e*x+d)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{9} \, B c^{3} x^{9} e + \frac{1}{8} \, B c^{3} d x^{8} + \frac{1}{8} \, A c^{3} x^{8} e + \frac{1}{7} \, A c^{3} d x^{7} + \frac{3}{7} \, B a c^{2} x^{7} e + \frac{1}{2} \, B a c^{2} d x^{6} + \frac{1}{2} \, A a c^{2} x^{6} e + \frac{3}{5} \, A a c^{2} d x^{5} + \frac{3}{5} \, B a^{2} c x^{5} e + \frac{3}{4} \, B a^{2} c d x^{4} + \frac{3}{4} \, A a^{2} c x^{4} e + A a^{2} c d x^{3} + \frac{1}{3} \, B a^{3} x^{3} e + \frac{1}{2} \, B a^{3} d x^{2} + \frac{1}{2} \, A a^{3} x^{2} e + A a^{3} d x"," ",0,"1/9*B*c^3*x^9*e + 1/8*B*c^3*d*x^8 + 1/8*A*c^3*x^8*e + 1/7*A*c^3*d*x^7 + 3/7*B*a*c^2*x^7*e + 1/2*B*a*c^2*d*x^6 + 1/2*A*a*c^2*x^6*e + 3/5*A*a*c^2*d*x^5 + 3/5*B*a^2*c*x^5*e + 3/4*B*a^2*c*d*x^4 + 3/4*A*a^2*c*x^4*e + A*a^2*c*d*x^3 + 1/3*B*a^3*x^3*e + 1/2*B*a^3*d*x^2 + 1/2*A*a^3*x^2*e + A*a^3*d*x","A",0
1318,1,73,0,0.173702," ","integrate((B*x+A)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{8} \, B c^{3} x^{8} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{2} \, B a c^{2} x^{6} + \frac{3}{5} \, A a c^{2} x^{5} + \frac{3}{4} \, B a^{2} c x^{4} + A a^{2} c x^{3} + \frac{1}{2} \, B a^{3} x^{2} + A a^{3} x"," ",0,"1/8*B*c^3*x^8 + 1/7*A*c^3*x^7 + 1/2*B*a*c^2*x^6 + 3/5*A*a*c^2*x^5 + 3/4*B*a^2*c*x^4 + A*a^2*c*x^3 + 1/2*B*a^3*x^2 + A*a^3*x","A",0
1319,1,459,0,0.179491," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d),x, algorithm=""giac"")","-{\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)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{420} \, {\left(60 \, B c^{3} x^{7} e^{6} - 70 \, B c^{3} d x^{6} e^{5} + 84 \, B c^{3} d^{2} x^{5} e^{4} - 105 \, B c^{3} d^{3} x^{4} e^{3} + 140 \, B c^{3} d^{4} x^{3} e^{2} - 210 \, B c^{3} d^{5} x^{2} e + 420 \, B c^{3} d^{6} x + 70 \, A c^{3} x^{6} e^{6} - 84 \, A c^{3} d x^{5} e^{5} + 105 \, A c^{3} d^{2} x^{4} e^{4} - 140 \, A c^{3} d^{3} x^{3} e^{3} + 210 \, A c^{3} d^{4} x^{2} e^{2} - 420 \, A c^{3} d^{5} x e + 252 \, B a c^{2} x^{5} e^{6} - 315 \, B a c^{2} d x^{4} e^{5} + 420 \, B a c^{2} d^{2} x^{3} e^{4} - 630 \, B a c^{2} d^{3} x^{2} e^{3} + 1260 \, B a c^{2} d^{4} x e^{2} + 315 \, A a c^{2} x^{4} e^{6} - 420 \, A a c^{2} d x^{3} e^{5} + 630 \, A a c^{2} d^{2} x^{2} e^{4} - 1260 \, A a c^{2} d^{3} x e^{3} + 420 \, B a^{2} c x^{3} e^{6} - 630 \, B a^{2} c d x^{2} e^{5} + 1260 \, B a^{2} c d^{2} x e^{4} + 630 \, A a^{2} c x^{2} e^{6} - 1260 \, A a^{2} c d x e^{5} + 420 \, B a^{3} x e^{6}\right)} e^{\left(-7\right)}"," ",0,"-(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)*e^(-8)*log(abs(x*e + d)) + 1/420*(60*B*c^3*x^7*e^6 - 70*B*c^3*d*x^6*e^5 + 84*B*c^3*d^2*x^5*e^4 - 105*B*c^3*d^3*x^4*e^3 + 140*B*c^3*d^4*x^3*e^2 - 210*B*c^3*d^5*x^2*e + 420*B*c^3*d^6*x + 70*A*c^3*x^6*e^6 - 84*A*c^3*d*x^5*e^5 + 105*A*c^3*d^2*x^4*e^4 - 140*A*c^3*d^3*x^3*e^3 + 210*A*c^3*d^4*x^2*e^2 - 420*A*c^3*d^5*x*e + 252*B*a*c^2*x^5*e^6 - 315*B*a*c^2*d*x^4*e^5 + 420*B*a*c^2*d^2*x^3*e^4 - 630*B*a*c^2*d^3*x^2*e^3 + 1260*B*a*c^2*d^4*x*e^2 + 315*A*a*c^2*x^4*e^6 - 420*A*a*c^2*d*x^3*e^5 + 630*A*a*c^2*d^2*x^2*e^4 - 1260*A*a*c^2*d^3*x*e^3 + 420*B*a^2*c*x^3*e^6 - 630*B*a^2*c*d*x^2*e^5 + 1260*B*a^2*c*d^2*x*e^4 + 630*A*a^2*c*x^2*e^6 - 1260*A*a^2*c*d*x*e^5 + 420*B*a^3*x*e^6)*e^(-7)","A",0
1320,1,539,0,0.196091," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{60} \, {\left(10 \, B c^{3} - \frac{12 \, {\left(7 \, B c^{3} d e - A c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{45 \, {\left(7 \, B c^{3} d^{2} e^{2} - 2 \, A c^{3} d e^{3} + B a c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{20 \, {\left(35 \, B c^{3} d^{3} e^{3} - 15 \, A c^{3} d^{2} e^{4} + 15 \, B a c^{2} d e^{5} - 3 \, A a c^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{30 \, {\left(35 \, B c^{3} d^{4} e^{4} - 20 \, A c^{3} d^{3} e^{5} + 30 \, B a c^{2} d^{2} e^{6} - 12 \, A a c^{2} d e^{7} + 3 \, B a^{2} c e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{180 \, {\left(7 \, B c^{3} d^{5} e^{5} - 5 \, A c^{3} d^{4} e^{6} + 10 \, B a c^{2} d^{3} e^{7} - 6 \, A a c^{2} d^{2} e^{8} + 3 \, B a^{2} c d e^{9} - A a^{2} c e^{10}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}}\right)} {\left(x e + d\right)}^{6} e^{\left(-8\right)} - {\left(7 \, B c^{3} d^{6} - 6 \, A c^{3} d^{5} e + 15 \, B a c^{2} d^{4} e^{2} - 12 \, A a c^{2} d^{3} e^{3} + 9 \, B a^{2} c d^{2} e^{4} - 6 \, A a^{2} c d e^{5} + B a^{3} e^{6}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c^{3} d^{7} e^{6}}{x e + d} - \frac{A c^{3} d^{6} e^{7}}{x e + d} + \frac{3 \, B a c^{2} d^{5} e^{8}}{x e + d} - \frac{3 \, A a c^{2} d^{4} e^{9}}{x e + d} + \frac{3 \, B a^{2} c d^{3} e^{10}}{x e + d} - \frac{3 \, A a^{2} c d^{2} e^{11}}{x e + d} + \frac{B a^{3} d e^{12}}{x e + d} - \frac{A a^{3} e^{13}}{x e + d}\right)} e^{\left(-14\right)}"," ",0,"1/60*(10*B*c^3 - 12*(7*B*c^3*d*e - A*c^3*e^2)*e^(-1)/(x*e + d) + 45*(7*B*c^3*d^2*e^2 - 2*A*c^3*d*e^3 + B*a*c^2*e^4)*e^(-2)/(x*e + d)^2 - 20*(35*B*c^3*d^3*e^3 - 15*A*c^3*d^2*e^4 + 15*B*a*c^2*d*e^5 - 3*A*a*c^2*e^6)*e^(-3)/(x*e + d)^3 + 30*(35*B*c^3*d^4*e^4 - 20*A*c^3*d^3*e^5 + 30*B*a*c^2*d^2*e^6 - 12*A*a*c^2*d*e^7 + 3*B*a^2*c*e^8)*e^(-4)/(x*e + d)^4 - 180*(7*B*c^3*d^5*e^5 - 5*A*c^3*d^4*e^6 + 10*B*a*c^2*d^3*e^7 - 6*A*a*c^2*d^2*e^8 + 3*B*a^2*c*d*e^9 - A*a^2*c*e^10)*e^(-5)/(x*e + d)^5)*(x*e + d)^6*e^(-8) - (7*B*c^3*d^6 - 6*A*c^3*d^5*e + 15*B*a*c^2*d^4*e^2 - 12*A*a*c^2*d^3*e^3 + 9*B*a^2*c*d^2*e^4 - 6*A*a^2*c*d*e^5 + B*a^3*e^6)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c^3*d^7*e^6/(x*e + d) - A*c^3*d^6*e^7/(x*e + d) + 3*B*a*c^2*d^5*e^8/(x*e + d) - 3*A*a*c^2*d^4*e^9/(x*e + d) + 3*B*a^2*c*d^3*e^10/(x*e + d) - 3*A*a^2*c*d^2*e^11/(x*e + d) + B*a^3*d*e^12/(x*e + d) - A*a^3*e^13/(x*e + d))*e^(-14)","A",0
1321,1,440,0,0.162642," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^3,x, algorithm=""giac"")","-3 \, {\left(7 \, B c^{3} d^{5} - 5 \, A c^{3} d^{4} e + 10 \, B a c^{2} d^{3} e^{2} - 6 \, A a c^{2} d^{2} e^{3} + 3 \, B a^{2} c d e^{4} - A a^{2} c e^{5}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{20} \, {\left(4 \, B c^{3} x^{5} e^{12} - 15 \, B c^{3} d x^{4} e^{11} + 40 \, B c^{3} d^{2} x^{3} e^{10} - 100 \, B c^{3} d^{3} x^{2} e^{9} + 300 \, B c^{3} d^{4} x e^{8} + 5 \, A c^{3} x^{4} e^{12} - 20 \, A c^{3} d x^{3} e^{11} + 60 \, A c^{3} d^{2} x^{2} e^{10} - 200 \, A c^{3} d^{3} x e^{9} + 20 \, B a c^{2} x^{3} e^{12} - 90 \, B a c^{2} d x^{2} e^{11} + 360 \, B a c^{2} d^{2} x e^{10} + 30 \, A a c^{2} x^{2} e^{12} - 180 \, A a c^{2} d x e^{11} + 60 \, B a^{2} c x e^{12}\right)} e^{\left(-15\right)} - \frac{{\left(13 \, B c^{3} d^{7} - 11 \, A c^{3} d^{6} e + 27 \, B a c^{2} d^{5} e^{2} - 21 \, A a c^{2} d^{4} e^{3} + 15 \, B a^{2} c d^{3} e^{4} - 9 \, A a^{2} c d^{2} e^{5} + B a^{3} d e^{6} + A a^{3} e^{7} + 2 \, {\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)} e^{\left(-8\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-3*(7*B*c^3*d^5 - 5*A*c^3*d^4*e + 10*B*a*c^2*d^3*e^2 - 6*A*a*c^2*d^2*e^3 + 3*B*a^2*c*d*e^4 - A*a^2*c*e^5)*e^(-8)*log(abs(x*e + d)) + 1/20*(4*B*c^3*x^5*e^12 - 15*B*c^3*d*x^4*e^11 + 40*B*c^3*d^2*x^3*e^10 - 100*B*c^3*d^3*x^2*e^9 + 300*B*c^3*d^4*x*e^8 + 5*A*c^3*x^4*e^12 - 20*A*c^3*d*x^3*e^11 + 60*A*c^3*d^2*x^2*e^10 - 200*A*c^3*d^3*x*e^9 + 20*B*a*c^2*x^3*e^12 - 90*B*a*c^2*d*x^2*e^11 + 360*B*a*c^2*d^2*x*e^10 + 30*A*a*c^2*x^2*e^12 - 180*A*a*c^2*d*x*e^11 + 60*B*a^2*c*x*e^12)*e^(-15) - 1/2*(13*B*c^3*d^7 - 11*A*c^3*d^6*e + 27*B*a*c^2*d^5*e^2 - 21*A*a*c^2*d^4*e^3 + 15*B*a^2*c*d^3*e^4 - 9*A*a^2*c*d^2*e^5 + B*a^3*d*e^6 + A*a^3*e^7 + 2*(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)*e^(-8)/(x*e + d)^2","A",0
1322,1,435,0,0.158061," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^4,x, algorithm=""giac"")","{\left(35 \, B c^{3} d^{4} - 20 \, A c^{3} d^{3} e + 30 \, B a c^{2} d^{2} e^{2} - 12 \, A a c^{2} d e^{3} + 3 \, B a^{2} c e^{4}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, B c^{3} x^{4} e^{12} - 16 \, B c^{3} d x^{3} e^{11} + 60 \, B c^{3} d^{2} x^{2} e^{10} - 240 \, B c^{3} d^{3} x e^{9} + 4 \, A c^{3} x^{3} e^{12} - 24 \, A c^{3} d x^{2} e^{11} + 120 \, A c^{3} d^{2} x e^{10} + 18 \, B a c^{2} x^{2} e^{12} - 144 \, B a c^{2} d x e^{11} + 36 \, A a c^{2} x e^{12}\right)} e^{\left(-16\right)} + \frac{{\left(107 \, B c^{3} d^{7} - 74 \, A c^{3} d^{6} e + 141 \, B a c^{2} d^{5} e^{2} - 78 \, A a c^{2} d^{4} e^{3} + 33 \, B a^{2} c d^{3} e^{4} - 6 \, A a^{2} c d^{2} e^{5} - B a^{3} d e^{6} - 2 \, A a^{3} e^{7} + 18 \, {\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} + 3 \, {\left(77 \, B c^{3} d^{6} e - 54 \, A c^{3} d^{5} e^{2} + 105 \, B a c^{2} d^{4} e^{3} - 60 \, 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\right)} e^{\left(-8\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"(35*B*c^3*d^4 - 20*A*c^3*d^3*e + 30*B*a*c^2*d^2*e^2 - 12*A*a*c^2*d*e^3 + 3*B*a^2*c*e^4)*e^(-8)*log(abs(x*e + d)) + 1/12*(3*B*c^3*x^4*e^12 - 16*B*c^3*d*x^3*e^11 + 60*B*c^3*d^2*x^2*e^10 - 240*B*c^3*d^3*x*e^9 + 4*A*c^3*x^3*e^12 - 24*A*c^3*d*x^2*e^11 + 120*A*c^3*d^2*x*e^10 + 18*B*a*c^2*x^2*e^12 - 144*B*a*c^2*d*x*e^11 + 36*A*a*c^2*x*e^12)*e^(-16) + 1/6*(107*B*c^3*d^7 - 74*A*c^3*d^6*e + 141*B*a*c^2*d^5*e^2 - 78*A*a*c^2*d^4*e^3 + 33*B*a^2*c*d^3*e^4 - 6*A*a^2*c*d^2*e^5 - B*a^3*d*e^6 - 2*A*a^3*e^7 + 18*(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 + 3*(77*B*c^3*d^6*e - 54*A*c^3*d^5*e^2 + 105*B*a*c^2*d^4*e^3 - 60*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)*e^(-8)/(x*e + d)^3","A",0
1323,1,647,0,0.182780," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{6} \, {\left(2 \, B c^{3} - \frac{3 \, {\left(7 \, B c^{3} d e - A c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{18 \, {\left(7 \, B c^{3} d^{2} e^{2} - 2 \, A c^{3} d e^{3} + B a c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-8\right)} + {\left(35 \, B c^{3} d^{3} - 15 \, A c^{3} d^{2} e + 15 \, B a c^{2} d e^{2} - 3 \, A a c^{2} e^{3}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{420 \, B c^{3} d^{4} e^{36}}{x e + d} - \frac{126 \, B c^{3} d^{5} e^{36}}{{\left(x e + d\right)}^{2}} + \frac{28 \, B c^{3} d^{6} e^{36}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c^{3} d^{7} e^{36}}{{\left(x e + d\right)}^{4}} - \frac{240 \, A c^{3} d^{3} e^{37}}{x e + d} + \frac{90 \, A c^{3} d^{4} e^{37}}{{\left(x e + d\right)}^{2}} - \frac{24 \, A c^{3} d^{5} e^{37}}{{\left(x e + d\right)}^{3}} + \frac{3 \, A c^{3} d^{6} e^{37}}{{\left(x e + d\right)}^{4}} + \frac{360 \, B a c^{2} d^{2} e^{38}}{x e + d} - \frac{180 \, B a c^{2} d^{3} e^{38}}{{\left(x e + d\right)}^{2}} + \frac{60 \, B a c^{2} d^{4} e^{38}}{{\left(x e + d\right)}^{3}} - \frac{9 \, B a c^{2} d^{5} e^{38}}{{\left(x e + d\right)}^{4}} - \frac{144 \, A a c^{2} d e^{39}}{x e + d} + \frac{108 \, A a c^{2} d^{2} e^{39}}{{\left(x e + d\right)}^{2}} - \frac{48 \, A a c^{2} d^{3} e^{39}}{{\left(x e + d\right)}^{3}} + \frac{9 \, A a c^{2} d^{4} e^{39}}{{\left(x e + d\right)}^{4}} + \frac{36 \, B a^{2} c e^{40}}{x e + d} - \frac{54 \, B a^{2} c d e^{40}}{{\left(x e + d\right)}^{2}} + \frac{36 \, B a^{2} c d^{2} e^{40}}{{\left(x e + d\right)}^{3}} - \frac{9 \, B a^{2} c d^{3} e^{40}}{{\left(x e + d\right)}^{4}} + \frac{18 \, A a^{2} c e^{41}}{{\left(x e + d\right)}^{2}} - \frac{24 \, A a^{2} c d e^{41}}{{\left(x e + d\right)}^{3}} + \frac{9 \, A a^{2} c d^{2} e^{41}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a^{3} e^{42}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a^{3} d e^{42}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a^{3} e^{43}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-44\right)}"," ",0,"1/6*(2*B*c^3 - 3*(7*B*c^3*d*e - A*c^3*e^2)*e^(-1)/(x*e + d) + 18*(7*B*c^3*d^2*e^2 - 2*A*c^3*d*e^3 + B*a*c^2*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-8) + (35*B*c^3*d^3 - 15*A*c^3*d^2*e + 15*B*a*c^2*d*e^2 - 3*A*a*c^2*e^3)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(420*B*c^3*d^4*e^36/(x*e + d) - 126*B*c^3*d^5*e^36/(x*e + d)^2 + 28*B*c^3*d^6*e^36/(x*e + d)^3 - 3*B*c^3*d^7*e^36/(x*e + d)^4 - 240*A*c^3*d^3*e^37/(x*e + d) + 90*A*c^3*d^4*e^37/(x*e + d)^2 - 24*A*c^3*d^5*e^37/(x*e + d)^3 + 3*A*c^3*d^6*e^37/(x*e + d)^4 + 360*B*a*c^2*d^2*e^38/(x*e + d) - 180*B*a*c^2*d^3*e^38/(x*e + d)^2 + 60*B*a*c^2*d^4*e^38/(x*e + d)^3 - 9*B*a*c^2*d^5*e^38/(x*e + d)^4 - 144*A*a*c^2*d*e^39/(x*e + d) + 108*A*a*c^2*d^2*e^39/(x*e + d)^2 - 48*A*a*c^2*d^3*e^39/(x*e + d)^3 + 9*A*a*c^2*d^4*e^39/(x*e + d)^4 + 36*B*a^2*c*e^40/(x*e + d) - 54*B*a^2*c*d*e^40/(x*e + d)^2 + 36*B*a^2*c*d^2*e^40/(x*e + d)^3 - 9*B*a^2*c*d^3*e^40/(x*e + d)^4 + 18*A*a^2*c*e^41/(x*e + d)^2 - 24*A*a^2*c*d*e^41/(x*e + d)^3 + 9*A*a^2*c*d^2*e^41/(x*e + d)^4 + 4*B*a^3*e^42/(x*e + d)^3 - 3*B*a^3*d*e^42/(x*e + d)^4 + 3*A*a^3*e^43/(x*e + d)^4)*e^(-44)","B",0
1324,1,429,0,0.162781," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^6,x, algorithm=""giac"")","3 \, {\left(7 \, B c^{3} d^{2} - 2 \, A c^{3} d e + B a c^{2} e^{2}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B c^{3} x^{2} e^{6} - 12 \, B c^{3} d x e^{5} + 2 \, A c^{3} x e^{6}\right)} e^{\left(-12\right)} + \frac{{\left(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} + 20 \, {\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 \, A a^{3} e^{7} + 10 \, {\left(245 \, B c^{3} d^{4} e^{3} - 100 \, 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(329 \, B c^{3} d^{5} e^{2} - 130 \, 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(399 \, B c^{3} d^{6} e - 154 \, 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\right)} e^{\left(-8\right)}}{20 \, {\left(x e + d\right)}^{5}}"," ",0,"3*(7*B*c^3*d^2 - 2*A*c^3*d*e + B*a*c^2*e^2)*e^(-8)*log(abs(x*e + d)) + 1/2*(B*c^3*x^2*e^6 - 12*B*c^3*d*x*e^5 + 2*A*c^3*x*e^6)*e^(-12) + 1/20*(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 + 20*(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*A*a^3*e^7 + 10*(245*B*c^3*d^4*e^3 - 100*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*(329*B*c^3*d^5*e^2 - 130*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*(399*B*c^3*d^6*e - 154*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)*e^(-8)/(x*e + d)^5","A",0
1325,1,426,0,0.162953," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^7,x, algorithm=""giac"")","B c^{3} x e^{\left(-7\right)} - {\left(7 \, B c^{3} d - A c^{3} e\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(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} + 180 \, {\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} + 2 \, B a^{3} d e^{6} + 30 \, {\left(175 \, B c^{3} d^{3} e^{4} - 45 \, 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 \, A a^{3} e^{7} + 20 \, {\left(455 \, 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(539 \, 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(609 \, 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\right)} e^{\left(-8\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"B*c^3*x*e^(-7) - (7*B*c^3*d - A*c^3*e)*e^(-8)*log(abs(x*e + d)) - 1/60*(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 + 180*(7*B*c^3*d^2*e^5 - 2*A*c^3*d*e^6 + B*a*c^2*e^7)*x^5 + 2*B*a^3*d*e^6 + 30*(175*B*c^3*d^3*e^4 - 45*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*A*a^3*e^7 + 20*(455*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*(539*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*(609*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)*e^(-8)/(x*e + d)^6","A",0
1326,1,431,0,0.193362," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^8,x, algorithm=""giac"")","B c^{3} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(420 \, {\left(7 \, B c^{3} d e^{5} - A c^{3} e^{6}\right)} x^{6} + 630 \, {\left(21 \, B c^{3} d^{2} e^{4} - 2 \, A c^{3} d e^{5} - B a c^{2} e^{6}\right)} x^{5} + 70 \, {\left(385 \, B c^{3} d^{3} e^{3} - 30 \, A c^{3} d^{2} e^{4} - 15 \, B a c^{2} d e^{5} - 6 \, A a c^{2} e^{6}\right)} x^{4} + 35 \, {\left(875 \, B c^{3} d^{4} e^{2} - 60 \, A c^{3} d^{3} e^{3} - 30 \, B a c^{2} d^{2} e^{4} - 12 \, A a c^{2} d e^{5} - 9 \, B a^{2} c e^{6}\right)} x^{3} + 21 \, {\left(959 \, B c^{3} d^{5} e - 60 \, A c^{3} d^{4} e^{2} - 30 \, B a c^{2} d^{3} e^{3} - 12 \, A a c^{2} d^{2} e^{4} - 9 \, B a^{2} c d e^{5} - 12 \, A a^{2} c e^{6}\right)} x^{2} + 7 \, {\left(1029 \, B c^{3} d^{6} - 60 \, A c^{3} d^{5} e - 30 \, B a c^{2} d^{4} e^{2} - 12 \, A a c^{2} d^{3} e^{3} - 9 \, B a^{2} c d^{2} e^{4} - 12 \, A a^{2} c d e^{5} - 10 \, B a^{3} e^{6}\right)} x + {\left(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}\right)} e^{\left(-1\right)}\right)} e^{\left(-7\right)}}{420 \, {\left(x e + d\right)}^{7}}"," ",0,"B*c^3*e^(-8)*log(abs(x*e + d)) + 1/420*(420*(7*B*c^3*d*e^5 - A*c^3*e^6)*x^6 + 630*(21*B*c^3*d^2*e^4 - 2*A*c^3*d*e^5 - B*a*c^2*e^6)*x^5 + 70*(385*B*c^3*d^3*e^3 - 30*A*c^3*d^2*e^4 - 15*B*a*c^2*d*e^5 - 6*A*a*c^2*e^6)*x^4 + 35*(875*B*c^3*d^4*e^2 - 60*A*c^3*d^3*e^3 - 30*B*a*c^2*d^2*e^4 - 12*A*a*c^2*d*e^5 - 9*B*a^2*c*e^6)*x^3 + 21*(959*B*c^3*d^5*e - 60*A*c^3*d^4*e^2 - 30*B*a*c^2*d^3*e^3 - 12*A*a*c^2*d^2*e^4 - 9*B*a^2*c*d*e^5 - 12*A*a^2*c*e^6)*x^2 + 7*(1029*B*c^3*d^6 - 60*A*c^3*d^5*e - 30*B*a*c^2*d^4*e^2 - 12*A*a*c^2*d^3*e^3 - 9*B*a^2*c*d^2*e^4 - 12*A*a^2*c*d*e^5 - 10*B*a^3*e^6)*x + (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)*e^(-1))*e^(-7)/(x*e + d)^7","A",0
1327,1,457,0,0.191599," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(280 \, B c^{3} x^{7} e^{7} + 980 \, B c^{3} d x^{6} e^{6} + 1960 \, B c^{3} d^{2} x^{5} e^{5} + 2450 \, B c^{3} d^{3} x^{4} e^{4} + 1960 \, B c^{3} d^{4} x^{3} e^{3} + 980 \, B c^{3} d^{5} x^{2} e^{2} + 280 \, B c^{3} d^{6} x e + 35 \, B c^{3} d^{7} + 140 \, A c^{3} x^{6} e^{7} + 280 \, A c^{3} d x^{5} e^{6} + 350 \, A c^{3} d^{2} x^{4} e^{5} + 280 \, A c^{3} d^{3} x^{3} e^{4} + 140 \, A c^{3} d^{4} x^{2} e^{3} + 40 \, A c^{3} d^{5} x e^{2} + 5 \, A c^{3} d^{6} e + 280 \, B a c^{2} x^{5} e^{7} + 350 \, B a c^{2} d x^{4} e^{6} + 280 \, B a c^{2} d^{2} x^{3} e^{5} + 140 \, B a c^{2} d^{3} x^{2} e^{4} + 40 \, B a c^{2} d^{4} x e^{3} + 5 \, B a c^{2} d^{5} e^{2} + 210 \, A a c^{2} x^{4} e^{7} + 168 \, A a c^{2} d x^{3} e^{6} + 84 \, A a c^{2} d^{2} x^{2} e^{5} + 24 \, A a c^{2} d^{3} x e^{4} + 3 \, A a c^{2} d^{4} e^{3} + 168 \, B a^{2} c x^{3} e^{7} + 84 \, B a^{2} c d x^{2} e^{6} + 24 \, B a^{2} c d^{2} x e^{5} + 3 \, B a^{2} c d^{3} e^{4} + 140 \, A a^{2} c x^{2} e^{7} + 40 \, A a^{2} c d x e^{6} + 5 \, A a^{2} c d^{2} e^{5} + 40 \, B a^{3} x e^{7} + 5 \, B a^{3} d e^{6} + 35 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(280*B*c^3*x^7*e^7 + 980*B*c^3*d*x^6*e^6 + 1960*B*c^3*d^2*x^5*e^5 + 2450*B*c^3*d^3*x^4*e^4 + 1960*B*c^3*d^4*x^3*e^3 + 980*B*c^3*d^5*x^2*e^2 + 280*B*c^3*d^6*x*e + 35*B*c^3*d^7 + 140*A*c^3*x^6*e^7 + 280*A*c^3*d*x^5*e^6 + 350*A*c^3*d^2*x^4*e^5 + 280*A*c^3*d^3*x^3*e^4 + 140*A*c^3*d^4*x^2*e^3 + 40*A*c^3*d^5*x*e^2 + 5*A*c^3*d^6*e + 280*B*a*c^2*x^5*e^7 + 350*B*a*c^2*d*x^4*e^6 + 280*B*a*c^2*d^2*x^3*e^5 + 140*B*a*c^2*d^3*x^2*e^4 + 40*B*a*c^2*d^4*x*e^3 + 5*B*a*c^2*d^5*e^2 + 210*A*a*c^2*x^4*e^7 + 168*A*a*c^2*d*x^3*e^6 + 84*A*a*c^2*d^2*x^2*e^5 + 24*A*a*c^2*d^3*x*e^4 + 3*A*a*c^2*d^4*e^3 + 168*B*a^2*c*x^3*e^7 + 84*B*a^2*c*d*x^2*e^6 + 24*B*a^2*c*d^2*x*e^5 + 3*B*a^2*c*d^3*e^4 + 140*A*a^2*c*x^2*e^7 + 40*A*a^2*c*d*x*e^6 + 5*A*a^2*c*d^2*e^5 + 40*B*a^3*x*e^7 + 5*B*a^3*d*e^6 + 35*A*a^3*e^7)*e^(-8)/(x*e + d)^8","A",0
1328,1,457,0,0.197456," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(1260 \, B c^{3} x^{7} e^{7} + 2940 \, B c^{3} d x^{6} e^{6} + 4410 \, B c^{3} d^{2} x^{5} e^{5} + 4410 \, B c^{3} d^{3} x^{4} e^{4} + 2940 \, B c^{3} d^{4} x^{3} e^{3} + 1260 \, B c^{3} d^{5} x^{2} e^{2} + 315 \, B c^{3} d^{6} x e + 35 \, B c^{3} d^{7} + 840 \, A c^{3} x^{6} e^{7} + 1260 \, A c^{3} d x^{5} e^{6} + 1260 \, A c^{3} d^{2} x^{4} e^{5} + 840 \, A c^{3} d^{3} x^{3} e^{4} + 360 \, A c^{3} d^{4} x^{2} e^{3} + 90 \, A c^{3} d^{5} x e^{2} + 10 \, A c^{3} d^{6} e + 1890 \, B a c^{2} x^{5} e^{7} + 1890 \, B a c^{2} d x^{4} e^{6} + 1260 \, B a c^{2} d^{2} x^{3} e^{5} + 540 \, B a c^{2} d^{3} x^{2} e^{4} + 135 \, B a c^{2} d^{4} x e^{3} + 15 \, B a c^{2} d^{5} e^{2} + 1512 \, A a c^{2} x^{4} e^{7} + 1008 \, A a c^{2} d x^{3} e^{6} + 432 \, A a c^{2} d^{2} x^{2} e^{5} + 108 \, A a c^{2} d^{3} x e^{4} + 12 \, A a c^{2} d^{4} e^{3} + 1260 \, B a^{2} c x^{3} e^{7} + 540 \, B a^{2} c d x^{2} e^{6} + 135 \, B a^{2} c d^{2} x e^{5} + 15 \, B a^{2} c d^{3} e^{4} + 1080 \, A a^{2} c x^{2} e^{7} + 270 \, A a^{2} c d x e^{6} + 30 \, A a^{2} c d^{2} e^{5} + 315 \, B a^{3} x e^{7} + 35 \, B a^{3} d e^{6} + 280 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{2520 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/2520*(1260*B*c^3*x^7*e^7 + 2940*B*c^3*d*x^6*e^6 + 4410*B*c^3*d^2*x^5*e^5 + 4410*B*c^3*d^3*x^4*e^4 + 2940*B*c^3*d^4*x^3*e^3 + 1260*B*c^3*d^5*x^2*e^2 + 315*B*c^3*d^6*x*e + 35*B*c^3*d^7 + 840*A*c^3*x^6*e^7 + 1260*A*c^3*d*x^5*e^6 + 1260*A*c^3*d^2*x^4*e^5 + 840*A*c^3*d^3*x^3*e^4 + 360*A*c^3*d^4*x^2*e^3 + 90*A*c^3*d^5*x*e^2 + 10*A*c^3*d^6*e + 1890*B*a*c^2*x^5*e^7 + 1890*B*a*c^2*d*x^4*e^6 + 1260*B*a*c^2*d^2*x^3*e^5 + 540*B*a*c^2*d^3*x^2*e^4 + 135*B*a*c^2*d^4*x*e^3 + 15*B*a*c^2*d^5*e^2 + 1512*A*a*c^2*x^4*e^7 + 1008*A*a*c^2*d*x^3*e^6 + 432*A*a*c^2*d^2*x^2*e^5 + 108*A*a*c^2*d^3*x*e^4 + 12*A*a*c^2*d^4*e^3 + 1260*B*a^2*c*x^3*e^7 + 540*B*a^2*c*d*x^2*e^6 + 135*B*a^2*c*d^2*x*e^5 + 15*B*a^2*c*d^3*e^4 + 1080*A*a^2*c*x^2*e^7 + 270*A*a^2*c*d*x*e^6 + 30*A*a^2*c*d^2*e^5 + 315*B*a^3*x*e^7 + 35*B*a^3*d*e^6 + 280*A*a^3*e^7)*e^(-8)/(x*e + d)^9","A",0
1329,1,457,0,0.168786," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(840 \, B c^{3} x^{7} e^{7} + 1470 \, B c^{3} d x^{6} e^{6} + 1764 \, B c^{3} d^{2} x^{5} e^{5} + 1470 \, B c^{3} d^{3} x^{4} e^{4} + 840 \, B c^{3} d^{4} x^{3} e^{3} + 315 \, B c^{3} d^{5} x^{2} e^{2} + 70 \, B c^{3} d^{6} x e + 7 \, B c^{3} d^{7} + 630 \, A c^{3} x^{6} e^{7} + 756 \, A c^{3} d x^{5} e^{6} + 630 \, A c^{3} d^{2} x^{4} e^{5} + 360 \, A c^{3} d^{3} x^{3} e^{4} + 135 \, A c^{3} d^{4} x^{2} e^{3} + 30 \, A c^{3} d^{5} x e^{2} + 3 \, A c^{3} d^{6} e + 1512 \, B a c^{2} x^{5} e^{7} + 1260 \, B a c^{2} d x^{4} e^{6} + 720 \, B a c^{2} d^{2} x^{3} e^{5} + 270 \, B a c^{2} d^{3} x^{2} e^{4} + 60 \, B a c^{2} d^{4} x e^{3} + 6 \, B a c^{2} d^{5} e^{2} + 1260 \, A a c^{2} x^{4} e^{7} + 720 \, A a c^{2} d x^{3} e^{6} + 270 \, A a c^{2} d^{2} x^{2} e^{5} + 60 \, A a c^{2} d^{3} x e^{4} + 6 \, A a c^{2} d^{4} e^{3} + 1080 \, B a^{2} c x^{3} e^{7} + 405 \, B a^{2} c d x^{2} e^{6} + 90 \, B a^{2} c d^{2} x e^{5} + 9 \, B a^{2} c d^{3} e^{4} + 945 \, A a^{2} c x^{2} e^{7} + 210 \, A a^{2} c d x e^{6} + 21 \, A a^{2} c d^{2} e^{5} + 280 \, B a^{3} x e^{7} + 28 \, B a^{3} d e^{6} + 252 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{2520 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/2520*(840*B*c^3*x^7*e^7 + 1470*B*c^3*d*x^6*e^6 + 1764*B*c^3*d^2*x^5*e^5 + 1470*B*c^3*d^3*x^4*e^4 + 840*B*c^3*d^4*x^3*e^3 + 315*B*c^3*d^5*x^2*e^2 + 70*B*c^3*d^6*x*e + 7*B*c^3*d^7 + 630*A*c^3*x^6*e^7 + 756*A*c^3*d*x^5*e^6 + 630*A*c^3*d^2*x^4*e^5 + 360*A*c^3*d^3*x^3*e^4 + 135*A*c^3*d^4*x^2*e^3 + 30*A*c^3*d^5*x*e^2 + 3*A*c^3*d^6*e + 1512*B*a*c^2*x^5*e^7 + 1260*B*a*c^2*d*x^4*e^6 + 720*B*a*c^2*d^2*x^3*e^5 + 270*B*a*c^2*d^3*x^2*e^4 + 60*B*a*c^2*d^4*x*e^3 + 6*B*a*c^2*d^5*e^2 + 1260*A*a*c^2*x^4*e^7 + 720*A*a*c^2*d*x^3*e^6 + 270*A*a*c^2*d^2*x^2*e^5 + 60*A*a*c^2*d^3*x*e^4 + 6*A*a*c^2*d^4*e^3 + 1080*B*a^2*c*x^3*e^7 + 405*B*a^2*c*d*x^2*e^6 + 90*B*a^2*c*d^2*x*e^5 + 9*B*a^2*c*d^3*e^4 + 945*A*a^2*c*x^2*e^7 + 210*A*a^2*c*d*x*e^6 + 21*A*a^2*c*d^2*e^5 + 280*B*a^3*x*e^7 + 28*B*a^3*d*e^6 + 252*A*a^3*e^7)*e^(-8)/(x*e + d)^10","A",0
1330,1,245,0,0.161084," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+a),x, algorithm=""giac"")","\frac{{\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)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{{\left(B c^{2} d^{4} + 4 \, A c^{2} d^{3} e - 6 \, B a c d^{2} e^{2} - 4 \, A a c d e^{3} + B a^{2} e^{4}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{3 \, B c^{3} x^{4} e^{4} + 16 \, B c^{3} d x^{3} e^{3} + 36 \, B c^{3} d^{2} x^{2} e^{2} + 48 \, B c^{3} d^{3} x e + 4 \, A c^{3} x^{3} e^{4} + 24 \, A c^{3} d x^{2} e^{3} + 72 \, A c^{3} d^{2} x e^{2} - 6 \, B a c^{2} x^{2} e^{4} - 48 \, B a c^{2} d x e^{3} - 12 \, A a c^{2} x e^{4}}{12 \, c^{4}}"," ",0,"(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)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/2*(B*c^2*d^4 + 4*A*c^2*d^3*e - 6*B*a*c*d^2*e^2 - 4*A*a*c*d*e^3 + B*a^2*e^4)*log(c*x^2 + a)/c^3 + 1/12*(3*B*c^3*x^4*e^4 + 16*B*c^3*d*x^3*e^3 + 36*B*c^3*d^2*x^2*e^2 + 48*B*c^3*d^3*x*e + 4*A*c^3*x^3*e^4 + 24*A*c^3*d*x^2*e^3 + 72*A*c^3*d^2*x*e^2 - 6*B*a*c^2*x^2*e^4 - 48*B*a*c^2*d*x*e^3 - 12*A*a*c^2*x*e^4)/c^4","A",0
1331,1,165,0,0.153180," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(B c d^{3} + 3 \, A c d^{2} e - 3 \, B a d e^{2} - A a e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{{\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)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{2 \, B c^{2} x^{3} e^{3} + 9 \, B c^{2} d x^{2} e^{2} + 18 \, B c^{2} d^{2} x e + 3 \, A c^{2} x^{2} e^{3} + 18 \, A c^{2} d x e^{2} - 6 \, B a c x e^{3}}{6 \, c^{3}}"," ",0,"1/2*(B*c*d^3 + 3*A*c*d^2*e - 3*B*a*d*e^2 - A*a*e^3)*log(c*x^2 + a)/c^2 + (A*c^2*d^3 - 3*B*a*c*d^2*e - 3*A*a*c*d*e^2 + B*a^2*e^3)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/6*(2*B*c^2*x^3*e^3 + 9*B*c^2*d*x^2*e^2 + 18*B*c^2*d^2*x*e + 3*A*c^2*x^2*e^3 + 18*A*c^2*d*x*e^2 - 6*B*a*c*x*e^3)/c^3","A",0
1332,1,101,0,0.162134," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(A c d^{2} - 2 \, B a d e - A a e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c} + \frac{{\left(B c d^{2} + 2 \, A c d e - B a e^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{B c x^{2} e^{2} + 4 \, B c d x e + 2 \, A c x e^{2}}{2 \, c^{2}}"," ",0,"(A*c*d^2 - 2*B*a*d*e - A*a*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) + 1/2*(B*c*d^2 + 2*A*c*d*e - B*a*e^2)*log(c*x^2 + a)/c^2 + 1/2*(B*c*x^2*e^2 + 4*B*c*d*x*e + 2*A*c*x*e^2)/c^2","A",0
1333,1,59,0,0.154311," ","integrate((B*x+A)*(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{B x e}{c} + \frac{{\left(B d + A e\right)} \log\left(c x^{2} + a\right)}{2 \, c} + \frac{{\left(A c d - B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c}"," ",0,"B*x*e/c + 1/2*(B*d + A*e)*log(c*x^2 + a)/c + (A*c*d - B*a*e)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c)","A",0
1334,1,31,0,0.154212," ","integrate((B*x+A)/(c*x^2+a),x, algorithm=""giac"")","\frac{A \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}} + \frac{B \log\left(c x^{2} + a\right)}{2 \, c}"," ",0,"A*arctan(c*x/sqrt(a*c))/sqrt(a*c) + 1/2*B*log(c*x^2 + a)/c","A",0
1335,1,104,0,0.158329," ","integrate((B*x+A)/(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(B d - A e\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c d^{2} + a e^{2}\right)}} - \frac{{\left(B d e - A e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{c d^{2} e + a e^{3}} + \frac{{\left(A c d + B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c d^{2} + a e^{2}\right)} \sqrt{a c}}"," ",0,"1/2*(B*d - A*e)*log(c*x^2 + a)/(c*d^2 + a*e^2) - (B*d*e - A*e^2)*log(abs(x*e + d))/(c*d^2*e + a*e^3) + (A*c*d + B*a*e)*arctan(c*x/sqrt(a*c))/((c*d^2 + a*e^2)*sqrt(a*c))","A",0
1336,1,229,0,0.162660," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(A c^{2} d^{2} e^{2} + 2 \, B a c d e^{3} - A a c e^{4}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a c}} + \frac{{\left(B c d^{2} - 2 \, A c d e - B a e^{2}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} + \frac{\frac{B d e^{2}}{x e + d} - \frac{A e^{3}}{x e + d}}{c d^{2} e^{2} + a e^{4}}"," ",0,"(A*c^2*d^2*e^2 + 2*B*a*c*d*e^3 - A*a*c*e^4)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*c)) + 1/2*(B*c*d^2 - 2*A*c*d*e - B*a*e^2)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + (B*d*e^2/(x*e + d) - A*e^3/(x*e + d))/(c*d^2*e^2 + a*e^4)","A",0
1337,1,383,0,0.166784," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(B c^{2} d^{3} - 3 \, A c^{2} d^{2} e - 3 \, B a c d e^{2} + A a c e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} - \frac{{\left(B c^{2} d^{3} e - 3 \, A c^{2} d^{2} e^{2} - 3 \, B a c d e^{3} + A a c e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}} + \frac{{\left(A c^{3} d^{3} + 3 \, B a c^{2} d^{2} e - 3 \, A a c^{2} d e^{2} - B a^{2} c e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{a c}} + \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(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}{2 \, {\left(c d^{2} + a e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"1/2*(B*c^2*d^3 - 3*A*c^2*d^2*e - 3*B*a*c*d*e^2 + A*a*c*e^3)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) - (B*c^2*d^3*e - 3*A*c^2*d^2*e^2 - 3*B*a*c*d*e^3 + A*a*c*e^4)*log(abs(x*e + d))/(c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7) + (A*c^3*d^3 + 3*B*a*c^2*d^2*e - 3*A*a*c^2*d*e^2 - B*a^2*c*e^3)*arctan(c*x/sqrt(a*c))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(a*c)) + 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*(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)/((c*d^2 + a*e^2)^3*(x*e + d)^2)","A",0
1338,1,347,0,0.159264," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, B c d^{3} e^{2} + 5 \, A c d^{2} e^{3} - 5 \, B a d e^{4} - A a e^{5}\right)} \log\left(c x^{2} + a\right)}{c^{3}} + \frac{{\left(A c^{3} d^{5} + 5 \, B a c^{2} d^{4} e + 10 \, A a c^{2} d^{3} e^{2} - 30 \, B a^{2} c d^{2} e^{3} - 15 \, A a^{2} c d e^{4} + 5 \, B a^{3} e^{5}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{3}} - \frac{B a c^{2} d^{5} + 5 \, A a c^{2} d^{4} e - 10 \, B a^{2} c d^{3} e^{2} - 10 \, A a^{2} c d^{2} e^{3} + 5 \, B a^{3} d e^{4} + A a^{3} e^{5} - {\left(A c^{3} d^{5} - 5 \, B a c^{2} d^{4} e - 10 \, A a c^{2} d^{3} e^{2} + 10 \, B a^{2} c d^{2} e^{3} + 5 \, A a^{2} c d e^{4} - B a^{3} e^{5}\right)} x}{2 \, {\left(c x^{2} + a\right)} a c^{3}} + \frac{2 \, B c^{4} x^{3} e^{5} + 15 \, B c^{4} d x^{2} e^{4} + 60 \, B c^{4} d^{2} x e^{3} + 3 \, A c^{4} x^{2} e^{5} + 30 \, A c^{4} d x e^{4} - 12 \, B a c^{3} x e^{5}}{6 \, c^{6}}"," ",0,"(5*B*c*d^3*e^2 + 5*A*c*d^2*e^3 - 5*B*a*d*e^4 - A*a*e^5)*log(c*x^2 + a)/c^3 + 1/2*(A*c^3*d^5 + 5*B*a*c^2*d^4*e + 10*A*a*c^2*d^3*e^2 - 30*B*a^2*c*d^2*e^3 - 15*A*a^2*c*d*e^4 + 5*B*a^3*e^5)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^3) - 1/2*(B*a*c^2*d^5 + 5*A*a*c^2*d^4*e - 10*B*a^2*c*d^3*e^2 - 10*A*a^2*c*d^2*e^3 + 5*B*a^3*d*e^4 + A*a^3*e^5 - (A*c^3*d^5 - 5*B*a*c^2*d^4*e - 10*A*a*c^2*d^3*e^2 + 10*B*a^2*c*d^2*e^3 + 5*A*a^2*c*d*e^4 - B*a^3*e^5)*x)/((c*x^2 + a)*a*c^3) + 1/6*(2*B*c^4*x^3*e^5 + 15*B*c^4*d*x^2*e^4 + 60*B*c^4*d^2*x*e^3 + 3*A*c^4*x^2*e^5 + 30*A*c^4*d*x*e^4 - 12*B*a*c^3*x*e^5)/c^6","A",0
1339,1,261,0,0.204235," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, B c d^{2} e^{2} + 2 \, A c d e^{3} - B a e^{4}\right)} \log\left(c x^{2} + a\right)}{c^{3}} + \frac{{\left(A c^{2} d^{4} + 4 \, B a c d^{3} e + 6 \, A a c d^{2} e^{2} - 12 \, B a^{2} d e^{3} - 3 \, A a^{2} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}} + \frac{B c^{2} x^{2} e^{4} + 8 \, B c^{2} d x e^{3} + 2 \, A c^{2} x e^{4}}{2 \, c^{4}} - \frac{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} - {\left(A c^{3} d^{4} - 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}{2 \, {\left(c x^{2} + a\right)} a c^{3}}"," ",0,"(3*B*c*d^2*e^2 + 2*A*c*d*e^3 - B*a*e^4)*log(c*x^2 + a)/c^3 + 1/2*(A*c^2*d^4 + 4*B*a*c*d^3*e + 6*A*a*c*d^2*e^2 - 12*B*a^2*d*e^3 - 3*A*a^2*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2) + 1/2*(B*c^2*x^2*e^4 + 8*B*c^2*d*x*e^3 + 2*A*c^2*x*e^4)/c^4 - 1/2*(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 - (A*c^3*d^4 - 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)/((c*x^2 + a)*a*c^3)","A",0
1340,1,179,0,0.194824," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{B x e^{3}}{c^{2}} + \frac{{\left(3 \, B d e^{2} + A e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{{\left(A c^{2} d^{3} + 3 \, B a c d^{2} e + 3 \, A a c d e^{2} - 3 \, B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}} - \frac{B a c d^{3} + 3 \, A a c d^{2} e - 3 \, B a^{2} d e^{2} - A a^{2} e^{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)} x}{2 \, {\left(c x^{2} + a\right)} a c^{2}}"," ",0,"B*x*e^3/c^2 + 1/2*(3*B*d*e^2 + A*e^3)*log(c*x^2 + a)/c^2 + 1/2*(A*c^2*d^3 + 3*B*a*c*d^2*e + 3*A*a*c*d*e^2 - 3*B*a^2*e^3)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2) - 1/2*(B*a*c*d^3 + 3*A*a*c*d^2*e - 3*B*a^2*d*e^2 - A*a^2*e^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)*x)/((c*x^2 + a)*a*c^2)","A",0
1341,1,127,0,0.161235," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{B e^{2} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{{\left(A c d^{2} + 2 \, B a d e + A a e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c} + \frac{{\left(A c d^{2} - 2 \, B a d e - A a e^{2}\right)} x - \frac{B a c d^{2} + 2 \, A a c d e - B a^{2} e^{2}}{c}}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*B*e^2*log(c*x^2 + a)/c^2 + 1/2*(A*c*d^2 + 2*B*a*d*e + A*a*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c) + 1/2*((A*c*d^2 - 2*B*a*d*e - A*a*e^2)*x - (B*a*c*d^2 + 2*A*a*c*d*e - B*a^2*e^2)/c)/((c*x^2 + a)*a*c)","A",0
1342,1,74,0,0.154866," ","integrate((B*x+A)*(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(A c d + B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c} + \frac{A c d x - B a x e - B a d - A a e}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*(A*c*d + B*a*e)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c) + 1/2*(A*c*d*x - B*a*x*e - B*a*d - A*a*e)/((c*x^2 + a)*a*c)","A",0
1343,1,47,0,0.172750," ","integrate((B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{A \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a} + \frac{A c x - B a}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*A*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a) + 1/2*(A*c*x - B*a)/((c*x^2 + a)*a*c)","A",0
1344,1,268,0,0.182864," ","integrate((B*x+A)/(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(B d e^{2} - A e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} - \frac{{\left(B d e^{3} - A e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}} + \frac{{\left(A c^{2} d^{3} - B a c d^{2} e + 3 \, A a c d e^{2} + B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{a c}} - \frac{B a c d^{3} - A a c d^{2} e + B a^{2} d e^{2} - A a^{2} e^{3} - {\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}{2 \, {\left(c d^{2} + a e^{2}\right)}^{2} {\left(c x^{2} + a\right)} a}"," ",0,"1/2*(B*d*e^2 - A*e^3)*log(c*x^2 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) - (B*d*e^3 - A*e^4)*log(abs(x*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) + 1/2*(A*c^2*d^3 - B*a*c*d^2*e + 3*A*a*c*d*e^2 + B*a^2*e^3)*arctan(c*x/sqrt(a*c))/((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(a*c)) - 1/2*(B*a*c*d^3 - A*a*c*d^2*e + B*a^2*d*e^2 - A*a^2*e^3 - (A*c^2*d^3 + B*a*c*d^2*e + A*a*c*d*e^2 + B*a^2*e^3)*x)/((c*d^2 + a*e^2)^2*(c*x^2 + a)*a)","A",0
1345,1,494,0,0.180429," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(A c^{3} d^{4} e^{2} - 2 \, B a c^{2} d^{3} e^{3} + 6 \, A a c^{2} d^{2} e^{4} + 6 \, B a^{2} c d e^{5} - 3 \, A a^{2} c e^{6}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{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{a c}} + \frac{{\left(3 \, B c d^{2} e^{2} - 4 \, A c d e^{3} - B a e^{4}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} + \frac{\frac{B d e^{6}}{x e + d} - \frac{A e^{7}}{x e + d}}{c^{2} d^{4} e^{4} + 2 \, a c d^{2} e^{6} + a^{2} e^{8}} + \frac{\frac{A c^{3} d^{3} e + 3 \, B a c^{2} d^{2} e^{2} - 3 \, A a c^{2} d e^{3} - B a^{2} c e^{4}}{c d^{2} + a e^{2}} - \frac{{\left(A c^{3} d^{4} e^{2} + 4 \, B a c^{2} d^{3} e^{3} - 6 \, A a c^{2} d^{2} e^{4} - 4 \, B a^{2} c d e^{5} + A a^{2} c e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} + a e^{2}\right)} {\left(x e + d\right)}}}{2 \, {\left(c d^{2} + a e^{2}\right)}^{2} a {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}}"," ",0,"1/2*(A*c^3*d^4*e^2 - 2*B*a*c^2*d^3*e^3 + 6*A*a*c^2*d^2*e^4 + 6*B*a^2*c*d*e^5 - 3*A*a^2*c*e^6)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*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(a*c)) + 1/2*(3*B*c*d^2*e^2 - 4*A*c*d*e^3 - B*a*e^4)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + (B*d*e^6/(x*e + d) - A*e^7/(x*e + d))/(c^2*d^4*e^4 + 2*a*c*d^2*e^6 + a^2*e^8) + 1/2*((A*c^3*d^3*e + 3*B*a*c^2*d^2*e^2 - 3*A*a*c^2*d*e^3 - B*a^2*c*e^4)/(c*d^2 + a*e^2) - (A*c^3*d^4*e^2 + 4*B*a*c^2*d^3*e^3 - 6*A*a*c^2*d^2*e^4 - 4*B*a^2*c*d*e^5 + A*a^2*c*e^6)*e^(-1)/((c*d^2 + a*e^2)*(x*e + d)))/((c*d^2 + a*e^2)^2*a*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2))","A",0
1346,1,403,0,0.161795," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{B x e^{5}}{c^{3}} + \frac{{\left(5 \, B d e^{4} + A e^{5}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{{\left(3 \, A c^{3} d^{5} + 5 \, B a c^{2} d^{4} e + 10 \, A a c^{2} d^{3} e^{2} + 30 \, B a^{2} c d^{2} e^{3} + 15 \, A a^{2} c d e^{4} - 15 \, B a^{3} e^{5}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{3}} - \frac{2 \, B a^{2} c^{2} d^{5} + 10 \, A a^{2} c^{2} d^{4} e + 20 \, B a^{3} c d^{3} e^{2} + 20 \, A a^{3} c d^{2} e^{3} - 30 \, B a^{4} d e^{4} - 6 \, A a^{4} e^{5} - {\left(3 \, A c^{4} d^{5} + 5 \, B a c^{3} d^{4} e + 10 \, A a c^{3} d^{3} e^{2} - 50 \, B a^{2} c^{2} d^{2} e^{3} - 25 \, A a^{2} c^{2} d e^{4} + 9 \, B a^{3} c e^{5}\right)} x^{3} + 8 \, {\left(5 \, B a^{2} c^{2} d^{3} e^{2} + 5 \, A a^{2} c^{2} d^{2} e^{3} - 5 \, B a^{3} c d e^{4} - A a^{3} c e^{5}\right)} x^{2} - {\left(5 \, 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} + 7 \, B a^{4} e^{5}\right)} x}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{3}}"," ",0,"B*x*e^5/c^3 + 1/2*(5*B*d*e^4 + A*e^5)*log(c*x^2 + a)/c^3 + 1/8*(3*A*c^3*d^5 + 5*B*a*c^2*d^4*e + 10*A*a*c^2*d^3*e^2 + 30*B*a^2*c*d^2*e^3 + 15*A*a^2*c*d*e^4 - 15*B*a^3*e^5)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^3) - 1/8*(2*B*a^2*c^2*d^5 + 10*A*a^2*c^2*d^4*e + 20*B*a^3*c*d^3*e^2 + 20*A*a^3*c*d^2*e^3 - 30*B*a^4*d*e^4 - 6*A*a^4*e^5 - (3*A*c^4*d^5 + 5*B*a*c^3*d^4*e + 10*A*a*c^3*d^3*e^2 - 50*B*a^2*c^2*d^2*e^3 - 25*A*a^2*c^2*d*e^4 + 9*B*a^3*c*e^5)*x^3 + 8*(5*B*a^2*c^2*d^3*e^2 + 5*A*a^2*c^2*d^2*e^3 - 5*B*a^3*c*d*e^4 - A*a^3*c*e^5)*x^2 - (5*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 + 7*B*a^4*e^5)*x)/((c*x^2 + a)^2*a^2*c^3)","A",0
1347,1,312,0,0.161574," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{B e^{4} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{{\left(3 \, A c^{2} d^{4} + 4 \, B a c d^{3} e + 6 \, A a c d^{2} e^{2} + 12 \, B a^{2} d e^{3} + 3 \, A a^{2} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}} + \frac{{\left(3 \, A c^{3} d^{4} + 4 \, B a c^{2} d^{3} e + 6 \, A a c^{2} d^{2} e^{2} - 20 \, B a^{2} c d e^{3} - 5 \, A a^{2} c e^{4}\right)} x^{3} - 8 \, {\left(3 \, B a^{2} c d^{2} e^{2} + 2 \, A a^{2} c d e^{3} - B a^{3} e^{4}\right)} x^{2} + {\left(5 \, 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}\right)} x - \frac{2 \, {\left(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} - 3 \, B a^{4} e^{4}\right)}}{c}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"1/2*B*e^4*log(c*x^2 + a)/c^3 + 1/8*(3*A*c^2*d^4 + 4*B*a*c*d^3*e + 6*A*a*c*d^2*e^2 + 12*B*a^2*d*e^3 + 3*A*a^2*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2) + 1/8*((3*A*c^3*d^4 + 4*B*a*c^2*d^3*e + 6*A*a*c^2*d^2*e^2 - 20*B*a^2*c*d*e^3 - 5*A*a^2*c*e^4)*x^3 - 8*(3*B*a^2*c*d^2*e^2 + 2*A*a^2*c*d*e^3 - B*a^3*e^4)*x^2 + (5*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)*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 - 3*B*a^4*e^4)/c)/((c*x^2 + a)^2*a^2*c^2)","A",0
1348,1,233,0,0.193673," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(A c^{2} d^{3} + B a c d^{2} e + A a c d e^{2} + B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}} + \frac{3 \, A c^{3} d^{3} x^{3} + 3 \, B a c^{2} d^{2} x^{3} e + 3 \, A a c^{2} d x^{3} e^{2} + 5 \, A a c^{2} d^{3} x - 5 \, B a^{2} c x^{3} e^{3} - 12 \, B a^{2} c d x^{2} e^{2} - 3 \, B a^{2} c d^{2} x e - 2 \, B a^{2} c d^{3} - 4 \, A a^{2} c x^{2} e^{3} - 3 \, A a^{2} c d x e^{2} - 6 \, A a^{2} c d^{2} e - 3 \, B a^{3} x e^{3} - 6 \, B a^{3} d e^{2} - 2 \, A a^{3} e^{3}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"3/8*(A*c^2*d^3 + B*a*c*d^2*e + A*a*c*d*e^2 + B*a^2*e^3)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2) + 1/8*(3*A*c^3*d^3*x^3 + 3*B*a*c^2*d^2*x^3*e + 3*A*a*c^2*d*x^3*e^2 + 5*A*a*c^2*d^3*x - 5*B*a^2*c*x^3*e^3 - 12*B*a^2*c*d*x^2*e^2 - 3*B*a^2*c*d^2*x*e - 2*B*a^2*c*d^3 - 4*A*a^2*c*x^2*e^3 - 3*A*a^2*c*d*x*e^2 - 6*A*a^2*c*d^2*e - 3*B*a^3*x*e^3 - 6*B*a^3*d*e^2 - 2*A*a^3*e^3)/((c*x^2 + a)^2*a^2*c^2)","B",0
1349,1,169,0,0.157925," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, A c d^{2} + 2 \, B a d e + A a e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c} + \frac{3 \, A c^{3} d^{2} x^{3} + 2 \, B a c^{2} d x^{3} e + A a c^{2} x^{3} e^{2} + 5 \, A a c^{2} d^{2} x - 4 \, B a^{2} c x^{2} e^{2} - 2 \, B a^{2} c d x e - 2 \, B a^{2} c d^{2} - A a^{2} c x e^{2} - 4 \, A a^{2} c d e - 2 \, B a^{3} e^{2}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"1/8*(3*A*c*d^2 + 2*B*a*d*e + A*a*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c) + 1/8*(3*A*c^3*d^2*x^3 + 2*B*a*c^2*d*x^3*e + A*a*c^2*x^3*e^2 + 5*A*a*c^2*d^2*x - 4*B*a^2*c*x^2*e^2 - 2*B*a^2*c*d*x*e - 2*B*a^2*c*d^2 - A*a^2*c*x*e^2 - 4*A*a^2*c*d*e - 2*B*a^3*e^2)/((c*x^2 + a)^2*a^2*c^2)","A",0
1350,1,102,0,0.157167," ","integrate((B*x+A)*(e*x+d)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, A c d + B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c} + \frac{3 \, A c^{2} d x^{3} + B a c x^{3} e + 5 \, A a c d x - B a^{2} x e - 2 \, B a^{2} d - 2 \, A a^{2} e}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c}"," ",0,"1/8*(3*A*c*d + B*a*e)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c) + 1/8*(3*A*c^2*d*x^3 + B*a*c*x^3*e + 5*A*a*c*d*x - B*a^2*x*e - 2*B*a^2*d - 2*A*a^2*e)/((c*x^2 + a)^2*a^2*c)","A",0
1351,1,60,0,0.192549," ","integrate((B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, A \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2}} + \frac{3 \, A c^{2} x^{3} + 5 \, A a c x - 2 \, B a^{2}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c}"," ",0,"3/8*A*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2) + 1/8*(3*A*c^2*x^3 + 5*A*a*c*x - 2*B*a^2)/((c*x^2 + a)^2*a^2*c)","A",0
1352,1,534,0,0.186532," ","integrate((B*x+A)/(e*x+d)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(B d e^{4} - A e^{5}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} - \frac{{\left(B d e^{5} - A e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}} + \frac{{\left(3 \, A c^{3} d^{5} - B a c^{2} d^{4} e + 10 \, A a c^{2} d^{3} e^{2} - 6 \, B a^{2} c d^{2} e^{3} + 15 \, A a^{2} c d e^{4} + 3 \, B a^{3} e^{5}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} \sqrt{a c}} - \frac{2 \, B a^{2} c^{2} d^{5} - 2 \, A a^{2} c^{2} d^{4} e + 8 \, B a^{3} c d^{3} e^{2} - 8 \, A a^{3} c d^{2} e^{3} + 6 \, B a^{4} d e^{4} - 6 \, A a^{4} e^{5} - {\left(3 \, A c^{4} d^{5} - B a c^{3} d^{4} e + 10 \, A a c^{3} d^{3} e^{2} + 2 \, B a^{2} c^{2} d^{2} e^{3} + 7 \, A a^{2} c^{2} d e^{4} + 3 \, B a^{3} c e^{5}\right)} x^{3} + 4 \, {\left(B a^{2} c^{2} d^{3} e^{2} - A a^{2} c^{2} d^{2} e^{3} + B a^{3} c d e^{4} - A a^{3} c e^{5}\right)} x^{2} - {\left(5 \, A a c^{3} d^{5} + B a^{2} c^{2} d^{4} e + 14 \, A a^{2} c^{2} d^{3} e^{2} + 6 \, B a^{3} c d^{2} e^{3} + 9 \, A a^{3} c d e^{4} + 5 \, B a^{4} e^{5}\right)} x}{8 \, {\left(c d^{2} + a e^{2}\right)}^{3} {\left(c x^{2} + a\right)}^{2} a^{2}}"," ",0,"1/2*(B*d*e^4 - A*e^5)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) - (B*d*e^5 - A*e^6)*log(abs(x*e + d))/(c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7) + 1/8*(3*A*c^3*d^5 - B*a*c^2*d^4*e + 10*A*a*c^2*d^3*e^2 - 6*B*a^2*c*d^2*e^3 + 15*A*a^2*c*d*e^4 + 3*B*a^3*e^5)*arctan(c*x/sqrt(a*c))/((a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*sqrt(a*c)) - 1/8*(2*B*a^2*c^2*d^5 - 2*A*a^2*c^2*d^4*e + 8*B*a^3*c*d^3*e^2 - 8*A*a^3*c*d^2*e^3 + 6*B*a^4*d*e^4 - 6*A*a^4*e^5 - (3*A*c^4*d^5 - B*a*c^3*d^4*e + 10*A*a*c^3*d^3*e^2 + 2*B*a^2*c^2*d^2*e^3 + 7*A*a^2*c^2*d*e^4 + 3*B*a^3*c*e^5)*x^3 + 4*(B*a^2*c^2*d^3*e^2 - A*a^2*c^2*d^2*e^3 + B*a^3*c*d*e^4 - A*a^3*c*e^5)*x^2 - (5*A*a*c^3*d^5 + B*a^2*c^2*d^4*e + 14*A*a^2*c^2*d^3*e^2 + 6*B*a^3*c*d^2*e^3 + 9*A*a^3*c*d*e^4 + 5*B*a^4*e^5)*x)/((c*d^2 + a*e^2)^3*(c*x^2 + a)^2*a^2)","A",0
1353,1,836,0,0.223623," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, A c^{4} d^{6} e^{2} - 2 \, B a c^{3} d^{5} e^{3} + 15 \, A a c^{3} d^{4} e^{4} - 20 \, B a^{2} c^{2} d^{3} e^{5} + 45 \, A a^{2} c^{2} d^{2} e^{6} + 30 \, B a^{3} c d e^{7} - 15 \, A a^{3} c e^{8}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{8 \, {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{a c}} + \frac{{\left(5 \, B c d^{2} e^{4} - 6 \, A c d e^{5} - B a e^{6}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)}} + \frac{\frac{B d e^{10}}{x e + d} - \frac{A e^{11}}{x e + d}}{c^{3} d^{6} e^{6} + 3 \, a c^{2} d^{4} e^{8} + 3 \, a^{2} c d^{2} e^{10} + a^{3} e^{12}} + \frac{3 \, A c^{5} d^{5} e - 2 \, B a c^{4} d^{4} e^{2} + 14 \, A a c^{4} d^{3} e^{3} + 32 \, B a^{2} c^{3} d^{2} e^{4} - 29 \, A a^{2} c^{3} d e^{5} - 6 \, B a^{3} c^{2} e^{6} - \frac{{\left(9 \, A c^{5} d^{6} e^{2} - 6 \, B a c^{4} d^{5} e^{3} + 41 \, A a c^{4} d^{4} e^{4} + 116 \, B a^{2} c^{3} d^{3} e^{5} - 121 \, A a^{2} c^{3} d^{2} e^{6} - 38 \, B a^{3} c^{2} d e^{7} + 7 \, A a^{3} c^{2} e^{8}\right)} e^{\left(-1\right)}}{x e + d} + \frac{{\left(9 \, A c^{5} d^{7} e^{3} - 6 \, B a c^{4} d^{6} e^{4} + 45 \, A a c^{4} d^{5} e^{5} + 140 \, B a^{2} c^{3} d^{4} e^{6} - 145 \, A a^{2} c^{3} d^{3} e^{7} - 22 \, B a^{3} c^{2} d^{2} e^{8} - 21 \, A a^{3} c^{2} d e^{9} - 8 \, B a^{4} c e^{10}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{{\left(3 \, A c^{5} d^{8} e^{4} - 2 \, B a c^{4} d^{7} e^{5} + 18 \, A a c^{4} d^{6} e^{6} + 58 \, B a^{2} c^{3} d^{5} e^{7} - 60 \, A a^{2} c^{3} d^{4} e^{8} + 26 \, B a^{3} c^{2} d^{3} e^{9} - 66 \, A a^{3} c^{2} d^{2} e^{10} - 34 \, B a^{4} c d e^{11} + 9 \, A a^{4} c e^{12}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{8 \, {\left(c d^{2} + a e^{2}\right)}^{4} a^{2} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{2}}"," ",0,"1/8*(3*A*c^4*d^6*e^2 - 2*B*a*c^3*d^5*e^3 + 15*A*a*c^3*d^4*e^4 - 20*B*a^2*c^2*d^3*e^5 + 45*A*a^2*c^2*d^2*e^6 + 30*B*a^3*c*d*e^7 - 15*A*a^3*c*e^8)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(a*c)) + 1/2*(5*B*c*d^2*e^4 - 6*A*c*d*e^5 - B*a*e^6)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) + (B*d*e^10/(x*e + d) - A*e^11/(x*e + d))/(c^3*d^6*e^6 + 3*a*c^2*d^4*e^8 + 3*a^2*c*d^2*e^10 + a^3*e^12) + 1/8*(3*A*c^5*d^5*e - 2*B*a*c^4*d^4*e^2 + 14*A*a*c^4*d^3*e^3 + 32*B*a^2*c^3*d^2*e^4 - 29*A*a^2*c^3*d*e^5 - 6*B*a^3*c^2*e^6 - (9*A*c^5*d^6*e^2 - 6*B*a*c^4*d^5*e^3 + 41*A*a*c^4*d^4*e^4 + 116*B*a^2*c^3*d^3*e^5 - 121*A*a^2*c^3*d^2*e^6 - 38*B*a^3*c^2*d*e^7 + 7*A*a^3*c^2*e^8)*e^(-1)/(x*e + d) + (9*A*c^5*d^7*e^3 - 6*B*a*c^4*d^6*e^4 + 45*A*a*c^4*d^5*e^5 + 140*B*a^2*c^3*d^4*e^6 - 145*A*a^2*c^3*d^3*e^7 - 22*B*a^3*c^2*d^2*e^8 - 21*A*a^3*c^2*d*e^9 - 8*B*a^4*c*e^10)*e^(-2)/(x*e + d)^2 - (3*A*c^5*d^8*e^4 - 2*B*a*c^4*d^7*e^5 + 18*A*a*c^4*d^6*e^6 + 58*B*a^2*c^3*d^5*e^7 - 60*A*a^2*c^3*d^4*e^8 + 26*B*a^3*c^2*d^3*e^9 - 66*A*a^3*c^2*d^2*e^10 - 34*B*a^4*c*d*e^11 + 9*A*a^4*c*e^12)*e^(-3)/(x*e + d)^3)/((c*d^2 + a*e^2)^4*a^2*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)^2)","A",0
1354,1,24,0,0.170873," ","integrate((-11+6*x)/(-1+2*x)/(x^2-1),x, algorithm=""giac"")","\frac{16}{3} \, \log\left({\left| 2 \, x - 1 \right|}\right) - \frac{17}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{5}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"16/3*log(abs(2*x - 1)) - 17/6*log(abs(x + 1)) - 5/2*log(abs(x - 1))","A",0
1355,1,27,0,0.152227," ","integrate(x*(1+x)^2/(x^2+1)^3,x, algorithm=""giac"")","\frac{x^{3} - 2 \, x^{2} - x - 2}{4 \, {\left(x^{2} + 1\right)}^{2}} + \frac{1}{4} \, \arctan\left(x\right)"," ",0,"1/4*(x^3 - 2*x^2 - x - 2)/(x^2 + 1)^2 + 1/4*arctan(x)","A",0
1356,1,64,0,0.185179," ","integrate((5-x)*(3+2*x)^4*(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{5670} \, {\left(3 \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(5 \, {\left(6 \, x + 7\right)} x - 689\right)} x - 16975\right)} x - 326029\right)} x - 519645\right)} x - 1167988\right)} \sqrt{3 \, x^{2} + 2} - \frac{2341}{27} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/5670*(3*(2*(12*(6*(5*(6*x + 7)*x - 689)*x - 16975)*x - 326029)*x - 519645)*x - 1167988)*sqrt(3*x^2 + 2) - 2341/27*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1357,1,57,0,0.171941," ","integrate((5-x)*(3+2*x)^3*(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{270} \, {\left(3 \, {\left({\left({\left(24 \, {\left(5 \, x - 3\right)} x - 2815\right)} x - 7306\right)} x - 7040\right)} x - 14516\right)} \sqrt{3 \, x^{2} + 2} - \frac{1022}{27} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/270*(3*(((24*(5*x - 3)*x - 2815)*x - 7306)*x - 7040)*x - 14516)*sqrt(3*x^2 + 2) - 1022/27*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1358,1,54,0,0.164741," ","integrate((5-x)*(3+2*x)^2*(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{270} \, {\left(3 \, {\left(2 \, {\left(18 \, {\left(2 \, x - 5\right)} x - 757\right)} x - 2085\right)} x - 3124\right)} \sqrt{3 \, x^{2} + 2} - \frac{131}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/270*(3*(2*(18*(2*x - 5)*x - 757)*x - 2085)*x - 3124)*sqrt(3*x^2 + 2) - 131/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1359,1,48,0,0.221354," ","integrate((5-x)*(3+2*x)*(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{18} \, {\left(3 \, {\left({\left(3 \, x - 14\right)} x - 44\right)} x - 28\right)} \sqrt{3 \, x^{2} + 2} - \frac{46}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/18*(3*((3*x - 14)*x - 44)*x - 28)*sqrt(3*x^2 + 2) - 46/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1360,1,44,0,0.159620," ","integrate((5-x)*(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{18} \, {\left(3 \, {\left(2 \, x - 15\right)} x + 4\right)} \sqrt{3 \, x^{2} + 2} - \frac{5}{3} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/18*(3*(2*x - 15)*x + 4)*sqrt(3*x^2 + 2) - 5/3*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1361,1,104,0,0.251781," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{3 \, x^{2} + 2} {\left(x - 13\right)} + \frac{121}{24} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{13}{8} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right)"," ",0,"-1/4*sqrt(3*x^2 + 2)*(x - 13) + 121/24*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 13/8*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2)))","A",0
1362,1,285,0,0.567356," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^2,x, algorithm=""giac"")","\frac{19}{35} \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 2 \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{35}}{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{3} + \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{13}{8} \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{3 \, {\left(3 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \sqrt{35} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{4 \, {\left({\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{2} - 3\right)}}"," ",0,"19/35*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)*sgn(1/(2*x + 3)) - 2*sqrt(3)*log(1/2*abs(-2*sqrt(3) + 2*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + 2*sqrt(35)/(2*x + 3))/(sqrt(3) + sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)))*sgn(1/(2*x + 3)) - 13/8*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3)*sgn(1/(2*x + 3)) + 3/4*(3*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))*sgn(1/(2*x + 3)) - sqrt(35)*sgn(1/(2*x + 3)))/((sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^2 - 3)","B",0
1363,1,205,0,0.267623," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^3,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{471}{9800} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{3048 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 4301 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 7368 \, \sqrt{3} x + 1496 \, \sqrt{3} + 7368 \, \sqrt{3 \, x^{2} + 2}}{560 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"1/8*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 471/9800*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/560*(3048*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 4301*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 7368*sqrt(3)*x + 1496*sqrt(3) + 7368*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","B",0
1364,1,232,0,0.308323," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^4,x, algorithm=""giac"")","\frac{123}{42875} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{\sqrt{3} {\left(1553 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 30 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 3870 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 25740 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 20 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 1376\right)}}{9800 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{3}}"," ",0,"123/42875*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 1/9800*sqrt(3)*(1553*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 30*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 3870*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 25740*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 20*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 1376)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^3","B",0
1365,1,181,0,0.218690," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^5,x, algorithm=""giac"")","\frac{1}{9604000} \, \sqrt{35} {\left(739 \, \sqrt{35} \sqrt{3} + 6336 \, \log\left(\sqrt{35} \sqrt{3} - 9\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{198}{300125} \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1}{823200} \, {\left(\frac{35 \, {\left(\frac{7 \, {\left(\frac{1365 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 257 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} + 9 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} + 2217 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)} \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3}"," ",0,"1/9604000*sqrt(35)*(739*sqrt(35)*sqrt(3) + 6336*log(sqrt(35)*sqrt(3) - 9))*sgn(1/(2*x + 3)) - 198/300125*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)*sgn(1/(2*x + 3)) - 1/823200*(35*(7*(1365*sgn(1/(2*x + 3))/(2*x + 3) - 257*sgn(1/(2*x + 3)))/(2*x + 3) + 9*sgn(1/(2*x + 3)))/(2*x + 3) + 2217*sgn(1/(2*x + 3)))*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3)","B",0
1366,1,322,0,0.261996," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^6,x, algorithm=""giac"")","\frac{1017}{7503125} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{3 \, \sqrt{3} {\left(904 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 36612 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} + 254217 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} - 142464 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 338184 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} - 4315808 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 1676892 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 1737184 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 219776 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 31232\right)}}{1715000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{5}}"," ",0,"1017/7503125*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 3/1715000*sqrt(3)*(904*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 36612*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 + 254217*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 142464*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 338184*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 4315808*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 1676892*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 1737184*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 219776*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 31232)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^5","B",0
1367,1,367,0,0.266737," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^7,x, algorithm=""giac"")","\frac{6102}{262609375} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{3 \, \sqrt{3} {\left(21696 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} + 1073952 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} + 6978880 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 87678735 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} - 66333990 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} - 258582989 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 426764436 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 755892540 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} - 355133440 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 207134880 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 19853952 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} + 2283136\right)}}{240100000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{6}}"," ",0,"6102/262609375*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 3/240100000*sqrt(3)*(21696*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 + 1073952*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 + 6978880*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 87678735*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 - 66333990*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 258582989*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 426764436*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 755892540*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 - 355133440*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 207134880*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 19853952*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) + 2283136)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^6","B",0
1368,1,72,0,0.188636," ","integrate((5-x)*(3+2*x)^4*(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{34020} \, {\left(3 \, {\left({\left(9 \, {\left(4 \, {\left(10 \, {\left({\left(21 \, {\left(8 \, x + 9\right)} x - 3404\right)} x - 13419\right)} x - 226763\right)} x - 1017345\right)} x - 9179024\right)} x - 6561135\right)} x - 8598544\right)} \sqrt{3 \, x^{2} + 2} - \frac{2777}{18} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/34020*(3*((9*(4*(10*((21*(8*x + 9)*x - 3404)*x - 13419)*x - 226763)*x - 1017345)*x - 9179024)*x - 6561135)*x - 8598544)*sqrt(3*x^2 + 2) - 2777/18*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1369,1,66,0,0.177271," ","integrate((5-x)*(3+2*x)^3*(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{1260} \, {\left(3 \, {\left({\left({\left(12 \, {\left(15 \, {\left({\left(7 \, x - 4\right)} x - 140\right)} x - 5167\right)} x - 73325\right)} x - 81712\right)} x - 75355\right)} x - 81392\right)} \sqrt{3 \, x^{2} + 2} - \frac{1087}{18} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/1260*(3*(((12*(15*((7*x - 4)*x - 140)*x - 5167)*x - 73325)*x - 81712)*x - 75355)*x - 81392)*sqrt(3*x^2 + 2) - 1087/18*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1370,1,62,0,0.168613," ","integrate((5-x)*(3+2*x)^2*(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{1260} \, {\left(3 \, {\left({\left({\left(12 \, {\left(20 \, {\left(3 \, x - 7\right)} x - 1007\right)} x - 16135\right)} x - 17072\right)} x - 23905\right)} x - 17392\right)} \sqrt{3 \, x^{2} + 2} - \frac{397}{18} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/1260*(3*(((12*(20*(3*x - 7)*x - 1007)*x - 16135)*x - 17072)*x - 23905)*x - 17392)*sqrt(3*x^2 + 2) - 397/18*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1371,1,56,0,0.193083," ","integrate((5-x)*(3+2*x)*(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{60} \, {\left({\left({\left({\left(12 \, {\left(5 \, x - 21\right)} x - 605\right)} x - 336\right)} x - 1115\right)} x - 112\right)} \sqrt{3 \, x^{2} + 2} - \frac{137}{18} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/60*((((12*(5*x - 21)*x - 605)*x - 336)*x - 1115)*x - 112)*sqrt(3*x^2 + 2) - 137/18*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1372,1,53,0,0.174165," ","integrate((5-x)*(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{60} \, {\left(3 \, {\left({\left(3 \, {\left(4 \, x - 25\right)} x + 16\right)} x - 125\right)} x + 16\right)} \sqrt{3 \, x^{2} + 2} - \frac{5}{2} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/60*(3*((3*(4*x - 25)*x + 16)*x - 125)*x + 16)*sqrt(3*x^2 + 2) - 5/2*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1373,1,116,0,0.265822," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x),x, algorithm=""giac"")","-\frac{1}{48} \, {\left(3 \, {\left(2 \, {\left(3 \, x - 26\right)} x + 127\right)} x - 1469\right)} \sqrt{3 \, x^{2} + 2} + \frac{1529}{32} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{455}{32} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right)"," ",0,"-1/48*(3*(2*(3*x - 26)*x + 127)*x - 1469)*sqrt(3*x^2 + 2) + 1529/32*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 455/32*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2)))","A",0
1374,1,475,0,0.732790," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^2,x, algorithm=""giac"")","\frac{193}{16} \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{663}{16} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{35}}{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{3} + \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{455}{32} \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{3 \, {\left(704 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 323 \, \sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 1944 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 1158 \, \sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 1872 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 1263 \, \sqrt{35} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{8 \, {\left({\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{2} - 3\right)}^{3}}"," ",0,"193/16*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)*sgn(1/(2*x + 3)) - 663/16*sqrt(3)*log(1/2*abs(-2*sqrt(3) + 2*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + 2*sqrt(35)/(2*x + 3))/(sqrt(3) + sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)))*sgn(1/(2*x + 3)) - 455/32*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3)*sgn(1/(2*x + 3)) + 3/8*(704*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^5*sgn(1/(2*x + 3)) - 323*sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^4*sgn(1/(2*x + 3)) - 1944*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^3*sgn(1/(2*x + 3)) + 1158*sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^2*sgn(1/(2*x + 3)) + 1872*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))*sgn(1/(2*x + 3)) - 1263*sqrt(35)*sgn(1/(2*x + 3)))/((sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^2 - 3)^3","B",0
1375,1,219,0,0.281301," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^3,x, algorithm=""giac"")","-\frac{3}{16} \, \sqrt{3 \, x^{2} + 2} {\left(x - 19\right)} + \frac{111}{8} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{1143}{280} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{5 \, {\left(1452 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 3013 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 6528 \, \sqrt{3} x + 1048 \, \sqrt{3} + 6528 \, \sqrt{3 \, x^{2} + 2}\right)}}{64 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"-3/16*sqrt(3*x^2 + 2)*(x - 19) + 111/8*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 1143/280*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 5/64*(1452*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 3013*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 6528*sqrt(3)*x + 1048*sqrt(3) + 6528*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","B",0
1376,1,265,0,0.277787," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^4,x, algorithm=""giac"")","-\frac{33}{16} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{11727}{19600} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{3}{16} \, \sqrt{3 \, x^{2} + 2} - \frac{\sqrt{3} {\left(14792 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 189285 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 141030 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 561630 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 166480 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 50144\right)}}{1120 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{3}}"," ",0,"-33/16*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 11727/19600*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 3/16*sqrt(3*x^2 + 2) - 1/1120*sqrt(3)*(14792*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 189285*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 141030*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 561630*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 166480*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 50144)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^3","B",0
1377,1,106,0,0.236137," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^5,x, algorithm=""giac"")","-\frac{1}{470400} \, {\left(\frac{35 \, {\left(\frac{35 \, {\left(\frac{1365 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 1193 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} + 16227 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} - 125301 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)} \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} - \frac{41767}{156800} \, \sqrt{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)"," ",0,"-1/470400*(35*(35*(1365*sgn(1/(2*x + 3))/(2*x + 3) - 1193*sgn(1/(2*x + 3)))/(2*x + 3) + 16227*sgn(1/(2*x + 3)))/(2*x + 3) - 125301*sgn(1/(2*x + 3)))*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) - 41767/156800*sqrt(3)*sgn(1/(2*x + 3))","A",0
1378,1,318,0,0.266530," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^6,x, algorithm=""giac"")","\frac{1107}{3001250} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{9 \, {\left(89686 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 138886 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} + 1224478 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} + 245133 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 1224531 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} - 4374874 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 4855928 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 1339152 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 586816 \, \sqrt{3} x - 37696 \, \sqrt{3} + 586816 \, \sqrt{3 \, x^{2} + 2}\right)}}{2744000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{5}}"," ",0,"1107/3001250*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/2744000*(89686*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 138886*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 + 1224478*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 + 245133*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 1224531*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 4374874*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 4855928*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 1339152*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 586816*sqrt(3)*x - 37696*sqrt(3) + 586816*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^5","B",0
1379,1,367,0,0.314277," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^7,x, algorithm=""giac"")","\frac{27}{306250} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{3 \, \sqrt{3} {\left(96 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} + 17877 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} - 4120 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 25860 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} - 225240 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} - 173964 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 648336 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 641040 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} - 309440 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 135120 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 10752 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} + 1536\right)}}{280000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{6}}"," ",0,"27/306250*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 3/280000*sqrt(3)*(96*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 + 17877*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 - 4120*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 25860*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 - 225240*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 173964*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 648336*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 641040*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 - 309440*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 135120*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 10752*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) + 1536)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^6","B",0
1380,1,408,0,0.279596," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^8,x, algorithm=""giac"")","\frac{72603}{3676531250} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{9 \, {\left(258144 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{13} + 5033808 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{12} + 225898166 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} + 26360013 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} + 555459995 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} - 2679767547 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} - 4252091247 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} - 6029804778 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} + 11677158028 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} - 7324195080 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 2245361152 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 675266496 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 174039168 \, \sqrt{3} x - 6049536 \, \sqrt{3} - 174039168 \, \sqrt{3 \, x^{2} + 2}\right)}}{3361400000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{7}}"," ",0,"72603/3676531250*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/3361400000*(258144*(sqrt(3)*x - sqrt(3*x^2 + 2))^13 + 5033808*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^12 + 225898166*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 + 26360013*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 + 555459995*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 - 2679767547*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 - 4252091247*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 6029804778*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 + 11677158028*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 7324195080*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 2245361152*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 675266496*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 174039168*sqrt(3)*x - 6049536*sqrt(3) - 174039168*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^7","B",0
1381,1,82,0,0.179431," ","integrate((5-x)*(3+2*x)^4*(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{53460} \, {\left(3 \, {\left({\left(9 \, {\left(2 \, {\left({\left(2 \, {\left(6 \, {\left(4 \, {\left(27 \, {\left(10 \, x + 11\right)} x - 4985\right)} x - 78111\right)} x - 867095\right)} x - 2406789\right)} x - 2791900\right)} x - 4708275\right)} x - 30720080\right)} x - 21456765\right)} x - 19537120\right)} \sqrt{3 \, x^{2} + 2} - \frac{4991}{18} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/53460*(3*((9*(2*((2*(6*(4*(27*(10*x + 11)*x - 4985)*x - 78111)*x - 867095)*x - 2406789)*x - 2791900)*x - 4708275)*x - 30720080)*x - 21456765)*x - 19537120)*sqrt(3*x^2 + 2) - 4991/18*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1382,1,76,0,0.233967," ","integrate((5-x)*(3+2*x)^3*(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{3240} \, {\left(3 \, {\left({\left(9 \, {\left(2 \, {\left({\left({\left(3 \, {\left(16 \, {\left(9 \, x - 5\right)} x - 2583\right)} x - 19180\right)} x - 27843\right)} x - 37720\right)} x - 71215\right)} x - 450080\right)} x - 415305\right)} x - 299200\right)} \sqrt{3 \, x^{2} + 2} - \frac{3731}{36} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/3240*(3*((9*(2*(((3*(16*(9*x - 5)*x - 2583)*x - 19180)*x - 27843)*x - 37720)*x - 71215)*x - 450080)*x - 415305)*x - 299200)*sqrt(3*x^2 + 2) - 3731/36*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1383,1,72,0,0.192006," ","integrate((5-x)*(3+2*x)^2*(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{324} \, {\left(3 \, {\left({\left(9 \, {\left(2 \, {\left({\left(2 \, {\left(3 \, {\left(4 \, x - 9\right)} x - 175\right)} x - 507\right)} x - 764\right)} x - 1873\right)} x - 9424\right)} x - 13455\right)} x - 6368\right)} \sqrt{3 \, x^{2} + 2} - \frac{665}{18} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/324*(3*((9*(2*((2*(3*(4*x - 9)*x - 175)*x - 507)*x - 764)*x - 1873)*x - 9424)*x - 13455)*x - 6368)*sqrt(3*x^2 + 2) - 665/18*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1384,1,63,0,0.205692," ","integrate((5-x)*(3+2*x)*(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{24} \, {\left({\left({\left({\left(6 \, {\left({\left(9 \, {\left(x - 4\right)} x - 73\right)} x - 72\right)} x - 1111\right)} x - 288\right)} x - 985\right)} x - 64\right)} \sqrt{3 \, x^{2} + 2} - \frac{455}{36} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/24*((((6*((9*(x - 4)*x - 73)*x - 72)*x - 1111)*x - 288)*x - 985)*x - 64)*sqrt(3*x^2 + 2) - 455/36*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1385,1,61,0,0.168442," ","integrate((5-x)*(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{84} \, {\left(3 \, {\left({\left({\left(6 \, {\left({\left(6 \, x - 35\right)} x + 12\right)} x - 455\right)} x + 48\right)} x - 385\right)} x + 32\right)} \sqrt{3 \, x^{2} + 2} - \frac{25}{6} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/84*(3*(((6*((6*x - 35)*x + 12)*x - 455)*x + 48)*x - 385)*x + 32)*sqrt(3*x^2 + 2) - 25/6*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1386,1,125,0,0.283386," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x),x, algorithm=""giac"")","-\frac{1}{960} \, {\left(3 \, {\left(2 \, {\left({\left(24 \, {\left(5 \, x - 39\right)} x + 2015\right)} x - 5798\right)} x + 26765\right)} x - 259571\right)} \sqrt{3 \, x^{2} + 2} + \frac{162673}{384} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{15925}{128} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right)"," ",0,"-1/960*(3*(2*((24*(5*x - 39)*x + 2015)*x - 5798)*x + 26765)*x - 259571)*sqrt(3*x^2 + 2) + 162673/384*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 15925/128*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2)))","A",0
1387,1,665,0,1.020975," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^2,x, algorithm=""giac"")","\frac{5425}{32} \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{18543}{32} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{35}}{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{3} + \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{15925}{128} \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{9 \, {\left(238455 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{9} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 149045 \, \sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{8} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 697600 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 719040 \, \sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 4150566 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 2707250 \, \sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 6756120 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 4557000 \, \sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 3563595 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 2833425 \, \sqrt{35} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{320 \, {\left({\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{2} - 3\right)}^{5}}"," ",0,"5425/32*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)*sgn(1/(2*x + 3)) - 18543/32*sqrt(3)*log(1/2*abs(-2*sqrt(3) + 2*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + 2*sqrt(35)/(2*x + 3))/(sqrt(3) + sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)))*sgn(1/(2*x + 3)) - 15925/128*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3)*sgn(1/(2*x + 3)) + 9/320*(238455*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^9*sgn(1/(2*x + 3)) - 149045*sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^8*sgn(1/(2*x + 3)) - 697600*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^7*sgn(1/(2*x + 3)) + 719040*sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^6*sgn(1/(2*x + 3)) + 4150566*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^5*sgn(1/(2*x + 3)) - 2707250*sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^4*sgn(1/(2*x + 3)) - 6756120*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^3*sgn(1/(2*x + 3)) + 4557000*sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^2*sgn(1/(2*x + 3)) + 3563595*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))*sgn(1/(2*x + 3)) - 2833425*sqrt(35)*sgn(1/(2*x + 3)))/((sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^2 - 3)^5","B",0
1388,1,230,0,0.289639," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^3,x, algorithm=""giac"")","-\frac{1}{32} \, {\left(3 \, {\left({\left(3 \, x - 38\right)} x + 225\right)} x - 4177\right)} \sqrt{3 \, x^{2} + 2} + \frac{43995}{128} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{12885}{128} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{35 \, {\left(11472 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 25829 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 57912 \, \sqrt{3} x + 8984 \, \sqrt{3} + 57912 \, \sqrt{3 \, x^{2} + 2}\right)}}{256 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"-1/32*(3*((3*x - 38)*x + 225)*x - 4177)*sqrt(3*x^2 + 2) + 43995/128*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 12885/128*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 35/256*(11472*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 25829*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 57912*sqrt(3)*x + 8984*sqrt(3) + 57912*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","B",0
1389,1,275,0,0.365145," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^4,x, algorithm=""giac"")","-\frac{1}{32} \, {\left(3 \, {\left(2 \, x - 33\right)} x + 973\right)} \sqrt{3 \, x^{2} + 2} - \frac{1785}{16} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{3657}{112} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{\sqrt{3} {\left(40667 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 589140 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 467730 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 1939920 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 585700 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 166304\right)}}{128 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{3}}"," ",0,"-1/32*(3*(2*x - 33)*x + 973)*sqrt(3*x^2 + 2) - 1785/16*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 3657/112*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 1/128*sqrt(3)*(40667*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 589140*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 467730*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 1939920*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 585700*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 166304)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^3","B",0
1390,1,440,0,0.822877," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^5,x, algorithm=""giac"")","-\frac{188379}{31360} \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{2625}{128} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{35}}{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{3} + \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1}{10752} \, {\left(\frac{7 \, {\left(\frac{35 \, {\left(\frac{1365 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 2129 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} + 57681 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} - 242979 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)} \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} - \frac{9 \, {\left(256 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 93 \, \sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 582 \, {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 225 \, \sqrt{35} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{64 \, {\left({\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)}^{2} - 3\right)}^{2}}"," ",0,"-188379/31360*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)*sgn(1/(2*x + 3)) + 2625/128*sqrt(3)*log(1/2*abs(-2*sqrt(3) + 2*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + 2*sqrt(35)/(2*x + 3))/(sqrt(3) + sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)))*sgn(1/(2*x + 3)) - 1/10752*(7*(35*(1365*sgn(1/(2*x + 3))/(2*x + 3) - 2129*sgn(1/(2*x + 3)))/(2*x + 3) + 57681*sgn(1/(2*x + 3)))/(2*x + 3) - 242979*sgn(1/(2*x + 3)))*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) - 9/64*(256*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^3*sgn(1/(2*x + 3)) - 93*sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^2*sgn(1/(2*x + 3)) - 582*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))*sgn(1/(2*x + 3)) + 225*sqrt(35)*sgn(1/(2*x + 3)))/((sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3))^2 - 3)^2","B",0
1391,1,355,0,0.324499," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^6,x, algorithm=""giac"")","-\frac{63}{32} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{789723}{1372000} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{9}{64} \, \sqrt{3 \, x^{2} + 2} - \frac{3 \, \sqrt{3} {\left(1034487 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 28143036 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} + 94364251 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} + 328235733 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 120044232 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} - 774358774 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 578739476 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 495467552 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 66595728 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 11086336\right)}}{156800 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{5}}"," ",0,"-63/32*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 789723/1372000*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/64*sqrt(3*x^2 + 2) - 3/156800*sqrt(3)*(1034487*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 28143036*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 + 94364251*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 + 328235733*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 120044232*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 774358774*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 578739476*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 495467552*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 66595728*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 11086336)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^5","B",0
1392,1,389,0,0.340318," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^7,x, algorithm=""giac"")","\frac{9}{128} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{159759}{7683200} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{3 \, \sqrt{3} {\left(566976 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} + 16427322 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} + 70792520 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 421378065 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} + 244013814 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} - 879808433 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 512612604 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 2079633300 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} - 831934400 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 500387712 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 51770496 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} + 7768192\right)}}{878080 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{6}}"," ",0,"9/128*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 159759/7683200*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 3/878080*sqrt(3)*(566976*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 + 16427322*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 + 70792520*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 421378065*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 + 244013814*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 879808433*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 512612604*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 2079633300*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 - 831934400*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 500387712*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 51770496*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) + 7768192)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^6","B",0
1393,1,408,0,0.315720," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^8,x, algorithm=""giac"")","\frac{1107}{21008750} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{9 \, {\left(908247 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{13} + 3755004 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{12} + 52905908 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} + 114259794 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} + 422075810 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} - 16674486 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} - 1093657086 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} - 205745364 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} + 1886581864 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} - 1023977040 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 660654976 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 94952448 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 9114816 \, \sqrt{3} x - 1555968 \, \sqrt{3} + 9114816 \, \sqrt{3 \, x^{2} + 2}\right)}}{38416000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{7}}"," ",0,"1107/21008750*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/38416000*(908247*(sqrt(3)*x - sqrt(3*x^2 + 2))^13 + 3755004*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^12 + 52905908*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 + 114259794*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 + 422075810*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 - 16674486*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 - 1093657086*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 205745364*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 + 1886581864*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 1023977040*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 660654976*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 94952448*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 9114816*sqrt(3)*x - 1555968*sqrt(3) + 9114816*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^7","B",0
1394,1,457,0,0.327944," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^9,x, algorithm=""giac"")","\frac{18873}{1470612500} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{9 \, \sqrt{3} {\left(178944 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{15} + 138131220 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{14} + 30787400 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{13} + 573375810 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{12} - 3328877720 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} - 8681082564 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} - 13787031160 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 1566458475 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} - 28541438480 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} + 30582301680 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 23140527424 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} - 12885596640 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 1726278400 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 9101541120 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 39843840 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 1411584\right)}}{10756480000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{8}}"," ",0,"18873/1470612500*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/10756480000*sqrt(3)*(178944*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^15 + 138131220*(sqrt(3)*x - sqrt(3*x^2 + 2))^14 + 30787400*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^13 + 573375810*(sqrt(3)*x - sqrt(3*x^2 + 2))^12 - 3328877720*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 - 8681082564*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 - 13787031160*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 1566458475*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 - 28541438480*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 + 30582301680*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 23140527424*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 12885596640*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 1726278400*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 9101541120*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 39843840*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 1411584)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^8","B",0
1395,1,502,0,0.306368," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^10,x, algorithm=""giac"")","\frac{76869}{25735718750} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{9 \, \sqrt{3} {\left(364416 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{17} + 27877824 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{16} + 1042205258 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{15} - 956098170 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{14} + 1003625490 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{13} - 85987901496 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{12} - 60468401868 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} - 331045664193 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} - 22913148915 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} - 544736640510 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} + 284856270864 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} - 908850124224 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} + 90616216992 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} - 115517223360 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} - 52895204480 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 565618176 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 140708352 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 17333248\right)}}{94119200000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{9}}"," ",0,"76869/25735718750*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/94119200000*sqrt(3)*(364416*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^17 + 27877824*(sqrt(3)*x - sqrt(3*x^2 + 2))^16 + 1042205258*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^15 - 956098170*(sqrt(3)*x - sqrt(3*x^2 + 2))^14 + 1003625490*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^13 - 85987901496*(sqrt(3)*x - sqrt(3*x^2 + 2))^12 - 60468401868*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 - 331045664193*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 - 22913148915*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 - 544736640510*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 + 284856270864*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 908850124224*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 + 90616216992*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 115517223360*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 - 52895204480*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 565618176*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 140708352*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 17333248)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^9","B",0
1396,1,547,0,0.530200," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^11,x, algorithm=""giac"")","\frac{5931873}{9007501562500} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{9 \, \sqrt{3} {\left(56242944 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{19} + 4808771712 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{18} + 60161202432 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{17} + 2449600006086 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{16} + 650003734476 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{15} + 11324343251586 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{14} - 43249498138224 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{13} - 114750161469717 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{12} - 263561308381422 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{11} - 64560900263031 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{10} - 173527579922724 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 409007369125548 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} - 812515292998272 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} + 775661489485344 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} - 309262645005696 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 53888888658816 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} - 21200045958144 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 6293205518848 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 348990277632 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} + 25185777664\right)}}{65883440000000 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{10}}"," ",0,"5931873/9007501562500*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/65883440000000*sqrt(3)*(56242944*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^19 + 4808771712*(sqrt(3)*x - sqrt(3*x^2 + 2))^18 + 60161202432*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^17 + 2449600006086*(sqrt(3)*x - sqrt(3*x^2 + 2))^16 + 650003734476*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^15 + 11324343251586*(sqrt(3)*x - sqrt(3*x^2 + 2))^14 - 43249498138224*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^13 - 114750161469717*(sqrt(3)*x - sqrt(3*x^2 + 2))^12 - 263561308381422*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 - 64560900263031*(sqrt(3)*x - sqrt(3*x^2 + 2))^10 - 173527579922724*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 409007369125548*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 - 812515292998272*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 + 775661489485344*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 - 309262645005696*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 53888888658816*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 - 21200045958144*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 6293205518848*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 348990277632*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) + 25185777664)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^10","B",0
1397,1,53,0,0.194322," ","integrate((5-x)*(3+2*x)^4/(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{405} \, {\left(12 \, {\left({\left(9 \, {\left(4 \, x + 5\right)} x - 1022\right)} x - 4905\right)} x - 118513\right)} \sqrt{3 \, x^{2} + 2} - \frac{343}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/405*(12*((9*(4*x + 5)*x - 1022)*x - 4905)*x - 118513)*sqrt(3*x^2 + 2) - 343/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1398,1,49,0,0.246738," ","integrate((5-x)*(3+2*x)^3/(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{27} \, {\left(3 \, {\left(2 \, {\left(3 \, x - 2\right)} x - 195\right)} x - 2171\right)} \sqrt{3 \, x^{2} + 2} - \frac{275}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/27*(3*(2*(3*x - 2)*x - 195)*x - 2171)*sqrt(3*x^2 + 2) - 275/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1399,1,42,0,0.176454," ","integrate((5-x)*(3+2*x)^2/(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{27} \, {\left(12 \, {\left(x - 3\right)} x - 475\right)} \sqrt{3 \, x^{2} + 2} - \frac{127}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/27*(12*(x - 3)*x - 475)*sqrt(3*x^2 + 2) - 127/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1400,1,37,0,0.168751," ","integrate((5-x)*(3+2*x)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3 \, x^{2} + 2} {\left(x - 7\right)} - \frac{47}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"-1/3*sqrt(3*x^2 + 2)*(x - 7) - 47/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
1401,1,34,0,0.190815," ","integrate((5-x)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{5}{3} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{1}{3} \, \sqrt{3 \, x^{2} + 2}"," ",0,"-5/3*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/3*sqrt(3*x^2 + 2)","A",0
1402,1,90,0,0.247675," ","integrate((5-x)/(3+2*x)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{13}{70} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right)"," ",0,"1/6*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 13/70*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2)))","B",0
1403,1,125,0,0.271144," ","integrate((5-x)/(3+2*x)^2/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{2450} \, \sqrt{35} {\left(13 \, \sqrt{35} \sqrt{3} + 82 \, \log\left(\sqrt{35} \sqrt{3} - 9\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{41 \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right)}{1225 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} - \frac{13 \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3}}{70 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"1/2450*sqrt(35)*(13*sqrt(35)*sqrt(3) + 82*log(sqrt(35)*sqrt(3) - 9))*sgn(1/(2*x + 3)) - 41/1225*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)/sgn(1/(2*x + 3)) - 13/70*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3)/sgn(1/(2*x + 3))","B",0
1404,1,183,0,0.294626," ","integrate((5-x)/(3+2*x)^3/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{291}{42875} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{1164 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 6463 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 17904 \, \sqrt{3} x + 2248 \, \sqrt{3} + 17904 \, \sqrt{3 \, x^{2} + 2}}{4900 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"291/42875*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 1/4900*(1164*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 6463*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 17904*sqrt(3)*x + 2248*sqrt(3) + 17904*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","B",0
1405,1,232,0,0.319324," ","integrate((5-x)/(3+2*x)^4/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{57}{60025} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{\sqrt{3} {\left(38 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 855 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 2250 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 13290 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3448 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 800\right)}}{3430 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{3}}"," ",0,"57/60025*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 1/3430*sqrt(3)*(38*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 855*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 2250*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 13290*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3448*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 800)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^3","B",0
1406,1,191,0,0.255088," ","integrate((5-x)/(3+2*x)^5/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{12005000} \, \sqrt{35} {\left(991 \, \sqrt{35} \sqrt{3} - 216 \, \log\left(\sqrt{35} \sqrt{3} - 9\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1}{1029000} \, {\left(\frac{35 \, {\left(\frac{7 \, {\left(\frac{97}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{195}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} + \frac{261}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} + \frac{2973}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)} \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{27 \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right)}{1500625 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"1/12005000*sqrt(35)*(991*sqrt(35)*sqrt(3) - 216*log(sqrt(35)*sqrt(3) - 9))*sgn(1/(2*x + 3)) - 1/1029000*(35*(7*(97/sgn(1/(2*x + 3)) + 195/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) + 261/sgn(1/(2*x + 3)))/(2*x + 3) + 2973/sgn(1/(2*x + 3)))*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + 27/1500625*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)/sgn(1/(2*x + 3))","A",0
1407,1,322,0,0.271467," ","integrate((5-x)/(3+2*x)^6/(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{19737}{262609375} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{3 \, \sqrt{3} {\left(8772 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{9} + 355266 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{8} + 1773406 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{7} + 11098773 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{6} + 2315313 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 49794206 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} - 25535944 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 16740688 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 1744032 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} + 213824\right)}}{30012500 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{5}}"," ",0,"-19737/262609375*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 3/30012500*sqrt(3)*(8772*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 + 355266*(sqrt(3)*x - sqrt(3*x^2 + 2))^8 + 1773406*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 + 11098773*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 + 2315313*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 49794206*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 - 25535944*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 16740688*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 1744032*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) + 213824)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^5","B",0
1408,1,54,0,0.188475," ","integrate((5-x)*(3+2*x)^4/(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{880}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{3 \, {\left(16 \, {\left(3 \, {\left(2 \, x + 3\right)} x - 313\right)} x + 4905\right)} x + 33914}{162 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"-880/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/162*(3*(16*(3*(2*x + 3)*x - 313)*x + 4905)*x + 33914)/sqrt(3*x^2 + 2)","A",0
1409,1,47,0,0.180542," ","integrate((5-x)*(3+2*x)^3/(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{134}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{3 \, {\left(8 \, {\left(x - 1\right)} x - 137\right)} x + 1426}{18 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"-134/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/18*(3*(8*(x - 1)*x - 137)*x + 1426)/sqrt(3*x^2 + 2)","A",0
1410,1,44,0,0.172374," ","integrate((5-x)*(3+2*x)^2/(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{8}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{3 \, {\left(8 \, x - 119\right)} x + 338}{18 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"-8/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/18*(3*(8*x - 119)*x + 338)/sqrt(3*x^2 + 2)","A",0
1411,1,39,0,0.180964," ","integrate((5-x)*(3+2*x)/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{7 \, {\left(7 \, x - 2\right)}}{6 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"2/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 7/6*(7*x - 2)/sqrt(3*x^2 + 2)","A",0
1412,1,16,0,0.166929," ","integrate((5-x)/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{15 \, x + 2}{6 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"1/6*(15*x + 2)/sqrt(3*x^2 + 2)","A",0
1413,1,84,0,0.209059," ","integrate((5-x)/(3+2*x)/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{26}{1225} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{41 \, x + 26}{70 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"26/1225*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/70*(41*x + 26)/sqrt(3*x^2 + 2)","A",0
1414,1,168,0,0.266434," ","integrate((5-x)/(3+2*x)^2/(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{85750} \, \sqrt{35} {\left(19 \, \sqrt{35} \sqrt{3} - 1264 \, \log\left(\sqrt{35} \sqrt{3} - 9\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{\frac{\frac{1093}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} - \frac{1820}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} + \frac{57}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2450 \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3}} - \frac{632 \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right)}{42875 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"-1/85750*sqrt(35)*(19*sqrt(35)*sqrt(3) - 1264*log(sqrt(35)*sqrt(3) - 9))*sgn(1/(2*x + 3)) + 1/2450*((1093/sgn(1/(2*x + 3)) - 1820/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) + 57/sgn(1/(2*x + 3)))/sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) - 632/42875*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)/sgn(1/(2*x + 3))","B",0
1415,1,199,0,0.254789," ","integrate((5-x)/(3+2*x)^3/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{1962}{300125} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{3 \, {\left(157 \, x - 1478\right)}}{85750 \, \sqrt{3 \, x^{2} + 2}} - \frac{768 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 2461 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 6168 \, \sqrt{3} x + 856 \, \sqrt{3} + 6168 \, \sqrt{3 \, x^{2} + 2}}{6125 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"1962/300125*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 3/85750*(157*x - 1478)/sqrt(3*x^2 + 2) - 1/6125*(768*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 2461*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 6168*sqrt(3)*x + 856*sqrt(3) + 6168*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","B",0
1416,1,248,0,0.288126," ","integrate((5-x)/(3+2*x)^4/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{3312}{1500625} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) - \frac{3 \, {\left(10281 \, x - 12674\right)}}{3001250 \, \sqrt{3 \, x^{2} + 2}} - \frac{2 \, \sqrt{3} {\left(12983 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 253320 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 298170 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 1481160 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 425140 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 106016\right)}}{1500625 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{3}}"," ",0,"3312/1500625*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 3/3001250*(10281*x - 12674)/sqrt(3*x^2 + 2) - 2/1500625*sqrt(3)*(12983*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 253320*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 298170*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 1481160*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 425140*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 106016)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^3","B",0
1417,1,234,0,0.293324," ","integrate((5-x)/(3+2*x)^5/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{2}{52521875} \, \sqrt{35} {\left(3736 \, \sqrt{35} \sqrt{3} + 15039 \, \log\left(\sqrt{35} \sqrt{3} - 9\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{\frac{\frac{35 \, {\left(\frac{7 \, {\left(\frac{5 \, {\left(\frac{913}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{1365}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} + \frac{2646}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} + \frac{12858}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} - \frac{583956}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} + \frac{134496}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{9003750 \, \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3}} - \frac{30078 \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right)}{52521875 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"2/52521875*sqrt(35)*(3736*sqrt(35)*sqrt(3) + 15039*log(sqrt(35)*sqrt(3) - 9))*sgn(1/(2*x + 3)) - 1/9003750*((35*(7*(5*(913/sgn(1/(2*x + 3)) + 1365/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) + 2646/sgn(1/(2*x + 3)))/(2*x + 3) + 12858/sgn(1/(2*x + 3)))/(2*x + 3) - 583956/sgn(1/(2*x + 3)))/(2*x + 3) + 134496/sgn(1/(2*x + 3)))/sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) - 30078/52521875*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)/sgn(1/(2*x + 3))","A",0
1418,1,60,0,0.183948," ","integrate((5-x)*(3+2*x)^6/(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{20720}{81} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{9 \, {\left({\left({\left(96 \, {\left(4 \, {\left(x + 6\right)} x - 151\right)} x - 125111\right)} x + 262664\right)} x - 15535\right)} x + 1798610}{486 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"-20720/81*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/486*(9*(((96*(4*(x + 6)*x - 151)*x - 125111)*x + 262664)*x - 15535)*x + 1798610)/(3*x^2 + 2)^(3/2)","A",0
1419,1,55,0,0.246118," ","integrate((5-x)*(3+2*x)^5/(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1600}{81} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{3 \, {\left({\left({\left(288 \, {\left(x + 5\right)} x - 61315\right)} x + 49200\right)} x - 26405\right)} x + 134126}{162 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"-1600/81*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/162*(3*(((288*(x + 5)*x - 61315)*x + 49200)*x - 26405)*x + 134126)/(3*x^2 + 2)^(3/2)","A",0
1420,1,52,0,0.181754," ","integrate((5-x)*(3+2*x)^4/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{16}{27} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{9 \, {\left({\left({\left(96 \, x - 6365\right)} x + 1840\right)} x - 3709\right)} x + 25342}{162 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"16/27*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/162*(9*(((96*x - 6365)*x + 1840)*x - 3709)*x + 25342)/(3*x^2 + 2)^(3/2)","A",0
1421,1,48,0,0.202594," ","integrate((5-x)*(3+2*x)^3/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{8}{27} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{3 \, {\left({\left(1657 \, x - 24\right)} x + 1247\right)} x - 1490}{54 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"8/27*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 1/54*(3*((1657*x - 24)*x + 1247)*x - 1490)/(3*x^2 + 2)^(3/2)","A",0
1422,1,25,0,0.179628," ","integrate((5-x)*(3+2*x)^2/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{9 \, {\left({\left(143 \, x + 8\right)} x + 135\right)} x - 274}{54 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"1/54*(9*((143*x + 8)*x + 135)*x - 274)/(3*x^2 + 2)^(3/2)","A",0
1423,1,23,0,0.182639," ","integrate((5-x)*(3+2*x)/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{3 \, {\left(43 \, x^{2} + 45\right)} x - 14}{18 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"1/18*(3*(43*x^2 + 45)*x - 14)/(3*x^2 + 2)^(3/2)","A",0
1424,1,21,0,0.182823," ","integrate((5-x)/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{45 \, {\left(x^{2} + 1\right)} x + 2}{18 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"1/18*(45*(x^2 + 1)*x + 2)/(3*x^2 + 2)^(3/2)","A",0
1425,1,93,0,0.213183," ","integrate((5-x)/(3+2*x)/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{104}{42875} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{3 \, {\left({\left(2137 \, x + 312\right)} x + 1903\right)} x + 1534}{7350 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"104/42875*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/7350*(3*((2137*x + 312)*x + 1903)*x + 1534)/(3*x^2 + 2)^(3/2)","A",0
1426,1,233,0,0.307367," ","integrate((5-x)/(3+2*x)^2/(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{360150} \, \sqrt{35} {\left(277 \, \sqrt{35} \sqrt{3} - 1056 \, \log\left(\sqrt{35} \sqrt{3} - 9\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{176 \, \sqrt{35} \log\left(\sqrt{35} {\left(\sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{35}}{2 \, x + 3}\right)} - 9\right)}{60025 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{\frac{\frac{\frac{7 \, {\left(\frac{4813}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{4368}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} - \frac{53523}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} + \frac{19269}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} - \frac{2493}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{10290 \, {\left(\frac{18}{2 \, x + 3} - \frac{35}{{\left(2 \, x + 3\right)}^{2}} - 3\right)} \sqrt{-\frac{18}{2 \, x + 3} + \frac{35}{{\left(2 \, x + 3\right)}^{2}} + 3}}"," ",0,"-1/360150*sqrt(35)*(277*sqrt(35)*sqrt(3) - 1056*log(sqrt(35)*sqrt(3) - 9))*sgn(1/(2*x + 3)) - 176/60025*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3) + sqrt(35)/(2*x + 3)) - 9)/sgn(1/(2*x + 3)) + 1/10290*(((7*(4813/sgn(1/(2*x + 3)) + 4368/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) - 53523/sgn(1/(2*x + 3)))/(2*x + 3) + 19269/sgn(1/(2*x + 3)))/(2*x + 3) - 2493/sgn(1/(2*x + 3)))/((18/(2*x + 3) - 35/(2*x + 3)^2 - 3)*sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 + 3))","B",0
1427,1,208,0,0.274790," ","integrate((5-x)/(3+2*x)^3/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{3072}{1500625} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{3 \, {\left({\left(59203 \, x + 69168\right)} x + 37637\right)} x + 190066}{3001250 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{4 \, {\left(9588 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} + 27991 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 68448 \, \sqrt{3} x + 9736 \, \sqrt{3} + 68448 \, \sqrt{3 \, x^{2} + 2}\right)}}{1500625 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"3072/1500625*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/3001250*(3*((59203*x + 69168)*x + 37637)*x + 190066)/(3*x^2 + 2)^(3/2) - 4/1500625*(9588*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 + 27991*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 68448*sqrt(3)*x + 9736*sqrt(3) + 68448*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","A",0
1428,1,257,0,0.466892," ","integrate((5-x)/(3+2*x)^4/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{55344}{52521875} \, \sqrt{35} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{9 \, {\left({\left(49879 \, x + 344464\right)} x - 6729\right)} x + 2510374}{105043750 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{8 \, \sqrt{3} {\left(37652 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{5} + 695865 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{4} + 729630 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 3472470 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 1016800 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 259424\right)}}{52521875 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 3 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{3}}"," ",0,"55344/52521875*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/105043750*(9*((49879*x + 344464)*x - 6729)*x + 2510374)/(3*x^2 + 2)^(3/2) - 8/52521875*sqrt(3)*(37652*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 695865*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 + 729630*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 3472470*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 1016800*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 259424)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^3","B",0
1429,1,580,0,0.347486," ","integrate((B*x+A)*(e*x+d)^(3/2)*(c*x^2+a),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a d^{2} e^{\left(-1\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c d^{2} e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c d^{2} e^{\left(-3\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a d e^{\left(-1\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A c d e^{\left(-2\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B c d e^{\left(-3\right)} + 3465 \, \sqrt{x e + d} A a d^{2} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a d + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a e^{\left(-1\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c e^{\left(-2\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c e^{\left(-3\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*d^2*e^(-1) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*d^2*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*d^2*e^(-3) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*d*e^(-1) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*c*d*e^(-2) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*c*d*e^(-3) + 3465*sqrt(x*e + d)*A*a*d^2 + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*d + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*e^(-1) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c*e^(-2) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c*e^(-3) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a)*e^(-1)","B",0
1430,1,327,0,0.164297," ","integrate((B*x+A)*(c*x^2+a)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a d e^{\left(-1\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c d e^{\left(-2\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c d e^{\left(-3\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a e^{\left(-1\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A c e^{\left(-2\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B c e^{\left(-3\right)} + 315 \, \sqrt{x e + d} A a d + 105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*d*e^(-1) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*d*e^(-2) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*d*e^(-3) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*e^(-1) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*c*e^(-2) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*c*e^(-3) + 315*sqrt(x*e + d)*A*a*d + 105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a)*e^(-1)","B",0
1431,1,138,0,0.195756," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a e^{\left(-1\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A c e^{\left(-2\right)} + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B c e^{\left(-3\right)} + 105 \, \sqrt{x e + d} A a\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*e^(-1) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*c*e^(-2) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*c*e^(-3) + 105*sqrt(x*e + d)*A*a)*e^(-1)","A",0
1432,1,135,0,0.170164," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c e^{16} - 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B c d e^{16} + 45 \, \sqrt{x e + d} B c d^{2} e^{16} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c e^{17} - 30 \, \sqrt{x e + d} A c d e^{17} + 15 \, \sqrt{x e + d} B a e^{18}\right)} e^{\left(-20\right)} + \frac{2 \, {\left(B c d^{3} - A c d^{2} e + B a d e^{2} - A a e^{3}\right)} e^{\left(-4\right)}}{\sqrt{x e + d}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*c*e^16 - 15*(x*e + d)^(3/2)*B*c*d*e^16 + 45*sqrt(x*e + d)*B*c*d^2*e^16 + 5*(x*e + d)^(3/2)*A*c*e^17 - 30*sqrt(x*e + d)*A*c*d*e^17 + 15*sqrt(x*e + d)*B*a*e^18)*e^(-20) + 2*(B*c*d^3 - A*c*d^2*e + B*a*d*e^2 - A*a*e^3)*e^(-4)/sqrt(x*e + d)","A",0
1433,1,126,0,0.172554," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B c e^{8} - 9 \, \sqrt{x e + d} B c d e^{8} + 3 \, \sqrt{x e + d} A c e^{9}\right)} e^{\left(-12\right)} - \frac{2 \, {\left(9 \, {\left(x e + d\right)} B c d^{2} - B c d^{3} - 6 \, {\left(x e + d\right)} A c d e + A c d^{2} e + 3 \, {\left(x e + d\right)} B a e^{2} - B a d e^{2} + A a e^{3}\right)} e^{\left(-4\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*B*c*e^8 - 9*sqrt(x*e + d)*B*c*d*e^8 + 3*sqrt(x*e + d)*A*c*e^9)*e^(-12) - 2/3*(9*(x*e + d)*B*c*d^2 - B*c*d^3 - 6*(x*e + d)*A*c*d*e + A*c*d^2*e + 3*(x*e + d)*B*a*e^2 - B*a*d*e^2 + A*a*e^3)*e^(-4)/(x*e + d)^(3/2)","A",0
1434,1,122,0,0.172898," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(7/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} B c e^{\left(-4\right)} + \frac{2 \, {\left(45 \, {\left(x e + d\right)}^{2} B c d - 15 \, {\left(x e + d\right)} B c d^{2} + 3 \, B c d^{3} - 15 \, {\left(x e + d\right)}^{2} A c e + 10 \, {\left(x e + d\right)} A c d e - 3 \, A c d^{2} e - 5 \, {\left(x e + d\right)} B a e^{2} + 3 \, B a d e^{2} - 3 \, A a e^{3}\right)} e^{\left(-4\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2*sqrt(x*e + d)*B*c*e^(-4) + 2/15*(45*(x*e + d)^2*B*c*d - 15*(x*e + d)*B*c*d^2 + 3*B*c*d^3 - 15*(x*e + d)^2*A*c*e + 10*(x*e + d)*A*c*d*e - 3*A*c*d^2*e - 5*(x*e + d)*B*a*e^2 + 3*B*a*d*e^2 - 3*A*a*e^3)*e^(-4)/(x*e + d)^(5/2)","A",0
1435,1,670,0,0.189989," ","integrate((B*x+A)*(c*x^2+a)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{2} d e^{\left(-1\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a c d e^{\left(-2\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a c d e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c^{2} d e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c^{2} d e^{\left(-5\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} e^{\left(-1\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a c e^{\left(-2\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a c e^{\left(-3\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A c^{2} e^{\left(-4\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B c^{2} e^{\left(-5\right)} + 45045 \, \sqrt{x e + d} A a^{2} d + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^2*d*e^(-1) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*c*d*e^(-2) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*c*d*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c^2*d*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c^2*d*e^(-5) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*e^(-1) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*c*e^(-2) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*c*e^(-3) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*c^2*e^(-4) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*c^2*e^(-5) + 45045*sqrt(x*e + d)*A*a^2*d + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2)*e^(-1)","B",0
1436,1,295,0,0.176866," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{2} e^{\left(-1\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a c e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a c e^{\left(-3\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A c^{2} e^{\left(-4\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B c^{2} e^{\left(-5\right)} + 3465 \, \sqrt{x e + d} A a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^2*e^(-1) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*c*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*c*e^(-3) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*c^2*e^(-4) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*c^2*e^(-5) + 3465*sqrt(x*e + d)*A*a^2)*e^(-1)","A",0
1437,1,331,0,0.193308," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} B c^{2} e^{48} - 225 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{2} d e^{48} + 630 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{2} d^{2} e^{48} - 1050 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{2} d^{3} e^{48} + 1575 \, \sqrt{x e + d} B c^{2} d^{4} e^{48} + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{2} e^{49} - 252 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{2} d e^{49} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d^{2} e^{49} - 1260 \, \sqrt{x e + d} A c^{2} d^{3} e^{49} + 126 \, {\left(x e + d\right)}^{\frac{5}{2}} B a c e^{50} - 630 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c d e^{50} + 1890 \, \sqrt{x e + d} B a c d^{2} e^{50} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} A a c e^{51} - 1260 \, \sqrt{x e + d} A a c d e^{51} + 315 \, \sqrt{x e + d} B a^{2} e^{52}\right)} e^{\left(-54\right)} + \frac{2 \, {\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)} e^{\left(-6\right)}}{\sqrt{x e + d}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*B*c^2*e^48 - 225*(x*e + d)^(7/2)*B*c^2*d*e^48 + 630*(x*e + d)^(5/2)*B*c^2*d^2*e^48 - 1050*(x*e + d)^(3/2)*B*c^2*d^3*e^48 + 1575*sqrt(x*e + d)*B*c^2*d^4*e^48 + 45*(x*e + d)^(7/2)*A*c^2*e^49 - 252*(x*e + d)^(5/2)*A*c^2*d*e^49 + 630*(x*e + d)^(3/2)*A*c^2*d^2*e^49 - 1260*sqrt(x*e + d)*A*c^2*d^3*e^49 + 126*(x*e + d)^(5/2)*B*a*c*e^50 - 630*(x*e + d)^(3/2)*B*a*c*d*e^50 + 1890*sqrt(x*e + d)*B*a*c*d^2*e^50 + 210*(x*e + d)^(3/2)*A*a*c*e^51 - 1260*sqrt(x*e + d)*A*a*c*d*e^51 + 315*sqrt(x*e + d)*B*a^2*e^52)*e^(-54) + 2*(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)*e^(-6)/sqrt(x*e + d)","A",0
1438,1,319,0,0.274920," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{2} e^{36} - 105 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{2} d e^{36} + 350 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{2} d^{2} e^{36} - 1050 \, \sqrt{x e + d} B c^{2} d^{3} e^{36} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{2} e^{37} - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d e^{37} + 630 \, \sqrt{x e + d} A c^{2} d^{2} e^{37} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c e^{38} - 630 \, \sqrt{x e + d} B a c d e^{38} + 210 \, \sqrt{x e + d} A a c e^{39}\right)} e^{\left(-42\right)} - \frac{2 \, {\left(15 \, {\left(x e + d\right)} B c^{2} d^{4} - B c^{2} d^{5} - 12 \, {\left(x e + d\right)} A c^{2} d^{3} e + A c^{2} d^{4} e + 18 \, {\left(x e + d\right)} B a c d^{2} e^{2} - 2 \, B a c d^{3} e^{2} - 12 \, {\left(x e + d\right)} A a c d e^{3} + 2 \, A a c d^{2} e^{3} + 3 \, {\left(x e + d\right)} B a^{2} e^{4} - B a^{2} d e^{4} + A a^{2} e^{5}\right)} e^{\left(-6\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/105*(15*(x*e + d)^(7/2)*B*c^2*e^36 - 105*(x*e + d)^(5/2)*B*c^2*d*e^36 + 350*(x*e + d)^(3/2)*B*c^2*d^2*e^36 - 1050*sqrt(x*e + d)*B*c^2*d^3*e^36 + 21*(x*e + d)^(5/2)*A*c^2*e^37 - 140*(x*e + d)^(3/2)*A*c^2*d*e^37 + 630*sqrt(x*e + d)*A*c^2*d^2*e^37 + 70*(x*e + d)^(3/2)*B*a*c*e^38 - 630*sqrt(x*e + d)*B*a*c*d*e^38 + 210*sqrt(x*e + d)*A*a*c*e^39)*e^(-42) - 2/3*(15*(x*e + d)*B*c^2*d^4 - B*c^2*d^5 - 12*(x*e + d)*A*c^2*d^3*e + A*c^2*d^4*e + 18*(x*e + d)*B*a*c*d^2*e^2 - 2*B*a*c*d^3*e^2 - 12*(x*e + d)*A*a*c*d*e^3 + 2*A*a*c*d^2*e^3 + 3*(x*e + d)*B*a^2*e^4 - B*a^2*d*e^4 + A*a^2*e^5)*e^(-6)/(x*e + d)^(3/2)","A",0
1439,1,319,0,0.206147," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{2} e^{24} - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{2} d e^{24} + 150 \, \sqrt{x e + d} B c^{2} d^{2} e^{24} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} e^{25} - 60 \, \sqrt{x e + d} A c^{2} d e^{25} + 30 \, \sqrt{x e + d} B a c e^{26}\right)} e^{\left(-30\right)} + \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} B c^{2} d^{3} - 25 \, {\left(x e + d\right)} B c^{2} d^{4} + 3 \, B c^{2} d^{5} - 90 \, {\left(x e + d\right)}^{2} A c^{2} d^{2} e + 20 \, {\left(x e + d\right)} A c^{2} d^{3} e - 3 \, A c^{2} d^{4} e + 90 \, {\left(x e + d\right)}^{2} B a c d e^{2} - 30 \, {\left(x e + d\right)} B a c d^{2} e^{2} + 6 \, B a c d^{3} e^{2} - 30 \, {\left(x e + d\right)}^{2} A a c e^{3} + 20 \, {\left(x e + d\right)} A a c d e^{3} - 6 \, A a c d^{2} e^{3} - 5 \, {\left(x e + d\right)} B a^{2} e^{4} + 3 \, B a^{2} d e^{4} - 3 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*c^2*e^24 - 25*(x*e + d)^(3/2)*B*c^2*d*e^24 + 150*sqrt(x*e + d)*B*c^2*d^2*e^24 + 5*(x*e + d)^(3/2)*A*c^2*e^25 - 60*sqrt(x*e + d)*A*c^2*d*e^25 + 30*sqrt(x*e + d)*B*a*c*e^26)*e^(-30) + 2/15*(150*(x*e + d)^2*B*c^2*d^3 - 25*(x*e + d)*B*c^2*d^4 + 3*B*c^2*d^5 - 90*(x*e + d)^2*A*c^2*d^2*e + 20*(x*e + d)*A*c^2*d^3*e - 3*A*c^2*d^4*e + 90*(x*e + d)^2*B*a*c*d*e^2 - 30*(x*e + d)*B*a*c*d^2*e^2 + 6*B*a*c*d^3*e^2 - 30*(x*e + d)^2*A*a*c*e^3 + 20*(x*e + d)*A*a*c*d*e^3 - 6*A*a*c*d^2*e^3 - 5*(x*e + d)*B*a^2*e^4 + 3*B*a^2*d*e^4 - 3*A*a^2*e^5)*e^(-6)/(x*e + d)^(5/2)","A",0
1440,1,316,0,0.223394," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(9/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B c^{2} e^{12} - 15 \, \sqrt{x e + d} B c^{2} d e^{12} + 3 \, \sqrt{x e + d} A c^{2} e^{13}\right)} e^{\left(-18\right)} - \frac{2 \, {\left(1050 \, {\left(x e + d\right)}^{3} B c^{2} d^{2} - 350 \, {\left(x e + d\right)}^{2} B c^{2} d^{3} + 105 \, {\left(x e + d\right)} B c^{2} d^{4} - 15 \, B c^{2} d^{5} - 420 \, {\left(x e + d\right)}^{3} A c^{2} d e + 210 \, {\left(x e + d\right)}^{2} A c^{2} d^{2} e - 84 \, {\left(x e + d\right)} A c^{2} d^{3} e + 15 \, A c^{2} d^{4} e + 210 \, {\left(x e + d\right)}^{3} B a c e^{2} - 210 \, {\left(x e + d\right)}^{2} B a c d e^{2} + 126 \, {\left(x e + d\right)} B a c d^{2} e^{2} - 30 \, B a c d^{3} e^{2} + 70 \, {\left(x e + d\right)}^{2} A a c e^{3} - 84 \, {\left(x e + d\right)} A a c d e^{3} + 30 \, A a c d^{2} e^{3} + 21 \, {\left(x e + d\right)} B a^{2} e^{4} - 15 \, B a^{2} d e^{4} + 15 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{105 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*B*c^2*e^12 - 15*sqrt(x*e + d)*B*c^2*d*e^12 + 3*sqrt(x*e + d)*A*c^2*e^13)*e^(-18) - 2/105*(1050*(x*e + d)^3*B*c^2*d^2 - 350*(x*e + d)^2*B*c^2*d^3 + 105*(x*e + d)*B*c^2*d^4 - 15*B*c^2*d^5 - 420*(x*e + d)^3*A*c^2*d*e + 210*(x*e + d)^2*A*c^2*d^2*e - 84*(x*e + d)*A*c^2*d^3*e + 15*A*c^2*d^4*e + 210*(x*e + d)^3*B*a*c*e^2 - 210*(x*e + d)^2*B*a*c*d*e^2 + 126*(x*e + d)*B*a*c*d^2*e^2 - 30*B*a*c*d^3*e^2 + 70*(x*e + d)^2*A*a*c*e^3 - 84*(x*e + d)*A*a*c*d*e^3 + 30*A*a*c*d^2*e^3 + 21*(x*e + d)*B*a^2*e^4 - 15*B*a^2*d*e^4 + 15*A*a^2*e^5)*e^(-6)/(x*e + d)^(7/2)","A",0
1441,1,504,0,0.217126," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{3} e^{\left(-1\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} c e^{\left(-2\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} c e^{\left(-3\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a c^{2} e^{\left(-4\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a c^{2} e^{\left(-5\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A c^{3} e^{\left(-6\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B c^{3} e^{\left(-7\right)} + 45045 \, \sqrt{x e + d} A a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^3*e^(-1) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*c*e^(-2) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*c*e^(-3) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*c^2*e^(-4) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*c^2*e^(-5) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*c^3*e^(-6) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*c^3*e^(-7) + 45045*sqrt(x*e + d)*A*a^3)*e^(-1)","A",0
1442,1,615,0,0.286285," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(1155 \, {\left(x e + d\right)}^{\frac{13}{2}} B c^{3} e^{96} - 9555 \, {\left(x e + d\right)}^{\frac{11}{2}} B c^{3} d e^{96} + 35035 \, {\left(x e + d\right)}^{\frac{9}{2}} B c^{3} d^{2} e^{96} - 75075 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{3} d^{3} e^{96} + 105105 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{3} d^{4} e^{96} - 105105 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{3} d^{5} e^{96} + 105105 \, \sqrt{x e + d} B c^{3} d^{6} e^{96} + 1365 \, {\left(x e + d\right)}^{\frac{11}{2}} A c^{3} e^{97} - 10010 \, {\left(x e + d\right)}^{\frac{9}{2}} A c^{3} d e^{97} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{3} d^{2} e^{97} - 60060 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{3} d^{3} e^{97} + 75075 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d^{4} e^{97} - 90090 \, \sqrt{x e + d} A c^{3} d^{5} e^{97} + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} B a c^{2} e^{98} - 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} B a c^{2} d e^{98} + 90090 \, {\left(x e + d\right)}^{\frac{5}{2}} B a c^{2} d^{2} e^{98} - 150150 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c^{2} d^{3} e^{98} + 225225 \, \sqrt{x e + d} B a c^{2} d^{4} e^{98} + 6435 \, {\left(x e + d\right)}^{\frac{7}{2}} A a c^{2} e^{99} - 36036 \, {\left(x e + d\right)}^{\frac{5}{2}} A a c^{2} d e^{99} + 90090 \, {\left(x e + d\right)}^{\frac{3}{2}} A a c^{2} d^{2} e^{99} - 180180 \, \sqrt{x e + d} A a c^{2} d^{3} e^{99} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} c e^{100} - 45045 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} c d e^{100} + 135135 \, \sqrt{x e + d} B a^{2} c d^{2} e^{100} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} c e^{101} - 90090 \, \sqrt{x e + d} A a^{2} c d e^{101} + 15015 \, \sqrt{x e + d} B a^{3} e^{102}\right)} e^{\left(-104\right)} + \frac{2 \, {\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)} e^{\left(-8\right)}}{\sqrt{x e + d}}"," ",0,"2/15015*(1155*(x*e + d)^(13/2)*B*c^3*e^96 - 9555*(x*e + d)^(11/2)*B*c^3*d*e^96 + 35035*(x*e + d)^(9/2)*B*c^3*d^2*e^96 - 75075*(x*e + d)^(7/2)*B*c^3*d^3*e^96 + 105105*(x*e + d)^(5/2)*B*c^3*d^4*e^96 - 105105*(x*e + d)^(3/2)*B*c^3*d^5*e^96 + 105105*sqrt(x*e + d)*B*c^3*d^6*e^96 + 1365*(x*e + d)^(11/2)*A*c^3*e^97 - 10010*(x*e + d)^(9/2)*A*c^3*d*e^97 + 32175*(x*e + d)^(7/2)*A*c^3*d^2*e^97 - 60060*(x*e + d)^(5/2)*A*c^3*d^3*e^97 + 75075*(x*e + d)^(3/2)*A*c^3*d^4*e^97 - 90090*sqrt(x*e + d)*A*c^3*d^5*e^97 + 5005*(x*e + d)^(9/2)*B*a*c^2*e^98 - 32175*(x*e + d)^(7/2)*B*a*c^2*d*e^98 + 90090*(x*e + d)^(5/2)*B*a*c^2*d^2*e^98 - 150150*(x*e + d)^(3/2)*B*a*c^2*d^3*e^98 + 225225*sqrt(x*e + d)*B*a*c^2*d^4*e^98 + 6435*(x*e + d)^(7/2)*A*a*c^2*e^99 - 36036*(x*e + d)^(5/2)*A*a*c^2*d*e^99 + 90090*(x*e + d)^(3/2)*A*a*c^2*d^2*e^99 - 180180*sqrt(x*e + d)*A*a*c^2*d^3*e^99 + 9009*(x*e + d)^(5/2)*B*a^2*c*e^100 - 45045*(x*e + d)^(3/2)*B*a^2*c*d*e^100 + 135135*sqrt(x*e + d)*B*a^2*c*d^2*e^100 + 15015*(x*e + d)^(3/2)*A*a^2*c*e^101 - 90090*sqrt(x*e + d)*A*a^2*c*d*e^101 + 15015*sqrt(x*e + d)*B*a^3*e^102)*e^(-104) + 2*(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)*e^(-8)/sqrt(x*e + d)","A",0
1443,1,599,0,0.232602," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(315 \, {\left(x e + d\right)}^{\frac{11}{2}} B c^{3} e^{80} - 2695 \, {\left(x e + d\right)}^{\frac{9}{2}} B c^{3} d e^{80} + 10395 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{3} d^{2} e^{80} - 24255 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{3} d^{3} e^{80} + 40425 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{3} d^{4} e^{80} - 72765 \, \sqrt{x e + d} B c^{3} d^{5} e^{80} + 385 \, {\left(x e + d\right)}^{\frac{9}{2}} A c^{3} e^{81} - 2970 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{3} d e^{81} + 10395 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{3} d^{2} e^{81} - 23100 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d^{3} e^{81} + 51975 \, \sqrt{x e + d} A c^{3} d^{4} e^{81} + 1485 \, {\left(x e + d\right)}^{\frac{7}{2}} B a c^{2} e^{82} - 10395 \, {\left(x e + d\right)}^{\frac{5}{2}} B a c^{2} d e^{82} + 34650 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c^{2} d^{2} e^{82} - 103950 \, \sqrt{x e + d} B a c^{2} d^{3} e^{82} + 2079 \, {\left(x e + d\right)}^{\frac{5}{2}} A a c^{2} e^{83} - 13860 \, {\left(x e + d\right)}^{\frac{3}{2}} A a c^{2} d e^{83} + 62370 \, \sqrt{x e + d} A a c^{2} d^{2} e^{83} + 3465 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} c e^{84} - 31185 \, \sqrt{x e + d} B a^{2} c d e^{84} + 10395 \, \sqrt{x e + d} A a^{2} c e^{85}\right)} e^{\left(-88\right)} - \frac{2 \, {\left(21 \, {\left(x e + d\right)} B c^{3} d^{6} - B c^{3} d^{7} - 18 \, {\left(x e + d\right)} A c^{3} d^{5} e + A c^{3} d^{6} e + 45 \, {\left(x e + d\right)} B a c^{2} d^{4} e^{2} - 3 \, B a c^{2} d^{5} e^{2} - 36 \, {\left(x e + d\right)} A a c^{2} d^{3} e^{3} + 3 \, A a c^{2} d^{4} e^{3} + 27 \, {\left(x e + d\right)} B a^{2} c d^{2} e^{4} - 3 \, B a^{2} c d^{3} e^{4} - 18 \, {\left(x e + d\right)} A a^{2} c d e^{5} + 3 \, A a^{2} c d^{2} e^{5} + 3 \, {\left(x e + d\right)} B a^{3} e^{6} - B a^{3} d e^{6} + A a^{3} e^{7}\right)} e^{\left(-8\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/3465*(315*(x*e + d)^(11/2)*B*c^3*e^80 - 2695*(x*e + d)^(9/2)*B*c^3*d*e^80 + 10395*(x*e + d)^(7/2)*B*c^3*d^2*e^80 - 24255*(x*e + d)^(5/2)*B*c^3*d^3*e^80 + 40425*(x*e + d)^(3/2)*B*c^3*d^4*e^80 - 72765*sqrt(x*e + d)*B*c^3*d^5*e^80 + 385*(x*e + d)^(9/2)*A*c^3*e^81 - 2970*(x*e + d)^(7/2)*A*c^3*d*e^81 + 10395*(x*e + d)^(5/2)*A*c^3*d^2*e^81 - 23100*(x*e + d)^(3/2)*A*c^3*d^3*e^81 + 51975*sqrt(x*e + d)*A*c^3*d^4*e^81 + 1485*(x*e + d)^(7/2)*B*a*c^2*e^82 - 10395*(x*e + d)^(5/2)*B*a*c^2*d*e^82 + 34650*(x*e + d)^(3/2)*B*a*c^2*d^2*e^82 - 103950*sqrt(x*e + d)*B*a*c^2*d^3*e^82 + 2079*(x*e + d)^(5/2)*A*a*c^2*e^83 - 13860*(x*e + d)^(3/2)*A*a*c^2*d*e^83 + 62370*sqrt(x*e + d)*A*a*c^2*d^2*e^83 + 3465*(x*e + d)^(3/2)*B*a^2*c*e^84 - 31185*sqrt(x*e + d)*B*a^2*c*d*e^84 + 10395*sqrt(x*e + d)*A*a^2*c*e^85)*e^(-88) - 2/3*(21*(x*e + d)*B*c^3*d^6 - B*c^3*d^7 - 18*(x*e + d)*A*c^3*d^5*e + A*c^3*d^6*e + 45*(x*e + d)*B*a*c^2*d^4*e^2 - 3*B*a*c^2*d^5*e^2 - 36*(x*e + d)*A*a*c^2*d^3*e^3 + 3*A*a*c^2*d^4*e^3 + 27*(x*e + d)*B*a^2*c*d^2*e^4 - 3*B*a^2*c*d^3*e^4 - 18*(x*e + d)*A*a^2*c*d*e^5 + 3*A*a^2*c*d^2*e^5 + 3*(x*e + d)*B*a^3*e^6 - B*a^3*d*e^6 + A*a^3*e^7)*e^(-8)/(x*e + d)^(3/2)","A",0
1444,1,599,0,0.225439," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} B c^{3} e^{64} - 315 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{3} d e^{64} + 1323 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{3} d^{2} e^{64} - 3675 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{3} d^{3} e^{64} + 11025 \, \sqrt{x e + d} B c^{3} d^{4} e^{64} + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{3} e^{65} - 378 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{3} d e^{65} + 1575 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d^{2} e^{65} - 6300 \, \sqrt{x e + d} A c^{3} d^{3} e^{65} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} B a c^{2} e^{66} - 1575 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c^{2} d e^{66} + 9450 \, \sqrt{x e + d} B a c^{2} d^{2} e^{66} + 315 \, {\left(x e + d\right)}^{\frac{3}{2}} A a c^{2} e^{67} - 3780 \, \sqrt{x e + d} A a c^{2} d e^{67} + 945 \, \sqrt{x e + d} B a^{2} c e^{68}\right)} e^{\left(-72\right)} + \frac{2 \, {\left(315 \, {\left(x e + d\right)}^{2} B c^{3} d^{5} - 35 \, {\left(x e + d\right)} B c^{3} d^{6} + 3 \, B c^{3} d^{7} - 225 \, {\left(x e + d\right)}^{2} A c^{3} d^{4} e + 30 \, {\left(x e + d\right)} A c^{3} d^{5} e - 3 \, A c^{3} d^{6} e + 450 \, {\left(x e + d\right)}^{2} B a c^{2} d^{3} e^{2} - 75 \, {\left(x e + d\right)} B a c^{2} d^{4} e^{2} + 9 \, B a c^{2} d^{5} e^{2} - 270 \, {\left(x e + d\right)}^{2} A a c^{2} d^{2} e^{3} + 60 \, {\left(x e + d\right)} A a c^{2} d^{3} e^{3} - 9 \, A a c^{2} d^{4} e^{3} + 135 \, {\left(x e + d\right)}^{2} B a^{2} c d e^{4} - 45 \, {\left(x e + d\right)} B a^{2} c d^{2} e^{4} + 9 \, B a^{2} c d^{3} e^{4} - 45 \, {\left(x e + d\right)}^{2} A a^{2} c e^{5} + 30 \, {\left(x e + d\right)} A a^{2} c d e^{5} - 9 \, A a^{2} c d^{2} e^{5} - 5 \, {\left(x e + d\right)} B a^{3} e^{6} + 3 \, B a^{3} d e^{6} - 3 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*B*c^3*e^64 - 315*(x*e + d)^(7/2)*B*c^3*d*e^64 + 1323*(x*e + d)^(5/2)*B*c^3*d^2*e^64 - 3675*(x*e + d)^(3/2)*B*c^3*d^3*e^64 + 11025*sqrt(x*e + d)*B*c^3*d^4*e^64 + 45*(x*e + d)^(7/2)*A*c^3*e^65 - 378*(x*e + d)^(5/2)*A*c^3*d*e^65 + 1575*(x*e + d)^(3/2)*A*c^3*d^2*e^65 - 6300*sqrt(x*e + d)*A*c^3*d^3*e^65 + 189*(x*e + d)^(5/2)*B*a*c^2*e^66 - 1575*(x*e + d)^(3/2)*B*a*c^2*d*e^66 + 9450*sqrt(x*e + d)*B*a*c^2*d^2*e^66 + 315*(x*e + d)^(3/2)*A*a*c^2*e^67 - 3780*sqrt(x*e + d)*A*a*c^2*d*e^67 + 945*sqrt(x*e + d)*B*a^2*c*e^68)*e^(-72) + 2/15*(315*(x*e + d)^2*B*c^3*d^5 - 35*(x*e + d)*B*c^3*d^6 + 3*B*c^3*d^7 - 225*(x*e + d)^2*A*c^3*d^4*e + 30*(x*e + d)*A*c^3*d^5*e - 3*A*c^3*d^6*e + 450*(x*e + d)^2*B*a*c^2*d^3*e^2 - 75*(x*e + d)*B*a*c^2*d^4*e^2 + 9*B*a*c^2*d^5*e^2 - 270*(x*e + d)^2*A*a*c^2*d^2*e^3 + 60*(x*e + d)*A*a*c^2*d^3*e^3 - 9*A*a*c^2*d^4*e^3 + 135*(x*e + d)^2*B*a^2*c*d*e^4 - 45*(x*e + d)*B*a^2*c*d^2*e^4 + 9*B*a^2*c*d^3*e^4 - 45*(x*e + d)^2*A*a^2*c*e^5 + 30*(x*e + d)*A*a^2*c*d*e^5 - 9*A*a^2*c*d^2*e^5 - 5*(x*e + d)*B*a^3*e^6 + 3*B*a^3*d*e^6 - 3*A*a^3*e^7)*e^(-8)/(x*e + d)^(5/2)","A",0
1445,1,597,0,0.251326," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(9/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} B c^{3} e^{48} - 49 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{3} d e^{48} + 245 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{3} d^{2} e^{48} - 1225 \, \sqrt{x e + d} B c^{3} d^{3} e^{48} + 7 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{3} e^{49} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d e^{49} + 525 \, \sqrt{x e + d} A c^{3} d^{2} e^{49} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c^{2} e^{50} - 525 \, \sqrt{x e + d} B a c^{2} d e^{50} + 105 \, \sqrt{x e + d} A a c^{2} e^{51}\right)} e^{\left(-56\right)} - \frac{2 \, {\left(1225 \, {\left(x e + d\right)}^{3} B c^{3} d^{4} - 245 \, {\left(x e + d\right)}^{2} B c^{3} d^{5} + 49 \, {\left(x e + d\right)} B c^{3} d^{6} - 5 \, B c^{3} d^{7} - 700 \, {\left(x e + d\right)}^{3} A c^{3} d^{3} e + 175 \, {\left(x e + d\right)}^{2} A c^{3} d^{4} e - 42 \, {\left(x e + d\right)} A c^{3} d^{5} e + 5 \, A c^{3} d^{6} e + 1050 \, {\left(x e + d\right)}^{3} B a c^{2} d^{2} e^{2} - 350 \, {\left(x e + d\right)}^{2} B a c^{2} d^{3} e^{2} + 105 \, {\left(x e + d\right)} B a c^{2} d^{4} e^{2} - 15 \, B a c^{2} d^{5} e^{2} - 420 \, {\left(x e + d\right)}^{3} A a c^{2} d e^{3} + 210 \, {\left(x e + d\right)}^{2} A a c^{2} d^{2} e^{3} - 84 \, {\left(x e + d\right)} A a c^{2} d^{3} e^{3} + 15 \, A a c^{2} d^{4} e^{3} + 105 \, {\left(x e + d\right)}^{3} B a^{2} c e^{4} - 105 \, {\left(x e + d\right)}^{2} B a^{2} c d e^{4} + 63 \, {\left(x e + d\right)} B a^{2} c d^{2} e^{4} - 15 \, B a^{2} c d^{3} e^{4} + 35 \, {\left(x e + d\right)}^{2} A a^{2} c e^{5} - 42 \, {\left(x e + d\right)} A a^{2} c d e^{5} + 15 \, A a^{2} c d^{2} e^{5} + 7 \, {\left(x e + d\right)} B a^{3} e^{6} - 5 \, B a^{3} d e^{6} + 5 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{35 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*B*c^3*e^48 - 49*(x*e + d)^(5/2)*B*c^3*d*e^48 + 245*(x*e + d)^(3/2)*B*c^3*d^2*e^48 - 1225*sqrt(x*e + d)*B*c^3*d^3*e^48 + 7*(x*e + d)^(5/2)*A*c^3*e^49 - 70*(x*e + d)^(3/2)*A*c^3*d*e^49 + 525*sqrt(x*e + d)*A*c^3*d^2*e^49 + 35*(x*e + d)^(3/2)*B*a*c^2*e^50 - 525*sqrt(x*e + d)*B*a*c^2*d*e^50 + 105*sqrt(x*e + d)*A*a*c^2*e^51)*e^(-56) - 2/35*(1225*(x*e + d)^3*B*c^3*d^4 - 245*(x*e + d)^2*B*c^3*d^5 + 49*(x*e + d)*B*c^3*d^6 - 5*B*c^3*d^7 - 700*(x*e + d)^3*A*c^3*d^3*e + 175*(x*e + d)^2*A*c^3*d^4*e - 42*(x*e + d)*A*c^3*d^5*e + 5*A*c^3*d^6*e + 1050*(x*e + d)^3*B*a*c^2*d^2*e^2 - 350*(x*e + d)^2*B*a*c^2*d^3*e^2 + 105*(x*e + d)*B*a*c^2*d^4*e^2 - 15*B*a*c^2*d^5*e^2 - 420*(x*e + d)^3*A*a*c^2*d*e^3 + 210*(x*e + d)^2*A*a*c^2*d^2*e^3 - 84*(x*e + d)*A*a*c^2*d^3*e^3 + 15*A*a*c^2*d^4*e^3 + 105*(x*e + d)^3*B*a^2*c*e^4 - 105*(x*e + d)^2*B*a^2*c*d*e^4 + 63*(x*e + d)*B*a^2*c*d^2*e^4 - 15*B*a^2*c*d^3*e^4 + 35*(x*e + d)^2*A*a^2*c*e^5 - 42*(x*e + d)*A*a^2*c*d*e^5 + 15*A*a^2*c*d^2*e^5 + 7*(x*e + d)*B*a^3*e^6 - 5*B*a^3*d*e^6 + 5*A*a^3*e^7)*e^(-8)/(x*e + d)^(7/2)","A",0
1446,1,595,0,0.242034," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(11/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{3} e^{32} - 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{3} d e^{32} + 315 \, \sqrt{x e + d} B c^{3} d^{2} e^{32} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} e^{33} - 90 \, \sqrt{x e + d} A c^{3} d e^{33} + 45 \, \sqrt{x e + d} B a c^{2} e^{34}\right)} e^{\left(-40\right)} + \frac{2 \, {\left(11025 \, {\left(x e + d\right)}^{4} B c^{3} d^{3} - 3675 \, {\left(x e + d\right)}^{3} B c^{3} d^{4} + 1323 \, {\left(x e + d\right)}^{2} B c^{3} d^{5} - 315 \, {\left(x e + d\right)} B c^{3} d^{6} + 35 \, B c^{3} d^{7} - 4725 \, {\left(x e + d\right)}^{4} A c^{3} d^{2} e + 2100 \, {\left(x e + d\right)}^{3} A c^{3} d^{3} e - 945 \, {\left(x e + d\right)}^{2} A c^{3} d^{4} e + 270 \, {\left(x e + d\right)} A c^{3} d^{5} e - 35 \, A c^{3} d^{6} e + 4725 \, {\left(x e + d\right)}^{4} B a c^{2} d e^{2} - 3150 \, {\left(x e + d\right)}^{3} B a c^{2} d^{2} e^{2} + 1890 \, {\left(x e + d\right)}^{2} B a c^{2} d^{3} e^{2} - 675 \, {\left(x e + d\right)} B a c^{2} d^{4} e^{2} + 105 \, B a c^{2} d^{5} e^{2} - 945 \, {\left(x e + d\right)}^{4} A a c^{2} e^{3} + 1260 \, {\left(x e + d\right)}^{3} A a c^{2} d e^{3} - 1134 \, {\left(x e + d\right)}^{2} A a c^{2} d^{2} e^{3} + 540 \, {\left(x e + d\right)} A a c^{2} d^{3} e^{3} - 105 \, A a c^{2} d^{4} e^{3} - 315 \, {\left(x e + d\right)}^{3} B a^{2} c e^{4} + 567 \, {\left(x e + d\right)}^{2} B a^{2} c d e^{4} - 405 \, {\left(x e + d\right)} B a^{2} c d^{2} e^{4} + 105 \, B a^{2} c d^{3} e^{4} - 189 \, {\left(x e + d\right)}^{2} A a^{2} c e^{5} + 270 \, {\left(x e + d\right)} A a^{2} c d e^{5} - 105 \, A a^{2} c d^{2} e^{5} - 45 \, {\left(x e + d\right)} B a^{3} e^{6} + 35 \, B a^{3} d e^{6} - 35 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{315 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*c^3*e^32 - 35*(x*e + d)^(3/2)*B*c^3*d*e^32 + 315*sqrt(x*e + d)*B*c^3*d^2*e^32 + 5*(x*e + d)^(3/2)*A*c^3*e^33 - 90*sqrt(x*e + d)*A*c^3*d*e^33 + 45*sqrt(x*e + d)*B*a*c^2*e^34)*e^(-40) + 2/315*(11025*(x*e + d)^4*B*c^3*d^3 - 3675*(x*e + d)^3*B*c^3*d^4 + 1323*(x*e + d)^2*B*c^3*d^5 - 315*(x*e + d)*B*c^3*d^6 + 35*B*c^3*d^7 - 4725*(x*e + d)^4*A*c^3*d^2*e + 2100*(x*e + d)^3*A*c^3*d^3*e - 945*(x*e + d)^2*A*c^3*d^4*e + 270*(x*e + d)*A*c^3*d^5*e - 35*A*c^3*d^6*e + 4725*(x*e + d)^4*B*a*c^2*d*e^2 - 3150*(x*e + d)^3*B*a*c^2*d^2*e^2 + 1890*(x*e + d)^2*B*a*c^2*d^3*e^2 - 675*(x*e + d)*B*a*c^2*d^4*e^2 + 105*B*a*c^2*d^5*e^2 - 945*(x*e + d)^4*A*a*c^2*e^3 + 1260*(x*e + d)^3*A*a*c^2*d*e^3 - 1134*(x*e + d)^2*A*a*c^2*d^2*e^3 + 540*(x*e + d)*A*a*c^2*d^3*e^3 - 105*A*a*c^2*d^4*e^3 - 315*(x*e + d)^3*B*a^2*c*e^4 + 567*(x*e + d)^2*B*a^2*c*d*e^4 - 405*(x*e + d)*B*a^2*c*d^2*e^4 + 105*B*a^2*c*d^3*e^4 - 189*(x*e + d)^2*A*a^2*c*e^5 + 270*(x*e + d)*A*a^2*c*d*e^5 - 105*A*a^2*c*d^2*e^5 - 45*(x*e + d)*B*a^3*e^6 + 35*B*a^3*d*e^6 - 35*A*a^3*e^7)*e^(-8)/(x*e + d)^(9/2)","A",0
1447,1,655,0,0.437821," ","integrate((B*x+A)*(e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""giac"")","\frac{{\left({\left(3 \, \sqrt{a c} a c d^{2} e^{2} + \sqrt{a c} a^{2} e^{4}\right)} A c^{2} + {\left(\sqrt{a c} a c d^{3} e + 3 \, \sqrt{a c} a^{2} d e^{3}\right)} B c^{2} - 2 \, {\left(a c^{3} d^{3} e - a^{2} c^{2} d e^{3}\right)} A {\left| c \right|} - {\left(a c^{3} d^{4} - a^{3} c e^{4}\right)} B {\left| c \right|} - {\left(\sqrt{a c} c^{4} d^{4} + 3 \, \sqrt{a c} a c^{3} d^{2} e^{2}\right)} A - {\left(3 \, \sqrt{a c} a c^{3} d^{3} e + \sqrt{a c} a^{2} c^{2} d e^{3}\right)} B\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{6} d + \sqrt{c^{12} d^{2} - {\left(c^{6} d^{2} - a c^{5} e^{2}\right)} c^{6}}}{c^{6}}}}\right)}{{\left(a c^{4} d - \sqrt{a c} a c^{3} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} - \frac{{\left({\left(3 \, \sqrt{a c} a c d^{2} e^{2} + \sqrt{a c} a^{2} e^{4}\right)} A c^{2} + {\left(\sqrt{a c} a c d^{3} e + 3 \, \sqrt{a c} a^{2} d e^{3}\right)} B c^{2} + 2 \, {\left(a c^{3} d^{3} e - a^{2} c^{2} d e^{3}\right)} A {\left| c \right|} + {\left(a c^{3} d^{4} - a^{3} c e^{4}\right)} B {\left| c \right|} - {\left(\sqrt{a c} c^{4} d^{4} + 3 \, \sqrt{a c} a c^{3} d^{2} e^{2}\right)} A - {\left(3 \, \sqrt{a c} a c^{3} d^{3} e + \sqrt{a c} a^{2} c^{2} d e^{3}\right)} B\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{6} d - \sqrt{c^{12} d^{2} - {\left(c^{6} d^{2} - a c^{5} e^{2}\right)} c^{6}}}{c^{6}}}}\right)}{{\left(a c^{4} d + \sqrt{a c} a c^{3} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B c^{4} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} B c^{4} d + 15 \, \sqrt{x e + d} B c^{4} d^{2} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{4} e + 30 \, \sqrt{x e + d} A c^{4} d e + 15 \, \sqrt{x e + d} B a c^{3} e^{2}\right)}}{15 \, c^{5}}"," ",0,"((3*sqrt(a*c)*a*c*d^2*e^2 + sqrt(a*c)*a^2*e^4)*A*c^2 + (sqrt(a*c)*a*c*d^3*e + 3*sqrt(a*c)*a^2*d*e^3)*B*c^2 - 2*(a*c^3*d^3*e - a^2*c^2*d*e^3)*A*abs(c) - (a*c^3*d^4 - a^3*c*e^4)*B*abs(c) - (sqrt(a*c)*c^4*d^4 + 3*sqrt(a*c)*a*c^3*d^2*e^2)*A - (3*sqrt(a*c)*a*c^3*d^3*e + sqrt(a*c)*a^2*c^2*d*e^3)*B)*arctan(sqrt(x*e + d)/sqrt(-(c^6*d + sqrt(c^12*d^2 - (c^6*d^2 - a*c^5*e^2)*c^6))/c^6))/((a*c^4*d - sqrt(a*c)*a*c^3*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) - ((3*sqrt(a*c)*a*c*d^2*e^2 + sqrt(a*c)*a^2*e^4)*A*c^2 + (sqrt(a*c)*a*c*d^3*e + 3*sqrt(a*c)*a^2*d*e^3)*B*c^2 + 2*(a*c^3*d^3*e - a^2*c^2*d*e^3)*A*abs(c) + (a*c^3*d^4 - a^3*c*e^4)*B*abs(c) - (sqrt(a*c)*c^4*d^4 + 3*sqrt(a*c)*a*c^3*d^2*e^2)*A - (3*sqrt(a*c)*a*c^3*d^3*e + sqrt(a*c)*a^2*c^2*d*e^3)*B)*arctan(sqrt(x*e + d)/sqrt(-(c^6*d - sqrt(c^12*d^2 - (c^6*d^2 - a*c^5*e^2)*c^6))/c^6))/((a*c^4*d + sqrt(a*c)*a*c^3*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 2/15*(3*(x*e + d)^(5/2)*B*c^4 + 5*(x*e + d)^(3/2)*B*c^4*d + 15*sqrt(x*e + d)*B*c^4*d^2 + 5*(x*e + d)^(3/2)*A*c^4*e + 30*sqrt(x*e + d)*A*c^4*d*e + 15*sqrt(x*e + d)*B*a*c^3*e^2)/c^5","B",0
1448,1,528,0,0.412501," ","integrate((B*x+A)*(e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, \sqrt{a c} B a c^{3} d^{2} e - 2 \, \sqrt{a c} A a c^{3} d e^{2} - {\left(\sqrt{a c} a c d^{2} e + \sqrt{a c} a^{2} e^{3}\right)} B c^{2} + {\left(a c^{3} d^{2} e - a^{2} c^{2} e^{3}\right)} A {\left| c \right|} + {\left(a c^{3} d^{3} - a^{2} c^{2} d e^{2}\right)} B {\left| c \right|} + {\left(\sqrt{a c} c^{4} d^{3} + \sqrt{a c} a c^{3} d e^{2}\right)} A\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{4} d + \sqrt{c^{8} d^{2} - {\left(c^{4} d^{2} - a c^{3} e^{2}\right)} c^{4}}}{c^{4}}}}\right)}{{\left(a c^{4} d - \sqrt{a c} a c^{3} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} + \frac{{\left(2 \, \sqrt{a c} B a c^{3} d^{2} e - 2 \, \sqrt{a c} A a c^{3} d e^{2} - {\left(\sqrt{a c} a c d^{2} e + \sqrt{a c} a^{2} e^{3}\right)} B c^{2} - {\left(a c^{3} d^{2} e - a^{2} c^{2} e^{3}\right)} A {\left| c \right|} - {\left(a c^{3} d^{3} - a^{2} c^{2} d e^{2}\right)} B {\left| c \right|} + {\left(\sqrt{a c} c^{4} d^{3} + \sqrt{a c} a c^{3} d e^{2}\right)} A\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{4} d - \sqrt{c^{8} d^{2} - {\left(c^{4} d^{2} - a c^{3} e^{2}\right)} c^{4}}}{c^{4}}}}\right)}{{\left(a c^{4} d + \sqrt{a c} a c^{3} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B c^{2} + 3 \, \sqrt{x e + d} B c^{2} d + 3 \, \sqrt{x e + d} A c^{2} e\right)}}{3 \, c^{3}}"," ",0,"-(2*sqrt(a*c)*B*a*c^3*d^2*e - 2*sqrt(a*c)*A*a*c^3*d*e^2 - (sqrt(a*c)*a*c*d^2*e + sqrt(a*c)*a^2*e^3)*B*c^2 + (a*c^3*d^2*e - a^2*c^2*e^3)*A*abs(c) + (a*c^3*d^3 - a^2*c^2*d*e^2)*B*abs(c) + (sqrt(a*c)*c^4*d^3 + sqrt(a*c)*a*c^3*d*e^2)*A)*arctan(sqrt(x*e + d)/sqrt(-(c^4*d + sqrt(c^8*d^2 - (c^4*d^2 - a*c^3*e^2)*c^4))/c^4))/((a*c^4*d - sqrt(a*c)*a*c^3*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) + (2*sqrt(a*c)*B*a*c^3*d^2*e - 2*sqrt(a*c)*A*a*c^3*d*e^2 - (sqrt(a*c)*a*c*d^2*e + sqrt(a*c)*a^2*e^3)*B*c^2 - (a*c^3*d^2*e - a^2*c^2*e^3)*A*abs(c) - (a*c^3*d^3 - a^2*c^2*d*e^2)*B*abs(c) + (sqrt(a*c)*c^4*d^3 + sqrt(a*c)*a*c^3*d*e^2)*A)*arctan(sqrt(x*e + d)/sqrt(-(c^4*d - sqrt(c^8*d^2 - (c^4*d^2 - a*c^3*e^2)*c^4))/c^4))/((a*c^4*d + sqrt(a*c)*a*c^3*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 2/3*((x*e + d)^(3/2)*B*c^2 + 3*sqrt(x*e + d)*B*c^2*d + 3*sqrt(x*e + d)*A*c^2*e)/c^3","B",0
1449,1,303,0,0.372040," ","integrate((B*x+A)*(e*x+d)^(1/2)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{2 \, \sqrt{x e + d} B}{c} - \frac{{\left(\sqrt{a c} A c^{3} d^{2} - \sqrt{a c} A a c^{2} e^{2} + {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d + \sqrt{c^{4} d^{2} - {\left(c^{2} d^{2} - a c e^{2}\right)} c^{2}}}{c^{2}}}}\right)}{{\left(a c^{3} d - \sqrt{a c} a c^{2} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} + \frac{{\left(\sqrt{a c} A c^{3} d^{2} - \sqrt{a c} A a c^{2} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d - \sqrt{c^{4} d^{2} - {\left(c^{2} d^{2} - a c e^{2}\right)} c^{2}}}{c^{2}}}}\right)}{{\left(a c^{3} d + \sqrt{a c} a c^{2} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}}"," ",0,"-2*sqrt(x*e + d)*B/c - (sqrt(a*c)*A*c^3*d^2 - sqrt(a*c)*A*a*c^2*e^2 + (a*c^2*d^2 - a^2*c*e^2)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d + sqrt(c^4*d^2 - (c^2*d^2 - a*c*e^2)*c^2))/c^2))/((a*c^3*d - sqrt(a*c)*a*c^2*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) + (sqrt(a*c)*A*c^3*d^2 - sqrt(a*c)*A*a*c^2*e^2 - (a*c^2*d^2 - a^2*c*e^2)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d - sqrt(c^4*d^2 - (c^2*d^2 - a*c*e^2)*c^2))/c^2))/((a*c^3*d + sqrt(a*c)*a*c^2*e)*sqrt(-c^2*d + sqrt(a*c)*c*e))","B",0
1450,1,177,0,0.259375," ","integrate((B*x+A)/(e*x+d)^(1/2)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(B a {\left| c \right|} + \sqrt{a c} A {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c d + \sqrt{c^{2} d^{2} - {\left(c d^{2} - a e^{2}\right)} c}}{c}}}\right)}{\sqrt{-c^{2} d - \sqrt{a c} c e} a c} - \frac{{\left(B a {\left| c \right|} - \sqrt{a c} A {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c d - \sqrt{c^{2} d^{2} - {\left(c d^{2} - a e^{2}\right)} c}}{c}}}\right)}{\sqrt{-c^{2} d + \sqrt{a c} c e} a c}"," ",0,"-(B*a*abs(c) + sqrt(a*c)*A*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c*d + sqrt(c^2*d^2 - (c*d^2 - a*e^2)*c))/c))/(sqrt(-c^2*d - sqrt(a*c)*c*e)*a*c) - (B*a*abs(c) - sqrt(a*c)*A*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c*d - sqrt(c^2*d^2 - (c*d^2 - a*e^2)*c))/c))/(sqrt(-c^2*d + sqrt(a*c)*c*e)*a*c)","A",0
1451,1,920,0,0.701935," ","integrate((B*x+A)/(e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{2 \, {\left(B d - A e\right)}}{{\left(c d^{2} - a e^{2}\right)} \sqrt{x e + d}} + \frac{{\left({\left(c d^{2} e - a e^{3}\right)}^{2} \sqrt{a c} B a d {\left| c \right|} - {\left(c d^{2} e - a e^{3}\right)}^{2} \sqrt{a c} A a {\left| c \right|} e + 2 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} A {\left| c d^{2} e - a e^{3} \right|} {\left| c \right|} - {\left(a c^{2} d^{4} - a^{3} e^{4}\right)} B {\left| c d^{2} e - a e^{3} \right|} {\left| c \right|} - {\left(\sqrt{a c} c^{3} d^{6} e - 2 \, \sqrt{a c} a c^{2} d^{4} e^{3} + \sqrt{a c} a^{2} c d^{2} e^{5}\right)} A {\left| c \right|} + {\left(\sqrt{a c} a c^{2} d^{5} e^{2} - 2 \, \sqrt{a c} a^{2} c d^{3} e^{4} + \sqrt{a c} a^{3} d e^{6}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d^{3} - a c d e^{2} + \sqrt{{\left(c^{2} d^{3} - a c d e^{2}\right)}^{2} - {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - a c e^{2}\right)}}}{c^{2} d^{2} - a c e^{2}}}}\right)}{{\left(a c^{3} d^{5} - \sqrt{a c} a c^{2} d^{4} e - 2 \, a^{2} c^{2} d^{3} e^{2} + 2 \, \sqrt{a c} a^{2} c d^{2} e^{3} + a^{3} c d e^{4} - \sqrt{a c} a^{3} e^{5}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| c d^{2} e - a e^{3} \right|}} - \frac{{\left({\left(c d^{2} e - a e^{3}\right)}^{2} \sqrt{a c} B a d {\left| c \right|} - {\left(c d^{2} e - a e^{3}\right)}^{2} \sqrt{a c} A a {\left| c \right|} e - 2 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} A {\left| c d^{2} e - a e^{3} \right|} {\left| c \right|} + {\left(a c^{2} d^{4} - a^{3} e^{4}\right)} B {\left| c d^{2} e - a e^{3} \right|} {\left| c \right|} - {\left(\sqrt{a c} c^{3} d^{6} e - 2 \, \sqrt{a c} a c^{2} d^{4} e^{3} + \sqrt{a c} a^{2} c d^{2} e^{5}\right)} A {\left| c \right|} + {\left(\sqrt{a c} a c^{2} d^{5} e^{2} - 2 \, \sqrt{a c} a^{2} c d^{3} e^{4} + \sqrt{a c} a^{3} d e^{6}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d^{3} - a c d e^{2} - \sqrt{{\left(c^{2} d^{3} - a c d e^{2}\right)}^{2} - {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - a c e^{2}\right)}}}{c^{2} d^{2} - a c e^{2}}}}\right)}{{\left(a c^{3} d^{5} + \sqrt{a c} a c^{2} d^{4} e - 2 \, a^{2} c^{2} d^{3} e^{2} - 2 \, \sqrt{a c} a^{2} c d^{2} e^{3} + a^{3} c d e^{4} + \sqrt{a c} a^{3} e^{5}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| c d^{2} e - a e^{3} \right|}}"," ",0,"-2*(B*d - A*e)/((c*d^2 - a*e^2)*sqrt(x*e + d)) + ((c*d^2*e - a*e^3)^2*sqrt(a*c)*B*a*d*abs(c) - (c*d^2*e - a*e^3)^2*sqrt(a*c)*A*a*abs(c)*e + 2*(a*c^2*d^3*e - a^2*c*d*e^3)*A*abs(c*d^2*e - a*e^3)*abs(c) - (a*c^2*d^4 - a^3*e^4)*B*abs(c*d^2*e - a*e^3)*abs(c) - (sqrt(a*c)*c^3*d^6*e - 2*sqrt(a*c)*a*c^2*d^4*e^3 + sqrt(a*c)*a^2*c*d^2*e^5)*A*abs(c) + (sqrt(a*c)*a*c^2*d^5*e^2 - 2*sqrt(a*c)*a^2*c*d^3*e^4 + sqrt(a*c)*a^3*d*e^6)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d^3 - a*c*d*e^2 + sqrt((c^2*d^3 - a*c*d*e^2)^2 - (c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c^2*d^2 - a*c*e^2)))/(c^2*d^2 - a*c*e^2)))/((a*c^3*d^5 - sqrt(a*c)*a*c^2*d^4*e - 2*a^2*c^2*d^3*e^2 + 2*sqrt(a*c)*a^2*c*d^2*e^3 + a^3*c*d*e^4 - sqrt(a*c)*a^3*e^5)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(c*d^2*e - a*e^3)) - ((c*d^2*e - a*e^3)^2*sqrt(a*c)*B*a*d*abs(c) - (c*d^2*e - a*e^3)^2*sqrt(a*c)*A*a*abs(c)*e - 2*(a*c^2*d^3*e - a^2*c*d*e^3)*A*abs(c*d^2*e - a*e^3)*abs(c) + (a*c^2*d^4 - a^3*e^4)*B*abs(c*d^2*e - a*e^3)*abs(c) - (sqrt(a*c)*c^3*d^6*e - 2*sqrt(a*c)*a*c^2*d^4*e^3 + sqrt(a*c)*a^2*c*d^2*e^5)*A*abs(c) + (sqrt(a*c)*a*c^2*d^5*e^2 - 2*sqrt(a*c)*a^2*c*d^3*e^4 + sqrt(a*c)*a^3*d*e^6)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d^3 - a*c*d*e^2 - sqrt((c^2*d^3 - a*c*d*e^2)^2 - (c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c^2*d^2 - a*c*e^2)))/(c^2*d^2 - a*c*e^2)))/((a*c^3*d^5 + sqrt(a*c)*a*c^2*d^4*e - 2*a^2*c^2*d^3*e^2 - 2*sqrt(a*c)*a^2*c*d^2*e^3 + a^3*c*d*e^4 + sqrt(a*c)*a^3*e^5)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(c*d^2*e - a*e^3))","B",0
1452,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1453,1,728,0,0.782941," ","integrate((B*x+A)*(e*x+d)^(5/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e^{2}}{c^{2}} - \frac{{\left(10 \, \sqrt{a c} B a^{3} d {\left| c \right|} e^{3} - {\left(\sqrt{a c} c d^{2} e^{2} - 3 \, \sqrt{a c} a e^{4}\right)} A a^{2} {\left| c \right|} - {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} A {\left| a \right|} {\left| c \right|} - 5 \, {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} B {\left| a \right|} {\left| c \right|} + 2 \, {\left(\sqrt{a c} a c^{2} d^{4} - 2 \, \sqrt{a c} a^{2} c d^{2} e^{2}\right)} A {\left| c \right|} - 5 \, {\left(\sqrt{a c} a^{2} c d^{3} e + \sqrt{a c} a^{3} d e^{3}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d + \sqrt{a^{2} c^{6} d^{2} - {\left(a c^{3} d^{2} - a^{2} c^{2} e^{2}\right)} a c^{3}}}{a c^{3}}}}\right)}{4 \, {\left(a^{2} c^{3} d - \sqrt{a c} a^{2} c^{2} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a \right|}} + \frac{{\left(10 \, B a^{3} c d {\left| c \right|} e^{3} - {\left(c^{2} d^{2} e^{2} - 3 \, a c e^{4}\right)} A a^{2} {\left| c \right|} + {\left(\sqrt{a c} c^{2} d^{3} e - \sqrt{a c} a c d e^{3}\right)} A {\left| a \right|} {\left| c \right|} + 5 \, {\left(\sqrt{a c} a c d^{2} e^{2} - \sqrt{a c} a^{2} e^{4}\right)} B {\left| a \right|} {\left| c \right|} + 2 \, {\left(a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2}\right)} A {\left| c \right|} - 5 \, {\left(a^{2} c^{2} d^{3} e + a^{3} c d e^{3}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d - \sqrt{a^{2} c^{6} d^{2} - {\left(a c^{3} d^{2} - a^{2} c^{2} e^{2}\right)} a c^{3}}}{a c^{3}}}}\right)}{4 \, {\left(a^{2} c^{3} e + \sqrt{a c} a c^{3} d\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d^{2} e - \sqrt{x e + d} A c^{2} d^{3} e + 2 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c d e^{2} - \sqrt{x e + d} B a c d^{2} e^{2} + {\left(x e + d\right)}^{\frac{3}{2}} A a c e^{3} + \sqrt{x e + d} A a c d e^{3} + \sqrt{x e + d} B a^{2} e^{4}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)} a c^{2}}"," ",0,"2*sqrt(x*e + d)*B*e^2/c^2 - 1/4*(10*sqrt(a*c)*B*a^3*d*abs(c)*e^3 - (sqrt(a*c)*c*d^2*e^2 - 3*sqrt(a*c)*a*e^4)*A*a^2*abs(c) - (a*c^2*d^3*e - a^2*c*d*e^3)*A*abs(a)*abs(c) - 5*(a^2*c*d^2*e^2 - a^3*e^4)*B*abs(a)*abs(c) + 2*(sqrt(a*c)*a*c^2*d^4 - 2*sqrt(a*c)*a^2*c*d^2*e^2)*A*abs(c) - 5*(sqrt(a*c)*a^2*c*d^3*e + sqrt(a*c)*a^3*d*e^3)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d + sqrt(a^2*c^6*d^2 - (a*c^3*d^2 - a^2*c^2*e^2)*a*c^3))/(a*c^3)))/((a^2*c^3*d - sqrt(a*c)*a^2*c^2*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a)) + 1/4*(10*B*a^3*c*d*abs(c)*e^3 - (c^2*d^2*e^2 - 3*a*c*e^4)*A*a^2*abs(c) + (sqrt(a*c)*c^2*d^3*e - sqrt(a*c)*a*c*d*e^3)*A*abs(a)*abs(c) + 5*(sqrt(a*c)*a*c*d^2*e^2 - sqrt(a*c)*a^2*e^4)*B*abs(a)*abs(c) + 2*(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2)*A*abs(c) - 5*(a^2*c^2*d^3*e + a^3*c*d*e^3)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d - sqrt(a^2*c^6*d^2 - (a*c^3*d^2 - a^2*c^2*e^2)*a*c^3))/(a*c^3)))/((a^2*c^3*e + sqrt(a*c)*a*c^3*d)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a)) - 1/2*((x*e + d)^(3/2)*A*c^2*d^2*e - sqrt(x*e + d)*A*c^2*d^3*e + 2*(x*e + d)^(3/2)*B*a*c*d*e^2 - sqrt(x*e + d)*B*a*c*d^2*e^2 + (x*e + d)^(3/2)*A*a*c*e^3 + sqrt(x*e + d)*A*a*c*d*e^3 + sqrt(x*e + d)*B*a^2*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)*a*c^2)","B",0
1454,1,533,0,0.707001," ","integrate((B*x+A)*(e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{a c} B a^{2} c^{3} d^{2} e + \sqrt{a c} A a^{2} c^{3} d e^{2} - 3 \, \sqrt{a c} B a^{3} c^{2} e^{3} + {\left(a c^{3} d^{2} e - a^{2} c^{2} e^{3}\right)} A {\left| a \right|} {\left| c \right|} - {\left(2 \, \sqrt{a c} a c^{4} d^{3} - \sqrt{a c} a^{2} c^{3} d e^{2}\right)} A\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d + \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{4} d - \sqrt{a c} a^{2} c^{3} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left(3 \, B a^{2} c^{3} d^{2} e + A a^{2} c^{3} d e^{2} - 3 \, B a^{3} c^{2} e^{3} - {\left(\sqrt{a c} c^{2} d^{2} e - \sqrt{a c} a c e^{3}\right)} A {\left| a \right|} {\left| c \right|} - {\left(2 \, a c^{4} d^{3} - a^{2} c^{3} d e^{2}\right)} A\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d - \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} e + \sqrt{a c} a c^{3} d\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} A c d e - \sqrt{x e + d} A c d^{2} e + {\left(x e + d\right)}^{\frac{3}{2}} B a e^{2} + \sqrt{x e + d} A a e^{3}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)} a c}"," ",0,"1/4*(3*sqrt(a*c)*B*a^2*c^3*d^2*e + sqrt(a*c)*A*a^2*c^3*d*e^2 - 3*sqrt(a*c)*B*a^3*c^2*e^3 + (a*c^3*d^2*e - a^2*c^2*e^3)*A*abs(a)*abs(c) - (2*sqrt(a*c)*a*c^4*d^3 - sqrt(a*c)*a^2*c^3*d*e^2)*A)*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d + sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^4*d - sqrt(a*c)*a^2*c^3*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a)) - 1/4*(3*B*a^2*c^3*d^2*e + A*a^2*c^3*d*e^2 - 3*B*a^3*c^2*e^3 - (sqrt(a*c)*c^2*d^2*e - sqrt(a*c)*a*c*e^3)*A*abs(a)*abs(c) - (2*a*c^4*d^3 - a^2*c^3*d*e^2)*A)*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d - sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^3*e + sqrt(a*c)*a*c^3*d)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a)) - 1/2*((x*e + d)^(3/2)*A*c*d*e - sqrt(x*e + d)*A*c*d^2*e + (x*e + d)^(3/2)*B*a*e^2 + sqrt(x*e + d)*A*a*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)*a*c)","B",0
1455,1,436,0,0.536415," ","integrate((B*x+A)*(e*x+d)^(1/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, A a c^{3} d^{2} - B a^{2} c^{2} d e - \sqrt{a c} A c d {\left| a \right|} {\left| c \right|} e - A a^{2} c^{2} e^{2} + \sqrt{a c} B a {\left| a \right|} {\left| c \right|} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d + \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{2} e - \sqrt{a c} a c^{2} d\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a \right|}} + \frac{{\left(2 \, A a c^{3} d^{2} - B a^{2} c^{2} d e + \sqrt{a c} A c d {\left| a \right|} {\left| c \right|} e - A a^{2} c^{2} e^{2} - \sqrt{a c} B a {\left| a \right|} {\left| c \right|} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d - \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{2} e + \sqrt{a c} a c^{2} d\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} A c e - \sqrt{x e + d} A c d e + \sqrt{x e + d} B a e^{2}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)} a c}"," ",0,"1/4*(2*A*a*c^3*d^2 - B*a^2*c^2*d*e - sqrt(a*c)*A*c*d*abs(a)*abs(c)*e - A*a^2*c^2*e^2 + sqrt(a*c)*B*a*abs(a)*abs(c)*e^2)*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d + sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^2*e - sqrt(a*c)*a*c^2*d)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a)) + 1/4*(2*A*a*c^3*d^2 - B*a^2*c^2*d*e + sqrt(a*c)*A*c*d*abs(a)*abs(c)*e - A*a^2*c^2*e^2 - sqrt(a*c)*B*a*abs(a)*abs(c)*e^2)*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d - sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^2*e + sqrt(a*c)*a*c^2*d)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a)) - 1/2*((x*e + d)^(3/2)*A*c*e - sqrt(x*e + d)*A*c*d*e + sqrt(x*e + d)*B*a*e^2)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)*a*c)","B",0
1456,1,1156,0,0.914320," ","integrate((B*x+A)/(e*x+d)^(1/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(a c d^{2} e - a^{2} e^{3}\right)}^{2} A c d {\left| c \right|} e - {\left(a c d^{2} e - a^{2} e^{3}\right)}^{2} B a {\left| c \right|} e^{2} + {\left(\sqrt{a c} c^{2} d^{4} e - 4 \, \sqrt{a c} a c d^{2} e^{3} + 3 \, \sqrt{a c} a^{2} e^{5}\right)} A {\left| a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} + 2 \, {\left(\sqrt{a c} a c d^{3} e^{2} - \sqrt{a c} a^{2} d e^{4}\right)} B {\left| a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} - {\left(2 \, a c^{4} d^{7} e - 7 \, a^{2} c^{3} d^{5} e^{3} + 8 \, a^{3} c^{2} d^{3} e^{5} - 3 \, a^{4} c d e^{7}\right)} A {\left| c \right|} - {\left(a^{2} c^{3} d^{6} e^{2} - 2 \, a^{3} c^{2} d^{4} e^{4} + a^{4} c d^{2} e^{6}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d^{3} - a^{2} c d e^{2} + \sqrt{{\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)}^{2} - {\left(a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)}}}{a c^{2} d^{2} - a^{2} c e^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} d^{4} e - \sqrt{a c} a c^{3} d^{5} + 2 \, \sqrt{a c} a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c^{2} d^{2} e^{3} - \sqrt{a c} a^{3} c d e^{4} + a^{4} c e^{5}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a c d^{2} e - a^{2} e^{3} \right|}} - \frac{{\left({\left(a c d^{2} e - a^{2} e^{3}\right)}^{2} \sqrt{a c} A c d {\left| c \right|} e - {\left(a c d^{2} e - a^{2} e^{3}\right)}^{2} \sqrt{a c} B a {\left| c \right|} e^{2} - {\left(a c^{3} d^{4} e - 4 \, a^{2} c^{2} d^{2} e^{3} + 3 \, a^{3} c e^{5}\right)} A {\left| a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} - 2 \, {\left(a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} B {\left| a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} - {\left(2 \, \sqrt{a c} a c^{4} d^{7} e - 7 \, \sqrt{a c} a^{2} c^{3} d^{5} e^{3} + 8 \, \sqrt{a c} a^{3} c^{2} d^{3} e^{5} - 3 \, \sqrt{a c} a^{4} c d e^{7}\right)} A {\left| c \right|} - {\left(\sqrt{a c} a^{2} c^{3} d^{6} e^{2} - 2 \, \sqrt{a c} a^{3} c^{2} d^{4} e^{4} + \sqrt{a c} a^{4} c d^{2} e^{6}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d^{3} - a^{2} c d e^{2} - \sqrt{{\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)}^{2} - {\left(a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)}}}{a c^{2} d^{2} - a^{2} c e^{2}}}}\right)}{4 \, {\left(a^{2} c^{4} d^{5} + \sqrt{a c} a^{2} c^{3} d^{4} e - 2 \, a^{3} c^{3} d^{3} e^{2} - 2 \, \sqrt{a c} a^{3} c^{2} d^{2} e^{3} + a^{4} c^{2} d e^{4} + \sqrt{a c} a^{4} c e^{5}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a c d^{2} e - a^{2} e^{3} \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} A c d e - \sqrt{x e + d} A c d^{2} e - {\left(x e + d\right)}^{\frac{3}{2}} B a e^{2} + 2 \, \sqrt{x e + d} B a d e^{2} - \sqrt{x e + d} A a e^{3}}{2 \, {\left(a c d^{2} - a^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}}"," ",0,"-1/4*((a*c*d^2*e - a^2*e^3)^2*A*c*d*abs(c)*e - (a*c*d^2*e - a^2*e^3)^2*B*a*abs(c)*e^2 + (sqrt(a*c)*c^2*d^4*e - 4*sqrt(a*c)*a*c*d^2*e^3 + 3*sqrt(a*c)*a^2*e^5)*A*abs(a*c*d^2*e - a^2*e^3)*abs(c) + 2*(sqrt(a*c)*a*c*d^3*e^2 - sqrt(a*c)*a^2*d*e^4)*B*abs(a*c*d^2*e - a^2*e^3)*abs(c) - (2*a*c^4*d^7*e - 7*a^2*c^3*d^5*e^3 + 8*a^3*c^2*d^3*e^5 - 3*a^4*c*d*e^7)*A*abs(c) - (a^2*c^3*d^6*e^2 - 2*a^3*c^2*d^4*e^4 + a^4*c*d^2*e^6)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d^3 - a^2*c*d*e^2 + sqrt((a*c^2*d^3 - a^2*c*d*e^2)^2 - (a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)*(a*c^2*d^2 - a^2*c*e^2)))/(a*c^2*d^2 - a^2*c*e^2)))/((a^2*c^3*d^4*e - sqrt(a*c)*a*c^3*d^5 + 2*sqrt(a*c)*a^2*c^2*d^3*e^2 - 2*a^3*c^2*d^2*e^3 - sqrt(a*c)*a^3*c*d*e^4 + a^4*c*e^5)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a*c*d^2*e - a^2*e^3)) - 1/4*((a*c*d^2*e - a^2*e^3)^2*sqrt(a*c)*A*c*d*abs(c)*e - (a*c*d^2*e - a^2*e^3)^2*sqrt(a*c)*B*a*abs(c)*e^2 - (a*c^3*d^4*e - 4*a^2*c^2*d^2*e^3 + 3*a^3*c*e^5)*A*abs(a*c*d^2*e - a^2*e^3)*abs(c) - 2*(a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*B*abs(a*c*d^2*e - a^2*e^3)*abs(c) - (2*sqrt(a*c)*a*c^4*d^7*e - 7*sqrt(a*c)*a^2*c^3*d^5*e^3 + 8*sqrt(a*c)*a^3*c^2*d^3*e^5 - 3*sqrt(a*c)*a^4*c*d*e^7)*A*abs(c) - (sqrt(a*c)*a^2*c^3*d^6*e^2 - 2*sqrt(a*c)*a^3*c^2*d^4*e^4 + sqrt(a*c)*a^4*c*d^2*e^6)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d^3 - a^2*c*d*e^2 - sqrt((a*c^2*d^3 - a^2*c*d*e^2)^2 - (a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)*(a*c^2*d^2 - a^2*c*e^2)))/(a*c^2*d^2 - a^2*c*e^2)))/((a^2*c^4*d^5 + sqrt(a*c)*a^2*c^3*d^4*e - 2*a^3*c^3*d^3*e^2 - 2*sqrt(a*c)*a^3*c^2*d^2*e^3 + a^4*c^2*d*e^4 + sqrt(a*c)*a^4*c*e^5)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a*c*d^2*e - a^2*e^3)) - 1/2*((x*e + d)^(3/2)*A*c*d*e - sqrt(x*e + d)*A*c*d^2*e - (x*e + d)^(3/2)*B*a*e^2 + 2*sqrt(x*e + d)*B*a*d*e^2 - sqrt(x*e + d)*A*a*e^3)/((a*c*d^2 - a^2*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2))","B",0
1457,1,1895,0,2.068138," ","integrate((B*x+A)/(e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(6 \, {\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} B a c d {\left| c \right|} e^{2} - {\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} {\left(c^{2} d^{2} e + 5 \, a c e^{3}\right)} A {\left| c \right|} - {\left(\sqrt{a c} c^{4} d^{7} e - 15 \, \sqrt{a c} a c^{3} d^{5} e^{3} + 27 \, \sqrt{a c} a^{2} c^{2} d^{3} e^{5} - 13 \, \sqrt{a c} a^{3} c d e^{7}\right)} A {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} - 3 \, {\left(3 \, \sqrt{a c} a c^{3} d^{6} e^{2} - 5 \, \sqrt{a c} a^{2} c^{2} d^{4} e^{4} + \sqrt{a c} a^{3} c d^{2} e^{6} + \sqrt{a c} a^{4} e^{8}\right)} B {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} + 2 \, {\left(a c^{7} d^{12} e - 8 \, a^{2} c^{6} d^{10} e^{3} + 22 \, a^{3} c^{5} d^{8} e^{5} - 28 \, a^{4} c^{4} d^{6} e^{7} + 17 \, a^{5} c^{3} d^{4} e^{9} - 4 \, a^{6} c^{2} d^{2} e^{11}\right)} A {\left| c \right|} + 3 \, {\left(a^{2} c^{6} d^{11} e^{2} - 3 \, a^{3} c^{5} d^{9} e^{4} + 2 \, a^{4} c^{4} d^{7} e^{6} + 2 \, a^{5} c^{3} d^{5} e^{8} - 3 \, a^{6} c^{2} d^{3} e^{10} + a^{7} c d e^{12}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4} + \sqrt{{\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)}^{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)} {\left(a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}\right)}{4 \, {\left(a^{2} c^{5} d^{8} e - \sqrt{a c} a c^{5} d^{9} + 4 \, \sqrt{a c} a^{2} c^{4} d^{7} e^{2} - 4 \, a^{3} c^{4} d^{6} e^{3} - 6 \, \sqrt{a c} a^{3} c^{3} d^{5} e^{4} + 6 \, a^{4} c^{3} d^{4} e^{5} + 4 \, \sqrt{a c} a^{4} c^{2} d^{3} e^{6} - 4 \, a^{5} c^{2} d^{2} e^{7} - \sqrt{a c} a^{5} c d e^{8} + a^{6} c e^{9}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|}} + \frac{{\left(6 \, {\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} \sqrt{a c} B a d {\left| c \right|} e^{2} - {\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} {\left(\sqrt{a c} c d^{2} e + 5 \, \sqrt{a c} a e^{3}\right)} A {\left| c \right|} + {\left(a c^{4} d^{7} e - 15 \, a^{2} c^{3} d^{5} e^{3} + 27 \, a^{3} c^{2} d^{3} e^{5} - 13 \, a^{4} c d e^{7}\right)} A {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} + 3 \, {\left(3 \, a^{2} c^{3} d^{6} e^{2} - 5 \, a^{3} c^{2} d^{4} e^{4} + a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} B {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} + 2 \, {\left(\sqrt{a c} a c^{6} d^{12} e - 8 \, \sqrt{a c} a^{2} c^{5} d^{10} e^{3} + 22 \, \sqrt{a c} a^{3} c^{4} d^{8} e^{5} - 28 \, \sqrt{a c} a^{4} c^{3} d^{6} e^{7} + 17 \, \sqrt{a c} a^{5} c^{2} d^{4} e^{9} - 4 \, \sqrt{a c} a^{6} c d^{2} e^{11}\right)} A {\left| c \right|} + 3 \, {\left(\sqrt{a c} a^{2} c^{5} d^{11} e^{2} - 3 \, \sqrt{a c} a^{3} c^{4} d^{9} e^{4} + 2 \, \sqrt{a c} a^{4} c^{3} d^{7} e^{6} + 2 \, \sqrt{a c} a^{5} c^{2} d^{5} e^{8} - 3 \, \sqrt{a c} a^{6} c d^{3} e^{10} + \sqrt{a c} a^{7} d e^{12}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4} - \sqrt{{\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)}^{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)} {\left(a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}\right)}{4 \, {\left(a^{2} c^{5} d^{9} + \sqrt{a c} a^{2} c^{4} d^{8} e - 4 \, a^{3} c^{4} d^{7} e^{2} - 4 \, \sqrt{a c} a^{3} c^{3} d^{6} e^{3} + 6 \, a^{4} c^{3} d^{5} e^{4} + 6 \, \sqrt{a c} a^{4} c^{2} d^{4} e^{5} - 4 \, a^{5} c^{2} d^{3} e^{6} - 4 \, \sqrt{a c} a^{5} c d^{2} e^{7} + a^{6} c d e^{8} + \sqrt{a c} a^{6} e^{9}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|}} - \frac{{\left(x e + d\right)}^{2} A c^{2} d^{2} e - {\left(x e + d\right)} A c^{2} d^{3} e - 6 \, {\left(x e + d\right)}^{2} B a c d e^{2} + 11 \, {\left(x e + d\right)} B a c d^{2} e^{2} - 4 \, B a c d^{3} e^{2} + 5 \, {\left(x e + d\right)}^{2} A a c e^{3} - 11 \, {\left(x e + d\right)} A a c d e^{3} + 4 \, A a c d^{2} e^{3} + {\left(x e + d\right)} B a^{2} e^{4} + 4 \, B a^{2} d e^{4} - 4 \, A a^{2} e^{5}}{2 \, {\left(a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left({\left(x e + d\right)}^{\frac{5}{2}} c - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d + \sqrt{x e + d} c d^{2} - \sqrt{x e + d} a e^{2}\right)}}"," ",0,"1/4*(6*(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)^2*B*a*c*d*abs(c)*e^2 - (a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)^2*(c^2*d^2*e + 5*a*c*e^3)*A*abs(c) - (sqrt(a*c)*c^4*d^7*e - 15*sqrt(a*c)*a*c^3*d^5*e^3 + 27*sqrt(a*c)*a^2*c^2*d^3*e^5 - 13*sqrt(a*c)*a^3*c*d*e^7)*A*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) - 3*(3*sqrt(a*c)*a*c^3*d^6*e^2 - 5*sqrt(a*c)*a^2*c^2*d^4*e^4 + sqrt(a*c)*a^3*c*d^2*e^6 + sqrt(a*c)*a^4*e^8)*B*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) + 2*(a*c^7*d^12*e - 8*a^2*c^6*d^10*e^3 + 22*a^3*c^5*d^8*e^5 - 28*a^4*c^4*d^6*e^7 + 17*a^5*c^3*d^4*e^9 - 4*a^6*c^2*d^2*e^11)*A*abs(c) + 3*(a^2*c^6*d^11*e^2 - 3*a^3*c^5*d^9*e^4 + 2*a^4*c^4*d^7*e^6 + 2*a^5*c^3*d^5*e^8 - 3*a^6*c^2*d^3*e^10 + a^7*c*d*e^12)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4 + sqrt((a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)^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)*(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/((a^2*c^5*d^8*e - sqrt(a*c)*a*c^5*d^9 + 4*sqrt(a*c)*a^2*c^4*d^7*e^2 - 4*a^3*c^4*d^6*e^3 - 6*sqrt(a*c)*a^3*c^3*d^5*e^4 + 6*a^4*c^3*d^4*e^5 + 4*sqrt(a*c)*a^4*c^2*d^3*e^6 - 4*a^5*c^2*d^2*e^7 - sqrt(a*c)*a^5*c*d*e^8 + a^6*c*e^9)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)) + 1/4*(6*(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)^2*sqrt(a*c)*B*a*d*abs(c)*e^2 - (a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)^2*(sqrt(a*c)*c*d^2*e + 5*sqrt(a*c)*a*e^3)*A*abs(c) + (a*c^4*d^7*e - 15*a^2*c^3*d^5*e^3 + 27*a^3*c^2*d^3*e^5 - 13*a^4*c*d*e^7)*A*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) + 3*(3*a^2*c^3*d^6*e^2 - 5*a^3*c^2*d^4*e^4 + a^4*c*d^2*e^6 + a^5*e^8)*B*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) + 2*(sqrt(a*c)*a*c^6*d^12*e - 8*sqrt(a*c)*a^2*c^5*d^10*e^3 + 22*sqrt(a*c)*a^3*c^4*d^8*e^5 - 28*sqrt(a*c)*a^4*c^3*d^6*e^7 + 17*sqrt(a*c)*a^5*c^2*d^4*e^9 - 4*sqrt(a*c)*a^6*c*d^2*e^11)*A*abs(c) + 3*(sqrt(a*c)*a^2*c^5*d^11*e^2 - 3*sqrt(a*c)*a^3*c^4*d^9*e^4 + 2*sqrt(a*c)*a^4*c^3*d^7*e^6 + 2*sqrt(a*c)*a^5*c^2*d^5*e^8 - 3*sqrt(a*c)*a^6*c*d^3*e^10 + sqrt(a*c)*a^7*d*e^12)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4 - sqrt((a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)^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)*(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/((a^2*c^5*d^9 + sqrt(a*c)*a^2*c^4*d^8*e - 4*a^3*c^4*d^7*e^2 - 4*sqrt(a*c)*a^3*c^3*d^6*e^3 + 6*a^4*c^3*d^5*e^4 + 6*sqrt(a*c)*a^4*c^2*d^4*e^5 - 4*a^5*c^2*d^3*e^6 - 4*sqrt(a*c)*a^5*c*d^2*e^7 + a^6*c*d*e^8 + sqrt(a*c)*a^6*e^9)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)) - 1/2*((x*e + d)^2*A*c^2*d^2*e - (x*e + d)*A*c^2*d^3*e - 6*(x*e + d)^2*B*a*c*d*e^2 + 11*(x*e + d)*B*a*c*d^2*e^2 - 4*B*a*c*d^3*e^2 + 5*(x*e + d)^2*A*a*c*e^3 - 11*(x*e + d)*A*a*c*d*e^3 + 4*A*a*c*d^2*e^3 + (x*e + d)*B*a^2*e^4 + 4*B*a^2*d*e^4 - 4*A*a^2*e^5)/((a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)*((x*e + d)^(5/2)*c - 2*(x*e + d)^(3/2)*c*d + sqrt(x*e + d)*c*d^2 - sqrt(x*e + d)*a*e^2))","B",0
1458,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(7/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
1459,1,728,0,0.604137," ","integrate((B*x+A)*(e*x+d)^(5/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","-\frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{3} d^{2} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{3} d^{3} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d^{4} e - 6 \, \sqrt{x e + d} A c^{3} d^{5} e - 5 \, {\left(x e + d\right)}^{\frac{7}{2}} B a c^{2} d e^{2} + 15 \, {\left(x e + d\right)}^{\frac{5}{2}} B a c^{2} d^{2} e^{2} - 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c^{2} d^{3} e^{2} + 5 \, \sqrt{x e + d} B a c^{2} d^{4} e^{2} - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} A a c^{2} e^{3} + 8 \, {\left(x e + d\right)}^{\frac{5}{2}} A a c^{2} d e^{3} - 17 \, {\left(x e + d\right)}^{\frac{3}{2}} A a c^{2} d^{2} e^{3} + 12 \, \sqrt{x e + d} A a c^{2} d^{3} e^{3} - 9 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} c e^{4} + 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} c d e^{4} - 10 \, \sqrt{x e + d} B a^{2} c d^{2} e^{4} - {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} c e^{5} - 6 \, \sqrt{x e + d} A a^{2} c d e^{5} + 5 \, \sqrt{x e + d} B a^{3} e^{6}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2} a^{2} c^{2}} - \frac{{\left(3 \, {\left(2 \, a c d e - 4 \, \sqrt{a c} c d^{2} + \sqrt{a c} a e^{2}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} A {\left| c \right|} + 5 \, {\left(2 \, \sqrt{a c} a d e - a^{2} e^{2}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d + \sqrt{a^{4} c^{6} d^{2} - {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} a^{2} c^{3}}}{a^{2} c^{3}}}}\right)}{32 \, a^{3} c^{4}} - \frac{{\left(3 \, {\left(2 \, a c d e + 4 \, \sqrt{a c} c d^{2} - \sqrt{a c} a e^{2}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} A {\left| c \right|} - 5 \, {\left(2 \, \sqrt{a c} a d e + a^{2} e^{2}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d - \sqrt{a^{4} c^{6} d^{2} - {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} a^{2} c^{3}}}{a^{2} c^{3}}}}\right)}{32 \, a^{3} c^{4}}"," ",0,"-1/16*(6*(x*e + d)^(7/2)*A*c^3*d^2*e - 18*(x*e + d)^(5/2)*A*c^3*d^3*e + 18*(x*e + d)^(3/2)*A*c^3*d^4*e - 6*sqrt(x*e + d)*A*c^3*d^5*e - 5*(x*e + d)^(7/2)*B*a*c^2*d*e^2 + 15*(x*e + d)^(5/2)*B*a*c^2*d^2*e^2 - 15*(x*e + d)^(3/2)*B*a*c^2*d^3*e^2 + 5*sqrt(x*e + d)*B*a*c^2*d^4*e^2 - 3*(x*e + d)^(7/2)*A*a*c^2*e^3 + 8*(x*e + d)^(5/2)*A*a*c^2*d*e^3 - 17*(x*e + d)^(3/2)*A*a*c^2*d^2*e^3 + 12*sqrt(x*e + d)*A*a*c^2*d^3*e^3 - 9*(x*e + d)^(5/2)*B*a^2*c*e^4 + 15*(x*e + d)^(3/2)*B*a^2*c*d*e^4 - 10*sqrt(x*e + d)*B*a^2*c*d^2*e^4 - (x*e + d)^(3/2)*A*a^2*c*e^5 - 6*sqrt(x*e + d)*A*a^2*c*d*e^5 + 5*sqrt(x*e + d)*B*a^3*e^6)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2*a^2*c^2) - 1/32*(3*(2*a*c*d*e - 4*sqrt(a*c)*c*d^2 + sqrt(a*c)*a*e^2)*sqrt(-c^2*d - sqrt(a*c)*c*e)*A*abs(c) + 5*(2*sqrt(a*c)*a*d*e - a^2*e^2)*sqrt(-c^2*d - sqrt(a*c)*c*e)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d + sqrt(a^4*c^6*d^2 - (a^2*c^3*d^2 - a^3*c^2*e^2)*a^2*c^3))/(a^2*c^3)))/(a^3*c^4) - 1/32*(3*(2*a*c*d*e + 4*sqrt(a*c)*c*d^2 - sqrt(a*c)*a*e^2)*sqrt(-c^2*d + sqrt(a*c)*c*e)*A*abs(c) - 5*(2*sqrt(a*c)*a*d*e + a^2*e^2)*sqrt(-c^2*d + sqrt(a*c)*c*e)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d - sqrt(a^4*c^6*d^2 - (a^2*c^3*d^2 - a^3*c^2*e^2)*a^2*c^3))/(a^2*c^3)))/(a^3*c^4)","B",0
1460,1,754,0,0.743342," ","integrate((B*x+A)*(e*x+d)^(3/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, \sqrt{a c} B a c^{3} d^{2} e - B a^{2} c^{2} d {\left| c \right|} e^{2} + 2 \, \sqrt{a c} A a c^{3} d e^{2} - \sqrt{a c} B a^{2} c^{2} e^{3} + {\left(2 \, a c^{3} d^{2} e - a^{2} c^{2} e^{3}\right)} A {\left| c \right|} - {\left(4 \, \sqrt{a c} c^{4} d^{3} - \sqrt{a c} a c^{3} d e^{2}\right)} A\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d + \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{4} d - \sqrt{a c} a^{3} c^{3} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} - \frac{3 \, {\left(2 \, \sqrt{a c} B a c^{3} d^{2} e + B a^{2} c^{2} d {\left| c \right|} e^{2} + 2 \, \sqrt{a c} A a c^{3} d e^{2} - \sqrt{a c} B a^{2} c^{2} e^{3} - {\left(2 \, a c^{3} d^{2} e - a^{2} c^{2} e^{3}\right)} A {\left| c \right|} - {\left(4 \, \sqrt{a c} c^{4} d^{3} - \sqrt{a c} a c^{3} d e^{2}\right)} A\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d - \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{4} d + \sqrt{a c} a^{3} c^{3} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{2} d e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{2} d^{2} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{2} d^{3} e - 6 \, \sqrt{x e + d} A c^{2} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} B a c e^{2} + 9 \, {\left(x e + d\right)}^{\frac{5}{2}} B a c d e^{2} - 9 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c d^{2} e^{2} + 3 \, \sqrt{x e + d} B a c d^{3} e^{2} - {\left(x e + d\right)}^{\frac{5}{2}} A a c e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} A a c d e^{3} + 9 \, \sqrt{x e + d} A a c d^{2} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} e^{4} - 3 \, \sqrt{x e + d} B a^{2} d e^{4} - 3 \, \sqrt{x e + d} A a^{2} e^{5}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2} a^{2} c}"," ",0,"3/32*(2*sqrt(a*c)*B*a*c^3*d^2*e - B*a^2*c^2*d*abs(c)*e^2 + 2*sqrt(a*c)*A*a*c^3*d*e^2 - sqrt(a*c)*B*a^2*c^2*e^3 + (2*a*c^3*d^2*e - a^2*c^2*e^3)*A*abs(c) - (4*sqrt(a*c)*c^4*d^3 - sqrt(a*c)*a*c^3*d*e^2)*A)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d + sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 - a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^4*d - sqrt(a*c)*a^3*c^3*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) - 3/32*(2*sqrt(a*c)*B*a*c^3*d^2*e + B*a^2*c^2*d*abs(c)*e^2 + 2*sqrt(a*c)*A*a*c^3*d*e^2 - sqrt(a*c)*B*a^2*c^2*e^3 - (2*a*c^3*d^2*e - a^2*c^2*e^3)*A*abs(c) - (4*sqrt(a*c)*c^4*d^3 - sqrt(a*c)*a*c^3*d*e^2)*A)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d - sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 - a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^4*d + sqrt(a*c)*a^3*c^3*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 1/16*(6*(x*e + d)^(7/2)*A*c^2*d*e - 18*(x*e + d)^(5/2)*A*c^2*d^2*e + 18*(x*e + d)^(3/2)*A*c^2*d^3*e - 6*sqrt(x*e + d)*A*c^2*d^4*e - 3*(x*e + d)^(7/2)*B*a*c*e^2 + 9*(x*e + d)^(5/2)*B*a*c*d*e^2 - 9*(x*e + d)^(3/2)*B*a*c*d^2*e^2 + 3*sqrt(x*e + d)*B*a*c*d^3*e^2 - (x*e + d)^(5/2)*A*a*c*e^3 - 8*(x*e + d)^(3/2)*A*a*c*d*e^3 + 9*sqrt(x*e + d)*A*a*c*d^2*e^3 - (x*e + d)^(3/2)*B*a^2*e^4 - 3*sqrt(x*e + d)*B*a^2*d*e^4 - 3*sqrt(x*e + d)*A*a^2*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2*a^2*c)","B",0
1461,1,1637,0,1.246833," ","integrate((B*x+A)*(e*x+d)^(1/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left({\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3}\right)}^{2} B a d {\left| c \right|} e^{2} - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3}\right)}^{2} {\left(6 \, c d^{2} e - 5 \, a e^{3}\right)} A {\left| c \right|} - 2 \, {\left(3 \, \sqrt{a c} a c^{3} d^{5} e - 7 \, \sqrt{a c} a^{2} c^{2} d^{3} e^{3} + 4 \, \sqrt{a c} a^{3} c d e^{5}\right)} A {\left| a^{2} c^{2} d^{2} e - a^{3} c e^{3} \right|} {\left| c \right|} + {\left(\sqrt{a c} a^{2} c^{2} d^{4} e^{2} - 4 \, \sqrt{a c} a^{3} c d^{2} e^{4} + 3 \, \sqrt{a c} a^{4} e^{6}\right)} B {\left| a^{2} c^{2} d^{2} e - a^{3} c e^{3} \right|} {\left| c \right|} + {\left(12 \, a^{3} c^{6} d^{8} e - 37 \, a^{4} c^{5} d^{6} e^{3} + 38 \, a^{5} c^{4} d^{4} e^{5} - 13 \, a^{6} c^{3} d^{2} e^{7}\right)} A {\left| c \right|} - {\left(2 \, a^{4} c^{5} d^{7} e^{2} - 7 \, a^{5} c^{4} d^{5} e^{4} + 8 \, a^{6} c^{3} d^{3} e^{6} - 3 \, a^{7} c^{2} d e^{8}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} + \sqrt{{\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2}\right)}^{2} - {\left(a^{2} c^{3} d^{4} - 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)}}}{a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}}}}\right)}{32 \, {\left(a^{4} c^{4} d^{4} e - \sqrt{a c} a^{3} c^{4} d^{5} + 2 \, \sqrt{a c} a^{4} c^{3} d^{3} e^{2} - 2 \, a^{5} c^{3} d^{2} e^{3} - \sqrt{a c} a^{5} c^{2} d e^{4} + a^{6} c^{2} e^{5}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a^{2} c^{2} d^{2} e - a^{3} c e^{3} \right|}} + \frac{{\left({\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3}\right)}^{2} \sqrt{a c} B a d {\left| c \right|} e^{2} - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3}\right)}^{2} {\left(6 \, \sqrt{a c} c d^{2} e - 5 \, \sqrt{a c} a e^{3}\right)} A {\left| c \right|} + 2 \, {\left(3 \, a^{2} c^{4} d^{5} e - 7 \, a^{3} c^{3} d^{3} e^{3} + 4 \, a^{4} c^{2} d e^{5}\right)} A {\left| a^{2} c^{2} d^{2} e - a^{3} c e^{3} \right|} {\left| c \right|} - {\left(a^{3} c^{3} d^{4} e^{2} - 4 \, a^{4} c^{2} d^{2} e^{4} + 3 \, a^{5} c e^{6}\right)} B {\left| a^{2} c^{2} d^{2} e - a^{3} c e^{3} \right|} {\left| c \right|} + {\left(12 \, \sqrt{a c} a^{3} c^{6} d^{8} e - 37 \, \sqrt{a c} a^{4} c^{5} d^{6} e^{3} + 38 \, \sqrt{a c} a^{5} c^{4} d^{4} e^{5} - 13 \, \sqrt{a c} a^{6} c^{3} d^{2} e^{7}\right)} A {\left| c \right|} - {\left(2 \, \sqrt{a c} a^{4} c^{5} d^{7} e^{2} - 7 \, \sqrt{a c} a^{5} c^{4} d^{5} e^{4} + 8 \, \sqrt{a c} a^{6} c^{3} d^{3} e^{6} - 3 \, \sqrt{a c} a^{7} c^{2} d e^{8}\right)} B {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} - \sqrt{{\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2}\right)}^{2} - {\left(a^{2} c^{3} d^{4} - 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)}}}{a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}}}}\right)}{32 \, {\left(a^{4} c^{5} d^{5} + \sqrt{a c} a^{4} c^{4} d^{4} e - 2 \, a^{5} c^{4} d^{3} e^{2} - 2 \, \sqrt{a c} a^{5} c^{3} d^{2} e^{3} + a^{6} c^{3} d e^{4} + \sqrt{a c} a^{6} c^{2} e^{5}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a^{2} c^{2} d^{2} e - a^{3} c e^{3} \right|}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} A c^{3} d^{2} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} A c^{3} d^{3} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} A c^{3} d^{4} e - 6 \, \sqrt{x e + d} A c^{3} d^{5} e - {\left(x e + d\right)}^{\frac{7}{2}} B a c^{2} d e^{2} + 3 \, {\left(x e + d\right)}^{\frac{5}{2}} B a c^{2} d^{2} e^{2} - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} B a c^{2} d^{3} e^{2} + \sqrt{x e + d} B a c^{2} d^{4} e^{2} - 5 \, {\left(x e + d\right)}^{\frac{7}{2}} A a c^{2} e^{3} + 14 \, {\left(x e + d\right)}^{\frac{5}{2}} A a c^{2} d e^{3} - 23 \, {\left(x e + d\right)}^{\frac{3}{2}} A a c^{2} d^{2} e^{3} + 14 \, \sqrt{x e + d} A a c^{2} d^{3} e^{3} + {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} c e^{4} - {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} c d e^{4} - 4 \, \sqrt{x e + d} B a^{2} c d^{2} e^{4} + 9 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} c e^{5} - 8 \, \sqrt{x e + d} A a^{2} c d e^{5} + 3 \, \sqrt{x e + d} B a^{3} e^{6}}{16 \, {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2}}"," ",0,"1/32*((a^2*c^2*d^2*e - a^3*c*e^3)^2*B*a*d*abs(c)*e^2 - (a^2*c^2*d^2*e - a^3*c*e^3)^2*(6*c*d^2*e - 5*a*e^3)*A*abs(c) - 2*(3*sqrt(a*c)*a*c^3*d^5*e - 7*sqrt(a*c)*a^2*c^2*d^3*e^3 + 4*sqrt(a*c)*a^3*c*d*e^5)*A*abs(a^2*c^2*d^2*e - a^3*c*e^3)*abs(c) + (sqrt(a*c)*a^2*c^2*d^4*e^2 - 4*sqrt(a*c)*a^3*c*d^2*e^4 + 3*sqrt(a*c)*a^4*e^6)*B*abs(a^2*c^2*d^2*e - a^3*c*e^3)*abs(c) + (12*a^3*c^6*d^8*e - 37*a^4*c^5*d^6*e^3 + 38*a^5*c^4*d^4*e^5 - 13*a^6*c^3*d^2*e^7)*A*abs(c) - (2*a^4*c^5*d^7*e^2 - 7*a^5*c^4*d^5*e^4 + 8*a^6*c^3*d^3*e^6 - 3*a^7*c^2*d*e^8)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d^3 - a^3*c^2*d*e^2 + sqrt((a^2*c^3*d^3 - a^3*c^2*d*e^2)^2 - (a^2*c^3*d^4 - 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*(a^2*c^3*d^2 - a^3*c^2*e^2)))/(a^2*c^3*d^2 - a^3*c^2*e^2)))/((a^4*c^4*d^4*e - sqrt(a*c)*a^3*c^4*d^5 + 2*sqrt(a*c)*a^4*c^3*d^3*e^2 - 2*a^5*c^3*d^2*e^3 - sqrt(a*c)*a^5*c^2*d*e^4 + a^6*c^2*e^5)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a^2*c^2*d^2*e - a^3*c*e^3)) + 1/32*((a^2*c^2*d^2*e - a^3*c*e^3)^2*sqrt(a*c)*B*a*d*abs(c)*e^2 - (a^2*c^2*d^2*e - a^3*c*e^3)^2*(6*sqrt(a*c)*c*d^2*e - 5*sqrt(a*c)*a*e^3)*A*abs(c) + 2*(3*a^2*c^4*d^5*e - 7*a^3*c^3*d^3*e^3 + 4*a^4*c^2*d*e^5)*A*abs(a^2*c^2*d^2*e - a^3*c*e^3)*abs(c) - (a^3*c^3*d^4*e^2 - 4*a^4*c^2*d^2*e^4 + 3*a^5*c*e^6)*B*abs(a^2*c^2*d^2*e - a^3*c*e^3)*abs(c) + (12*sqrt(a*c)*a^3*c^6*d^8*e - 37*sqrt(a*c)*a^4*c^5*d^6*e^3 + 38*sqrt(a*c)*a^5*c^4*d^4*e^5 - 13*sqrt(a*c)*a^6*c^3*d^2*e^7)*A*abs(c) - (2*sqrt(a*c)*a^4*c^5*d^7*e^2 - 7*sqrt(a*c)*a^5*c^4*d^5*e^4 + 8*sqrt(a*c)*a^6*c^3*d^3*e^6 - 3*sqrt(a*c)*a^7*c^2*d*e^8)*B*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d^3 - a^3*c^2*d*e^2 - sqrt((a^2*c^3*d^3 - a^3*c^2*d*e^2)^2 - (a^2*c^3*d^4 - 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*(a^2*c^3*d^2 - a^3*c^2*e^2)))/(a^2*c^3*d^2 - a^3*c^2*e^2)))/((a^4*c^5*d^5 + sqrt(a*c)*a^4*c^4*d^4*e - 2*a^5*c^4*d^3*e^2 - 2*sqrt(a*c)*a^5*c^3*d^2*e^3 + a^6*c^3*d*e^4 + sqrt(a*c)*a^6*c^2*e^5)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a^2*c^2*d^2*e - a^3*c*e^3)) - 1/16*(6*(x*e + d)^(7/2)*A*c^3*d^2*e - 18*(x*e + d)^(5/2)*A*c^3*d^3*e + 18*(x*e + d)^(3/2)*A*c^3*d^4*e - 6*sqrt(x*e + d)*A*c^3*d^5*e - (x*e + d)^(7/2)*B*a*c^2*d*e^2 + 3*(x*e + d)^(5/2)*B*a*c^2*d^2*e^2 - 3*(x*e + d)^(3/2)*B*a*c^2*d^3*e^2 + sqrt(x*e + d)*B*a*c^2*d^4*e^2 - 5*(x*e + d)^(7/2)*A*a*c^2*e^3 + 14*(x*e + d)^(5/2)*A*a*c^2*d*e^3 - 23*(x*e + d)^(3/2)*A*a*c^2*d^2*e^3 + 14*sqrt(x*e + d)*A*a*c^2*d^3*e^3 + (x*e + d)^(5/2)*B*a^2*c*e^4 - (x*e + d)^(3/2)*B*a^2*c*d*e^4 - 4*sqrt(x*e + d)*B*a^2*c*d^2*e^4 + 9*(x*e + d)^(3/2)*A*a^2*c*e^5 - 8*sqrt(x*e + d)*A*a^2*c*d*e^5 + 3*sqrt(x*e + d)*B*a^3*e^6)/((a^2*c^2*d^2 - a^3*c*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2)","B",0
1462,-2,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(1/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
1463,1,2892,0,1.850524," ","integrate((B*x+A)/(-B^2*e*x^2-A^2*e+2*A*B*d)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, A B^{6} d^{2} e - 2 \, A^{2} B^{5} d e^{2} - 8 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d^{2} e - 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d^{2} + 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} d e^{2} - 2 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} B^{5} d - \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d - {\left(8 \, A B^{4} d^{2} e - 8 \, A^{2} B^{3} d e^{2} - 16 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{2} d^{2} e - 8 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{3} d^{2} + 2 \, A^{3} B^{2} e^{3} + 16 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B d e^{2} + 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{2} d e - 4 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} B^{3} d - 2 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{3} d - 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{3} e^{3} + 2 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} A B^{2} e + \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{2} e\right)} B^{2} - {\left(16 \, A B^{5} d^{3} e + 16 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d^{3} e - 32 \, A^{2} B^{4} d^{2} e^{2} + 8 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d^{3} - 32 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} d^{2} e^{2} - 12 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d^{2} e + 20 \, A^{3} B^{3} d e^{3} + 2 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d^{2} + 20 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{3} B^{2} d e^{3} + 4 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} d e^{2} - 3 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d e - 8 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} B^{4} d^{2} - 4 \, A^{4} B^{2} e^{4} + 12 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} A B^{3} d e - 4 \, \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{4} B e^{4} + \sqrt{-B^{2} d - \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} e^{2} - 4 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} A^{2} B^{2} e^{2}\right)} {\left| B \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{{\left(B^{2} d e + \sqrt{B^{4} d^{2} e^{2} - {\left(B^{2} d^{2} e - 2 \, A B d e^{2} + A^{2} e^{3}\right)} B^{2} e}\right)} e^{\left(-1\right)}}{B^{2}}}}\right)}{16 \, A B^{7} d^{4} e^{2} + 8 \, B^{8} d^{4} e - 48 \, A^{2} B^{6} d^{3} e^{3} - 20 \, A B^{7} d^{3} e^{2} + 2 \, B^{8} d^{3} e + 52 \, A^{3} B^{5} d^{2} e^{4} + 16 \, A^{2} B^{6} d^{2} e^{3} - 5 \, A B^{7} d^{2} e^{2} - 24 \, A^{4} B^{4} d e^{5} - 4 \, A^{3} B^{5} d e^{4} + 4 \, A^{2} B^{6} d e^{3} + 4 \, A^{5} B^{3} e^{6} - A^{3} B^{5} e^{4}} + \frac{{\left(4 \, A B^{6} d^{2} e - 2 \, A^{2} B^{5} d e^{2} - 8 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d^{2} e - 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d^{2} + 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} d e^{2} - 2 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} B^{5} d - \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d - {\left(8 \, A B^{4} d^{2} e - 8 \, A^{2} B^{3} d e^{2} - 16 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{2} d^{2} e - 8 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{3} d^{2} + 2 \, A^{3} B^{2} e^{3} + 16 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B d e^{2} + 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{2} d e - 4 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} B^{3} d - 2 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{3} d - 4 \, \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{3} e^{3} + 2 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} A B^{2} e + \sqrt{2 \, A B d e - A^{2} e^{2}} \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{2} e\right)} B^{2} - {\left(16 \, A B^{5} d^{3} e - 16 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d^{3} e - 32 \, A^{2} B^{4} d^{2} e^{2} - 8 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d^{3} + 32 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} d^{2} e^{2} + 12 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d^{2} e + 20 \, A^{3} B^{3} d e^{3} - 2 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} B^{5} d^{2} - 20 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{3} B^{2} d e^{3} - 4 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} d e^{2} + 3 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A B^{4} d e - 8 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} B^{4} d^{2} - 4 \, A^{4} B^{2} e^{4} + 12 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} A B^{3} d e + 4 \, \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{4} B e^{4} - \sqrt{-B^{2} d + \sqrt{2 \, A B d e - A^{2} e^{2}} B} A^{2} B^{3} e^{2} - 4 \, {\left(2 \, A B d e - A^{2} e^{2}\right)} A^{2} B^{2} e^{2}\right)} {\left| B \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{{\left(B^{2} d e - \sqrt{B^{4} d^{2} e^{2} - {\left(B^{2} d^{2} e - 2 \, A B d e^{2} + A^{2} e^{3}\right)} B^{2} e}\right)} e^{\left(-1\right)}}{B^{2}}}}\right)}{16 \, A B^{7} d^{4} e^{2} + 8 \, B^{8} d^{4} e - 48 \, A^{2} B^{6} d^{3} e^{3} - 20 \, A B^{7} d^{3} e^{2} + 2 \, B^{8} d^{3} e + 52 \, A^{3} B^{5} d^{2} e^{4} + 16 \, A^{2} B^{6} d^{2} e^{3} - 5 \, A B^{7} d^{2} e^{2} - 24 \, A^{4} B^{4} d e^{5} - 4 \, A^{3} B^{5} d e^{4} + 4 \, A^{2} B^{6} d e^{3} + 4 \, A^{5} B^{3} e^{6} - A^{3} B^{5} e^{4}}"," ",0,"-(4*A*B^6*d^2*e - 2*A^2*B^5*d*e^2 - 8*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d^2*e - 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d^2 + 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*d*e^2 - 2*(2*A*B*d*e - A^2*e^2)*B^5*d - sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d - (8*A*B^4*d^2*e - 8*A^2*B^3*d*e^2 - 16*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^2*d^2*e - 8*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*B^3*d^2 + 2*A^3*B^2*e^3 + 16*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B*d*e^2 + 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^2*d*e - 4*(2*A*B*d*e - A^2*e^2)*B^3*d - 2*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*B^3*d - 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^3*e^3 + 2*(2*A*B*d*e - A^2*e^2)*A*B^2*e + sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^2*e)*B^2 - (16*A*B^5*d^3*e + 16*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d^3*e - 32*A^2*B^4*d^2*e^2 + 8*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d^3 - 32*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*d^2*e^2 - 12*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d^2*e + 20*A^3*B^3*d*e^3 + 2*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d^2 + 20*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^3*B^2*d*e^3 + 4*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*d*e^2 - 3*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d*e - 8*(2*A*B*d*e - A^2*e^2)*B^4*d^2 - 4*A^4*B^2*e^4 + 12*(2*A*B*d*e - A^2*e^2)*A*B^3*d*e - 4*sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^4*B*e^4 + sqrt(-B^2*d - sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*e^2 - 4*(2*A*B*d*e - A^2*e^2)*A^2*B^2*e^2)*abs(B))*arctan(sqrt(x*e + d)/sqrt(-(B^2*d*e + sqrt(B^4*d^2*e^2 - (B^2*d^2*e - 2*A*B*d*e^2 + A^2*e^3)*B^2*e))*e^(-1)/B^2))/(16*A*B^7*d^4*e^2 + 8*B^8*d^4*e - 48*A^2*B^6*d^3*e^3 - 20*A*B^7*d^3*e^2 + 2*B^8*d^3*e + 52*A^3*B^5*d^2*e^4 + 16*A^2*B^6*d^2*e^3 - 5*A*B^7*d^2*e^2 - 24*A^4*B^4*d*e^5 - 4*A^3*B^5*d*e^4 + 4*A^2*B^6*d*e^3 + 4*A^5*B^3*e^6 - A^3*B^5*e^4) + (4*A*B^6*d^2*e - 2*A^2*B^5*d*e^2 - 8*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d^2*e - 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d^2 + 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*d*e^2 - 2*(2*A*B*d*e - A^2*e^2)*B^5*d - sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d - (8*A*B^4*d^2*e - 8*A^2*B^3*d*e^2 - 16*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^2*d^2*e - 8*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*B^3*d^2 + 2*A^3*B^2*e^3 + 16*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B*d*e^2 + 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^2*d*e - 4*(2*A*B*d*e - A^2*e^2)*B^3*d - 2*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*B^3*d - 4*sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^3*e^3 + 2*(2*A*B*d*e - A^2*e^2)*A*B^2*e + sqrt(2*A*B*d*e - A^2*e^2)*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^2*e)*B^2 - (16*A*B^5*d^3*e - 16*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d^3*e - 32*A^2*B^4*d^2*e^2 - 8*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d^3 + 32*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*d^2*e^2 + 12*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d^2*e + 20*A^3*B^3*d*e^3 - 2*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*B^5*d^2 - 20*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^3*B^2*d*e^3 - 4*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*d*e^2 + 3*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A*B^4*d*e - 8*(2*A*B*d*e - A^2*e^2)*B^4*d^2 - 4*A^4*B^2*e^4 + 12*(2*A*B*d*e - A^2*e^2)*A*B^3*d*e + 4*sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^4*B*e^4 - sqrt(-B^2*d + sqrt(2*A*B*d*e - A^2*e^2)*B)*A^2*B^3*e^2 - 4*(2*A*B*d*e - A^2*e^2)*A^2*B^2*e^2)*abs(B))*arctan(sqrt(x*e + d)/sqrt(-(B^2*d*e - sqrt(B^4*d^2*e^2 - (B^2*d^2*e - 2*A*B*d*e^2 + A^2*e^3)*B^2*e))*e^(-1)/B^2))/(16*A*B^7*d^4*e^2 + 8*B^8*d^4*e - 48*A^2*B^6*d^3*e^3 - 20*A*B^7*d^3*e^2 + 2*B^8*d^3*e + 52*A^3*B^5*d^2*e^4 + 16*A^2*B^6*d^2*e^3 - 5*A*B^7*d^2*e^2 - 24*A^4*B^4*d*e^5 - 4*A^3*B^5*d*e^4 + 4*A^2*B^6*d*e^3 + 4*A^5*B^3*e^6 - A^3*B^5*e^4)","B",0
1464,-2,0,0,0.000000," ","integrate(2*(B*x+A)/(x^2+1)/(2*(A^2*e-B^2*e)/A/B+4*e*x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Undef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf 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limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf 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limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in 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limit2*((8*(A^2*B^8*exp(1)^2-A^4*B^6*exp(1)^2-A^6*B^4*exp(1)^2+A^8*B^2*exp(1)^2)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+16*(-A^3*B^7*exp(1)^2+A^7*B^3*exp(1)^2)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+16*(-A^3*B^7*exp(1)^2+A^7*B^3*exp(1)^2)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+8*(A^2*B^8*exp(1)^2-A^4*B^6*exp(1)^2-A^6*B^4*exp(1)^2+A^8*B^2*exp(1)^2)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+8*(A^4*B^12*exp(1)^4-2*A^8*B^8*exp(1)^4+A^12*B^4*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2-A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3+48*(-A^6*B^12*exp(1)^4-A^8*B^10*exp(1)^4+A^10*B^8*exp(1)^4+A^12*B^6*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^5*B^11*exp(1)^4-A^7*B^9*exp(1)^4+A^9*B^7*exp(1)^4+A^11*B^5*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2-A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^5*B^13*exp(1)^4-2*A^9*B^9*exp(1)^4+A^13*B^5*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^5*B^13*exp(1)^4-2*A^9*B^9*exp(1)^4+A^13*B^5*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+48*(A^5*B^13*exp(1)^4-2*A^9*B^9*exp(1)^4+A^13*B^5*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+96*(-A^6*B^12*exp(1)^4-A^8*B^10*exp(1)^4+A^10*B^8*exp(1)^4+A^12*B^6*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^4*B^12*exp(1)^4-2*A^8*B^8*exp(1)^4+A^12*B^4*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2-A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+96*(-A^6*B^12*exp(1)^4-A^8*B^10*exp(1)^4+A^10*B^8*exp(1)^4+A^12*B^6*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^5*B^13*exp(1)^4-2*A^9*B^9*exp(1)^4+A^13*B^5*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+16*(-A^5*B^11*exp(1)^4-A^7*B^9*exp(1)^4+A^9*B^7*exp(1)^4+A^11*B^5*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2+A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3+48*(-A^6*B^12*exp(1)^4-A^8*B^10*exp(1)^4+A^10*B^8*exp(1)^4+A^12*B^6*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^4*B^12*exp(1)^4-2*A^8*B^8*exp(1)^4+A^12*B^4*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2+A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^6*B^12*exp(1)^4-A^8*B^10*exp(1)^4+A^10*B^8*exp(1)^4+A^12*B^6*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+48*(A^5*B^13*exp(1)^4-2*A^9*B^9*exp(1)^4+A^13*B^5*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^5*B^11*exp(1)^4-A^7*B^9*exp(1)^4+A^9*B^7*exp(1)^4+A^11*B^5*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2+A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+16*(-A^5*B^11*exp(1)^4-A^7*B^9*exp(1)^4+A^9*B^7*exp(1)^4+A^11*B^5*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2-A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3+24*(A^5*B^13*exp(1)^4-2*A^9*B^9*exp(1)^4+A^13*B^5*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2-A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)+A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^6*B^12*exp(1)^4-A^8*B^10*exp(1)^4+A^10*B^8*exp(1)^4+A^12*B^6*exp(1)^4)*sqrt(A^2*B^6*exp(1)^2+2*A^4*B^4*exp(1)^2+A^6*B^2*exp(1)^2+A*B^3*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^3*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+8*(A^4*B^12*exp(1)^4-2*A^8*B^8*exp(1)^4+A^12*B^4*exp(1)^4)*sqrt(A^2*B^10*exp(1)^2+A^4*B^8*exp(1)^2+A^8*B^4*exp(1)^2+A^10*B^2*exp(1)^2+A*B^7*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1)-A^7*B*abs(A*B^3*exp(1)+A^3*B*exp(1))*exp(1))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3)/(-64*A^3*exp(1)+64*A*B^2*exp(1))/sqrt(-A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*B*exp(1)+A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)/(A^3*exp(1)*B+A*exp(1)*B^3)^2*ln((A^2*exp(1)+2*A*B*x*exp(1)-B^2*exp(1))/A/B-2*((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4)*sqrt((1+(A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)*sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2))*sqrt((A^2*exp(1)+2*A*B*x*exp(1)-B^2*exp(1))/A/B)+((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4)*((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4))+(16*(A^4*B^8*exp(1)^3-A^8*B^4*exp(1)^3)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+8*(A^3*B^9*exp(1)^3-A^5*B^7*exp(1)^3-A^7*B^5*exp(1)^3+A^9*B^3*exp(1)^3)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+8*(A^3*B^9*exp(1)^3-A^5*B^7*exp(1)^3-A^7*B^5*exp(1)^3+A^9*B^3*exp(1)^3)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+16*(A^4*B^8*exp(1)^3-A^8*B^4*exp(1)^3)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*(A^3*exp(1)*B+A*exp(1)*B^3)^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+16*(-A^6*B^12*exp(1)^5-A^8*B^10*exp(1)^5+A^10*B^8*exp(1)^5+A^12*B^6*exp(1)^5)*sqrt(-A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)+A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)-A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3+24*(A^6*B^14*exp(1)^5-2*A^10*B^10*exp(1)^5+A^14*B^6*exp(1)^5)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^5*B^13*exp(1)^5-2*A^9*B^9*exp(1)^5+A^13*B^5*exp(1)^5)*sqrt(-A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)+A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)-A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^7*B^13*exp(1)^5-A^9*B^11*exp(1)^5+A^11*B^9*exp(1)^5+A^13*B^7*exp(1)^5)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^7*B^13*exp(1)^5-A^9*B^11*exp(1)^5+A^11*B^9*exp(1)^5+A^13*B^7*exp(1)^5)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+96*(-A^7*B^13*exp(1)^5-A^9*B^11*exp(1)^5+A^11*B^9*exp(1)^5+A^13*B^7*exp(1)^5)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(A^6*B^14*exp(1)^5-2*A^10*B^10*exp(1)^5+A^14*B^6*exp(1)^5)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^6*B^12*exp(1)^5-A^8*B^10*exp(1)^5+A^10*B^8*exp(1)^5+A^12*B^6*exp(1)^5)*sqrt(-A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)+A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)-A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+48*(A^6*B^14*exp(1)^5-2*A^10*B^10*exp(1)^5+A^14*B^6*exp(1)^5)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^7*B^13*exp(1)^5-A^9*B^11*exp(1)^5+A^11*B^9*exp(1)^5+A^13*B^7*exp(1)^5)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+8*(A^5*B^13*exp(1)^5-2*A^9*B^9*exp(1)^5+A^13*B^5*exp(1)^5)*sqrt(A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)-A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)+A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3+24*(A^6*B^14*exp(1)^5-2*A^10*B^10*exp(1)^5+A^14*B^6*exp(1)^5)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+48*(-A^6*B^12*exp(1)^5-A^8*B^10*exp(1)^5+A^10*B^8*exp(1)^5+A^12*B^6*exp(1)^5)*sqrt(A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)-A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)+A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^6*B^14*exp(1)^5-2*A^10*B^10*exp(1)^5+A^14*B^6*exp(1)^5)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+96*(-A^7*B^13*exp(1)^5-A^9*B^11*exp(1)^5+A^11*B^9*exp(1)^5+A^13*B^7*exp(1)^5)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^5*B^13*exp(1)^5-2*A^9*B^9*exp(1)^5+A^13*B^5*exp(1)^5)*sqrt(A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)-A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)+A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*im(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+8*(A^5*B^13*exp(1)^5-2*A^9*B^9*exp(1)^5+A^13*B^5*exp(1)^5)*sqrt(-A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)+A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)-A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3+48*(-A^7*B^13*exp(1)^5-A^9*B^11*exp(1)^5+A^11*B^9*exp(1)^5+A^13*B^7*exp(1)^5)*sqrt(-A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))+B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))+24*(A^6*B^14*exp(1)^5-2*A^10*B^10*exp(1)^5+A^14*B^6*exp(1)^5)*sqrt(A^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^4*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^7*exp(1)-3*A^3*B^5*exp(1)-3*A^5*B^3*exp(1)-A^7*B*exp(1))*re(sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^2+16*(-A^6*B^12*exp(1)^5-A^8*B^10*exp(1)^5+A^10*B^8*exp(1)^5+A^12*B^6*exp(1)^5)*sqrt(A^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-B^8*abs(A*B^3*exp(1)+A^3*B*exp(1))-A*B^11*exp(1)-A^2*B^6*abs(A*B^3*exp(1)+A^3*B*exp(1))-2*A^3*B^9*exp(1)-A^5*B^7*exp(1)+A^6*B^2*abs(A*B^3*exp(1)+A^3*B*exp(1))-A^7*B^5*exp(1)-2*A^9*B^3*exp(1)-A^11*B*exp(1))*re(sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)))^3)/(32*A^6*B*exp(1)^2-32*A^2*B^5*exp(1)^2)/abs(A^3*B*exp(1)+A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)/(A^3*exp(1)*B+A*exp(1)*B^3)^2*atan((sqrt((A^2*exp(1)+2*A*B*x*exp(1)-B^2*exp(1))/A/B)-sign(cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2))*sqrt((1+(A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)*((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4))/sign(sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2))/sqrt((1-(A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)/((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4))+(-2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)-6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2+2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+(3*A^2-3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(-9*A^2+9*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(9*A^2-9*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2+(-3*A^2+3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2-18*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+18*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2+2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)-6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3-2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(-A^2+B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+(3*A^2-3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(-3*A^2+3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2+(-A^2+B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(A^2-B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+(A^2-B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2))/(4*sqrt(2)*A^3*exp(1)+4*sqrt(2)*A*B^2*exp(1))*ln((A^2*exp(1)+2*A*B*x*exp(1)-B^2*exp(1))/A/B+2*((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4)*cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)*sqrt((A^2*exp(1)+2*A*B*x*exp(1)-B^2*exp(1))/A/B)+((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4)*((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4))-((A^2-B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+(-3*A^2+3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(3*A^2-3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2+(-A^2+B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)-18*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+18*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2-6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+(-3*A^2+3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2+(9*A^2-9*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(-9*A^2+9*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2+(-A^2+B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+(3*A^2-3*B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+(A^2-B^2)*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cos(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)-2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)-6*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^2-2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*cosh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)+2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)^3+2*A*B*sqrt(-A^3*B*exp(1)-A*B^3*exp(1))*sin(re(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2)*sinh(im(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3)))/2))/(2*sqrt(2)*A^3*exp(1)+2*sqrt(2)*A*B^2*exp(1))*atan((sqrt((A^2*exp(1)+2*A*B*x*exp(1)-B^2*exp(1))/A/B)+cos(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)*((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4))/sin(acos((A^3*B*exp(1)-A*B^3*exp(1))/abs(A^3*exp(1)*B+A*exp(1)*B^3))/2)/((A^4*exp(1)^2+2*A^2*B^2*exp(1)^2+B^4*exp(1)^2)/A^2/B^2)^(1/4)))","F(-2)",0
1465,1,68,0,0.192041," ","integrate((B*x+A)/(-x^2+1)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{{\left(A - B\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d + e}}\right)}{\sqrt{-d + e}} - \frac{{\left(A + B\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d - e}}\right)}{\sqrt{-d - e}}"," ",0,"(A - B)*arctan(sqrt(x*e + d)/sqrt(-d + e))/sqrt(-d + e) - (A + B)*arctan(sqrt(x*e + d)/sqrt(-d - e))/sqrt(-d - e)","A",0
1466,-1,0,0,0.000000," ","integrate((B*x+A)/(x^2+1)/(e*x+d)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1467,1,157,0,0.930957," ","integrate((1-x)*(1+x)^(1/2)/(x^2+1),x, algorithm=""giac"")","\sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{2} \, \sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right) - \frac{1}{2} \, \sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right) - 2 \, \sqrt{x + 1}"," ",0,"sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) + sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) + 1/2*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1) - 1/2*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1) - 2*sqrt(x + 1)","A",0
1468,1,63,0,0.240826," ","integrate((3+x)/(x^2+1)/(4+3*x)^(1/2),x, algorithm=""giac"")","\sqrt{2} \arctan\left(\frac{1}{250} \cdot 25^{\frac{3}{4}} \sqrt{10} {\left(3 \cdot 25^{\frac{1}{4}} \sqrt{10} + 10 \, \sqrt{3 \, x + 4}\right)}\right) + \sqrt{2} \arctan\left(-\frac{1}{250} \cdot 25^{\frac{3}{4}} \sqrt{10} {\left(3 \cdot 25^{\frac{1}{4}} \sqrt{10} - 10 \, \sqrt{3 \, x + 4}\right)}\right)"," ",0,"sqrt(2)*arctan(1/250*25^(3/4)*sqrt(10)*(3*25^(1/4)*sqrt(10) + 10*sqrt(3*x + 4))) + sqrt(2)*arctan(-1/250*25^(3/4)*sqrt(10)*(3*25^(1/4)*sqrt(10) - 10*sqrt(3*x + 4)))","A",0
1469,1,53,0,0.217629," ","integrate((1-3*x)/(x^2+1)/(4+3*x)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{3}{5} \cdot 25^{\frac{1}{4}} \sqrt{10} \sqrt{3 \, x + 4} + 3 \, x + 9\right) - \frac{1}{2} \, \sqrt{2} \log\left(-\frac{3}{5} \cdot 25^{\frac{1}{4}} \sqrt{10} \sqrt{3 \, x + 4} + 3 \, x + 9\right)"," ",0,"1/2*sqrt(2)*log(3/5*25^(1/4)*sqrt(10)*sqrt(3*x + 4) + 3*x + 9) - 1/2*sqrt(2)*log(-3/5*25^(1/4)*sqrt(10)*sqrt(3*x + 4) + 3*x + 9)","A",0
1470,1,21,0,0.185080," ","integrate((2+x)/(x^2+1)/(3+4*x)^(1/2),x, algorithm=""giac"")","\arctan\left(\sqrt{4 \, x + 3} + 2\right) + \arctan\left(\sqrt{4 \, x + 3} - 2\right)"," ",0,"arctan(sqrt(4*x + 3) + 2) + arctan(sqrt(4*x + 3) - 2)","A",0
1471,1,23,0,0.183575," ","integrate((-2+x)/(x^2-8)/(-3+x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} {\left(\pi + 2 \, \arctan\left(\frac{\sqrt{2} {\left(x - 4\right)}}{4 \, \sqrt{x - 3}}\right)\right)}"," ",0,"1/4*sqrt(2)*(pi + 2*arctan(1/4*sqrt(2)*(x - 4)/sqrt(x - 3)))","A",0
1472,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d), x)","F",0
1473,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)/sqrt(e*x + d), x)","F",0
1474,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(B*x + A)/(e*x + d)^(3/2), x)","F",0
1475,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 1.8Unable to transpose Error: Bad Argument Value","F(-2)",0
1476,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/sqrt(e*x + d), x)","F",0
1477,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/(e*x + d)^(3/2), x)","F",0
1478,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/(e*x + d)^(5/2), x)","F",0
1479,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(B x + A\right)}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(B*x + A)/(e*x + d)^(7/2), x)","F",0
1480,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(3/2)/sqrt(c*x^2 + a), x)","F",0
1481,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + a), x)","F",0
1482,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + a} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + a)*sqrt(e*x + d)), x)","F",0
1483,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + a)*(e*x + d)^(3/2)), x)","F",0
1484,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(3/2)/(c*x^2 + a)^(3/2), x)","F",0
1485,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x + d}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x + d)/(c*x^2 + a)^(3/2), x)","F",0
1486,0,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + a)^(3/2)*sqrt(e*x + d)), x)","F",0
1487,1,5560,0,0.383990," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c^{3} m^{7} x^{8} e^{8} + {\left(x e + d\right)}^{m} B c^{3} d m^{7} x^{7} e^{7} + {\left(x e + d\right)}^{m} A c^{3} m^{7} x^{7} e^{8} + 28 \, {\left(x e + d\right)}^{m} B c^{3} m^{6} x^{8} e^{8} + {\left(x e + d\right)}^{m} A c^{3} d m^{7} x^{6} e^{7} + 21 \, {\left(x e + d\right)}^{m} B c^{3} d m^{6} x^{7} e^{7} - 7 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{6} x^{6} e^{6} + 3 \, {\left(x e + d\right)}^{m} B a c^{2} m^{7} x^{6} e^{8} + 29 \, {\left(x e + d\right)}^{m} A c^{3} m^{6} x^{7} e^{8} + 322 \, {\left(x e + d\right)}^{m} B c^{3} m^{5} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{7} x^{5} e^{7} + 23 \, {\left(x e + d\right)}^{m} A c^{3} d m^{6} x^{6} e^{7} + 175 \, {\left(x e + d\right)}^{m} B c^{3} d m^{5} x^{7} e^{7} - 6 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{6} x^{5} e^{6} - 105 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{5} x^{6} e^{6} + 42 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{5} x^{5} e^{5} + 3 \, {\left(x e + d\right)}^{m} A a c^{2} m^{7} x^{5} e^{8} + 90 \, {\left(x e + d\right)}^{m} B a c^{2} m^{6} x^{6} e^{8} + 343 \, {\left(x e + d\right)}^{m} A c^{3} m^{5} x^{7} e^{8} + 1960 \, {\left(x e + d\right)}^{m} B c^{3} m^{4} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{7} x^{4} e^{7} + 75 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{6} x^{5} e^{7} + 205 \, {\left(x e + d\right)}^{m} A c^{3} d m^{5} x^{6} e^{7} + 735 \, {\left(x e + d\right)}^{m} B c^{3} d m^{4} x^{7} e^{7} - 15 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{6} x^{4} e^{6} - 108 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{5} x^{5} e^{6} - 595 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{4} x^{6} e^{6} + 30 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{5} x^{4} e^{5} + 420 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{4} x^{5} e^{5} - 210 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{4} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} B a^{2} c m^{7} x^{4} e^{8} + 93 \, {\left(x e + d\right)}^{m} A a c^{2} m^{6} x^{5} e^{8} + 1098 \, {\left(x e + d\right)}^{m} B a c^{2} m^{5} x^{6} e^{8} + 2135 \, {\left(x e + d\right)}^{m} A c^{3} m^{4} x^{7} e^{8} + 6769 \, {\left(x e + d\right)}^{m} B c^{3} m^{3} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{7} x^{3} e^{7} + 81 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{6} x^{4} e^{7} + 723 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{5} x^{5} e^{7} + 905 \, {\left(x e + d\right)}^{m} A c^{3} d m^{4} x^{6} e^{7} + 1624 \, {\left(x e + d\right)}^{m} B c^{3} d m^{3} x^{7} e^{7} - 12 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{6} x^{3} e^{6} - 315 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{5} x^{4} e^{6} - 690 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{4} x^{5} e^{6} - 1575 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{3} x^{6} e^{6} + 60 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{5} x^{3} e^{5} + 420 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{4} x^{4} e^{5} + 1470 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{3} x^{5} e^{5} - 120 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{4} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{3} x^{4} e^{4} + 840 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m^{3} x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} A a^{2} c m^{7} x^{3} e^{8} + 96 \, {\left(x e + d\right)}^{m} B a^{2} c m^{6} x^{4} e^{8} + 1173 \, {\left(x e + d\right)}^{m} A a c^{2} m^{5} x^{5} e^{8} + 7020 \, {\left(x e + d\right)}^{m} B a c^{2} m^{4} x^{6} e^{8} + 7504 \, {\left(x e + d\right)}^{m} A c^{3} m^{3} x^{7} e^{8} + 13132 \, {\left(x e + d\right)}^{m} B c^{3} m^{2} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{7} x^{2} e^{7} + 87 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{6} x^{3} e^{7} + 849 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{5} x^{4} e^{7} + 3405 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{4} x^{5} e^{7} + 2074 \, {\left(x e + d\right)}^{m} A c^{3} d m^{3} x^{6} e^{7} + 1764 \, {\left(x e + d\right)}^{m} B c^{3} d m^{2} x^{7} e^{7} - 9 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{6} x^{2} e^{6} - 288 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{5} x^{3} e^{6} - 2355 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{4} x^{4} e^{6} - 1980 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{3} x^{5} e^{6} - 1918 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{2} x^{6} e^{6} + 36 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{5} x^{2} e^{5} + 1080 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{4} x^{3} e^{5} + 1770 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{3} x^{4} e^{5} + 2100 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{2} x^{5} e^{5} - 180 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m^{4} x^{2} e^{4} - 1320 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{3} x^{3} e^{4} - 2310 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{2} x^{4} e^{4} + 360 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m^{3} x^{2} e^{3} + 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m^{2} x^{3} e^{3} - 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{6} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a^{3} m^{7} x^{2} e^{8} + 99 \, {\left(x e + d\right)}^{m} A a^{2} c m^{6} x^{3} e^{8} + 1254 \, {\left(x e + d\right)}^{m} B a^{2} c m^{5} x^{4} e^{8} + 7743 \, {\left(x e + d\right)}^{m} A a c^{2} m^{4} x^{5} e^{8} + 25227 \, {\left(x e + d\right)}^{m} B a c^{2} m^{3} x^{6} e^{8} + 14756 \, {\left(x e + d\right)}^{m} A c^{3} m^{2} x^{7} e^{8} + 13068 \, {\left(x e + d\right)}^{m} B c^{3} m x^{8} e^{8} + {\left(x e + d\right)}^{m} B a^{3} d m^{7} x e^{7} + 93 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{6} x^{2} e^{7} + 993 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{5} x^{3} e^{7} + 4347 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{4} x^{4} e^{7} + 8202 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{3} x^{5} e^{7} + 2312 \, {\left(x e + d\right)}^{m} A c^{3} d m^{2} x^{6} e^{7} + 720 \, {\left(x e + d\right)}^{m} B c^{3} d m x^{7} e^{7} - 6 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{6} x e^{6} - 243 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{5} x^{2} e^{6} - 2532 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{4} x^{3} e^{6} - 7605 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{3} x^{4} e^{6} - 2544 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{2} x^{5} e^{6} - 840 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m x^{6} e^{6} + 18 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{5} x e^{5} + 792 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{4} x^{2} e^{5} + 6180 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{3} x^{3} e^{5} + 2820 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{2} x^{4} e^{5} + 1008 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m x^{5} e^{5} - 72 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m^{4} x e^{4} - 2880 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m^{3} x^{2} e^{4} - 3120 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{2} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m x^{4} e^{4} + 360 \, {\left(x e + d\right)}^{m} B a c^{2} d^{5} m^{3} x e^{3} + 3240 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m^{2} x^{2} e^{3} + 1680 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m x^{3} e^{3} - 720 \, {\left(x e + d\right)}^{m} A c^{3} d^{6} m^{2} x e^{2} - 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{6} m x^{2} e^{2} + 5040 \, {\left(x e + d\right)}^{m} B c^{3} d^{7} m x e + {\left(x e + d\right)}^{m} A a^{3} m^{7} x e^{8} + 34 \, {\left(x e + d\right)}^{m} B a^{3} m^{6} x^{2} e^{8} + 1341 \, {\left(x e + d\right)}^{m} A a^{2} c m^{5} x^{3} e^{8} + 8592 \, {\left(x e + d\right)}^{m} B a^{2} c m^{4} x^{4} e^{8} + 28632 \, {\left(x e + d\right)}^{m} A a c^{2} m^{3} x^{5} e^{8} + 50490 \, {\left(x e + d\right)}^{m} B a c^{2} m^{2} x^{6} e^{8} + 14832 \, {\left(x e + d\right)}^{m} A c^{3} m x^{7} e^{8} + 5040 \, {\left(x e + d\right)}^{m} B c^{3} x^{8} e^{8} + {\left(x e + d\right)}^{m} A a^{3} d m^{7} e^{7} + 33 \, {\left(x e + d\right)}^{m} B a^{3} d m^{6} x e^{7} + 1155 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{5} x^{2} e^{7} + 5613 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{4} x^{3} e^{7} + 11244 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{3} x^{4} e^{7} + 9480 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{2} x^{5} e^{7} + 960 \, {\left(x e + d\right)}^{m} A c^{3} d m x^{6} e^{7} - {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{6} e^{6} - 180 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{5} x e^{6} - 2493 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{4} x^{2} e^{6} - 9792 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{3} x^{3} e^{6} - 10590 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{2} x^{4} e^{6} - 1152 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m x^{5} e^{6} + 6 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{5} e^{5} + 468 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{4} x e^{5} + 6012 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{3} x^{2} e^{5} + 11880 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{2} x^{3} e^{5} + 1440 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m x^{4} e^{5} - 18 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m^{4} e^{4} - 1512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m^{3} x e^{4} - 12780 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m^{2} x^{2} e^{4} - 1920 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m x^{3} e^{4} + 72 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} m^{3} e^{3} + 5400 \, {\left(x e + d\right)}^{m} B a c^{2} d^{5} m^{2} x e^{3} + 2880 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m x^{2} e^{3} - 360 \, {\left(x e + d\right)}^{m} B a c^{2} d^{6} m^{2} e^{2} - 5760 \, {\left(x e + d\right)}^{m} A c^{3} d^{6} m x e^{2} + 720 \, {\left(x e + d\right)}^{m} A c^{3} d^{7} m e - 5040 \, {\left(x e + d\right)}^{m} B c^{3} d^{8} + 35 \, {\left(x e + d\right)}^{m} A a^{3} m^{6} x e^{8} + 478 \, {\left(x e + d\right)}^{m} B a^{3} m^{5} x^{2} e^{8} + 9585 \, {\left(x e + d\right)}^{m} A a^{2} c m^{4} x^{3} e^{8} + 32979 \, {\left(x e + d\right)}^{m} B a^{2} c m^{3} x^{4} e^{8} + 58692 \, {\left(x e + d\right)}^{m} A a c^{2} m^{2} x^{5} e^{8} + 51432 \, {\left(x e + d\right)}^{m} B a c^{2} m x^{6} e^{8} + 5760 \, {\left(x e + d\right)}^{m} A c^{3} x^{7} e^{8} + 35 \, {\left(x e + d\right)}^{m} A a^{3} d m^{6} e^{7} + 445 \, {\left(x e + d\right)}^{m} B a^{3} d m^{5} x e^{7} + 7275 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{4} x^{2} e^{7} + 16140 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{3} x^{3} e^{7} + 13716 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{2} x^{4} e^{7} + 4032 \, {\left(x e + d\right)}^{m} B a c^{2} d m x^{5} e^{7} - 33 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{5} e^{6} - 2130 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{4} x e^{6} - 11853 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{3} x^{2} e^{6} - 15600 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{2} x^{3} e^{6} - 5040 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m x^{4} e^{6} + 180 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{4} e^{5} + 4518 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{3} x e^{5} + 17352 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{2} x^{2} e^{5} + 6720 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m x^{3} e^{5} - 468 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m^{3} e^{4} - 10512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m^{2} x e^{4} - 10080 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m x^{2} e^{4} + 1512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} m^{2} e^{3} + 20160 \, {\left(x e + d\right)}^{m} B a c^{2} d^{5} m x e^{3} - 5400 \, {\left(x e + d\right)}^{m} B a c^{2} d^{6} m e^{2} + 5760 \, {\left(x e + d\right)}^{m} A c^{3} d^{7} e + 511 \, {\left(x e + d\right)}^{m} A a^{3} m^{5} x e^{8} + 3580 \, {\left(x e + d\right)}^{m} B a^{3} m^{4} x^{2} e^{8} + 38592 \, {\left(x e + d\right)}^{m} A a^{2} c m^{3} x^{3} e^{8} + 69936 \, {\left(x e + d\right)}^{m} B a^{2} c m^{2} x^{4} e^{8} + 60912 \, {\left(x e + d\right)}^{m} A a c^{2} m x^{5} e^{8} + 20160 \, {\left(x e + d\right)}^{m} B a c^{2} x^{6} e^{8} + 511 \, {\left(x e + d\right)}^{m} A a^{3} d m^{5} e^{7} + 3135 \, {\left(x e + d\right)}^{m} B a^{3} d m^{4} x e^{7} + 24042 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{3} x^{2} e^{7} + 21516 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{2} x^{3} e^{7} + 6048 \, {\left(x e + d\right)}^{m} A a c^{2} d m x^{4} e^{7} - 445 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{4} e^{6} - 12420 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{3} x e^{6} - 24714 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{2} x^{2} e^{6} - 8064 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m x^{3} e^{6} + 2130 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{3} e^{5} + 19188 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{2} x e^{5} + 12096 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m x^{2} e^{5} - 4518 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m^{2} e^{4} - 24192 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m x e^{4} + 10512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} m e^{3} - 20160 \, {\left(x e + d\right)}^{m} B a c^{2} d^{6} e^{2} + 4025 \, {\left(x e + d\right)}^{m} A a^{3} m^{4} x e^{8} + 15289 \, {\left(x e + d\right)}^{m} B a^{3} m^{3} x^{2} e^{8} + 86076 \, {\left(x e + d\right)}^{m} A a^{2} c m^{2} x^{3} e^{8} + 74628 \, {\left(x e + d\right)}^{m} B a^{2} c m x^{4} e^{8} + 24192 \, {\left(x e + d\right)}^{m} A a c^{2} x^{5} e^{8} + 4025 \, {\left(x e + d\right)}^{m} A a^{3} d m^{4} e^{7} + 12154 \, {\left(x e + d\right)}^{m} B a^{3} d m^{3} x e^{7} + 37992 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{2} x^{2} e^{7} + 10080 \, {\left(x e + d\right)}^{m} B a^{2} c d m x^{3} e^{7} - 3135 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{3} e^{6} - 35664 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{2} x e^{6} - 15120 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m x^{2} e^{6} + 12420 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{2} e^{5} + 30240 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m x e^{5} - 19188 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m e^{4} + 24192 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} e^{3} + 18424 \, {\left(x e + d\right)}^{m} A a^{3} m^{3} x e^{8} + 36706 \, {\left(x e + d\right)}^{m} B a^{3} m^{2} x^{2} e^{8} + 96144 \, {\left(x e + d\right)}^{m} A a^{2} c m x^{3} e^{8} + 30240 \, {\left(x e + d\right)}^{m} B a^{2} c x^{4} e^{8} + 18424 \, {\left(x e + d\right)}^{m} A a^{3} d m^{3} e^{7} + 24552 \, {\left(x e + d\right)}^{m} B a^{3} d m^{2} x e^{7} + 20160 \, {\left(x e + d\right)}^{m} A a^{2} c d m x^{2} e^{7} - 12154 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{2} e^{6} - 40320 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m x e^{6} + 35664 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m e^{5} - 30240 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} e^{4} + 48860 \, {\left(x e + d\right)}^{m} A a^{3} m^{2} x e^{8} + 44712 \, {\left(x e + d\right)}^{m} B a^{3} m x^{2} e^{8} + 40320 \, {\left(x e + d\right)}^{m} A a^{2} c x^{3} e^{8} + 48860 \, {\left(x e + d\right)}^{m} A a^{3} d m^{2} e^{7} + 20160 \, {\left(x e + d\right)}^{m} B a^{3} d m x e^{7} - 24552 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m e^{6} + 40320 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} e^{5} + 69264 \, {\left(x e + d\right)}^{m} A a^{3} m x e^{8} + 20160 \, {\left(x e + d\right)}^{m} B a^{3} x^{2} e^{8} + 69264 \, {\left(x e + d\right)}^{m} A a^{3} d m e^{7} - 20160 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} e^{6} + 40320 \, {\left(x e + d\right)}^{m} A a^{3} x e^{8} + 40320 \, {\left(x e + d\right)}^{m} A a^{3} d e^{7}}{m^{8} e^{8} + 36 \, m^{7} e^{8} + 546 \, m^{6} e^{8} + 4536 \, m^{5} e^{8} + 22449 \, m^{4} e^{8} + 67284 \, m^{3} e^{8} + 118124 \, m^{2} e^{8} + 109584 \, m e^{8} + 40320 \, e^{8}}"," ",0,"((x*e + d)^m*B*c^3*m^7*x^8*e^8 + (x*e + d)^m*B*c^3*d*m^7*x^7*e^7 + (x*e + d)^m*A*c^3*m^7*x^7*e^8 + 28*(x*e + d)^m*B*c^3*m^6*x^8*e^8 + (x*e + d)^m*A*c^3*d*m^7*x^6*e^7 + 21*(x*e + d)^m*B*c^3*d*m^6*x^7*e^7 - 7*(x*e + d)^m*B*c^3*d^2*m^6*x^6*e^6 + 3*(x*e + d)^m*B*a*c^2*m^7*x^6*e^8 + 29*(x*e + d)^m*A*c^3*m^6*x^7*e^8 + 322*(x*e + d)^m*B*c^3*m^5*x^8*e^8 + 3*(x*e + d)^m*B*a*c^2*d*m^7*x^5*e^7 + 23*(x*e + d)^m*A*c^3*d*m^6*x^6*e^7 + 175*(x*e + d)^m*B*c^3*d*m^5*x^7*e^7 - 6*(x*e + d)^m*A*c^3*d^2*m^6*x^5*e^6 - 105*(x*e + d)^m*B*c^3*d^2*m^5*x^6*e^6 + 42*(x*e + d)^m*B*c^3*d^3*m^5*x^5*e^5 + 3*(x*e + d)^m*A*a*c^2*m^7*x^5*e^8 + 90*(x*e + d)^m*B*a*c^2*m^6*x^6*e^8 + 343*(x*e + d)^m*A*c^3*m^5*x^7*e^8 + 1960*(x*e + d)^m*B*c^3*m^4*x^8*e^8 + 3*(x*e + d)^m*A*a*c^2*d*m^7*x^4*e^7 + 75*(x*e + d)^m*B*a*c^2*d*m^6*x^5*e^7 + 205*(x*e + d)^m*A*c^3*d*m^5*x^6*e^7 + 735*(x*e + d)^m*B*c^3*d*m^4*x^7*e^7 - 15*(x*e + d)^m*B*a*c^2*d^2*m^6*x^4*e^6 - 108*(x*e + d)^m*A*c^3*d^2*m^5*x^5*e^6 - 595*(x*e + d)^m*B*c^3*d^2*m^4*x^6*e^6 + 30*(x*e + d)^m*A*c^3*d^3*m^5*x^4*e^5 + 420*(x*e + d)^m*B*c^3*d^3*m^4*x^5*e^5 - 210*(x*e + d)^m*B*c^3*d^4*m^4*x^4*e^4 + 3*(x*e + d)^m*B*a^2*c*m^7*x^4*e^8 + 93*(x*e + d)^m*A*a*c^2*m^6*x^5*e^8 + 1098*(x*e + d)^m*B*a*c^2*m^5*x^6*e^8 + 2135*(x*e + d)^m*A*c^3*m^4*x^7*e^8 + 6769*(x*e + d)^m*B*c^3*m^3*x^8*e^8 + 3*(x*e + d)^m*B*a^2*c*d*m^7*x^3*e^7 + 81*(x*e + d)^m*A*a*c^2*d*m^6*x^4*e^7 + 723*(x*e + d)^m*B*a*c^2*d*m^5*x^5*e^7 + 905*(x*e + d)^m*A*c^3*d*m^4*x^6*e^7 + 1624*(x*e + d)^m*B*c^3*d*m^3*x^7*e^7 - 12*(x*e + d)^m*A*a*c^2*d^2*m^6*x^3*e^6 - 315*(x*e + d)^m*B*a*c^2*d^2*m^5*x^4*e^6 - 690*(x*e + d)^m*A*c^3*d^2*m^4*x^5*e^6 - 1575*(x*e + d)^m*B*c^3*d^2*m^3*x^6*e^6 + 60*(x*e + d)^m*B*a*c^2*d^3*m^5*x^3*e^5 + 420*(x*e + d)^m*A*c^3*d^3*m^4*x^4*e^5 + 1470*(x*e + d)^m*B*c^3*d^3*m^3*x^5*e^5 - 120*(x*e + d)^m*A*c^3*d^4*m^4*x^3*e^4 - 1260*(x*e + d)^m*B*c^3*d^4*m^3*x^4*e^4 + 840*(x*e + d)^m*B*c^3*d^5*m^3*x^3*e^3 + 3*(x*e + d)^m*A*a^2*c*m^7*x^3*e^8 + 96*(x*e + d)^m*B*a^2*c*m^6*x^4*e^8 + 1173*(x*e + d)^m*A*a*c^2*m^5*x^5*e^8 + 7020*(x*e + d)^m*B*a*c^2*m^4*x^6*e^8 + 7504*(x*e + d)^m*A*c^3*m^3*x^7*e^8 + 13132*(x*e + d)^m*B*c^3*m^2*x^8*e^8 + 3*(x*e + d)^m*A*a^2*c*d*m^7*x^2*e^7 + 87*(x*e + d)^m*B*a^2*c*d*m^6*x^3*e^7 + 849*(x*e + d)^m*A*a*c^2*d*m^5*x^4*e^7 + 3405*(x*e + d)^m*B*a*c^2*d*m^4*x^5*e^7 + 2074*(x*e + d)^m*A*c^3*d*m^3*x^6*e^7 + 1764*(x*e + d)^m*B*c^3*d*m^2*x^7*e^7 - 9*(x*e + d)^m*B*a^2*c*d^2*m^6*x^2*e^6 - 288*(x*e + d)^m*A*a*c^2*d^2*m^5*x^3*e^6 - 2355*(x*e + d)^m*B*a*c^2*d^2*m^4*x^4*e^6 - 1980*(x*e + d)^m*A*c^3*d^2*m^3*x^5*e^6 - 1918*(x*e + d)^m*B*c^3*d^2*m^2*x^6*e^6 + 36*(x*e + d)^m*A*a*c^2*d^3*m^5*x^2*e^5 + 1080*(x*e + d)^m*B*a*c^2*d^3*m^4*x^3*e^5 + 1770*(x*e + d)^m*A*c^3*d^3*m^3*x^4*e^5 + 2100*(x*e + d)^m*B*c^3*d^3*m^2*x^5*e^5 - 180*(x*e + d)^m*B*a*c^2*d^4*m^4*x^2*e^4 - 1320*(x*e + d)^m*A*c^3*d^4*m^3*x^3*e^4 - 2310*(x*e + d)^m*B*c^3*d^4*m^2*x^4*e^4 + 360*(x*e + d)^m*A*c^3*d^5*m^3*x^2*e^3 + 2520*(x*e + d)^m*B*c^3*d^5*m^2*x^3*e^3 - 2520*(x*e + d)^m*B*c^3*d^6*m^2*x^2*e^2 + (x*e + d)^m*B*a^3*m^7*x^2*e^8 + 99*(x*e + d)^m*A*a^2*c*m^6*x^3*e^8 + 1254*(x*e + d)^m*B*a^2*c*m^5*x^4*e^8 + 7743*(x*e + d)^m*A*a*c^2*m^4*x^5*e^8 + 25227*(x*e + d)^m*B*a*c^2*m^3*x^6*e^8 + 14756*(x*e + d)^m*A*c^3*m^2*x^7*e^8 + 13068*(x*e + d)^m*B*c^3*m*x^8*e^8 + (x*e + d)^m*B*a^3*d*m^7*x*e^7 + 93*(x*e + d)^m*A*a^2*c*d*m^6*x^2*e^7 + 993*(x*e + d)^m*B*a^2*c*d*m^5*x^3*e^7 + 4347*(x*e + d)^m*A*a*c^2*d*m^4*x^4*e^7 + 8202*(x*e + d)^m*B*a*c^2*d*m^3*x^5*e^7 + 2312*(x*e + d)^m*A*c^3*d*m^2*x^6*e^7 + 720*(x*e + d)^m*B*c^3*d*m*x^7*e^7 - 6*(x*e + d)^m*A*a^2*c*d^2*m^6*x*e^6 - 243*(x*e + d)^m*B*a^2*c*d^2*m^5*x^2*e^6 - 2532*(x*e + d)^m*A*a*c^2*d^2*m^4*x^3*e^6 - 7605*(x*e + d)^m*B*a*c^2*d^2*m^3*x^4*e^6 - 2544*(x*e + d)^m*A*c^3*d^2*m^2*x^5*e^6 - 840*(x*e + d)^m*B*c^3*d^2*m*x^6*e^6 + 18*(x*e + d)^m*B*a^2*c*d^3*m^5*x*e^5 + 792*(x*e + d)^m*A*a*c^2*d^3*m^4*x^2*e^5 + 6180*(x*e + d)^m*B*a*c^2*d^3*m^3*x^3*e^5 + 2820*(x*e + d)^m*A*c^3*d^3*m^2*x^4*e^5 + 1008*(x*e + d)^m*B*c^3*d^3*m*x^5*e^5 - 72*(x*e + d)^m*A*a*c^2*d^4*m^4*x*e^4 - 2880*(x*e + d)^m*B*a*c^2*d^4*m^3*x^2*e^4 - 3120*(x*e + d)^m*A*c^3*d^4*m^2*x^3*e^4 - 1260*(x*e + d)^m*B*c^3*d^4*m*x^4*e^4 + 360*(x*e + d)^m*B*a*c^2*d^5*m^3*x*e^3 + 3240*(x*e + d)^m*A*c^3*d^5*m^2*x^2*e^3 + 1680*(x*e + d)^m*B*c^3*d^5*m*x^3*e^3 - 720*(x*e + d)^m*A*c^3*d^6*m^2*x*e^2 - 2520*(x*e + d)^m*B*c^3*d^6*m*x^2*e^2 + 5040*(x*e + d)^m*B*c^3*d^7*m*x*e + (x*e + d)^m*A*a^3*m^7*x*e^8 + 34*(x*e + d)^m*B*a^3*m^6*x^2*e^8 + 1341*(x*e + d)^m*A*a^2*c*m^5*x^3*e^8 + 8592*(x*e + d)^m*B*a^2*c*m^4*x^4*e^8 + 28632*(x*e + d)^m*A*a*c^2*m^3*x^5*e^8 + 50490*(x*e + d)^m*B*a*c^2*m^2*x^6*e^8 + 14832*(x*e + d)^m*A*c^3*m*x^7*e^8 + 5040*(x*e + d)^m*B*c^3*x^8*e^8 + (x*e + d)^m*A*a^3*d*m^7*e^7 + 33*(x*e + d)^m*B*a^3*d*m^6*x*e^7 + 1155*(x*e + d)^m*A*a^2*c*d*m^5*x^2*e^7 + 5613*(x*e + d)^m*B*a^2*c*d*m^4*x^3*e^7 + 11244*(x*e + d)^m*A*a*c^2*d*m^3*x^4*e^7 + 9480*(x*e + d)^m*B*a*c^2*d*m^2*x^5*e^7 + 960*(x*e + d)^m*A*c^3*d*m*x^6*e^7 - (x*e + d)^m*B*a^3*d^2*m^6*e^6 - 180*(x*e + d)^m*A*a^2*c*d^2*m^5*x*e^6 - 2493*(x*e + d)^m*B*a^2*c*d^2*m^4*x^2*e^6 - 9792*(x*e + d)^m*A*a*c^2*d^2*m^3*x^3*e^6 - 10590*(x*e + d)^m*B*a*c^2*d^2*m^2*x^4*e^6 - 1152*(x*e + d)^m*A*c^3*d^2*m*x^5*e^6 + 6*(x*e + d)^m*A*a^2*c*d^3*m^5*e^5 + 468*(x*e + d)^m*B*a^2*c*d^3*m^4*x*e^5 + 6012*(x*e + d)^m*A*a*c^2*d^3*m^3*x^2*e^5 + 11880*(x*e + d)^m*B*a*c^2*d^3*m^2*x^3*e^5 + 1440*(x*e + d)^m*A*c^3*d^3*m*x^4*e^5 - 18*(x*e + d)^m*B*a^2*c*d^4*m^4*e^4 - 1512*(x*e + d)^m*A*a*c^2*d^4*m^3*x*e^4 - 12780*(x*e + d)^m*B*a*c^2*d^4*m^2*x^2*e^4 - 1920*(x*e + d)^m*A*c^3*d^4*m*x^3*e^4 + 72*(x*e + d)^m*A*a*c^2*d^5*m^3*e^3 + 5400*(x*e + d)^m*B*a*c^2*d^5*m^2*x*e^3 + 2880*(x*e + d)^m*A*c^3*d^5*m*x^2*e^3 - 360*(x*e + d)^m*B*a*c^2*d^6*m^2*e^2 - 5760*(x*e + d)^m*A*c^3*d^6*m*x*e^2 + 720*(x*e + d)^m*A*c^3*d^7*m*e - 5040*(x*e + d)^m*B*c^3*d^8 + 35*(x*e + d)^m*A*a^3*m^6*x*e^8 + 478*(x*e + d)^m*B*a^3*m^5*x^2*e^8 + 9585*(x*e + d)^m*A*a^2*c*m^4*x^3*e^8 + 32979*(x*e + d)^m*B*a^2*c*m^3*x^4*e^8 + 58692*(x*e + d)^m*A*a*c^2*m^2*x^5*e^8 + 51432*(x*e + d)^m*B*a*c^2*m*x^6*e^8 + 5760*(x*e + d)^m*A*c^3*x^7*e^8 + 35*(x*e + d)^m*A*a^3*d*m^6*e^7 + 445*(x*e + d)^m*B*a^3*d*m^5*x*e^7 + 7275*(x*e + d)^m*A*a^2*c*d*m^4*x^2*e^7 + 16140*(x*e + d)^m*B*a^2*c*d*m^3*x^3*e^7 + 13716*(x*e + d)^m*A*a*c^2*d*m^2*x^4*e^7 + 4032*(x*e + d)^m*B*a*c^2*d*m*x^5*e^7 - 33*(x*e + d)^m*B*a^3*d^2*m^5*e^6 - 2130*(x*e + d)^m*A*a^2*c*d^2*m^4*x*e^6 - 11853*(x*e + d)^m*B*a^2*c*d^2*m^3*x^2*e^6 - 15600*(x*e + d)^m*A*a*c^2*d^2*m^2*x^3*e^6 - 5040*(x*e + d)^m*B*a*c^2*d^2*m*x^4*e^6 + 180*(x*e + d)^m*A*a^2*c*d^3*m^4*e^5 + 4518*(x*e + d)^m*B*a^2*c*d^3*m^3*x*e^5 + 17352*(x*e + d)^m*A*a*c^2*d^3*m^2*x^2*e^5 + 6720*(x*e + d)^m*B*a*c^2*d^3*m*x^3*e^5 - 468*(x*e + d)^m*B*a^2*c*d^4*m^3*e^4 - 10512*(x*e + d)^m*A*a*c^2*d^4*m^2*x*e^4 - 10080*(x*e + d)^m*B*a*c^2*d^4*m*x^2*e^4 + 1512*(x*e + d)^m*A*a*c^2*d^5*m^2*e^3 + 20160*(x*e + d)^m*B*a*c^2*d^5*m*x*e^3 - 5400*(x*e + d)^m*B*a*c^2*d^6*m*e^2 + 5760*(x*e + d)^m*A*c^3*d^7*e + 511*(x*e + d)^m*A*a^3*m^5*x*e^8 + 3580*(x*e + d)^m*B*a^3*m^4*x^2*e^8 + 38592*(x*e + d)^m*A*a^2*c*m^3*x^3*e^8 + 69936*(x*e + d)^m*B*a^2*c*m^2*x^4*e^8 + 60912*(x*e + d)^m*A*a*c^2*m*x^5*e^8 + 20160*(x*e + d)^m*B*a*c^2*x^6*e^8 + 511*(x*e + d)^m*A*a^3*d*m^5*e^7 + 3135*(x*e + d)^m*B*a^3*d*m^4*x*e^7 + 24042*(x*e + d)^m*A*a^2*c*d*m^3*x^2*e^7 + 21516*(x*e + d)^m*B*a^2*c*d*m^2*x^3*e^7 + 6048*(x*e + d)^m*A*a*c^2*d*m*x^4*e^7 - 445*(x*e + d)^m*B*a^3*d^2*m^4*e^6 - 12420*(x*e + d)^m*A*a^2*c*d^2*m^3*x*e^6 - 24714*(x*e + d)^m*B*a^2*c*d^2*m^2*x^2*e^6 - 8064*(x*e + d)^m*A*a*c^2*d^2*m*x^3*e^6 + 2130*(x*e + d)^m*A*a^2*c*d^3*m^3*e^5 + 19188*(x*e + d)^m*B*a^2*c*d^3*m^2*x*e^5 + 12096*(x*e + d)^m*A*a*c^2*d^3*m*x^2*e^5 - 4518*(x*e + d)^m*B*a^2*c*d^4*m^2*e^4 - 24192*(x*e + d)^m*A*a*c^2*d^4*m*x*e^4 + 10512*(x*e + d)^m*A*a*c^2*d^5*m*e^3 - 20160*(x*e + d)^m*B*a*c^2*d^6*e^2 + 4025*(x*e + d)^m*A*a^3*m^4*x*e^8 + 15289*(x*e + d)^m*B*a^3*m^3*x^2*e^8 + 86076*(x*e + d)^m*A*a^2*c*m^2*x^3*e^8 + 74628*(x*e + d)^m*B*a^2*c*m*x^4*e^8 + 24192*(x*e + d)^m*A*a*c^2*x^5*e^8 + 4025*(x*e + d)^m*A*a^3*d*m^4*e^7 + 12154*(x*e + d)^m*B*a^3*d*m^3*x*e^7 + 37992*(x*e + d)^m*A*a^2*c*d*m^2*x^2*e^7 + 10080*(x*e + d)^m*B*a^2*c*d*m*x^3*e^7 - 3135*(x*e + d)^m*B*a^3*d^2*m^3*e^6 - 35664*(x*e + d)^m*A*a^2*c*d^2*m^2*x*e^6 - 15120*(x*e + d)^m*B*a^2*c*d^2*m*x^2*e^6 + 12420*(x*e + d)^m*A*a^2*c*d^3*m^2*e^5 + 30240*(x*e + d)^m*B*a^2*c*d^3*m*x*e^5 - 19188*(x*e + d)^m*B*a^2*c*d^4*m*e^4 + 24192*(x*e + d)^m*A*a*c^2*d^5*e^3 + 18424*(x*e + d)^m*A*a^3*m^3*x*e^8 + 36706*(x*e + d)^m*B*a^3*m^2*x^2*e^8 + 96144*(x*e + d)^m*A*a^2*c*m*x^3*e^8 + 30240*(x*e + d)^m*B*a^2*c*x^4*e^8 + 18424*(x*e + d)^m*A*a^3*d*m^3*e^7 + 24552*(x*e + d)^m*B*a^3*d*m^2*x*e^7 + 20160*(x*e + d)^m*A*a^2*c*d*m*x^2*e^7 - 12154*(x*e + d)^m*B*a^3*d^2*m^2*e^6 - 40320*(x*e + d)^m*A*a^2*c*d^2*m*x*e^6 + 35664*(x*e + d)^m*A*a^2*c*d^3*m*e^5 - 30240*(x*e + d)^m*B*a^2*c*d^4*e^4 + 48860*(x*e + d)^m*A*a^3*m^2*x*e^8 + 44712*(x*e + d)^m*B*a^3*m*x^2*e^8 + 40320*(x*e + d)^m*A*a^2*c*x^3*e^8 + 48860*(x*e + d)^m*A*a^3*d*m^2*e^7 + 20160*(x*e + d)^m*B*a^3*d*m*x*e^7 - 24552*(x*e + d)^m*B*a^3*d^2*m*e^6 + 40320*(x*e + d)^m*A*a^2*c*d^3*e^5 + 69264*(x*e + d)^m*A*a^3*m*x*e^8 + 20160*(x*e + d)^m*B*a^3*x^2*e^8 + 69264*(x*e + d)^m*A*a^3*d*m*e^7 - 20160*(x*e + d)^m*B*a^3*d^2*e^6 + 40320*(x*e + d)^m*A*a^3*x*e^8 + 40320*(x*e + d)^m*A*a^3*d*e^7)/(m^8*e^8 + 36*m^7*e^8 + 546*m^6*e^8 + 4536*m^5*e^8 + 22449*m^4*e^8 + 67284*m^3*e^8 + 118124*m^2*e^8 + 109584*m*e^8 + 40320*e^8)","B",0
1488,1,2435,0,0.261770," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c^{2} m^{5} x^{6} e^{6} + {\left(x e + d\right)}^{m} B c^{2} d m^{5} x^{5} e^{5} + {\left(x e + d\right)}^{m} A c^{2} m^{5} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} B c^{2} m^{4} x^{6} e^{6} + {\left(x e + d\right)}^{m} A c^{2} d m^{5} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} B c^{2} d m^{4} x^{5} e^{5} - 5 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{4} x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} B a c m^{5} x^{4} e^{6} + 16 \, {\left(x e + d\right)}^{m} A c^{2} m^{4} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} B c^{2} m^{3} x^{6} e^{6} + 2 \, {\left(x e + d\right)}^{m} B a c d m^{5} x^{3} e^{5} + 12 \, {\left(x e + d\right)}^{m} A c^{2} d m^{4} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} B c^{2} d m^{3} x^{5} e^{5} - 4 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{4} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{3} x^{4} e^{4} + 20 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m^{3} x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} A a c m^{5} x^{3} e^{6} + 34 \, {\left(x e + d\right)}^{m} B a c m^{4} x^{4} e^{6} + 95 \, {\left(x e + d\right)}^{m} A c^{2} m^{3} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} B c^{2} m^{2} x^{6} e^{6} + 2 \, {\left(x e + d\right)}^{m} A a c d m^{5} x^{2} e^{5} + 28 \, {\left(x e + d\right)}^{m} B a c d m^{4} x^{3} e^{5} + 47 \, {\left(x e + d\right)}^{m} A c^{2} d m^{3} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} B c^{2} d m^{2} x^{5} e^{5} - 6 \, {\left(x e + d\right)}^{m} B a c d^{2} m^{4} x^{2} e^{4} - 36 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{3} x^{3} e^{4} - 55 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{2} x^{4} e^{4} + 12 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m^{3} x^{2} e^{3} + 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m^{2} x^{3} e^{3} - 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{4} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a^{2} m^{5} x^{2} e^{6} + 36 \, {\left(x e + d\right)}^{m} A a c m^{4} x^{3} e^{6} + 214 \, {\left(x e + d\right)}^{m} B a c m^{3} x^{4} e^{6} + 260 \, {\left(x e + d\right)}^{m} A c^{2} m^{2} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} B c^{2} m x^{6} e^{6} + {\left(x e + d\right)}^{m} B a^{2} d m^{5} x e^{5} + 32 \, {\left(x e + d\right)}^{m} A a c d m^{4} x^{2} e^{5} + 130 \, {\left(x e + d\right)}^{m} B a c d m^{3} x^{3} e^{5} + 72 \, {\left(x e + d\right)}^{m} A c^{2} d m^{2} x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} B c^{2} d m x^{5} e^{5} - 4 \, {\left(x e + d\right)}^{m} A a c d^{2} m^{4} x e^{4} - 72 \, {\left(x e + d\right)}^{m} B a c d^{2} m^{3} x^{2} e^{4} - 80 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{2} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m x^{4} e^{4} + 12 \, {\left(x e + d\right)}^{m} B a c d^{3} m^{3} x e^{3} + 84 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m^{2} x^{2} e^{3} + 40 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m x^{3} e^{3} - 24 \, {\left(x e + d\right)}^{m} A c^{2} d^{4} m^{2} x e^{2} - 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{4} m x^{2} e^{2} + 120 \, {\left(x e + d\right)}^{m} B c^{2} d^{5} m x e + {\left(x e + d\right)}^{m} A a^{2} m^{5} x e^{6} + 19 \, {\left(x e + d\right)}^{m} B a^{2} m^{4} x^{2} e^{6} + 242 \, {\left(x e + d\right)}^{m} A a c m^{3} x^{3} e^{6} + 614 \, {\left(x e + d\right)}^{m} B a c m^{2} x^{4} e^{6} + 324 \, {\left(x e + d\right)}^{m} A c^{2} m x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} B c^{2} x^{6} e^{6} + {\left(x e + d\right)}^{m} A a^{2} d m^{5} e^{5} + 18 \, {\left(x e + d\right)}^{m} B a^{2} d m^{4} x e^{5} + 178 \, {\left(x e + d\right)}^{m} A a c d m^{3} x^{2} e^{5} + 224 \, {\left(x e + d\right)}^{m} B a c d m^{2} x^{3} e^{5} + 36 \, {\left(x e + d\right)}^{m} A c^{2} d m x^{4} e^{5} - {\left(x e + d\right)}^{m} B a^{2} d^{2} m^{4} e^{4} - 60 \, {\left(x e + d\right)}^{m} A a c d^{2} m^{3} x e^{4} - 246 \, {\left(x e + d\right)}^{m} B a c d^{2} m^{2} x^{2} e^{4} - 48 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m x^{3} e^{4} + 4 \, {\left(x e + d\right)}^{m} A a c d^{3} m^{3} e^{3} + 132 \, {\left(x e + d\right)}^{m} B a c d^{3} m^{2} x e^{3} + 72 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m x^{2} e^{3} - 12 \, {\left(x e + d\right)}^{m} B a c d^{4} m^{2} e^{2} - 144 \, {\left(x e + d\right)}^{m} A c^{2} d^{4} m x e^{2} + 24 \, {\left(x e + d\right)}^{m} A c^{2} d^{5} m e - 120 \, {\left(x e + d\right)}^{m} B c^{2} d^{6} + 20 \, {\left(x e + d\right)}^{m} A a^{2} m^{4} x e^{6} + 137 \, {\left(x e + d\right)}^{m} B a^{2} m^{3} x^{2} e^{6} + 744 \, {\left(x e + d\right)}^{m} A a c m^{2} x^{3} e^{6} + 792 \, {\left(x e + d\right)}^{m} B a c m x^{4} e^{6} + 144 \, {\left(x e + d\right)}^{m} A c^{2} x^{5} e^{6} + 20 \, {\left(x e + d\right)}^{m} A a^{2} d m^{4} e^{5} + 119 \, {\left(x e + d\right)}^{m} B a^{2} d m^{3} x e^{5} + 388 \, {\left(x e + d\right)}^{m} A a c d m^{2} x^{2} e^{5} + 120 \, {\left(x e + d\right)}^{m} B a c d m x^{3} e^{5} - 18 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} m^{3} e^{4} - 296 \, {\left(x e + d\right)}^{m} A a c d^{2} m^{2} x e^{4} - 180 \, {\left(x e + d\right)}^{m} B a c d^{2} m x^{2} e^{4} + 60 \, {\left(x e + d\right)}^{m} A a c d^{3} m^{2} e^{3} + 360 \, {\left(x e + d\right)}^{m} B a c d^{3} m x e^{3} - 132 \, {\left(x e + d\right)}^{m} B a c d^{4} m e^{2} + 144 \, {\left(x e + d\right)}^{m} A c^{2} d^{5} e + 155 \, {\left(x e + d\right)}^{m} A a^{2} m^{3} x e^{6} + 461 \, {\left(x e + d\right)}^{m} B a^{2} m^{2} x^{2} e^{6} + 1016 \, {\left(x e + d\right)}^{m} A a c m x^{3} e^{6} + 360 \, {\left(x e + d\right)}^{m} B a c x^{4} e^{6} + 155 \, {\left(x e + d\right)}^{m} A a^{2} d m^{3} e^{5} + 342 \, {\left(x e + d\right)}^{m} B a^{2} d m^{2} x e^{5} + 240 \, {\left(x e + d\right)}^{m} A a c d m x^{2} e^{5} - 119 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} m^{2} e^{4} - 480 \, {\left(x e + d\right)}^{m} A a c d^{2} m x e^{4} + 296 \, {\left(x e + d\right)}^{m} A a c d^{3} m e^{3} - 360 \, {\left(x e + d\right)}^{m} B a c d^{4} e^{2} + 580 \, {\left(x e + d\right)}^{m} A a^{2} m^{2} x e^{6} + 702 \, {\left(x e + d\right)}^{m} B a^{2} m x^{2} e^{6} + 480 \, {\left(x e + d\right)}^{m} A a c x^{3} e^{6} + 580 \, {\left(x e + d\right)}^{m} A a^{2} d m^{2} e^{5} + 360 \, {\left(x e + d\right)}^{m} B a^{2} d m x e^{5} - 342 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} m e^{4} + 480 \, {\left(x e + d\right)}^{m} A a c d^{3} e^{3} + 1044 \, {\left(x e + d\right)}^{m} A a^{2} m x e^{6} + 360 \, {\left(x e + d\right)}^{m} B a^{2} x^{2} e^{6} + 1044 \, {\left(x e + d\right)}^{m} A a^{2} d m e^{5} - 360 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} e^{4} + 720 \, {\left(x e + d\right)}^{m} A a^{2} x e^{6} + 720 \, {\left(x e + d\right)}^{m} A a^{2} d e^{5}}{m^{6} e^{6} + 21 \, m^{5} e^{6} + 175 \, m^{4} e^{6} + 735 \, m^{3} e^{6} + 1624 \, m^{2} e^{6} + 1764 \, m e^{6} + 720 \, e^{6}}"," ",0,"((x*e + d)^m*B*c^2*m^5*x^6*e^6 + (x*e + d)^m*B*c^2*d*m^5*x^5*e^5 + (x*e + d)^m*A*c^2*m^5*x^5*e^6 + 15*(x*e + d)^m*B*c^2*m^4*x^6*e^6 + (x*e + d)^m*A*c^2*d*m^5*x^4*e^5 + 10*(x*e + d)^m*B*c^2*d*m^4*x^5*e^5 - 5*(x*e + d)^m*B*c^2*d^2*m^4*x^4*e^4 + 2*(x*e + d)^m*B*a*c*m^5*x^4*e^6 + 16*(x*e + d)^m*A*c^2*m^4*x^5*e^6 + 85*(x*e + d)^m*B*c^2*m^3*x^6*e^6 + 2*(x*e + d)^m*B*a*c*d*m^5*x^3*e^5 + 12*(x*e + d)^m*A*c^2*d*m^4*x^4*e^5 + 35*(x*e + d)^m*B*c^2*d*m^3*x^5*e^5 - 4*(x*e + d)^m*A*c^2*d^2*m^4*x^3*e^4 - 30*(x*e + d)^m*B*c^2*d^2*m^3*x^4*e^4 + 20*(x*e + d)^m*B*c^2*d^3*m^3*x^3*e^3 + 2*(x*e + d)^m*A*a*c*m^5*x^3*e^6 + 34*(x*e + d)^m*B*a*c*m^4*x^4*e^6 + 95*(x*e + d)^m*A*c^2*m^3*x^5*e^6 + 225*(x*e + d)^m*B*c^2*m^2*x^6*e^6 + 2*(x*e + d)^m*A*a*c*d*m^5*x^2*e^5 + 28*(x*e + d)^m*B*a*c*d*m^4*x^3*e^5 + 47*(x*e + d)^m*A*c^2*d*m^3*x^4*e^5 + 50*(x*e + d)^m*B*c^2*d*m^2*x^5*e^5 - 6*(x*e + d)^m*B*a*c*d^2*m^4*x^2*e^4 - 36*(x*e + d)^m*A*c^2*d^2*m^3*x^3*e^4 - 55*(x*e + d)^m*B*c^2*d^2*m^2*x^4*e^4 + 12*(x*e + d)^m*A*c^2*d^3*m^3*x^2*e^3 + 60*(x*e + d)^m*B*c^2*d^3*m^2*x^3*e^3 - 60*(x*e + d)^m*B*c^2*d^4*m^2*x^2*e^2 + (x*e + d)^m*B*a^2*m^5*x^2*e^6 + 36*(x*e + d)^m*A*a*c*m^4*x^3*e^6 + 214*(x*e + d)^m*B*a*c*m^3*x^4*e^6 + 260*(x*e + d)^m*A*c^2*m^2*x^5*e^6 + 274*(x*e + d)^m*B*c^2*m*x^6*e^6 + (x*e + d)^m*B*a^2*d*m^5*x*e^5 + 32*(x*e + d)^m*A*a*c*d*m^4*x^2*e^5 + 130*(x*e + d)^m*B*a*c*d*m^3*x^3*e^5 + 72*(x*e + d)^m*A*c^2*d*m^2*x^4*e^5 + 24*(x*e + d)^m*B*c^2*d*m*x^5*e^5 - 4*(x*e + d)^m*A*a*c*d^2*m^4*x*e^4 - 72*(x*e + d)^m*B*a*c*d^2*m^3*x^2*e^4 - 80*(x*e + d)^m*A*c^2*d^2*m^2*x^3*e^4 - 30*(x*e + d)^m*B*c^2*d^2*m*x^4*e^4 + 12*(x*e + d)^m*B*a*c*d^3*m^3*x*e^3 + 84*(x*e + d)^m*A*c^2*d^3*m^2*x^2*e^3 + 40*(x*e + d)^m*B*c^2*d^3*m*x^3*e^3 - 24*(x*e + d)^m*A*c^2*d^4*m^2*x*e^2 - 60*(x*e + d)^m*B*c^2*d^4*m*x^2*e^2 + 120*(x*e + d)^m*B*c^2*d^5*m*x*e + (x*e + d)^m*A*a^2*m^5*x*e^6 + 19*(x*e + d)^m*B*a^2*m^4*x^2*e^6 + 242*(x*e + d)^m*A*a*c*m^3*x^3*e^6 + 614*(x*e + d)^m*B*a*c*m^2*x^4*e^6 + 324*(x*e + d)^m*A*c^2*m*x^5*e^6 + 120*(x*e + d)^m*B*c^2*x^6*e^6 + (x*e + d)^m*A*a^2*d*m^5*e^5 + 18*(x*e + d)^m*B*a^2*d*m^4*x*e^5 + 178*(x*e + d)^m*A*a*c*d*m^3*x^2*e^5 + 224*(x*e + d)^m*B*a*c*d*m^2*x^3*e^5 + 36*(x*e + d)^m*A*c^2*d*m*x^4*e^5 - (x*e + d)^m*B*a^2*d^2*m^4*e^4 - 60*(x*e + d)^m*A*a*c*d^2*m^3*x*e^4 - 246*(x*e + d)^m*B*a*c*d^2*m^2*x^2*e^4 - 48*(x*e + d)^m*A*c^2*d^2*m*x^3*e^4 + 4*(x*e + d)^m*A*a*c*d^3*m^3*e^3 + 132*(x*e + d)^m*B*a*c*d^3*m^2*x*e^3 + 72*(x*e + d)^m*A*c^2*d^3*m*x^2*e^3 - 12*(x*e + d)^m*B*a*c*d^4*m^2*e^2 - 144*(x*e + d)^m*A*c^2*d^4*m*x*e^2 + 24*(x*e + d)^m*A*c^2*d^5*m*e - 120*(x*e + d)^m*B*c^2*d^6 + 20*(x*e + d)^m*A*a^2*m^4*x*e^6 + 137*(x*e + d)^m*B*a^2*m^3*x^2*e^6 + 744*(x*e + d)^m*A*a*c*m^2*x^3*e^6 + 792*(x*e + d)^m*B*a*c*m*x^4*e^6 + 144*(x*e + d)^m*A*c^2*x^5*e^6 + 20*(x*e + d)^m*A*a^2*d*m^4*e^5 + 119*(x*e + d)^m*B*a^2*d*m^3*x*e^5 + 388*(x*e + d)^m*A*a*c*d*m^2*x^2*e^5 + 120*(x*e + d)^m*B*a*c*d*m*x^3*e^5 - 18*(x*e + d)^m*B*a^2*d^2*m^3*e^4 - 296*(x*e + d)^m*A*a*c*d^2*m^2*x*e^4 - 180*(x*e + d)^m*B*a*c*d^2*m*x^2*e^4 + 60*(x*e + d)^m*A*a*c*d^3*m^2*e^3 + 360*(x*e + d)^m*B*a*c*d^3*m*x*e^3 - 132*(x*e + d)^m*B*a*c*d^4*m*e^2 + 144*(x*e + d)^m*A*c^2*d^5*e + 155*(x*e + d)^m*A*a^2*m^3*x*e^6 + 461*(x*e + d)^m*B*a^2*m^2*x^2*e^6 + 1016*(x*e + d)^m*A*a*c*m*x^3*e^6 + 360*(x*e + d)^m*B*a*c*x^4*e^6 + 155*(x*e + d)^m*A*a^2*d*m^3*e^5 + 342*(x*e + d)^m*B*a^2*d*m^2*x*e^5 + 240*(x*e + d)^m*A*a*c*d*m*x^2*e^5 - 119*(x*e + d)^m*B*a^2*d^2*m^2*e^4 - 480*(x*e + d)^m*A*a*c*d^2*m*x*e^4 + 296*(x*e + d)^m*A*a*c*d^3*m*e^3 - 360*(x*e + d)^m*B*a*c*d^4*e^2 + 580*(x*e + d)^m*A*a^2*m^2*x*e^6 + 702*(x*e + d)^m*B*a^2*m*x^2*e^6 + 480*(x*e + d)^m*A*a*c*x^3*e^6 + 580*(x*e + d)^m*A*a^2*d*m^2*e^5 + 360*(x*e + d)^m*B*a^2*d*m*x*e^5 - 342*(x*e + d)^m*B*a^2*d^2*m*e^4 + 480*(x*e + d)^m*A*a*c*d^3*e^3 + 1044*(x*e + d)^m*A*a^2*m*x*e^6 + 360*(x*e + d)^m*B*a^2*x^2*e^6 + 1044*(x*e + d)^m*A*a^2*d*m*e^5 - 360*(x*e + d)^m*B*a^2*d^2*e^4 + 720*(x*e + d)^m*A*a^2*x*e^6 + 720*(x*e + d)^m*A*a^2*d*e^5)/(m^6*e^6 + 21*m^5*e^6 + 175*m^4*e^6 + 735*m^3*e^6 + 1624*m^2*e^6 + 1764*m*e^6 + 720*e^6)","B",0
1489,1,770,0,0.180244," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} B c d m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} A c m^{3} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B c m^{2} x^{4} e^{4} + {\left(x e + d\right)}^{m} A c d m^{3} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} B c d m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} B c d^{2} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a m^{3} x^{2} e^{4} + 7 \, {\left(x e + d\right)}^{m} A c m^{2} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} B c m x^{4} e^{4} + {\left(x e + d\right)}^{m} B a d m^{3} x e^{3} + 5 \, {\left(x e + d\right)}^{m} A c d m^{2} x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} B c d m x^{3} e^{3} - 2 \, {\left(x e + d\right)}^{m} A c d^{2} m^{2} x e^{2} - 3 \, {\left(x e + d\right)}^{m} B c d^{2} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} B c d^{3} m x e + {\left(x e + d\right)}^{m} A a m^{3} x e^{4} + 8 \, {\left(x e + d\right)}^{m} B a m^{2} x^{2} e^{4} + 14 \, {\left(x e + d\right)}^{m} A c m x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B c x^{4} e^{4} + {\left(x e + d\right)}^{m} A a d m^{3} e^{3} + 7 \, {\left(x e + d\right)}^{m} B a d m^{2} x e^{3} + 4 \, {\left(x e + d\right)}^{m} A c d m x^{2} e^{3} - {\left(x e + d\right)}^{m} B a d^{2} m^{2} e^{2} - 8 \, {\left(x e + d\right)}^{m} A c d^{2} m x e^{2} + 2 \, {\left(x e + d\right)}^{m} A c d^{3} m e - 6 \, {\left(x e + d\right)}^{m} B c d^{4} + 9 \, {\left(x e + d\right)}^{m} A a m^{2} x e^{4} + 19 \, {\left(x e + d\right)}^{m} B a m x^{2} e^{4} + 8 \, {\left(x e + d\right)}^{m} A c x^{3} e^{4} + 9 \, {\left(x e + d\right)}^{m} A a d m^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} B a d m x e^{3} - 7 \, {\left(x e + d\right)}^{m} B a d^{2} m e^{2} + 8 \, {\left(x e + d\right)}^{m} A c d^{3} e + 26 \, {\left(x e + d\right)}^{m} A a m x e^{4} + 12 \, {\left(x e + d\right)}^{m} B a x^{2} e^{4} + 26 \, {\left(x e + d\right)}^{m} A a d m e^{3} - 12 \, {\left(x e + d\right)}^{m} B a d^{2} e^{2} + 24 \, {\left(x e + d\right)}^{m} A a x e^{4} + 24 \, {\left(x e + d\right)}^{m} A a d e^{3}}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"((x*e + d)^m*B*c*m^3*x^4*e^4 + (x*e + d)^m*B*c*d*m^3*x^3*e^3 + (x*e + d)^m*A*c*m^3*x^3*e^4 + 6*(x*e + d)^m*B*c*m^2*x^4*e^4 + (x*e + d)^m*A*c*d*m^3*x^2*e^3 + 3*(x*e + d)^m*B*c*d*m^2*x^3*e^3 - 3*(x*e + d)^m*B*c*d^2*m^2*x^2*e^2 + (x*e + d)^m*B*a*m^3*x^2*e^4 + 7*(x*e + d)^m*A*c*m^2*x^3*e^4 + 11*(x*e + d)^m*B*c*m*x^4*e^4 + (x*e + d)^m*B*a*d*m^3*x*e^3 + 5*(x*e + d)^m*A*c*d*m^2*x^2*e^3 + 2*(x*e + d)^m*B*c*d*m*x^3*e^3 - 2*(x*e + d)^m*A*c*d^2*m^2*x*e^2 - 3*(x*e + d)^m*B*c*d^2*m*x^2*e^2 + 6*(x*e + d)^m*B*c*d^3*m*x*e + (x*e + d)^m*A*a*m^3*x*e^4 + 8*(x*e + d)^m*B*a*m^2*x^2*e^4 + 14*(x*e + d)^m*A*c*m*x^3*e^4 + 6*(x*e + d)^m*B*c*x^4*e^4 + (x*e + d)^m*A*a*d*m^3*e^3 + 7*(x*e + d)^m*B*a*d*m^2*x*e^3 + 4*(x*e + d)^m*A*c*d*m*x^2*e^3 - (x*e + d)^m*B*a*d^2*m^2*e^2 - 8*(x*e + d)^m*A*c*d^2*m*x*e^2 + 2*(x*e + d)^m*A*c*d^3*m*e - 6*(x*e + d)^m*B*c*d^4 + 9*(x*e + d)^m*A*a*m^2*x*e^4 + 19*(x*e + d)^m*B*a*m*x^2*e^4 + 8*(x*e + d)^m*A*c*x^3*e^4 + 9*(x*e + d)^m*A*a*d*m^2*e^3 + 12*(x*e + d)^m*B*a*d*m*x*e^3 - 7*(x*e + d)^m*B*a*d^2*m*e^2 + 8*(x*e + d)^m*A*c*d^3*e + 26*(x*e + d)^m*A*a*m*x*e^4 + 12*(x*e + d)^m*B*a*x^2*e^4 + 26*(x*e + d)^m*A*a*d*m*e^3 - 12*(x*e + d)^m*B*a*d^2*e^2 + 24*(x*e + d)^m*A*a*x*e^4 + 24*(x*e + d)^m*A*a*d*e^3)/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
1490,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{c x^{2} + a}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/(c*x^2 + a), x)","F",0
1491,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{{\left(c x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/(c*x^2 + a)^2, x)","F",0
1492,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1+m)/(c*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m + 1}}{c x^{2} + a}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(m + 1)/(c*x^2 + a), x)","F",0
1493,0,0,0,0.000000," ","integrate((c*d*x-a*e)*(e*x+d)^(-3-2*p)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c d x - a e\right)} {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((c*d*x - a*e)*(c*x^2 + a)^p*(e*x + d)^(-2*p - 3), x)","F",0
1494,1,270,0,0.156893," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{4} \, c^{2} x^{8} e^{4} + \frac{8}{7} \, c^{2} d x^{7} e^{3} + 2 \, c^{2} d^{2} x^{6} e^{2} + \frac{8}{5} \, c^{2} d^{3} x^{5} e + \frac{1}{2} \, c^{2} d^{4} x^{4} + \frac{3}{7} \, b c x^{7} e^{4} + 2 \, b c d x^{6} e^{3} + \frac{18}{5} \, b c d^{2} x^{5} e^{2} + 3 \, b c d^{3} x^{4} e + b c d^{4} x^{3} + \frac{1}{6} \, b^{2} x^{6} e^{4} + \frac{1}{3} \, a c x^{6} e^{4} + \frac{4}{5} \, b^{2} d x^{5} e^{3} + \frac{8}{5} \, a c d x^{5} e^{3} + \frac{3}{2} \, b^{2} d^{2} x^{4} e^{2} + 3 \, a c d^{2} x^{4} e^{2} + \frac{4}{3} \, b^{2} d^{3} x^{3} e + \frac{8}{3} \, a c d^{3} x^{3} e + \frac{1}{2} \, b^{2} d^{4} x^{2} + a c d^{4} x^{2} + \frac{1}{5} \, a b x^{5} e^{4} + a b d x^{4} e^{3} + 2 \, a b d^{2} x^{3} e^{2} + 2 \, a b d^{3} x^{2} e + a b d^{4} x"," ",0,"1/4*c^2*x^8*e^4 + 8/7*c^2*d*x^7*e^3 + 2*c^2*d^2*x^6*e^2 + 8/5*c^2*d^3*x^5*e + 1/2*c^2*d^4*x^4 + 3/7*b*c*x^7*e^4 + 2*b*c*d*x^6*e^3 + 18/5*b*c*d^2*x^5*e^2 + 3*b*c*d^3*x^4*e + b*c*d^4*x^3 + 1/6*b^2*x^6*e^4 + 1/3*a*c*x^6*e^4 + 4/5*b^2*d*x^5*e^3 + 8/5*a*c*d*x^5*e^3 + 3/2*b^2*d^2*x^4*e^2 + 3*a*c*d^2*x^4*e^2 + 4/3*b^2*d^3*x^3*e + 8/3*a*c*d^3*x^3*e + 1/2*b^2*d^4*x^2 + a*c*d^4*x^2 + 1/5*a*b*x^5*e^4 + a*b*d*x^4*e^3 + 2*a*b*d^2*x^3*e^2 + 2*a*b*d^3*x^2*e + a*b*d^4*x","B",0
1495,1,206,0,0.156241," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{7} \, c^{2} x^{7} e^{3} + c^{2} d x^{6} e^{2} + \frac{6}{5} \, c^{2} d^{2} x^{5} e + \frac{1}{2} \, c^{2} d^{3} x^{4} + \frac{1}{2} \, b c x^{6} e^{3} + \frac{9}{5} \, b c d x^{5} e^{2} + \frac{9}{4} \, b c d^{2} x^{4} e + b c d^{3} x^{3} + \frac{1}{5} \, b^{2} x^{5} e^{3} + \frac{2}{5} \, a c x^{5} e^{3} + \frac{3}{4} \, b^{2} d x^{4} e^{2} + \frac{3}{2} \, a c d x^{4} e^{2} + b^{2} d^{2} x^{3} e + 2 \, a c d^{2} x^{3} e + \frac{1}{2} \, b^{2} d^{3} x^{2} + a c d^{3} x^{2} + \frac{1}{4} \, a b x^{4} e^{3} + a b d x^{3} e^{2} + \frac{3}{2} \, a b d^{2} x^{2} e + a b d^{3} x"," ",0,"2/7*c^2*x^7*e^3 + c^2*d*x^6*e^2 + 6/5*c^2*d^2*x^5*e + 1/2*c^2*d^3*x^4 + 1/2*b*c*x^6*e^3 + 9/5*b*c*d*x^5*e^2 + 9/4*b*c*d^2*x^4*e + b*c*d^3*x^3 + 1/5*b^2*x^5*e^3 + 2/5*a*c*x^5*e^3 + 3/4*b^2*d*x^4*e^2 + 3/2*a*c*d*x^4*e^2 + b^2*d^2*x^3*e + 2*a*c*d^2*x^3*e + 1/2*b^2*d^3*x^2 + a*c*d^3*x^2 + 1/4*a*b*x^4*e^3 + a*b*d*x^3*e^2 + 3/2*a*b*d^2*x^2*e + a*b*d^3*x","A",0
1496,1,146,0,0.180243," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{3} \, c^{2} x^{6} e^{2} + \frac{4}{5} \, c^{2} d x^{5} e + \frac{1}{2} \, c^{2} d^{2} x^{4} + \frac{3}{5} \, b c x^{5} e^{2} + \frac{3}{2} \, b c d x^{4} e + b c d^{2} x^{3} + \frac{1}{4} \, b^{2} x^{4} e^{2} + \frac{1}{2} \, a c x^{4} e^{2} + \frac{2}{3} \, b^{2} d x^{3} e + \frac{4}{3} \, a c d x^{3} e + \frac{1}{2} \, b^{2} d^{2} x^{2} + a c d^{2} x^{2} + \frac{1}{3} \, a b x^{3} e^{2} + a b d x^{2} e + a b d^{2} x"," ",0,"1/3*c^2*x^6*e^2 + 4/5*c^2*d*x^5*e + 1/2*c^2*d^2*x^4 + 3/5*b*c*x^5*e^2 + 3/2*b*c*d*x^4*e + b*c*d^2*x^3 + 1/4*b^2*x^4*e^2 + 1/2*a*c*x^4*e^2 + 2/3*b^2*d*x^3*e + 4/3*a*c*d*x^3*e + 1/2*b^2*d^2*x^2 + a*c*d^2*x^2 + 1/3*a*b*x^3*e^2 + a*b*d*x^2*e + a*b*d^2*x","A",0
1497,1,85,0,0.189414," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{5} \, c^{2} x^{5} e + \frac{1}{2} \, c^{2} d x^{4} + \frac{3}{4} \, b c x^{4} e + b c d x^{3} + \frac{1}{3} \, b^{2} x^{3} e + \frac{2}{3} \, a c x^{3} e + \frac{1}{2} \, b^{2} d x^{2} + a c d x^{2} + \frac{1}{2} \, a b x^{2} e + a b d x"," ",0,"2/5*c^2*x^5*e + 1/2*c^2*d*x^4 + 3/4*b*c*x^4*e + b*c*d*x^3 + 1/3*b^2*x^3*e + 2/3*a*c*x^3*e + 1/2*b^2*d*x^2 + a*c*d*x^2 + 1/2*a*b*x^2*e + a*b*d*x","A",0
1498,1,25,0,0.148833," ","integrate((2*c*x+b)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{2} \, {\left(c x^{2} + b x\right)}^{2} + {\left(c x^{2} + b x\right)} a"," ",0,"1/2*(c*x^2 + b*x)^2 + (c*x^2 + b*x)*a","A",0
1499,1,118,0,0.150816," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d),x, algorithm=""giac"")","-{\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(4 \, c^{2} x^{3} e^{2} - 6 \, c^{2} d x^{2} e + 12 \, c^{2} d^{2} x + 9 \, b c x^{2} e^{2} - 18 \, b c d x e + 6 \, b^{2} x e^{2} + 12 \, a c x e^{2}\right)} e^{\left(-3\right)}"," ",0,"-(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)*e^(-4)*log(abs(x*e + d)) + 1/6*(4*c^2*x^3*e^2 - 6*c^2*d*x^2*e + 12*c^2*d^2*x + 9*b*c*x^2*e^2 - 18*b*c*d*x*e + 6*b^2*x*e^2 + 12*a*c*x*e^2)*e^(-3)","A",0
1500,1,177,0,0.165699," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""giac"")","{\left(c^{2} - \frac{3 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)} - {\left(6 \, c^{2} d^{2} - 6 \, b c d e + b^{2} e^{2} + 2 \, a c e^{2}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{2 \, c^{2} d^{3} e^{2}}{x e + d} - \frac{3 \, b c d^{2} e^{3}}{x e + d} + \frac{b^{2} d e^{4}}{x e + d} + \frac{2 \, a c d e^{4}}{x e + d} - \frac{a b e^{5}}{x e + d}\right)} e^{\left(-6\right)}"," ",0,"(c^2 - 3*(2*c^2*d*e - b*c*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4) - (6*c^2*d^2 - 6*b*c*d*e + b^2*e^2 + 2*a*c*e^2)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (2*c^2*d^3*e^2/(x*e + d) - 3*b*c*d^2*e^3/(x*e + d) + b^2*d*e^4/(x*e + d) + 2*a*c*d*e^4/(x*e + d) - a*b*e^5/(x*e + d))*e^(-6)","A",0
1501,1,116,0,0.148907," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""giac"")","2 \, c^{2} x e^{\left(-3\right)} - 3 \, {\left(2 \, c^{2} d - b c e\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(10 \, c^{2} d^{3} - 9 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} + a b e^{3} + 2 \, {\left(6 \, c^{2} d^{2} e - 6 \, b c d e^{2} + b^{2} e^{3} + 2 \, a c e^{3}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"2*c^2*x*e^(-3) - 3*(2*c^2*d - b*c*e)*e^(-4)*log(abs(x*e + d)) - 1/2*(10*c^2*d^3 - 9*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 + a*b*e^3 + 2*(6*c^2*d^2*e - 6*b*c*d*e^2 + b^2*e^3 + 2*a*c*e^3)*x)*e^(-4)/(x*e + d)^2","A",0
1502,1,123,0,0.150770," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""giac"")","2 \, c^{2} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(18 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{2} + 3 \, {\left(18 \, c^{2} d^{2} - 6 \, b c d e - b^{2} e^{2} - 2 \, a c e^{2}\right)} x + {\left(22 \, c^{2} d^{3} - 6 \, b c d^{2} e - b^{2} d e^{2} - 2 \, a c d e^{2} - 2 \, a b e^{3}\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"2*c^2*e^(-4)*log(abs(x*e + d)) + 1/6*(18*(2*c^2*d*e - b*c*e^2)*x^2 + 3*(18*c^2*d^2 - 6*b*c*d*e - b^2*e^2 - 2*a*c*e^2)*x + (22*c^2*d^3 - 6*b*c*d^2*e - b^2*d*e^2 - 2*a*c*d*e^2 - 2*a*b*e^3)*e^(-1))*e^(-3)/(x*e + d)^3","A",0
1503,1,186,0,0.194139," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{24 \, c^{2} e^{\left(-1\right)}}{x e + d} - \frac{36 \, c^{2} d e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}} + \frac{24 \, c^{2} d^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{6 \, c^{2} d^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{18 \, b c}{{\left(x e + d\right)}^{2}} - \frac{24 \, b c d}{{\left(x e + d\right)}^{3}} + \frac{9 \, b c d^{2}}{{\left(x e + d\right)}^{4}} + \frac{4 \, b^{2} e}{{\left(x e + d\right)}^{3}} + \frac{8 \, a c e}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{2} d e}{{\left(x e + d\right)}^{4}} - \frac{6 \, a c d e}{{\left(x e + d\right)}^{4}} + \frac{3 \, a b e^{2}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-3\right)}"," ",0,"-1/12*(24*c^2*e^(-1)/(x*e + d) - 36*c^2*d*e^(-1)/(x*e + d)^2 + 24*c^2*d^2*e^(-1)/(x*e + d)^3 - 6*c^2*d^3*e^(-1)/(x*e + d)^4 + 18*b*c/(x*e + d)^2 - 24*b*c*d/(x*e + d)^3 + 9*b*c*d^2/(x*e + d)^4 + 4*b^2*e/(x*e + d)^3 + 8*a*c*e/(x*e + d)^3 - 3*b^2*d*e/(x*e + d)^4 - 6*a*c*d*e/(x*e + d)^4 + 3*a*b*e^2/(x*e + d)^4)*e^(-3)","A",0
1504,1,543,0,0.173357," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{5} \, c^{3} x^{10} e^{4} + \frac{8}{9} \, c^{3} d x^{9} e^{3} + \frac{3}{2} \, c^{3} d^{2} x^{8} e^{2} + \frac{8}{7} \, c^{3} d^{3} x^{7} e + \frac{1}{3} \, c^{3} d^{4} x^{6} + \frac{5}{9} \, b c^{2} x^{9} e^{4} + \frac{5}{2} \, b c^{2} d x^{8} e^{3} + \frac{30}{7} \, b c^{2} d^{2} x^{7} e^{2} + \frac{10}{3} \, b c^{2} d^{3} x^{6} e + b c^{2} d^{4} x^{5} + \frac{1}{2} \, b^{2} c x^{8} e^{4} + \frac{1}{2} \, a c^{2} x^{8} e^{4} + \frac{16}{7} \, b^{2} c d x^{7} e^{3} + \frac{16}{7} \, a c^{2} d x^{7} e^{3} + 4 \, b^{2} c d^{2} x^{6} e^{2} + 4 \, a c^{2} d^{2} x^{6} e^{2} + \frac{16}{5} \, b^{2} c d^{3} x^{5} e + \frac{16}{5} \, a c^{2} d^{3} x^{5} e + b^{2} c d^{4} x^{4} + a c^{2} d^{4} x^{4} + \frac{1}{7} \, b^{3} x^{7} e^{4} + \frac{6}{7} \, a b c x^{7} e^{4} + \frac{2}{3} \, b^{3} d x^{6} e^{3} + 4 \, a b c d x^{6} e^{3} + \frac{6}{5} \, b^{3} d^{2} x^{5} e^{2} + \frac{36}{5} \, a b c d^{2} x^{5} e^{2} + b^{3} d^{3} x^{4} e + 6 \, a b c d^{3} x^{4} e + \frac{1}{3} \, b^{3} d^{4} x^{3} + 2 \, a b c d^{4} x^{3} + \frac{1}{3} \, a b^{2} x^{6} e^{4} + \frac{1}{3} \, a^{2} c x^{6} e^{4} + \frac{8}{5} \, a b^{2} d x^{5} e^{3} + \frac{8}{5} \, a^{2} c d x^{5} e^{3} + 3 \, a b^{2} d^{2} x^{4} e^{2} + 3 \, a^{2} c d^{2} x^{4} e^{2} + \frac{8}{3} \, a b^{2} d^{3} x^{3} e + \frac{8}{3} \, a^{2} c d^{3} x^{3} e + a b^{2} d^{4} x^{2} + a^{2} c d^{4} x^{2} + \frac{1}{5} \, a^{2} b x^{5} e^{4} + a^{2} b d x^{4} e^{3} + 2 \, a^{2} b d^{2} x^{3} e^{2} + 2 \, a^{2} b d^{3} x^{2} e + a^{2} b d^{4} x"," ",0,"1/5*c^3*x^10*e^4 + 8/9*c^3*d*x^9*e^3 + 3/2*c^3*d^2*x^8*e^2 + 8/7*c^3*d^3*x^7*e + 1/3*c^3*d^4*x^6 + 5/9*b*c^2*x^9*e^4 + 5/2*b*c^2*d*x^8*e^3 + 30/7*b*c^2*d^2*x^7*e^2 + 10/3*b*c^2*d^3*x^6*e + b*c^2*d^4*x^5 + 1/2*b^2*c*x^8*e^4 + 1/2*a*c^2*x^8*e^4 + 16/7*b^2*c*d*x^7*e^3 + 16/7*a*c^2*d*x^7*e^3 + 4*b^2*c*d^2*x^6*e^2 + 4*a*c^2*d^2*x^6*e^2 + 16/5*b^2*c*d^3*x^5*e + 16/5*a*c^2*d^3*x^5*e + b^2*c*d^4*x^4 + a*c^2*d^4*x^4 + 1/7*b^3*x^7*e^4 + 6/7*a*b*c*x^7*e^4 + 2/3*b^3*d*x^6*e^3 + 4*a*b*c*d*x^6*e^3 + 6/5*b^3*d^2*x^5*e^2 + 36/5*a*b*c*d^2*x^5*e^2 + b^3*d^3*x^4*e + 6*a*b*c*d^3*x^4*e + 1/3*b^3*d^4*x^3 + 2*a*b*c*d^4*x^3 + 1/3*a*b^2*x^6*e^4 + 1/3*a^2*c*x^6*e^4 + 8/5*a*b^2*d*x^5*e^3 + 8/5*a^2*c*d*x^5*e^3 + 3*a*b^2*d^2*x^4*e^2 + 3*a^2*c*d^2*x^4*e^2 + 8/3*a*b^2*d^3*x^3*e + 8/3*a^2*c*d^3*x^3*e + a*b^2*d^4*x^2 + a^2*c*d^4*x^2 + 1/5*a^2*b*x^5*e^4 + a^2*b*d*x^4*e^3 + 2*a^2*b*d^2*x^3*e^2 + 2*a^2*b*d^3*x^2*e + a^2*b*d^4*x","B",0
1505,1,420,0,0.160142," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{9} \, c^{3} x^{9} e^{3} + \frac{3}{4} \, c^{3} d x^{8} e^{2} + \frac{6}{7} \, c^{3} d^{2} x^{7} e + \frac{1}{3} \, c^{3} d^{3} x^{6} + \frac{5}{8} \, b c^{2} x^{8} e^{3} + \frac{15}{7} \, b c^{2} d x^{7} e^{2} + \frac{5}{2} \, b c^{2} d^{2} x^{6} e + b c^{2} d^{3} x^{5} + \frac{4}{7} \, b^{2} c x^{7} e^{3} + \frac{4}{7} \, a c^{2} x^{7} e^{3} + 2 \, b^{2} c d x^{6} e^{2} + 2 \, a c^{2} d x^{6} e^{2} + \frac{12}{5} \, b^{2} c d^{2} x^{5} e + \frac{12}{5} \, a c^{2} d^{2} x^{5} e + b^{2} c d^{3} x^{4} + a c^{2} d^{3} x^{4} + \frac{1}{6} \, b^{3} x^{6} e^{3} + a b c x^{6} e^{3} + \frac{3}{5} \, b^{3} d x^{5} e^{2} + \frac{18}{5} \, a b c d x^{5} e^{2} + \frac{3}{4} \, b^{3} d^{2} x^{4} e + \frac{9}{2} \, a b c d^{2} x^{4} e + \frac{1}{3} \, b^{3} d^{3} x^{3} + 2 \, a b c d^{3} x^{3} + \frac{2}{5} \, a b^{2} x^{5} e^{3} + \frac{2}{5} \, a^{2} c x^{5} e^{3} + \frac{3}{2} \, a b^{2} d x^{4} e^{2} + \frac{3}{2} \, a^{2} c d x^{4} e^{2} + 2 \, a b^{2} d^{2} x^{3} e + 2 \, a^{2} c d^{2} x^{3} e + a b^{2} d^{3} x^{2} + a^{2} c d^{3} x^{2} + \frac{1}{4} \, a^{2} b x^{4} e^{3} + a^{2} b d x^{3} e^{2} + \frac{3}{2} \, a^{2} b d^{2} x^{2} e + a^{2} b d^{3} x"," ",0,"2/9*c^3*x^9*e^3 + 3/4*c^3*d*x^8*e^2 + 6/7*c^3*d^2*x^7*e + 1/3*c^3*d^3*x^6 + 5/8*b*c^2*x^8*e^3 + 15/7*b*c^2*d*x^7*e^2 + 5/2*b*c^2*d^2*x^6*e + b*c^2*d^3*x^5 + 4/7*b^2*c*x^7*e^3 + 4/7*a*c^2*x^7*e^3 + 2*b^2*c*d*x^6*e^2 + 2*a*c^2*d*x^6*e^2 + 12/5*b^2*c*d^2*x^5*e + 12/5*a*c^2*d^2*x^5*e + b^2*c*d^3*x^4 + a*c^2*d^3*x^4 + 1/6*b^3*x^6*e^3 + a*b*c*x^6*e^3 + 3/5*b^3*d*x^5*e^2 + 18/5*a*b*c*d*x^5*e^2 + 3/4*b^3*d^2*x^4*e + 9/2*a*b*c*d^2*x^4*e + 1/3*b^3*d^3*x^3 + 2*a*b*c*d^3*x^3 + 2/5*a*b^2*x^5*e^3 + 2/5*a^2*c*x^5*e^3 + 3/2*a*b^2*d*x^4*e^2 + 3/2*a^2*c*d*x^4*e^2 + 2*a*b^2*d^2*x^3*e + 2*a^2*c*d^2*x^3*e + a*b^2*d^3*x^2 + a^2*c*d^3*x^2 + 1/4*a^2*b*x^4*e^3 + a^2*b*d*x^3*e^2 + 3/2*a^2*b*d^2*x^2*e + a^2*b*d^3*x","A",0
1506,1,298,0,0.167377," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{4} \, c^{3} x^{8} e^{2} + \frac{4}{7} \, c^{3} d x^{7} e + \frac{1}{3} \, c^{3} d^{2} x^{6} + \frac{5}{7} \, b c^{2} x^{7} e^{2} + \frac{5}{3} \, b c^{2} d x^{6} e + b c^{2} d^{2} x^{5} + \frac{2}{3} \, b^{2} c x^{6} e^{2} + \frac{2}{3} \, a c^{2} x^{6} e^{2} + \frac{8}{5} \, b^{2} c d x^{5} e + \frac{8}{5} \, a c^{2} d x^{5} e + b^{2} c d^{2} x^{4} + a c^{2} d^{2} x^{4} + \frac{1}{5} \, b^{3} x^{5} e^{2} + \frac{6}{5} \, a b c x^{5} e^{2} + \frac{1}{2} \, b^{3} d x^{4} e + 3 \, a b c d x^{4} e + \frac{1}{3} \, b^{3} d^{2} x^{3} + 2 \, a b c d^{2} x^{3} + \frac{1}{2} \, a b^{2} x^{4} e^{2} + \frac{1}{2} \, a^{2} c x^{4} e^{2} + \frac{4}{3} \, a b^{2} d x^{3} e + \frac{4}{3} \, a^{2} c d x^{3} e + a b^{2} d^{2} x^{2} + a^{2} c d^{2} x^{2} + \frac{1}{3} \, a^{2} b x^{3} e^{2} + a^{2} b d x^{2} e + a^{2} b d^{2} x"," ",0,"1/4*c^3*x^8*e^2 + 4/7*c^3*d*x^7*e + 1/3*c^3*d^2*x^6 + 5/7*b*c^2*x^7*e^2 + 5/3*b*c^2*d*x^6*e + b*c^2*d^2*x^5 + 2/3*b^2*c*x^6*e^2 + 2/3*a*c^2*x^6*e^2 + 8/5*b^2*c*d*x^5*e + 8/5*a*c^2*d*x^5*e + b^2*c*d^2*x^4 + a*c^2*d^2*x^4 + 1/5*b^3*x^5*e^2 + 6/5*a*b*c*x^5*e^2 + 1/2*b^3*d*x^4*e + 3*a*b*c*d*x^4*e + 1/3*b^3*d^2*x^3 + 2*a*b*c*d^2*x^3 + 1/2*a*b^2*x^4*e^2 + 1/2*a^2*c*x^4*e^2 + 4/3*a*b^2*d*x^3*e + 4/3*a^2*c*d*x^3*e + a*b^2*d^2*x^2 + a^2*c*d^2*x^2 + 1/3*a^2*b*x^3*e^2 + a^2*b*d*x^2*e + a^2*b*d^2*x","A",0
1507,1,176,0,0.194782," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{7} \, c^{3} x^{7} e + \frac{1}{3} \, c^{3} d x^{6} + \frac{5}{6} \, b c^{2} x^{6} e + b c^{2} d x^{5} + \frac{4}{5} \, b^{2} c x^{5} e + \frac{4}{5} \, a c^{2} x^{5} e + b^{2} c d x^{4} + a c^{2} d x^{4} + \frac{1}{4} \, b^{3} x^{4} e + \frac{3}{2} \, a b c x^{4} e + \frac{1}{3} \, b^{3} d x^{3} + 2 \, a b c d x^{3} + \frac{2}{3} \, a b^{2} x^{3} e + \frac{2}{3} \, a^{2} c x^{3} e + a b^{2} d x^{2} + a^{2} c d x^{2} + \frac{1}{2} \, a^{2} b x^{2} e + a^{2} b d x"," ",0,"2/7*c^3*x^7*e + 1/3*c^3*d*x^6 + 5/6*b*c^2*x^6*e + b*c^2*d*x^5 + 4/5*b^2*c*x^5*e + 4/5*a*c^2*x^5*e + b^2*c*d*x^4 + a*c^2*d*x^4 + 1/4*b^3*x^4*e + 3/2*a*b*c*x^4*e + 1/3*b^3*d*x^3 + 2*a*b*c*d*x^3 + 2/3*a*b^2*x^3*e + 2/3*a^2*c*x^3*e + a*b^2*d*x^2 + a^2*c*d*x^2 + 1/2*a^2*b*x^2*e + a^2*b*d*x","A",0
1508,1,40,0,0.162370," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(c x^{2} + b x\right)}^{3} + {\left(c x^{2} + b x\right)}^{2} a + {\left(c x^{2} + b x\right)} a^{2}"," ",0,"1/3*(c*x^2 + b*x)^3 + (c*x^2 + b*x)^2*a + (c*x^2 + b*x)*a^2","B",0
1509,1,337,0,0.155705," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""giac"")","-{\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(24 \, c^{3} x^{5} e^{4} - 30 \, c^{3} d x^{4} e^{3} + 40 \, c^{3} d^{2} x^{3} e^{2} - 60 \, c^{3} d^{3} x^{2} e + 120 \, c^{3} d^{4} x + 75 \, b c^{2} x^{4} e^{4} - 100 \, b c^{2} d x^{3} e^{3} + 150 \, b c^{2} d^{2} x^{2} e^{2} - 300 \, b c^{2} d^{3} x e + 80 \, b^{2} c x^{3} e^{4} + 80 \, a c^{2} x^{3} e^{4} - 120 \, b^{2} c d x^{2} e^{3} - 120 \, a c^{2} d x^{2} e^{3} + 240 \, b^{2} c d^{2} x e^{2} + 240 \, a c^{2} d^{2} x e^{2} + 30 \, b^{3} x^{2} e^{4} + 180 \, a b c x^{2} e^{4} - 60 \, b^{3} d x e^{3} - 360 \, a b c d x e^{3} + 120 \, a b^{2} x e^{4} + 120 \, a^{2} c x e^{4}\right)} e^{\left(-5\right)}"," ",0,"-(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)*e^(-6)*log(abs(x*e + d)) + 1/60*(24*c^3*x^5*e^4 - 30*c^3*d*x^4*e^3 + 40*c^3*d^2*x^3*e^2 - 60*c^3*d^3*x^2*e + 120*c^3*d^4*x + 75*b*c^2*x^4*e^4 - 100*b*c^2*d*x^3*e^3 + 150*b*c^2*d^2*x^2*e^2 - 300*b*c^2*d^3*x*e + 80*b^2*c*x^3*e^4 + 80*a*c^2*x^3*e^4 - 120*b^2*c*d*x^2*e^3 - 120*a*c^2*d*x^2*e^3 + 240*b^2*c*d^2*x*e^2 + 240*a*c^2*d^2*x*e^2 + 30*b^3*x^2*e^4 + 180*a*b*c*x^2*e^4 - 60*b^3*d*x*e^3 - 360*a*b*c*d*x*e^3 + 120*a*b^2*x*e^4 + 120*a^2*c*x*e^4)*e^(-5)","A",0
1510,1,420,0,0.172568," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{6} \, {\left(3 \, c^{3} - \frac{10 \, {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{12 \, {\left(5 \, c^{3} d^{2} e^{2} - 5 \, b c^{2} d e^{3} + b^{2} c e^{4} + a c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{6 \, {\left(20 \, c^{3} d^{3} e^{3} - 30 \, b c^{2} d^{2} e^{4} + 12 \, b^{2} c d e^{5} + 12 \, a c^{2} d e^{5} - b^{3} e^{6} - 6 \, a b c e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{4} e^{\left(-6\right)} - 2 \, {\left(5 \, c^{3} d^{4} - 10 \, b c^{2} d^{3} e + 6 \, b^{2} c d^{2} e^{2} + 6 \, a c^{2} d^{2} e^{2} - b^{3} d e^{3} - 6 \, a b c d e^{3} + a b^{2} e^{4} + a^{2} c e^{4}\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{2 \, c^{3} d^{5} e^{4}}{x e + d} - \frac{5 \, b c^{2} d^{4} e^{5}}{x e + d} + \frac{4 \, b^{2} c d^{3} e^{6}}{x e + d} + \frac{4 \, a c^{2} d^{3} e^{6}}{x e + d} - \frac{b^{3} d^{2} e^{7}}{x e + d} - \frac{6 \, a b c d^{2} e^{7}}{x e + d} + \frac{2 \, a b^{2} d e^{8}}{x e + d} + \frac{2 \, a^{2} c d e^{8}}{x e + d} - \frac{a^{2} b e^{9}}{x e + d}\right)} e^{\left(-10\right)}"," ",0,"1/6*(3*c^3 - 10*(2*c^3*d*e - b*c^2*e^2)*e^(-1)/(x*e + d) + 12*(5*c^3*d^2*e^2 - 5*b*c^2*d*e^3 + b^2*c*e^4 + a*c^2*e^4)*e^(-2)/(x*e + d)^2 - 6*(20*c^3*d^3*e^3 - 30*b*c^2*d^2*e^4 + 12*b^2*c*d*e^5 + 12*a*c^2*d*e^5 - b^3*e^6 - 6*a*b*c*e^6)*e^(-3)/(x*e + d)^3)*(x*e + d)^4*e^(-6) - 2*(5*c^3*d^4 - 10*b*c^2*d^3*e + 6*b^2*c*d^2*e^2 + 6*a*c^2*d^2*e^2 - b^3*d*e^3 - 6*a*b*c*d*e^3 + a*b^2*e^4 + a^2*c*e^4)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (2*c^3*d^5*e^4/(x*e + d) - 5*b*c^2*d^4*e^5/(x*e + d) + 4*b^2*c*d^3*e^6/(x*e + d) + 4*a*c^2*d^3*e^6/(x*e + d) - b^3*d^2*e^7/(x*e + d) - 6*a*b*c*d^2*e^7/(x*e + d) + 2*a*b^2*d*e^8/(x*e + d) + 2*a^2*c*d*e^8/(x*e + d) - a^2*b*e^9/(x*e + d))*e^(-10)","A",0
1511,1,317,0,0.159440," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^3,x, algorithm=""giac"")","-{\left(20 \, c^{3} d^{3} - 30 \, b c^{2} d^{2} e + 12 \, b^{2} c d e^{2} + 12 \, a c^{2} d e^{2} - b^{3} e^{3} - 6 \, a b c e^{3}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(4 \, c^{3} x^{3} e^{6} - 18 \, c^{3} d x^{2} e^{5} + 72 \, c^{3} d^{2} x e^{4} + 15 \, b c^{2} x^{2} e^{6} - 90 \, b c^{2} d x e^{5} + 24 \, b^{2} c x e^{6} + 24 \, a c^{2} x e^{6}\right)} e^{\left(-9\right)} - \frac{{\left(18 \, c^{3} d^{5} - 35 \, b c^{2} d^{4} e + 20 \, b^{2} c d^{3} e^{2} + 20 \, a c^{2} d^{3} e^{2} - 3 \, b^{3} d^{2} e^{3} - 18 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} + a^{2} b e^{5} + 4 \, {\left(5 \, c^{3} d^{4} e - 10 \, b c^{2} d^{3} e^{2} + 6 \, b^{2} c d^{2} e^{3} + 6 \, a c^{2} d^{2} e^{3} - b^{3} d e^{4} - 6 \, a b c d e^{4} + a b^{2} e^{5} + a^{2} c e^{5}\right)} x\right)} e^{\left(-6\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-(20*c^3*d^3 - 30*b*c^2*d^2*e + 12*b^2*c*d*e^2 + 12*a*c^2*d*e^2 - b^3*e^3 - 6*a*b*c*e^3)*e^(-6)*log(abs(x*e + d)) + 1/6*(4*c^3*x^3*e^6 - 18*c^3*d*x^2*e^5 + 72*c^3*d^2*x*e^4 + 15*b*c^2*x^2*e^6 - 90*b*c^2*d*x*e^5 + 24*b^2*c*x*e^6 + 24*a*c^2*x*e^6)*e^(-9) - 1/2*(18*c^3*d^5 - 35*b*c^2*d^4*e + 20*b^2*c*d^3*e^2 + 20*a*c^2*d^3*e^2 - 3*b^3*d^2*e^3 - 18*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 + a^2*b*e^5 + 4*(5*c^3*d^4*e - 10*b*c^2*d^3*e^2 + 6*b^2*c*d^2*e^3 + 6*a*c^2*d^2*e^3 - b^3*d*e^4 - 6*a*b*c*d*e^4 + a*b^2*e^5 + a^2*c*e^5)*x)*e^(-6)/(x*e + d)^2","A",0
1512,1,314,0,0.157003," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^4,x, algorithm=""giac"")","4 \, {\left(5 \, c^{3} d^{2} - 5 \, b c^{2} d e + b^{2} c e^{2} + a c^{2} e^{2}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + {\left(c^{3} x^{2} e^{4} - 8 \, c^{3} d x e^{3} + 5 \, b c^{2} x e^{4}\right)} e^{\left(-8\right)} + \frac{{\left(47 \, c^{3} d^{5} - 65 \, b c^{2} d^{4} e + 22 \, b^{2} c d^{3} e^{2} + 22 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} - a b^{2} d e^{4} - a^{2} c d e^{4} - a^{2} b e^{5} + 3 \, {\left(20 \, c^{3} d^{3} e^{2} - 30 \, b c^{2} d^{2} e^{3} + 12 \, b^{2} c d e^{4} + 12 \, a c^{2} d e^{4} - b^{3} e^{5} - 6 \, a b c e^{5}\right)} x^{2} + 3 \, {\left(35 \, c^{3} d^{4} e - 50 \, b c^{2} d^{3} e^{2} + 18 \, b^{2} c d^{2} e^{3} + 18 \, a c^{2} d^{2} e^{3} - b^{3} d e^{4} - 6 \, a b c d e^{4} - a b^{2} e^{5} - a^{2} c e^{5}\right)} x\right)} e^{\left(-6\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"4*(5*c^3*d^2 - 5*b*c^2*d*e + b^2*c*e^2 + a*c^2*e^2)*e^(-6)*log(abs(x*e + d)) + (c^3*x^2*e^4 - 8*c^3*d*x*e^3 + 5*b*c^2*x*e^4)*e^(-8) + 1/3*(47*c^3*d^5 - 65*b*c^2*d^4*e + 22*b^2*c*d^3*e^2 + 22*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 - a*b^2*d*e^4 - a^2*c*d*e^4 - a^2*b*e^5 + 3*(20*c^3*d^3*e^2 - 30*b*c^2*d^2*e^3 + 12*b^2*c*d*e^4 + 12*a*c^2*d*e^4 - b^3*e^5 - 6*a*b*c*e^5)*x^2 + 3*(35*c^3*d^4*e - 50*b*c^2*d^3*e^2 + 18*b^2*c*d^2*e^3 + 18*a*c^2*d^2*e^3 - b^3*d*e^4 - 6*a*b*c*d*e^4 - a*b^2*e^5 - a^2*c*e^5)*x)*e^(-6)/(x*e + d)^3","A",0
1513,1,525,0,0.202152," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^5,x, algorithm=""giac"")","2 \, {\left(x e + d\right)} c^{3} e^{\left(-6\right)} + 5 \, {\left(2 \, c^{3} d - b c^{2} e\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{240 \, c^{3} d^{2} e^{22}}{x e + d} - \frac{120 \, c^{3} d^{3} e^{22}}{{\left(x e + d\right)}^{2}} + \frac{40 \, c^{3} d^{4} e^{22}}{{\left(x e + d\right)}^{3}} - \frac{6 \, c^{3} d^{5} e^{22}}{{\left(x e + d\right)}^{4}} - \frac{240 \, b c^{2} d e^{23}}{x e + d} + \frac{180 \, b c^{2} d^{2} e^{23}}{{\left(x e + d\right)}^{2}} - \frac{80 \, b c^{2} d^{3} e^{23}}{{\left(x e + d\right)}^{3}} + \frac{15 \, b c^{2} d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{48 \, b^{2} c e^{24}}{x e + d} + \frac{48 \, a c^{2} e^{24}}{x e + d} - \frac{72 \, b^{2} c d e^{24}}{{\left(x e + d\right)}^{2}} - \frac{72 \, a c^{2} d e^{24}}{{\left(x e + d\right)}^{2}} + \frac{48 \, b^{2} c d^{2} e^{24}}{{\left(x e + d\right)}^{3}} + \frac{48 \, a c^{2} d^{2} e^{24}}{{\left(x e + d\right)}^{3}} - \frac{12 \, b^{2} c d^{3} e^{24}}{{\left(x e + d\right)}^{4}} - \frac{12 \, a c^{2} d^{3} e^{24}}{{\left(x e + d\right)}^{4}} + \frac{6 \, b^{3} e^{25}}{{\left(x e + d\right)}^{2}} + \frac{36 \, a b c e^{25}}{{\left(x e + d\right)}^{2}} - \frac{8 \, b^{3} d e^{25}}{{\left(x e + d\right)}^{3}} - \frac{48 \, a b c d e^{25}}{{\left(x e + d\right)}^{3}} + \frac{3 \, b^{3} d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{18 \, a b c d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{8 \, a b^{2} e^{26}}{{\left(x e + d\right)}^{3}} + \frac{8 \, a^{2} c e^{26}}{{\left(x e + d\right)}^{3}} - \frac{6 \, a b^{2} d e^{26}}{{\left(x e + d\right)}^{4}} - \frac{6 \, a^{2} c d e^{26}}{{\left(x e + d\right)}^{4}} + \frac{3 \, a^{2} b e^{27}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-28\right)}"," ",0,"2*(x*e + d)*c^3*e^(-6) + 5*(2*c^3*d - b*c^2*e)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(240*c^3*d^2*e^22/(x*e + d) - 120*c^3*d^3*e^22/(x*e + d)^2 + 40*c^3*d^4*e^22/(x*e + d)^3 - 6*c^3*d^5*e^22/(x*e + d)^4 - 240*b*c^2*d*e^23/(x*e + d) + 180*b*c^2*d^2*e^23/(x*e + d)^2 - 80*b*c^2*d^3*e^23/(x*e + d)^3 + 15*b*c^2*d^4*e^23/(x*e + d)^4 + 48*b^2*c*e^24/(x*e + d) + 48*a*c^2*e^24/(x*e + d) - 72*b^2*c*d*e^24/(x*e + d)^2 - 72*a*c^2*d*e^24/(x*e + d)^2 + 48*b^2*c*d^2*e^24/(x*e + d)^3 + 48*a*c^2*d^2*e^24/(x*e + d)^3 - 12*b^2*c*d^3*e^24/(x*e + d)^4 - 12*a*c^2*d^3*e^24/(x*e + d)^4 + 6*b^3*e^25/(x*e + d)^2 + 36*a*b*c*e^25/(x*e + d)^2 - 8*b^3*d*e^25/(x*e + d)^3 - 48*a*b*c*d*e^25/(x*e + d)^3 + 3*b^3*d^2*e^25/(x*e + d)^4 + 18*a*b*c*d^2*e^25/(x*e + d)^4 + 8*a*b^2*e^26/(x*e + d)^3 + 8*a^2*c*e^26/(x*e + d)^3 - 6*a*b^2*d*e^26/(x*e + d)^4 - 6*a^2*c*d*e^26/(x*e + d)^4 + 3*a^2*b*e^27/(x*e + d)^4)*e^(-28)","B",0
1514,1,908,0,0.166952," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{6} \, c^{4} x^{12} e^{4} + \frac{8}{11} \, c^{4} d x^{11} e^{3} + \frac{6}{5} \, c^{4} d^{2} x^{10} e^{2} + \frac{8}{9} \, c^{4} d^{3} x^{9} e + \frac{1}{4} \, c^{4} d^{4} x^{8} + \frac{7}{11} \, b c^{3} x^{11} e^{4} + \frac{14}{5} \, b c^{3} d x^{10} e^{3} + \frac{14}{3} \, b c^{3} d^{2} x^{9} e^{2} + \frac{7}{2} \, b c^{3} d^{3} x^{8} e + b c^{3} d^{4} x^{7} + \frac{9}{10} \, b^{2} c^{2} x^{10} e^{4} + \frac{3}{5} \, a c^{3} x^{10} e^{4} + 4 \, b^{2} c^{2} d x^{9} e^{3} + \frac{8}{3} \, a c^{3} d x^{9} e^{3} + \frac{27}{4} \, b^{2} c^{2} d^{2} x^{8} e^{2} + \frac{9}{2} \, a c^{3} d^{2} x^{8} e^{2} + \frac{36}{7} \, b^{2} c^{2} d^{3} x^{7} e + \frac{24}{7} \, a c^{3} d^{3} x^{7} e + \frac{3}{2} \, b^{2} c^{2} d^{4} x^{6} + a c^{3} d^{4} x^{6} + \frac{5}{9} \, b^{3} c x^{9} e^{4} + \frac{5}{3} \, a b c^{2} x^{9} e^{4} + \frac{5}{2} \, b^{3} c d x^{8} e^{3} + \frac{15}{2} \, a b c^{2} d x^{8} e^{3} + \frac{30}{7} \, b^{3} c d^{2} x^{7} e^{2} + \frac{90}{7} \, a b c^{2} d^{2} x^{7} e^{2} + \frac{10}{3} \, b^{3} c d^{3} x^{6} e + 10 \, a b c^{2} d^{3} x^{6} e + b^{3} c d^{4} x^{5} + 3 \, a b c^{2} d^{4} x^{5} + \frac{1}{8} \, b^{4} x^{8} e^{4} + \frac{3}{2} \, a b^{2} c x^{8} e^{4} + \frac{3}{4} \, a^{2} c^{2} x^{8} e^{4} + \frac{4}{7} \, b^{4} d x^{7} e^{3} + \frac{48}{7} \, a b^{2} c d x^{7} e^{3} + \frac{24}{7} \, a^{2} c^{2} d x^{7} e^{3} + b^{4} d^{2} x^{6} e^{2} + 12 \, a b^{2} c d^{2} x^{6} e^{2} + 6 \, a^{2} c^{2} d^{2} x^{6} e^{2} + \frac{4}{5} \, b^{4} d^{3} x^{5} e + \frac{48}{5} \, a b^{2} c d^{3} x^{5} e + \frac{24}{5} \, a^{2} c^{2} d^{3} x^{5} e + \frac{1}{4} \, b^{4} d^{4} x^{4} + 3 \, a b^{2} c d^{4} x^{4} + \frac{3}{2} \, a^{2} c^{2} d^{4} x^{4} + \frac{3}{7} \, a b^{3} x^{7} e^{4} + \frac{9}{7} \, a^{2} b c x^{7} e^{4} + 2 \, a b^{3} d x^{6} e^{3} + 6 \, a^{2} b c d x^{6} e^{3} + \frac{18}{5} \, a b^{3} d^{2} x^{5} e^{2} + \frac{54}{5} \, a^{2} b c d^{2} x^{5} e^{2} + 3 \, a b^{3} d^{3} x^{4} e + 9 \, a^{2} b c d^{3} x^{4} e + a b^{3} d^{4} x^{3} + 3 \, a^{2} b c d^{4} x^{3} + \frac{1}{2} \, a^{2} b^{2} x^{6} e^{4} + \frac{1}{3} \, a^{3} c x^{6} e^{4} + \frac{12}{5} \, a^{2} b^{2} d x^{5} e^{3} + \frac{8}{5} \, a^{3} c d x^{5} e^{3} + \frac{9}{2} \, a^{2} b^{2} d^{2} x^{4} e^{2} + 3 \, a^{3} c d^{2} x^{4} e^{2} + 4 \, a^{2} b^{2} d^{3} x^{3} e + \frac{8}{3} \, a^{3} c d^{3} x^{3} e + \frac{3}{2} \, a^{2} b^{2} d^{4} x^{2} + a^{3} c d^{4} x^{2} + \frac{1}{5} \, a^{3} b x^{5} e^{4} + a^{3} b d x^{4} e^{3} + 2 \, a^{3} b d^{2} x^{3} e^{2} + 2 \, a^{3} b d^{3} x^{2} e + a^{3} b d^{4} x"," ",0,"1/6*c^4*x^12*e^4 + 8/11*c^4*d*x^11*e^3 + 6/5*c^4*d^2*x^10*e^2 + 8/9*c^4*d^3*x^9*e + 1/4*c^4*d^4*x^8 + 7/11*b*c^3*x^11*e^4 + 14/5*b*c^3*d*x^10*e^3 + 14/3*b*c^3*d^2*x^9*e^2 + 7/2*b*c^3*d^3*x^8*e + b*c^3*d^4*x^7 + 9/10*b^2*c^2*x^10*e^4 + 3/5*a*c^3*x^10*e^4 + 4*b^2*c^2*d*x^9*e^3 + 8/3*a*c^3*d*x^9*e^3 + 27/4*b^2*c^2*d^2*x^8*e^2 + 9/2*a*c^3*d^2*x^8*e^2 + 36/7*b^2*c^2*d^3*x^7*e + 24/7*a*c^3*d^3*x^7*e + 3/2*b^2*c^2*d^4*x^6 + a*c^3*d^4*x^6 + 5/9*b^3*c*x^9*e^4 + 5/3*a*b*c^2*x^9*e^4 + 5/2*b^3*c*d*x^8*e^3 + 15/2*a*b*c^2*d*x^8*e^3 + 30/7*b^3*c*d^2*x^7*e^2 + 90/7*a*b*c^2*d^2*x^7*e^2 + 10/3*b^3*c*d^3*x^6*e + 10*a*b*c^2*d^3*x^6*e + b^3*c*d^4*x^5 + 3*a*b*c^2*d^4*x^5 + 1/8*b^4*x^8*e^4 + 3/2*a*b^2*c*x^8*e^4 + 3/4*a^2*c^2*x^8*e^4 + 4/7*b^4*d*x^7*e^3 + 48/7*a*b^2*c*d*x^7*e^3 + 24/7*a^2*c^2*d*x^7*e^3 + b^4*d^2*x^6*e^2 + 12*a*b^2*c*d^2*x^6*e^2 + 6*a^2*c^2*d^2*x^6*e^2 + 4/5*b^4*d^3*x^5*e + 48/5*a*b^2*c*d^3*x^5*e + 24/5*a^2*c^2*d^3*x^5*e + 1/4*b^4*d^4*x^4 + 3*a*b^2*c*d^4*x^4 + 3/2*a^2*c^2*d^4*x^4 + 3/7*a*b^3*x^7*e^4 + 9/7*a^2*b*c*x^7*e^4 + 2*a*b^3*d*x^6*e^3 + 6*a^2*b*c*d*x^6*e^3 + 18/5*a*b^3*d^2*x^5*e^2 + 54/5*a^2*b*c*d^2*x^5*e^2 + 3*a*b^3*d^3*x^4*e + 9*a^2*b*c*d^3*x^4*e + a*b^3*d^4*x^3 + 3*a^2*b*c*d^4*x^3 + 1/2*a^2*b^2*x^6*e^4 + 1/3*a^3*c*x^6*e^4 + 12/5*a^2*b^2*d*x^5*e^3 + 8/5*a^3*c*d*x^5*e^3 + 9/2*a^2*b^2*d^2*x^4*e^2 + 3*a^3*c*d^2*x^4*e^2 + 4*a^2*b^2*d^3*x^3*e + 8/3*a^3*c*d^3*x^3*e + 3/2*a^2*b^2*d^4*x^2 + a^3*c*d^4*x^2 + 1/5*a^3*b*x^5*e^4 + a^3*b*d*x^4*e^3 + 2*a^3*b*d^2*x^3*e^2 + 2*a^3*b*d^3*x^2*e + a^3*b*d^4*x","B",0
1515,1,705,0,0.177012," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{11} \, c^{4} x^{11} e^{3} + \frac{3}{5} \, c^{4} d x^{10} e^{2} + \frac{2}{3} \, c^{4} d^{2} x^{9} e + \frac{1}{4} \, c^{4} d^{3} x^{8} + \frac{7}{10} \, b c^{3} x^{10} e^{3} + \frac{7}{3} \, b c^{3} d x^{9} e^{2} + \frac{21}{8} \, b c^{3} d^{2} x^{8} e + b c^{3} d^{3} x^{7} + b^{2} c^{2} x^{9} e^{3} + \frac{2}{3} \, a c^{3} x^{9} e^{3} + \frac{27}{8} \, b^{2} c^{2} d x^{8} e^{2} + \frac{9}{4} \, a c^{3} d x^{8} e^{2} + \frac{27}{7} \, b^{2} c^{2} d^{2} x^{7} e + \frac{18}{7} \, a c^{3} d^{2} x^{7} e + \frac{3}{2} \, b^{2} c^{2} d^{3} x^{6} + a c^{3} d^{3} x^{6} + \frac{5}{8} \, b^{3} c x^{8} e^{3} + \frac{15}{8} \, a b c^{2} x^{8} e^{3} + \frac{15}{7} \, b^{3} c d x^{7} e^{2} + \frac{45}{7} \, a b c^{2} d x^{7} e^{2} + \frac{5}{2} \, b^{3} c d^{2} x^{6} e + \frac{15}{2} \, a b c^{2} d^{2} x^{6} e + b^{3} c d^{3} x^{5} + 3 \, a b c^{2} d^{3} x^{5} + \frac{1}{7} \, b^{4} x^{7} e^{3} + \frac{12}{7} \, a b^{2} c x^{7} e^{3} + \frac{6}{7} \, a^{2} c^{2} x^{7} e^{3} + \frac{1}{2} \, b^{4} d x^{6} e^{2} + 6 \, a b^{2} c d x^{6} e^{2} + 3 \, a^{2} c^{2} d x^{6} e^{2} + \frac{3}{5} \, b^{4} d^{2} x^{5} e + \frac{36}{5} \, a b^{2} c d^{2} x^{5} e + \frac{18}{5} \, a^{2} c^{2} d^{2} x^{5} e + \frac{1}{4} \, b^{4} d^{3} x^{4} + 3 \, a b^{2} c d^{3} x^{4} + \frac{3}{2} \, a^{2} c^{2} d^{3} x^{4} + \frac{1}{2} \, a b^{3} x^{6} e^{3} + \frac{3}{2} \, a^{2} b c x^{6} e^{3} + \frac{9}{5} \, a b^{3} d x^{5} e^{2} + \frac{27}{5} \, a^{2} b c d x^{5} e^{2} + \frac{9}{4} \, a b^{3} d^{2} x^{4} e + \frac{27}{4} \, a^{2} b c d^{2} x^{4} e + a b^{3} d^{3} x^{3} + 3 \, a^{2} b c d^{3} x^{3} + \frac{3}{5} \, a^{2} b^{2} x^{5} e^{3} + \frac{2}{5} \, a^{3} c x^{5} e^{3} + \frac{9}{4} \, a^{2} b^{2} d x^{4} e^{2} + \frac{3}{2} \, a^{3} c d x^{4} e^{2} + 3 \, a^{2} b^{2} d^{2} x^{3} e + 2 \, a^{3} c d^{2} x^{3} e + \frac{3}{2} \, a^{2} b^{2} d^{3} x^{2} + a^{3} c d^{3} x^{2} + \frac{1}{4} \, a^{3} b x^{4} e^{3} + a^{3} b d x^{3} e^{2} + \frac{3}{2} \, a^{3} b d^{2} x^{2} e + a^{3} b d^{3} x"," ",0,"2/11*c^4*x^11*e^3 + 3/5*c^4*d*x^10*e^2 + 2/3*c^4*d^2*x^9*e + 1/4*c^4*d^3*x^8 + 7/10*b*c^3*x^10*e^3 + 7/3*b*c^3*d*x^9*e^2 + 21/8*b*c^3*d^2*x^8*e + b*c^3*d^3*x^7 + b^2*c^2*x^9*e^3 + 2/3*a*c^3*x^9*e^3 + 27/8*b^2*c^2*d*x^8*e^2 + 9/4*a*c^3*d*x^8*e^2 + 27/7*b^2*c^2*d^2*x^7*e + 18/7*a*c^3*d^2*x^7*e + 3/2*b^2*c^2*d^3*x^6 + a*c^3*d^3*x^6 + 5/8*b^3*c*x^8*e^3 + 15/8*a*b*c^2*x^8*e^3 + 15/7*b^3*c*d*x^7*e^2 + 45/7*a*b*c^2*d*x^7*e^2 + 5/2*b^3*c*d^2*x^6*e + 15/2*a*b*c^2*d^2*x^6*e + b^3*c*d^3*x^5 + 3*a*b*c^2*d^3*x^5 + 1/7*b^4*x^7*e^3 + 12/7*a*b^2*c*x^7*e^3 + 6/7*a^2*c^2*x^7*e^3 + 1/2*b^4*d*x^6*e^2 + 6*a*b^2*c*d*x^6*e^2 + 3*a^2*c^2*d*x^6*e^2 + 3/5*b^4*d^2*x^5*e + 36/5*a*b^2*c*d^2*x^5*e + 18/5*a^2*c^2*d^2*x^5*e + 1/4*b^4*d^3*x^4 + 3*a*b^2*c*d^3*x^4 + 3/2*a^2*c^2*d^3*x^4 + 1/2*a*b^3*x^6*e^3 + 3/2*a^2*b*c*x^6*e^3 + 9/5*a*b^3*d*x^5*e^2 + 27/5*a^2*b*c*d*x^5*e^2 + 9/4*a*b^3*d^2*x^4*e + 27/4*a^2*b*c*d^2*x^4*e + a*b^3*d^3*x^3 + 3*a^2*b*c*d^3*x^3 + 3/5*a^2*b^2*x^5*e^3 + 2/5*a^3*c*x^5*e^3 + 9/4*a^2*b^2*d*x^4*e^2 + 3/2*a^3*c*d*x^4*e^2 + 3*a^2*b^2*d^2*x^3*e + 2*a^3*c*d^2*x^3*e + 3/2*a^2*b^2*d^3*x^2 + a^3*c*d^3*x^2 + 1/4*a^3*b*x^4*e^3 + a^3*b*d*x^3*e^2 + 3/2*a^3*b*d^2*x^2*e + a^3*b*d^3*x","A",0
1516,1,502,0,0.156549," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{5} \, c^{4} x^{10} e^{2} + \frac{4}{9} \, c^{4} d x^{9} e + \frac{1}{4} \, c^{4} d^{2} x^{8} + \frac{7}{9} \, b c^{3} x^{9} e^{2} + \frac{7}{4} \, b c^{3} d x^{8} e + b c^{3} d^{2} x^{7} + \frac{9}{8} \, b^{2} c^{2} x^{8} e^{2} + \frac{3}{4} \, a c^{3} x^{8} e^{2} + \frac{18}{7} \, b^{2} c^{2} d x^{7} e + \frac{12}{7} \, a c^{3} d x^{7} e + \frac{3}{2} \, b^{2} c^{2} d^{2} x^{6} + a c^{3} d^{2} x^{6} + \frac{5}{7} \, b^{3} c x^{7} e^{2} + \frac{15}{7} \, a b c^{2} x^{7} e^{2} + \frac{5}{3} \, b^{3} c d x^{6} e + 5 \, a b c^{2} d x^{6} e + b^{3} c d^{2} x^{5} + 3 \, a b c^{2} d^{2} x^{5} + \frac{1}{6} \, b^{4} x^{6} e^{2} + 2 \, a b^{2} c x^{6} e^{2} + a^{2} c^{2} x^{6} e^{2} + \frac{2}{5} \, b^{4} d x^{5} e + \frac{24}{5} \, a b^{2} c d x^{5} e + \frac{12}{5} \, a^{2} c^{2} d x^{5} e + \frac{1}{4} \, b^{4} d^{2} x^{4} + 3 \, a b^{2} c d^{2} x^{4} + \frac{3}{2} \, a^{2} c^{2} d^{2} x^{4} + \frac{3}{5} \, a b^{3} x^{5} e^{2} + \frac{9}{5} \, a^{2} b c x^{5} e^{2} + \frac{3}{2} \, a b^{3} d x^{4} e + \frac{9}{2} \, a^{2} b c d x^{4} e + a b^{3} d^{2} x^{3} + 3 \, a^{2} b c d^{2} x^{3} + \frac{3}{4} \, a^{2} b^{2} x^{4} e^{2} + \frac{1}{2} \, a^{3} c x^{4} e^{2} + 2 \, a^{2} b^{2} d x^{3} e + \frac{4}{3} \, a^{3} c d x^{3} e + \frac{3}{2} \, a^{2} b^{2} d^{2} x^{2} + a^{3} c d^{2} x^{2} + \frac{1}{3} \, a^{3} b x^{3} e^{2} + a^{3} b d x^{2} e + a^{3} b d^{2} x"," ",0,"1/5*c^4*x^10*e^2 + 4/9*c^4*d*x^9*e + 1/4*c^4*d^2*x^8 + 7/9*b*c^3*x^9*e^2 + 7/4*b*c^3*d*x^8*e + b*c^3*d^2*x^7 + 9/8*b^2*c^2*x^8*e^2 + 3/4*a*c^3*x^8*e^2 + 18/7*b^2*c^2*d*x^7*e + 12/7*a*c^3*d*x^7*e + 3/2*b^2*c^2*d^2*x^6 + a*c^3*d^2*x^6 + 5/7*b^3*c*x^7*e^2 + 15/7*a*b*c^2*x^7*e^2 + 5/3*b^3*c*d*x^6*e + 5*a*b*c^2*d*x^6*e + b^3*c*d^2*x^5 + 3*a*b*c^2*d^2*x^5 + 1/6*b^4*x^6*e^2 + 2*a*b^2*c*x^6*e^2 + a^2*c^2*x^6*e^2 + 2/5*b^4*d*x^5*e + 24/5*a*b^2*c*d*x^5*e + 12/5*a^2*c^2*d*x^5*e + 1/4*b^4*d^2*x^4 + 3*a*b^2*c*d^2*x^4 + 3/2*a^2*c^2*d^2*x^4 + 3/5*a*b^3*x^5*e^2 + 9/5*a^2*b*c*x^5*e^2 + 3/2*a*b^3*d*x^4*e + 9/2*a^2*b*c*d*x^4*e + a*b^3*d^2*x^3 + 3*a^2*b*c*d^2*x^3 + 3/4*a^2*b^2*x^4*e^2 + 1/2*a^3*c*x^4*e^2 + 2*a^2*b^2*d*x^3*e + 4/3*a^3*c*d*x^3*e + 3/2*a^2*b^2*d^2*x^2 + a^3*c*d^2*x^2 + 1/3*a^3*b*x^3*e^2 + a^3*b*d*x^2*e + a^3*b*d^2*x","A",0
1517,1,300,0,0.175117," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{9} \, c^{4} x^{9} e + \frac{1}{4} \, c^{4} d x^{8} + \frac{7}{8} \, b c^{3} x^{8} e + b c^{3} d x^{7} + \frac{9}{7} \, b^{2} c^{2} x^{7} e + \frac{6}{7} \, a c^{3} x^{7} e + \frac{3}{2} \, b^{2} c^{2} d x^{6} + a c^{3} d x^{6} + \frac{5}{6} \, b^{3} c x^{6} e + \frac{5}{2} \, a b c^{2} x^{6} e + b^{3} c d x^{5} + 3 \, a b c^{2} d x^{5} + \frac{1}{5} \, b^{4} x^{5} e + \frac{12}{5} \, a b^{2} c x^{5} e + \frac{6}{5} \, a^{2} c^{2} x^{5} e + \frac{1}{4} \, b^{4} d x^{4} + 3 \, a b^{2} c d x^{4} + \frac{3}{2} \, a^{2} c^{2} d x^{4} + \frac{3}{4} \, a b^{3} x^{4} e + \frac{9}{4} \, a^{2} b c x^{4} e + a b^{3} d x^{3} + 3 \, a^{2} b c d x^{3} + a^{2} b^{2} x^{3} e + \frac{2}{3} \, a^{3} c x^{3} e + \frac{3}{2} \, a^{2} b^{2} d x^{2} + a^{3} c d x^{2} + \frac{1}{2} \, a^{3} b x^{2} e + a^{3} b d x"," ",0,"2/9*c^4*x^9*e + 1/4*c^4*d*x^8 + 7/8*b*c^3*x^8*e + b*c^3*d*x^7 + 9/7*b^2*c^2*x^7*e + 6/7*a*c^3*x^7*e + 3/2*b^2*c^2*d*x^6 + a*c^3*d*x^6 + 5/6*b^3*c*x^6*e + 5/2*a*b*c^2*x^6*e + b^3*c*d*x^5 + 3*a*b*c^2*d*x^5 + 1/5*b^4*x^5*e + 12/5*a*b^2*c*x^5*e + 6/5*a^2*c^2*x^5*e + 1/4*b^4*d*x^4 + 3*a*b^2*c*d*x^4 + 3/2*a^2*c^2*d*x^4 + 3/4*a*b^3*x^4*e + 9/4*a^2*b*c*x^4*e + a*b^3*d*x^3 + 3*a^2*b*c*d*x^3 + a^2*b^2*x^3*e + 2/3*a^3*c*x^3*e + 3/2*a^2*b^2*d*x^2 + a^3*c*d*x^2 + 1/2*a^3*b*x^2*e + a^3*b*d*x","A",0
1518,1,56,0,0.149878," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{4} \, {\left(c x^{2} + b x\right)}^{4} + {\left(c x^{2} + b x\right)}^{3} a + \frac{3}{2} \, {\left(c x^{2} + b x\right)}^{2} a^{2} + {\left(c x^{2} + b x\right)} a^{3}"," ",0,"1/4*(c*x^2 + b*x)^4 + (c*x^2 + b*x)^3*a + 3/2*(c*x^2 + b*x)^2*a^2 + (c*x^2 + b*x)*a^3","B",0
1519,1,742,0,0.169550," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d),x, algorithm=""giac"")","-{\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e + 9 \, b^{2} c^{2} d^{5} e^{2} + 6 \, a c^{3} d^{5} e^{2} - 5 \, b^{3} c d^{4} e^{3} - 15 \, a b c^{2} d^{4} e^{3} + b^{4} d^{3} e^{4} + 12 \, a b^{2} c d^{3} e^{4} + 6 \, a^{2} c^{2} d^{3} e^{4} - 3 \, a b^{3} d^{2} e^{5} - 9 \, a^{2} b c d^{2} e^{5} + 3 \, a^{2} b^{2} d e^{6} + 2 \, a^{3} c d e^{6} - a^{3} b e^{7}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{420} \, {\left(120 \, c^{4} x^{7} e^{6} - 140 \, c^{4} d x^{6} e^{5} + 168 \, c^{4} d^{2} x^{5} e^{4} - 210 \, c^{4} d^{3} x^{4} e^{3} + 280 \, c^{4} d^{4} x^{3} e^{2} - 420 \, c^{4} d^{5} x^{2} e + 840 \, c^{4} d^{6} x + 490 \, b c^{3} x^{6} e^{6} - 588 \, b c^{3} d x^{5} e^{5} + 735 \, b c^{3} d^{2} x^{4} e^{4} - 980 \, b c^{3} d^{3} x^{3} e^{3} + 1470 \, b c^{3} d^{4} x^{2} e^{2} - 2940 \, b c^{3} d^{5} x e + 756 \, b^{2} c^{2} x^{5} e^{6} + 504 \, a c^{3} x^{5} e^{6} - 945 \, b^{2} c^{2} d x^{4} e^{5} - 630 \, a c^{3} d x^{4} e^{5} + 1260 \, b^{2} c^{2} d^{2} x^{3} e^{4} + 840 \, a c^{3} d^{2} x^{3} e^{4} - 1890 \, b^{2} c^{2} d^{3} x^{2} e^{3} - 1260 \, a c^{3} d^{3} x^{2} e^{3} + 3780 \, b^{2} c^{2} d^{4} x e^{2} + 2520 \, a c^{3} d^{4} x e^{2} + 525 \, b^{3} c x^{4} e^{6} + 1575 \, a b c^{2} x^{4} e^{6} - 700 \, b^{3} c d x^{3} e^{5} - 2100 \, a b c^{2} d x^{3} e^{5} + 1050 \, b^{3} c d^{2} x^{2} e^{4} + 3150 \, a b c^{2} d^{2} x^{2} e^{4} - 2100 \, b^{3} c d^{3} x e^{3} - 6300 \, a b c^{2} d^{3} x e^{3} + 140 \, b^{4} x^{3} e^{6} + 1680 \, a b^{2} c x^{3} e^{6} + 840 \, a^{2} c^{2} x^{3} e^{6} - 210 \, b^{4} d x^{2} e^{5} - 2520 \, a b^{2} c d x^{2} e^{5} - 1260 \, a^{2} c^{2} d x^{2} e^{5} + 420 \, b^{4} d^{2} x e^{4} + 5040 \, a b^{2} c d^{2} x e^{4} + 2520 \, a^{2} c^{2} d^{2} x e^{4} + 630 \, a b^{3} x^{2} e^{6} + 1890 \, a^{2} b c x^{2} e^{6} - 1260 \, a b^{3} d x e^{5} - 3780 \, a^{2} b c d x e^{5} + 1260 \, a^{2} b^{2} x e^{6} + 840 \, a^{3} c x e^{6}\right)} e^{\left(-7\right)}"," ",0,"-(2*c^4*d^7 - 7*b*c^3*d^6*e + 9*b^2*c^2*d^5*e^2 + 6*a*c^3*d^5*e^2 - 5*b^3*c*d^4*e^3 - 15*a*b*c^2*d^4*e^3 + b^4*d^3*e^4 + 12*a*b^2*c*d^3*e^4 + 6*a^2*c^2*d^3*e^4 - 3*a*b^3*d^2*e^5 - 9*a^2*b*c*d^2*e^5 + 3*a^2*b^2*d*e^6 + 2*a^3*c*d*e^6 - a^3*b*e^7)*e^(-8)*log(abs(x*e + d)) + 1/420*(120*c^4*x^7*e^6 - 140*c^4*d*x^6*e^5 + 168*c^4*d^2*x^5*e^4 - 210*c^4*d^3*x^4*e^3 + 280*c^4*d^4*x^3*e^2 - 420*c^4*d^5*x^2*e + 840*c^4*d^6*x + 490*b*c^3*x^6*e^6 - 588*b*c^3*d*x^5*e^5 + 735*b*c^3*d^2*x^4*e^4 - 980*b*c^3*d^3*x^3*e^3 + 1470*b*c^3*d^4*x^2*e^2 - 2940*b*c^3*d^5*x*e + 756*b^2*c^2*x^5*e^6 + 504*a*c^3*x^5*e^6 - 945*b^2*c^2*d*x^4*e^5 - 630*a*c^3*d*x^4*e^5 + 1260*b^2*c^2*d^2*x^3*e^4 + 840*a*c^3*d^2*x^3*e^4 - 1890*b^2*c^2*d^3*x^2*e^3 - 1260*a*c^3*d^3*x^2*e^3 + 3780*b^2*c^2*d^4*x*e^2 + 2520*a*c^3*d^4*x*e^2 + 525*b^3*c*x^4*e^6 + 1575*a*b*c^2*x^4*e^6 - 700*b^3*c*d*x^3*e^5 - 2100*a*b*c^2*d*x^3*e^5 + 1050*b^3*c*d^2*x^2*e^4 + 3150*a*b*c^2*d^2*x^2*e^4 - 2100*b^3*c*d^3*x*e^3 - 6300*a*b*c^2*d^3*x*e^3 + 140*b^4*x^3*e^6 + 1680*a*b^2*c*x^3*e^6 + 840*a^2*c^2*x^3*e^6 - 210*b^4*d*x^2*e^5 - 2520*a*b^2*c*d*x^2*e^5 - 1260*a^2*c^2*d*x^2*e^5 + 420*b^4*d^2*x*e^4 + 5040*a*b^2*c*d^2*x*e^4 + 2520*a^2*c^2*d^2*x*e^4 + 630*a*b^3*x^2*e^6 + 1890*a^2*b*c*x^2*e^6 - 1260*a*b^3*d*x*e^5 - 3780*a^2*b*c*d*x*e^5 + 1260*a^2*b^2*x*e^6 + 840*a^3*c*x*e^6)*e^(-7)","A",0
1520,1,828,0,0.197853," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{60} \, {\left(20 \, c^{4} - \frac{84 \, {\left(2 \, c^{4} d e - b c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{45 \, {\left(14 \, c^{4} d^{2} e^{2} - 14 \, b c^{3} d e^{3} + 3 \, b^{2} c^{2} e^{4} + 2 \, a c^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{100 \, {\left(14 \, c^{4} d^{3} e^{3} - 21 \, b c^{3} d^{2} e^{4} + 9 \, b^{2} c^{2} d e^{5} + 6 \, a c^{3} d e^{5} - b^{3} c e^{6} - 3 \, a b c^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{30 \, {\left(70 \, c^{4} d^{4} e^{4} - 140 \, b c^{3} d^{3} e^{5} + 90 \, b^{2} c^{2} d^{2} e^{6} + 60 \, a c^{3} d^{2} e^{6} - 20 \, b^{3} c d e^{7} - 60 \, a b c^{2} d e^{7} + b^{4} e^{8} + 12 \, a b^{2} c e^{8} + 6 \, a^{2} c^{2} e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{180 \, {\left(14 \, c^{4} d^{5} e^{5} - 35 \, b c^{3} d^{4} e^{6} + 30 \, b^{2} c^{2} d^{3} e^{7} + 20 \, a c^{3} d^{3} e^{7} - 10 \, b^{3} c d^{2} e^{8} - 30 \, a b c^{2} d^{2} e^{8} + b^{4} d e^{9} + 12 \, a b^{2} c d e^{9} + 6 \, a^{2} c^{2} d e^{9} - a b^{3} e^{10} - 3 \, a^{2} b c e^{10}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}}\right)} {\left(x e + d\right)}^{6} e^{\left(-8\right)} - {\left(14 \, c^{4} d^{6} - 42 \, b c^{3} d^{5} e + 45 \, b^{2} c^{2} d^{4} e^{2} + 30 \, a c^{3} d^{4} e^{2} - 20 \, b^{3} c d^{3} e^{3} - 60 \, a b c^{2} d^{3} e^{3} + 3 \, b^{4} d^{2} e^{4} + 36 \, a b^{2} c d^{2} e^{4} + 18 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a b^{3} d e^{5} - 18 \, a^{2} b c d e^{5} + 3 \, a^{2} b^{2} e^{6} + 2 \, a^{3} c e^{6}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{2 \, c^{4} d^{7} e^{6}}{x e + d} - \frac{7 \, b c^{3} d^{6} e^{7}}{x e + d} + \frac{9 \, b^{2} c^{2} d^{5} e^{8}}{x e + d} + \frac{6 \, a c^{3} d^{5} e^{8}}{x e + d} - \frac{5 \, b^{3} c d^{4} e^{9}}{x e + d} - \frac{15 \, a b c^{2} d^{4} e^{9}}{x e + d} + \frac{b^{4} d^{3} e^{10}}{x e + d} + \frac{12 \, a b^{2} c d^{3} e^{10}}{x e + d} + \frac{6 \, a^{2} c^{2} d^{3} e^{10}}{x e + d} - \frac{3 \, a b^{3} d^{2} e^{11}}{x e + d} - \frac{9 \, a^{2} b c d^{2} e^{11}}{x e + d} + \frac{3 \, a^{2} b^{2} d e^{12}}{x e + d} + \frac{2 \, a^{3} c d e^{12}}{x e + d} - \frac{a^{3} b e^{13}}{x e + d}\right)} e^{\left(-14\right)}"," ",0,"1/60*(20*c^4 - 84*(2*c^4*d*e - b*c^3*e^2)*e^(-1)/(x*e + d) + 45*(14*c^4*d^2*e^2 - 14*b*c^3*d*e^3 + 3*b^2*c^2*e^4 + 2*a*c^3*e^4)*e^(-2)/(x*e + d)^2 - 100*(14*c^4*d^3*e^3 - 21*b*c^3*d^2*e^4 + 9*b^2*c^2*d*e^5 + 6*a*c^3*d*e^5 - b^3*c*e^6 - 3*a*b*c^2*e^6)*e^(-3)/(x*e + d)^3 + 30*(70*c^4*d^4*e^4 - 140*b*c^3*d^3*e^5 + 90*b^2*c^2*d^2*e^6 + 60*a*c^3*d^2*e^6 - 20*b^3*c*d*e^7 - 60*a*b*c^2*d*e^7 + b^4*e^8 + 12*a*b^2*c*e^8 + 6*a^2*c^2*e^8)*e^(-4)/(x*e + d)^4 - 180*(14*c^4*d^5*e^5 - 35*b*c^3*d^4*e^6 + 30*b^2*c^2*d^3*e^7 + 20*a*c^3*d^3*e^7 - 10*b^3*c*d^2*e^8 - 30*a*b*c^2*d^2*e^8 + b^4*d*e^9 + 12*a*b^2*c*d*e^9 + 6*a^2*c^2*d*e^9 - a*b^3*e^10 - 3*a^2*b*c*e^10)*e^(-5)/(x*e + d)^5)*(x*e + d)^6*e^(-8) - (14*c^4*d^6 - 42*b*c^3*d^5*e + 45*b^2*c^2*d^4*e^2 + 30*a*c^3*d^4*e^2 - 20*b^3*c*d^3*e^3 - 60*a*b*c^2*d^3*e^3 + 3*b^4*d^2*e^4 + 36*a*b^2*c*d^2*e^4 + 18*a^2*c^2*d^2*e^4 - 6*a*b^3*d*e^5 - 18*a^2*b*c*d*e^5 + 3*a^2*b^2*e^6 + 2*a^3*c*e^6)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (2*c^4*d^7*e^6/(x*e + d) - 7*b*c^3*d^6*e^7/(x*e + d) + 9*b^2*c^2*d^5*e^8/(x*e + d) + 6*a*c^3*d^5*e^8/(x*e + d) - 5*b^3*c*d^4*e^9/(x*e + d) - 15*a*b*c^2*d^4*e^9/(x*e + d) + b^4*d^3*e^10/(x*e + d) + 12*a*b^2*c*d^3*e^10/(x*e + d) + 6*a^2*c^2*d^3*e^10/(x*e + d) - 3*a*b^3*d^2*e^11/(x*e + d) - 9*a^2*b*c*d^2*e^11/(x*e + d) + 3*a^2*b^2*d*e^12/(x*e + d) + 2*a^3*c*d*e^12/(x*e + d) - a^3*b*e^13/(x*e + d))*e^(-14)","B",0
1521,1,694,0,0.169903," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^3,x, algorithm=""giac"")","-3 \, {\left(14 \, c^{4} d^{5} - 35 \, b c^{3} d^{4} e + 30 \, b^{2} c^{2} d^{3} e^{2} + 20 \, a c^{3} d^{3} e^{2} - 10 \, b^{3} c d^{2} e^{3} - 30 \, a b c^{2} d^{2} e^{3} + b^{4} d e^{4} + 12 \, a b^{2} c d e^{4} + 6 \, a^{2} c^{2} d e^{4} - a b^{3} e^{5} - 3 \, a^{2} b c e^{5}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{20} \, {\left(8 \, c^{4} x^{5} e^{12} - 30 \, c^{4} d x^{4} e^{11} + 80 \, c^{4} d^{2} x^{3} e^{10} - 200 \, c^{4} d^{3} x^{2} e^{9} + 600 \, c^{4} d^{4} x e^{8} + 35 \, b c^{3} x^{4} e^{12} - 140 \, b c^{3} d x^{3} e^{11} + 420 \, b c^{3} d^{2} x^{2} e^{10} - 1400 \, b c^{3} d^{3} x e^{9} + 60 \, b^{2} c^{2} x^{3} e^{12} + 40 \, a c^{3} x^{3} e^{12} - 270 \, b^{2} c^{2} d x^{2} e^{11} - 180 \, a c^{3} d x^{2} e^{11} + 1080 \, b^{2} c^{2} d^{2} x e^{10} + 720 \, a c^{3} d^{2} x e^{10} + 50 \, b^{3} c x^{2} e^{12} + 150 \, a b c^{2} x^{2} e^{12} - 300 \, b^{3} c d x e^{11} - 900 \, a b c^{2} d x e^{11} + 20 \, b^{4} x e^{12} + 240 \, a b^{2} c x e^{12} + 120 \, a^{2} c^{2} x e^{12}\right)} e^{\left(-15\right)} - \frac{{\left(26 \, c^{4} d^{7} - 77 \, b c^{3} d^{6} e + 81 \, b^{2} c^{2} d^{5} e^{2} + 54 \, a c^{3} d^{5} e^{2} - 35 \, b^{3} c d^{4} e^{3} - 105 \, a b c^{2} d^{4} e^{3} + 5 \, b^{4} d^{3} e^{4} + 60 \, a b^{2} c d^{3} e^{4} + 30 \, a^{2} c^{2} d^{3} e^{4} - 9 \, a b^{3} d^{2} e^{5} - 27 \, a^{2} b c d^{2} e^{5} + 3 \, a^{2} b^{2} d e^{6} + 2 \, a^{3} c d e^{6} + a^{3} b e^{7} + 2 \, {\left(14 \, c^{4} d^{6} e - 42 \, b c^{3} d^{5} e^{2} + 45 \, b^{2} c^{2} d^{4} e^{3} + 30 \, a c^{3} d^{4} e^{3} - 20 \, b^{3} c d^{3} e^{4} - 60 \, a b c^{2} d^{3} e^{4} + 3 \, b^{4} d^{2} e^{5} + 36 \, a b^{2} c d^{2} e^{5} + 18 \, a^{2} c^{2} d^{2} e^{5} - 6 \, a b^{3} d e^{6} - 18 \, a^{2} b c d e^{6} + 3 \, a^{2} b^{2} e^{7} + 2 \, a^{3} c e^{7}\right)} x\right)} e^{\left(-8\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-3*(14*c^4*d^5 - 35*b*c^3*d^4*e + 30*b^2*c^2*d^3*e^2 + 20*a*c^3*d^3*e^2 - 10*b^3*c*d^2*e^3 - 30*a*b*c^2*d^2*e^3 + b^4*d*e^4 + 12*a*b^2*c*d*e^4 + 6*a^2*c^2*d*e^4 - a*b^3*e^5 - 3*a^2*b*c*e^5)*e^(-8)*log(abs(x*e + d)) + 1/20*(8*c^4*x^5*e^12 - 30*c^4*d*x^4*e^11 + 80*c^4*d^2*x^3*e^10 - 200*c^4*d^3*x^2*e^9 + 600*c^4*d^4*x*e^8 + 35*b*c^3*x^4*e^12 - 140*b*c^3*d*x^3*e^11 + 420*b*c^3*d^2*x^2*e^10 - 1400*b*c^3*d^3*x*e^9 + 60*b^2*c^2*x^3*e^12 + 40*a*c^3*x^3*e^12 - 270*b^2*c^2*d*x^2*e^11 - 180*a*c^3*d*x^2*e^11 + 1080*b^2*c^2*d^2*x*e^10 + 720*a*c^3*d^2*x*e^10 + 50*b^3*c*x^2*e^12 + 150*a*b*c^2*x^2*e^12 - 300*b^3*c*d*x*e^11 - 900*a*b*c^2*d*x*e^11 + 20*b^4*x*e^12 + 240*a*b^2*c*x*e^12 + 120*a^2*c^2*x*e^12)*e^(-15) - 1/2*(26*c^4*d^7 - 77*b*c^3*d^6*e + 81*b^2*c^2*d^5*e^2 + 54*a*c^3*d^5*e^2 - 35*b^3*c*d^4*e^3 - 105*a*b*c^2*d^4*e^3 + 5*b^4*d^3*e^4 + 60*a*b^2*c*d^3*e^4 + 30*a^2*c^2*d^3*e^4 - 9*a*b^3*d^2*e^5 - 27*a^2*b*c*d^2*e^5 + 3*a^2*b^2*d*e^6 + 2*a^3*c*d*e^6 + a^3*b*e^7 + 2*(14*c^4*d^6*e - 42*b*c^3*d^5*e^2 + 45*b^2*c^2*d^4*e^3 + 30*a*c^3*d^4*e^3 - 20*b^3*c*d^3*e^4 - 60*a*b*c^2*d^3*e^4 + 3*b^4*d^2*e^5 + 36*a*b^2*c*d^2*e^5 + 18*a^2*c^2*d^2*e^5 - 6*a*b^3*d*e^6 - 18*a^2*b*c*d*e^6 + 3*a^2*b^2*e^7 + 2*a^3*c*e^7)*x)*e^(-8)/(x*e + d)^2","A",0
1522,1,678,0,0.169926," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^4,x, algorithm=""giac"")","{\left(70 \, c^{4} d^{4} - 140 \, b c^{3} d^{3} e + 90 \, b^{2} c^{2} d^{2} e^{2} + 60 \, a c^{3} d^{2} e^{2} - 20 \, b^{3} c d e^{3} - 60 \, a b c^{2} d e^{3} + b^{4} e^{4} + 12 \, a b^{2} c e^{4} + 6 \, a^{2} c^{2} e^{4}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(3 \, c^{4} x^{4} e^{12} - 16 \, c^{4} d x^{3} e^{11} + 60 \, c^{4} d^{2} x^{2} e^{10} - 240 \, c^{4} d^{3} x e^{9} + 14 \, b c^{3} x^{3} e^{12} - 84 \, b c^{3} d x^{2} e^{11} + 420 \, b c^{3} d^{2} x e^{10} + 27 \, b^{2} c^{2} x^{2} e^{12} + 18 \, a c^{3} x^{2} e^{12} - 216 \, b^{2} c^{2} d x e^{11} - 144 \, a c^{3} d x e^{11} + 30 \, b^{3} c x e^{12} + 90 \, a b c^{2} x e^{12}\right)} e^{\left(-16\right)} + \frac{{\left(214 \, c^{4} d^{7} - 518 \, b c^{3} d^{6} e + 423 \, b^{2} c^{2} d^{5} e^{2} + 282 \, a c^{3} d^{5} e^{2} - 130 \, b^{3} c d^{4} e^{3} - 390 \, a b c^{2} d^{4} e^{3} + 11 \, b^{4} d^{3} e^{4} + 132 \, a b^{2} c d^{3} e^{4} + 66 \, a^{2} c^{2} d^{3} e^{4} - 6 \, a b^{3} d^{2} e^{5} - 18 \, a^{2} b c d^{2} e^{5} - 3 \, a^{2} b^{2} d e^{6} - 2 \, a^{3} c d e^{6} - 2 \, a^{3} b e^{7} + 18 \, {\left(14 \, c^{4} d^{5} e^{2} - 35 \, b c^{3} d^{4} e^{3} + 30 \, b^{2} c^{2} d^{3} e^{4} + 20 \, a c^{3} d^{3} e^{4} - 10 \, b^{3} c d^{2} e^{5} - 30 \, a b c^{2} d^{2} e^{5} + b^{4} d e^{6} + 12 \, a b^{2} c d e^{6} + 6 \, a^{2} c^{2} d e^{6} - a b^{3} e^{7} - 3 \, a^{2} b c e^{7}\right)} x^{2} + 3 \, {\left(154 \, c^{4} d^{6} e - 378 \, b c^{3} d^{5} e^{2} + 315 \, b^{2} c^{2} d^{4} e^{3} + 210 \, a c^{3} d^{4} e^{3} - 100 \, b^{3} c d^{3} e^{4} - 300 \, a b c^{2} d^{3} e^{4} + 9 \, b^{4} d^{2} e^{5} + 108 \, a b^{2} c d^{2} e^{5} + 54 \, a^{2} c^{2} d^{2} e^{5} - 6 \, a b^{3} d e^{6} - 18 \, a^{2} b c d e^{6} - 3 \, a^{2} b^{2} e^{7} - 2 \, a^{3} c e^{7}\right)} x\right)} e^{\left(-8\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"(70*c^4*d^4 - 140*b*c^3*d^3*e + 90*b^2*c^2*d^2*e^2 + 60*a*c^3*d^2*e^2 - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3 + b^4*e^4 + 12*a*b^2*c*e^4 + 6*a^2*c^2*e^4)*e^(-8)*log(abs(x*e + d)) + 1/6*(3*c^4*x^4*e^12 - 16*c^4*d*x^3*e^11 + 60*c^4*d^2*x^2*e^10 - 240*c^4*d^3*x*e^9 + 14*b*c^3*x^3*e^12 - 84*b*c^3*d*x^2*e^11 + 420*b*c^3*d^2*x*e^10 + 27*b^2*c^2*x^2*e^12 + 18*a*c^3*x^2*e^12 - 216*b^2*c^2*d*x*e^11 - 144*a*c^3*d*x*e^11 + 30*b^3*c*x*e^12 + 90*a*b*c^2*x*e^12)*e^(-16) + 1/6*(214*c^4*d^7 - 518*b*c^3*d^6*e + 423*b^2*c^2*d^5*e^2 + 282*a*c^3*d^5*e^2 - 130*b^3*c*d^4*e^3 - 390*a*b*c^2*d^4*e^3 + 11*b^4*d^3*e^4 + 132*a*b^2*c*d^3*e^4 + 66*a^2*c^2*d^3*e^4 - 6*a*b^3*d^2*e^5 - 18*a^2*b*c*d^2*e^5 - 3*a^2*b^2*d*e^6 - 2*a^3*c*d*e^6 - 2*a^3*b*e^7 + 18*(14*c^4*d^5*e^2 - 35*b*c^3*d^4*e^3 + 30*b^2*c^2*d^3*e^4 + 20*a*c^3*d^3*e^4 - 10*b^3*c*d^2*e^5 - 30*a*b*c^2*d^2*e^5 + b^4*d*e^6 + 12*a*b^2*c*d*e^6 + 6*a^2*c^2*d*e^6 - a*b^3*e^7 - 3*a^2*b*c*e^7)*x^2 + 3*(154*c^4*d^6*e - 378*b*c^3*d^5*e^2 + 315*b^2*c^2*d^4*e^3 + 210*a*c^3*d^4*e^3 - 100*b^3*c*d^3*e^4 - 300*a*b*c^2*d^3*e^4 + 9*b^4*d^2*e^5 + 108*a*b^2*c*d^2*e^5 + 54*a^2*c^2*d^2*e^5 - 6*a*b^3*d*e^6 - 18*a^2*b*c*d*e^6 - 3*a^2*b^2*e^7 - 2*a^3*c*e^7)*x)*e^(-8)/(x*e + d)^3","A",0
1523,1,1057,0,0.220178," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{6} \, {\left(4 \, c^{4} - \frac{21 \, {\left(2 \, c^{4} d e - b c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{18 \, {\left(14 \, c^{4} d^{2} e^{2} - 14 \, b c^{3} d e^{3} + 3 \, b^{2} c^{2} e^{4} + 2 \, a c^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-8\right)} + 5 \, {\left(14 \, c^{4} d^{3} - 21 \, b c^{3} d^{2} e + 9 \, b^{2} c^{2} d e^{2} + 6 \, a c^{3} d e^{2} - b^{3} c e^{3} - 3 \, a b c^{2} e^{3}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{840 \, c^{4} d^{4} e^{36}}{x e + d} - \frac{252 \, c^{4} d^{5} e^{36}}{{\left(x e + d\right)}^{2}} + \frac{56 \, c^{4} d^{6} e^{36}}{{\left(x e + d\right)}^{3}} - \frac{6 \, c^{4} d^{7} e^{36}}{{\left(x e + d\right)}^{4}} - \frac{1680 \, b c^{3} d^{3} e^{37}}{x e + d} + \frac{630 \, b c^{3} d^{4} e^{37}}{{\left(x e + d\right)}^{2}} - \frac{168 \, b c^{3} d^{5} e^{37}}{{\left(x e + d\right)}^{3}} + \frac{21 \, b c^{3} d^{6} e^{37}}{{\left(x e + d\right)}^{4}} + \frac{1080 \, b^{2} c^{2} d^{2} e^{38}}{x e + d} + \frac{720 \, a c^{3} d^{2} e^{38}}{x e + d} - \frac{540 \, b^{2} c^{2} d^{3} e^{38}}{{\left(x e + d\right)}^{2}} - \frac{360 \, a c^{3} d^{3} e^{38}}{{\left(x e + d\right)}^{2}} + \frac{180 \, b^{2} c^{2} d^{4} e^{38}}{{\left(x e + d\right)}^{3}} + \frac{120 \, a c^{3} d^{4} e^{38}}{{\left(x e + d\right)}^{3}} - \frac{27 \, b^{2} c^{2} d^{5} e^{38}}{{\left(x e + d\right)}^{4}} - \frac{18 \, a c^{3} d^{5} e^{38}}{{\left(x e + d\right)}^{4}} - \frac{240 \, b^{3} c d e^{39}}{x e + d} - \frac{720 \, a b c^{2} d e^{39}}{x e + d} + \frac{180 \, b^{3} c d^{2} e^{39}}{{\left(x e + d\right)}^{2}} + \frac{540 \, a b c^{2} d^{2} e^{39}}{{\left(x e + d\right)}^{2}} - \frac{80 \, b^{3} c d^{3} e^{39}}{{\left(x e + d\right)}^{3}} - \frac{240 \, a b c^{2} d^{3} e^{39}}{{\left(x e + d\right)}^{3}} + \frac{15 \, b^{3} c d^{4} e^{39}}{{\left(x e + d\right)}^{4}} + \frac{45 \, a b c^{2} d^{4} e^{39}}{{\left(x e + d\right)}^{4}} + \frac{12 \, b^{4} e^{40}}{x e + d} + \frac{144 \, a b^{2} c e^{40}}{x e + d} + \frac{72 \, a^{2} c^{2} e^{40}}{x e + d} - \frac{18 \, b^{4} d e^{40}}{{\left(x e + d\right)}^{2}} - \frac{216 \, a b^{2} c d e^{40}}{{\left(x e + d\right)}^{2}} - \frac{108 \, a^{2} c^{2} d e^{40}}{{\left(x e + d\right)}^{2}} + \frac{12 \, b^{4} d^{2} e^{40}}{{\left(x e + d\right)}^{3}} + \frac{144 \, a b^{2} c d^{2} e^{40}}{{\left(x e + d\right)}^{3}} + \frac{72 \, a^{2} c^{2} d^{2} e^{40}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{4} d^{3} e^{40}}{{\left(x e + d\right)}^{4}} - \frac{36 \, a b^{2} c d^{3} e^{40}}{{\left(x e + d\right)}^{4}} - \frac{18 \, a^{2} c^{2} d^{3} e^{40}}{{\left(x e + d\right)}^{4}} + \frac{18 \, a b^{3} e^{41}}{{\left(x e + d\right)}^{2}} + \frac{54 \, a^{2} b c e^{41}}{{\left(x e + d\right)}^{2}} - \frac{24 \, a b^{3} d e^{41}}{{\left(x e + d\right)}^{3}} - \frac{72 \, a^{2} b c d e^{41}}{{\left(x e + d\right)}^{3}} + \frac{9 \, a b^{3} d^{2} e^{41}}{{\left(x e + d\right)}^{4}} + \frac{27 \, a^{2} b c d^{2} e^{41}}{{\left(x e + d\right)}^{4}} + \frac{12 \, a^{2} b^{2} e^{42}}{{\left(x e + d\right)}^{3}} + \frac{8 \, a^{3} c e^{42}}{{\left(x e + d\right)}^{3}} - \frac{9 \, a^{2} b^{2} d e^{42}}{{\left(x e + d\right)}^{4}} - \frac{6 \, a^{3} c d e^{42}}{{\left(x e + d\right)}^{4}} + \frac{3 \, a^{3} b e^{43}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-44\right)}"," ",0,"1/6*(4*c^4 - 21*(2*c^4*d*e - b*c^3*e^2)*e^(-1)/(x*e + d) + 18*(14*c^4*d^2*e^2 - 14*b*c^3*d*e^3 + 3*b^2*c^2*e^4 + 2*a*c^3*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-8) + 5*(14*c^4*d^3 - 21*b*c^3*d^2*e + 9*b^2*c^2*d*e^2 + 6*a*c^3*d*e^2 - b^3*c*e^3 - 3*a*b*c^2*e^3)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(840*c^4*d^4*e^36/(x*e + d) - 252*c^4*d^5*e^36/(x*e + d)^2 + 56*c^4*d^6*e^36/(x*e + d)^3 - 6*c^4*d^7*e^36/(x*e + d)^4 - 1680*b*c^3*d^3*e^37/(x*e + d) + 630*b*c^3*d^4*e^37/(x*e + d)^2 - 168*b*c^3*d^5*e^37/(x*e + d)^3 + 21*b*c^3*d^6*e^37/(x*e + d)^4 + 1080*b^2*c^2*d^2*e^38/(x*e + d) + 720*a*c^3*d^2*e^38/(x*e + d) - 540*b^2*c^2*d^3*e^38/(x*e + d)^2 - 360*a*c^3*d^3*e^38/(x*e + d)^2 + 180*b^2*c^2*d^4*e^38/(x*e + d)^3 + 120*a*c^3*d^4*e^38/(x*e + d)^3 - 27*b^2*c^2*d^5*e^38/(x*e + d)^4 - 18*a*c^3*d^5*e^38/(x*e + d)^4 - 240*b^3*c*d*e^39/(x*e + d) - 720*a*b*c^2*d*e^39/(x*e + d) + 180*b^3*c*d^2*e^39/(x*e + d)^2 + 540*a*b*c^2*d^2*e^39/(x*e + d)^2 - 80*b^3*c*d^3*e^39/(x*e + d)^3 - 240*a*b*c^2*d^3*e^39/(x*e + d)^3 + 15*b^3*c*d^4*e^39/(x*e + d)^4 + 45*a*b*c^2*d^4*e^39/(x*e + d)^4 + 12*b^4*e^40/(x*e + d) + 144*a*b^2*c*e^40/(x*e + d) + 72*a^2*c^2*e^40/(x*e + d) - 18*b^4*d*e^40/(x*e + d)^2 - 216*a*b^2*c*d*e^40/(x*e + d)^2 - 108*a^2*c^2*d*e^40/(x*e + d)^2 + 12*b^4*d^2*e^40/(x*e + d)^3 + 144*a*b^2*c*d^2*e^40/(x*e + d)^3 + 72*a^2*c^2*d^2*e^40/(x*e + d)^3 - 3*b^4*d^3*e^40/(x*e + d)^4 - 36*a*b^2*c*d^3*e^40/(x*e + d)^4 - 18*a^2*c^2*d^3*e^40/(x*e + d)^4 + 18*a*b^3*e^41/(x*e + d)^2 + 54*a^2*b*c*e^41/(x*e + d)^2 - 24*a*b^3*d*e^41/(x*e + d)^3 - 72*a^2*b*c*d*e^41/(x*e + d)^3 + 9*a*b^3*d^2*e^41/(x*e + d)^4 + 27*a^2*b*c*d^2*e^41/(x*e + d)^4 + 12*a^2*b^2*e^42/(x*e + d)^3 + 8*a^3*c*e^42/(x*e + d)^3 - 9*a^2*b^2*d*e^42/(x*e + d)^4 - 6*a^3*c*d*e^42/(x*e + d)^4 + 3*a^3*b*e^43/(x*e + d)^4)*e^(-44)","B",0
1524,1,401,0,0.159024," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, b^{2} c^{2} d^{2} e^{2} - 12 \, a c^{3} d^{2} e^{2} - 4 \, b^{3} c d e^{3} + 12 \, a b c^{2} d e^{3} + b^{4} e^{4} - 4 \, a b^{2} c e^{4} + 2 \, a^{2} c^{2} e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{{\left(4 \, b^{2} c^{3} d^{3} e - 16 \, a c^{4} d^{3} e - 6 \, b^{3} c^{2} d^{2} e^{2} + 24 \, a b c^{3} d^{2} e^{2} + 4 \, b^{4} c d e^{3} - 20 \, a b^{2} c^{2} d e^{3} + 16 \, a^{2} c^{3} d e^{3} - b^{5} e^{4} + 6 \, a b^{3} c e^{4} - 8 \, a^{2} b c^{2} e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{4}} + \frac{3 \, c^{4} x^{4} e^{4} + 16 \, c^{4} d x^{3} e^{3} + 36 \, c^{4} d^{2} x^{2} e^{2} + 48 \, c^{4} d^{3} x e - 2 \, b c^{3} x^{3} e^{4} - 12 \, b c^{3} d x^{2} e^{3} - 36 \, b c^{3} d^{2} x e^{2} + 3 \, b^{2} c^{2} x^{2} e^{4} - 6 \, a c^{3} x^{2} e^{4} + 24 \, b^{2} c^{2} d x e^{3} - 48 \, a c^{3} d x e^{3} - 6 \, b^{3} c x e^{4} + 18 \, a b c^{2} x e^{4}}{6 \, c^{4}}"," ",0,"1/2*(2*c^4*d^4 - 4*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 12*a*c^3*d^2*e^2 - 4*b^3*c*d*e^3 + 12*a*b*c^2*d*e^3 + b^4*e^4 - 4*a*b^2*c*e^4 + 2*a^2*c^2*e^4)*log(c*x^2 + b*x + a)/c^4 + (4*b^2*c^3*d^3*e - 16*a*c^4*d^3*e - 6*b^3*c^2*d^2*e^2 + 24*a*b*c^3*d^2*e^2 + 4*b^4*c*d*e^3 - 20*a*b^2*c^2*d*e^3 + 16*a^2*c^3*d*e^3 - b^5*e^4 + 6*a*b^3*c*e^4 - 8*a^2*b*c^2*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4) + 1/6*(3*c^4*x^4*e^4 + 16*c^4*d*x^3*e^3 + 36*c^4*d^2*x^2*e^2 + 48*c^4*d^3*x*e - 2*b*c^3*x^3*e^4 - 12*b*c^3*d*x^2*e^3 - 36*b*c^3*d^2*x*e^2 + 3*b^2*c^2*x^2*e^4 - 6*a*c^3*x^2*e^4 + 24*b^2*c^2*d*x*e^3 - 48*a*c^3*d*x*e^3 - 6*b^3*c*x*e^4 + 18*a*b*c^2*x*e^4)/c^4","A",0
1525,1,251,0,0.156439," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - 6 \, a c^{2} d e^{2} - b^{3} e^{3} + 3 \, a b c e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} + \frac{{\left(3 \, b^{2} c^{2} d^{2} e - 12 \, a c^{3} d^{2} e - 3 \, b^{3} c d e^{2} + 12 \, a b c^{2} d e^{2} + b^{4} e^{3} - 5 \, a b^{2} c e^{3} + 4 \, a^{2} c^{2} e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{3}} + \frac{4 \, c^{3} x^{3} e^{3} + 18 \, c^{3} d x^{2} e^{2} + 36 \, c^{3} d^{2} x e - 3 \, b c^{2} x^{2} e^{3} - 18 \, b c^{2} d x e^{2} + 6 \, b^{2} c x e^{3} - 12 \, a c^{2} x e^{3}}{6 \, c^{3}}"," ",0,"1/2*(2*c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 6*a*c^2*d*e^2 - b^3*e^3 + 3*a*b*c*e^3)*log(c*x^2 + b*x + a)/c^3 + (3*b^2*c^2*d^2*e - 12*a*c^3*d^2*e - 3*b^3*c*d*e^2 + 12*a*b*c^2*d*e^2 + b^4*e^3 - 5*a*b^2*c*e^3 + 4*a^2*c^2*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3) + 1/6*(4*c^3*x^3*e^3 + 18*c^3*d*x^2*e^2 + 36*c^3*d^2*x*e - 3*b*c^2*x^2*e^3 - 18*b*c^2*d*x*e^2 + 6*b^2*c*x*e^3 - 12*a*c^2*x*e^3)/c^3","A",0
1526,1,144,0,0.176567," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(2 \, c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, a c e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{{\left(2 \, b^{2} c d e - 8 \, a c^{2} d e - b^{3} e^{2} + 4 \, a b c e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}} + \frac{c^{2} x^{2} e^{2} + 4 \, c^{2} d x e - b c x e^{2}}{c^{2}}"," ",0,"1/2*(2*c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*a*c*e^2)*log(c*x^2 + b*x + a)/c^2 + (2*b^2*c*d*e - 8*a*c^2*d*e - b^3*e^2 + 4*a*b*c*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2) + (c^2*x^2*e^2 + 4*c^2*d*x*e - b*c*x*e^2)/c^2","A",0
1527,1,81,0,0.157624," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","2 \, x e + \frac{{\left(2 \, c d - b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c} + \frac{{\left(b^{2} e - 4 \, a c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c}"," ",0,"2*x*e + 1/2*(2*c*d - b*e)*log(c*x^2 + b*x + a)/c + (b^2*e - 4*a*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c)","A",0
1528,1,12,0,0.147745," ","integrate((2*c*x+b)/(c*x^2+b*x+a),x, algorithm=""giac"")","\log\left({\left| c x^{2} + b x + a \right|}\right)"," ",0,"log(abs(c*x^2 + b*x + a))","A",0
1529,1,149,0,0.158062," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(2 \, c d - b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}} - \frac{{\left(2 \, c d e - b e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{c d^{2} e - b d e^{2} + a e^{3}} - \frac{{\left(b^{2} e - 4 \, a c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"1/2*(2*c*d - b*e)*log(c*x^2 + b*x + a)/(c*d^2 - b*d*e + a*e^2) - (2*c*d*e - b*e^2)*log(abs(x*e + d))/(c*d^2*e - b*d*e^2 + a*e^3) - (b^2*e - 4*a*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c*d^2 - b*d*e + a*e^2)*sqrt(-b^2 + 4*a*c))","A",0
1530,1,362,0,0.263993," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{{\left(2 \, b^{2} c d e^{3} - 8 \, a c^{2} d e^{3} - b^{3} e^{4} + 4 \, a b c e^{4}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(2 \, c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, a c e^{2}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}} + \frac{\frac{2 \, c d e^{2}}{x e + d} - \frac{b e^{3}}{x e + d}}{c d^{2} e^{2} - b d e^{3} + a e^{4}}"," ",0,"-(2*b^2*c*d*e^3 - 8*a*c^2*d*e^3 - b^3*e^4 + 4*a*b*c*e^4)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-b^2 + 4*a*c)) + 1/2*(2*c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*a*c*e^2)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) + (2*c*d*e^2/(x*e + d) - b*e^3/(x*e + d))/(c*d^2*e^2 - b*d*e^3 + a*e^4)","A",0
1531,1,710,0,0.195396," ","integrate((2*c*x+b)/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - 6 \, a c^{2} d e^{2} - b^{3} e^{3} + 3 \, a b c e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} - \frac{{\left(2 \, c^{3} d^{3} e - 3 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3} - 6 \, a c^{2} d e^{3} - b^{3} e^{4} + 3 \, a b c e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}} - \frac{{\left(3 \, b^{2} c^{2} d^{2} e - 12 \, a c^{3} d^{2} e - 3 \, b^{3} c d e^{2} + 12 \, a b c^{2} d e^{2} + b^{4} e^{3} - 5 \, a b^{2} c e^{3} + 4 \, a^{2} c^{2} e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{6 \, c^{3} d^{5} - 13 \, b c^{2} d^{4} e + 10 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - 3 \, b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 4 \, a b^{2} d e^{4} - 2 \, a^{2} c d e^{4} - a^{2} b e^{5} + 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} + a b^{2} e^{5} - 2 \, a^{2} c e^{5}\right)} x}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"1/2*(2*c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 6*a*c^2*d*e^2 - b^3*e^3 + 3*a*b*c*e^3)*log(c*x^2 + b*x + a)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) - (2*c^3*d^3*e - 3*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3 - 6*a*c^2*d*e^3 - b^3*e^4 + 3*a*b*c*e^4)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7) - (3*b^2*c^2*d^2*e - 12*a*c^3*d^2*e - 3*b^3*c*d*e^2 + 12*a*b*c^2*d*e^2 + b^4*e^3 - 5*a*b^2*c*e^3 + 4*a^2*c^2*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-b^2 + 4*a*c)) + 1/2*(6*c^3*d^5 - 13*b*c^2*d^4*e + 10*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - 3*b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 4*a*b^2*d*e^4 - 2*a^2*c*d*e^4 - a^2*b*e^5 + 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*e^5 - 2*a^2*c*e^5)*x)/((c*d^2 - b*d*e + a*e^2)^3*(x*e + d)^2)","B",0
1532,1,285,0,0.164021," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4} - a c e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{c^{3}} + \frac{4 \, {\left(2 \, c^{3} d^{3} e - 3 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3} - 6 \, a c^{2} d e^{3} - b^{3} e^{4} + 3 \, a b c e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{3}} + \frac{c^{3} x^{2} e^{4} + 8 \, c^{3} d x e^{3} - 3 \, b c^{2} x e^{4}}{c^{4}} - \frac{c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2} + 4 \, a b c d e^{3} - a b^{2} e^{4} + a^{2} c e^{4} + {\left(4 \, c^{3} d^{3} e - 6 \, b c^{2} d^{2} e^{2} + 4 \, b^{2} c d e^{3} - 4 \, a c^{2} d e^{3} - b^{3} e^{4} + 2 \, a b c e^{4}\right)} x}{{\left(c x^{2} + b x + a\right)} c^{3}}"," ",0,"2*(3*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4 - a*c*e^4)*log(c*x^2 + b*x + a)/c^3 + 4*(2*c^3*d^3*e - 3*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3 - 6*a*c^2*d*e^3 - b^3*e^4 + 3*a*b*c*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3) + (c^3*x^2*e^4 + 8*c^3*d*x*e^3 - 3*b*c^2*x*e^4)/c^4 - (c^3*d^4 - 6*a*c^2*d^2*e^2 + 4*a*b*c*d*e^3 - a*b^2*e^4 + a^2*c*e^4 + (4*c^3*d^3*e - 6*b*c^2*d^2*e^2 + 4*b^2*c*d*e^3 - 4*a*c^2*d*e^3 - b^3*e^4 + 2*a*b*c*e^4)*x)/((c*x^2 + b*x + a)*c^3)","A",0
1533,1,173,0,0.160297," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2 \, x e^{3}}{c} + \frac{3 \, {\left(2 \, c d e^{2} - b e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{3 \, {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + b^{2} e^{3} - 2 \, a c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}} - \frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(3 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3} - a c e^{3}\right)} x}{{\left(c x^{2} + b x + a\right)} c^{2}}"," ",0,"2*x*e^3/c + 3/2*(2*c*d*e^2 - b*e^3)*log(c*x^2 + b*x + a)/c^2 + 3*(2*c^2*d^2*e - 2*b*c*d*e^2 + b^2*e^3 - 2*a*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2) - (c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (3*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3 - a*c*e^3)*x)/((c*x^2 + b*x + a)*c^2)","A",0
1534,1,114,0,0.175018," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{e^{2} \log\left(c x^{2} + b x + a\right)}{c} + \frac{2 \, {\left(2 \, c d e - b e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c} - \frac{\frac{{\left(2 \, c d e - b e^{2}\right)} x}{c} + \frac{c d^{2} - a e^{2}}{c}}{c x^{2} + b x + a}"," ",0,"e^2*log(c*x^2 + b*x + a)/c + 2*(2*c*d*e - b*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c) - ((2*c*d*e - b*e^2)*x/c + (c*d^2 - a*e^2)/c)/(c*x^2 + b*x + a)","A",0
1535,1,57,0,0.158085," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e}{\sqrt{-b^{2} + 4 \, a c}} - \frac{x e + d}{c x^{2} + b x + a}"," ",0,"2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))*e/sqrt(-b^2 + 4*a*c) - (x*e + d)/(c*x^2 + b*x + a)","A",0
1536,1,14,0,0.170041," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{1}{c x^{2} + b x + a}"," ",0,"-1/(c*x^2 + b*x + a)","A",0
1537,1,357,0,0.209558," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, c d e^{2} - b e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}} - \frac{{\left(2 \, c d e^{3} - b e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3} + 2 \, a c d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}} - \frac{{\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + b^{2} e^{3} - 2 \, a c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{c^{2} d^{3} - 2 \, b c d^{2} e + b^{2} d e^{2} + a c d e^{2} - a b e^{3} - {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} x}{{\left(c d^{2} - b d e + a e^{2}\right)}^{2} {\left(c x^{2} + b x + a\right)}}"," ",0,"1/2*(2*c*d*e^2 - b*e^3)*log(c*x^2 + b*x + a)/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) - (2*c*d*e^3 - b*e^4)*log(abs(x*e + d))/(c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3 + 2*a*c*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5) - (2*c^2*d^2*e - 2*b*c*d*e^2 + b^2*e^3 - 2*a*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-b^2 + 4*a*c)) - (c^2*d^3 - 2*b*c*d^2*e + b^2*d*e^2 + a*c*d*e^2 - a*b*e^3 - (c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*x)/((c*d^2 - b*d*e + a*e^2)^2*(c*x^2 + b*x + a))","A",0
1538,1,741,0,0.240534," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, b^{2} c d e^{5} - 6 \, a c^{2} d e^{5} - b^{3} e^{6} + 3 \, a b c e^{6}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(3 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4} - a c e^{4}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}} + \frac{\frac{2 \, c d e^{6}}{x e + d} - \frac{b e^{7}}{x e + d}}{c^{2} d^{4} e^{4} - 2 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6} + 2 \, a c d^{2} e^{6} - 2 \, a b d e^{7} + a^{2} e^{8}} + \frac{\frac{3 \, c^{3} d^{2} e^{2} - 3 \, b c^{2} d e^{3} + b^{2} c e^{4} - a c^{2} e^{4}}{c d^{2} - b d e + a e^{2}} - \frac{{\left(4 \, c^{3} d^{3} e^{3} - 6 \, b c^{2} d^{2} e^{4} + 4 \, b^{2} c d e^{5} - 4 \, a c^{2} d e^{5} - b^{3} e^{6} + 2 \, a b c e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} - b d e + a e^{2}\right)} {\left(x e + d\right)}}}{{\left(c d^{2} - b d e + a e^{2}\right)}^{2} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}}"," ",0,"-2*(2*c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*b^2*c*d*e^5 - 6*a*c^2*d*e^5 - b^3*e^6 + 3*a*b*c*e^6)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-b^2 + 4*a*c)) + (3*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4 - a*c*e^4)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) + (2*c*d*e^6/(x*e + d) - b*e^7/(x*e + d))/(c^2*d^4*e^4 - 2*b*c*d^3*e^5 + b^2*d^2*e^6 + 2*a*c*d^2*e^6 - 2*a*b*d*e^7 + a^2*e^8) + ((3*c^3*d^2*e^2 - 3*b*c^2*d*e^3 + b^2*c*e^4 - a*c^2*e^4)/(c*d^2 - b*d*e + a*e^2) - (4*c^3*d^3*e^3 - 6*b*c^2*d^2*e^4 + 4*b^2*c*d*e^5 - 4*a*c^2*d*e^5 - b^3*e^6 + 2*a*b*c*e^6)*e^(-1)/((c*d^2 - b*d*e + a*e^2)*(x*e + d)))/((c*d^2 - b*d*e + a*e^2)^2*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2))","B",0
1539,1,636,0,0.210201," ","integrate((2*c*x+b)*(e*x+d)^5/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(2 \, c^{4} d^{4} e - 4 \, b c^{3} d^{3} e^{2} + 12 \, a c^{3} d^{2} e^{3} + 2 \, b^{3} c d e^{4} - 12 \, a b c^{2} d e^{4} - b^{4} e^{5} + 6 \, a b^{2} c e^{5} - 6 \, a^{2} c^{2} e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, x e^{5}}{c^{2}} + \frac{5 \, {\left(2 \, c d e^{4} - b e^{5}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} - \frac{b^{2} c^{3} d^{5} - 4 \, a c^{4} d^{5} + 5 \, a b c^{3} d^{4} e - 40 \, a^{2} c^{3} d^{3} e^{2} + 30 \, a^{2} b c^{2} d^{2} e^{3} - 25 \, a^{2} b^{2} c d e^{4} + 60 \, a^{3} c^{2} d e^{4} + 7 \, a^{2} b^{3} e^{5} - 23 \, a^{3} b c e^{5} + 2 \, {\left(5 \, c^{5} d^{4} e - 10 \, b c^{4} d^{3} e^{2} + 20 \, b^{2} c^{3} d^{2} e^{3} - 50 \, a c^{4} d^{2} e^{3} - 15 \, b^{3} c^{2} d e^{4} + 50 \, a b c^{3} d e^{4} + 4 \, b^{4} c e^{5} - 17 \, a b^{2} c^{2} e^{5} + 9 \, a^{2} c^{3} e^{5}\right)} x^{3} + {\left(15 \, b c^{4} d^{4} e - 10 \, b^{2} c^{3} d^{3} e^{2} - 80 \, a c^{4} d^{3} e^{2} + 30 \, b^{3} c^{2} d^{2} e^{3} - 30 \, a b c^{3} d^{2} e^{3} - 25 \, b^{4} c d e^{4} + 50 \, a b^{2} c^{2} d e^{4} + 80 \, a^{2} c^{3} d e^{4} + 7 \, b^{5} e^{5} - 21 \, a b^{3} c e^{5} - 13 \, a^{2} b c^{2} e^{5}\right)} x^{2} + 2 \, {\left(5 \, b^{2} c^{3} d^{4} e - 5 \, a c^{4} d^{4} e - 30 \, a b c^{3} d^{3} e^{2} + 30 \, a b^{2} c^{2} d^{2} e^{3} - 30 \, a^{2} c^{3} d^{2} e^{3} - 25 \, a b^{3} c d e^{4} + 70 \, a^{2} b c^{2} d e^{4} + 7 \, a b^{4} e^{5} - 26 \, a^{2} b^{2} c e^{5} + 7 \, a^{3} c^{2} e^{5}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)} c^{3}}"," ",0,"-5*(2*c^4*d^4*e - 4*b*c^3*d^3*e^2 + 12*a*c^3*d^2*e^3 + 2*b^3*c*d*e^4 - 12*a*b*c^2*d*e^4 - b^4*e^5 + 6*a*b^2*c*e^5 - 6*a^2*c^2*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^3 - 4*a*c^4)*sqrt(-b^2 + 4*a*c)) + 2*x*e^5/c^2 + 5/2*(2*c*d*e^4 - b*e^5)*log(c*x^2 + b*x + a)/c^3 - 1/2*(b^2*c^3*d^5 - 4*a*c^4*d^5 + 5*a*b*c^3*d^4*e - 40*a^2*c^3*d^3*e^2 + 30*a^2*b*c^2*d^2*e^3 - 25*a^2*b^2*c*d*e^4 + 60*a^3*c^2*d*e^4 + 7*a^2*b^3*e^5 - 23*a^3*b*c*e^5 + 2*(5*c^5*d^4*e - 10*b*c^4*d^3*e^2 + 20*b^2*c^3*d^2*e^3 - 50*a*c^4*d^2*e^3 - 15*b^3*c^2*d*e^4 + 50*a*b*c^3*d*e^4 + 4*b^4*c*e^5 - 17*a*b^2*c^2*e^5 + 9*a^2*c^3*e^5)*x^3 + (15*b*c^4*d^4*e - 10*b^2*c^3*d^3*e^2 - 80*a*c^4*d^3*e^2 + 30*b^3*c^2*d^2*e^3 - 30*a*b*c^3*d^2*e^3 - 25*b^4*c*d*e^4 + 50*a*b^2*c^2*d*e^4 + 80*a^2*c^3*d*e^4 + 7*b^5*e^5 - 21*a*b^3*c*e^5 - 13*a^2*b*c^2*e^5)*x^2 + 2*(5*b^2*c^3*d^4*e - 5*a*c^4*d^4*e - 30*a*b*c^3*d^3*e^2 + 30*a*b^2*c^2*d^2*e^3 - 30*a^2*c^3*d^2*e^3 - 25*a*b^3*c*d*e^4 + 70*a^2*b*c^2*d*e^4 + 7*a*b^4*e^5 - 26*a^2*b^2*c*e^5 + 7*a^3*c^2*e^5)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)*c^3)","B",0
1540,1,439,0,0.180428," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(4 \, c^{3} d^{3} e - 6 \, b c^{2} d^{2} e^{2} + 12 \, a c^{2} d e^{3} + b^{3} e^{4} - 6 \, a b c e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{e^{4} \log\left(c x^{2} + b x + a\right)}{c^{2}} - \frac{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} + 4 \, a b c^{2} d^{3} e - 24 \, a^{2} c^{2} d^{2} e^{2} + 12 \, a^{2} b c d e^{3} - 5 \, a^{2} b^{2} e^{4} + 12 \, a^{3} c e^{4} + 2 \, {\left(4 \, c^{4} d^{3} e - 6 \, b c^{3} d^{2} e^{2} + 8 \, b^{2} c^{2} d e^{3} - 20 \, a c^{3} d e^{3} - 3 \, b^{3} c e^{4} + 10 \, a b c^{2} e^{4}\right)} x^{3} + {\left(12 \, b c^{3} d^{3} e - 6 \, b^{2} c^{2} d^{2} e^{2} - 48 \, a c^{3} d^{2} e^{2} + 12 \, b^{3} c d e^{3} - 12 \, a b c^{2} d e^{3} - 5 \, b^{4} e^{4} + 10 \, a b^{2} c e^{4} + 16 \, a^{2} c^{2} e^{4}\right)} x^{2} + 2 \, {\left(4 \, b^{2} c^{2} d^{3} e - 4 \, a c^{3} d^{3} e - 18 \, a b c^{2} d^{2} e^{2} + 12 \, a b^{2} c d e^{3} - 12 \, a^{2} c^{2} d e^{3} - 5 \, a b^{3} e^{4} + 14 \, a^{2} b c e^{4}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"-2*(4*c^3*d^3*e - 6*b*c^2*d^2*e^2 + 12*a*c^2*d*e^3 + b^3*e^4 - 6*a*b*c*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2 - 4*a*c^3)*sqrt(-b^2 + 4*a*c)) + e^4*log(c*x^2 + b*x + a)/c^2 - 1/2*(b^2*c^2*d^4 - 4*a*c^3*d^4 + 4*a*b*c^2*d^3*e - 24*a^2*c^2*d^2*e^2 + 12*a^2*b*c*d*e^3 - 5*a^2*b^2*e^4 + 12*a^3*c*e^4 + 2*(4*c^4*d^3*e - 6*b*c^3*d^2*e^2 + 8*b^2*c^2*d*e^3 - 20*a*c^3*d*e^3 - 3*b^3*c*e^4 + 10*a*b*c^2*e^4)*x^3 + (12*b*c^3*d^3*e - 6*b^2*c^2*d^2*e^2 - 48*a*c^3*d^2*e^2 + 12*b^3*c*d*e^3 - 12*a*b*c^2*d*e^3 - 5*b^4*e^4 + 10*a*b^2*c*e^4 + 16*a^2*c^2*e^4)*x^2 + 2*(4*b^2*c^2*d^3*e - 4*a*c^3*d^3*e - 18*a*b*c^2*d^2*e^2 + 12*a*b^2*c*d*e^3 - 12*a^2*c^2*d*e^3 - 5*a*b^3*e^4 + 14*a^2*b*c*e^4)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)*c^2)","B",0
1541,1,292,0,0.183698," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{6 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, c^{3} d^{2} x^{3} e - 6 \, b c^{2} d x^{3} e^{2} + 9 \, b c^{2} d^{2} x^{2} e + 4 \, b^{2} c x^{3} e^{3} - 10 \, a c^{2} x^{3} e^{3} - 3 \, b^{2} c d x^{2} e^{2} - 24 \, a c^{2} d x^{2} e^{2} + 6 \, b^{2} c d^{2} x e - 6 \, a c^{2} d^{2} x e + b^{2} c d^{3} - 4 \, a c^{2} d^{3} + 3 \, b^{3} x^{2} e^{3} - 3 \, a b c x^{2} e^{3} - 18 \, a b c d x e^{2} + 3 \, a b c d^{2} e + 6 \, a b^{2} x e^{3} - 6 \, a^{2} c x e^{3} - 12 \, a^{2} c d e^{2} + 3 \, a^{2} b e^{3}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"-6*(c*d^2*e - b*d*e^2 + a*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(6*c^3*d^2*x^3*e - 6*b*c^2*d*x^3*e^2 + 9*b*c^2*d^2*x^2*e + 4*b^2*c*x^3*e^3 - 10*a*c^2*x^3*e^3 - 3*b^2*c*d*x^2*e^2 - 24*a*c^2*d*x^2*e^2 + 6*b^2*c*d^2*x*e - 6*a*c^2*d^2*x*e + b^2*c*d^3 - 4*a*c^2*d^3 + 3*b^3*x^2*e^3 - 3*a*b*c*x^2*e^3 - 18*a*b*c*d*x*e^2 + 3*a*b*c*d^2*e + 6*a*b^2*x*e^3 - 6*a^2*c*x*e^3 - 12*a^2*c*d*e^2 + 3*a^2*b*e^3)/((b^2*c - 4*a*c^2)*(c*x^2 + b*x + a)^2)","B",0
1542,1,183,0,0.170958," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c d e - b e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{4 \, c^{2} d x^{3} e - 2 \, b c x^{3} e^{2} + 6 \, b c d x^{2} e - b^{2} x^{2} e^{2} - 8 \, a c x^{2} e^{2} + 4 \, b^{2} d x e - 4 \, a c d x e + b^{2} d^{2} - 4 \, a c d^{2} - 6 \, a b x e^{2} + 2 \, a b d e - 4 \, a^{2} e^{2}}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-2*(2*c*d*e - b*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(4*c^2*d*x^3*e - 2*b*c*x^3*e^2 + 6*b*c*d*x^2*e - b^2*x^2*e^2 - 8*a*c*x^2*e^2 + 4*b^2*d*x*e - 4*a*c*d*x*e + b^2*d^2 - 4*a*c*d^2 - 6*a*b*x*e^2 + 2*a*b*d*e - 4*a^2*e^2)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c))","A",0
1543,1,122,0,0.163548," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{2 \, c \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c^{2} x^{3} e + 3 \, b c x^{2} e + 2 \, b^{2} x e - 2 \, a c x e + b^{2} d - 4 \, a c d + a b e}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-2*c*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))*e/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*c^2*x^3*e + 3*b*c*x^2*e + 2*b^2*x*e - 2*a*c*x*e + b^2*d - 4*a*c*d + a*b*e)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c))","A",0
1544,1,14,0,0.155612," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"-1/2/(c*x^2 + b*x + a)^2","A",0
1545,1,1117,0,0.282840," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(2 \, c d e^{4} - b e^{5}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} - \frac{{\left(2 \, c d e^{5} - b e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}} + \frac{{\left(2 \, c^{4} d^{4} e - 4 \, b c^{3} d^{3} e^{2} + 12 \, a c^{3} d^{2} e^{3} + 2 \, b^{3} c d e^{4} - 12 \, a b c^{2} d e^{4} - b^{4} e^{5} + 6 \, a b^{2} c e^{5} - 6 \, a^{2} c^{2} e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{3} d^{6} - 4 \, a c^{4} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 12 \, a b c^{3} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - 9 \, a b^{2} c^{2} d^{4} e^{2} - 12 \, a^{2} c^{3} d^{4} e^{2} - b^{5} d^{3} e^{3} - 2 \, a b^{3} c d^{3} e^{3} + 24 \, a^{2} b c^{2} d^{3} e^{3} + 3 \, a b^{4} d^{2} e^{4} - 9 \, a^{2} b^{2} c d^{2} e^{4} - 12 \, a^{3} c^{2} d^{2} e^{4} - 3 \, a^{2} b^{3} d e^{5} + 12 \, a^{3} b c d e^{5} + a^{3} b^{2} e^{6} - 4 \, a^{4} c e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b^{2} c^{3} d^{5} - 4 \, a c^{4} d^{5} - 3 \, b^{3} c^{2} d^{4} e + 11 \, a b c^{3} d^{4} e + 3 \, b^{4} c d^{3} e^{2} - 6 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 5 \, a b^{3} c d^{2} e^{3} + 30 \, a^{2} b c^{2} d^{2} e^{3} + 4 \, a b^{4} d e^{4} - 11 \, a^{2} b^{2} c d e^{4} - 12 \, a^{3} c^{2} d e^{4} - 3 \, a^{2} b^{3} e^{5} + 11 \, a^{3} b c e^{5} - 2 \, {\left(c^{5} d^{4} e - 2 \, b c^{4} d^{3} e^{2} + 2 \, b^{2} c^{3} d^{2} e^{3} - 2 \, a c^{4} d^{2} e^{3} - b^{3} c^{2} d e^{4} + 2 \, a b c^{3} d e^{4} + a b^{2} c^{2} e^{5} - 3 \, a^{2} c^{3} e^{5}\right)} x^{3} - {\left(3 \, b c^{4} d^{4} e - 8 \, b^{2} c^{3} d^{3} e^{2} + 8 \, a c^{4} d^{3} e^{2} + 9 \, b^{3} c^{2} d^{2} e^{3} - 18 \, a b c^{3} d^{2} e^{3} - 4 \, b^{4} c d e^{4} + 8 \, a b^{2} c^{2} d e^{4} + 8 \, a^{2} c^{3} d e^{4} + 4 \, a b^{3} c e^{5} - 13 \, a^{2} b c^{2} e^{5}\right)} x^{2} - 2 \, {\left(b^{2} c^{3} d^{4} e - a c^{4} d^{4} e - 3 \, b^{3} c^{2} d^{3} e^{2} + 6 \, a b c^{3} d^{3} e^{2} + 3 \, b^{4} c d^{2} e^{3} - 6 \, a b^{2} c^{2} d^{2} e^{3} - 6 \, a^{2} c^{3} d^{2} e^{3} - b^{5} d e^{4} + 10 \, a^{2} b c^{2} d e^{4} + a b^{4} e^{5} - 2 \, a^{2} b^{2} c e^{5} - 5 \, a^{3} c^{2} e^{5}\right)} x}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{3} {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(2*c*d*e^4 - b*e^5)*log(c*x^2 + b*x + a)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) - (2*c*d*e^5 - b*e^6)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7) + (2*c^4*d^4*e - 4*b*c^3*d^3*e^2 + 12*a*c^3*d^2*e^3 + 2*b^3*c*d*e^4 - 12*a*b*c^2*d*e^4 - b^4*e^5 + 6*a*b^2*c*e^5 - 6*a^2*c^2*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*sqrt(-b^2 + 4*a*c)) - 1/2*(b^2*c^3*d^5 - 4*a*c^4*d^5 - 3*b^3*c^2*d^4*e + 11*a*b*c^3*d^4*e + 3*b^4*c*d^3*e^2 - 6*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 5*a*b^3*c*d^2*e^3 + 30*a^2*b*c^2*d^2*e^3 + 4*a*b^4*d*e^4 - 11*a^2*b^2*c*d*e^4 - 12*a^3*c^2*d*e^4 - 3*a^2*b^3*e^5 + 11*a^3*b*c*e^5 - 2*(c^5*d^4*e - 2*b*c^4*d^3*e^2 + 2*b^2*c^3*d^2*e^3 - 2*a*c^4*d^2*e^3 - b^3*c^2*d*e^4 + 2*a*b*c^3*d*e^4 + a*b^2*c^2*e^5 - 3*a^2*c^3*e^5)*x^3 - (3*b*c^4*d^4*e - 8*b^2*c^3*d^3*e^2 + 8*a*c^4*d^3*e^2 + 9*b^3*c^2*d^2*e^3 - 18*a*b*c^3*d^2*e^3 - 4*b^4*c*d*e^4 + 8*a*b^2*c^2*d*e^4 + 8*a^2*c^3*d*e^4 + 4*a*b^3*c*e^5 - 13*a^2*b*c^2*e^5)*x^2 - 2*(b^2*c^3*d^4*e - a*c^4*d^4*e - 3*b^3*c^2*d^3*e^2 + 6*a*b*c^3*d^3*e^2 + 3*b^4*c*d^2*e^3 - 6*a*b^2*c^2*d^2*e^3 - 6*a^2*c^3*d^2*e^3 - b^5*d*e^4 + 10*a^2*b*c^2*d*e^4 + a*b^4*e^5 - 2*a^2*b^2*c*e^5 - 5*a^3*c^2*e^5)*x)/((c*d^2 - b*d*e + a*e^2)^3*(c*x^2 + b*x + a)^2*(b^2 - 4*a*c))","B",0
1546,1,759,0,0.252015," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{13440} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(3 \, c x e^{4} + \frac{2 \, {\left(7 \, c^{7} d e^{3} + b c^{6} e^{4}\right)}}{c^{6}}\right)} x + \frac{252 \, c^{7} d^{2} e^{2} + 98 \, b c^{6} d e^{3} - b^{2} c^{5} e^{4} + 6 \, a c^{6} e^{4}}{c^{6}}\right)} x + \frac{1680 \, c^{7} d^{3} e + 1512 \, b c^{6} d^{2} e^{2} - 42 \, b^{2} c^{5} d e^{3} + 280 \, a c^{6} d e^{3} + 9 \, b^{3} c^{4} e^{4} - 44 \, a b c^{5} e^{4}}{c^{6}}\right)} x + \frac{1120 \, c^{7} d^{4} + 2800 \, b c^{6} d^{3} e - 168 \, b^{2} c^{5} d^{2} e^{2} + 1344 \, a c^{6} d^{2} e^{2} + 98 \, b^{3} c^{4} d e^{3} - 504 \, a b c^{5} d e^{3} - 21 \, b^{4} c^{3} e^{4} + 124 \, a b^{2} c^{4} e^{4} - 128 \, a^{2} c^{5} e^{4}}{c^{6}}\right)} x + \frac{4480 \, b c^{6} d^{4} - 560 \, b^{2} c^{5} d^{3} e + 6720 \, a c^{6} d^{3} e + 840 \, b^{3} c^{4} d^{2} e^{2} - 4704 \, a b c^{5} d^{2} e^{2} - 490 \, b^{4} c^{3} d e^{3} + 3024 \, a b^{2} c^{4} d e^{3} - 3360 \, a^{2} c^{5} d e^{3} + 105 \, b^{5} c^{2} e^{4} - 728 \, a b^{3} c^{3} e^{4} + 1168 \, a^{2} b c^{4} e^{4}}{c^{6}}\right)} x + \frac{8960 \, a c^{6} d^{4} + 1680 \, b^{3} c^{4} d^{3} e - 11200 \, a b c^{5} d^{3} e - 2520 \, b^{4} c^{3} d^{2} e^{2} + 16800 \, a b^{2} c^{4} d^{2} e^{2} - 21504 \, a^{2} c^{5} d^{2} e^{2} + 1470 \, b^{5} c^{2} d e^{3} - 10640 \, a b^{3} c^{3} d e^{3} + 18144 \, a^{2} b c^{4} d e^{3} - 315 \, b^{6} c e^{4} + 2520 \, a b^{4} c^{2} e^{4} - 5488 \, a^{2} b^{2} c^{3} e^{4} + 2048 \, a^{3} c^{4} e^{4}}{c^{6}}\right)} + \frac{{\left(16 \, b^{4} c^{3} d^{3} e - 128 \, a b^{2} c^{4} d^{3} e + 256 \, a^{2} c^{5} d^{3} e - 24 \, b^{5} c^{2} d^{2} e^{2} + 192 \, a b^{3} c^{3} d^{2} e^{2} - 384 \, a^{2} b c^{4} d^{2} e^{2} + 14 \, b^{6} c d e^{3} - 120 \, a b^{4} c^{2} d e^{3} + 288 \, a^{2} b^{2} c^{3} d e^{3} - 128 \, a^{3} c^{4} d e^{3} - 3 \, b^{7} e^{4} + 28 \, a b^{5} c e^{4} - 80 \, a^{2} b^{3} c^{2} e^{4} + 64 \, a^{3} b c^{3} e^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{11}{2}}}"," ",0,"1/13440*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(3*c*x*e^4 + 2*(7*c^7*d*e^3 + b*c^6*e^4)/c^6)*x + (252*c^7*d^2*e^2 + 98*b*c^6*d*e^3 - b^2*c^5*e^4 + 6*a*c^6*e^4)/c^6)*x + (1680*c^7*d^3*e + 1512*b*c^6*d^2*e^2 - 42*b^2*c^5*d*e^3 + 280*a*c^6*d*e^3 + 9*b^3*c^4*e^4 - 44*a*b*c^5*e^4)/c^6)*x + (1120*c^7*d^4 + 2800*b*c^6*d^3*e - 168*b^2*c^5*d^2*e^2 + 1344*a*c^6*d^2*e^2 + 98*b^3*c^4*d*e^3 - 504*a*b*c^5*d*e^3 - 21*b^4*c^3*e^4 + 124*a*b^2*c^4*e^4 - 128*a^2*c^5*e^4)/c^6)*x + (4480*b*c^6*d^4 - 560*b^2*c^5*d^3*e + 6720*a*c^6*d^3*e + 840*b^3*c^4*d^2*e^2 - 4704*a*b*c^5*d^2*e^2 - 490*b^4*c^3*d*e^3 + 3024*a*b^2*c^4*d*e^3 - 3360*a^2*c^5*d*e^3 + 105*b^5*c^2*e^4 - 728*a*b^3*c^3*e^4 + 1168*a^2*b*c^4*e^4)/c^6)*x + (8960*a*c^6*d^4 + 1680*b^3*c^4*d^3*e - 11200*a*b*c^5*d^3*e - 2520*b^4*c^3*d^2*e^2 + 16800*a*b^2*c^4*d^2*e^2 - 21504*a^2*c^5*d^2*e^2 + 1470*b^5*c^2*d*e^3 - 10640*a*b^3*c^3*d*e^3 + 18144*a^2*b*c^4*d*e^3 - 315*b^6*c*e^4 + 2520*a*b^4*c^2*e^4 - 5488*a^2*b^2*c^3*e^4 + 2048*a^3*c^4*e^4)/c^6) + 1/256*(16*b^4*c^3*d^3*e - 128*a*b^2*c^4*d^3*e + 256*a^2*c^5*d^3*e - 24*b^5*c^2*d^2*e^2 + 192*a*b^3*c^3*d^2*e^2 - 384*a^2*b*c^4*d^2*e^2 + 14*b^6*c*d*e^3 - 120*a*b^4*c^2*d*e^3 + 288*a^2*b^2*c^3*d*e^3 - 128*a^3*c^4*d*e^3 - 3*b^7*e^4 + 28*a*b^5*c*e^4 - 80*a^2*b^3*c^2*e^4 + 64*a^3*b*c^3*e^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
1547,1,506,0,0.243847," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{3840} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c x e^{3} + \frac{36 \, c^{6} d e^{2} + 7 \, b c^{5} e^{3}}{c^{5}}\right)} x + \frac{360 \, c^{6} d^{2} e + 216 \, b c^{5} d e^{2} - 3 \, b^{2} c^{4} e^{3} + 20 \, a c^{5} e^{3}}{c^{5}}\right)} x + \frac{320 \, c^{6} d^{3} + 600 \, b c^{5} d^{2} e - 24 \, b^{2} c^{4} d e^{2} + 192 \, a c^{5} d e^{2} + 7 \, b^{3} c^{3} e^{3} - 36 \, a b c^{4} e^{3}}{c^{5}}\right)} x + \frac{1280 \, b c^{5} d^{3} - 120 \, b^{2} c^{4} d^{2} e + 1440 \, a c^{5} d^{2} e + 120 \, b^{3} c^{3} d e^{2} - 672 \, a b c^{4} d e^{2} - 35 \, b^{4} c^{2} e^{3} + 216 \, a b^{2} c^{3} e^{3} - 240 \, a^{2} c^{4} e^{3}}{c^{5}}\right)} x + \frac{2560 \, a c^{5} d^{3} + 360 \, b^{3} c^{3} d^{2} e - 2400 \, a b c^{4} d^{2} e - 360 \, b^{4} c^{2} d e^{2} + 2400 \, a b^{2} c^{3} d e^{2} - 3072 \, a^{2} c^{4} d e^{2} + 105 \, b^{5} c e^{3} - 760 \, a b^{3} c^{2} e^{3} + 1296 \, a^{2} b c^{3} e^{3}}{c^{5}}\right)} + \frac{{\left(24 \, b^{4} c^{2} d^{2} e - 192 \, a b^{2} c^{3} d^{2} e + 384 \, a^{2} c^{4} d^{2} e - 24 \, b^{5} c d e^{2} + 192 \, a b^{3} c^{2} d e^{2} - 384 \, a^{2} b c^{3} d e^{2} + 7 \, b^{6} e^{3} - 60 \, a b^{4} c e^{3} + 144 \, a^{2} b^{2} c^{2} e^{3} - 64 \, a^{3} c^{3} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{512 \, c^{\frac{9}{2}}}"," ",0,"1/3840*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*c*x*e^3 + (36*c^6*d*e^2 + 7*b*c^5*e^3)/c^5)*x + (360*c^6*d^2*e + 216*b*c^5*d*e^2 - 3*b^2*c^4*e^3 + 20*a*c^5*e^3)/c^5)*x + (320*c^6*d^3 + 600*b*c^5*d^2*e - 24*b^2*c^4*d*e^2 + 192*a*c^5*d*e^2 + 7*b^3*c^3*e^3 - 36*a*b*c^4*e^3)/c^5)*x + (1280*b*c^5*d^3 - 120*b^2*c^4*d^2*e + 1440*a*c^5*d^2*e + 120*b^3*c^3*d*e^2 - 672*a*b*c^4*d*e^2 - 35*b^4*c^2*e^3 + 216*a*b^2*c^3*e^3 - 240*a^2*c^4*e^3)/c^5)*x + (2560*a*c^5*d^3 + 360*b^3*c^3*d^2*e - 2400*a*b*c^4*d^2*e - 360*b^4*c^2*d*e^2 + 2400*a*b^2*c^3*d*e^2 - 3072*a^2*c^4*d*e^2 + 105*b^5*c*e^3 - 760*a*b^3*c^2*e^3 + 1296*a^2*b*c^3*e^3)/c^5) + 1/512*(24*b^4*c^2*d^2*e - 192*a*b^2*c^3*d^2*e + 384*a^2*c^4*d^2*e - 24*b^5*c*d*e^2 + 192*a*b^3*c^2*d*e^2 - 384*a^2*b*c^3*d*e^2 + 7*b^6*e^3 - 60*a*b^4*c*e^3 + 144*a^2*b^2*c^2*e^3 - 64*a^3*c^3*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
1548,1,308,0,0.235365," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{480} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(4 \, c x e^{2} + \frac{10 \, c^{5} d e + 3 \, b c^{4} e^{2}}{c^{4}}\right)} x + \frac{40 \, c^{5} d^{2} + 50 \, b c^{4} d e - b^{2} c^{3} e^{2} + 8 \, a c^{4} e^{2}}{c^{4}}\right)} x + \frac{160 \, b c^{4} d^{2} - 10 \, b^{2} c^{3} d e + 120 \, a c^{4} d e + 5 \, b^{3} c^{2} e^{2} - 28 \, a b c^{3} e^{2}}{c^{4}}\right)} x + \frac{320 \, a c^{4} d^{2} + 30 \, b^{3} c^{2} d e - 200 \, a b c^{3} d e - 15 \, b^{4} c e^{2} + 100 \, a b^{2} c^{2} e^{2} - 128 \, a^{2} c^{3} e^{2}}{c^{4}}\right)} + \frac{{\left(2 \, b^{4} c d e - 16 \, a b^{2} c^{2} d e + 32 \, a^{2} c^{3} d e - b^{5} e^{2} + 8 \, a b^{3} c e^{2} - 16 \, a^{2} b c^{2} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{64 \, c^{\frac{7}{2}}}"," ",0,"1/480*sqrt(c*x^2 + b*x + a)*(2*(4*(6*(4*c*x*e^2 + (10*c^5*d*e + 3*b*c^4*e^2)/c^4)*x + (40*c^5*d^2 + 50*b*c^4*d*e - b^2*c^3*e^2 + 8*a*c^4*e^2)/c^4)*x + (160*b*c^4*d^2 - 10*b^2*c^3*d*e + 120*a*c^4*d*e + 5*b^3*c^2*e^2 - 28*a*b*c^3*e^2)/c^4)*x + (320*a*c^4*d^2 + 30*b^3*c^2*d*e - 200*a*b*c^3*d*e - 15*b^4*c*e^2 + 100*a*b^2*c^2*e^2 - 128*a^2*c^3*e^2)/c^4) + 1/64*(2*b^4*c*d*e - 16*a*b^2*c^2*d*e + 32*a^2*c^3*d*e - b^5*e^2 + 8*a*b^3*c*e^2 - 16*a^2*b*c^2*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
1549,1,170,0,0.221992," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, c x e + \frac{8 \, c^{4} d + 5 \, b c^{3} e}{c^{3}}\right)} x + \frac{32 \, b c^{3} d - b^{2} c^{2} e + 12 \, a c^{3} e}{c^{3}}\right)} x + \frac{64 \, a c^{3} d + 3 \, b^{3} c e - 20 \, a b c^{2} e}{c^{3}}\right)} + \frac{{\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{64 \, c^{\frac{5}{2}}}"," ",0,"1/96*sqrt(c*x^2 + b*x + a)*(2*(4*(6*c*x*e + (8*c^4*d + 5*b*c^3*e)/c^3)*x + (32*b*c^3*d - b^2*c^2*e + 12*a*c^3*e)/c^3)*x + (64*a*c^3*d + 3*b^3*c*e - 20*a*b*c^2*e)/c^3) + 1/64*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
1550,1,14,0,0.167506," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1552,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Unable to divide, perhaps due to rounding error%%%{%%%{32,[2,11,0,0,2]%%%}+%%%{-16,[1,11,2,0,1]%%%}+%%%{2,[0,11,4,0,0]%%%},[4]%%%}+%%%{%%%{-64,[2,11,0,0,3]%%%}+%%%{32,[1,11,2,0,2]%%%}+%%%{-4,[0,11,4,0,1]%%%},[2]%%%}+%%%{%%%{32,[2,11,0,0,4]%%%}+%%%{-16,[1,11,2,0,3]%%%}+%%%{2,[0,11,4,0,2]%%%},[0]%%%} / %%%{%%%{1,[1,2,0,0,0]%%%}+%%%{-1,[0,1,1,1,0]%%%}+%%%{1,[0,0,0,2,1]%%%},[4]%%%}+%%%{%%%{-2,[1,2,0,0,1]%%%}+%%%{2,[0,1,1,1,1]%%%}+%%%{-2,[0,0,0,2,2]%%%},[2]%%%}+%%%{%%%{1,[1,2,0,0,2]%%%}+%%%{-1,[0,1,1,1,2]%%%}+%%%{1,[0,0,0,2,3]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
1553,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.51Unable to divide, perhaps due to rounding error%%%{1,[6,0,0,6,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,5,1]%%%}+%%%{3,[4,1,0,5,1]%%%}+%%%{-3,[4,0,1,6,0]%%%}+%%%{%%%{12,[1]%%%},[4,0,0,4,2]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,4,2]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,5,1]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,3,3]%%%}+%%%{3,[2,2,0,4,2]%%%}+%%%{-6,[2,1,1,5,1]%%%}+%%%{%%%{12,[1]%%%},[2,1,0,3,3]%%%}+%%%{3,[2,0,2,6,0]%%%}+%%%{%%%{-12,[1]%%%},[2,0,1,4,2]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,0,3,3]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,1,4,2]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,2,5,1]%%%}+%%%{1,[0,3,0,3,3]%%%}+%%%{-3,[0,2,1,4,2]%%%}+%%%{3,[0,1,2,5,1]%%%}+%%%{-1,[0,0,3,6,0]%%%} / %%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,3,0]%%%}+%%%{%%%{-6,[2]%%%},[5,0,0,2,1]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,0,2,1]%%%}+%%%{%%{poly1[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,3,0]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,1,2]%%%}+%%%{%%%{-12,[2]%%%},[3,1,0,1,2]%%%}+%%%{%%%{12,[2]%%%},[3,0,1,2,1]%%%}+%%%{%%%{-8,[3]%%%},[3,0,0,0,3]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,0,1,2]%%%}+%%%{%%{[%%%{-6,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,1,2,1]%%%}+%%%{%%{[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0,0,3]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,3,0]%%%}+%%%{%%{poly1[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,1,2]%%%}+%%%{%%%{-6,[2]%%%},[1,2,0,0,3]%%%}+%%%{%%%{12,[2]%%%},[1,1,1,1,2]%%%}+%%%{%%%{-6,[2]%%%},[1,0,2,2,1]%%%}+%%%{%%{[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,0,0,3]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,1,1,2]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,2,2,1]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,3,3,0]%%%} Error: Bad Argument Value","F(-2)",0
1554,1,2611,0,0.767200," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","\frac{{\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{8 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{\frac{9}{2}} d^{5} e + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{5} d^{6} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{4} d^{4} e^{2} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{9}{2}} d^{6} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{\frac{7}{2}} d^{4} e^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{7}{2}} d^{5} e - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{9}{2}} d^{5} e + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{4} d^{6} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{3} d^{3} e^{3} - 272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{3} d^{4} e^{2} + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{4} d^{4} e^{2} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{3} d^{5} e - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{4} d^{5} e + 16 \, b^{3} c^{\frac{7}{2}} d^{6} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{5}{2}} d^{3} e^{3} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{7}{2}} d^{3} e^{3} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{5}{2}} d^{4} e^{2} + 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{\frac{7}{2}} d^{4} e^{2} - 24 \, b^{4} c^{\frac{5}{2}} d^{5} e - 48 \, a b^{2} c^{\frac{7}{2}} d^{5} e + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{2} d^{2} e^{4} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{3} d^{2} e^{4} + 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{2} d^{3} e^{3} + 512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{3} d^{3} e^{3} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{2} d^{4} e^{2} + 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{3} d^{4} e^{2} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{4} d^{4} e^{2} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c^{\frac{3}{2}} d^{2} e^{4} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{5}{2}} d^{2} e^{4} + 42 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c^{\frac{3}{2}} d^{3} e^{3} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{5}{2}} d^{3} e^{3} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{7}{2}} d^{3} e^{3} + 2 \, b^{5} c^{\frac{3}{2}} d^{4} e^{2} + 112 \, a b^{3} c^{\frac{5}{2}} d^{4} e^{2} + 48 \, a^{2} b c^{\frac{7}{2}} d^{4} e^{2} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{2} d e^{5} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} c d^{2} e^{4} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{2} d^{2} e^{4} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{3} d^{2} e^{4} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} c d^{3} e^{3} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{2} d^{3} e^{3} - 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{3} d^{3} e^{3} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} \sqrt{c} d e^{5} - 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{3}{2}} d e^{5} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{5}{2}} d e^{5} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{5} \sqrt{c} d^{2} e^{4} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c^{\frac{3}{2}} d^{2} e^{4} + 3 \, b^{6} \sqrt{c} d^{3} e^{3} - 26 \, a b^{4} c^{\frac{3}{2}} d^{3} e^{3} - 192 \, a^{2} b^{2} c^{\frac{5}{2}} d^{3} e^{3} - 32 \, a^{3} c^{\frac{7}{2}} d^{3} e^{3} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{4} e^{6} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} c e^{6} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{2} e^{6} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} d e^{5} - 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} c d e^{5} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{2} d e^{5} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{6} d^{2} e^{4} - 42 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} c d^{2} e^{4} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{2} d^{2} e^{4} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{3} d^{2} e^{4} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b c^{\frac{3}{2}} e^{6} - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{4} \sqrt{c} d e^{5} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c^{\frac{3}{2}} d e^{5} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{5}{2}} d e^{5} - 6 \, a b^{5} \sqrt{c} d^{2} e^{4} + 48 \, a^{2} b^{3} c^{\frac{3}{2}} d^{2} e^{4} + 192 \, a^{3} b c^{\frac{5}{2}} d^{2} e^{4} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{4} e^{6} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} c e^{6} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{5} d e^{5} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{2} d e^{5} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{3} \sqrt{c} e^{6} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b c^{\frac{3}{2}} e^{6} + 3 \, a^{2} b^{4} \sqrt{c} d e^{5} - 40 \, a^{3} b^{2} c^{\frac{3}{2}} d e^{5} - 80 \, a^{4} c^{\frac{5}{2}} d e^{5} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{4} e^{6} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{2} c e^{6} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} c^{2} e^{6} + 16 \, a^{4} b c^{\frac{3}{2}} e^{6}}{24 \, {\left(c^{2} d^{4} e^{3} - 2 \, b c d^{3} e^{4} + b^{2} d^{2} e^{5} + 2 \, a c d^{2} e^{5} - 2 \, a b d e^{6} + a^{2} e^{7}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{3}}"," ",0,"1/8*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/24*(192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^(9/2)*d^5*e + 128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^5*d^6 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^4*d^4*e^2 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(9/2)*d^6 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^(7/2)*d^4*e^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(7/2)*d^5*e - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(9/2)*d^5*e + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^4*d^6 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^3*d^3*e^3 - 272*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^3*d^4*e^2 + 128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^4*d^4*e^2 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^3*d^5*e - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^4*d^5*e + 16*b^3*c^(7/2)*d^6 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(5/2)*d^3*e^3 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(7/2)*d^3*e^3 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(5/2)*d^4*e^2 + 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^(7/2)*d^4*e^2 - 24*b^4*c^(5/2)*d^5*e - 48*a*b^2*c^(7/2)*d^5*e + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^2*d^2*e^4 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^3*d^2*e^4 + 32*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^2*d^3*e^3 + 512*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^3*d^3*e^3 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^2*d^4*e^2 + 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^3*d^4*e^2 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^4*d^4*e^2 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c^(3/2)*d^2*e^4 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(5/2)*d^2*e^4 + 42*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(3/2)*d^3*e^3 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(5/2)*d^3*e^3 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(7/2)*d^3*e^3 + 2*b^5*c^(3/2)*d^4*e^2 + 112*a*b^3*c^(5/2)*d^4*e^2 + 48*a^2*b*c^(7/2)*d^4*e^2 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^2*d*e^5 + 90*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c*d^2*e^4 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^2*d^2*e^4 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^3*d^2*e^4 + 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c*d^3*e^3 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^2*d^3*e^3 - 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^3*d^3*e^3 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*sqrt(c)*d*e^5 - 168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(3/2)*d*e^5 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(5/2)*d*e^5 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*sqrt(c)*d^2*e^4 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c^(3/2)*d^2*e^4 + 3*b^6*sqrt(c)*d^3*e^3 - 26*a*b^4*c^(3/2)*d^3*e^3 - 192*a^2*b^2*c^(5/2)*d^3*e^3 - 32*a^3*c^(7/2)*d^3*e^3 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^4*e^6 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*c*e^6 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^2*e^6 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*d*e^5 - 160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c*d*e^5 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^2*d*e^5 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*d^2*e^4 - 42*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c*d^2*e^4 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^2*d^2*e^4 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^3*d^2*e^4 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c^(3/2)*e^6 - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*sqrt(c)*d*e^5 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(3/2)*d*e^5 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(5/2)*d*e^5 - 6*a*b^5*sqrt(c)*d^2*e^4 + 48*a^2*b^3*c^(3/2)*d^2*e^4 + 192*a^3*b*c^(5/2)*d^2*e^4 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^4*e^6 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*c*e^6 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*d*e^5 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^2*d*e^5 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^3*sqrt(c)*e^6 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c^(3/2)*e^6 + 3*a^2*b^4*sqrt(c)*d*e^5 - 40*a^3*b^2*c^(3/2)*d*e^5 - 80*a^4*c^(5/2)*d*e^5 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^4*e^6 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*c*e^6 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c^2*e^6 + 16*a^4*b*c^(3/2)*e^6)/((c^2*d^4*e^3 - 2*b*c*d^3*e^4 + b^2*d^2*e^5 + 2*a*c*d^2*e^5 - 2*a*b*d*e^6 + a^2*e^7)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^3)","B",0
1555,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1556,1,10103,0,73.158790," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","\frac{{\left(24 \, b^{4} c^{2} d^{2} e - 192 \, a b^{2} c^{3} d^{2} e + 384 \, a^{2} c^{4} d^{2} e - 24 \, b^{5} c d e^{2} + 192 \, a b^{3} c^{2} d e^{2} - 384 \, a^{2} b c^{3} d e^{2} + 7 \, b^{6} e^{3} - 60 \, a b^{4} c e^{3} + 144 \, a^{2} b^{2} c^{2} e^{3} - 64 \, a^{3} c^{3} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{128 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} c^{\frac{15}{2}} d^{9} e + 4096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{8} d^{10} + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} c^{7} d^{8} e^{2} + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{7} d^{9} e + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{\frac{15}{2}} d^{10} - 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b c^{\frac{13}{2}} d^{8} e^{2} - 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{13}{2}} d^{9} e - 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{15}{2}} d^{9} e + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{7} d^{10} - 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b c^{6} d^{7} e^{3} - 40448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{6} d^{8} e^{2} + 8192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{7} d^{8} e^{2} - 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{6} d^{9} e - 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{7} d^{9} e + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{13}{2}} d^{10} - 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{2} c^{\frac{11}{2}} d^{7} e^{3} + 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a c^{\frac{13}{2}} d^{7} e^{3} - 29440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c^{\frac{11}{2}} d^{8} e^{2} + 66560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{13}{2}} d^{8} e^{2} - 12160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c^{\frac{11}{2}} d^{9} e - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{13}{2}} d^{9} e + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{6} d^{10} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{2} c^{5} d^{6} e^{4} + 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a c^{6} d^{6} e^{4} - 22528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} c^{5} d^{7} e^{3} + 90112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{6} d^{7} e^{3} - 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} c^{5} d^{8} e^{2} + 107520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{6} d^{8} e^{2} + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{7} d^{8} e^{2} - 3200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} c^{5} d^{9} e - 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{6} d^{9} e + 128 \, b^{5} c^{\frac{11}{2}} d^{10} + 143360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{3} c^{\frac{9}{2}} d^{6} e^{4} + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} c^{\frac{9}{2}} d^{7} e^{3} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{11}{2}} d^{7} e^{3} - 71680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{13}{2}} d^{7} e^{3} + 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{5} c^{\frac{9}{2}} d^{8} e^{2} + 71680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c^{\frac{11}{2}} d^{8} e^{2} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{\frac{13}{2}} d^{8} e^{2} - 320 \, b^{6} c^{\frac{9}{2}} d^{9} e - 640 \, a b^{4} c^{\frac{11}{2}} d^{9} e - 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{3} c^{4} d^{5} e^{5} - 122880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b c^{5} d^{5} e^{5} + 133280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{4} c^{4} d^{6} e^{4} - 48384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} c^{5} d^{6} e^{4} - 218624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{6} d^{6} e^{4} + 16640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} c^{4} d^{7} e^{3} - 71680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} c^{5} d^{7} e^{3} - 184320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{6} d^{7} e^{3} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{6} c^{4} d^{8} e^{2} + 21760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} c^{5} d^{8} e^{2} + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{6} d^{8} e^{2} - 131120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{4} c^{\frac{7}{2}} d^{5} e^{5} - 97920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{2} c^{\frac{9}{2}} d^{5} e^{5} - 234240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} c^{\frac{11}{2}} d^{5} e^{5} + 53200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{5} c^{\frac{7}{2}} d^{6} e^{4} + 40320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{3} c^{\frac{9}{2}} d^{6} e^{4} - 295680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b c^{\frac{11}{2}} d^{6} e^{4} + 7520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{6} c^{\frac{7}{2}} d^{7} e^{3} - 58240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{4} c^{\frac{9}{2}} d^{7} e^{3} - 161280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c^{\frac{11}{2}} d^{7} e^{3} - 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{13}{2}} d^{7} e^{3} + 96 \, b^{7} c^{\frac{7}{2}} d^{8} e^{2} + 2496 \, a b^{5} c^{\frac{9}{2}} d^{8} e^{2} + 1280 \, a^{2} b^{3} c^{\frac{11}{2}} d^{8} e^{2} - 1040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{4} c^{3} d^{4} e^{6} + 213120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{2} c^{4} d^{4} e^{6} - 119040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} c^{5} d^{4} e^{6} - 155248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{5} c^{3} d^{5} e^{5} - 33920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{3} c^{4} d^{5} e^{5} - 46848 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b c^{5} d^{5} e^{5} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{6} c^{3} d^{6} e^{4} + 93440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{4} c^{4} d^{6} e^{4} - 42240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} c^{5} d^{6} e^{4} + 92160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} c^{6} d^{6} e^{4} + 1760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{7} c^{3} d^{7} e^{3} - 17280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{5} c^{4} d^{7} e^{3} - 58880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} c^{5} d^{7} e^{3} - 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{6} d^{7} e^{3} - 3240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{4} c^{\frac{5}{2}} d^{3} e^{7} + 25920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{2} c^{\frac{7}{2}} d^{3} e^{7} - 51840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} c^{\frac{9}{2}} d^{3} e^{7} + 37440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{5} c^{\frac{5}{2}} d^{4} e^{6} + 273920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{3} c^{\frac{7}{2}} d^{4} e^{6} + 168960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b c^{\frac{9}{2}} d^{4} e^{6} - 85120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{6} c^{\frac{5}{2}} d^{5} e^{5} - 74000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{4} c^{\frac{7}{2}} d^{5} e^{5} + 90240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{2} c^{\frac{9}{2}} d^{5} e^{5} + 392960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} c^{\frac{11}{2}} d^{5} e^{5} - 7480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{7} c^{\frac{5}{2}} d^{6} e^{4} + 52800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{5} c^{\frac{7}{2}} d^{6} e^{4} + 80000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{3} c^{\frac{9}{2}} d^{6} e^{4} + 174080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b c^{\frac{11}{2}} d^{6} e^{4} + 176 \, b^{8} c^{\frac{5}{2}} d^{7} e^{3} - 1824 \, a b^{6} c^{\frac{7}{2}} d^{7} e^{3} - 7680 \, a^{2} b^{4} c^{\frac{9}{2}} d^{7} e^{3} - 2560 \, a^{3} b^{2} c^{\frac{11}{2}} d^{7} e^{3} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{4} c^{2} d^{2} e^{8} + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b^{2} c^{3} d^{2} e^{8} - 5760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} c^{4} d^{2} e^{8} + 9600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{5} c^{2} d^{3} e^{7} - 117760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{3} c^{3} d^{3} e^{7} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b c^{4} d^{3} e^{7} + 63700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{6} c^{2} d^{4} e^{6} + 236480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{4} c^{3} d^{4} e^{6} - 39360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{2} c^{4} d^{4} e^{6} + 468480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} c^{5} d^{4} e^{6} - 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{7} c^{2} d^{5} e^{5} - 55200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{5} c^{3} d^{5} e^{5} - 152320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{3} c^{4} d^{5} e^{5} + 509440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b c^{5} d^{5} e^{5} - 2540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{8} c^{2} d^{6} e^{4} + 13360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{6} c^{3} d^{6} e^{4} + 33120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{4} c^{4} d^{6} e^{4} + 102400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{2} c^{5} d^{6} e^{4} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} c^{6} d^{6} e^{4} + 3240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{5} c^{\frac{3}{2}} d^{2} e^{8} - 25920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{3} c^{\frac{5}{2}} d^{2} e^{8} + 51840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} b c^{\frac{7}{2}} d^{2} e^{8} + 6370 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{6} c^{\frac{3}{2}} d^{3} e^{7} - 159000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{4} c^{\frac{5}{2}} d^{3} e^{7} - 324000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b^{2} c^{\frac{7}{2}} d^{3} e^{7} + 278400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{3} c^{\frac{9}{2}} d^{3} e^{7} + 39170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{7} c^{\frac{3}{2}} d^{4} e^{6} + 195720 \, {\left(\sqrt{c} x - 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5310 \, a^{3} b^{6} c^{\frac{3}{2}} d^{3} e^{7} - 7840 \, a^{4} b^{4} c^{\frac{5}{2}} d^{3} e^{7} + 25248 \, a^{5} b^{2} c^{\frac{7}{2}} d^{3} e^{7} - 1792 \, a^{6} c^{\frac{9}{2}} d^{3} e^{7} - 896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{6} e^{10} + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{4} c e^{10} + 23040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b^{2} c^{2} e^{10} - 2370 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{7} d e^{9} - 41640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{5} c d e^{9} + 37280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{3} c^{2} d e^{9} - 48000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b c^{3} d e^{9} + 630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{8} d^{2} e^{8} + 6510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{6} c d^{2} e^{8} + 28720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{4} c^{2} d^{2} e^{8} - 68640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{2} c^{3} d^{2} e^{8} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} c^{4} d^{2} e^{8} + 32000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b^{3} c^{\frac{3}{2}} e^{10} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} b c^{\frac{5}{2}} e^{10} - 12990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{6} \sqrt{c} d e^{9} - 1480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{4} c^{\frac{3}{2}} d e^{9} + 31200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{2} c^{\frac{5}{2}} d e^{9} - 17280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} c^{\frac{7}{2}} d e^{9} - 420 \, a^{3} b^{7} \sqrt{c} d^{2} e^{8} + 7080 \, a^{4} b^{5} c^{\frac{3}{2}} d^{2} e^{8} - 3712 \, a^{5} b^{3} c^{\frac{5}{2}} d^{2} e^{8} - 20352 \, a^{6} b c^{\frac{7}{2}} d^{2} e^{8} + 790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{6} e^{10} + 8040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{4} c e^{10} + 5280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b^{2} c^{2} e^{10} - 5760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} c^{3} e^{10} - 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{7} d e^{9} - 8280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{5} c d e^{9} + 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{3} c^{2} d e^{9} + 28800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b c^{3} d e^{9} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{5} \sqrt{c} e^{10} - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{3} c^{\frac{3}{2}} e^{10} + 105 \, a^{4} b^{6} \sqrt{c} d e^{9} - 4740 \, a^{5} b^{4} c^{\frac{3}{2}} d e^{9} + 8304 \, a^{6} b^{2} c^{\frac{5}{2}} d e^{9} + 5184 \, a^{7} c^{\frac{7}{2}} d e^{9} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{6} e^{10} + 2940 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{4} c e^{10} - 5520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b^{2} c^{2} e^{10} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} c^{3} e^{10} + 1280 \, a^{6} b^{3} c^{\frac{3}{2}} e^{10} - 3072 \, a^{7} b c^{\frac{5}{2}} e^{10}}{1920 \, {\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 \, a c^{3} d^{6} e^{5} - 4 \, b^{3} c d^{5} e^{6} - 12 \, a b c^{2} d^{5} e^{6} + b^{4} d^{4} e^{7} + 12 \, a b^{2} c d^{4} e^{7} + 6 \, a^{2} c^{2} d^{4} e^{7} - 4 \, a b^{3} d^{3} e^{8} - 12 \, a^{2} b c d^{3} e^{8} + 6 \, a^{2} b^{2} d^{2} e^{9} + 4 \, a^{3} c d^{2} e^{9} - 4 \, a^{3} b d e^{10} + a^{4} e^{11}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{5}}"," ",0,"1/128*(24*b^4*c^2*d^2*e - 192*a*b^2*c^3*d^2*e + 384*a^2*c^4*d^2*e - 24*b^5*c*d*e^2 + 192*a*b^3*c^2*d*e^2 - 384*a^2*b*c^3*d*e^2 + 7*b^6*e^3 - 60*a*b^4*c*e^3 + 144*a^2*b^2*c^2*e^3 - 64*a^3*c^3*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/1920*(10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*c^(15/2)*d^9*e + 4096*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^8*d^10 + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*c^7*d^8*e^2 + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^7*d^9*e + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^(15/2)*d^10 - 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b*c^(13/2)*d^8*e^2 - 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(13/2)*d^9*e - 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(15/2)*d^9*e + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^7*d^10 - 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b*c^6*d^7*e^3 - 40448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^6*d^8*e^2 + 8192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^7*d^8*e^2 - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^6*d^9*e - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^7*d^9*e + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(13/2)*d^10 - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^2*c^(11/2)*d^7*e^3 + 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*c^(13/2)*d^7*e^3 - 29440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c^(11/2)*d^8*e^2 + 66560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(13/2)*d^8*e^2 - 12160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(11/2)*d^9*e - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(13/2)*d^9*e + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^6*d^10 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^2*c^5*d^6*e^4 + 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*c^6*d^6*e^4 - 22528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*c^5*d^7*e^3 + 90112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^6*d^7*e^3 - 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c^5*d^8*e^2 + 107520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^6*d^8*e^2 + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^7*d^8*e^2 - 3200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c^5*d^9*e - 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^6*d^9*e + 128*b^5*c^(11/2)*d^10 + 143360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^3*c^(9/2)*d^6*e^4 + 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*c^(9/2)*d^7*e^3 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(11/2)*d^7*e^3 - 71680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(13/2)*d^7*e^3 + 2240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*c^(9/2)*d^8*e^2 + 71680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c^(11/2)*d^8*e^2 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^(13/2)*d^8*e^2 - 320*b^6*c^(9/2)*d^9*e - 640*a*b^4*c^(11/2)*d^9*e - 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^3*c^4*d^5*e^5 - 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b*c^5*d^5*e^5 + 133280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^4*c^4*d^6*e^4 - 48384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*c^5*d^6*e^4 - 218624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^6*d^6*e^4 + 16640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*c^4*d^7*e^3 - 71680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c^5*d^7*e^3 - 184320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^6*d^7*e^3 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*c^4*d^8*e^2 + 21760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c^5*d^8*e^2 + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^6*d^8*e^2 - 131120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^4*c^(7/2)*d^5*e^5 - 97920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^2*c^(9/2)*d^5*e^5 - 234240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*c^(11/2)*d^5*e^5 + 53200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^5*c^(7/2)*d^6*e^4 + 40320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^3*c^(9/2)*d^6*e^4 - 295680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c^(11/2)*d^6*e^4 + 7520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^6*c^(7/2)*d^7*e^3 - 58240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*c^(9/2)*d^7*e^3 - 161280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(11/2)*d^7*e^3 - 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(13/2)*d^7*e^3 + 96*b^7*c^(7/2)*d^8*e^2 + 2496*a*b^5*c^(9/2)*d^8*e^2 + 1280*a^2*b^3*c^(11/2)*d^8*e^2 - 1040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^4*c^3*d^4*e^6 + 213120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^2*c^4*d^4*e^6 - 119040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*c^5*d^4*e^6 - 155248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^5*c^3*d^5*e^5 - 33920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^3*c^4*d^5*e^5 - 46848*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*c^5*d^5*e^5 + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^6*c^3*d^6*e^4 + 93440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^4*c^4*d^6*e^4 - 42240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*c^5*d^6*e^4 + 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*c^6*d^6*e^4 + 1760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^7*c^3*d^7*e^3 - 17280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*c^4*d^7*e^3 - 58880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c^5*d^7*e^3 - 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^6*d^7*e^3 - 3240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^4*c^(5/2)*d^3*e^7 + 25920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^2*c^(7/2)*d^3*e^7 - 51840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*c^(9/2)*d^3*e^7 + 37440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^5*c^(5/2)*d^4*e^6 + 273920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^3*c^(7/2)*d^4*e^6 + 168960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b*c^(9/2)*d^4*e^6 - 85120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^6*c^(5/2)*d^5*e^5 - 74000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^4*c^(7/2)*d^5*e^5 + 90240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^2*c^(9/2)*d^5*e^5 + 392960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*c^(11/2)*d^5*e^5 - 7480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^7*c^(5/2)*d^6*e^4 + 52800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^5*c^(7/2)*d^6*e^4 + 80000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^3*c^(9/2)*d^6*e^4 + 174080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c^(11/2)*d^6*e^4 + 176*b^8*c^(5/2)*d^7*e^3 - 1824*a*b^6*c^(7/2)*d^7*e^3 - 7680*a^2*b^4*c^(9/2)*d^7*e^3 - 2560*a^3*b^2*c^(11/2)*d^7*e^3 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^4*c^2*d^2*e^8 + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^2*c^3*d^2*e^8 - 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*c^4*d^2*e^8 + 9600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^5*c^2*d^3*e^7 - 117760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*c^3*d^3*e^7 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c^4*d^3*e^7 + 63700*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^6*c^2*d^4*e^6 + 236480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^4*c^3*d^4*e^6 - 39360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^2*c^4*d^4*e^6 + 468480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*c^5*d^4*e^6 - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^7*c^2*d^5*e^5 - 55200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^5*c^3*d^5*e^5 - 152320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^3*c^4*d^5*e^5 + 509440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b*c^5*d^5*e^5 - 2540*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^8*c^2*d^6*e^4 + 13360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^6*c^3*d^6*e^4 + 33120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^4*c^4*d^6*e^4 + 102400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*c^5*d^6*e^4 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c^6*d^6*e^4 + 3240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^5*c^(3/2)*d^2*e^8 - 25920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^3*c^(5/2)*d^2*e^8 + 51840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b*c^(7/2)*d^2*e^8 + 6370*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^6*c^(3/2)*d^3*e^7 - 159000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^4*c^(5/2)*d^3*e^7 - 324000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^2*c^(7/2)*d^3*e^7 + 278400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*c^(9/2)*d^3*e^7 + 39170*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^7*c^(3/2)*d^4*e^6 + 195720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^5*c^(5/2)*d^4*e^6 - 202400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^3*c^(7/2)*d^4*e^6 + 188800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b*c^(9/2)*d^4*e^6 - 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^8*c^(3/2)*d^5*e^5 - 8720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^6*c^(5/2)*d^5*e^5 - 188880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^4*c^(7/2)*d^5*e^5 + 191360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^2*c^(9/2)*d^5*e^5 - 70400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*c^(11/2)*d^5*e^5 - 290*b^9*c^(3/2)*d^6*e^4 + 1448*a*b^7*c^(5/2)*d^6*e^4 + 2928*a^2*b^5*c^(7/2)*d^6*e^4 + 19200*a^3*b^3*c^(9/2)*d^6*e^4 + 1280*a^4*b*c^(11/2)*d^6*e^4 + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^5*c*d*e^9 - 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^3*c^2*d*e^9 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b*c^3*d*e^9 - 1610*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^6*c*d^2*e^8 + 16440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^4*c^2*d^2*e^8 + 7200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^2*c^3*d^2*e^8 + 97920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*c^4*d^2*e^8 - 5426*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^7*c*d^3*e^7 - 140616*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^5*c^2*d^3*e^7 - 246880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*c^3*d^3*e^7 - 101760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b*c^4*d^3*e^7 + 10930*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^8*c*d^4*e^6 + 84200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^6*c^2*d^4*e^6 + 24240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^4*c^3*d^4*e^6 - 80640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^2*c^4*d^4*e^6 - 367360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*c^5*d^4*e^6 + 690*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^9*c*d^5*e^5 + 1840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^7*c^2*d^5*e^5 - 61680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^5*c^3*d^5*e^5 + 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^3*c^4*d^5*e^5 - 78080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b*c^5*d^5*e^5 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^6*sqrt(c)*d*e^9 + 8100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^4*c^(3/2)*d*e^9 - 19440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^2*c^(5/2)*d*e^9 + 8640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*c^(7/2)*d*e^9 - 3430*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^7*sqrt(c)*d^2*e^8 + 17640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^5*c^(3/2)*d^2*e^8 + 207840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^3*c^(5/2)*d^2*e^8 - 74880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b*c^(7/2)*d^2*e^8 - 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^8*sqrt(c)*d^3*e^7 - 112130*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^6*c^(3/2)*d^3*e^7 - 70200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^4*c^(5/2)*d^3*e^7 + 45600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^2*c^(7/2)*d^3*e^7 - 361600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*c^(9/2)*d^3*e^7 + 1470*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^9*sqrt(c)*d^4*e^6 + 8780*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^7*c^(3/2)*d^4*e^6 + 86640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^5*c^(5/2)*d^4*e^6 + 50240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^3*c^(7/2)*d^4*e^6 - 375040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b*c^(9/2)*d^4*e^6 + 105*b^10*sqrt(c)*d^5*e^5 + 330*a*b^8*c^(3/2)*d^5*e^5 - 6064*a^2*b^6*c^(5/2)*d^5*e^5 - 2160*a^3*b^4*c^(7/2)*d^5*e^5 - 21120*a^4*b^2*c^(9/2)*d^5*e^5 - 256*a^5*c^(11/2)*d^5*e^5 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^6*e^10 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^4*c*e^10 - 2160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^2*c^2*e^10 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*c^3*e^10 - 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^7*d*e^9 + 2520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^5*c*d*e^9 + 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^3*c^2*d*e^9 - 63360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b*c^3*d*e^9 - 896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^8*d^2*e^8 + 10034*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^6*c*d^2*e^8 + 203640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^4*c^2*d^2*e^8 + 119520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^2*c^3*d^2*e^8 - 155520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*c^4*d^2*e^8 - 790*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^9*d^3*e^7 - 47420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^7*c*d^3*e^7 - 60720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^5*c^2*d^3*e^7 + 76480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^3*c^3*d^3*e^7 + 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c^4*d^3*e^7 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^10*d^4*e^6 - 2610*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^8*c*d^4*e^6 + 25060*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^6*c^2*d^4*e^6 + 60320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^4*c^3*d^4*e^6 - 112320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^2*c^4*d^4*e^6 + 17920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*c^5*d^4*e^6 + 3430*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^6*sqrt(c)*d*e^9 - 29400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^4*c^(3/2)*d*e^9 - 52320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^2*c^(5/2)*d*e^9 - 21120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*c^(7/2)*d*e^9 + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^7*sqrt(c)*d^2*e^8 + 130560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^5*c^(3/2)*d^2*e^8 - 25600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^3*c^(5/2)*d^2*e^8 + 153600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b*c^(7/2)*d^2*e^8 - 8250*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^8*sqrt(c)*d^3*e^7 - 22690*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^6*c^(3/2)*d^3*e^7 - 85480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^4*c^(5/2)*d^3*e^7 + 178080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*c^(7/2)*d^3*e^7 + 164480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*c^(9/2)*d^3*e^7 - 420*a*b^9*sqrt(c)*d^4*e^6 + 1650*a^2*b^7*c^(3/2)*d^4*e^6 + 10760*a^3*b^5*c^(5/2)*d^4*e^6 - 9120*a^4*b^3*c^(7/2)*d^4*e^6 + 9600*a^5*b*c^(9/2)*d^4*e^6 + 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^6*e^10 - 4200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^4*c*e^10 + 10080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^2*c^2*e^10 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*c^3*e^10 + 1792*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^7*d*e^9 - 12288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^5*c*d*e^9 - 153600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^3*c^2*d*e^9 + 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*c^3*d*e^9 + 2370*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^8*d^2*e^8 + 70090*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^6*c*d^2*e^8 - 45560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^4*c^2*d^2*e^8 + 8160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^2*c^3*d^2*e^8 + 109440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*c^4*d^2*e^8 - 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^9*d^3*e^7 + 750*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^7*c*d^3*e^7 - 52040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^5*c^2*d^3*e^7 + 27040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^3*c^3*d^3*e^7 + 128640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b*c^4*d^3*e^7 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b*c^(5/2)*e^10 - 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^6*sqrt(c)*d*e^9 - 89600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^4*c^(3/2)*d*e^9 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*c^(7/2)*d*e^9 + 15930*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^7*sqrt(c)*d^2*e^8 + 18440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^5*c^(3/2)*d^2*e^8 - 16160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^3*c^(5/2)*d^2*e^8 - 82560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b*c^(7/2)*d^2*e^8 + 630*a^2*b^8*sqrt(c)*d^3*e^7 - 5310*a^3*b^6*c^(3/2)*d^3*e^7 - 7840*a^4*b^4*c^(5/2)*d^3*e^7 + 25248*a^5*b^2*c^(7/2)*d^3*e^7 - 1792*a^6*c^(9/2)*d^3*e^7 - 896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^6*e^10 + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^4*c*e^10 + 23040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^2*c^2*e^10 - 2370*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^7*d*e^9 - 41640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^5*c*d*e^9 + 37280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^3*c^2*d*e^9 - 48000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b*c^3*d*e^9 + 630*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^8*d^2*e^8 + 6510*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^6*c*d^2*e^8 + 28720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^4*c^2*d^2*e^8 - 68640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^2*c^3*d^2*e^8 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*c^4*d^2*e^8 + 32000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^3*c^(3/2)*e^10 - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b*c^(5/2)*e^10 - 12990*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^6*sqrt(c)*d*e^9 - 1480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^4*c^(3/2)*d*e^9 + 31200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^2*c^(5/2)*d*e^9 - 17280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*c^(7/2)*d*e^9 - 420*a^3*b^7*sqrt(c)*d^2*e^8 + 7080*a^4*b^5*c^(3/2)*d^2*e^8 - 3712*a^5*b^3*c^(5/2)*d^2*e^8 - 20352*a^6*b*c^(7/2)*d^2*e^8 + 790*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^6*e^10 + 8040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^4*c*e^10 + 5280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^2*c^2*e^10 - 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*c^3*e^10 - 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^7*d*e^9 - 8280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^5*c*d*e^9 + 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^3*c^2*d*e^9 + 28800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*c^3*d*e^9 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^5*sqrt(c)*e^10 - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^3*c^(3/2)*e^10 + 105*a^4*b^6*sqrt(c)*d*e^9 - 4740*a^5*b^4*c^(3/2)*d*e^9 + 8304*a^6*b^2*c^(5/2)*d*e^9 + 5184*a^7*c^(7/2)*d*e^9 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^6*e^10 + 2940*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^4*c*e^10 - 5520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^2*c^2*e^10 - 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*c^3*e^10 + 1280*a^6*b^3*c^(3/2)*e^10 - 3072*a^7*b*c^(5/2)*e^10)/((c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 + 6*b^2*c^2*d^6*e^5 + 4*a*c^3*d^6*e^5 - 4*b^3*c*d^5*e^6 - 12*a*b*c^2*d^5*e^6 + b^4*d^4*e^7 + 12*a*b^2*c*d^4*e^7 + 6*a^2*c^2*d^4*e^7 - 4*a*b^3*d^3*e^8 - 12*a^2*b*c*d^3*e^8 + 6*a^2*b^2*d^2*e^9 + 4*a^3*c*d^2*e^9 - 4*a^3*b*d*e^10 + a^4*e^11)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^5)","B",0
1557,1,856,0,0.270802," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{286720} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, c^{2} x e^{3} + \frac{48 \, c^{9} d e^{2} + 25 \, b c^{8} e^{3}}{c^{7}}\right)} x + \frac{224 \, c^{9} d^{2} e + 352 \, b c^{8} d e^{2} + 41 \, b^{2} c^{7} e^{3} + 84 \, a c^{8} e^{3}}{c^{7}}\right)} x + \frac{896 \, c^{9} d^{3} + 4256 \, b c^{8} d^{2} e + 1504 \, b^{2} c^{7} d e^{2} + 3072 \, a c^{8} d e^{2} - 3 \, b^{3} c^{6} e^{3} + 564 \, a b c^{7} e^{3}}{c^{7}}\right)} x + \frac{14336 \, b c^{8} d^{3} + 15456 \, b^{2} c^{7} d^{2} e + 31360 \, a c^{8} d^{2} e - 96 \, b^{3} c^{6} d e^{2} + 17792 \, a b c^{7} d e^{2} + 27 \, b^{4} c^{5} e^{3} - 216 \, a b^{2} c^{6} e^{3} + 560 \, a^{2} c^{7} e^{3}}{c^{7}}\right)} x + \frac{14336 \, b^{2} c^{7} d^{3} + 28672 \, a c^{8} d^{3} - 224 \, b^{3} c^{6} d^{2} e + 51072 \, a b c^{7} d^{2} e + 224 \, b^{4} c^{5} d e^{2} - 1920 \, a b^{2} c^{6} d e^{2} + 6144 \, a^{2} c^{7} d e^{2} - 63 \, b^{5} c^{4} e^{3} + 568 \, a b^{3} c^{5} e^{3} - 1392 \, a^{2} b c^{6} e^{3}}{c^{7}}\right)} x + \frac{114688 \, a b c^{7} d^{3} + 1120 \, b^{4} c^{5} d^{2} e - 10752 \, a b^{2} c^{6} d^{2} e + 53760 \, a^{2} c^{7} d^{2} e - 1120 \, b^{5} c^{4} d e^{2} + 10752 \, a b^{3} c^{5} d e^{2} - 29184 \, a^{2} b c^{6} d e^{2} + 315 \, b^{6} c^{3} e^{3} - 3164 \, a b^{4} c^{4} e^{3} + 9552 \, a^{2} b^{2} c^{5} e^{3} - 6720 \, a^{3} c^{6} e^{3}}{c^{7}}\right)} x + \frac{114688 \, a^{2} c^{7} d^{3} - 3360 \, b^{5} c^{4} d^{2} e + 35840 \, a b^{3} c^{5} d^{2} e - 118272 \, a^{2} b c^{6} d^{2} e + 3360 \, b^{6} c^{3} d e^{2} - 35840 \, a b^{4} c^{4} d e^{2} + 118272 \, a^{2} b^{2} c^{5} d e^{2} - 98304 \, a^{3} c^{6} d e^{2} - 945 \, b^{7} c^{2} e^{3} + 10500 \, a b^{5} c^{3} e^{3} - 37744 \, a^{2} b^{3} c^{4} e^{3} + 42432 \, a^{3} b c^{5} e^{3}}{c^{7}}\right)} - \frac{3 \, {\left(32 \, b^{6} c^{2} d^{2} e - 384 \, a b^{4} c^{3} d^{2} e + 1536 \, a^{2} b^{2} c^{4} d^{2} e - 2048 \, a^{3} c^{5} d^{2} e - 32 \, b^{7} c d e^{2} + 384 \, a b^{5} c^{2} d e^{2} - 1536 \, a^{2} b^{3} c^{3} d e^{2} + 2048 \, a^{3} b c^{4} d e^{2} + 9 \, b^{8} e^{3} - 112 \, a b^{6} c e^{3} + 480 \, a^{2} b^{4} c^{2} e^{3} - 768 \, a^{3} b^{2} c^{3} e^{3} + 256 \, a^{4} c^{4} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16384 \, c^{\frac{11}{2}}}"," ",0,"1/286720*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(4*(14*c^2*x*e^3 + (48*c^9*d*e^2 + 25*b*c^8*e^3)/c^7)*x + (224*c^9*d^2*e + 352*b*c^8*d*e^2 + 41*b^2*c^7*e^3 + 84*a*c^8*e^3)/c^7)*x + (896*c^9*d^3 + 4256*b*c^8*d^2*e + 1504*b^2*c^7*d*e^2 + 3072*a*c^8*d*e^2 - 3*b^3*c^6*e^3 + 564*a*b*c^7*e^3)/c^7)*x + (14336*b*c^8*d^3 + 15456*b^2*c^7*d^2*e + 31360*a*c^8*d^2*e - 96*b^3*c^6*d*e^2 + 17792*a*b*c^7*d*e^2 + 27*b^4*c^5*e^3 - 216*a*b^2*c^6*e^3 + 560*a^2*c^7*e^3)/c^7)*x + (14336*b^2*c^7*d^3 + 28672*a*c^8*d^3 - 224*b^3*c^6*d^2*e + 51072*a*b*c^7*d^2*e + 224*b^4*c^5*d*e^2 - 1920*a*b^2*c^6*d*e^2 + 6144*a^2*c^7*d*e^2 - 63*b^5*c^4*e^3 + 568*a*b^3*c^5*e^3 - 1392*a^2*b*c^6*e^3)/c^7)*x + (114688*a*b*c^7*d^3 + 1120*b^4*c^5*d^2*e - 10752*a*b^2*c^6*d^2*e + 53760*a^2*c^7*d^2*e - 1120*b^5*c^4*d*e^2 + 10752*a*b^3*c^5*d*e^2 - 29184*a^2*b*c^6*d*e^2 + 315*b^6*c^3*e^3 - 3164*a*b^4*c^4*e^3 + 9552*a^2*b^2*c^5*e^3 - 6720*a^3*c^6*e^3)/c^7)*x + (114688*a^2*c^7*d^3 - 3360*b^5*c^4*d^2*e + 35840*a*b^3*c^5*d^2*e - 118272*a^2*b*c^6*d^2*e + 3360*b^6*c^3*d*e^2 - 35840*a*b^4*c^4*d*e^2 + 118272*a^2*b^2*c^5*d*e^2 - 98304*a^3*c^6*d*e^2 - 945*b^7*c^2*e^3 + 10500*a*b^5*c^3*e^3 - 37744*a^2*b^3*c^4*e^3 + 42432*a^3*b*c^5*e^3)/c^7) - 3/16384*(32*b^6*c^2*d^2*e - 384*a*b^4*c^3*d^2*e + 1536*a^2*b^2*c^4*d^2*e - 2048*a^3*c^5*d^2*e - 32*b^7*c*d*e^2 + 384*a*b^5*c^2*d*e^2 - 1536*a^2*b^3*c^3*d*e^2 + 2048*a^3*b*c^4*d*e^2 + 9*b^8*e^3 - 112*a*b^6*c*e^3 + 480*a^2*b^4*c^2*e^3 - 768*a^3*b^2*c^3*e^3 + 256*a^4*c^4*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","B",0
1558,1,534,0,0.251424," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{26880} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(6 \, c^{2} x e^{2} + \frac{14 \, c^{8} d e + 11 \, b c^{7} e^{2}}{c^{6}}\right)} x + \frac{84 \, c^{8} d^{2} + 266 \, b c^{7} d e + 47 \, b^{2} c^{6} e^{2} + 96 \, a c^{7} e^{2}}{c^{6}}\right)} x + \frac{1344 \, b c^{7} d^{2} + 966 \, b^{2} c^{6} d e + 1960 \, a c^{7} d e - 3 \, b^{3} c^{5} e^{2} + 556 \, a b c^{6} e^{2}}{c^{6}}\right)} x + \frac{1344 \, b^{2} c^{6} d^{2} + 2688 \, a c^{7} d^{2} - 14 \, b^{3} c^{5} d e + 3192 \, a b c^{6} d e + 7 \, b^{4} c^{4} e^{2} - 60 \, a b^{2} c^{5} e^{2} + 192 \, a^{2} c^{6} e^{2}}{c^{6}}\right)} x + \frac{10752 \, a b c^{6} d^{2} + 70 \, b^{4} c^{4} d e - 672 \, a b^{2} c^{5} d e + 3360 \, a^{2} c^{6} d e - 35 \, b^{5} c^{3} e^{2} + 336 \, a b^{3} c^{4} e^{2} - 912 \, a^{2} b c^{5} e^{2}}{c^{6}}\right)} x + \frac{10752 \, a^{2} c^{6} d^{2} - 210 \, b^{5} c^{3} d e + 2240 \, a b^{3} c^{4} d e - 7392 \, a^{2} b c^{5} d e + 105 \, b^{6} c^{2} e^{2} - 1120 \, a b^{4} c^{3} e^{2} + 3696 \, a^{2} b^{2} c^{4} e^{2} - 3072 \, a^{3} c^{5} e^{2}}{c^{6}}\right)} - \frac{{\left(2 \, b^{6} c d e - 24 \, a b^{4} c^{2} d e + 96 \, a^{2} b^{2} c^{3} d e - 128 \, a^{3} c^{4} d e - b^{7} e^{2} + 12 \, a b^{5} c e^{2} - 48 \, a^{2} b^{3} c^{2} e^{2} + 64 \, a^{3} b c^{3} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{512 \, c^{\frac{9}{2}}}"," ",0,"1/26880*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(6*c^2*x*e^2 + (14*c^8*d*e + 11*b*c^7*e^2)/c^6)*x + (84*c^8*d^2 + 266*b*c^7*d*e + 47*b^2*c^6*e^2 + 96*a*c^7*e^2)/c^6)*x + (1344*b*c^7*d^2 + 966*b^2*c^6*d*e + 1960*a*c^7*d*e - 3*b^3*c^5*e^2 + 556*a*b*c^6*e^2)/c^6)*x + (1344*b^2*c^6*d^2 + 2688*a*c^7*d^2 - 14*b^3*c^5*d*e + 3192*a*b*c^6*d*e + 7*b^4*c^4*e^2 - 60*a*b^2*c^5*e^2 + 192*a^2*c^6*e^2)/c^6)*x + (10752*a*b*c^6*d^2 + 70*b^4*c^4*d*e - 672*a*b^2*c^5*d*e + 3360*a^2*c^6*d*e - 35*b^5*c^3*e^2 + 336*a*b^3*c^4*e^2 - 912*a^2*b*c^5*e^2)/c^6)*x + (10752*a^2*c^6*d^2 - 210*b^5*c^3*d*e + 2240*a*b^3*c^4*d*e - 7392*a^2*b*c^5*d*e + 105*b^6*c^2*e^2 - 1120*a*b^4*c^3*e^2 + 3696*a^2*b^2*c^4*e^2 - 3072*a^3*c^5*e^2)/c^6) - 1/512*(2*b^6*c*d*e - 24*a*b^4*c^2*d*e + 96*a^2*b^2*c^3*d*e - 128*a^3*c^4*d*e - b^7*e^2 + 12*a*b^5*c*e^2 - 48*a^2*b^3*c^2*e^2 + 64*a^3*b*c^3*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","B",0
1559,1,294,0,0.257699," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{3840} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c^{2} x e + \frac{12 \, c^{7} d + 19 \, b c^{6} e}{c^{5}}\right)} x + \frac{192 \, b c^{6} d + 69 \, b^{2} c^{5} e + 140 \, a c^{6} e}{c^{5}}\right)} x + \frac{192 \, b^{2} c^{5} d + 384 \, a c^{6} d - b^{3} c^{4} e + 228 \, a b c^{5} e}{c^{5}}\right)} x + \frac{1536 \, a b c^{5} d + 5 \, b^{4} c^{3} e - 48 \, a b^{2} c^{4} e + 240 \, a^{2} c^{5} e}{c^{5}}\right)} x + \frac{1536 \, a^{2} c^{5} d - 15 \, b^{5} c^{2} e + 160 \, a b^{3} c^{3} e - 528 \, a^{2} b c^{4} e}{c^{5}}\right)} - \frac{{\left(b^{6} e - 12 \, a b^{4} c e + 48 \, a^{2} b^{2} c^{2} e - 64 \, a^{3} c^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{512 \, c^{\frac{7}{2}}}"," ",0,"1/3840*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*c^2*x*e + (12*c^7*d + 19*b*c^6*e)/c^5)*x + (192*b*c^6*d + 69*b^2*c^5*e + 140*a*c^6*e)/c^5)*x + (192*b^2*c^5*d + 384*a*c^6*d - b^3*c^4*e + 228*a*b*c^5*e)/c^5)*x + (1536*a*b*c^5*d + 5*b^4*c^3*e - 48*a*b^2*c^4*e + 240*a^2*c^5*e)/c^5)*x + (1536*a^2*c^5*d - 15*b^5*c^2*e + 160*a*b^3*c^3*e - 528*a^2*b*c^4*e)/c^5) - 1/512*(b^6*e - 12*a*b^4*c*e + 48*a^2*b^2*c^2*e - 64*a^3*c^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","B",0
1560,1,14,0,0.188910," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}"," ",0,"2/5*(c*x^2 + b*x + a)^(5/2)","A",0
1561,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1562,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1563,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.82Unable to divide, perhaps due to rounding error%%%{1,[6,0,8,0,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,7,0,1]%%%}+%%%{-3,[4,1,8,0,0]%%%}+%%%{3,[4,0,7,1,1]%%%}+%%%{%%%{12,[1]%%%},[4,0,6,0,2]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,7,0,1]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,6,1,2]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,5,0,3]%%%}+%%%{3,[2,2,8,0,0]%%%}+%%%{-6,[2,1,7,1,1]%%%}+%%%{%%%{-12,[1]%%%},[2,1,6,0,2]%%%}+%%%{3,[2,0,6,2,2]%%%}+%%%{%%%{12,[1]%%%},[2,0,5,1,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,7,0,1]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,6,1,2]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,5,2,3]%%%}+%%%{-1,[0,3,8,0,0]%%%}+%%%{3,[0,2,7,1,1]%%%}+%%%{-3,[0,1,6,2,2]%%%}+%%%{1,[0,0,5,3,3]%%%} / %%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,3,0,0]%%%}+%%%{%%%{-6,[2]%%%},[5,0,2,0,1]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,3,0,0]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,1,1]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,0,2]%%%}+%%%{%%%{12,[2]%%%},[3,1,2,0,1]%%%}+%%%{%%%{-12,[2]%%%},[3,0,1,1,2]%%%}+%%%{%%%{-8,[3]%%%},[3,0,0,0,3]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,3,0,0]%%%}+%%%{%%{[%%%{-6,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,2,1,1]%%%}+%%%{%%{[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,1,0,2]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,2,2]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,1,3]%%%}+%%%{%%%{-6,[2]%%%},[1,2,2,0,1]%%%}+%%%{%%%{12,[2]%%%},[1,1,1,1,2]%%%}+%%%{%%%{-6,[2]%%%},[1,0,0,2,3]%%%}+%%%{%%{[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,3,0,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,2,1,1]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,1,2,2]%%%}+%%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,3,3]%%%} Error: Bad Argument Value","F(-2)",0
1564,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 42.28Unable to divide, perhaps due to rounding error%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,9,0,0]%%%}+%%%{%%%{8,[1]%%%},[7,0,8,1,0]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,1,8,1,0]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,9,0,1]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,7,2,0]%%%}+%%%{%%%{24,[1]%%%},[5,1,7,2,0]%%%}+%%%{%%%{-24,[1]%%%},[5,0,8,1,1]%%%}+%%%{%%%{32,[2]%%%},[5,0,6,3,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,2,7,2,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,8,1,1]%%%}+%%%{%%{[%%%{-48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,6,3,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,9,0,2]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,7,2,1]%%%}+%%%{%%{[%%%{-16,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,5,4,0]%%%}+%%%{%%%{24,[1]%%%},[3,2,6,3,0]%%%}+%%%{%%%{-48,[1]%%%},[3,1,7,2,1]%%%}+%%%{%%%{32,[2]%%%},[3,1,5,4,0]%%%}+%%%{%%%{24,[1]%%%},[3,0,8,1,2]%%%}+%%%{%%%{-32,[2]%%%},[3,0,6,3,1]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,3,6,3,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,7,2,1]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,5,4,0]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,8,1,2]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,6,3,1]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,9,0,3]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,7,2,2]%%%}+%%%{%%%{8,[1]%%%},[1,3,5,4,0]%%%}+%%%{%%%{-24,[1]%%%},[1,2,6,3,1]%%%}+%%%{%%%{24,[1]%%%},[1,1,7,2,2]%%%}+%%%{%%%{-8,[1]%%%},[1,0,8,1,3]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,4,5,4,0]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,6,3,1]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,7,2,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,8,1,3]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,9,0,4]%%%} / %%%{%%%{1,[2]%%%},[8,0,4,0,0]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,3,1,0]%%%}+%%%{%%%{4,[2]%%%},[6,1,3,1,0]%%%}+%%%{%%%{-4,[2]%%%},[6,0,4,0,1]%%%}+%%%{%%%{24,[3]%%%},[6,0,2,2,0]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,2,2,0]%%%}+%%%{%%{poly1[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,3,1,1]%%%}+%%%{%%{poly1[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,1,3,0]%%%}+%%%{%%%{6,[2]%%%},[4,2,2,2,0]%%%}+%%%{%%%{-12,[2]%%%},[4,1,3,1,1]%%%}+%%%{%%%{48,[3]%%%},[4,1,1,3,0]%%%}+%%%{%%%{6,[2]%%%},[4,0,4,0,2]%%%}+%%%{%%%{-48,[3]%%%},[4,0,2,2,1]%%%}+%%%{%%%{16,[4]%%%},[4,0,0,4,0]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,1,3,0]%%%}+%%%{%%{[%%%{48,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,2,2,1]%%%}+%%%{%%{[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,4,0]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,3,1,2]%%%}+%%%{%%{poly1[%%%{32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,3,1]%%%}+%%%{%%%{4,[2]%%%},[2,3,1,3,0]%%%}+%%%{%%%{-12,[2]%%%},[2,2,2,2,1]%%%}+%%%{%%%{24,[3]%%%},[2,2,0,4,0]%%%}+%%%{%%%{12,[2]%%%},[2,1,3,1,2]%%%}+%%%{%%%{-48,[3]%%%},[2,1,1,3,1]%%%}+%%%{%%%{-4,[2]%%%},[2,0,4,0,3]%%%}+%%%{%%%{24,[3]%%%},[2,0,2,2,2]%%%}+%%%{%%{[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,0,4,0]%%%}+%%%{%%{poly1[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,1,3,1]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,2,2,2]%%%}+%%%{%%{poly1[%%%{8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,1,3]%%%}+%%%{%%%{1,[2]%%%},[0,4,0,4,0]%%%}+%%%{%%%{-4,[2]%%%},[0,3,1,3,1]%%%}+%%%{%%%{6,[2]%%%},[0,2,2,2,2]%%%}+%%%{%%%{-4,[2]%%%},[0,1,3,1,3]%%%}+%%%{%%%{1,[2]%%%},[0,0,4,0,4]%%%} Error: Bad Argument Value","F(-2)",0
1565,1,1302,0,0.320452," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{6881280} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, {\left(6 \, c^{3} x e^{3} + \frac{20 \, c^{12} d e^{2} + 17 \, b c^{11} e^{3}}{c^{9}}\right)} x + \frac{360 \, c^{12} d^{2} e + 920 \, b c^{11} d e^{2} + 251 \, b^{2} c^{10} e^{3} + 252 \, a c^{11} e^{3}}{c^{9}}\right)} x + \frac{1920 \, c^{12} d^{3} + 14760 \, b c^{11} d^{2} e + 12120 \, b^{2} c^{10} d e^{2} + 12160 \, a c^{11} d e^{2} + 1035 \, b^{3} c^{9} e^{3} + 6268 \, a b c^{10} e^{3}}{c^{9}}\right)} x + \frac{23040 \, b c^{11} d^{3} + 57000 \, b^{2} c^{10} d^{2} e + 57120 \, a c^{11} d^{2} e + 14680 \, b^{3} c^{9} d e^{2} + 88800 \, a b c^{10} d e^{2} - 5 \, b^{4} c^{8} e^{3} + 10200 \, a b^{2} c^{9} e^{3} + 10416 \, a^{2} c^{10} e^{3}}{c^{9}}\right)} x + \frac{46080 \, b^{2} c^{10} d^{3} + 46080 \, a c^{11} d^{3} + 35880 \, b^{3} c^{9} d^{2} e + 216480 \, a b c^{10} d^{2} e - 40 \, b^{4} c^{8} d e^{2} + 75360 \, a b^{2} c^{9} d e^{2} + 76800 \, a^{2} c^{10} d e^{2} + 11 \, b^{5} c^{7} e^{3} - 120 \, a b^{3} c^{8} e^{3} + 13680 \, a^{2} b c^{9} e^{3}}{c^{9}}\right)} x + \frac{122880 \, b^{3} c^{9} d^{3} + 737280 \, a b c^{10} d^{3} - 360 \, b^{4} c^{8} d^{2} e + 782400 \, a b^{2} c^{9} d^{2} e + 792960 \, a^{2} c^{10} d^{2} e + 360 \, b^{5} c^{7} d e^{2} - 4160 \, a b^{3} c^{8} d e^{2} + 435840 \, a^{2} b c^{9} d e^{2} - 99 \, b^{6} c^{6} e^{3} + 1180 \, a b^{4} c^{7} e^{3} - 4560 \, a^{2} b^{2} c^{8} e^{3} + 6720 \, a^{3} c^{9} e^{3}}{c^{9}}\right)} x + \frac{737280 \, a b^{2} c^{9} d^{3} + 737280 \, a^{2} c^{10} d^{3} + 840 \, b^{5} c^{7} d^{2} e - 10560 \, a b^{3} c^{8} d^{2} e + 1272960 \, a^{2} b c^{9} d^{2} e - 840 \, b^{6} c^{6} d e^{2} + 10560 \, a b^{4} c^{7} d e^{2} - 44160 \, a^{2} b^{2} c^{8} d e^{2} + 81920 \, a^{3} c^{9} d e^{2} + 231 \, b^{7} c^{5} e^{3} - 2988 \, a b^{5} c^{6} e^{3} + 13200 \, a^{2} b^{3} c^{7} e^{3} - 20800 \, a^{3} b c^{8} e^{3}}{c^{9}}\right)} x + \frac{2949120 \, a^{2} b c^{9} d^{3} - 4200 \, b^{6} c^{6} d^{2} e + 57120 \, a b^{4} c^{7} d^{2} e - 270720 \, a^{2} b^{2} c^{8} d^{2} e + 806400 \, a^{3} c^{9} d^{2} e + 4200 \, b^{7} c^{5} d e^{2} - 57120 \, a b^{5} c^{6} d e^{2} + 270720 \, a^{2} b^{3} c^{7} d e^{2} - 478720 \, a^{3} b c^{8} d e^{2} - 1155 \, b^{8} c^{4} e^{3} + 16128 \, a b^{6} c^{5} e^{3} - 80160 \, a^{2} b^{4} c^{6} e^{3} + 158720 \, a^{3} b^{2} c^{7} e^{3} - 80640 \, a^{4} c^{8} e^{3}}{c^{9}}\right)} x + \frac{1966080 \, a^{3} c^{9} d^{3} + 12600 \, b^{7} c^{5} d^{2} e - 184800 \, a b^{5} c^{6} d^{2} e + 981120 \, a^{2} b^{3} c^{7} d^{2} e - 2142720 \, a^{3} b c^{8} d^{2} e - 12600 \, b^{8} c^{4} d e^{2} + 184800 \, a b^{6} c^{5} d e^{2} - 981120 \, a^{2} b^{4} c^{6} d e^{2} + 2142720 \, a^{3} b^{2} c^{7} d e^{2} - 1310720 \, a^{4} c^{8} d e^{2} + 3465 \, b^{9} c^{3} e^{3} - 52080 \, a b^{7} c^{4} e^{3} + 288288 \, a^{2} b^{5} c^{5} e^{3} - 687360 \, a^{3} b^{3} c^{6} e^{3} + 574720 \, a^{4} b c^{7} e^{3}}{c^{9}}\right)} + \frac{3 \, {\left(40 \, b^{8} c^{2} d^{2} e - 640 \, a b^{6} c^{3} d^{2} e + 3840 \, a^{2} b^{4} c^{4} d^{2} e - 10240 \, a^{3} b^{2} c^{5} d^{2} e + 10240 \, a^{4} c^{6} d^{2} e - 40 \, b^{9} c d e^{2} + 640 \, a b^{7} c^{2} d e^{2} - 3840 \, a^{2} b^{5} c^{3} d e^{2} + 10240 \, a^{3} b^{3} c^{4} d e^{2} - 10240 \, a^{4} b c^{5} d e^{2} + 11 \, b^{10} e^{3} - 180 \, a b^{8} c e^{3} + 1120 \, a^{2} b^{6} c^{2} e^{3} - 3200 \, a^{3} b^{4} c^{3} e^{3} + 3840 \, a^{4} b^{2} c^{4} e^{3} - 1024 \, a^{5} c^{5} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{131072 \, c^{\frac{13}{2}}}"," ",0,"1/6881280*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(14*(16*(6*c^3*x*e^3 + (20*c^12*d*e^2 + 17*b*c^11*e^3)/c^9)*x + (360*c^12*d^2*e + 920*b*c^11*d*e^2 + 251*b^2*c^10*e^3 + 252*a*c^11*e^3)/c^9)*x + (1920*c^12*d^3 + 14760*b*c^11*d^2*e + 12120*b^2*c^10*d*e^2 + 12160*a*c^11*d*e^2 + 1035*b^3*c^9*e^3 + 6268*a*b*c^10*e^3)/c^9)*x + (23040*b*c^11*d^3 + 57000*b^2*c^10*d^2*e + 57120*a*c^11*d^2*e + 14680*b^3*c^9*d*e^2 + 88800*a*b*c^10*d*e^2 - 5*b^4*c^8*e^3 + 10200*a*b^2*c^9*e^3 + 10416*a^2*c^10*e^3)/c^9)*x + (46080*b^2*c^10*d^3 + 46080*a*c^11*d^3 + 35880*b^3*c^9*d^2*e + 216480*a*b*c^10*d^2*e - 40*b^4*c^8*d*e^2 + 75360*a*b^2*c^9*d*e^2 + 76800*a^2*c^10*d*e^2 + 11*b^5*c^7*e^3 - 120*a*b^3*c^8*e^3 + 13680*a^2*b*c^9*e^3)/c^9)*x + (122880*b^3*c^9*d^3 + 737280*a*b*c^10*d^3 - 360*b^4*c^8*d^2*e + 782400*a*b^2*c^9*d^2*e + 792960*a^2*c^10*d^2*e + 360*b^5*c^7*d*e^2 - 4160*a*b^3*c^8*d*e^2 + 435840*a^2*b*c^9*d*e^2 - 99*b^6*c^6*e^3 + 1180*a*b^4*c^7*e^3 - 4560*a^2*b^2*c^8*e^3 + 6720*a^3*c^9*e^3)/c^9)*x + (737280*a*b^2*c^9*d^3 + 737280*a^2*c^10*d^3 + 840*b^5*c^7*d^2*e - 10560*a*b^3*c^8*d^2*e + 1272960*a^2*b*c^9*d^2*e - 840*b^6*c^6*d*e^2 + 10560*a*b^4*c^7*d*e^2 - 44160*a^2*b^2*c^8*d*e^2 + 81920*a^3*c^9*d*e^2 + 231*b^7*c^5*e^3 - 2988*a*b^5*c^6*e^3 + 13200*a^2*b^3*c^7*e^3 - 20800*a^3*b*c^8*e^3)/c^9)*x + (2949120*a^2*b*c^9*d^3 - 4200*b^6*c^6*d^2*e + 57120*a*b^4*c^7*d^2*e - 270720*a^2*b^2*c^8*d^2*e + 806400*a^3*c^9*d^2*e + 4200*b^7*c^5*d*e^2 - 57120*a*b^5*c^6*d*e^2 + 270720*a^2*b^3*c^7*d*e^2 - 478720*a^3*b*c^8*d*e^2 - 1155*b^8*c^4*e^3 + 16128*a*b^6*c^5*e^3 - 80160*a^2*b^4*c^6*e^3 + 158720*a^3*b^2*c^7*e^3 - 80640*a^4*c^8*e^3)/c^9)*x + (1966080*a^3*c^9*d^3 + 12600*b^7*c^5*d^2*e - 184800*a*b^5*c^6*d^2*e + 981120*a^2*b^3*c^7*d^2*e - 2142720*a^3*b*c^8*d^2*e - 12600*b^8*c^4*d*e^2 + 184800*a*b^6*c^5*d*e^2 - 981120*a^2*b^4*c^6*d*e^2 + 2142720*a^3*b^2*c^7*d*e^2 - 1310720*a^4*c^8*d*e^2 + 3465*b^9*c^3*e^3 - 52080*a*b^7*c^4*e^3 + 288288*a^2*b^5*c^5*e^3 - 687360*a^3*b^3*c^6*e^3 + 574720*a^4*b*c^7*e^3)/c^9) + 3/131072*(40*b^8*c^2*d^2*e - 640*a*b^6*c^3*d^2*e + 3840*a^2*b^4*c^4*d^2*e - 10240*a^3*b^2*c^5*d^2*e + 10240*a^4*c^6*d^2*e - 40*b^9*c*d*e^2 + 640*a*b^7*c^2*d*e^2 - 3840*a^2*b^5*c^3*d*e^2 + 10240*a^3*b^3*c^4*d*e^2 - 10240*a^4*b*c^5*d*e^2 + 11*b^10*e^3 - 180*a*b^8*c*e^3 + 1120*a^2*b^6*c^2*e^3 - 3200*a^3*b^4*c^3*e^3 + 3840*a^4*b^2*c^4*e^3 - 1024*a^5*c^5*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","B",0
1566,1,824,0,0.298326," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{516096} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(8 \, c^{3} x e^{2} + \frac{18 \, c^{11} d e + 23 \, b c^{10} e^{2}}{c^{8}}\right)} x + \frac{144 \, c^{11} d^{2} + 738 \, b c^{10} d e + 303 \, b^{2} c^{9} e^{2} + 304 \, a c^{10} e^{2}}{c^{8}}\right)} x + \frac{1728 \, b c^{10} d^{2} + 2850 \, b^{2} c^{9} d e + 2856 \, a c^{10} d e + 367 \, b^{3} c^{8} e^{2} + 2220 \, a b c^{9} e^{2}}{c^{8}}\right)} x + \frac{3456 \, b^{2} c^{9} d^{2} + 3456 \, a c^{10} d^{2} + 1794 \, b^{3} c^{8} d e + 10824 \, a b c^{9} d e - b^{4} c^{7} e^{2} + 1884 \, a b^{2} c^{8} e^{2} + 1920 \, a^{2} c^{9} e^{2}}{c^{8}}\right)} x + \frac{9216 \, b^{3} c^{8} d^{2} + 55296 \, a b c^{9} d^{2} - 18 \, b^{4} c^{7} d e + 39120 \, a b^{2} c^{8} d e + 39648 \, a^{2} c^{9} d e + 9 \, b^{5} c^{6} e^{2} - 104 \, a b^{3} c^{7} e^{2} + 10896 \, a^{2} b c^{8} e^{2}}{c^{8}}\right)} x + \frac{55296 \, a b^{2} c^{8} d^{2} + 55296 \, a^{2} c^{9} d^{2} + 42 \, b^{5} c^{6} d e - 528 \, a b^{3} c^{7} d e + 63648 \, a^{2} b c^{8} d e - 21 \, b^{6} c^{5} e^{2} + 264 \, a b^{4} c^{6} e^{2} - 1104 \, a^{2} b^{2} c^{7} e^{2} + 2048 \, a^{3} c^{8} e^{2}}{c^{8}}\right)} x + \frac{221184 \, a^{2} b c^{8} d^{2} - 210 \, b^{6} c^{5} d e + 2856 \, a b^{4} c^{6} d e - 13536 \, a^{2} b^{2} c^{7} d e + 40320 \, a^{3} c^{8} d e + 105 \, b^{7} c^{4} e^{2} - 1428 \, a b^{5} c^{5} e^{2} + 6768 \, a^{2} b^{3} c^{6} e^{2} - 11968 \, a^{3} b c^{7} e^{2}}{c^{8}}\right)} x + \frac{147456 \, a^{3} c^{8} d^{2} + 630 \, b^{7} c^{4} d e - 9240 \, a b^{5} c^{5} d e + 49056 \, a^{2} b^{3} c^{6} d e - 107136 \, a^{3} b c^{7} d e - 315 \, b^{8} c^{3} e^{2} + 4620 \, a b^{6} c^{4} e^{2} - 24528 \, a^{2} b^{4} c^{5} e^{2} + 53568 \, a^{3} b^{2} c^{6} e^{2} - 32768 \, a^{4} c^{7} e^{2}}{c^{8}}\right)} + \frac{5 \, {\left(2 \, b^{8} c d e - 32 \, a b^{6} c^{2} d e + 192 \, a^{2} b^{4} c^{3} d e - 512 \, a^{3} b^{2} c^{4} d e + 512 \, a^{4} c^{5} d e - b^{9} e^{2} + 16 \, a b^{7} c e^{2} - 96 \, a^{2} b^{5} c^{2} e^{2} + 256 \, a^{3} b^{3} c^{3} e^{2} - 256 \, a^{4} b c^{4} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16384 \, c^{\frac{11}{2}}}"," ",0,"1/516096*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(14*(8*c^3*x*e^2 + (18*c^11*d*e + 23*b*c^10*e^2)/c^8)*x + (144*c^11*d^2 + 738*b*c^10*d*e + 303*b^2*c^9*e^2 + 304*a*c^10*e^2)/c^8)*x + (1728*b*c^10*d^2 + 2850*b^2*c^9*d*e + 2856*a*c^10*d*e + 367*b^3*c^8*e^2 + 2220*a*b*c^9*e^2)/c^8)*x + (3456*b^2*c^9*d^2 + 3456*a*c^10*d^2 + 1794*b^3*c^8*d*e + 10824*a*b*c^9*d*e - b^4*c^7*e^2 + 1884*a*b^2*c^8*e^2 + 1920*a^2*c^9*e^2)/c^8)*x + (9216*b^3*c^8*d^2 + 55296*a*b*c^9*d^2 - 18*b^4*c^7*d*e + 39120*a*b^2*c^8*d*e + 39648*a^2*c^9*d*e + 9*b^5*c^6*e^2 - 104*a*b^3*c^7*e^2 + 10896*a^2*b*c^8*e^2)/c^8)*x + (55296*a*b^2*c^8*d^2 + 55296*a^2*c^9*d^2 + 42*b^5*c^6*d*e - 528*a*b^3*c^7*d*e + 63648*a^2*b*c^8*d*e - 21*b^6*c^5*e^2 + 264*a*b^4*c^6*e^2 - 1104*a^2*b^2*c^7*e^2 + 2048*a^3*c^8*e^2)/c^8)*x + (221184*a^2*b*c^8*d^2 - 210*b^6*c^5*d*e + 2856*a*b^4*c^6*d*e - 13536*a^2*b^2*c^7*d*e + 40320*a^3*c^8*d*e + 105*b^7*c^4*e^2 - 1428*a*b^5*c^5*e^2 + 6768*a^2*b^3*c^6*e^2 - 11968*a^3*b*c^7*e^2)/c^8)*x + (147456*a^3*c^8*d^2 + 630*b^7*c^4*d*e - 9240*a*b^5*c^5*d*e + 49056*a^2*b^3*c^6*d*e - 107136*a^3*b*c^7*d*e - 315*b^8*c^3*e^2 + 4620*a*b^6*c^4*e^2 - 24528*a^2*b^4*c^5*e^2 + 53568*a^3*b^2*c^6*e^2 - 32768*a^4*c^7*e^2)/c^8) + 5/16384*(2*b^8*c*d*e - 32*a*b^6*c^2*d*e + 192*a^2*b^4*c^3*d*e - 512*a^3*b^2*c^4*d*e + 512*a^4*c^5*d*e - b^9*e^2 + 16*a*b^7*c*e^2 - 96*a^2*b^5*c^2*e^2 + 256*a^3*b^3*c^3*e^2 - 256*a^4*b*c^4*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","B",0
1567,1,452,0,0.268690," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{172032} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, c^{3} x e + \frac{16 \, c^{10} d + 41 \, b c^{9} e}{c^{7}}\right)} x + \frac{576 \, b c^{9} d + 475 \, b^{2} c^{8} e + 476 \, a c^{9} e}{c^{7}}\right)} x + \frac{1152 \, b^{2} c^{8} d + 1152 \, a c^{9} d + 299 \, b^{3} c^{7} e + 1804 \, a b c^{8} e}{c^{7}}\right)} x + \frac{3072 \, b^{3} c^{7} d + 18432 \, a b c^{8} d - 3 \, b^{4} c^{6} e + 6520 \, a b^{2} c^{7} e + 6608 \, a^{2} c^{8} e}{c^{7}}\right)} x + \frac{18432 \, a b^{2} c^{7} d + 18432 \, a^{2} c^{8} d + 7 \, b^{5} c^{5} e - 88 \, a b^{3} c^{6} e + 10608 \, a^{2} b c^{7} e}{c^{7}}\right)} x + \frac{73728 \, a^{2} b c^{7} d - 35 \, b^{6} c^{4} e + 476 \, a b^{4} c^{5} e - 2256 \, a^{2} b^{2} c^{6} e + 6720 \, a^{3} c^{7} e}{c^{7}}\right)} x + \frac{49152 \, a^{3} c^{7} d + 105 \, b^{7} c^{3} e - 1540 \, a b^{5} c^{4} e + 8176 \, a^{2} b^{3} c^{5} e - 17856 \, a^{3} b c^{6} e}{c^{7}}\right)} + \frac{5 \, {\left(b^{8} e - 16 \, a b^{6} c e + 96 \, a^{2} b^{4} c^{2} e - 256 \, a^{3} b^{2} c^{3} e + 256 \, a^{4} c^{4} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16384 \, c^{\frac{9}{2}}}"," ",0,"1/172032*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(12*(14*c^3*x*e + (16*c^10*d + 41*b*c^9*e)/c^7)*x + (576*b*c^9*d + 475*b^2*c^8*e + 476*a*c^9*e)/c^7)*x + (1152*b^2*c^8*d + 1152*a*c^9*d + 299*b^3*c^7*e + 1804*a*b*c^8*e)/c^7)*x + (3072*b^3*c^7*d + 18432*a*b*c^8*d - 3*b^4*c^6*e + 6520*a*b^2*c^7*e + 6608*a^2*c^8*e)/c^7)*x + (18432*a*b^2*c^7*d + 18432*a^2*c^8*d + 7*b^5*c^5*e - 88*a*b^3*c^6*e + 10608*a^2*b*c^7*e)/c^7)*x + (73728*a^2*b*c^7*d - 35*b^6*c^4*e + 476*a*b^4*c^5*e - 2256*a^2*b^2*c^6*e + 6720*a^3*c^7*e)/c^7)*x + (49152*a^3*c^7*d + 105*b^7*c^3*e - 1540*a*b^5*c^4*e + 8176*a^2*b^3*c^5*e - 17856*a^3*b*c^6*e)/c^7) + 5/16384*(b^8*e - 16*a*b^6*c*e + 96*a^2*b^4*c^2*e - 256*a^3*b^2*c^3*e + 256*a^4*c^4*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","B",0
1568,1,14,0,0.153172," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}}"," ",0,"2/7*(c*x^2 + b*x + a)^(7/2)","A",0
1569,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1571,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.07Unable to divide, perhaps due to rounding error%%%{1,[6,0,10,0,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,9,0,1]%%%}+%%%{-3,[4,1,10,0,0]%%%}+%%%{3,[4,0,9,1,1]%%%}+%%%{%%%{12,[1]%%%},[4,0,8,0,2]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,9,0,1]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,8,1,2]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,7,0,3]%%%}+%%%{3,[2,2,10,0,0]%%%}+%%%{-6,[2,1,9,1,1]%%%}+%%%{%%%{-12,[1]%%%},[2,1,8,0,2]%%%}+%%%{3,[2,0,8,2,2]%%%}+%%%{%%%{12,[1]%%%},[2,0,7,1,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,9,0,1]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,8,1,2]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,7,2,3]%%%}+%%%{-1,[0,3,10,0,0]%%%}+%%%{3,[0,2,9,1,1]%%%}+%%%{-3,[0,1,8,2,2]%%%}+%%%{1,[0,0,7,3,3]%%%} / %%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,3,0,0]%%%}+%%%{%%%{-6,[2]%%%},[5,0,2,0,1]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,3,0,0]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,1,1]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,0,2]%%%}+%%%{%%%{12,[2]%%%},[3,1,2,0,1]%%%}+%%%{%%%{-12,[2]%%%},[3,0,1,1,2]%%%}+%%%{%%%{-8,[3]%%%},[3,0,0,0,3]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,3,0,0]%%%}+%%%{%%{[%%%{-6,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,2,1,1]%%%}+%%%{%%{[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,1,0,2]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,2,2]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,1,3]%%%}+%%%{%%%{-6,[2]%%%},[1,2,2,0,1]%%%}+%%%{%%%{12,[2]%%%},[1,1,1,1,2]%%%}+%%%{%%%{-6,[2]%%%},[1,0,0,2,3]%%%}+%%%{%%{[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,3,0,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,2,1,1]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,1,2,2]%%%}+%%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,3,3]%%%} Error: Bad Argument Value","F(-2)",0
1572,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 42.98Unable to divide, perhaps due to rounding error%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,11,0]%%%}+%%%{%%%{8,[1]%%%},[7,0,0,10,1]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,1,0,11,0]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,1,10,1]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,9,2]%%%}+%%%{%%%{-24,[1]%%%},[5,1,0,10,1]%%%}+%%%{%%%{24,[1]%%%},[5,0,1,9,2]%%%}+%%%{%%%{32,[2]%%%},[5,0,0,8,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,2,0,11,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,1,10,1]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,0,9,2]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,9,2]%%%}+%%%{%%{[%%%{-48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,8,3]%%%}+%%%{%%{[%%%{-16,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,7,4]%%%}+%%%{%%%{24,[1]%%%},[3,2,0,10,1]%%%}+%%%{%%%{-48,[1]%%%},[3,1,1,9,2]%%%}+%%%{%%%{-32,[2]%%%},[3,1,0,8,3]%%%}+%%%{%%%{24,[1]%%%},[3,0,2,8,3]%%%}+%%%{%%%{32,[2]%%%},[3,0,1,7,4]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,3,0,11,0]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,1,10,1]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,0,9,2]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,2,9,2]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,1,8,3]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,3,8,3]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,7,4]%%%}+%%%{%%%{-8,[1]%%%},[1,3,0,10,1]%%%}+%%%{%%%{24,[1]%%%},[1,2,1,9,2]%%%}+%%%{%%%{-24,[1]%%%},[1,1,2,8,3]%%%}+%%%{%%%{8,[1]%%%},[1,0,3,7,4]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,4,0,11,0]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,1,10,1]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,2,9,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,3,8,3]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,7,4]%%%} / %%%{%%%{1,[2]%%%},[8,0,0,4,0]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,0,3,1]%%%}+%%%{%%%{-4,[2]%%%},[6,1,0,4,0]%%%}+%%%{%%%{4,[2]%%%},[6,0,1,3,1]%%%}+%%%{%%%{24,[3]%%%},[6,0,0,2,2]%%%}+%%%{%%{[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,0,3,1]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,1,2,2]%%%}+%%%{%%{poly1[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,1,3]%%%}+%%%{%%%{6,[2]%%%},[4,2,0,4,0]%%%}+%%%{%%%{-12,[2]%%%},[4,1,1,3,1]%%%}+%%%{%%%{-48,[3]%%%},[4,1,0,2,2]%%%}+%%%{%%%{6,[2]%%%},[4,0,2,2,2]%%%}+%%%{%%%{48,[3]%%%},[4,0,1,1,3]%%%}+%%%{%%%{16,[4]%%%},[4,0,0,0,4]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,0,3,1]%%%}+%%%{%%{[%%%{48,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,1,2,2]%%%}+%%%{%%{[%%%{32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,1,3]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,2,1,3]%%%}+%%%{%%{poly1[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,0,4]%%%}+%%%{%%%{-4,[2]%%%},[2,3,0,4,0]%%%}+%%%{%%%{12,[2]%%%},[2,2,1,3,1]%%%}+%%%{%%%{24,[3]%%%},[2,2,0,2,2]%%%}+%%%{%%%{-12,[2]%%%},[2,1,2,2,2]%%%}+%%%{%%%{-48,[3]%%%},[2,1,1,1,3]%%%}+%%%{%%%{4,[2]%%%},[2,0,3,1,3]%%%}+%%%{%%%{24,[3]%%%},[2,0,2,0,4]%%%}+%%%{%%{[%%%{8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,0,3,1]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,1,2,2]%%%}+%%%{%%{[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,2,1,3]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,0,4]%%%}+%%%{%%%{1,[2]%%%},[0,4,0,4,0]%%%}+%%%{%%%{-4,[2]%%%},[0,3,1,3,1]%%%}+%%%{%%%{6,[2]%%%},[0,2,2,2,2]%%%}+%%%{%%%{-4,[2]%%%},[0,1,3,1,3]%%%}+%%%{%%%{1,[2]%%%},[0,0,4,0,4]%%%} Error: Bad Argument Value","F(-2)",0
1573,1,252,0,0.263633," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{32} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, x e^{3} + \frac{8 \, c^{3} d e^{2} - b c^{2} e^{3}}{c^{3}}\right)} x + \frac{48 \, c^{3} d^{2} e - 16 \, b c^{2} d e^{2} + 5 \, b^{2} c e^{3} - 12 \, a c^{2} e^{3}}{c^{3}}\right)} x + \frac{64 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 48 \, b^{2} c d e^{2} - 128 \, a c^{2} d e^{2} - 15 \, b^{3} e^{3} + 52 \, a b c e^{3}}{c^{3}}\right)} - \frac{3 \, {\left(16 \, b^{2} c^{2} d^{2} e - 64 \, a c^{3} d^{2} e - 16 \, b^{3} c d e^{2} + 64 \, a b c^{2} d e^{2} + 5 \, b^{4} e^{3} - 24 \, a b^{2} c e^{3} + 16 \, a^{2} c^{2} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{64 \, c^{\frac{7}{2}}}"," ",0,"1/32*sqrt(c*x^2 + b*x + a)*(2*(4*(2*x*e^3 + (8*c^3*d*e^2 - b*c^2*e^3)/c^3)*x + (48*c^3*d^2*e - 16*b*c^2*d*e^2 + 5*b^2*c*e^3 - 12*a*c^2*e^3)/c^3)*x + (64*c^3*d^3 - 48*b*c^2*d^2*e + 48*b^2*c*d*e^2 - 128*a*c^2*d*e^2 - 15*b^3*e^3 + 52*a*b*c*e^3)/c^3) - 3/64*(16*b^2*c^2*d^2*e - 64*a*c^3*d^2*e - 16*b^3*c*d*e^2 + 64*a*b*c^2*d*e^2 + 5*b^4*e^3 - 24*a*b^2*c*e^3 + 16*a^2*c^2*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
1574,1,146,0,0.283016," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(2 \, x e^{2} + \frac{6 \, c^{2} d e - b c e^{2}}{c^{2}}\right)} x + \frac{12 \, c^{2} d^{2} - 6 \, b c d e + 3 \, b^{2} e^{2} - 8 \, a c e^{2}}{c^{2}}\right)} - \frac{{\left(2 \, b^{2} c d e - 8 \, a c^{2} d e - b^{3} e^{2} + 4 \, a b c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{5}{2}}}"," ",0,"1/6*sqrt(c*x^2 + b*x + a)*(2*(2*x*e^2 + (6*c^2*d*e - b*c*e^2)/c^2)*x + (12*c^2*d^2 - 6*b*c*d*e + 3*b^2*e^2 - 8*a*c*e^2)/c^2) - 1/4*(2*b^2*c*d*e - 8*a*c^2*d*e - b^3*e^2 + 4*a*b*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
1575,1,84,0,0.436346," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} + b x + a} {\left(2 \, x e + \frac{4 \, c d - b e}{c}\right)} - \frac{{\left(b^{2} e - 4 \, a c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{3}{2}}}"," ",0,"1/2*sqrt(c*x^2 + b*x + a)*(2*x*e + (4*c*d - b*e)/c) - 1/4*(b^2*e - 4*a*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
1576,1,14,0,0.152761," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{c x^{2} + b x + a}"," ",0,"2*sqrt(c*x^2 + b*x + a)","A",0
1577,-2,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1578,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1579,1,1046,0,0.392997," ","integrate((2*c*x+b)/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, b^{2} c d e - 8 \, a c^{2} d e - b^{3} e^{2} + 4 \, a b c e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{7}{2}} d^{4} - 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{5}{2}} d^{3} e + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{3} d^{4} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{2} d^{3} e - 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{3} d^{3} e + 4 \, b^{2} c^{\frac{5}{2}} d^{4} + 34 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{3}{2}} d^{2} e^{2} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{5}{2}} d^{2} e^{2} - 4 \, b^{3} c^{\frac{3}{2}} d^{3} e - 16 \, a b c^{\frac{5}{2}} d^{3} e + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c d e^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{2} d e^{3} + 22 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c d^{2} e^{2} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{2} d^{2} e^{2} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} \sqrt{c} d e^{3} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{\frac{3}{2}} d e^{3} + 3 \, b^{4} \sqrt{c} d^{2} e^{2} + 10 \, a b^{2} c^{\frac{3}{2}} d^{2} e^{2} + 8 \, a^{2} c^{\frac{5}{2}} d^{2} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} e^{4} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c e^{4} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} d e^{3} - 22 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c d e^{3} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{2} d e^{3} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{3}{2}} e^{4} - 11 \, a b^{3} \sqrt{c} d e^{3} + 12 \, a^{2} b c^{\frac{3}{2}} d e^{3} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} e^{4} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c e^{4} + 8 \, a^{2} b^{2} \sqrt{c} e^{4} - 16 \, a^{3} c^{\frac{3}{2}} e^{4}}{4 \, {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3} + 2 \, a c d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{2}}"," ",0,"-3/4*(2*b^2*c*d*e - 8*a*c^2*d*e - b^3*e^2 + 4*a*b*c*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/4*(16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(7/2)*d^4 - 32*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(5/2)*d^3*e + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^3*d^4 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^2*d^3*e - 32*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^3*d^3*e + 4*b^2*c^(5/2)*d^4 + 34*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(3/2)*d^2*e^2 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(5/2)*d^2*e^2 - 4*b^3*c^(3/2)*d^3*e - 16*a*b*c^(5/2)*d^3*e + 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c*d*e^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^2*d*e^3 + 22*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c*d^2*e^2 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^2*d^2*e^2 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*sqrt(c)*d*e^3 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^(3/2)*d*e^3 + 3*b^4*sqrt(c)*d^2*e^2 + 10*a*b^2*c^(3/2)*d^2*e^2 + 8*a^2*c^(5/2)*d^2*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*e^4 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c*e^4 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*d*e^3 - 22*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c*d*e^3 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^2*d*e^3 + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(3/2)*e^4 - 11*a*b^3*sqrt(c)*d*e^3 + 12*a^2*b*c^(3/2)*d*e^3 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*e^4 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c*e^4 + 8*a^2*b^2*sqrt(c)*e^4 - 16*a^3*c^(3/2)*e^4)/((c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3 + 2*a*c*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^2)","B",0
1580,1,2666,0,0.774637," ","integrate((2*c*x+b)/(e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(16 \, b^{2} c^{2} d^{2} e - 64 \, a c^{3} d^{2} e - 16 \, b^{3} c d e^{2} + 64 \, a b c^{2} d e^{2} + 5 \, b^{4} e^{3} - 24 \, a b^{2} c e^{3} + 16 \, a^{2} c^{2} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{8 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{5} d^{6} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{4} d^{5} e + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{9}{2}} d^{6} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{7}{2}} d^{5} e - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{9}{2}} d^{5} e + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{4} d^{6} + 736 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{3} d^{4} e^{2} - 1024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{4} d^{4} e^{2} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{3} d^{5} e - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{4} d^{5} e + 16 \, b^{3} c^{\frac{7}{2}} d^{6} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{5}{2}} d^{3} e^{3} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{7}{2}} d^{3} e^{3} + 864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{5}{2}} d^{4} e^{2} - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{\frac{7}{2}} d^{4} e^{2} - 24 \, b^{4} c^{\frac{5}{2}} d^{5} e - 96 \, a b^{2} c^{\frac{7}{2}} d^{5} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{2} d^{2} e^{4} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{3} d^{2} e^{4} - 352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{2} d^{3} e^{3} + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{3} d^{3} e^{3} + 324 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{2} d^{4} e^{2} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{3} d^{4} e^{2} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{4} d^{4} e^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c^{\frac{3}{2}} d^{2} e^{4} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{5}{2}} d^{2} e^{4} - 546 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c^{\frac{3}{2}} d^{3} e^{3} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{5}{2}} d^{3} e^{3} + 1632 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{7}{2}} d^{3} e^{3} + 38 \, b^{5} c^{\frac{3}{2}} d^{4} e^{2} + 64 \, a b^{3} c^{\frac{5}{2}} d^{4} e^{2} + 96 \, a^{2} b c^{\frac{7}{2}} d^{4} e^{2} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} c d e^{5} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{2} d e^{5} - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} c d^{2} e^{4} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{2} d^{2} e^{4} + 1248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{3} d^{2} e^{4} - 186 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} c d^{3} e^{3} - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{2} d^{3} e^{3} + 1248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{3} d^{3} e^{3} + 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} \sqrt{c} d e^{5} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{3}{2}} d e^{5} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{5}{2}} d e^{5} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{5} \sqrt{c} d^{2} e^{4} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c^{\frac{3}{2}} d^{2} e^{4} - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{\frac{5}{2}} d^{2} e^{4} - 15 \, b^{6} \sqrt{c} d^{3} e^{3} - 158 \, a b^{4} c^{\frac{3}{2}} d^{3} e^{3} + 240 \, a^{2} b^{2} c^{\frac{5}{2}} d^{3} e^{3} - 32 \, a^{3} c^{\frac{7}{2}} d^{3} e^{3} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{4} e^{6} - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} c e^{6} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{2} e^{6} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} d e^{5} - 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} c d e^{5} - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{2} d e^{5} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{6} d^{2} e^{4} + 402 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} c d^{2} e^{4} - 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{2} d^{2} e^{4} - 1056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{3} d^{2} e^{4} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{4} \sqrt{c} d e^{5} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{5}{2}} d e^{5} + 78 \, a b^{5} \sqrt{c} d^{2} e^{4} + 48 \, a^{2} b^{3} c^{\frac{3}{2}} d^{2} e^{4} - 480 \, a^{3} b c^{\frac{5}{2}} d^{2} e^{4} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{4} e^{6} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} c e^{6} - 66 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{5} d e^{5} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} c d e^{5} + 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{2} d e^{5} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b c^{\frac{3}{2}} e^{6} - 111 \, a^{2} b^{4} \sqrt{c} d e^{5} + 200 \, a^{3} b^{2} c^{\frac{3}{2}} d e^{5} + 208 \, a^{4} c^{\frac{5}{2}} d e^{5} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{4} e^{6} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{2} c e^{6} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} c^{2} e^{6} + 48 \, a^{3} b^{3} \sqrt{c} e^{6} - 128 \, a^{4} b c^{\frac{3}{2}} e^{6}}{24 \, {\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{3}}"," ",0,"-1/8*(16*b^2*c^2*d^2*e - 64*a*c^3*d^2*e - 16*b^3*c*d*e^2 + 64*a*b*c^2*d*e^2 + 5*b^4*e^3 - 24*a*b^2*c*e^3 + 16*a^2*c^2*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/24*(128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^5*d^6 - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^4*d^5*e + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(9/2)*d^6 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(7/2)*d^5*e - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(9/2)*d^5*e + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^4*d^6 + 736*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^3*d^4*e^2 - 1024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^4*d^4*e^2 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^3*d^5*e - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^4*d^5*e + 16*b^3*c^(7/2)*d^6 + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(5/2)*d^3*e^3 - 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(7/2)*d^3*e^3 + 864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(5/2)*d^4*e^2 - 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^(7/2)*d^4*e^2 - 24*b^4*c^(5/2)*d^5*e - 96*a*b^2*c^(7/2)*d^5*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^2*d^2*e^4 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^3*d^2*e^4 - 352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^2*d^3*e^3 + 128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^3*d^3*e^3 + 324*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^2*d^4*e^2 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^3*d^4*e^2 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^4*d^4*e^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c^(3/2)*d^2*e^4 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(5/2)*d^2*e^4 - 546*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(3/2)*d^3*e^3 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(5/2)*d^3*e^3 + 1632*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(7/2)*d^3*e^3 + 38*b^5*c^(3/2)*d^4*e^2 + 64*a*b^3*c^(5/2)*d^4*e^2 + 96*a^2*b*c^(7/2)*d^4*e^2 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*c*d*e^5 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^2*d*e^5 - 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c*d^2*e^4 + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^2*d^2*e^4 + 1248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^3*d^2*e^4 - 186*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c*d^3*e^3 - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^2*d^3*e^3 + 1248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^3*d^3*e^3 + 75*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*sqrt(c)*d*e^5 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(3/2)*d*e^5 + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(5/2)*d*e^5 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*sqrt(c)*d^2*e^4 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c^(3/2)*d^2*e^4 - 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^(5/2)*d^2*e^4 - 15*b^6*sqrt(c)*d^3*e^3 - 158*a*b^4*c^(3/2)*d^3*e^3 + 240*a^2*b^2*c^(5/2)*d^3*e^3 - 32*a^3*c^(7/2)*d^3*e^3 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^4*e^6 - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*c*e^6 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^2*e^6 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*d*e^5 - 64*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c*d*e^5 - 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^2*d*e^5 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*d^2*e^4 + 402*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c*d^2*e^4 - 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^2*d^2*e^4 - 1056*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^3*d^2*e^4 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*sqrt(c)*d*e^5 - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(5/2)*d*e^5 + 78*a*b^5*sqrt(c)*d^2*e^4 + 48*a^2*b^3*c^(3/2)*d^2*e^4 - 480*a^3*b*c^(5/2)*d^2*e^4 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^4*e^6 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*c*e^6 - 66*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*d*e^5 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c*d*e^5 + 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^2*d*e^5 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c^(3/2)*e^6 - 111*a^2*b^4*sqrt(c)*d*e^5 + 200*a^3*b^2*c^(3/2)*d*e^5 + 208*a^4*c^(5/2)*d*e^5 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^4*e^6 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*c*e^6 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c^2*e^6 + 48*a^3*b^3*sqrt(c)*e^6 - 128*a^4*b*c^(3/2)*e^6)/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^3)","B",0
1581,1,545,0,0.367929," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left(\frac{{\left(b^{2} c^{3} e^{4} - 4 \, a c^{4} e^{4}\right)} x}{b^{2} c^{3} - 4 \, a c^{4}} + \frac{6 \, b^{2} c^{3} d e^{3} - 24 \, a c^{4} d e^{3} - b^{3} c^{2} e^{4} + 4 \, a b c^{3} e^{4}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x + \frac{36 \, b^{2} c^{3} d^{2} e^{2} - 144 \, a c^{4} d^{2} e^{2} - 18 \, b^{3} c^{2} d e^{3} + 72 \, a b c^{3} d e^{3} + 5 \, b^{4} c e^{4} - 28 \, a b^{2} c^{2} e^{4} + 32 \, a^{2} c^{3} e^{4}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{24 \, b^{2} c^{3} d^{3} e - 96 \, a c^{4} d^{3} e - 72 \, b^{3} c^{2} d^{2} e^{2} + 288 \, a b c^{3} d^{2} e^{2} + 54 \, b^{4} c d e^{3} - 252 \, a b^{2} c^{2} d e^{3} + 144 \, a^{2} c^{3} d e^{3} - 15 \, b^{5} e^{4} + 86 \, a b^{3} c e^{4} - 104 \, a^{2} b c^{2} e^{4}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{6 \, b^{2} c^{3} d^{4} - 24 \, a c^{4} d^{4} - 72 \, a b^{2} c^{2} d^{2} e^{2} + 288 \, a^{2} c^{3} d^{2} e^{2} + 54 \, a b^{3} c d e^{3} - 216 \, a^{2} b c^{2} d e^{3} - 15 \, a b^{4} e^{4} + 76 \, a^{2} b^{2} c e^{4} - 64 \, a^{3} c^{2} e^{4}}{b^{2} c^{3} - 4 \, a c^{4}}}{3 \, \sqrt{c x^{2} + b x + a}} - \frac{{\left(16 \, c^{3} d^{3} e - 24 \, b c^{2} d^{2} e^{2} + 18 \, b^{2} c d e^{3} - 24 \, a c^{2} d e^{3} - 5 \, b^{3} e^{4} + 12 \, a b c e^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{7}{2}}}"," ",0,"1/3*(((2*((b^2*c^3*e^4 - 4*a*c^4*e^4)*x/(b^2*c^3 - 4*a*c^4) + (6*b^2*c^3*d*e^3 - 24*a*c^4*d*e^3 - b^3*c^2*e^4 + 4*a*b*c^3*e^4)/(b^2*c^3 - 4*a*c^4))*x + (36*b^2*c^3*d^2*e^2 - 144*a*c^4*d^2*e^2 - 18*b^3*c^2*d*e^3 + 72*a*b*c^3*d*e^3 + 5*b^4*c*e^4 - 28*a*b^2*c^2*e^4 + 32*a^2*c^3*e^4)/(b^2*c^3 - 4*a*c^4))*x - (24*b^2*c^3*d^3*e - 96*a*c^4*d^3*e - 72*b^3*c^2*d^2*e^2 + 288*a*b*c^3*d^2*e^2 + 54*b^4*c*d*e^3 - 252*a*b^2*c^2*d*e^3 + 144*a^2*c^3*d*e^3 - 15*b^5*e^4 + 86*a*b^3*c*e^4 - 104*a^2*b*c^2*e^4)/(b^2*c^3 - 4*a*c^4))*x - (6*b^2*c^3*d^4 - 24*a*c^4*d^4 - 72*a*b^2*c^2*d^2*e^2 + 288*a^2*c^3*d^2*e^2 + 54*a*b^3*c*d*e^3 - 216*a^2*b*c^2*d*e^3 - 15*a*b^4*e^4 + 76*a^2*b^2*c*e^4 - 64*a^3*c^2*e^4)/(b^2*c^3 - 4*a*c^4))/sqrt(c*x^2 + b*x + a) - 1/2*(16*c^3*d^3*e - 24*b*c^2*d^2*e^2 + 18*b^2*c*d*e^3 - 24*a*c^2*d*e^3 - 5*b^3*e^4 + 12*a*b*c*e^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","B",0
1582,1,347,0,0.324431," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, {\left(b^{2} c^{2} e^{3} - 4 \, a c^{3} e^{3}\right)} x}{b^{2} c^{2} - 4 \, a c^{3}} + \frac{3 \, {\left(4 \, b^{2} c^{2} d e^{2} - 16 \, a c^{3} d e^{2} - b^{3} c e^{3} + 4 \, a b c^{2} e^{3}\right)}}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x - \frac{3 \, {\left(4 \, b^{2} c^{2} d^{2} e - 16 \, a c^{3} d^{2} e - 8 \, b^{3} c d e^{2} + 32 \, a b c^{2} d e^{2} + 3 \, b^{4} e^{3} - 14 \, a b^{2} c e^{3} + 8 \, a^{2} c^{2} e^{3}\right)}}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x - \frac{4 \, b^{2} c^{2} d^{3} - 16 \, a c^{3} d^{3} - 24 \, a b^{2} c d e^{2} + 96 \, a^{2} c^{2} d e^{2} + 9 \, a b^{3} e^{3} - 36 \, a^{2} b c e^{3}}{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, \sqrt{c x^{2} + b x + a}} - \frac{3 \, {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + 3 \, b^{2} e^{3} - 4 \, a c e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{5}{2}}}"," ",0,"1/2*(((2*(b^2*c^2*e^3 - 4*a*c^3*e^3)*x/(b^2*c^2 - 4*a*c^3) + 3*(4*b^2*c^2*d*e^2 - 16*a*c^3*d*e^2 - b^3*c*e^3 + 4*a*b*c^2*e^3)/(b^2*c^2 - 4*a*c^3))*x - 3*(4*b^2*c^2*d^2*e - 16*a*c^3*d^2*e - 8*b^3*c*d*e^2 + 32*a*b*c^2*d*e^2 + 3*b^4*e^3 - 14*a*b^2*c*e^3 + 8*a^2*c^2*e^3)/(b^2*c^2 - 4*a*c^3))*x - (4*b^2*c^2*d^3 - 16*a*c^3*d^3 - 24*a*b^2*c*d*e^2 + 96*a^2*c^2*d*e^2 + 9*a*b^3*e^3 - 36*a^2*b*c*e^3)/(b^2*c^2 - 4*a*c^3))/sqrt(c*x^2 + b*x + a) - 3/4*(8*c^2*d^2*e - 8*b*c*d*e^2 + 3*b^2*e^3 - 4*a*c*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","B",0
1583,1,197,0,0.331986," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(\frac{{\left(b^{2} c e^{2} - 4 \, a c^{2} e^{2}\right)} x}{b^{2} c - 4 \, a c^{2}} - \frac{2 \, {\left(b^{2} c d e - 4 \, a c^{2} d e - b^{3} e^{2} + 4 \, a b c e^{2}\right)}}{b^{2} c - 4 \, a c^{2}}\right)} x - \frac{b^{2} c d^{2} - 4 \, a c^{2} d^{2} - 2 \, a b^{2} e^{2} + 8 \, a^{2} c e^{2}}{b^{2} c - 4 \, a c^{2}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{2 \, {\left(2 \, c d e - b e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"2*(((b^2*c*e^2 - 4*a*c^2*e^2)*x/(b^2*c - 4*a*c^2) - 2*(b^2*c*d*e - 4*a*c^2*d*e - b^3*e^2 + 4*a*b*c*e^2)/(b^2*c - 4*a*c^2))*x - (b^2*c*d^2 - 4*a*c^2*d^2 - 2*a*b^2*e^2 + 8*a^2*c*e^2)/(b^2*c - 4*a*c^2))/sqrt(c*x^2 + b*x + a) - 2*(2*c*d*e - b*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","B",0
1584,1,101,0,0.304323," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, e \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{\sqrt{c}} - \frac{2 \, {\left(\frac{{\left(b^{2} e - 4 \, a c e\right)} x}{b^{2} - 4 \, a c} + \frac{b^{2} d - 4 \, a c d}{b^{2} - 4 \, a c}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2*e*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/sqrt(c) - 2*((b^2*e - 4*a*c*e)*x/(b^2 - 4*a*c) + (b^2*d - 4*a*c*d)/(b^2 - 4*a*c))/sqrt(c*x^2 + b*x + a)","B",0
1585,1,14,0,0.205024," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2/sqrt(c*x^2 + b*x + a)","A",0
1586,1,501,0,0.307580," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(b^{2} c^{2} d^{2} e - 4 \, a c^{3} d^{2} e - b^{3} c d e^{2} + 4 \, a b c^{2} d e^{2} + a b^{2} c e^{3} - 4 \, a^{2} c^{2} e^{3}\right)} x}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}} - \frac{b^{2} c^{2} d^{3} - 4 \, a c^{3} d^{3} - 2 \, b^{3} c d^{2} e + 8 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 3 \, a b^{2} c d e^{2} - 4 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{2 \, {\left(2 \, c d e - b e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}}"," ",0,"2*((b^2*c^2*d^2*e - 4*a*c^3*d^2*e - b^3*c*d*e^2 + 4*a*b*c^2*d*e^2 + a*b^2*c*e^3 - 4*a^2*c^2*e^3)*x/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4) - (b^2*c^2*d^3 - 4*a*c^3*d^3 - 2*b^3*c*d^2*e + 8*a*b*c^2*d^2*e + b^4*d*e^2 - 3*a*b^2*c*d*e^2 - 4*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3)/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4))/sqrt(c*x^2 + b*x + a) - 2*(2*c*d*e - b*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c*d^2 - b*d*e + a*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2))","B",0
1587,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1588,1,754,0,0.375450," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left(\frac{3 \, {\left(b^{4} c^{2} e^{4} - 8 \, a b^{2} c^{3} e^{4} + 16 \, a^{2} c^{4} e^{4}\right)} x}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}} - \frac{4 \, {\left(4 \, b^{2} c^{4} d^{3} e - 16 \, a c^{5} d^{3} e - 6 \, b^{3} c^{3} d^{2} e^{2} + 24 \, a b c^{4} d^{2} e^{2} + 7 \, b^{4} c^{2} d e^{3} - 44 \, a b^{2} c^{3} d e^{3} + 64 \, a^{2} c^{4} d e^{3} - 4 \, b^{5} c e^{4} + 30 \, a b^{3} c^{2} e^{4} - 56 \, a^{2} b c^{3} e^{4}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x - \frac{6 \, {\left(4 \, b^{3} c^{3} d^{3} e - 16 \, a b c^{4} d^{3} e - 3 \, b^{4} c^{2} d^{2} e^{2} + 48 \, a^{2} c^{4} d^{2} e^{2} + 4 \, b^{5} c d e^{3} - 20 \, a b^{3} c^{2} d e^{3} + 16 \, a^{2} b c^{3} d e^{3} - 2 \, b^{6} e^{4} + 12 \, a b^{4} c e^{4} - 8 \, a^{2} b^{2} c^{2} e^{4} - 32 \, a^{3} c^{3} e^{4}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x - \frac{12 \, {\left(b^{4} c^{2} d^{3} e - 4 \, a b^{2} c^{3} d^{3} e - 6 \, a b^{3} c^{2} d^{2} e^{2} + 24 \, a^{2} b c^{3} d^{2} e^{2} + 4 \, a b^{4} c d e^{3} - 20 \, a^{2} b^{2} c^{2} d e^{3} + 16 \, a^{3} c^{3} d e^{3} - 2 \, a b^{5} e^{4} + 14 \, a^{2} b^{3} c e^{4} - 24 \, a^{3} b c^{2} e^{4}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x - \frac{b^{4} c^{2} d^{4} - 8 \, a b^{2} c^{3} d^{4} + 16 \, a^{2} c^{4} d^{4} + 8 \, a b^{3} c^{2} d^{3} e - 32 \, a^{2} b c^{3} d^{3} e - 48 \, a^{2} b^{2} c^{2} d^{2} e^{2} + 192 \, a^{3} c^{3} d^{2} e^{2} + 24 \, a^{2} b^{3} c d e^{3} - 96 \, a^{3} b c^{2} d e^{3} - 12 \, a^{2} b^{4} e^{4} + 80 \, a^{3} b^{2} c e^{4} - 128 \, a^{4} c^{2} e^{4}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} - \frac{4 \, {\left(2 \, c d e^{3} - b e^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"2/3*((((3*(b^4*c^2*e^4 - 8*a*b^2*c^3*e^4 + 16*a^2*c^4*e^4)*x/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4) - 4*(4*b^2*c^4*d^3*e - 16*a*c^5*d^3*e - 6*b^3*c^3*d^2*e^2 + 24*a*b*c^4*d^2*e^2 + 7*b^4*c^2*d*e^3 - 44*a*b^2*c^3*d*e^3 + 64*a^2*c^4*d*e^3 - 4*b^5*c*e^4 + 30*a*b^3*c^2*e^4 - 56*a^2*b*c^3*e^4)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x - 6*(4*b^3*c^3*d^3*e - 16*a*b*c^4*d^3*e - 3*b^4*c^2*d^2*e^2 + 48*a^2*c^4*d^2*e^2 + 4*b^5*c*d*e^3 - 20*a*b^3*c^2*d*e^3 + 16*a^2*b*c^3*d*e^3 - 2*b^6*e^4 + 12*a*b^4*c*e^4 - 8*a^2*b^2*c^2*e^4 - 32*a^3*c^3*e^4)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x - 12*(b^4*c^2*d^3*e - 4*a*b^2*c^3*d^3*e - 6*a*b^3*c^2*d^2*e^2 + 24*a^2*b*c^3*d^2*e^2 + 4*a*b^4*c*d*e^3 - 20*a^2*b^2*c^2*d*e^3 + 16*a^3*c^3*d*e^3 - 2*a*b^5*e^4 + 14*a^2*b^3*c*e^4 - 24*a^3*b*c^2*e^4)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x - (b^4*c^2*d^4 - 8*a*b^2*c^3*d^4 + 16*a^2*c^4*d^4 + 8*a*b^3*c^2*d^3*e - 32*a^2*b*c^3*d^3*e - 48*a^2*b^2*c^2*d^2*e^2 + 192*a^3*c^3*d^2*e^2 + 24*a^2*b^3*c*d*e^3 - 96*a^3*b*c^2*d*e^3 - 12*a^2*b^4*e^4 + 80*a^3*b^2*c*e^4 - 128*a^4*c^2*e^4)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))/(c*x^2 + b*x + a)^(3/2) - 4*(2*c*d*e^3 - b*e^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","B",0
1589,1,492,0,0.348561," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, e^{3} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}} - \frac{2 \, {\left({\left({\left(\frac{{\left(12 \, b^{2} c^{3} d^{2} e - 48 \, a c^{4} d^{2} e - 12 \, b^{3} c^{2} d e^{2} + 48 \, a b c^{3} d e^{2} + 7 \, b^{4} c e^{3} - 44 \, a b^{2} c^{2} e^{3} + 64 \, a^{2} c^{3} e^{3}\right)} x}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}} + \frac{3 \, {\left(6 \, b^{3} c^{2} d^{2} e - 24 \, a b c^{3} d^{2} e - 3 \, b^{4} c d e^{2} + 48 \, a^{2} c^{3} d e^{2} + 2 \, b^{5} e^{3} - 10 \, a b^{3} c e^{3} + 8 \, a^{2} b c^{2} e^{3}\right)}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}\right)} x + \frac{3 \, {\left(3 \, b^{4} c d^{2} e - 12 \, a b^{2} c^{2} d^{2} e - 12 \, a b^{3} c d e^{2} + 48 \, a^{2} b c^{2} d e^{2} + 4 \, a b^{4} e^{3} - 20 \, a^{2} b^{2} c e^{3} + 16 \, a^{3} c^{2} e^{3}\right)}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}\right)} x + \frac{b^{4} c d^{3} - 8 \, a b^{2} c^{2} d^{3} + 16 \, a^{2} c^{3} d^{3} + 6 \, a b^{3} c d^{2} e - 24 \, a^{2} b c^{2} d^{2} e - 24 \, a^{2} b^{2} c d e^{2} + 96 \, a^{3} c^{2} d e^{2} + 6 \, a^{2} b^{3} e^{3} - 24 \, a^{3} b c e^{3}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2*e^3*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2) - 2/3*((((12*b^2*c^3*d^2*e - 48*a*c^4*d^2*e - 12*b^3*c^2*d*e^2 + 48*a*b*c^3*d*e^2 + 7*b^4*c*e^3 - 44*a*b^2*c^2*e^3 + 64*a^2*c^3*e^3)*x/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) + 3*(6*b^3*c^2*d^2*e - 24*a*b*c^3*d^2*e - 3*b^4*c*d*e^2 + 48*a^2*c^3*d*e^2 + 2*b^5*e^3 - 10*a*b^3*c*e^3 + 8*a^2*b*c^2*e^3)/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3))*x + 3*(3*b^4*c*d^2*e - 12*a*b^2*c^2*d^2*e - 12*a*b^3*c*d*e^2 + 48*a^2*b*c^2*d*e^2 + 4*a*b^4*e^3 - 20*a^2*b^2*c*e^3 + 16*a^3*c^2*e^3)/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3))*x + (b^4*c*d^3 - 8*a*b^2*c^2*d^3 + 16*a^2*c^3*d^3 + 6*a*b^3*c*d^2*e - 24*a^2*b*c^2*d^2*e - 24*a^2*b^2*c*d*e^2 + 96*a^3*c^2*d*e^2 + 6*a^2*b^3*e^3 - 24*a^3*b*c*e^3)/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3))/(c*x^2 + b*x + a)^(3/2)","B",0
1590,1,289,0,0.321723," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(\frac{4 \, {\left(2 \, b^{2} c^{2} d e - 8 \, a c^{3} d e - b^{3} c e^{2} + 4 \, a b c^{2} e^{2}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(4 \, b^{3} c d e - 16 \, a b c^{2} d e - b^{4} e^{2} + 16 \, a^{2} c^{2} e^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{6 \, {\left(b^{4} d e - 4 \, a b^{2} c d e - 2 \, a b^{3} e^{2} + 8 \, a^{2} b c e^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{b^{4} d^{2} - 8 \, a b^{2} c d^{2} + 16 \, a^{2} c^{2} d^{2} + 4 \, a b^{3} d e - 16 \, a^{2} b c d e - 8 \, a^{2} b^{2} e^{2} + 32 \, a^{3} c e^{2}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2/3*(((4*(2*b^2*c^2*d*e - 8*a*c^3*d*e - b^3*c*e^2 + 4*a*b*c^2*e^2)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(4*b^3*c*d*e - 16*a*b*c^2*d*e - b^4*e^2 + 16*a^2*c^2*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 6*(b^4*d*e - 4*a*b^2*c*d*e - 2*a*b^3*e^2 + 8*a^2*b*c*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (b^4*d^2 - 8*a*b^2*c*d^2 + 16*a^2*c^2*d^2 + 4*a*b^3*d*e - 16*a^2*b*c*d*e - 8*a^2*b^2*e^2 + 32*a^3*c*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
1591,1,205,0,0.278919," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(2 \, {\left(\frac{2 \, {\left(b^{2} c^{2} e - 4 \, a c^{3} e\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(b^{3} c e - 4 \, a b c^{2} e\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(b^{4} e - 4 \, a b^{2} c e\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d + 2 \, a b^{3} e - 8 \, a^{2} b c e}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((2*(2*(b^2*c^2*e - 4*a*c^3*e)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(b^3*c*e - 4*a*b*c^2*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(b^4*e - 4*a*b^2*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d + 2*a*b^3*e - 8*a^2*b*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
1592,1,14,0,0.280294," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\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
1593,1,8417,0,2.403504," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c d e^{3} - b e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{2 \, {\left({\left({\left(\frac{{\left(4 \, b^{2} c^{10} d^{14} e - 16 \, a c^{11} d^{14} e - 28 \, b^{3} c^{9} d^{13} e^{2} + 112 \, a b c^{10} d^{13} e^{2} + 87 \, b^{4} c^{8} d^{12} e^{3} - 332 \, a b^{2} c^{9} d^{12} e^{3} - 64 \, a^{2} c^{10} d^{12} e^{3} - 158 \, b^{5} c^{7} d^{11} e^{4} + 536 \, a b^{3} c^{8} d^{11} e^{4} + 384 \, a^{2} b c^{9} d^{11} e^{4} + 185 \, b^{6} c^{6} d^{10} e^{5} - 482 \, a b^{4} c^{7} d^{10} e^{5} - 1020 \, a^{2} b^{2} c^{8} d^{10} e^{5} - 48 \, a^{3} c^{9} d^{10} e^{5} - 144 \, b^{7} c^{5} d^{9} e^{6} + 166 \, a b^{5} c^{6} d^{9} e^{6} + 1580 \, a^{2} b^{3} c^{7} d^{9} e^{6} + 240 \, a^{3} b c^{8} d^{9} e^{6} + 73 \, b^{8} c^{4} d^{8} e^{7} + 128 \, a b^{6} c^{5} d^{8} e^{7} - 1515 \, a^{2} b^{4} c^{6} d^{8} e^{7} - 700 \, a^{3} b^{2} c^{7} d^{8} e^{7} + 160 \, a^{4} c^{8} d^{8} e^{7} - 22 \, b^{9} c^{3} d^{7} e^{8} - 188 \, a b^{7} c^{4} d^{7} e^{8} + 804 \, a^{2} b^{5} c^{5} d^{7} e^{8} + 1360 \, a^{3} b^{3} c^{6} d^{7} e^{8} - 640 \, a^{4} b c^{7} d^{7} e^{8} + 3 \, b^{10} c^{2} d^{6} e^{9} + 94 \, a b^{8} c^{3} d^{6} e^{9} - 94 \, a^{2} b^{6} c^{4} d^{6} e^{9} - 1500 \, a^{3} b^{4} c^{5} d^{6} e^{9} + 620 \, a^{4} b^{2} c^{6} d^{6} e^{9} + 400 \, a^{5} c^{7} d^{6} e^{9} - 18 \, a b^{9} c^{2} d^{5} e^{10} - 120 \, a^{2} b^{7} c^{3} d^{5} e^{10} + 748 \, a^{3} b^{5} c^{4} d^{5} e^{10} + 380 \, a^{4} b^{3} c^{5} d^{5} e^{10} - 1200 \, a^{5} b c^{6} d^{5} e^{10} + 45 \, a^{2} b^{8} c^{2} d^{4} e^{11} - 40 \, a^{3} b^{6} c^{3} d^{4} e^{11} - 815 \, a^{4} b^{4} c^{4} d^{4} e^{11} + 924 \, a^{5} b^{2} c^{5} d^{4} e^{11} + 384 \, a^{6} c^{6} d^{4} e^{11} - 60 \, a^{3} b^{7} c^{2} d^{3} e^{12} + 250 \, a^{4} b^{5} c^{3} d^{3} e^{12} + 152 \, a^{5} b^{3} c^{4} d^{3} e^{12} - 768 \, a^{6} b c^{5} d^{3} e^{12} + 45 \, a^{4} b^{6} c^{2} d^{2} e^{13} - 258 \, a^{5} b^{4} c^{3} d^{2} e^{13} + 268 \, a^{6} b^{2} c^{4} d^{2} e^{13} + 176 \, a^{7} c^{5} d^{2} e^{13} - 18 \, a^{5} b^{5} c^{2} d e^{14} + 116 \, a^{6} b^{3} c^{3} d e^{14} - 176 \, a^{7} b c^{4} d e^{14} + 3 \, a^{6} b^{4} c^{2} e^{15} - 20 \, a^{7} b^{2} c^{3} e^{15} + 32 \, a^{8} c^{4} e^{15}\right)} x}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}} + \frac{3 \, {\left(2 \, b^{3} c^{9} d^{14} e - 8 \, a b c^{10} d^{14} e - 15 \, b^{4} c^{8} d^{13} e^{2} + 64 \, a b^{2} c^{9} d^{13} e^{2} - 16 \, a^{2} c^{10} d^{13} e^{2} + 50 \, b^{5} c^{7} d^{12} e^{3} - 218 \, a b^{3} c^{8} d^{12} e^{3} + 72 \, a^{2} b c^{9} d^{12} e^{3} - 97 \, b^{6} c^{6} d^{11} e^{4} + 406 \, a b^{4} c^{7} d^{11} e^{4} - 48 \, a^{2} b^{2} c^{8} d^{11} e^{4} - 96 \, a^{3} c^{9} d^{11} e^{4} + 120 \, b^{7} c^{5} d^{10} e^{5} - 428 \, a b^{5} c^{6} d^{10} e^{5} - 334 \, a^{2} b^{3} c^{7} d^{10} e^{5} + 504 \, a^{3} b c^{8} d^{10} e^{5} - 97 \, b^{8} c^{4} d^{9} e^{6} + 208 \, a b^{6} c^{5} d^{9} e^{6} + 975 \, a^{2} b^{4} c^{6} d^{9} e^{6} - 960 \, a^{3} b^{2} c^{7} d^{9} e^{6} - 240 \, a^{4} c^{8} d^{9} e^{6} + 50 \, b^{9} c^{3} d^{8} e^{7} + 46 \, a b^{7} c^{4} d^{8} e^{7} - 1194 \, a^{2} b^{5} c^{5} d^{8} e^{7} + 550 \, a^{3} b^{3} c^{6} d^{8} e^{7} + 1160 \, a^{4} b c^{7} d^{8} e^{7} - 15 \, b^{10} c^{2} d^{7} e^{8} - 122 \, a b^{8} c^{3} d^{7} e^{8} + 698 \, a^{2} b^{6} c^{4} d^{7} e^{8} + 660 \, a^{3} b^{4} c^{5} d^{7} e^{8} - 2080 \, a^{4} b^{2} c^{6} d^{7} e^{8} - 320 \, a^{5} c^{7} d^{7} e^{8} + 2 \, b^{11} c d^{6} e^{9} + 64 \, a b^{9} c^{2} d^{6} e^{9} - 102 \, a^{2} b^{7} c^{3} d^{6} e^{9} - 1184 \, a^{3} b^{5} c^{4} d^{6} e^{9} + 1430 \, a^{4} b^{3} c^{5} d^{6} e^{9} + 1320 \, a^{5} b c^{6} d^{6} e^{9} - 12 \, a b^{10} c d^{5} e^{10} - 81 \, a^{2} b^{8} c^{2} d^{5} e^{10} + 596 \, a^{3} b^{6} c^{3} d^{5} e^{10} + 175 \, a^{4} b^{4} c^{4} d^{5} e^{10} - 1920 \, a^{5} b^{2} c^{5} d^{5} e^{10} - 240 \, a^{6} c^{6} d^{5} e^{10} + 30 \, a^{2} b^{9} c d^{4} e^{11} - 30 \, a^{3} b^{7} c^{2} d^{4} e^{11} - 650 \, a^{4} b^{5} c^{3} d^{4} e^{11} + 962 \, a^{5} b^{3} c^{4} d^{4} e^{11} + 792 \, a^{6} b c^{5} d^{4} e^{11} - 40 \, a^{3} b^{8} c d^{3} e^{12} + 175 \, a^{4} b^{6} c^{2} d^{3} e^{12} + 150 \, a^{5} b^{4} c^{3} d^{3} e^{12} - 816 \, a^{6} b^{2} c^{4} d^{3} e^{12} - 96 \, a^{7} c^{5} d^{3} e^{12} + 30 \, a^{4} b^{7} c d^{2} e^{13} - 180 \, a^{5} b^{5} c^{2} d^{2} e^{13} + 182 \, a^{6} b^{3} c^{3} d^{2} e^{13} + 232 \, a^{7} b c^{4} d^{2} e^{13} - 12 \, a^{5} b^{6} c d e^{14} + 81 \, a^{6} b^{4} c^{2} d e^{14} - 128 \, a^{7} b^{2} c^{3} d e^{14} - 16 \, a^{8} c^{4} d e^{14} + 2 \, a^{6} b^{5} c e^{15} - 14 \, a^{7} b^{3} c^{2} e^{15} + 24 \, a^{8} b c^{3} e^{15}\right)}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)} x + \frac{3 \, {\left(b^{4} c^{8} d^{14} e - 4 \, a b^{2} c^{9} d^{14} e - 8 \, b^{5} c^{7} d^{13} e^{2} + 36 \, a b^{3} c^{8} d^{13} e^{2} - 16 \, a^{2} b c^{9} d^{13} e^{2} + 28 \, b^{6} c^{6} d^{12} e^{3} - 132 \, a b^{4} c^{7} d^{12} e^{3} + 76 \, a^{2} b^{2} c^{8} d^{12} e^{3} + 16 \, a^{3} c^{9} d^{12} e^{3} - 56 \, b^{7} c^{5} d^{11} e^{4} + 254 \, a b^{5} c^{6} d^{11} e^{4} - 72 \, a^{2} b^{3} c^{7} d^{11} e^{4} - 192 \, a^{3} b c^{8} d^{11} e^{4} + 70 \, b^{8} c^{4} d^{10} e^{5} - 264 \, a b^{6} c^{5} d^{10} e^{5} - 241 \, a^{2} b^{4} c^{6} d^{10} e^{5} + 684 \, a^{3} b^{2} c^{7} d^{10} e^{5} + 96 \, a^{4} c^{8} d^{10} e^{5} - 56 \, b^{9} c^{3} d^{9} e^{6} + 114 \, a b^{7} c^{4} d^{9} e^{6} + 730 \, a^{2} b^{5} c^{5} d^{9} e^{6} - 980 \, a^{3} b^{3} c^{6} d^{9} e^{6} - 720 \, a^{4} b c^{7} d^{9} e^{6} + 28 \, b^{10} c^{2} d^{8} e^{7} + 44 \, a b^{8} c^{3} d^{8} e^{7} - 819 \, a^{2} b^{6} c^{4} d^{8} e^{7} + 290 \, a^{3} b^{4} c^{5} d^{8} e^{7} + 1900 \, a^{4} b^{2} c^{6} d^{8} e^{7} + 240 \, a^{5} c^{7} d^{8} e^{7} - 8 \, b^{11} c d^{7} e^{8} - 78 \, a b^{9} c^{2} d^{7} e^{8} + 404 \, a^{2} b^{7} c^{3} d^{7} e^{8} + 764 \, a^{3} b^{5} c^{4} d^{7} e^{8} - 2160 \, a^{4} b^{3} c^{5} d^{7} e^{8} - 1280 \, a^{5} b c^{6} d^{7} e^{8} + b^{12} d^{6} e^{9} + 36 \, a b^{10} c d^{6} e^{9} - 23 \, a^{2} b^{8} c^{2} d^{6} e^{9} - 888 \, a^{3} b^{6} c^{3} d^{6} e^{9} + 735 \, a^{4} b^{4} c^{4} d^{6} e^{9} + 2420 \, a^{5} b^{2} c^{5} d^{6} e^{9} + 320 \, a^{6} c^{6} d^{6} e^{9} - 6 \, a b^{11} d^{5} e^{10} - 54 \, a^{2} b^{9} c d^{5} e^{10} + 316 \, a^{3} b^{7} c^{2} d^{5} e^{10} + 524 \, a^{4} b^{5} c^{3} d^{5} e^{10} - 1860 \, a^{5} b^{3} c^{4} d^{5} e^{10} - 1200 \, a^{6} b c^{5} d^{5} e^{10} + 15 \, a^{2} b^{10} d^{4} e^{11} + 10 \, a^{3} b^{8} c d^{4} e^{11} - 450 \, a^{4} b^{6} c^{2} d^{4} e^{11} + 296 \, a^{5} b^{4} c^{3} d^{4} e^{11} + 1476 \, a^{6} b^{2} c^{4} d^{4} e^{11} + 240 \, a^{7} c^{5} d^{4} e^{11} - 20 \, a^{3} b^{9} d^{3} e^{12} + 60 \, a^{4} b^{7} c d^{3} e^{12} + 262 \, a^{5} b^{5} c^{2} d^{3} e^{12} - 584 \, a^{6} b^{3} c^{3} d^{3} e^{12} - 576 \, a^{7} b c^{4} d^{3} e^{12} + 15 \, a^{4} b^{8} d^{2} e^{13} - 72 \, a^{5} b^{6} c d^{2} e^{13} - 47 \, a^{6} b^{4} c^{2} d^{2} e^{13} + 356 \, a^{7} b^{2} c^{3} d^{2} e^{13} + 96 \, a^{8} c^{4} d^{2} e^{13} - 6 \, a^{5} b^{7} d e^{14} + 34 \, a^{6} b^{5} c d e^{14} - 12 \, a^{7} b^{3} c^{2} d e^{14} - 112 \, a^{8} b c^{3} d e^{14} + a^{6} b^{6} e^{15} - 6 \, a^{7} b^{4} c e^{15} + 4 \, a^{8} b^{2} c^{2} e^{15} + 16 \, a^{9} c^{3} e^{15}\right)}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)} x - \frac{b^{4} c^{8} d^{15} - 8 \, a b^{2} c^{9} d^{15} + 16 \, a^{2} c^{10} d^{15} - 8 \, b^{5} c^{7} d^{14} e + 62 \, a b^{3} c^{8} d^{14} e - 120 \, a^{2} b c^{9} d^{14} e + 28 \, b^{6} c^{6} d^{13} e^{2} - 200 \, a b^{4} c^{7} d^{13} e^{2} + 312 \, a^{2} b^{2} c^{8} d^{13} e^{2} + 160 \, a^{3} c^{9} d^{13} e^{2} - 56 \, b^{7} c^{5} d^{12} e^{3} + 336 \, a b^{5} c^{6} d^{12} e^{3} - 182 \, a^{2} b^{3} c^{7} d^{12} e^{3} - 1064 \, a^{3} b c^{8} d^{12} e^{3} + 70 \, b^{8} c^{4} d^{11} e^{4} - 280 \, a b^{6} c^{5} d^{11} e^{4} - 717 \, a^{2} b^{4} c^{6} d^{11} e^{4} + 2712 \, a^{3} b^{2} c^{7} d^{11} e^{4} + 624 \, a^{4} c^{8} d^{11} e^{4} - 56 \, b^{9} c^{3} d^{10} e^{5} + 28 \, a b^{7} c^{4} d^{10} e^{5} + 1740 \, a^{2} b^{5} c^{5} d^{10} e^{5} - 2930 \, a^{3} b^{3} c^{6} d^{10} e^{5} - 3576 \, a^{4} b c^{7} d^{10} e^{5} + 28 \, b^{10} c^{2} d^{9} e^{6} + 168 \, a b^{8} c^{3} d^{9} e^{6} - 1655 \, a^{2} b^{6} c^{4} d^{9} e^{6} + 90 \, a^{3} b^{4} c^{5} d^{9} e^{6} + 7880 \, a^{4} b^{2} c^{6} d^{9} e^{6} + 1280 \, a^{5} c^{7} d^{9} e^{6} - 8 \, b^{11} c d^{8} e^{7} - 160 \, a b^{9} c^{2} d^{8} e^{7} + 618 \, a^{2} b^{7} c^{3} d^{8} e^{7} + 2900 \, a^{3} b^{5} c^{4} d^{8} e^{7} - 7670 \, a^{4} b^{3} c^{5} d^{8} e^{7} - 6120 \, a^{5} b c^{6} d^{8} e^{7} + b^{12} d^{7} e^{8} + 64 \, a b^{10} c d^{7} e^{8} + 117 \, a^{2} b^{8} c^{2} d^{7} e^{8} - 2676 \, a^{3} b^{6} c^{3} d^{7} e^{8} + 1655 \, a^{4} b^{4} c^{4} d^{7} e^{8} + 10920 \, a^{5} b^{2} c^{5} d^{7} e^{8} + 1520 \, a^{6} c^{6} d^{7} e^{8} - 10 \, a b^{11} d^{6} e^{9} - 168 \, a^{2} b^{9} c d^{6} e^{9} + 758 \, a^{3} b^{7} c^{2} d^{6} e^{9} + 2696 \, a^{4} b^{5} c^{3} d^{6} e^{9} - 8150 \, a^{5} b^{3} c^{4} d^{6} e^{9} - 5800 \, a^{6} b c^{5} d^{6} e^{9} + 39 \, a^{2} b^{10} d^{5} e^{10} + 130 \, a^{3} b^{8} c d^{5} e^{10} - 1894 \, a^{4} b^{6} c^{2} d^{5} e^{10} + 996 \, a^{5} b^{4} c^{3} d^{5} e^{10} + 7752 \, a^{6} b^{2} c^{4} d^{5} e^{10} + 1056 \, a^{7} c^{5} d^{5} e^{10} - 80 \, a^{3} b^{9} d^{4} e^{11} + 190 \, a^{4} b^{7} c d^{4} e^{11} + 1632 \, a^{5} b^{5} c^{2} d^{4} e^{11} - 3698 \, a^{6} b^{3} c^{3} d^{4} e^{11} - 3000 \, a^{7} b c^{4} d^{4} e^{11} + 95 \, a^{4} b^{8} d^{3} e^{12} - 492 \, a^{5} b^{6} c d^{3} e^{12} - 235 \, a^{6} b^{4} c^{2} d^{3} e^{12} + 2632 \, a^{7} b^{2} c^{3} d^{3} e^{12} + 400 \, a^{8} c^{4} d^{3} e^{12} - 66 \, a^{5} b^{7} d^{2} e^{13} + 436 \, a^{6} b^{5} c d^{2} e^{13} - 502 \, a^{7} b^{3} c^{2} d^{2} e^{13} - 744 \, a^{8} b c^{3} d^{2} e^{13} + 25 \, a^{6} b^{6} d e^{14} - 182 \, a^{7} b^{4} c d e^{14} + 312 \, a^{8} b^{2} c^{2} d e^{14} + 64 \, a^{9} c^{3} d e^{14} - 4 \, a^{7} b^{5} e^{15} + 30 \, a^{8} b^{3} c e^{15} - 56 \, a^{9} b c^{2} e^{15}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2*(2*c*d*e^3 - b*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 2/3*((((4*b^2*c^10*d^14*e - 16*a*c^11*d^14*e - 28*b^3*c^9*d^13*e^2 + 112*a*b*c^10*d^13*e^2 + 87*b^4*c^8*d^12*e^3 - 332*a*b^2*c^9*d^12*e^3 - 64*a^2*c^10*d^12*e^3 - 158*b^5*c^7*d^11*e^4 + 536*a*b^3*c^8*d^11*e^4 + 384*a^2*b*c^9*d^11*e^4 + 185*b^6*c^6*d^10*e^5 - 482*a*b^4*c^7*d^10*e^5 - 1020*a^2*b^2*c^8*d^10*e^5 - 48*a^3*c^9*d^10*e^5 - 144*b^7*c^5*d^9*e^6 + 166*a*b^5*c^6*d^9*e^6 + 1580*a^2*b^3*c^7*d^9*e^6 + 240*a^3*b*c^8*d^9*e^6 + 73*b^8*c^4*d^8*e^7 + 128*a*b^6*c^5*d^8*e^7 - 1515*a^2*b^4*c^6*d^8*e^7 - 700*a^3*b^2*c^7*d^8*e^7 + 160*a^4*c^8*d^8*e^7 - 22*b^9*c^3*d^7*e^8 - 188*a*b^7*c^4*d^7*e^8 + 804*a^2*b^5*c^5*d^7*e^8 + 1360*a^3*b^3*c^6*d^7*e^8 - 640*a^4*b*c^7*d^7*e^8 + 3*b^10*c^2*d^6*e^9 + 94*a*b^8*c^3*d^6*e^9 - 94*a^2*b^6*c^4*d^6*e^9 - 1500*a^3*b^4*c^5*d^6*e^9 + 620*a^4*b^2*c^6*d^6*e^9 + 400*a^5*c^7*d^6*e^9 - 18*a*b^9*c^2*d^5*e^10 - 120*a^2*b^7*c^3*d^5*e^10 + 748*a^3*b^5*c^4*d^5*e^10 + 380*a^4*b^3*c^5*d^5*e^10 - 1200*a^5*b*c^6*d^5*e^10 + 45*a^2*b^8*c^2*d^4*e^11 - 40*a^3*b^6*c^3*d^4*e^11 - 815*a^4*b^4*c^4*d^4*e^11 + 924*a^5*b^2*c^5*d^4*e^11 + 384*a^6*c^6*d^4*e^11 - 60*a^3*b^7*c^2*d^3*e^12 + 250*a^4*b^5*c^3*d^3*e^12 + 152*a^5*b^3*c^4*d^3*e^12 - 768*a^6*b*c^5*d^3*e^12 + 45*a^4*b^6*c^2*d^2*e^13 - 258*a^5*b^4*c^3*d^2*e^13 + 268*a^6*b^2*c^4*d^2*e^13 + 176*a^7*c^5*d^2*e^13 - 18*a^5*b^5*c^2*d*e^14 + 116*a^6*b^3*c^3*d*e^14 - 176*a^7*b*c^4*d*e^14 + 3*a^6*b^4*c^2*e^15 - 20*a^7*b^2*c^3*e^15 + 32*a^8*c^4*e^15)*x/(b^4*c^8*d^16 - 8*a*b^2*c^9*d^16 + 16*a^2*c^10*d^16 - 8*b^5*c^7*d^15*e + 64*a*b^3*c^8*d^15*e - 128*a^2*b*c^9*d^15*e + 28*b^6*c^6*d^14*e^2 - 216*a*b^4*c^7*d^14*e^2 + 384*a^2*b^2*c^8*d^14*e^2 + 128*a^3*c^9*d^14*e^2 - 56*b^7*c^5*d^13*e^3 + 392*a*b^5*c^6*d^13*e^3 - 448*a^2*b^3*c^7*d^13*e^3 - 896*a^3*b*c^8*d^13*e^3 + 70*b^8*c^4*d^12*e^4 - 392*a*b^6*c^5*d^12*e^4 - 196*a^2*b^4*c^6*d^12*e^4 + 2464*a^3*b^2*c^7*d^12*e^4 + 448*a^4*c^8*d^12*e^4 - 56*b^9*c^3*d^11*e^5 + 168*a*b^7*c^4*d^11*e^5 + 1176*a^2*b^5*c^5*d^11*e^5 - 3136*a^3*b^3*c^6*d^11*e^5 - 2688*a^4*b*c^7*d^11*e^5 + 28*b^10*c^2*d^10*e^6 + 56*a*b^8*c^3*d^10*e^6 - 1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 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8*b^11*c*d^7*e^8 - 78*a*b^9*c^2*d^7*e^8 + 404*a^2*b^7*c^3*d^7*e^8 + 764*a^3*b^5*c^4*d^7*e^8 - 2160*a^4*b^3*c^5*d^7*e^8 - 1280*a^5*b*c^6*d^7*e^8 + b^12*d^6*e^9 + 36*a*b^10*c*d^6*e^9 - 23*a^2*b^8*c^2*d^6*e^9 - 888*a^3*b^6*c^3*d^6*e^9 + 735*a^4*b^4*c^4*d^6*e^9 + 2420*a^5*b^2*c^5*d^6*e^9 + 320*a^6*c^6*d^6*e^9 - 6*a*b^11*d^5*e^10 - 54*a^2*b^9*c*d^5*e^10 + 316*a^3*b^7*c^2*d^5*e^10 + 524*a^4*b^5*c^3*d^5*e^10 - 1860*a^5*b^3*c^4*d^5*e^10 - 1200*a^6*b*c^5*d^5*e^10 + 15*a^2*b^10*d^4*e^11 + 10*a^3*b^8*c*d^4*e^11 - 450*a^4*b^6*c^2*d^4*e^11 + 296*a^5*b^4*c^3*d^4*e^11 + 1476*a^6*b^2*c^4*d^4*e^11 + 240*a^7*c^5*d^4*e^11 - 20*a^3*b^9*d^3*e^12 + 60*a^4*b^7*c*d^3*e^12 + 262*a^5*b^5*c^2*d^3*e^12 - 584*a^6*b^3*c^3*d^3*e^12 - 576*a^7*b*c^4*d^3*e^12 + 15*a^4*b^8*d^2*e^13 - 72*a^5*b^6*c*d^2*e^13 - 47*a^6*b^4*c^2*d^2*e^13 + 356*a^7*b^2*c^3*d^2*e^13 + 96*a^8*c^4*d^2*e^13 - 6*a^5*b^7*d*e^14 + 34*a^6*b^5*c*d*e^14 - 12*a^7*b^3*c^2*d*e^14 - 112*a^8*b*c^3*d*e^14 + a^6*b^6*e^15 - 6*a^7*b^4*c*e^15 + 4*a^8*b^2*c^2*e^15 + 16*a^9*c^3*e^15)/(b^4*c^8*d^16 - 8*a*b^2*c^9*d^16 + 16*a^2*c^10*d^16 - 8*b^5*c^7*d^15*e + 64*a*b^3*c^8*d^15*e - 128*a^2*b*c^9*d^15*e + 28*b^6*c^6*d^14*e^2 - 216*a*b^4*c^7*d^14*e^2 + 384*a^2*b^2*c^8*d^14*e^2 + 128*a^3*c^9*d^14*e^2 - 56*b^7*c^5*d^13*e^3 + 392*a*b^5*c^6*d^13*e^3 - 448*a^2*b^3*c^7*d^13*e^3 - 896*a^3*b*c^8*d^13*e^3 + 70*b^8*c^4*d^12*e^4 - 392*a*b^6*c^5*d^12*e^4 - 196*a^2*b^4*c^6*d^12*e^4 + 2464*a^3*b^2*c^7*d^12*e^4 + 448*a^4*c^8*d^12*e^4 - 56*b^9*c^3*d^11*e^5 + 168*a*b^7*c^4*d^11*e^5 + 1176*a^2*b^5*c^5*d^11*e^5 - 3136*a^3*b^3*c^6*d^11*e^5 - 2688*a^4*b*c^7*d^11*e^5 + 28*b^10*c^2*d^10*e^6 + 56*a*b^8*c^3*d^10*e^6 - 1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 12*a^2*b^8*c^2*d^8*e^8 - 1904*a^3*b^6*c^3*d^8*e^8 + 2310*a^4*b^4*c^4*d^8*e^8 + 8400*a^5*b^2*c^5*d^8*e^8 + 1120*a^6*c^6*d^8*e^8 - 8*a*b^11*d^7*e^9 - 104*a^2*b^9*c*d^7*e^9 + 656*a^3*b^7*c^2*d^7*e^9 + 1512*a^4*b^5*c^3*d^7*e^9 - 6720*a^5*b^3*c^4*d^7*e^9 - 4480*a^6*b*c^5*d^7*e^9 + 28*a^2*b^10*d^6*e^10 + 56*a^3*b^8*c*d^6*e^10 - 1372*a^4*b^6*c^2*d^6*e^10 + 1176*a^5*b^4*c^3*d^6*e^10 + 6272*a^6*b^2*c^4*d^6*e^10 + 896*a^7*c^5*d^6*e^10 - 56*a^3*b^9*d^5*e^11 + 168*a^4*b^7*c*d^5*e^11 + 1176*a^5*b^5*c^2*d^5*e^11 - 3136*a^6*b^3*c^3*d^5*e^11 - 2688*a^7*b*c^4*d^5*e^11 + 70*a^4*b^8*d^4*e^12 - 392*a^5*b^6*c*d^4*e^12 - 196*a^6*b^4*c^2*d^4*e^12 + 2464*a^7*b^2*c^3*d^4*e^12 + 448*a^8*c^4*d^4*e^12 - 56*a^5*b^7*d^3*e^13 + 392*a^6*b^5*c*d^3*e^13 - 448*a^7*b^3*c^2*d^3*e^13 - 896*a^8*b*c^3*d^3*e^13 + 28*a^6*b^6*d^2*e^14 - 216*a^7*b^4*c*d^2*e^14 + 384*a^8*b^2*c^2*d^2*e^14 + 128*a^9*c^3*d^2*e^14 - 8*a^7*b^5*d*e^15 + 64*a^8*b^3*c*d*e^15 - 128*a^9*b*c^2*d*e^15 + a^8*b^4*e^16 - 8*a^9*b^2*c*e^16 + 16*a^10*c^2*e^16))*x - (b^4*c^8*d^15 - 8*a*b^2*c^9*d^15 + 16*a^2*c^10*d^15 - 8*b^5*c^7*d^14*e + 62*a*b^3*c^8*d^14*e - 120*a^2*b*c^9*d^14*e + 28*b^6*c^6*d^13*e^2 - 200*a*b^4*c^7*d^13*e^2 + 312*a^2*b^2*c^8*d^13*e^2 + 160*a^3*c^9*d^13*e^2 - 56*b^7*c^5*d^12*e^3 + 336*a*b^5*c^6*d^12*e^3 - 182*a^2*b^3*c^7*d^12*e^3 - 1064*a^3*b*c^8*d^12*e^3 + 70*b^8*c^4*d^11*e^4 - 280*a*b^6*c^5*d^11*e^4 - 717*a^2*b^4*c^6*d^11*e^4 + 2712*a^3*b^2*c^7*d^11*e^4 + 624*a^4*c^8*d^11*e^4 - 56*b^9*c^3*d^10*e^5 + 28*a*b^7*c^4*d^10*e^5 + 1740*a^2*b^5*c^5*d^10*e^5 - 2930*a^3*b^3*c^6*d^10*e^5 - 3576*a^4*b*c^7*d^10*e^5 + 28*b^10*c^2*d^9*e^6 + 168*a*b^8*c^3*d^9*e^6 - 1655*a^2*b^6*c^4*d^9*e^6 + 90*a^3*b^4*c^5*d^9*e^6 + 7880*a^4*b^2*c^6*d^9*e^6 + 1280*a^5*c^7*d^9*e^6 - 8*b^11*c*d^8*e^7 - 160*a*b^9*c^2*d^8*e^7 + 618*a^2*b^7*c^3*d^8*e^7 + 2900*a^3*b^5*c^4*d^8*e^7 - 7670*a^4*b^3*c^5*d^8*e^7 - 6120*a^5*b*c^6*d^8*e^7 + b^12*d^7*e^8 + 64*a*b^10*c*d^7*e^8 + 117*a^2*b^8*c^2*d^7*e^8 - 2676*a^3*b^6*c^3*d^7*e^8 + 1655*a^4*b^4*c^4*d^7*e^8 + 10920*a^5*b^2*c^5*d^7*e^8 + 1520*a^6*c^6*d^7*e^8 - 10*a*b^11*d^6*e^9 - 168*a^2*b^9*c*d^6*e^9 + 758*a^3*b^7*c^2*d^6*e^9 + 2696*a^4*b^5*c^3*d^6*e^9 - 8150*a^5*b^3*c^4*d^6*e^9 - 5800*a^6*b*c^5*d^6*e^9 + 39*a^2*b^10*d^5*e^10 + 130*a^3*b^8*c*d^5*e^10 - 1894*a^4*b^6*c^2*d^5*e^10 + 996*a^5*b^4*c^3*d^5*e^10 + 7752*a^6*b^2*c^4*d^5*e^10 + 1056*a^7*c^5*d^5*e^10 - 80*a^3*b^9*d^4*e^11 + 190*a^4*b^7*c*d^4*e^11 + 1632*a^5*b^5*c^2*d^4*e^11 - 3698*a^6*b^3*c^3*d^4*e^11 - 3000*a^7*b*c^4*d^4*e^11 + 95*a^4*b^8*d^3*e^12 - 492*a^5*b^6*c*d^3*e^12 - 235*a^6*b^4*c^2*d^3*e^12 + 2632*a^7*b^2*c^3*d^3*e^12 + 400*a^8*c^4*d^3*e^12 - 66*a^5*b^7*d^2*e^13 + 436*a^6*b^5*c*d^2*e^13 - 502*a^7*b^3*c^2*d^2*e^13 - 744*a^8*b*c^3*d^2*e^13 + 25*a^6*b^6*d*e^14 - 182*a^7*b^4*c*d*e^14 + 312*a^8*b^2*c^2*d*e^14 + 64*a^9*c^3*d*e^14 - 4*a^7*b^5*e^15 + 30*a^8*b^3*c*e^15 - 56*a^9*b*c^2*e^15)/(b^4*c^8*d^16 - 8*a*b^2*c^9*d^16 + 16*a^2*c^10*d^16 - 8*b^5*c^7*d^15*e + 64*a*b^3*c^8*d^15*e - 128*a^2*b*c^9*d^15*e + 28*b^6*c^6*d^14*e^2 - 216*a*b^4*c^7*d^14*e^2 + 384*a^2*b^2*c^8*d^14*e^2 + 128*a^3*c^9*d^14*e^2 - 56*b^7*c^5*d^13*e^3 + 392*a*b^5*c^6*d^13*e^3 - 448*a^2*b^3*c^7*d^13*e^3 - 896*a^3*b*c^8*d^13*e^3 + 70*b^8*c^4*d^12*e^4 - 392*a*b^6*c^5*d^12*e^4 - 196*a^2*b^4*c^6*d^12*e^4 + 2464*a^3*b^2*c^7*d^12*e^4 + 448*a^4*c^8*d^12*e^4 - 56*b^9*c^3*d^11*e^5 + 168*a*b^7*c^4*d^11*e^5 + 1176*a^2*b^5*c^5*d^11*e^5 - 3136*a^3*b^3*c^6*d^11*e^5 - 2688*a^4*b*c^7*d^11*e^5 + 28*b^10*c^2*d^10*e^6 + 56*a*b^8*c^3*d^10*e^6 - 1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 12*a^2*b^8*c^2*d^8*e^8 - 1904*a^3*b^6*c^3*d^8*e^8 + 2310*a^4*b^4*c^4*d^8*e^8 + 8400*a^5*b^2*c^5*d^8*e^8 + 1120*a^6*c^6*d^8*e^8 - 8*a*b^11*d^7*e^9 - 104*a^2*b^9*c*d^7*e^9 + 656*a^3*b^7*c^2*d^7*e^9 + 1512*a^4*b^5*c^3*d^7*e^9 - 6720*a^5*b^3*c^4*d^7*e^9 - 4480*a^6*b*c^5*d^7*e^9 + 28*a^2*b^10*d^6*e^10 + 56*a^3*b^8*c*d^6*e^10 - 1372*a^4*b^6*c^2*d^6*e^10 + 1176*a^5*b^4*c^3*d^6*e^10 + 6272*a^6*b^2*c^4*d^6*e^10 + 896*a^7*c^5*d^6*e^10 - 56*a^3*b^9*d^5*e^11 + 168*a^4*b^7*c*d^5*e^11 + 1176*a^5*b^5*c^2*d^5*e^11 - 3136*a^6*b^3*c^3*d^5*e^11 - 2688*a^7*b*c^4*d^5*e^11 + 70*a^4*b^8*d^4*e^12 - 392*a^5*b^6*c*d^4*e^12 - 196*a^6*b^4*c^2*d^4*e^12 + 2464*a^7*b^2*c^3*d^4*e^12 + 448*a^8*c^4*d^4*e^12 - 56*a^5*b^7*d^3*e^13 + 392*a^6*b^5*c*d^3*e^13 - 448*a^7*b^3*c^2*d^3*e^13 - 896*a^8*b*c^3*d^3*e^13 + 28*a^6*b^6*d^2*e^14 - 216*a^7*b^4*c*d^2*e^14 + 384*a^8*b^2*c^2*d^2*e^14 + 128*a^9*c^3*d^2*e^14 - 8*a^7*b^5*d*e^15 + 64*a^8*b^3*c*d*e^15 - 128*a^9*b*c^2*d*e^15 + a^8*b^4*e^16 - 8*a^9*b^2*c*e^16 + 16*a^10*c^2*e^16))/(c*x^2 + b*x + a)^(3/2)","B",0
1594,1,6103,0,3.182081," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\frac{{\left(32 \, \sqrt{c d^{2} - b d e + a e^{2}} c^{4} d^{3} e^{3} + 48 \, b^{2} c^{\frac{5}{2}} d^{2} e^{5} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 192 \, a c^{\frac{7}{2}} d^{2} e^{5} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 48 \, \sqrt{c d^{2} - b d e + a e^{2}} b c^{3} d^{2} e^{4} - 48 \, b^{3} c^{\frac{3}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 192 \, a b c^{\frac{5}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 76 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{2} c^{2} d e^{5} - 208 \, \sqrt{c d^{2} - b d e + a e^{2}} a c^{3} d e^{5} + 15 \, b^{4} \sqrt{c} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 72 \, a b^{2} c^{\frac{3}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 48 \, a^{2} c^{\frac{5}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 30 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{3} c e^{6} + 104 \, \sqrt{c d^{2} - b d e + a e^{2}} a b c^{2} e^{6}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e + a e^{2}} b^{2} c^{\frac{7}{2}} d^{6} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} a c^{\frac{9}{2}} d^{6} - 3 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{3} c^{\frac{5}{2}} d^{5} e + 12 \, \sqrt{c d^{2} - b d e + a e^{2}} a b c^{\frac{7}{2}} d^{5} e + 3 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{4} c^{\frac{3}{2}} d^{4} e^{2} - 9 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{2} c^{\frac{5}{2}} d^{4} e^{2} - 12 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} c^{\frac{7}{2}} d^{4} e^{2} - \sqrt{c d^{2} - b d e + a e^{2}} b^{5} \sqrt{c} d^{3} e^{3} - 2 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{3} c^{\frac{3}{2}} d^{3} e^{3} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b c^{\frac{5}{2}} d^{3} e^{3} + 3 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{4} \sqrt{c} d^{2} e^{4} - 9 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{2} c^{\frac{3}{2}} d^{2} e^{4} - 12 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} c^{\frac{5}{2}} d^{2} e^{4} - 3 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{3} \sqrt{c} d e^{5} + 12 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b c^{\frac{3}{2}} d e^{5} + \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b^{2} \sqrt{c} e^{6} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{4} c^{\frac{3}{2}} e^{6}} + \frac{2 \, {\left(\frac{{\left(\frac{{\left(\frac{{\left(\frac{4 \, {\left(4 \, b^{2} c^{5} d^{6} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, a c^{6} d^{6} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 12 \, b^{3} c^{4} d^{5} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a b c^{5} d^{5} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 31 \, b^{4} c^{3} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 188 \, a b^{2} c^{4} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 256 \, a^{2} c^{5} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 42 \, b^{5} c^{2} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 296 \, a b^{3} c^{3} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 512 \, a^{2} b c^{4} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, b^{6} c d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 162 \, a b^{4} c^{2} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 204 \, a^{2} b^{2} c^{3} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 240 \, a^{3} c^{4} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, b^{7} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 22 \, a b^{5} c d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 52 \, a^{2} b^{3} c^{2} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 240 \, a^{3} b c^{3} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, a b^{6} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 41 \, a^{2} b^{4} c e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 92 \, a^{3} b^{2} c^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, a^{4} c^{3} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}} - \frac{3 \, {\left(2 \, b^{4} c^{3} d^{5} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, a b^{2} c^{4} d^{5} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} c^{5} d^{5} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, b^{5} c^{2} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 40 \, a b^{3} c^{3} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 80 \, a^{2} b c^{4} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 4 \, b^{6} c d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 28 \, a b^{4} c^{2} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} b^{2} c^{3} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 64 \, a^{3} c^{4} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, a b^{5} c d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} b^{3} c^{2} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 96 \, a^{3} b c^{3} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, a b^{6} d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 14 \, a^{2} b^{4} c d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{3} b^{2} c^{2} d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{4} c^{3} d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - a^{2} b^{5} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 8 \, a^{3} b^{3} c e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, a^{4} b c^{2} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{3 \, {\left(16 \, b^{2} c^{5} d^{5} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 64 \, a c^{6} d^{5} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 40 \, b^{3} c^{4} d^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 160 \, a b c^{5} d^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 84 \, b^{4} c^{3} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 512 \, a b^{2} c^{4} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 704 \, a^{2} c^{5} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 86 \, b^{5} c^{2} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 608 \, a b^{3} c^{3} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 1056 \, a^{2} b c^{4} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 36 \, b^{6} c d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 260 \, a b^{4} c^{2} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 432 \, a^{2} b^{2} c^{3} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 128 \, a^{3} c^{4} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, b^{7} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 34 \, a b^{5} c e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 40 \, a^{2} b^{3} c^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 64 \, a^{3} b c^{3} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(8 \, b^{2} c^{5} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, a c^{6} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, b^{3} c^{4} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 64 \, a b c^{5} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 29 \, b^{4} c^{3} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 184 \, a b^{2} c^{4} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 272 \, a^{2} c^{5} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, b^{5} c^{2} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 152 \, a b^{3} c^{3} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 272 \, a^{2} b c^{4} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, b^{6} c e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 39 \, a b^{4} c^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 80 \, a^{2} b^{2} c^{3} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, a^{3} c^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{16 \, b^{2} c^{5} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 64 \, a c^{6} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, b^{3} c^{4} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 96 \, a b c^{5} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 38 \, b^{4} c^{3} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 256 \, a b^{2} c^{4} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 416 \, a^{2} c^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 15 \, b^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 112 \, a b^{3} c^{3} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 208 \, a^{2} b c^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)}}{{\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{\frac{3}{2}}} - \frac{3 \, {\left(16 \, c^{2} d^{2} e^{6} - 16 \, b c d e^{7} + 5 \, b^{2} e^{8} - 4 \, a c e^{8}\right)} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3} + a e^{4}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"-1/6*((32*sqrt(c*d^2 - b*d*e + a*e^2)*c^4*d^3*e^3 + 48*b^2*c^(5/2)*d^2*e^5*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 192*a*c^(7/2)*d^2*e^5*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 48*sqrt(c*d^2 - b*d*e + a*e^2)*b*c^3*d^2*e^4 - 48*b^3*c^(3/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 192*a*b*c^(5/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 76*sqrt(c*d^2 - b*d*e + a*e^2)*b^2*c^2*d*e^5 - 208*sqrt(c*d^2 - b*d*e + a*e^2)*a*c^3*d*e^5 + 15*b^4*sqrt(c)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 72*a*b^2*c^(3/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 48*a^2*c^(5/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 30*sqrt(c*d^2 - b*d*e + a*e^2)*b^3*c*e^6 + 104*sqrt(c*d^2 - b*d*e + a*e^2)*a*b*c^2*e^6)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e + a*e^2)*b^2*c^(7/2)*d^6 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*a*c^(9/2)*d^6 - 3*sqrt(c*d^2 - b*d*e + a*e^2)*b^3*c^(5/2)*d^5*e + 12*sqrt(c*d^2 - b*d*e + a*e^2)*a*b*c^(7/2)*d^5*e + 3*sqrt(c*d^2 - b*d*e + a*e^2)*b^4*c^(3/2)*d^4*e^2 - 9*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^2*c^(5/2)*d^4*e^2 - 12*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*c^(7/2)*d^4*e^2 - sqrt(c*d^2 - b*d*e + a*e^2)*b^5*sqrt(c)*d^3*e^3 - 2*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^3*c^(3/2)*d^3*e^3 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b*c^(5/2)*d^3*e^3 + 3*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^4*sqrt(c)*d^2*e^4 - 9*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^2*c^(3/2)*d^2*e^4 - 12*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*c^(5/2)*d^2*e^4 - 3*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^3*sqrt(c)*d*e^5 + 12*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b*c^(3/2)*d*e^5 + sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b^2*sqrt(c)*e^6 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*a^4*c^(3/2)*e^6) + 2*((((4*(4*b^2*c^5*d^6*e^17*sgn(1/(x*e + d)) - 16*a*c^6*d^6*e^17*sgn(1/(x*e + d)) - 12*b^3*c^4*d^5*e^18*sgn(1/(x*e + d)) + 48*a*b*c^5*d^5*e^18*sgn(1/(x*e + d)) + 31*b^4*c^3*d^4*e^19*sgn(1/(x*e + d)) - 188*a*b^2*c^4*d^4*e^19*sgn(1/(x*e + d)) + 256*a^2*c^5*d^4*e^19*sgn(1/(x*e + d)) - 42*b^5*c^2*d^3*e^20*sgn(1/(x*e + d)) + 296*a*b^3*c^3*d^3*e^20*sgn(1/(x*e + d)) - 512*a^2*b*c^4*d^3*e^20*sgn(1/(x*e + d)) + 24*b^6*c*d^2*e^21*sgn(1/(x*e + d)) - 162*a*b^4*c^2*d^2*e^21*sgn(1/(x*e + d)) + 204*a^2*b^2*c^3*d^2*e^21*sgn(1/(x*e + d)) + 240*a^3*c^4*d^2*e^21*sgn(1/(x*e + d)) - 5*b^7*d*e^22*sgn(1/(x*e + d)) + 22*a*b^5*c*d*e^22*sgn(1/(x*e + d)) + 52*a^2*b^3*c^2*d*e^22*sgn(1/(x*e + d)) - 240*a^3*b*c^3*d*e^22*sgn(1/(x*e + d)) + 5*a*b^6*e^23*sgn(1/(x*e + d)) - 41*a^2*b^4*c*e^23*sgn(1/(x*e + d)) + 92*a^3*b^2*c^2*e^23*sgn(1/(x*e + d)) - 32*a^4*c^3*e^23*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2) - 3*(2*b^4*c^3*d^5*e^20*sgn(1/(x*e + d)) - 16*a*b^2*c^4*d^5*e^20*sgn(1/(x*e + d)) + 32*a^2*c^5*d^5*e^20*sgn(1/(x*e + d)) - 5*b^5*c^2*d^4*e^21*sgn(1/(x*e + d)) + 40*a*b^3*c^3*d^4*e^21*sgn(1/(x*e + d)) - 80*a^2*b*c^4*d^4*e^21*sgn(1/(x*e + d)) + 4*b^6*c*d^3*e^22*sgn(1/(x*e + d)) - 28*a*b^4*c^2*d^3*e^22*sgn(1/(x*e + d)) + 32*a^2*b^2*c^3*d^3*e^22*sgn(1/(x*e + d)) + 64*a^3*c^4*d^3*e^22*sgn(1/(x*e + d)) - b^7*d^2*e^23*sgn(1/(x*e + d)) + 2*a*b^5*c*d^2*e^23*sgn(1/(x*e + d)) + 32*a^2*b^3*c^2*d^2*e^23*sgn(1/(x*e + d)) - 96*a^3*b*c^3*d^2*e^23*sgn(1/(x*e + d)) + 2*a*b^6*d*e^24*sgn(1/(x*e + d)) - 14*a^2*b^4*c*d*e^24*sgn(1/(x*e + d)) + 16*a^3*b^2*c^2*d*e^24*sgn(1/(x*e + d)) + 32*a^4*c^3*d*e^24*sgn(1/(x*e + d)) - a^2*b^5*e^25*sgn(1/(x*e + d)) + 8*a^3*b^3*c*e^25*sgn(1/(x*e + d)) - 16*a^4*b*c^2*e^25*sgn(1/(x*e + d)))*e^(-1)/((b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2)*(x*e + d)))*e^(-1)/(x*e + d) - 3*(16*b^2*c^5*d^5*e^16*sgn(1/(x*e + d)) - 64*a*c^6*d^5*e^16*sgn(1/(x*e + d)) - 40*b^3*c^4*d^4*e^17*sgn(1/(x*e + d)) + 160*a*b*c^5*d^4*e^17*sgn(1/(x*e + d)) + 84*b^4*c^3*d^3*e^18*sgn(1/(x*e + d)) - 512*a*b^2*c^4*d^3*e^18*sgn(1/(x*e + d)) + 704*a^2*c^5*d^3*e^18*sgn(1/(x*e + d)) - 86*b^5*c^2*d^2*e^19*sgn(1/(x*e + d)) + 608*a*b^3*c^3*d^2*e^19*sgn(1/(x*e + d)) - 1056*a^2*b*c^4*d^2*e^19*sgn(1/(x*e + d)) + 36*b^6*c*d*e^20*sgn(1/(x*e + d)) - 260*a*b^4*c^2*d*e^20*sgn(1/(x*e + d)) + 432*a^2*b^2*c^3*d*e^20*sgn(1/(x*e + d)) + 128*a^3*c^4*d*e^20*sgn(1/(x*e + d)) - 5*b^7*e^21*sgn(1/(x*e + d)) + 34*a*b^5*c*e^21*sgn(1/(x*e + d)) - 40*a^2*b^3*c^2*e^21*sgn(1/(x*e + d)) - 64*a^3*b*c^3*e^21*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2))*e^(-1)/(x*e + d) + 6*(8*b^2*c^5*d^4*e^15*sgn(1/(x*e + d)) - 32*a*c^6*d^4*e^15*sgn(1/(x*e + d)) - 16*b^3*c^4*d^3*e^16*sgn(1/(x*e + d)) + 64*a*b*c^5*d^3*e^16*sgn(1/(x*e + d)) + 29*b^4*c^3*d^2*e^17*sgn(1/(x*e + d)) - 184*a*b^2*c^4*d^2*e^17*sgn(1/(x*e + d)) + 272*a^2*c^5*d^2*e^17*sgn(1/(x*e + d)) - 21*b^5*c^2*d*e^18*sgn(1/(x*e + d)) + 152*a*b^3*c^3*d*e^18*sgn(1/(x*e + d)) - 272*a^2*b*c^4*d*e^18*sgn(1/(x*e + d)) + 5*b^6*c*e^19*sgn(1/(x*e + d)) - 39*a*b^4*c^2*e^19*sgn(1/(x*e + d)) + 80*a^2*b^2*c^3*e^19*sgn(1/(x*e + d)) - 16*a^3*c^4*e^19*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2))*e^(-1)/(x*e + d) - (16*b^2*c^5*d^3*e^14*sgn(1/(x*e + d)) - 64*a*c^6*d^3*e^14*sgn(1/(x*e + d)) - 24*b^3*c^4*d^2*e^15*sgn(1/(x*e + d)) + 96*a*b*c^5*d^2*e^15*sgn(1/(x*e + d)) + 38*b^4*c^3*d*e^16*sgn(1/(x*e + d)) - 256*a*b^2*c^4*d*e^16*sgn(1/(x*e + d)) + 416*a^2*c^5*d*e^16*sgn(1/(x*e + d)) - 15*b^5*c^2*e^17*sgn(1/(x*e + d)) + 112*a*b^3*c^3*e^17*sgn(1/(x*e + d)) - 208*a^2*b*c^4*e^17*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2))/(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)^(3/2) - 3*(16*c^2*d^2*e^6 - 16*b*c*d*e^7 + 5*b^2*e^8 - 4*a*c*e^8)*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3 + a*e^4)*e^(-1)/(x*e + d))))/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7)*sqrt(c*d^2 - b*d*e + a*e^2)*sgn(1/(x*e + d))))*e^(-2)","B",0
1595,1,1087,0,0.227152," ","integrate((2*c*x+b)*(e*x+d)^(5/2)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b^{2} d^{3} e^{\left(-1\right)} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a c d^{3} e^{\left(-1\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b c d^{3} e^{\left(-2\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{2} d^{3} e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{2} e^{\left(-1\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d^{2} e^{\left(-1\right)} + 11583 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d^{2} e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{2} e^{\left(-3\right)} + 45045 \, \sqrt{x e + d} a b d^{3} + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{2} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d e^{\left(-1\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c d e^{\left(-1\right)} + 1287 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c d e^{\left(-2\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} e^{\left(-1\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c e^{\left(-1\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c e^{\left(-2\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} e^{\left(-3\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b^2*d^3*e^(-1) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*c*d^3*e^(-1) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*c*d^3*e^(-2) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^2*d^3*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^2*e^(-1) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d^2*e^(-1) + 11583*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d^2*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^2*e^(-3) + 45045*sqrt(x*e + d)*a*b*d^3 + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^2 + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d*e^(-1) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*d*e^(-1) + 1287*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*d*e^(-2) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*e^(-1) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c*e^(-1) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c*e^(-2) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*e^(-3) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b)*e^(-1)","B",0
1596,1,711,0,0.194786," ","integrate((2*c*x+b)*(e*x+d)^(3/2)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b^{2} d^{2} e^{\left(-1\right)} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a c d^{2} e^{\left(-1\right)} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b c d^{2} e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{2} d^{2} e^{\left(-3\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d e^{\left(-1\right)} + 924 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d e^{\left(-1\right)} + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d e^{\left(-2\right)} + 44 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d e^{\left(-3\right)} + 3465 \, \sqrt{x e + d} a b d^{2} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} e^{\left(-1\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c e^{\left(-1\right)} + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c e^{\left(-2\right)} + 10 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} e^{\left(-3\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b^2*d^2*e^(-1) + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*c*d^2*e^(-1) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*c*d^2*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^2*d^2*e^(-3) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d*e^(-1) + 924*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d*e^(-1) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d*e^(-2) + 44*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d*e^(-3) + 3465*sqrt(x*e + d)*a*b*d^2 + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*e^(-1) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*e^(-1) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*e^(-2) + 10*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*e^(-3) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b)*e^(-1)","B",0
1597,1,400,0,0.270379," ","integrate((2*c*x+b)*(c*x^2+b*x+a)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b^{2} d e^{\left(-1\right)} + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a c d e^{\left(-1\right)} + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b c d e^{\left(-2\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{2} d e^{\left(-3\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} e^{\left(-1\right)} + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c e^{\left(-1\right)} + 27 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c e^{\left(-2\right)} + 2 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} e^{\left(-3\right)} + 315 \, \sqrt{x e + d} a b d + 105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b^2*d*e^(-1) + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*c*d*e^(-1) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*c*d*e^(-2) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^2*d*e^(-3) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*e^(-1) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*e^(-1) + 27*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*e^(-2) + 2*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*e^(-3) + 315*sqrt(x*e + d)*a*b*d + 105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b)*e^(-1)","B",0
1598,1,166,0,0.266675," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b^{2} e^{\left(-1\right)} + 70 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a c e^{\left(-1\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b c e^{\left(-2\right)} + 6 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{2} e^{\left(-3\right)} + 105 \, \sqrt{x e + d} a b\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b^2*e^(-1) + 70*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*c*e^(-1) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*c*e^(-2) + 6*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^2*e^(-3) + 105*sqrt(x*e + d)*a*b)*e^(-1)","A",0
1599,1,163,0,0.193115," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left(2 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} e^{16} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d e^{16} + 30 \, \sqrt{x e + d} c^{2} d^{2} e^{16} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b c e^{17} - 30 \, \sqrt{x e + d} b c d e^{17} + 5 \, \sqrt{x e + d} b^{2} e^{18} + 10 \, \sqrt{x e + d} a c e^{18}\right)} e^{\left(-20\right)} + \frac{2 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)} e^{\left(-4\right)}}{\sqrt{x e + d}}"," ",0,"2/5*(2*(x*e + d)^(5/2)*c^2*e^16 - 10*(x*e + d)^(3/2)*c^2*d*e^16 + 30*sqrt(x*e + d)*c^2*d^2*e^16 + 5*(x*e + d)^(3/2)*b*c*e^17 - 30*sqrt(x*e + d)*b*c*d*e^17 + 5*sqrt(x*e + d)*b^2*e^18 + 10*sqrt(x*e + d)*a*c*e^18)*e^(-20) + 2*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)*e^(-4)/sqrt(x*e + d)","A",0
1600,1,153,0,0.203283," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} e^{8} - 18 \, \sqrt{x e + d} c^{2} d e^{8} + 9 \, \sqrt{x e + d} b c e^{9}\right)} e^{\left(-12\right)} - \frac{2 \, {\left(18 \, {\left(x e + d\right)} c^{2} d^{2} - 2 \, c^{2} d^{3} - 18 \, {\left(x e + d\right)} b c d e + 3 \, b c d^{2} e + 3 \, {\left(x e + d\right)} b^{2} e^{2} + 6 \, {\left(x e + d\right)} a c e^{2} - b^{2} d e^{2} - 2 \, a c d e^{2} + a b e^{3}\right)} e^{\left(-4\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/3*(2*(x*e + d)^(3/2)*c^2*e^8 - 18*sqrt(x*e + d)*c^2*d*e^8 + 9*sqrt(x*e + d)*b*c*e^9)*e^(-12) - 2/3*(18*(x*e + d)*c^2*d^2 - 2*c^2*d^3 - 18*(x*e + d)*b*c*d*e + 3*b*c*d^2*e + 3*(x*e + d)*b^2*e^2 + 6*(x*e + d)*a*c*e^2 - b^2*d*e^2 - 2*a*c*d*e^2 + a*b*e^3)*e^(-4)/(x*e + d)^(3/2)","A",0
1601,1,2447,0,0.327180," ","integrate((2*c*x+b)*(e*x+d)^(5/2)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b^{2} d^{3} e^{\left(-1\right)} + 510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} c d^{3} e^{\left(-1\right)} + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{3} d^{3} e^{\left(-2\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b c d^{3} e^{\left(-2\right)} + 87516 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} c d^{3} e^{\left(-3\right)} + 87516 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c^{2} d^{3} e^{\left(-3\right)} + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c^{2} d^{3} e^{\left(-4\right)} + 2210 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{3} d^{3} e^{\left(-5\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{2} e^{\left(-1\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d^{2} e^{\left(-1\right)} + 65637 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{2} e^{\left(-2\right)} + 393822 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b c d^{2} e^{\left(-2\right)} + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d^{2} e^{\left(-3\right)} + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d^{2} e^{\left(-3\right)} + 16575 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d^{2} e^{\left(-4\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{2} e^{\left(-5\right)} + 765765 \, \sqrt{x e + d} a^{2} b d^{3} + 765765 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{2} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d e^{\left(-1\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c d e^{\left(-1\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d e^{\left(-2\right)} + 43758 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c d e^{\left(-2\right)} + 13260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c d e^{\left(-3\right)} + 13260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} d e^{\left(-3\right)} + 3825 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} d e^{\left(-4\right)} + 714 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d e^{\left(-5\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d + 4862 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} e^{\left(-1\right)} + 4862 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c e^{\left(-1\right)} + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} e^{\left(-2\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b c e^{\left(-2\right)} + 1020 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c e^{\left(-3\right)} + 1020 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{2} e^{\left(-3\right)} + 595 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{2} e^{\left(-4\right)} + 14 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} e^{\left(-5\right)} + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b\right)} e^{\left(-1\right)}"," ",0,"2/765765*(510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b^2*d^3*e^(-1) + 510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*c*d^3*e^(-1) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^3*d^3*e^(-2) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*c*d^3*e^(-2) + 87516*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*c*d^3*e^(-3) + 87516*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c^2*d^3*e^(-3) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c^2*d^3*e^(-4) + 2210*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^3*d^3*e^(-5) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^2*e^(-1) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d^2*e^(-1) + 65637*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^2*e^(-2) + 393822*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*c*d^2*e^(-2) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d^2*e^(-3) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d^2*e^(-3) + 16575*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d^2*e^(-4) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^2*e^(-5) + 765765*sqrt(x*e + d)*a^2*b*d^3 + 765765*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^2 + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d*e^(-1) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*d*e^(-1) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d*e^(-2) + 43758*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c*d*e^(-2) + 13260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*d*e^(-3) + 13260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*d*e^(-3) + 3825*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*d*e^(-4) + 714*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d*e^(-5) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d + 4862*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*e^(-1) + 4862*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c*e^(-1) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*e^(-2) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*c*e^(-2) + 1020*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c*e^(-3) + 1020*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^2*e^(-3) + 595*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^2*e^(-4) + 14*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*e^(-5) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b)*e^(-1)","B",0
1602,1,1648,0,0.288974," ","integrate((2*c*x+b)*(e*x+d)^(3/2)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b^{2} d^{2} e^{\left(-1\right)} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} c d^{2} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{3} d^{2} e^{\left(-2\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b c d^{2} e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} c d^{2} e^{\left(-3\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c^{2} d^{2} e^{\left(-3\right)} + 715 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c^{2} d^{2} e^{\left(-4\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{3} d^{2} e^{\left(-5\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d e^{\left(-1\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d e^{\left(-1\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d e^{\left(-2\right)} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b c d e^{\left(-2\right)} + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d e^{\left(-3\right)} + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d e^{\left(-3\right)} + 650 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d e^{\left(-4\right)} + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d e^{\left(-5\right)} + 45045 \, \sqrt{x e + d} a^{2} b d^{2} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} e^{\left(-1\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c e^{\left(-1\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c e^{\left(-2\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c e^{\left(-3\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} e^{\left(-3\right)} + 75 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} e^{\left(-4\right)} + 14 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} e^{\left(-5\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b\right)} e^{\left(-1\right)}"," ",0,"2/45045*(30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b^2*d^2*e^(-1) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*c*d^2*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^3*d^2*e^(-2) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*c*d^2*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*c*d^2*e^(-3) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c^2*d^2*e^(-3) + 715*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c^2*d^2*e^(-4) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^3*d^2*e^(-5) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d*e^(-1) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d*e^(-1) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d*e^(-2) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*c*d*e^(-2) + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d*e^(-3) + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d*e^(-3) + 650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d*e^(-4) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d*e^(-5) + 45045*sqrt(x*e + d)*a^2*b*d^2 + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*e^(-1) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*e^(-1) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c*e^(-2) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*e^(-3) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*e^(-3) + 75*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*e^(-4) + 14*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*e^(-5) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b)*e^(-1)","B",0
1603,1,966,0,0.220955," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b^{2} d e^{\left(-1\right)} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} c d e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{3} d e^{\left(-2\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b c d e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} c d e^{\left(-3\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c^{2} d e^{\left(-3\right)} + 715 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c^{2} d e^{\left(-4\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{3} d e^{\left(-5\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} e^{\left(-1\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c e^{\left(-1\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} e^{\left(-2\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b c e^{\left(-2\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c e^{\left(-3\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} e^{\left(-3\right)} + 325 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} e^{\left(-4\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} e^{\left(-5\right)} + 45045 \, \sqrt{x e + d} a^{2} b d + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b\right)} e^{\left(-1\right)}"," ",0,"2/45045*(30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b^2*d*e^(-1) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*c*d*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^3*d*e^(-2) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*c*d*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*c*d*e^(-3) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c^2*d*e^(-3) + 715*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c^2*d*e^(-4) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^3*d*e^(-5) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*e^(-1) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*e^(-1) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*e^(-2) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*c*e^(-2) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*e^(-3) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*e^(-3) + 325*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*e^(-4) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*e^(-5) + 45045*sqrt(x*e + d)*a^2*b*d + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b)*e^(-1)","B",0
1604,1,421,0,0.183481," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b^{2} e^{\left(-1\right)} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} c e^{\left(-1\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{3} e^{\left(-2\right)} + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b c e^{\left(-2\right)} + 396 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} c e^{\left(-3\right)} + 396 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c^{2} e^{\left(-3\right)} + 55 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c^{2} e^{\left(-4\right)} + 10 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{3} e^{\left(-5\right)} + 3465 \, \sqrt{x e + d} a^{2} b\right)} e^{\left(-1\right)}"," ",0,"2/3465*(2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b^2*e^(-1) + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*c*e^(-1) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^3*e^(-2) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*c*e^(-2) + 396*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*c*e^(-3) + 396*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c^2*e^(-3) + 55*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c^2*e^(-4) + 10*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^3*e^(-5) + 3465*sqrt(x*e + d)*a^2*b)*e^(-1)","A",0
1605,1,460,0,0.211802," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(70 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} e^{48} - 450 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d e^{48} + 1260 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{2} e^{48} - 2100 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e^{48} + 3150 \, \sqrt{x e + d} c^{3} d^{4} e^{48} + 225 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} e^{49} - 1260 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d e^{49} + 3150 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{49} - 6300 \, \sqrt{x e + d} b c^{2} d^{3} e^{49} + 252 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c e^{50} + 252 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} e^{50} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{50} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{50} + 3780 \, \sqrt{x e + d} b^{2} c d^{2} e^{50} + 3780 \, \sqrt{x e + d} a c^{2} d^{2} e^{50} + 105 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{51} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c e^{51} - 630 \, \sqrt{x e + d} b^{3} d e^{51} - 3780 \, \sqrt{x e + d} a b c d e^{51} + 630 \, \sqrt{x e + d} a b^{2} e^{52} + 630 \, \sqrt{x e + d} a^{2} c e^{52}\right)} e^{\left(-54\right)} + \frac{2 \, {\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)} e^{\left(-6\right)}}{\sqrt{x e + d}}"," ",0,"2/315*(70*(x*e + d)^(9/2)*c^3*e^48 - 450*(x*e + d)^(7/2)*c^3*d*e^48 + 1260*(x*e + d)^(5/2)*c^3*d^2*e^48 - 2100*(x*e + d)^(3/2)*c^3*d^3*e^48 + 3150*sqrt(x*e + d)*c^3*d^4*e^48 + 225*(x*e + d)^(7/2)*b*c^2*e^49 - 1260*(x*e + d)^(5/2)*b*c^2*d*e^49 + 3150*(x*e + d)^(3/2)*b*c^2*d^2*e^49 - 6300*sqrt(x*e + d)*b*c^2*d^3*e^49 + 252*(x*e + d)^(5/2)*b^2*c*e^50 + 252*(x*e + d)^(5/2)*a*c^2*e^50 - 1260*(x*e + d)^(3/2)*b^2*c*d*e^50 - 1260*(x*e + d)^(3/2)*a*c^2*d*e^50 + 3780*sqrt(x*e + d)*b^2*c*d^2*e^50 + 3780*sqrt(x*e + d)*a*c^2*d^2*e^50 + 105*(x*e + d)^(3/2)*b^3*e^51 + 630*(x*e + d)^(3/2)*a*b*c*e^51 - 630*sqrt(x*e + d)*b^3*d*e^51 - 3780*sqrt(x*e + d)*a*b*c*d*e^51 + 630*sqrt(x*e + d)*a*b^2*e^52 + 630*sqrt(x*e + d)*a^2*c*e^52)*e^(-54) + 2*(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)*e^(-6)/sqrt(x*e + d)","B",0
1606,1,440,0,0.221125," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{21} \, {\left(6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} e^{36} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d e^{36} + 140 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{2} e^{36} - 420 \, \sqrt{x e + d} c^{3} d^{3} e^{36} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} e^{37} - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d e^{37} + 630 \, \sqrt{x e + d} b c^{2} d^{2} e^{37} + 28 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c e^{38} + 28 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} e^{38} - 252 \, \sqrt{x e + d} b^{2} c d e^{38} - 252 \, \sqrt{x e + d} a c^{2} d e^{38} + 21 \, \sqrt{x e + d} b^{3} e^{39} + 126 \, \sqrt{x e + d} a b c e^{39}\right)} e^{\left(-42\right)} - \frac{2 \, {\left(30 \, {\left(x e + d\right)} c^{3} d^{4} - 2 \, c^{3} d^{5} - 60 \, {\left(x e + d\right)} b c^{2} d^{3} e + 5 \, b c^{2} d^{4} e + 36 \, {\left(x e + d\right)} b^{2} c d^{2} e^{2} + 36 \, {\left(x e + d\right)} a c^{2} d^{2} e^{2} - 4 \, b^{2} c d^{3} e^{2} - 4 \, a c^{2} d^{3} e^{2} - 6 \, {\left(x e + d\right)} b^{3} d e^{3} - 36 \, {\left(x e + d\right)} a b c d e^{3} + b^{3} d^{2} e^{3} + 6 \, a b c d^{2} e^{3} + 6 \, {\left(x e + d\right)} a b^{2} e^{4} + 6 \, {\left(x e + d\right)} a^{2} c e^{4} - 2 \, a b^{2} d e^{4} - 2 \, a^{2} c d e^{4} + a^{2} b e^{5}\right)} e^{\left(-6\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/21*(6*(x*e + d)^(7/2)*c^3*e^36 - 42*(x*e + d)^(5/2)*c^3*d*e^36 + 140*(x*e + d)^(3/2)*c^3*d^2*e^36 - 420*sqrt(x*e + d)*c^3*d^3*e^36 + 21*(x*e + d)^(5/2)*b*c^2*e^37 - 140*(x*e + d)^(3/2)*b*c^2*d*e^37 + 630*sqrt(x*e + d)*b*c^2*d^2*e^37 + 28*(x*e + d)^(3/2)*b^2*c*e^38 + 28*(x*e + d)^(3/2)*a*c^2*e^38 - 252*sqrt(x*e + d)*b^2*c*d*e^38 - 252*sqrt(x*e + d)*a*c^2*d*e^38 + 21*sqrt(x*e + d)*b^3*e^39 + 126*sqrt(x*e + d)*a*b*c*e^39)*e^(-42) - 2/3*(30*(x*e + d)*c^3*d^4 - 2*c^3*d^5 - 60*(x*e + d)*b*c^2*d^3*e + 5*b*c^2*d^4*e + 36*(x*e + d)*b^2*c*d^2*e^2 + 36*(x*e + d)*a*c^2*d^2*e^2 - 4*b^2*c*d^3*e^2 - 4*a*c^2*d^3*e^2 - 6*(x*e + d)*b^3*d*e^3 - 36*(x*e + d)*a*b*c*d*e^3 + b^3*d^2*e^3 + 6*a*b*c*d^2*e^3 + 6*(x*e + d)*a*b^2*e^4 + 6*(x*e + d)*a^2*c*e^4 - 2*a*b^2*d*e^4 - 2*a^2*c*d*e^4 + a^2*b*e^5)*e^(-6)/(x*e + d)^(3/2)","A",0
1607,1,4552,0,0.594209," ","integrate((2*c*x+b)*(e*x+d)^(5/2)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(14549535 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b^{2} d^{3} e^{\left(-1\right)} + 9699690 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} c d^{3} e^{\left(-1\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{3} d^{3} e^{\left(-2\right)} + 8729721 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b c d^{3} e^{\left(-2\right)} + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{4} d^{3} e^{\left(-3\right)} + 4988412 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} c d^{3} e^{\left(-3\right)} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c^{2} d^{3} e^{\left(-3\right)} + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} c d^{3} e^{\left(-4\right)} + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c^{2} d^{3} e^{\left(-4\right)} + 188955 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c^{2} d^{3} e^{\left(-5\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{3} d^{3} e^{\left(-5\right)} + 33915 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{3} d^{3} e^{\left(-6\right)} + 4522 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{4} d^{3} e^{\left(-7\right)} + 8729721 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d^{2} e^{\left(-1\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} c d^{2} e^{\left(-1\right)} + 3741309 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d^{2} e^{\left(-2\right)} + 11223927 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b c d^{2} e^{\left(-2\right)} + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d^{2} e^{\left(-3\right)} + 1662804 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} c d^{2} e^{\left(-3\right)} + 831402 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c^{2} d^{2} e^{\left(-3\right)} + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} c d^{2} e^{\left(-4\right)} + 944775 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b c^{2} d^{2} e^{\left(-4\right)} + 130815 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c^{2} d^{2} e^{\left(-5\right)} + 87210 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{3} d^{2} e^{\left(-5\right)} + 47481 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{3} d^{2} e^{\left(-6\right)} + 798 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{4} d^{2} e^{\left(-7\right)} + 14549535 \, \sqrt{x e + d} a^{3} b d^{3} + 14549535 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d^{2} + 3741309 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} d e^{\left(-1\right)} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} c d e^{\left(-1\right)} + 415701 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} d e^{\left(-2\right)} + 1247103 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b c d e^{\left(-2\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} d e^{\left(-3\right)} + 755820 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{2} c d e^{\left(-3\right)} + 377910 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} c^{2} d e^{\left(-3\right)} + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} c d e^{\left(-4\right)} + 218025 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b c^{2} d e^{\left(-4\right)} + 61047 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{2} c^{2} d e^{\left(-5\right)} + 40698 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a c^{3} d e^{\left(-5\right)} + 2793 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b c^{3} d e^{\left(-6\right)} + 378 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} c^{4} d e^{\left(-7\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b d + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{2} e^{\left(-1\right)} + 92378 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} c e^{\left(-1\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{3} e^{\left(-2\right)} + 188955 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b c e^{\left(-2\right)} + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{4} e^{\left(-3\right)} + 58140 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{2} c e^{\left(-3\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} c^{2} e^{\left(-3\right)} + 11305 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{3} c e^{\left(-4\right)} + 33915 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b c^{2} e^{\left(-4\right)} + 1197 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{2} c^{2} e^{\left(-5\right)} + 798 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a c^{3} e^{\left(-5\right)} + 441 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b c^{3} e^{\left(-6\right)} + 30 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} c^{4} e^{\left(-7\right)} + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(14549535*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b^2*d^3*e^(-1) + 9699690*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*c*d^3*e^(-1) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^3*d^3*e^(-2) + 8729721*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*c*d^3*e^(-2) + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^4*d^3*e^(-3) + 4988412*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*c*d^3*e^(-3) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c^2*d^3*e^(-3) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*c*d^3*e^(-4) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c^2*d^3*e^(-4) + 188955*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c^2*d^3*e^(-5) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^3*d^3*e^(-5) + 33915*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^3*d^3*e^(-6) + 4522*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^4*d^3*e^(-7) + 8729721*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d^2*e^(-1) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*c*d^2*e^(-1) + 3741309*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d^2*e^(-2) + 11223927*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*c*d^2*e^(-2) + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d^2*e^(-3) + 1662804*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*c*d^2*e^(-3) + 831402*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c^2*d^2*e^(-3) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*c*d^2*e^(-4) + 944775*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*c^2*d^2*e^(-4) + 130815*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c^2*d^2*e^(-5) + 87210*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^3*d^2*e^(-5) + 47481*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^3*d^2*e^(-6) + 798*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^4*d^2*e^(-7) + 14549535*sqrt(x*e + d)*a^3*b*d^3 + 14549535*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d^2 + 3741309*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*d*e^(-1) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*c*d*e^(-1) + 415701*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*d*e^(-2) + 1247103*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b*c*d*e^(-2) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*d*e^(-3) + 755820*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^2*c*d*e^(-3) + 377910*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*c^2*d*e^(-3) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*c*d*e^(-4) + 218025*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b*c^2*d*e^(-4) + 61047*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^2*c^2*d*e^(-5) + 40698*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*c^3*d*e^(-5) + 2793*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b*c^3*d*e^(-6) + 378*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*c^4*d*e^(-7) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*d + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^2*e^(-1) + 92378*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*c*e^(-1) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^3*e^(-2) + 188955*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b*c*e^(-2) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^4*e^(-3) + 58140*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^2*c*e^(-3) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*c^2*e^(-3) + 11305*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^3*c*e^(-4) + 33915*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b*c^2*e^(-4) + 1197*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^2*c^2*e^(-5) + 798*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*c^3*e^(-5) + 441*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b*c^3*e^(-6) + 30*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*c^4*e^(-7) + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b)*e^(-1)","B",0
1608,1,3123,0,0.371923," ","integrate((2*c*x+b)*(e*x+d)^(3/2)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(14549535 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b^{2} d^{2} e^{\left(-1\right)} + 9699690 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} c d^{2} e^{\left(-1\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{3} d^{2} e^{\left(-2\right)} + 8729721 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b c d^{2} e^{\left(-2\right)} + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{4} d^{2} e^{\left(-3\right)} + 4988412 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} c d^{2} e^{\left(-3\right)} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c^{2} d^{2} e^{\left(-3\right)} + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} c d^{2} e^{\left(-4\right)} + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c^{2} d^{2} e^{\left(-4\right)} + 188955 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c^{2} d^{2} e^{\left(-5\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{3} d^{2} e^{\left(-5\right)} + 33915 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{3} d^{2} e^{\left(-6\right)} + 4522 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{4} d^{2} e^{\left(-7\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d e^{\left(-1\right)} + 3879876 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} c d e^{\left(-1\right)} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d e^{\left(-2\right)} + 7482618 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b c d e^{\left(-2\right)} + 92378 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d e^{\left(-3\right)} + 1108536 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} c d e^{\left(-3\right)} + 554268 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c^{2} d e^{\left(-3\right)} + 209950 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} c d e^{\left(-4\right)} + 629850 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b c^{2} d e^{\left(-4\right)} + 87210 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c^{2} d e^{\left(-5\right)} + 58140 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{3} d e^{\left(-5\right)} + 31654 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{3} d e^{\left(-6\right)} + 532 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{4} d e^{\left(-7\right)} + 14549535 \, \sqrt{x e + d} a^{3} b d^{2} + 9699690 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d + 1247103 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} e^{\left(-1\right)} + 831402 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} c e^{\left(-1\right)} + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} e^{\left(-2\right)} + 415701 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b c e^{\left(-2\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} e^{\left(-3\right)} + 251940 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{2} c e^{\left(-3\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} c^{2} e^{\left(-3\right)} + 24225 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} c e^{\left(-4\right)} + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b c^{2} e^{\left(-4\right)} + 20349 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{2} c^{2} e^{\left(-5\right)} + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a c^{3} e^{\left(-5\right)} + 931 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b c^{3} e^{\left(-6\right)} + 126 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} c^{4} e^{\left(-7\right)} + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(14549535*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b^2*d^2*e^(-1) + 9699690*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*c*d^2*e^(-1) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^3*d^2*e^(-2) + 8729721*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*c*d^2*e^(-2) + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^4*d^2*e^(-3) + 4988412*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*c*d^2*e^(-3) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c^2*d^2*e^(-3) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*c*d^2*e^(-4) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c^2*d^2*e^(-4) + 188955*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c^2*d^2*e^(-5) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^3*d^2*e^(-5) + 33915*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^3*d^2*e^(-6) + 4522*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^4*d^2*e^(-7) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d*e^(-1) + 3879876*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*c*d*e^(-1) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d*e^(-2) + 7482618*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*c*d*e^(-2) + 92378*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d*e^(-3) + 1108536*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*c*d*e^(-3) + 554268*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c^2*d*e^(-3) + 209950*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*c*d*e^(-4) + 629850*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*c^2*d*e^(-4) + 87210*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c^2*d*e^(-5) + 58140*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^3*d*e^(-5) + 31654*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^3*d*e^(-6) + 532*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^4*d*e^(-7) + 14549535*sqrt(x*e + d)*a^3*b*d^2 + 9699690*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d + 1247103*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*e^(-1) + 831402*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*c*e^(-1) + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*e^(-2) + 415701*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b*c*e^(-2) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*e^(-3) + 251940*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^2*c*e^(-3) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*c^2*e^(-3) + 24225*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*c*e^(-4) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b*c^2*e^(-4) + 20349*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^2*c^2*e^(-5) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*c^3*e^(-5) + 931*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b*c^3*e^(-6) + 126*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*c^4*e^(-7) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b)*e^(-1)","B",0
1609,1,1876,0,0.284285," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{765765} \, {\left(765765 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b^{2} d e^{\left(-1\right)} + 510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} c d e^{\left(-1\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{3} d e^{\left(-2\right)} + 459459 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b c d e^{\left(-2\right)} + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{4} d e^{\left(-3\right)} + 262548 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} c d e^{\left(-3\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c^{2} d e^{\left(-3\right)} + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} c d e^{\left(-4\right)} + 36465 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c^{2} d e^{\left(-4\right)} + 9945 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c^{2} d e^{\left(-5\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{3} d e^{\left(-5\right)} + 1785 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{3} d e^{\left(-6\right)} + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{4} d e^{\left(-7\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} e^{\left(-1\right)} + 102102 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} c e^{\left(-1\right)} + 65637 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} e^{\left(-2\right)} + 196911 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b c e^{\left(-2\right)} + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} e^{\left(-3\right)} + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} c e^{\left(-3\right)} + 14586 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c^{2} e^{\left(-3\right)} + 5525 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} c e^{\left(-4\right)} + 16575 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b c^{2} e^{\left(-4\right)} + 2295 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c^{2} e^{\left(-5\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{3} e^{\left(-5\right)} + 833 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{3} e^{\left(-6\right)} + 14 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{4} e^{\left(-7\right)} + 765765 \, \sqrt{x e + d} a^{3} b d + 255255 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b\right)} e^{\left(-1\right)}"," ",0,"2/765765*(765765*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b^2*d*e^(-1) + 510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*c*d*e^(-1) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^3*d*e^(-2) + 459459*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*c*d*e^(-2) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^4*d*e^(-3) + 262548*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*c*d*e^(-3) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c^2*d*e^(-3) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*c*d*e^(-4) + 36465*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c^2*d*e^(-4) + 9945*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c^2*d*e^(-5) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^3*d*e^(-5) + 1785*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^3*d*e^(-6) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^4*d*e^(-7) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*e^(-1) + 102102*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*c*e^(-1) + 65637*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*e^(-2) + 196911*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*c*e^(-2) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*e^(-3) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*c*e^(-3) + 14586*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c^2*e^(-3) + 5525*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*c*e^(-4) + 16575*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*c^2*e^(-4) + 2295*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c^2*e^(-5) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^3*e^(-5) + 833*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^3*e^(-6) + 14*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^4*e^(-7) + 765765*sqrt(x*e + d)*a^3*b*d + 255255*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b)*e^(-1)","B",0
1610,1,841,0,0.225763," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b^{2} e^{\left(-1\right)} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} c e^{\left(-1\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{3} e^{\left(-2\right)} + 27027 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b c e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{4} e^{\left(-3\right)} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} c e^{\left(-3\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c^{2} e^{\left(-3\right)} + 715 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} c e^{\left(-4\right)} + 2145 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c^{2} e^{\left(-4\right)} + 585 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c^{2} e^{\left(-5\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{3} e^{\left(-5\right)} + 105 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{3} e^{\left(-6\right)} + 14 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{4} e^{\left(-7\right)} + 45045 \, \sqrt{x e + d} a^{3} b\right)} e^{\left(-1\right)}"," ",0,"2/45045*(45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b^2*e^(-1) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*c*e^(-1) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^3*e^(-2) + 27027*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*c*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^4*e^(-3) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*c*e^(-3) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c^2*e^(-3) + 715*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*c*e^(-4) + 2145*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c^2*e^(-4) + 585*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c^2*e^(-5) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^3*e^(-5) + 105*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^3*e^(-6) + 14*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^4*e^(-7) + 45045*sqrt(x*e + d)*a^3*b)*e^(-1)","B",0
1611,1,1000,0,0.311460," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(2310 \, {\left(x e + d\right)}^{\frac{13}{2}} c^{4} e^{96} - 19110 \, {\left(x e + d\right)}^{\frac{11}{2}} c^{4} d e^{96} + 70070 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{4} d^{2} e^{96} - 150150 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{4} d^{3} e^{96} + 210210 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} d^{4} e^{96} - 210210 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{5} e^{96} + 210210 \, \sqrt{x e + d} c^{4} d^{6} e^{96} + 9555 \, {\left(x e + d\right)}^{\frac{11}{2}} b c^{3} e^{97} - 70070 \, {\left(x e + d\right)}^{\frac{9}{2}} b c^{3} d e^{97} + 225225 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{3} d^{2} e^{97} - 420420 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{3} d^{3} e^{97} + 525525 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{4} e^{97} - 630630 \, \sqrt{x e + d} b c^{3} d^{5} e^{97} + 15015 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{2} c^{2} e^{98} + 10010 \, {\left(x e + d\right)}^{\frac{9}{2}} a c^{3} e^{98} - 96525 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{2} d e^{98} - 64350 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{3} d e^{98} + 270270 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{2} d^{2} e^{98} + 180180 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{3} d^{2} e^{98} - 450450 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{3} e^{98} - 300300 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{3} d^{3} e^{98} + 675675 \, \sqrt{x e + d} b^{2} c^{2} d^{4} e^{98} + 450450 \, \sqrt{x e + d} a c^{3} d^{4} e^{98} + 10725 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c e^{99} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} a b c^{2} e^{99} - 60060 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c d e^{99} - 180180 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c^{2} d e^{99} + 150150 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d^{2} e^{99} + 450450 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c^{2} d^{2} e^{99} - 300300 \, \sqrt{x e + d} b^{3} c d^{3} e^{99} - 900900 \, \sqrt{x e + d} a b c^{2} d^{3} e^{99} + 3003 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} e^{100} + 36036 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} c e^{100} + 18018 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c^{2} e^{100} - 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d e^{100} - 180180 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} c d e^{100} - 90090 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c^{2} d e^{100} + 45045 \, \sqrt{x e + d} b^{4} d^{2} e^{100} + 540540 \, \sqrt{x e + d} a b^{2} c d^{2} e^{100} + 270270 \, \sqrt{x e + d} a^{2} c^{2} d^{2} e^{100} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} e^{101} + 45045 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b c e^{101} - 90090 \, \sqrt{x e + d} a b^{3} d e^{101} - 270270 \, \sqrt{x e + d} a^{2} b c d e^{101} + 45045 \, \sqrt{x e + d} a^{2} b^{2} e^{102} + 30030 \, \sqrt{x e + d} a^{3} c e^{102}\right)} e^{\left(-104\right)} + \frac{2 \, {\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e + 9 \, b^{2} c^{2} d^{5} e^{2} + 6 \, a c^{3} d^{5} e^{2} - 5 \, b^{3} c d^{4} e^{3} - 15 \, a b c^{2} d^{4} e^{3} + b^{4} d^{3} e^{4} + 12 \, a b^{2} c d^{3} e^{4} + 6 \, a^{2} c^{2} d^{3} e^{4} - 3 \, a b^{3} d^{2} e^{5} - 9 \, a^{2} b c d^{2} e^{5} + 3 \, a^{2} b^{2} d e^{6} + 2 \, a^{3} c d e^{6} - a^{3} b e^{7}\right)} e^{\left(-8\right)}}{\sqrt{x e + d}}"," ",0,"2/15015*(2310*(x*e + d)^(13/2)*c^4*e^96 - 19110*(x*e + d)^(11/2)*c^4*d*e^96 + 70070*(x*e + d)^(9/2)*c^4*d^2*e^96 - 150150*(x*e + d)^(7/2)*c^4*d^3*e^96 + 210210*(x*e + d)^(5/2)*c^4*d^4*e^96 - 210210*(x*e + d)^(3/2)*c^4*d^5*e^96 + 210210*sqrt(x*e + d)*c^4*d^6*e^96 + 9555*(x*e + d)^(11/2)*b*c^3*e^97 - 70070*(x*e + d)^(9/2)*b*c^3*d*e^97 + 225225*(x*e + d)^(7/2)*b*c^3*d^2*e^97 - 420420*(x*e + d)^(5/2)*b*c^3*d^3*e^97 + 525525*(x*e + d)^(3/2)*b*c^3*d^4*e^97 - 630630*sqrt(x*e + d)*b*c^3*d^5*e^97 + 15015*(x*e + d)^(9/2)*b^2*c^2*e^98 + 10010*(x*e + d)^(9/2)*a*c^3*e^98 - 96525*(x*e + d)^(7/2)*b^2*c^2*d*e^98 - 64350*(x*e + d)^(7/2)*a*c^3*d*e^98 + 270270*(x*e + d)^(5/2)*b^2*c^2*d^2*e^98 + 180180*(x*e + d)^(5/2)*a*c^3*d^2*e^98 - 450450*(x*e + d)^(3/2)*b^2*c^2*d^3*e^98 - 300300*(x*e + d)^(3/2)*a*c^3*d^3*e^98 + 675675*sqrt(x*e + d)*b^2*c^2*d^4*e^98 + 450450*sqrt(x*e + d)*a*c^3*d^4*e^98 + 10725*(x*e + d)^(7/2)*b^3*c*e^99 + 32175*(x*e + d)^(7/2)*a*b*c^2*e^99 - 60060*(x*e + d)^(5/2)*b^3*c*d*e^99 - 180180*(x*e + d)^(5/2)*a*b*c^2*d*e^99 + 150150*(x*e + d)^(3/2)*b^3*c*d^2*e^99 + 450450*(x*e + d)^(3/2)*a*b*c^2*d^2*e^99 - 300300*sqrt(x*e + d)*b^3*c*d^3*e^99 - 900900*sqrt(x*e + d)*a*b*c^2*d^3*e^99 + 3003*(x*e + d)^(5/2)*b^4*e^100 + 36036*(x*e + d)^(5/2)*a*b^2*c*e^100 + 18018*(x*e + d)^(5/2)*a^2*c^2*e^100 - 15015*(x*e + d)^(3/2)*b^4*d*e^100 - 180180*(x*e + d)^(3/2)*a*b^2*c*d*e^100 - 90090*(x*e + d)^(3/2)*a^2*c^2*d*e^100 + 45045*sqrt(x*e + d)*b^4*d^2*e^100 + 540540*sqrt(x*e + d)*a*b^2*c*d^2*e^100 + 270270*sqrt(x*e + d)*a^2*c^2*d^2*e^100 + 15015*(x*e + d)^(3/2)*a*b^3*e^101 + 45045*(x*e + d)^(3/2)*a^2*b*c*e^101 - 90090*sqrt(x*e + d)*a*b^3*d*e^101 - 270270*sqrt(x*e + d)*a^2*b*c*d*e^101 + 45045*sqrt(x*e + d)*a^2*b^2*e^102 + 30030*sqrt(x*e + d)*a^3*c*e^102)*e^(-104) + 2*(2*c^4*d^7 - 7*b*c^3*d^6*e + 9*b^2*c^2*d^5*e^2 + 6*a*c^3*d^5*e^2 - 5*b^3*c*d^4*e^3 - 15*a*b*c^2*d^4*e^3 + b^4*d^3*e^4 + 12*a*b^2*c*d^3*e^4 + 6*a^2*c^2*d^3*e^4 - 3*a*b^3*d^2*e^5 - 9*a^2*b*c*d^2*e^5 + 3*a^2*b^2*d*e^6 + 2*a^3*c*d*e^6 - a^3*b*e^7)*e^(-8)/sqrt(x*e + d)","B",0
1612,1,972,0,0.303728," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{693} \, {\left(126 \, {\left(x e + d\right)}^{\frac{11}{2}} c^{4} e^{80} - 1078 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{4} d e^{80} + 4158 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{4} d^{2} e^{80} - 9702 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} d^{3} e^{80} + 16170 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{4} e^{80} - 29106 \, \sqrt{x e + d} c^{4} d^{5} e^{80} + 539 \, {\left(x e + d\right)}^{\frac{9}{2}} b c^{3} e^{81} - 4158 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{3} d e^{81} + 14553 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{3} d^{2} e^{81} - 32340 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{3} e^{81} + 72765 \, \sqrt{x e + d} b c^{3} d^{4} e^{81} + 891 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{2} e^{82} + 594 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{3} e^{82} - 6237 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{2} d e^{82} - 4158 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{3} d e^{82} + 20790 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{2} e^{82} + 13860 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{3} d^{2} e^{82} - 62370 \, \sqrt{x e + d} b^{2} c^{2} d^{3} e^{82} - 41580 \, \sqrt{x e + d} a c^{3} d^{3} e^{82} + 693 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c e^{83} + 2079 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c^{2} e^{83} - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d e^{83} - 13860 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c^{2} d e^{83} + 20790 \, \sqrt{x e + d} b^{3} c d^{2} e^{83} + 62370 \, \sqrt{x e + d} a b c^{2} d^{2} e^{83} + 231 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{84} + 2772 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} c e^{84} + 1386 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c^{2} e^{84} - 2079 \, \sqrt{x e + d} b^{4} d e^{84} - 24948 \, \sqrt{x e + d} a b^{2} c d e^{84} - 12474 \, \sqrt{x e + d} a^{2} c^{2} d e^{84} + 2079 \, \sqrt{x e + d} a b^{3} e^{85} + 6237 \, \sqrt{x e + d} a^{2} b c e^{85}\right)} e^{\left(-88\right)} - \frac{2 \, {\left(42 \, {\left(x e + d\right)} c^{4} d^{6} - 2 \, c^{4} d^{7} - 126 \, {\left(x e + d\right)} b c^{3} d^{5} e + 7 \, b c^{3} d^{6} e + 135 \, {\left(x e + d\right)} b^{2} c^{2} d^{4} e^{2} + 90 \, {\left(x e + d\right)} a c^{3} d^{4} e^{2} - 9 \, b^{2} c^{2} d^{5} e^{2} - 6 \, a c^{3} d^{5} e^{2} - 60 \, {\left(x e + d\right)} b^{3} c d^{3} e^{3} - 180 \, {\left(x e + d\right)} a b c^{2} d^{3} e^{3} + 5 \, b^{3} c d^{4} e^{3} + 15 \, a b c^{2} d^{4} e^{3} + 9 \, {\left(x e + d\right)} b^{4} d^{2} e^{4} + 108 \, {\left(x e + d\right)} a b^{2} c d^{2} e^{4} + 54 \, {\left(x e + d\right)} a^{2} c^{2} d^{2} e^{4} - b^{4} d^{3} e^{4} - 12 \, a b^{2} c d^{3} e^{4} - 6 \, a^{2} c^{2} d^{3} e^{4} - 18 \, {\left(x e + d\right)} a b^{3} d e^{5} - 54 \, {\left(x e + d\right)} a^{2} b c d e^{5} + 3 \, a b^{3} d^{2} e^{5} + 9 \, a^{2} b c d^{2} e^{5} + 9 \, {\left(x e + d\right)} a^{2} b^{2} e^{6} + 6 \, {\left(x e + d\right)} a^{3} c e^{6} - 3 \, a^{2} b^{2} d e^{6} - 2 \, a^{3} c d e^{6} + a^{3} b e^{7}\right)} e^{\left(-8\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/693*(126*(x*e + d)^(11/2)*c^4*e^80 - 1078*(x*e + d)^(9/2)*c^4*d*e^80 + 4158*(x*e + d)^(7/2)*c^4*d^2*e^80 - 9702*(x*e + d)^(5/2)*c^4*d^3*e^80 + 16170*(x*e + d)^(3/2)*c^4*d^4*e^80 - 29106*sqrt(x*e + d)*c^4*d^5*e^80 + 539*(x*e + d)^(9/2)*b*c^3*e^81 - 4158*(x*e + d)^(7/2)*b*c^3*d*e^81 + 14553*(x*e + d)^(5/2)*b*c^3*d^2*e^81 - 32340*(x*e + d)^(3/2)*b*c^3*d^3*e^81 + 72765*sqrt(x*e + d)*b*c^3*d^4*e^81 + 891*(x*e + d)^(7/2)*b^2*c^2*e^82 + 594*(x*e + d)^(7/2)*a*c^3*e^82 - 6237*(x*e + d)^(5/2)*b^2*c^2*d*e^82 - 4158*(x*e + d)^(5/2)*a*c^3*d*e^82 + 20790*(x*e + d)^(3/2)*b^2*c^2*d^2*e^82 + 13860*(x*e + d)^(3/2)*a*c^3*d^2*e^82 - 62370*sqrt(x*e + d)*b^2*c^2*d^3*e^82 - 41580*sqrt(x*e + d)*a*c^3*d^3*e^82 + 693*(x*e + d)^(5/2)*b^3*c*e^83 + 2079*(x*e + d)^(5/2)*a*b*c^2*e^83 - 4620*(x*e + d)^(3/2)*b^3*c*d*e^83 - 13860*(x*e + d)^(3/2)*a*b*c^2*d*e^83 + 20790*sqrt(x*e + d)*b^3*c*d^2*e^83 + 62370*sqrt(x*e + d)*a*b*c^2*d^2*e^83 + 231*(x*e + d)^(3/2)*b^4*e^84 + 2772*(x*e + d)^(3/2)*a*b^2*c*e^84 + 1386*(x*e + d)^(3/2)*a^2*c^2*e^84 - 2079*sqrt(x*e + d)*b^4*d*e^84 - 24948*sqrt(x*e + d)*a*b^2*c*d*e^84 - 12474*sqrt(x*e + d)*a^2*c^2*d*e^84 + 2079*sqrt(x*e + d)*a*b^3*e^85 + 6237*sqrt(x*e + d)*a^2*b*c*e^85)*e^(-88) - 2/3*(42*(x*e + d)*c^4*d^6 - 2*c^4*d^7 - 126*(x*e + d)*b*c^3*d^5*e + 7*b*c^3*d^6*e + 135*(x*e + d)*b^2*c^2*d^4*e^2 + 90*(x*e + d)*a*c^3*d^4*e^2 - 9*b^2*c^2*d^5*e^2 - 6*a*c^3*d^5*e^2 - 60*(x*e + d)*b^3*c*d^3*e^3 - 180*(x*e + d)*a*b*c^2*d^3*e^3 + 5*b^3*c*d^4*e^3 + 15*a*b*c^2*d^4*e^3 + 9*(x*e + d)*b^4*d^2*e^4 + 108*(x*e + d)*a*b^2*c*d^2*e^4 + 54*(x*e + d)*a^2*c^2*d^2*e^4 - b^4*d^3*e^4 - 12*a*b^2*c*d^3*e^4 - 6*a^2*c^2*d^3*e^4 - 18*(x*e + d)*a*b^3*d*e^5 - 54*(x*e + d)*a^2*b*c*d*e^5 + 3*a*b^3*d^2*e^5 + 9*a^2*b*c*d^2*e^5 + 9*(x*e + d)*a^2*b^2*e^6 + 6*(x*e + d)*a^3*c*e^6 - 3*a^2*b^2*d*e^6 - 2*a^3*c*d*e^6 + a^3*b*e^7)*e^(-8)/(x*e + d)^(3/2)","B",0
1613,1,813,0,0.480085," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left({\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{2} e - 2 \, \sqrt{b^{2} - 4 \, a c} b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2} - 2 \, {\left(2 \, c^{4} d^{3} - 3 \, b c^{3} d^{2} e - a b c^{2} e^{3} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(4 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{2} e - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d e^{2} + \sqrt{b^{2} - 4 \, a c} b^{2} c^{2} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{4} d - b c^{3} e + \sqrt{-4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{4} + {\left(2 \, c^{4} d - b c^{3} e\right)}^{2}}}{c^{4}}}}\right)}{4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{2}} - \frac{{\left({\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{2} e - 2 \, \sqrt{b^{2} - 4 \, a c} b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2} + 2 \, {\left(2 \, c^{4} d^{3} - 3 \, b c^{3} d^{2} e - a b c^{2} e^{3} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(4 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{2} e - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d e^{2} + \sqrt{b^{2} - 4 \, a c} b^{2} c^{2} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{4} d - b c^{3} e - \sqrt{-4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{4} + {\left(2 \, c^{4} d - b c^{3} e\right)}^{2}}}{c^{4}}}}\right)}{4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{2}} + \frac{2 \, {\left(2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} + 6 \, \sqrt{x e + d} c^{3} d - 3 \, \sqrt{x e + d} b c^{2} e\right)}}{3 \, c^{3}}"," ",0,"1/4*((2*sqrt(b^2 - 4*a*c)*c^2*d^2*e - 2*sqrt(b^2 - 4*a*c)*b*c*d*e^2 + (b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2 - 2*(2*c^4*d^3 - 3*b*c^3*d^2*e - a*b*c^2*e^3 + (b^2*c^2 + 2*a*c^3)*d*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (4*sqrt(b^2 - 4*a*c)*c^4*d^2*e - 4*sqrt(b^2 - 4*a*c)*b*c^3*d*e^2 + sqrt(b^2 - 4*a*c)*b^2*c^2*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^4*d - b*c^3*e + sqrt(-4*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^4 + (2*c^4*d - b*c^3*e)^2))/c^4))/((c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^2) - 1/4*((2*sqrt(b^2 - 4*a*c)*c^2*d^2*e - 2*sqrt(b^2 - 4*a*c)*b*c*d*e^2 + (b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2 + 2*(2*c^4*d^3 - 3*b*c^3*d^2*e - a*b*c^2*e^3 + (b^2*c^2 + 2*a*c^3)*d*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (4*sqrt(b^2 - 4*a*c)*c^4*d^2*e - 4*sqrt(b^2 - 4*a*c)*b*c^3*d*e^2 + sqrt(b^2 - 4*a*c)*b^2*c^2*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^4*d - b*c^3*e - sqrt(-4*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^4 + (2*c^4*d - b*c^3*e)^2))/c^4))/((c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^2) + 2/3*(2*(x*e + d)^(3/2)*c^3 + 6*sqrt(x*e + d)*c^3*d - 3*sqrt(x*e + d)*b*c^2*e)/c^3","B",0
1614,1,614,0,0.458264," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","4 \, \sqrt{x e + d} + \frac{{\left({\left(2 \, \sqrt{b^{2} - 4 \, a c} c d e - \sqrt{b^{2} - 4 \, a c} b e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2} - 4 \, {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d e - \sqrt{b^{2} - 4 \, a c} b c^{2} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e + \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{4 \, {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)} c^{2}} - \frac{{\left({\left(2 \, \sqrt{b^{2} - 4 \, a c} c d e - \sqrt{b^{2} - 4 \, a c} b e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2} + 4 \, {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d e - \sqrt{b^{2} - 4 \, a c} b c^{2} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e - \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{4 \, {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)} c^{2}}"," ",0,"4*sqrt(x*e + d) + 1/4*((2*sqrt(b^2 - 4*a*c)*c*d*e - sqrt(b^2 - 4*a*c)*b*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2 - 4*(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (2*sqrt(b^2 - 4*a*c)*c^3*d*e - sqrt(b^2 - 4*a*c)*b*c^2*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d - b*c*e + sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((c^3*d^2 - b*c^2*d*e + a*c^2*e^2)*c^2) - 1/4*((2*sqrt(b^2 - 4*a*c)*c*d*e - sqrt(b^2 - 4*a*c)*b*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2 + 4*(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (2*sqrt(b^2 - 4*a*c)*c^3*d*e - sqrt(b^2 - 4*a*c)*b*c^2*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d - b*c*e - sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((c^3*d^2 - b*c^2*d*e + a*c^2*e^2)*c^2)","B",0
1615,1,254,0,0.297475," ","integrate((2*c*x+b)/(c*x^2+b*x+a)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e + \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{{\left(2 \, c d - {\left(b - \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| c \right|}} - \frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e - \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{{\left(2 \, c d - {\left(b + \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| c \right|}}"," ",0,"-2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e + sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/((2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*abs(c)) - 2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e - sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*abs(c))","A",0
1616,1,1366,0,0.998656," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, c d - b e\right)}}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{x e + d}} + \frac{{\left({\left(c d^{2} e - b d e^{2} + a e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, \sqrt{b^{2} - 4 \, a c} c d - \sqrt{b^{2} - 4 \, a c} b e\right)} - 2 \, {\left(2 \, c^{3} d^{4} - 4 \, b c^{2} d^{3} e + 3 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} + {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{5} e^{2} - 5 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{4} e^{3} + 4 \, {\left(b^{2} c + a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{4} - \sqrt{b^{2} - 4 \, a c} a^{2} b e^{7} - {\left(b^{3} + 6 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{5} + 2 \, {\left(a b^{2} + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} d e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3} + \sqrt{{\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)}^{2} - 4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - 3 \, a^{2} b d e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + a^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(c d^{2} e - b d e^{2} + a e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, \sqrt{b^{2} - 4 \, a c} c d - \sqrt{b^{2} - 4 \, a c} b e\right)} + 2 \, {\left(2 \, c^{3} d^{4} - 4 \, b c^{2} d^{3} e + 3 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} + {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{5} e^{2} - 5 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{4} e^{3} + 4 \, {\left(b^{2} c + a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{4} - \sqrt{b^{2} - 4 \, a c} a^{2} b e^{7} - {\left(b^{3} + 6 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{5} + 2 \, {\left(a b^{2} + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} d e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3} - \sqrt{{\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)}^{2} - 4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - 3 \, a^{2} b d e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + a^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} {\left| c \right|}}"," ",0,"2*(2*c*d - b*e)/((c*d^2 - b*d*e + a*e^2)*sqrt(x*e + d)) + 1/4*((c*d^2*e - b*d*e^2 + a*e^3)^2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*sqrt(b^2 - 4*a*c)*c*d - sqrt(b^2 - 4*a*c)*b*e) - 2*(2*c^3*d^4 - 4*b*c^2*d^3*e + 3*b^2*c*d^2*e^2 - b^3*d*e^3 + (a*b^2 - 2*a^2*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c*d^2*e - b*d*e^2 + a*e^3) + (2*sqrt(b^2 - 4*a*c)*c^3*d^5*e^2 - 5*sqrt(b^2 - 4*a*c)*b*c^2*d^4*e^3 + 4*(b^2*c + a*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^4 - sqrt(b^2 - 4*a*c)*a^2*b*e^7 - (b^3 + 6*a*b*c)*sqrt(b^2 - 4*a*c)*d^2*e^5 + 2*(a*b^2 + a^2*c)*sqrt(b^2 - 4*a*c)*d*e^6)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3 + sqrt((2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)^2 - 4*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*(b^2*c + a*c^2)*d^4*e^2 - 3*a^2*b*d*e^5 - (b^3 + 6*a*b*c)*d^3*e^3 + a^3*e^6 + 3*(a*b^2 + a^2*c)*d^2*e^4)*abs(c*d^2*e - b*d*e^2 + a*e^3)*abs(c)) - 1/4*((c*d^2*e - b*d*e^2 + a*e^3)^2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*sqrt(b^2 - 4*a*c)*c*d - sqrt(b^2 - 4*a*c)*b*e) + 2*(2*c^3*d^4 - 4*b*c^2*d^3*e + 3*b^2*c*d^2*e^2 - b^3*d*e^3 + (a*b^2 - 2*a^2*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c*d^2*e - b*d*e^2 + a*e^3) + (2*sqrt(b^2 - 4*a*c)*c^3*d^5*e^2 - 5*sqrt(b^2 - 4*a*c)*b*c^2*d^4*e^3 + 4*(b^2*c + a*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^4 - sqrt(b^2 - 4*a*c)*a^2*b*e^7 - (b^3 + 6*a*b*c)*sqrt(b^2 - 4*a*c)*d^2*e^5 + 2*(a*b^2 + a^2*c)*sqrt(b^2 - 4*a*c)*d*e^6)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3 - sqrt((2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)^2 - 4*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*(b^2*c + a*c^2)*d^4*e^2 - 3*a^2*b*d*e^5 - (b^3 + 6*a*b*c)*d^3*e^3 + a^3*e^6 + 3*(a*b^2 + a^2*c)*d^2*e^4)*abs(c*d^2*e - b*d*e^2 + a*e^3)*abs(c))","B",0
1617,1,1255,0,4.004070," ","integrate((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{3} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5} + \sqrt{{\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)}^{2} - 4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right)}{{\left(2 \, c^{3} d^{3} - 3 \, {\left(b c^{2} - \sqrt{b^{2} - 4 \, a c} c^{2}\right)} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2} - \sqrt{b^{2} - 4 \, a c} b c\right)} d e^{2} - {\left(b^{3} - 3 \, a b c - {\left(b^{2} - a c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} - \frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{3} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5} - \sqrt{{\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)}^{2} - 4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right)}{{\left(2 \, c^{3} d^{3} - 3 \, {\left(b c^{2} + \sqrt{b^{2} - 4 \, a c} c^{2}\right)} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2} + \sqrt{b^{2} - 4 \, a c} b c\right)} d e^{2} - {\left(b^{3} - 3 \, a b c + {\left(b^{2} - a c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} + \frac{2 \, {\left(6 \, {\left(x e + d\right)} c^{2} d^{2} + 2 \, c^{2} d^{3} - 6 \, {\left(x e + d\right)} b c d e - 3 \, b c d^{2} e + 3 \, {\left(x e + d\right)} b^{2} e^{2} - 6 \, {\left(x e + d\right)} a c e^{2} + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)}}{3 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5 + sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((2*c^3*d^3 - 3*(b*c^2 - sqrt(b^2 - 4*a*c)*c^2)*d^2*e + 3*(b^2*c - 2*a*c^2 - sqrt(b^2 - 4*a*c)*b*c)*d*e^2 - (b^3 - 3*a*b*c - (b^2 - a*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) - 2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5 - sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((2*c^3*d^3 - 3*(b*c^2 + sqrt(b^2 - 4*a*c)*c^2)*d^2*e + 3*(b^2*c - 2*a*c^2 + sqrt(b^2 - 4*a*c)*b*c)*d*e^2 - (b^3 - 3*a*b*c + (b^2 - a*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) + 2/3*(6*(x*e + d)*c^2*d^2 + 2*c^2*d^3 - 6*(x*e + d)*b*c*d*e - 3*b*c*d^2*e + 3*(x*e + d)*b^2*e^2 - 6*(x*e + d)*a*c*e^2 + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(x*e + d)^(3/2))","B",0
1618,1,772,0,1.669790," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{4 \, \sqrt{x e + d} e^{2}}{c} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d e^{2} - \sqrt{x e + d} c d^{2} e^{2} - {\left(x e + d\right)}^{\frac{3}{2}} b e^{3} + \sqrt{x e + d} b d e^{3} - \sqrt{x e + d} a e^{4}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)} c} + \frac{5 \, {\left(4 \, c^{5} d^{3} e - 6 \, b c^{4} 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)} c^{2} + 4 \, {\left(b^{2} c^{3} - a c^{4}\right)} d e^{3} + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} b c^{2} d e^{3} + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{4}\right)} {\left| c \right|} - {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e + \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d - {\left(b^{2} c - 4 \, a c^{2} + \sqrt{b^{2} - 4 \, a c} b c\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} - \frac{5 \, {\left(4 \, c^{5} d^{3} e - 6 \, b c^{4} 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)} c^{2} + 4 \, {\left(b^{2} c^{3} - a c^{4}\right)} d e^{3} - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} b c^{2} d e^{3} + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{4}\right)} {\left| c \right|} - {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e - \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d + {\left(b^{2} c - 4 \, a c^{2} - \sqrt{b^{2} - 4 \, a c} b c\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}}"," ",0,"4*sqrt(x*e + d)*e^2/c - (2*(x*e + d)^(3/2)*c*d*e^2 - sqrt(x*e + d)*c*d^2*e^2 - (x*e + d)^(3/2)*b*e^3 + sqrt(x*e + d)*b*d*e^3 - sqrt(x*e + d)*a*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)*c) + 5*(4*c^5*d^3*e - 6*b*c^4*d^2*e^2 - (2*(b^2*c - 4*a*c^2)*d*e^3 - (b^3 - 4*a*b*c)*e^4)*c^2 + 4*(b^2*c^3 - a*c^4)*d*e^3 + 2*(sqrt(b^2 - 4*a*c)*c^3*d^2*e^2 - sqrt(b^2 - 4*a*c)*b*c^2*d*e^3 + sqrt(b^2 - 4*a*c)*a*c^2*e^4)*abs(c) - (b^3*c^2 - 2*a*b*c^3)*e^4)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d - b*c*e + sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((2*sqrt(b^2 - 4*a*c)*c^2*d - (b^2*c - 4*a*c^2 + sqrt(b^2 - 4*a*c)*b*c)*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2) - 5*(4*c^5*d^3*e - 6*b*c^4*d^2*e^2 - (2*(b^2*c - 4*a*c^2)*d*e^3 - (b^3 - 4*a*b*c)*e^4)*c^2 + 4*(b^2*c^3 - a*c^4)*d*e^3 - 2*(sqrt(b^2 - 4*a*c)*c^3*d^2*e^2 - sqrt(b^2 - 4*a*c)*b*c^2*d*e^3 + sqrt(b^2 - 4*a*c)*a*c^2*e^4)*abs(c) - (b^3*c^2 - 2*a*b*c^3)*e^4)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d - b*c*e - sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((2*sqrt(b^2 - 4*a*c)*c^2*d + (b^2*c - 4*a*c^2 - sqrt(b^2 - 4*a*c)*b*c)*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2)","B",0
1619,1,288,0,1.107403," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(x e + d\right)}^{\frac{3}{2}} e^{2}}{{\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}} - \frac{3 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e + \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right) e}{2 \, \sqrt{b^{2} - 4 \, a c} {\left| c \right|}} + \frac{3 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e - \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right) e}{2 \, \sqrt{b^{2} - 4 \, a c} {\left| c \right|}}"," ",0,"-(x*e + d)^(3/2)*e^2/((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2) - 3/2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e + sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))*e/(sqrt(b^2 - 4*a*c)*abs(c)) + 3/2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e - sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))*e/(sqrt(b^2 - 4*a*c)*abs(c))","A",0
1620,1,351,0,1.080371," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e + \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right) e}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c d + {\left(b^{2} - 4 \, a c - \sqrt{b^{2} - 4 \, a c} b\right)} e\right)} {\left| c \right|}} + \frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e - \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right) e}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c d - {\left(b^{2} - 4 \, a c + \sqrt{b^{2} - 4 \, a c} b\right)} e\right)} {\left| c \right|}} - \frac{\sqrt{x e + d} e^{2}}{{\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}}"," ",0,"-sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e + sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))*e/((2*sqrt(b^2 - 4*a*c)*c*d + (b^2 - 4*a*c - sqrt(b^2 - 4*a*c)*b)*e)*abs(c)) + sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e - sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))*e/((2*sqrt(b^2 - 4*a*c)*c*d - (b^2 - 4*a*c + sqrt(b^2 - 4*a*c)*b)*e)*abs(c)) - sqrt(x*e + d)*e^2/((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)","A",0
1621,1,1534,0,1.533237," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{\frac{3}{2}} c e^{2} - 2 \, \sqrt{x e + d} c d e^{2} + \sqrt{x e + d} b e^{3}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)} {\left(c d^{2} - b d e + a e^{2}\right)}} + \frac{{\left({\left(c d^{2} e - b d e^{2} + a e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} - 4 \, a c\right)} e^{2} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{3} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} b c d^{2} e^{3} - \sqrt{b^{2} - 4 \, a c} a b e^{5} + {\left(b^{2} + 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} d e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} + {\left(4 \, c^{4} d^{6} e^{2} - 12 \, b c^{3} d^{5} e^{3} + {\left(13 \, b^{2} c^{2} + 8 \, a c^{3}\right)} d^{4} e^{4} + a^{2} b^{2} e^{8} - 2 \, {\left(3 \, b^{3} c + 8 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 10 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d e^{7}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3} + \sqrt{{\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)}^{2} - 4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{6} - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{5} e + 3 \, {\left(b^{2} c + a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} a^{2} b d e^{5} - {\left(b^{3} + 6 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + \sqrt{b^{2} - 4 \, a c} a^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4}\right)} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(c d^{2} e - b d e^{2} + a e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} - 4 \, a c\right)} e^{2} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{3} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} b c d^{2} e^{3} - \sqrt{b^{2} - 4 \, a c} a b e^{5} + {\left(b^{2} + 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} d e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} + {\left(4 \, c^{4} d^{6} e^{2} - 12 \, b c^{3} d^{5} e^{3} + {\left(13 \, b^{2} c^{2} + 8 \, a c^{3}\right)} d^{4} e^{4} + a^{2} b^{2} e^{8} - 2 \, {\left(3 \, b^{3} c + 8 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 10 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d e^{7}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3} - \sqrt{{\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)}^{2} - 4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{6} - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{5} e + 3 \, {\left(b^{2} c + a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} a^{2} b d e^{5} - {\left(b^{3} + 6 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + \sqrt{b^{2} - 4 \, a c} a^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4}\right)} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} {\left| c \right|}}"," ",0,"((x*e + d)^(3/2)*c*e^2 - 2*sqrt(x*e + d)*c*d*e^2 + sqrt(x*e + d)*b*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)*(c*d^2 - b*d*e + a*e^2)) + 1/8*((c*d^2*e - b*d*e^2 + a*e^3)^2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(b^2 - 4*a*c)*e^2 - 2*(2*sqrt(b^2 - 4*a*c)*c^2*d^3*e^2 - 3*sqrt(b^2 - 4*a*c)*b*c*d^2*e^3 - sqrt(b^2 - 4*a*c)*a*b*e^5 + (b^2 + 2*a*c)*sqrt(b^2 - 4*a*c)*d*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c*d^2*e - b*d*e^2 + a*e^3) + (4*c^4*d^6*e^2 - 12*b*c^3*d^5*e^3 + (13*b^2*c^2 + 8*a*c^3)*d^4*e^4 + a^2*b^2*e^8 - 2*(3*b^3*c + 8*a*b*c^2)*d^3*e^5 + (b^4 + 10*a*b^2*c + 4*a^2*c^2)*d^2*e^6 - 2*(a*b^3 + 2*a^2*b*c)*d*e^7)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3 + sqrt((2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)^2 - 4*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((sqrt(b^2 - 4*a*c)*c^3*d^6 - 3*sqrt(b^2 - 4*a*c)*b*c^2*d^5*e + 3*(b^2*c + a*c^2)*sqrt(b^2 - 4*a*c)*d^4*e^2 - 3*sqrt(b^2 - 4*a*c)*a^2*b*d*e^5 - (b^3 + 6*a*b*c)*sqrt(b^2 - 4*a*c)*d^3*e^3 + sqrt(b^2 - 4*a*c)*a^3*e^6 + 3*(a*b^2 + a^2*c)*sqrt(b^2 - 4*a*c)*d^2*e^4)*abs(c*d^2*e - b*d*e^2 + a*e^3)*abs(c)) - 1/8*((c*d^2*e - b*d*e^2 + a*e^3)^2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(b^2 - 4*a*c)*e^2 + 2*(2*sqrt(b^2 - 4*a*c)*c^2*d^3*e^2 - 3*sqrt(b^2 - 4*a*c)*b*c*d^2*e^3 - sqrt(b^2 - 4*a*c)*a*b*e^5 + (b^2 + 2*a*c)*sqrt(b^2 - 4*a*c)*d*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c*d^2*e - b*d*e^2 + a*e^3) + (4*c^4*d^6*e^2 - 12*b*c^3*d^5*e^3 + (13*b^2*c^2 + 8*a*c^3)*d^4*e^4 + a^2*b^2*e^8 - 2*(3*b^3*c + 8*a*b*c^2)*d^3*e^5 + (b^4 + 10*a*b^2*c + 4*a^2*c^2)*d^2*e^6 - 2*(a*b^3 + 2*a^2*b*c)*d*e^7)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3 - sqrt((2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)^2 - 4*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((sqrt(b^2 - 4*a*c)*c^3*d^6 - 3*sqrt(b^2 - 4*a*c)*b*c^2*d^5*e + 3*(b^2*c + a*c^2)*sqrt(b^2 - 4*a*c)*d^4*e^2 - 3*sqrt(b^2 - 4*a*c)*a^2*b*d*e^5 - (b^3 + 6*a*b*c)*sqrt(b^2 - 4*a*c)*d^3*e^3 + sqrt(b^2 - 4*a*c)*a^3*e^6 + 3*(a*b^2 + a^2*c)*sqrt(b^2 - 4*a*c)*d^2*e^4)*abs(c*d^2*e - b*d*e^2 + a*e^3)*abs(c))","B",0
1622,1,1441,0,8.040780," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{3 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{3} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5} + \sqrt{{\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)}^{2} - 4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right) e}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{3} + 3 \, {\left(b^{2} c^{2} - 4 \, a c^{3} - \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} d^{2} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2} - {\left(b^{2} c - 2 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} - \frac{3 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{3} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5} - \sqrt{{\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)}^{2} - 4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right) e}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{3} - 3 \, {\left(b^{2} c^{2} - 4 \, a c^{3} + \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} d^{2} e + 3 \, {\left(b^{3} c - 4 \, a b c^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d e^{2} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} + \frac{6 \, {\left(x e + d\right)}^{2} c^{2} d e^{2} - 11 \, {\left(x e + d\right)} c^{2} d^{2} e^{2} + 4 \, c^{2} d^{3} e^{2} - 3 \, {\left(x e + d\right)}^{2} b c e^{3} + 11 \, {\left(x e + d\right)} b c d e^{3} - 6 \, b c d^{2} e^{3} - 3 \, {\left(x e + d\right)} b^{2} e^{4} + {\left(x e + d\right)} a c e^{4} + 2 \, b^{2} d e^{4} + 4 \, a c d e^{4} - 2 \, a b e^{5}}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left({\left(x e + d\right)}^{\frac{5}{2}} c - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d + \sqrt{x e + d} c d^{2} + {\left(x e + d\right)}^{\frac{3}{2}} b e - \sqrt{x e + d} b d e + \sqrt{x e + d} a e^{2}\right)}}"," ",0,"3*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5 + sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))*e/((2*sqrt(b^2 - 4*a*c)*c^3*d^3 + 3*(b^2*c^2 - 4*a*c^3 - sqrt(b^2 - 4*a*c)*b*c^2)*d^2*e - 3*(b^3*c - 4*a*b*c^2 - (b^2*c - 2*a*c^2)*sqrt(b^2 - 4*a*c))*d*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) - 3*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5 - sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))*e/((2*sqrt(b^2 - 4*a*c)*c^3*d^3 - 3*(b^2*c^2 - 4*a*c^3 + sqrt(b^2 - 4*a*c)*b*c^2)*d^2*e + 3*(b^3*c - 4*a*b*c^2 + (b^2*c - 2*a*c^2)*sqrt(b^2 - 4*a*c))*d*e^2 - (b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) + (6*(x*e + d)^2*c^2*d*e^2 - 11*(x*e + d)*c^2*d^2*e^2 + 4*c^2*d^3*e^2 - 3*(x*e + d)^2*b*c*e^3 + 11*(x*e + d)*b*c*d*e^3 - 6*b*c*d^2*e^3 - 3*(x*e + d)*b^2*e^4 + (x*e + d)*a*c*e^4 + 2*b^2*d*e^4 + 4*a*c*d*e^4 - 2*a*b*e^5)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*((x*e + d)^(5/2)*c - 2*(x*e + d)^(3/2)*c*d + sqrt(x*e + d)*c*d^2 + (x*e + d)^(3/2)*b*e - sqrt(x*e + d)*b*d*e + sqrt(x*e + d)*a*e^2))","B",0
1623,1,1749,0,6.053222," ","integrate((2*c*x+b)*(e*x+d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{7 \, {\left(16 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} e^{2} - 32 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e^{3} + 16 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{4} - {\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} - {\left(b^{2} - 6 \, a c\right)} e^{4}\right)} {\left(b^{2} c e - 4 \, a c^{2} e\right)}^{2} - 32 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{5} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{3} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e^{3} - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{4}\right)} {\left| -b^{2} c e + 4 \, a c^{2} e \right|} - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 32 \, a^{2} b^{2} c^{4}\right)} e^{6}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e + \sqrt{{\left(2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{4 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| -b^{2} c e + 4 \, a c^{2} e \right|} {\left| c \right|}} + \frac{7 \, {\left(16 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} e^{2} - 32 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e^{3} + 16 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{4} - {\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} - {\left(b^{2} - 6 \, a c\right)} e^{4}\right)} {\left(b^{2} c e - 4 \, a c^{2} e\right)}^{2} - 32 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{5} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{3} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e^{3} - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{4}\right)} {\left| -b^{2} c e + 4 \, a c^{2} e \right|} - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 32 \, a^{2} b^{2} c^{4}\right)} e^{6}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e - \sqrt{{\left(2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{4 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d - {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| -b^{2} c e + 4 \, a c^{2} e \right|} {\left| c \right|}} - \frac{14 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{2} e^{2} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{3} e^{2} + 42 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{4} e^{2} - 14 \, \sqrt{x e + d} c^{3} d^{5} e^{2} - 14 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} d e^{3} + 63 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d^{2} e^{3} - 84 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{3} e^{3} + 35 \, \sqrt{x e + d} b c^{2} d^{4} e^{3} + 9 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c e^{4} - 22 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} e^{4} - 35 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c d e^{4} + 14 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d e^{4} + 56 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d^{2} e^{4} + 28 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{2} e^{4} - 28 \, \sqrt{x e + d} b^{2} c d^{3} e^{4} - 28 \, \sqrt{x e + d} a c^{2} d^{3} e^{4} + 7 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{5} - 7 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c e^{5} - 14 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{5} - 28 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c d e^{5} + 7 \, \sqrt{x e + d} b^{3} d^{2} e^{5} + 42 \, \sqrt{x e + d} a b c d^{2} e^{5} + 14 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} e^{6} - 14 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c e^{6} - 14 \, \sqrt{x e + d} a b^{2} d e^{6} - 14 \, \sqrt{x e + d} a^{2} c d e^{6} + 7 \, \sqrt{x e + d} a^{2} b e^{7}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2} {\left(b^{2} c - 4 \, a c^{2}\right)}}"," ",0,"-7/4*(16*(b^2*c^6 - 4*a*c^7)*d^4*e^2 - 32*(b^3*c^5 - 4*a*b*c^6)*d^3*e^3 + 16*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^4 - (2*c^2*d^2*e^2 - 2*b*c*d*e^3 - (b^2 - 6*a*c)*e^4)*(b^2*c*e - 4*a*c^2*e)^2 - 32*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^5 - 2*(2*sqrt(b^2 - 4*a*c)*c^4*d^3*e^2 - 3*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e^3 - sqrt(b^2 - 4*a*c)*a*b*c^2*e^5 + (b^2*c^2 + 2*a*c^3)*sqrt(b^2 - 4*a*c)*d*e^4)*abs(-b^2*c*e + 4*a*c^2*e) - (b^6*c^2 - 12*a*b^4*c^3 + 32*a^2*b^2*c^4)*e^6)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e + sqrt((2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e)^2 - 4*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3 - (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c))*e)*abs(-b^2*c*e + 4*a*c^2*e)*abs(c)) + 7/4*(16*(b^2*c^6 - 4*a*c^7)*d^4*e^2 - 32*(b^3*c^5 - 4*a*b*c^6)*d^3*e^3 + 16*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^4 - (2*c^2*d^2*e^2 - 2*b*c*d*e^3 - (b^2 - 6*a*c)*e^4)*(b^2*c*e - 4*a*c^2*e)^2 - 32*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^5 + 2*(2*sqrt(b^2 - 4*a*c)*c^4*d^3*e^2 - 3*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e^3 - sqrt(b^2 - 4*a*c)*a*b*c^2*e^5 + (b^2*c^2 + 2*a*c^3)*sqrt(b^2 - 4*a*c)*d*e^4)*abs(-b^2*c*e + 4*a*c^2*e) - (b^6*c^2 - 12*a*b^4*c^3 + 32*a^2*b^2*c^4)*e^6)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e - sqrt((2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e)^2 - 4*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3 + (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c))*e)*abs(-b^2*c*e + 4*a*c^2*e)*abs(c)) - 1/4*(14*(x*e + d)^(7/2)*c^3*d^2*e^2 - 42*(x*e + d)^(5/2)*c^3*d^3*e^2 + 42*(x*e + d)^(3/2)*c^3*d^4*e^2 - 14*sqrt(x*e + d)*c^3*d^5*e^2 - 14*(x*e + d)^(7/2)*b*c^2*d*e^3 + 63*(x*e + d)^(5/2)*b*c^2*d^2*e^3 - 84*(x*e + d)^(3/2)*b*c^2*d^3*e^3 + 35*sqrt(x*e + d)*b*c^2*d^4*e^3 + 9*(x*e + d)^(7/2)*b^2*c*e^4 - 22*(x*e + d)^(7/2)*a*c^2*e^4 - 35*(x*e + d)^(5/2)*b^2*c*d*e^4 + 14*(x*e + d)^(5/2)*a*c^2*d*e^4 + 56*(x*e + d)^(3/2)*b^2*c*d^2*e^4 + 28*(x*e + d)^(3/2)*a*c^2*d^2*e^4 - 28*sqrt(x*e + d)*b^2*c*d^3*e^4 - 28*sqrt(x*e + d)*a*c^2*d^3*e^4 + 7*(x*e + d)^(5/2)*b^3*e^5 - 7*(x*e + d)^(5/2)*a*b*c*e^5 - 14*(x*e + d)^(3/2)*b^3*d*e^5 - 28*(x*e + d)^(3/2)*a*b*c*d*e^5 + 7*sqrt(x*e + d)*b^3*d^2*e^5 + 42*sqrt(x*e + d)*a*b*c*d^2*e^5 + 14*(x*e + d)^(3/2)*a*b^2*e^6 - 14*(x*e + d)^(3/2)*a^2*c*e^6 - 14*sqrt(x*e + d)*a*b^2*d*e^6 - 14*sqrt(x*e + d)*a^2*c*d*e^6 + 7*sqrt(x*e + d)*a^2*b*e^7)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2*(b^2*c - 4*a*c^2))","B",0
1624,1,1425,0,3.655234," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, c d e^{2} - b e^{3}\right)} {\left(b^{2} e - 4 \, a c e\right)}^{2} + 4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{2} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} b c d e^{3} + \sqrt{b^{2} - 4 \, a c} a c e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 24 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + 2 \, {\left(5 \, b^{4} c - 16 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 16 \, a^{2} b c^{2}\right)} e^{5}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e + \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{32 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}} + \frac{5 \, {\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, c d e^{2} - b e^{3}\right)} {\left(b^{2} e - 4 \, a c e\right)}^{2} - 4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{2} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} b c d e^{3} + \sqrt{b^{2} - 4 \, a c} a c e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 24 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + 2 \, {\left(5 \, b^{4} c - 16 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 16 \, a^{2} b c^{2}\right)} e^{5}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e - \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{32 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}} - \frac{10 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d e^{2} - 30 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{2} e^{2} + 30 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{3} e^{2} - 10 \, \sqrt{x e + d} c^{2} d^{4} e^{2} - 5 \, {\left(x e + d\right)}^{\frac{7}{2}} b c e^{3} + 30 \, {\left(x e + d\right)}^{\frac{5}{2}} b c d e^{3} - 45 \, {\left(x e + d\right)}^{\frac{3}{2}} b c d^{2} e^{3} + 20 \, \sqrt{x e + d} b c d^{3} e^{3} - 3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{4} - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} a c e^{4} + 15 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{4} + 30 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d e^{4} - 10 \, \sqrt{x e + d} b^{2} d^{2} e^{4} - 20 \, \sqrt{x e + d} a c d^{2} e^{4} - 15 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{5} + 20 \, \sqrt{x e + d} a b d e^{5} - 10 \, \sqrt{x e + d} a^{2} e^{6}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-5/32*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*c*d*e^2 - b*e^3)*(b^2*e - 4*a*c*e)^2 + 4*(sqrt(b^2 - 4*a*c)*c^2*d^2*e^2 - sqrt(b^2 - 4*a*c)*b*c*d*e^3 + sqrt(b^2 - 4*a*c)*a*c*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - (16*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 24*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + 2*(5*b^4*c - 16*a*b^2*c^2 - 16*a^2*c^3)*d*e^4 - (b^5 - 16*a^2*b*c^2)*e^5)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e + sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d^2 - (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2*c - 4*a^2*c^2)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c)) + 5/32*(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*c*d*e^2 - b*e^3)*(b^2*e - 4*a*c*e)^2 - 4*(sqrt(b^2 - 4*a*c)*c^2*d^2*e^2 - sqrt(b^2 - 4*a*c)*b*c*d*e^3 + sqrt(b^2 - 4*a*c)*a*c*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - (16*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 24*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + 2*(5*b^4*c - 16*a*b^2*c^2 - 16*a^2*c^3)*d*e^4 - (b^5 - 16*a^2*b*c^2)*e^5)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e - sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d^2 - (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2*c - 4*a^2*c^2)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c)) - 1/4*(10*(x*e + d)^(7/2)*c^2*d*e^2 - 30*(x*e + d)^(5/2)*c^2*d^2*e^2 + 30*(x*e + d)^(3/2)*c^2*d^3*e^2 - 10*sqrt(x*e + d)*c^2*d^4*e^2 - 5*(x*e + d)^(7/2)*b*c*e^3 + 30*(x*e + d)^(5/2)*b*c*d*e^3 - 45*(x*e + d)^(3/2)*b*c*d^2*e^3 + 20*sqrt(x*e + d)*b*c*d^3*e^3 - 3*(x*e + d)^(5/2)*b^2*e^4 - 18*(x*e + d)^(5/2)*a*c*e^4 + 15*(x*e + d)^(3/2)*b^2*d*e^4 + 30*(x*e + d)^(3/2)*a*c*d*e^4 - 10*sqrt(x*e + d)*b^2*d^2*e^4 - 20*sqrt(x*e + d)*a*c*d^2*e^4 - 15*(x*e + d)^(3/2)*a*b*e^5 + 20*sqrt(x*e + d)*a*b*d*e^5 - 10*sqrt(x*e + d)*a^2*e^6)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2*(b^2 - 4*a*c))","B",0
1625,1,1189,0,3.704759," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} e - 4 \, a c e\right)}^{2} e^{2} + {\left(2 \, \sqrt{b^{2} - 4 \, a c} c d e^{2} - \sqrt{b^{2} - 4 \, a c} b e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - 2 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 4 \, a b^{2} c\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e + \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} - 4 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}} + \frac{3 \, {\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} e - 4 \, a c e\right)}^{2} e^{2} - {\left(2 \, \sqrt{b^{2} - 4 \, a c} c d e^{2} - \sqrt{b^{2} - 4 \, a c} b e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - 2 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 4 \, a b^{2} c\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e - \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} - 4 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} e^{2} - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d e^{2} + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{2} e^{2} - 6 \, \sqrt{x e + d} c^{2} d^{3} e^{2} + 9 \, {\left(x e + d\right)}^{\frac{5}{2}} b c e^{3} - 18 \, {\left(x e + d\right)}^{\frac{3}{2}} b c d e^{3} + 9 \, \sqrt{x e + d} b c d^{2} e^{3} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{4} - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} a c e^{4} - 3 \, \sqrt{x e + d} b^{2} d e^{4} - 6 \, \sqrt{x e + d} a c d e^{4} + 3 \, \sqrt{x e + d} a b e^{5}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-3/16*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(b^2*e - 4*a*c*e)^2*e^2 + (2*sqrt(b^2 - 4*a*c)*c*d*e^2 - sqrt(b^2 - 4*a*c)*b*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - 2*(4*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 4*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 4*a*b^2*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e + sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c - 4*a*c^2)*sqrt(b^2 - 4*a*c)*d^2 - (b^3 - 4*a*b*c)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2 - 4*a^2*c)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c)) + 3/16*(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(b^2*e - 4*a*c*e)^2*e^2 - (2*sqrt(b^2 - 4*a*c)*c*d*e^2 - sqrt(b^2 - 4*a*c)*b*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - 2*(4*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 4*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 4*a*b^2*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e - sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c - 4*a*c^2)*sqrt(b^2 - 4*a*c)*d^2 - (b^3 - 4*a*b*c)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2 - 4*a^2*c)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c)) - 1/4*(6*(x*e + d)^(7/2)*c^2*e^2 - 18*(x*e + d)^(5/2)*c^2*d*e^2 + 18*(x*e + d)^(3/2)*c^2*d^2*e^2 - 6*sqrt(x*e + d)*c^2*d^3*e^2 + 9*(x*e + d)^(5/2)*b*c*e^3 - 18*(x*e + d)^(3/2)*b*c*d*e^3 + 9*sqrt(x*e + d)*b*c*d^2*e^3 + 5*(x*e + d)^(3/2)*b^2*e^4 - 2*(x*e + d)^(3/2)*a*c*e^4 - 3*sqrt(x*e + d)*b^2*d*e^4 - 6*sqrt(x*e + d)*a*c*d*e^4 + 3*sqrt(x*e + d)*a*b*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2*(b^2 - 4*a*c))","B",0
1626,1,3071,0,5.526875," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{{\left({\left(b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, c d e^{2} - b e^{3}\right)} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{4} e^{2} - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{3} e^{3} + {\left(b^{2} c + 8 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} + {\left(b^{3} - 8 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} - {\left(a b^{2} - 6 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| -b^{2} c d^{2} e + 4 \, a c^{2} d^{2} e + b^{3} d e^{2} - 4 \, a b c d e^{2} - a b^{2} e^{3} + 4 \, a^{2} c e^{3} \right|} - {\left(16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{7} e^{2} - 56 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} e^{3} + 14 \, {\left(5 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{5} e^{4} - 35 \, {\left(b^{5} c^{2} - 16 \, a^{2} b c^{4}\right)} d^{4} e^{5} + 4 \, {\left(b^{6} c + 23 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{3} e^{6} + {\left(b^{7} - 26 \, a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 384 \, a^{3} b c^{3}\right)} d^{2} e^{7} - 2 \, {\left(a b^{6} - 19 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{8} + {\left(a^{2} b^{5} - 16 \, a^{3} b^{3} c + 48 \, a^{4} b c^{2}\right)} e^{9}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3} + \sqrt{{\left(2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3}\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)}}}{b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}}}}\right)}{32 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} {\left| -b^{2} c d^{2} e + 4 \, a c^{2} d^{2} e + b^{3} d e^{2} - 4 \, a b c d e^{2} - a b^{2} e^{3} + 4 \, a^{2} c e^{3} \right|} {\left| c \right|}} + \frac{{\left({\left(b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, c d e^{2} - b e^{3}\right)} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{4} e^{2} - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{3} e^{3} + {\left(b^{2} c + 8 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} + {\left(b^{3} - 8 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} - {\left(a b^{2} - 6 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| -b^{2} c d^{2} e + 4 \, a c^{2} d^{2} e + b^{3} d e^{2} - 4 \, a b c d e^{2} - a b^{2} e^{3} + 4 \, a^{2} c e^{3} \right|} - {\left(16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{7} e^{2} - 56 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} e^{3} + 14 \, {\left(5 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{5} e^{4} - 35 \, {\left(b^{5} c^{2} - 16 \, a^{2} b c^{4}\right)} d^{4} e^{5} + 4 \, {\left(b^{6} c + 23 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{3} e^{6} + {\left(b^{7} - 26 \, a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 384 \, a^{3} b c^{3}\right)} d^{2} e^{7} - 2 \, {\left(a b^{6} - 19 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{8} + {\left(a^{2} b^{5} - 16 \, a^{3} b^{3} c + 48 \, a^{4} b c^{2}\right)} e^{9}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3} - \sqrt{{\left(2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3}\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)}}}{b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}}}}\right)}{32 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} {\left| -b^{2} c d^{2} e + 4 \, a c^{2} d^{2} e + b^{3} d e^{2} - 4 \, a b c d e^{2} - a b^{2} e^{3} + 4 \, a^{2} c e^{3} \right|} {\left| c \right|}} - \frac{2 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d e^{2} - 6 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{2} e^{2} + 6 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e^{2} - 2 \, \sqrt{x e + d} c^{3} d^{4} e^{2} - {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} e^{3} + 6 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d e^{3} - 9 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{3} + 4 \, \sqrt{x e + d} b c^{2} d^{3} e^{3} - 2 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c e^{4} + 2 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} e^{4} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{4} - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{4} - \sqrt{x e + d} b^{2} c d^{2} e^{4} - 8 \, \sqrt{x e + d} a c^{2} d^{2} e^{4} - {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{5} + {\left(x e + d\right)}^{\frac{3}{2}} a b c e^{5} - \sqrt{x e + d} b^{3} d e^{5} + 8 \, \sqrt{x e + d} a b c d e^{5} + \sqrt{x e + d} a b^{2} e^{6} - 6 \, \sqrt{x e + d} a^{2} c e^{6}}{4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2}}"," ",0,"-1/32*((b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3)^2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*c*d*e^2 - b*e^3) + 2*(2*sqrt(b^2 - 4*a*c)*c^3*d^4*e^2 - 4*sqrt(b^2 - 4*a*c)*b*c^2*d^3*e^3 + (b^2*c + 8*a*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^4 + (b^3 - 8*a*b*c)*sqrt(b^2 - 4*a*c)*d*e^5 - (a*b^2 - 6*a^2*c)*sqrt(b^2 - 4*a*c)*e^6)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(-b^2*c*d^2*e + 4*a*c^2*d^2*e + b^3*d*e^2 - 4*a*b*c*d*e^2 - a*b^2*e^3 + 4*a^2*c*e^3) - (16*(b^2*c^5 - 4*a*c^6)*d^7*e^2 - 56*(b^3*c^4 - 4*a*b*c^5)*d^6*e^3 + 14*(5*b^4*c^3 - 16*a*b^2*c^4 - 16*a^2*c^5)*d^5*e^4 - 35*(b^5*c^2 - 16*a^2*b*c^4)*d^4*e^5 + 4*(b^6*c + 23*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d^3*e^6 + (b^7 - 26*a*b^5*c - 8*a^2*b^3*c^2 + 384*a^3*b*c^3)*d^2*e^7 - 2*(a*b^6 - 19*a^2*b^4*c + 48*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^8 + (a^2*b^5 - 16*a^3*b^3*c + 48*a^4*b*c^2)*e^9)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3 + sqrt((2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3)^2 - 4*(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(((b^2*c^3 - 4*a*c^4)*sqrt(b^2 - 4*a*c)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*sqrt(b^2 - 4*a*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*sqrt(b^2 - 4*a*c)*e^6)*abs(-b^2*c*d^2*e + 4*a*c^2*d^2*e + b^3*d*e^2 - 4*a*b*c*d*e^2 - a*b^2*e^3 + 4*a^2*c*e^3)*abs(c)) + 1/32*((b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3)^2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*c*d*e^2 - b*e^3) - 2*(2*sqrt(b^2 - 4*a*c)*c^3*d^4*e^2 - 4*sqrt(b^2 - 4*a*c)*b*c^2*d^3*e^3 + (b^2*c + 8*a*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^4 + (b^3 - 8*a*b*c)*sqrt(b^2 - 4*a*c)*d*e^5 - (a*b^2 - 6*a^2*c)*sqrt(b^2 - 4*a*c)*e^6)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(-b^2*c*d^2*e + 4*a*c^2*d^2*e + b^3*d*e^2 - 4*a*b*c*d*e^2 - a*b^2*e^3 + 4*a^2*c*e^3) - (16*(b^2*c^5 - 4*a*c^6)*d^7*e^2 - 56*(b^3*c^4 - 4*a*b*c^5)*d^6*e^3 + 14*(5*b^4*c^3 - 16*a*b^2*c^4 - 16*a^2*c^5)*d^5*e^4 - 35*(b^5*c^2 - 16*a^2*b*c^4)*d^4*e^5 + 4*(b^6*c + 23*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d^3*e^6 + (b^7 - 26*a*b^5*c - 8*a^2*b^3*c^2 + 384*a^3*b*c^3)*d^2*e^7 - 2*(a*b^6 - 19*a^2*b^4*c + 48*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^8 + (a^2*b^5 - 16*a^3*b^3*c + 48*a^4*b*c^2)*e^9)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3 - sqrt((2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3)^2 - 4*(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(((b^2*c^3 - 4*a*c^4)*sqrt(b^2 - 4*a*c)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*sqrt(b^2 - 4*a*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*sqrt(b^2 - 4*a*c)*e^6)*abs(-b^2*c*d^2*e + 4*a*c^2*d^2*e + b^3*d*e^2 - 4*a*b*c*d*e^2 - a*b^2*e^3 + 4*a^2*c*e^3)*abs(c)) - 1/4*(2*(x*e + d)^(7/2)*c^3*d*e^2 - 6*(x*e + d)^(5/2)*c^3*d^2*e^2 + 6*(x*e + d)^(3/2)*c^3*d^3*e^2 - 2*sqrt(x*e + d)*c^3*d^4*e^2 - (x*e + d)^(7/2)*b*c^2*e^3 + 6*(x*e + d)^(5/2)*b*c^2*d*e^3 - 9*(x*e + d)^(3/2)*b*c^2*d^2*e^3 + 4*sqrt(x*e + d)*b*c^2*d^3*e^3 - 2*(x*e + d)^(5/2)*b^2*c*e^4 + 2*(x*e + d)^(5/2)*a*c^2*e^4 + 5*(x*e + d)^(3/2)*b^2*c*d*e^4 - 2*(x*e + d)^(3/2)*a*c^2*d*e^4 - sqrt(x*e + d)*b^2*c*d^2*e^4 - 8*sqrt(x*e + d)*a*c^2*d^2*e^4 - (x*e + d)^(3/2)*b^3*e^5 + (x*e + d)^(3/2)*a*b*c*e^5 - sqrt(x*e + d)*b^3*d*e^5 + 8*sqrt(x*e + d)*a*b*c*d*e^5 + sqrt(x*e + d)*a*b^2*e^6 - 6*sqrt(x*e + d)*a^2*c*e^6)/((b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)","B",0
1627,1,5779,0,10.015863," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{{\left({\left(b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5}\right)}^{2} {\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + {\left(3 \, b^{2} - 10 \, a c\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{5} d^{7} e^{2} - 7 \, \sqrt{b^{2} - 4 \, a c} b c^{4} d^{6} e^{3} + 3 \, {\left(b^{2} c^{3} + 10 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{4} + 5 \, {\left(2 \, b^{3} c^{2} - 15 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{5} - {\left(11 \, b^{4} c - 48 \, a b^{2} c^{2} - 54 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{6} + 3 \, {\left(b^{5} + a b^{3} c - 27 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{7} - {\left(6 \, a b^{4} - 21 \, a^{2} b^{2} c - 26 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e^{8} + {\left(3 \, a^{2} b^{3} - 13 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} e^{9}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} - {\left(16 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{12} e^{2} - 96 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{11} e^{3} + 8 \, {\left(29 \, b^{4} c^{6} - 100 \, a b^{2} c^{7} - 64 \, a^{2} c^{8}\right)} d^{10} e^{4} - 40 \, {\left(7 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} - 64 \, a^{2} b c^{7}\right)} d^{9} e^{5} + {\left(157 \, b^{6} c^{4} + 636 \, a b^{4} c^{5} - 4704 \, a^{2} b^{2} c^{6} - 1408 \, a^{3} c^{7}\right)} d^{8} e^{6} - 4 \, {\left(b^{7} c^{3} + 300 \, a b^{5} c^{4} - 864 \, a^{2} b^{3} c^{5} - 1408 \, a^{3} b c^{6}\right)} d^{7} e^{7} - 14 \, {\left(3 \, b^{8} c^{2} - 50 \, a b^{6} c^{3} + 576 \, a^{3} b^{2} c^{5} + 128 \, a^{4} c^{6}\right)} d^{6} e^{8} + 4 \, {\left(5 \, b^{9} c - 27 \, a b^{7} c^{2} - 336 \, a^{2} b^{5} c^{3} + 1120 \, a^{3} b^{3} c^{4} + 1344 \, a^{4} b c^{5}\right)} d^{5} e^{9} - {\left(3 \, b^{10} + 40 \, a b^{8} c - 590 \, a^{2} b^{6} c^{2} + 120 \, a^{3} b^{4} c^{3} + 5360 \, a^{4} b^{2} c^{4} + 1088 \, a^{5} c^{5}\right)} d^{4} e^{10} + 4 \, {\left(3 \, a b^{9} - 7 \, a^{2} b^{7} c - 164 \, a^{3} b^{5} c^{2} + 440 \, a^{4} b^{3} c^{3} + 544 \, a^{5} b c^{4}\right)} d^{3} e^{11} - 2 \, {\left(9 \, a^{2} b^{8} - 62 \, a^{3} b^{6} c - 60 \, a^{4} b^{4} c^{2} + 624 \, a^{5} b^{2} c^{3} + 128 \, a^{6} c^{4}\right)} d^{2} e^{12} + 4 \, {\left(3 \, a^{3} b^{7} - 26 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} + 64 \, a^{6} b c^{3}\right)} d e^{13} - {\left(3 \, a^{4} b^{6} - 28 \, a^{5} b^{4} c + 64 \, a^{6} b^{2} c^{2}\right)} e^{14}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5} + \sqrt{{\left(2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5}\right)}^{2} - 4 \, {\left(b^{2} c^{3} d^{6} - 4 \, a c^{4} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 12 \, a b c^{3} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - 9 \, a b^{2} c^{2} d^{4} e^{2} - 12 \, a^{2} c^{3} d^{4} e^{2} - b^{5} d^{3} e^{3} - 2 \, a b^{3} c d^{3} e^{3} + 24 \, a^{2} b c^{2} d^{3} e^{3} + 3 \, a b^{4} d^{2} e^{4} - 9 \, a^{2} b^{2} c d^{2} e^{4} - 12 \, a^{3} c^{2} d^{2} e^{4} - 3 \, a^{2} b^{3} d e^{5} + 12 \, a^{3} b c d e^{5} + a^{3} b^{2} e^{6} - 4 \, a^{4} c e^{6}\right)} {\left(b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}\right)}}}{b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}}}}\right)}{32 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{10} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{9} e + 5 \, {\left(2 \, b^{4} c^{3} - 7 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{8} e^{2} - 10 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{7} e^{3} + 5 \, {\left(b^{6} c + 2 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} e^{4} - {\left(b^{7} + 16 \, a b^{5} c - 50 \, a^{2} b^{3} c^{2} - 120 \, a^{3} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{5} + 5 \, {\left(a b^{6} + 2 \, a^{2} b^{4} c - 22 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{6} - 10 \, {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{7} + 5 \, {\left(2 \, a^{3} b^{4} - 7 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{8} - 5 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{b^{2} - 4 \, a c} e^{10}\right)} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} {\left| c \right|}} - \frac{{\left({\left(b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5}\right)}^{2} {\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + {\left(3 \, b^{2} - 10 \, a c\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{5} d^{7} e^{2} - 7 \, \sqrt{b^{2} - 4 \, a c} b c^{4} d^{6} e^{3} + 3 \, {\left(b^{2} c^{3} + 10 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{4} + 5 \, {\left(2 \, b^{3} c^{2} - 15 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{5} - {\left(11 \, b^{4} c - 48 \, a b^{2} c^{2} - 54 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{6} + 3 \, {\left(b^{5} + a b^{3} c - 27 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{7} - {\left(6 \, a b^{4} - 21 \, a^{2} b^{2} c - 26 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e^{8} + {\left(3 \, a^{2} b^{3} - 13 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} e^{9}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} - {\left(16 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{12} e^{2} - 96 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{11} e^{3} + 8 \, {\left(29 \, b^{4} c^{6} - 100 \, a b^{2} c^{7} - 64 \, a^{2} c^{8}\right)} d^{10} e^{4} - 40 \, {\left(7 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} - 64 \, a^{2} b c^{7}\right)} d^{9} e^{5} + {\left(157 \, b^{6} c^{4} + 636 \, a b^{4} c^{5} - 4704 \, a^{2} b^{2} c^{6} - 1408 \, a^{3} c^{7}\right)} d^{8} e^{6} - 4 \, {\left(b^{7} c^{3} + 300 \, a b^{5} c^{4} - 864 \, a^{2} b^{3} c^{5} - 1408 \, a^{3} b c^{6}\right)} d^{7} e^{7} - 14 \, {\left(3 \, b^{8} c^{2} - 50 \, a b^{6} c^{3} + 576 \, a^{3} b^{2} c^{5} + 128 \, a^{4} c^{6}\right)} d^{6} e^{8} + 4 \, {\left(5 \, b^{9} c - 27 \, a b^{7} c^{2} - 336 \, a^{2} b^{5} c^{3} + 1120 \, a^{3} b^{3} c^{4} + 1344 \, a^{4} b c^{5}\right)} d^{5} e^{9} - {\left(3 \, b^{10} + 40 \, a b^{8} c - 590 \, a^{2} b^{6} c^{2} + 120 \, a^{3} b^{4} c^{3} + 5360 \, a^{4} b^{2} c^{4} + 1088 \, a^{5} c^{5}\right)} d^{4} e^{10} + 4 \, {\left(3 \, a b^{9} - 7 \, a^{2} b^{7} c - 164 \, a^{3} b^{5} c^{2} + 440 \, a^{4} b^{3} c^{3} + 544 \, a^{5} b c^{4}\right)} d^{3} e^{11} - 2 \, {\left(9 \, a^{2} b^{8} - 62 \, a^{3} b^{6} c - 60 \, a^{4} b^{4} c^{2} + 624 \, a^{5} b^{2} c^{3} + 128 \, a^{6} c^{4}\right)} d^{2} e^{12} + 4 \, {\left(3 \, a^{3} b^{7} - 26 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} + 64 \, a^{6} b c^{3}\right)} d e^{13} - {\left(3 \, a^{4} b^{6} - 28 \, a^{5} b^{4} c + 64 \, a^{6} b^{2} c^{2}\right)} e^{14}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5} - \sqrt{{\left(2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5}\right)}^{2} - 4 \, {\left(b^{2} c^{3} d^{6} - 4 \, a c^{4} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 12 \, a b c^{3} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - 9 \, a b^{2} c^{2} d^{4} e^{2} - 12 \, a^{2} c^{3} d^{4} e^{2} - b^{5} d^{3} e^{3} - 2 \, a b^{3} c d^{3} e^{3} + 24 \, a^{2} b c^{2} d^{3} e^{3} + 3 \, a b^{4} d^{2} e^{4} - 9 \, a^{2} b^{2} c d^{2} e^{4} - 12 \, a^{3} c^{2} d^{2} e^{4} - 3 \, a^{2} b^{3} d e^{5} + 12 \, a^{3} b c d e^{5} + a^{3} b^{2} e^{6} - 4 \, a^{4} c e^{6}\right)} {\left(b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}\right)}}}{b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}}}}\right)}{32 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{10} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{9} e + 5 \, {\left(2 \, b^{4} c^{3} - 7 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{8} e^{2} - 10 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{7} e^{3} + 5 \, {\left(b^{6} c + 2 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} e^{4} - {\left(b^{7} + 16 \, a b^{5} c - 50 \, a^{2} b^{3} c^{2} - 120 \, a^{3} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{5} + 5 \, {\left(a b^{6} + 2 \, a^{2} b^{4} c - 22 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{6} - 10 \, {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{7} + 5 \, {\left(2 \, a^{3} b^{4} - 7 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{8} - 5 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{b^{2} - 4 \, a c} e^{10}\right)} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} {\left| c \right|}} + \frac{2 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{4} d^{2} e^{2} - 6 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} d^{3} e^{2} + 6 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{4} e^{2} - 2 \, \sqrt{x e + d} c^{4} d^{5} e^{2} - 2 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{3} d e^{3} + 9 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{3} d^{2} e^{3} - 12 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{3} e^{3} + 5 \, \sqrt{x e + d} b c^{3} d^{4} e^{3} + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{2} e^{4} - 10 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{3} e^{4} - 15 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{2} d e^{4} + 42 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{3} d e^{4} + 24 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{2} e^{4} - 60 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{3} d^{2} e^{4} - 14 \, \sqrt{x e + d} b^{2} c^{2} d^{3} e^{4} + 36 \, \sqrt{x e + d} a c^{3} d^{3} e^{4} + 6 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c e^{5} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c^{2} e^{5} - 18 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d e^{5} + 60 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c^{2} d e^{5} + 16 \, \sqrt{x e + d} b^{3} c d^{2} e^{5} - 54 \, \sqrt{x e + d} a b c^{2} d^{2} e^{5} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{6} - 6 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} c e^{6} - 18 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c^{2} e^{6} - 5 \, \sqrt{x e + d} b^{4} d e^{6} + 8 \, \sqrt{x e + d} a b^{2} c d e^{6} + 38 \, \sqrt{x e + d} a^{2} c^{2} d e^{6} + 5 \, \sqrt{x e + d} a b^{3} e^{7} - 19 \, \sqrt{x e + d} a^{2} b c e^{7}}{4 \, {\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2}}"," ",0,"1/32*((b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)^2*(2*c^2*d^2*e^2 - 2*b*c*d*e^3 + (3*b^2 - 10*a*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e) + 2*(2*sqrt(b^2 - 4*a*c)*c^5*d^7*e^2 - 7*sqrt(b^2 - 4*a*c)*b*c^4*d^6*e^3 + 3*(b^2*c^3 + 10*a*c^4)*sqrt(b^2 - 4*a*c)*d^5*e^4 + 5*(2*b^3*c^2 - 15*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^5 - (11*b^4*c - 48*a*b^2*c^2 - 54*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^3*e^6 + 3*(b^5 + a*b^3*c - 27*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^7 - (6*a*b^4 - 21*a^2*b^2*c - 26*a^3*c^2)*sqrt(b^2 - 4*a*c)*d*e^8 + (3*a^2*b^3 - 13*a^3*b*c)*sqrt(b^2 - 4*a*c)*e^9)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5) - (16*(b^2*c^8 - 4*a*c^9)*d^12*e^2 - 96*(b^3*c^7 - 4*a*b*c^8)*d^11*e^3 + 8*(29*b^4*c^6 - 100*a*b^2*c^7 - 64*a^2*c^8)*d^10*e^4 - 40*(7*b^5*c^5 - 12*a*b^3*c^6 - 64*a^2*b*c^7)*d^9*e^5 + (157*b^6*c^4 + 636*a*b^4*c^5 - 4704*a^2*b^2*c^6 - 1408*a^3*c^7)*d^8*e^6 - 4*(b^7*c^3 + 300*a*b^5*c^4 - 864*a^2*b^3*c^5 - 1408*a^3*b*c^6)*d^7*e^7 - 14*(3*b^8*c^2 - 50*a*b^6*c^3 + 576*a^3*b^2*c^5 + 128*a^4*c^6)*d^6*e^8 + 4*(5*b^9*c - 27*a*b^7*c^2 - 336*a^2*b^5*c^3 + 1120*a^3*b^3*c^4 + 1344*a^4*b*c^5)*d^5*e^9 - (3*b^10 + 40*a*b^8*c - 590*a^2*b^6*c^2 + 120*a^3*b^4*c^3 + 5360*a^4*b^2*c^4 + 1088*a^5*c^5)*d^4*e^10 + 4*(3*a*b^9 - 7*a^2*b^7*c - 164*a^3*b^5*c^2 + 440*a^4*b^3*c^3 + 544*a^5*b*c^4)*d^3*e^11 - 2*(9*a^2*b^8 - 62*a^3*b^6*c - 60*a^4*b^4*c^2 + 624*a^5*b^2*c^3 + 128*a^6*c^4)*d^2*e^12 + 4*(3*a^3*b^7 - 26*a^4*b^5*c + 40*a^5*b^3*c^2 + 64*a^6*b*c^3)*d*e^13 - (3*a^4*b^6 - 28*a^5*b^4*c + 64*a^6*b^2*c^2)*e^14)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5 + sqrt((2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5)^2 - 4*(b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(((b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^10 - 5*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^9*e + 5*(2*b^4*c^3 - 7*a*b^2*c^4 - 4*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^8*e^2 - 10*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d^7*e^3 + 5*(b^6*c + 2*a*b^4*c^2 - 22*a^2*b^2*c^3 - 8*a^3*c^4)*sqrt(b^2 - 4*a*c)*d^6*e^4 - (b^7 + 16*a*b^5*c - 50*a^2*b^3*c^2 - 120*a^3*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e^5 + 5*(a*b^6 + 2*a^2*b^4*c - 22*a^3*b^2*c^2 - 8*a^4*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^6 - 10*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^7 + 5*(2*a^3*b^4 - 7*a^4*b^2*c - 4*a^5*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^8 - 5*(a^4*b^3 - 4*a^5*b*c)*sqrt(b^2 - 4*a*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*sqrt(b^2 - 4*a*c)*e^10)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)*abs(c)) - 1/32*((b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)^2*(2*c^2*d^2*e^2 - 2*b*c*d*e^3 + (3*b^2 - 10*a*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e) - 2*(2*sqrt(b^2 - 4*a*c)*c^5*d^7*e^2 - 7*sqrt(b^2 - 4*a*c)*b*c^4*d^6*e^3 + 3*(b^2*c^3 + 10*a*c^4)*sqrt(b^2 - 4*a*c)*d^5*e^4 + 5*(2*b^3*c^2 - 15*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^5 - (11*b^4*c - 48*a*b^2*c^2 - 54*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^3*e^6 + 3*(b^5 + a*b^3*c - 27*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^7 - (6*a*b^4 - 21*a^2*b^2*c - 26*a^3*c^2)*sqrt(b^2 - 4*a*c)*d*e^8 + (3*a^2*b^3 - 13*a^3*b*c)*sqrt(b^2 - 4*a*c)*e^9)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5) - (16*(b^2*c^8 - 4*a*c^9)*d^12*e^2 - 96*(b^3*c^7 - 4*a*b*c^8)*d^11*e^3 + 8*(29*b^4*c^6 - 100*a*b^2*c^7 - 64*a^2*c^8)*d^10*e^4 - 40*(7*b^5*c^5 - 12*a*b^3*c^6 - 64*a^2*b*c^7)*d^9*e^5 + (157*b^6*c^4 + 636*a*b^4*c^5 - 4704*a^2*b^2*c^6 - 1408*a^3*c^7)*d^8*e^6 - 4*(b^7*c^3 + 300*a*b^5*c^4 - 864*a^2*b^3*c^5 - 1408*a^3*b*c^6)*d^7*e^7 - 14*(3*b^8*c^2 - 50*a*b^6*c^3 + 576*a^3*b^2*c^5 + 128*a^4*c^6)*d^6*e^8 + 4*(5*b^9*c - 27*a*b^7*c^2 - 336*a^2*b^5*c^3 + 1120*a^3*b^3*c^4 + 1344*a^4*b*c^5)*d^5*e^9 - (3*b^10 + 40*a*b^8*c - 590*a^2*b^6*c^2 + 120*a^3*b^4*c^3 + 5360*a^4*b^2*c^4 + 1088*a^5*c^5)*d^4*e^10 + 4*(3*a*b^9 - 7*a^2*b^7*c - 164*a^3*b^5*c^2 + 440*a^4*b^3*c^3 + 544*a^5*b*c^4)*d^3*e^11 - 2*(9*a^2*b^8 - 62*a^3*b^6*c - 60*a^4*b^4*c^2 + 624*a^5*b^2*c^3 + 128*a^6*c^4)*d^2*e^12 + 4*(3*a^3*b^7 - 26*a^4*b^5*c + 40*a^5*b^3*c^2 + 64*a^6*b*c^3)*d*e^13 - (3*a^4*b^6 - 28*a^5*b^4*c + 64*a^6*b^2*c^2)*e^14)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5 - sqrt((2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5)^2 - 4*(b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(((b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^10 - 5*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^9*e + 5*(2*b^4*c^3 - 7*a*b^2*c^4 - 4*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^8*e^2 - 10*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d^7*e^3 + 5*(b^6*c + 2*a*b^4*c^2 - 22*a^2*b^2*c^3 - 8*a^3*c^4)*sqrt(b^2 - 4*a*c)*d^6*e^4 - (b^7 + 16*a*b^5*c - 50*a^2*b^3*c^2 - 120*a^3*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e^5 + 5*(a*b^6 + 2*a^2*b^4*c - 22*a^3*b^2*c^2 - 8*a^4*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^6 - 10*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^7 + 5*(2*a^3*b^4 - 7*a^4*b^2*c - 4*a^5*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^8 - 5*(a^4*b^3 - 4*a^5*b*c)*sqrt(b^2 - 4*a*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*sqrt(b^2 - 4*a*c)*e^10)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)*abs(c)) + 1/4*(2*(x*e + d)^(7/2)*c^4*d^2*e^2 - 6*(x*e + d)^(5/2)*c^4*d^3*e^2 + 6*(x*e + d)^(3/2)*c^4*d^4*e^2 - 2*sqrt(x*e + d)*c^4*d^5*e^2 - 2*(x*e + d)^(7/2)*b*c^3*d*e^3 + 9*(x*e + d)^(5/2)*b*c^3*d^2*e^3 - 12*(x*e + d)^(3/2)*b*c^3*d^3*e^3 + 5*sqrt(x*e + d)*b*c^3*d^4*e^3 + 3*(x*e + d)^(7/2)*b^2*c^2*e^4 - 10*(x*e + d)^(7/2)*a*c^3*e^4 - 15*(x*e + d)^(5/2)*b^2*c^2*d*e^4 + 42*(x*e + d)^(5/2)*a*c^3*d*e^4 + 24*(x*e + d)^(3/2)*b^2*c^2*d^2*e^4 - 60*(x*e + d)^(3/2)*a*c^3*d^2*e^4 - 14*sqrt(x*e + d)*b^2*c^2*d^3*e^4 + 36*sqrt(x*e + d)*a*c^3*d^3*e^4 + 6*(x*e + d)^(5/2)*b^3*c*e^5 - 21*(x*e + d)^(5/2)*a*b*c^2*e^5 - 18*(x*e + d)^(3/2)*b^3*c*d*e^5 + 60*(x*e + d)^(3/2)*a*b*c^2*d*e^5 + 16*sqrt(x*e + d)*b^3*c*d^2*e^5 - 54*sqrt(x*e + d)*a*b*c^2*d^2*e^5 + 3*(x*e + d)^(3/2)*b^4*e^6 - 6*(x*e + d)^(3/2)*a*b^2*c*e^6 - 18*(x*e + d)^(3/2)*a^2*c^2*e^6 - 5*sqrt(x*e + d)*b^4*d*e^6 + 8*sqrt(x*e + d)*a*b^2*c*d*e^6 + 38*sqrt(x*e + d)*a^2*c^2*d*e^6 + 5*sqrt(x*e + d)*a*b^3*e^7 - 19*sqrt(x*e + d)*a^2*b*c*e^7)/((b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)","B",0
1628,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d), x)","F",0
1629,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(2*c*x + b)/sqrt(e*x + d), x)","F",0
1630,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(2*c*x + b)/(e*x + d)^(3/2), x)","F",0
1631,-2,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 3.64Unable to transpose Error: Bad Argument Value","F(-2)",0
1632,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(2*c*x + b)/(e*x + d)^(7/2), x)","F",0
1633,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(2 \, c x + b\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(2*c*x + b)/sqrt(e*x + d), x)","F",0
1634,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(2 \, c x + b\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(2*c*x + b)/(e*x + d)^(3/2), x)","F",0
1635,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(2 \, c x + b\right)}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(2*c*x + b)/(e*x + d)^(5/2), x)","F",0
1636,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(2 \, c x + b\right)}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(2*c*x + b)/(e*x + d)^(7/2), x)","F",0
1637,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{5}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(5/2)/sqrt(c*x^2 + b*x + a), x)","F",0
1638,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
1639,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*x + b)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
1640,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, c x + b}{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((2*c*x + b)/(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)), x)","F",0
1641,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, c x + b}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2)), x)","F",0
1642,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, c x + b}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(5/2)), x)","F",0
1643,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(7/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1644,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(5/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1645,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(3/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1646,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} \sqrt{e x + d}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*sqrt(e*x + d)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1647,0,0,0,0.000000," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, c x + b}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((2*c*x + b)/((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d)), x)","F",0
1648,-2,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 3.17Unable to transpose Error: Bad Argument Value","F(-2)",0
1649,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(7/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(7/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1650,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(5/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1651,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^(3/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1652,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} \sqrt{e x + d}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*x + b)*sqrt(e*x + d)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1653,0,0,0,0.000000," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, c x + b}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((2*c*x + b)/((c*x^2 + b*x + a)^(5/2)*sqrt(e*x + d)), x)","F",0
1654,1,9689,0,0.503524," ","integrate((2*c*x+b)*(e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2 \, {\left(x e + d\right)}^{m} c^{4} m^{7} x^{8} e^{8} + 2 \, {\left(x e + d\right)}^{m} c^{4} d m^{7} x^{7} e^{7} + 7 \, {\left(x e + d\right)}^{m} b c^{3} m^{7} x^{7} e^{8} + 56 \, {\left(x e + d\right)}^{m} c^{4} m^{6} x^{8} e^{8} + 7 \, {\left(x e + d\right)}^{m} b c^{3} d m^{7} x^{6} e^{7} + 42 \, {\left(x e + d\right)}^{m} c^{4} d m^{6} x^{7} e^{7} - 14 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{6} x^{6} e^{6} + 9 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{7} x^{6} e^{8} + 6 \, {\left(x e + d\right)}^{m} a c^{3} m^{7} x^{6} e^{8} + 203 \, {\left(x e + d\right)}^{m} b c^{3} m^{6} x^{7} e^{8} + 644 \, {\left(x e + d\right)}^{m} c^{4} m^{5} x^{8} e^{8} + 9 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{7} x^{5} e^{7} + 6 \, {\left(x e + d\right)}^{m} a c^{3} d m^{7} x^{5} e^{7} + 161 \, {\left(x e + d\right)}^{m} b c^{3} d m^{6} x^{6} e^{7} + 350 \, {\left(x e + d\right)}^{m} c^{4} d m^{5} x^{7} e^{7} - 42 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{6} x^{5} e^{6} - 210 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{5} x^{6} e^{6} + 84 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{5} x^{5} e^{5} + 5 \, {\left(x e + d\right)}^{m} b^{3} c m^{7} x^{5} e^{8} + 15 \, {\left(x e + d\right)}^{m} a b c^{2} m^{7} x^{5} e^{8} + 270 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{6} x^{6} e^{8} + 180 \, {\left(x e + d\right)}^{m} a c^{3} m^{6} x^{6} e^{8} + 2401 \, {\left(x e + d\right)}^{m} b c^{3} m^{5} x^{7} e^{8} + 3920 \, {\left(x e + d\right)}^{m} c^{4} m^{4} x^{8} e^{8} + 5 \, {\left(x e + d\right)}^{m} b^{3} c d m^{7} x^{4} e^{7} + 15 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{7} x^{4} e^{7} + 225 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{6} x^{5} e^{7} + 150 \, {\left(x e + d\right)}^{m} a c^{3} d m^{6} x^{5} e^{7} + 1435 \, {\left(x e + d\right)}^{m} b c^{3} d m^{5} x^{6} e^{7} + 1470 \, {\left(x e + d\right)}^{m} c^{4} d m^{4} x^{7} e^{7} - 45 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{6} x^{4} e^{6} - 30 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{6} x^{4} e^{6} - 756 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{5} x^{5} e^{6} - 1190 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{4} x^{6} e^{6} + 210 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{5} x^{4} e^{5} + 840 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{4} x^{5} e^{5} - 420 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m^{4} x^{4} e^{4} + {\left(x e + d\right)}^{m} b^{4} m^{7} x^{4} e^{8} + 12 \, {\left(x e + d\right)}^{m} a b^{2} c m^{7} x^{4} e^{8} + 6 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{7} x^{4} e^{8} + 155 \, {\left(x e + d\right)}^{m} b^{3} c m^{6} x^{5} e^{8} + 465 \, {\left(x e + d\right)}^{m} a b c^{2} m^{6} x^{5} e^{8} + 3294 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{5} x^{6} e^{8} + 2196 \, {\left(x e + d\right)}^{m} a c^{3} m^{5} x^{6} e^{8} + 14945 \, {\left(x e + d\right)}^{m} b c^{3} m^{4} x^{7} e^{8} + 13538 \, {\left(x e + d\right)}^{m} c^{4} m^{3} x^{8} e^{8} + {\left(x e + d\right)}^{m} b^{4} d m^{7} x^{3} e^{7} + 12 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{7} x^{3} e^{7} + 6 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{7} x^{3} e^{7} + 135 \, {\left(x e + d\right)}^{m} b^{3} c d m^{6} x^{4} e^{7} + 405 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{6} x^{4} e^{7} + 2169 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{5} x^{5} e^{7} + 1446 \, {\left(x e + d\right)}^{m} a c^{3} d m^{5} x^{5} e^{7} + 6335 \, {\left(x e + d\right)}^{m} b c^{3} d m^{4} x^{6} e^{7} + 3248 \, {\left(x e + d\right)}^{m} c^{4} d m^{3} x^{7} e^{7} - 20 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{6} x^{3} e^{6} - 60 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{6} x^{3} e^{6} - 945 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{5} x^{4} e^{6} - 630 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{5} x^{4} e^{6} - 4830 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{4} x^{5} e^{6} - 3150 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{3} x^{6} e^{6} + 180 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{5} x^{3} e^{5} + 120 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{5} x^{3} e^{5} + 2940 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{4} x^{4} e^{5} + 2940 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{3} x^{5} e^{5} - 840 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m^{4} x^{3} e^{4} - 2520 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m^{3} x^{4} e^{4} + 1680 \, {\left(x e + d\right)}^{m} c^{4} d^{5} m^{3} x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} a b^{3} m^{7} x^{3} e^{8} + 9 \, {\left(x e + d\right)}^{m} a^{2} b c m^{7} x^{3} e^{8} + 32 \, {\left(x e + d\right)}^{m} b^{4} m^{6} x^{4} e^{8} + 384 \, {\left(x e + d\right)}^{m} a b^{2} c m^{6} x^{4} e^{8} + 192 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{6} x^{4} e^{8} + 1955 \, {\left(x e + d\right)}^{m} b^{3} c m^{5} x^{5} e^{8} + 5865 \, {\left(x e + d\right)}^{m} a b c^{2} m^{5} x^{5} e^{8} + 21060 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{4} x^{6} e^{8} + 14040 \, {\left(x e + d\right)}^{m} a c^{3} m^{4} x^{6} e^{8} + 52528 \, {\left(x e + d\right)}^{m} b c^{3} m^{3} x^{7} e^{8} + 26264 \, {\left(x e + d\right)}^{m} c^{4} m^{2} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} a b^{3} d m^{7} x^{2} e^{7} + 9 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{7} x^{2} e^{7} + 29 \, {\left(x e + d\right)}^{m} b^{4} d m^{6} x^{3} e^{7} + 348 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{6} x^{3} e^{7} + 174 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{6} x^{3} e^{7} + 1415 \, {\left(x e + d\right)}^{m} b^{3} c d m^{5} x^{4} e^{7} + 4245 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{5} x^{4} e^{7} + 10215 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{4} x^{5} e^{7} + 6810 \, {\left(x e + d\right)}^{m} a c^{3} d m^{4} x^{5} e^{7} + 14518 \, {\left(x e + d\right)}^{m} b c^{3} d m^{3} x^{6} e^{7} + 3528 \, {\left(x e + d\right)}^{m} c^{4} d m^{2} x^{7} e^{7} - 3 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{6} x^{2} e^{6} - 36 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{6} x^{2} e^{6} - 18 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{6} x^{2} e^{6} - 480 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{5} x^{3} e^{6} - 1440 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{5} x^{3} e^{6} - 7065 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{4} x^{4} e^{6} - 4710 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{4} x^{4} e^{6} - 13860 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{3} x^{5} e^{6} - 3836 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{2} x^{6} e^{6} + 60 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m^{5} x^{2} e^{5} + 180 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m^{5} x^{2} e^{5} + 3240 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{4} x^{3} e^{5} + 2160 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{4} x^{3} e^{5} + 12390 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{3} x^{4} e^{5} + 4200 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{2} x^{5} e^{5} - 540 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{4} m^{4} x^{2} e^{4} - 360 \, {\left(x e + d\right)}^{m} a c^{3} d^{4} m^{4} x^{2} e^{4} - 9240 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m^{3} x^{3} e^{4} - 4620 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m^{2} x^{4} e^{4} + 2520 \, {\left(x e + d\right)}^{m} b c^{3} d^{5} m^{3} x^{2} e^{3} + 5040 \, {\left(x e + d\right)}^{m} c^{4} d^{5} m^{2} x^{3} e^{3} - 5040 \, {\left(x e + d\right)}^{m} c^{4} d^{6} m^{2} x^{2} e^{2} + 3 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{7} x^{2} e^{8} + 2 \, {\left(x e + d\right)}^{m} a^{3} c m^{7} x^{2} e^{8} + 99 \, {\left(x e + d\right)}^{m} a b^{3} m^{6} x^{3} e^{8} + 297 \, {\left(x e + d\right)}^{m} a^{2} b c m^{6} x^{3} e^{8} + 418 \, {\left(x e + d\right)}^{m} b^{4} m^{5} x^{4} e^{8} + 5016 \, {\left(x e + d\right)}^{m} a b^{2} c m^{5} x^{4} e^{8} + 2508 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{5} x^{4} e^{8} + 12905 \, {\left(x e + d\right)}^{m} b^{3} c m^{4} x^{5} e^{8} + 38715 \, {\left(x e + d\right)}^{m} a b c^{2} m^{4} x^{5} e^{8} + 75681 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{3} x^{6} e^{8} + 50454 \, {\left(x e + d\right)}^{m} a c^{3} m^{3} x^{6} e^{8} + 103292 \, {\left(x e + d\right)}^{m} b c^{3} m^{2} x^{7} e^{8} + 26136 \, {\left(x e + d\right)}^{m} c^{4} m x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{7} x e^{7} + 2 \, {\left(x e + d\right)}^{m} a^{3} c d m^{7} x e^{7} + 93 \, {\left(x e + d\right)}^{m} a b^{3} d m^{6} x^{2} e^{7} + 279 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{6} x^{2} e^{7} + 331 \, {\left(x e + d\right)}^{m} b^{4} d m^{5} x^{3} e^{7} + 3972 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{5} x^{3} e^{7} + 1986 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{5} x^{3} e^{7} + 7245 \, {\left(x e + d\right)}^{m} b^{3} c d m^{4} x^{4} e^{7} + 21735 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{4} x^{4} e^{7} + 24606 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{3} x^{5} e^{7} + 16404 \, {\left(x e + d\right)}^{m} a c^{3} d m^{3} x^{5} e^{7} + 16184 \, {\left(x e + d\right)}^{m} b c^{3} d m^{2} x^{6} e^{7} + 1440 \, {\left(x e + d\right)}^{m} c^{4} d m x^{7} e^{7} - 6 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{6} x e^{6} - 18 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{6} x e^{6} - 81 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{5} x^{2} e^{6} - 972 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{5} x^{2} e^{6} - 486 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{5} x^{2} e^{6} - 4220 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{4} x^{3} e^{6} - 12660 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{4} x^{3} e^{6} - 22815 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{3} x^{4} e^{6} - 15210 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{3} x^{4} e^{6} - 17808 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{2} x^{5} e^{6} - 1680 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m x^{6} e^{6} + 6 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{5} x e^{5} + 72 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m^{5} x e^{5} + 36 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m^{5} x e^{5} + 1320 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m^{4} x^{2} e^{5} + 3960 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m^{4} x^{2} e^{5} + 18540 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{3} x^{3} e^{5} + 12360 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{3} x^{3} e^{5} + 19740 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{2} x^{4} e^{5} + 2016 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m x^{5} e^{5} - 120 \, {\left(x e + d\right)}^{m} b^{3} c d^{4} m^{4} x e^{4} - 360 \, {\left(x e + d\right)}^{m} a b c^{2} d^{4} m^{4} x e^{4} - 8640 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{4} m^{3} x^{2} e^{4} - 5760 \, {\left(x e + d\right)}^{m} a c^{3} d^{4} m^{3} x^{2} e^{4} - 21840 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m^{2} x^{3} e^{4} - 2520 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m x^{4} e^{4} + 1080 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{5} m^{3} x e^{3} + 720 \, {\left(x e + d\right)}^{m} a c^{3} d^{5} m^{3} x e^{3} + 22680 \, {\left(x e + d\right)}^{m} b c^{3} d^{5} m^{2} x^{2} e^{3} + 3360 \, {\left(x e + d\right)}^{m} c^{4} d^{5} m x^{3} e^{3} - 5040 \, {\left(x e + d\right)}^{m} b c^{3} d^{6} m^{2} x e^{2} - 5040 \, {\left(x e + d\right)}^{m} c^{4} d^{6} m x^{2} e^{2} + 10080 \, {\left(x e + d\right)}^{m} c^{4} d^{7} m x e + {\left(x e + d\right)}^{m} a^{3} b m^{7} x e^{8} + 102 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{6} x^{2} e^{8} + 68 \, {\left(x e + d\right)}^{m} a^{3} c m^{6} x^{2} e^{8} + 1341 \, {\left(x e + d\right)}^{m} a b^{3} m^{5} x^{3} e^{8} + 4023 \, {\left(x e + d\right)}^{m} a^{2} b c m^{5} x^{3} e^{8} + 2864 \, {\left(x e + d\right)}^{m} b^{4} m^{4} x^{4} e^{8} + 34368 \, {\left(x e + d\right)}^{m} a b^{2} c m^{4} x^{4} e^{8} + 17184 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{4} x^{4} e^{8} + 47720 \, {\left(x e + d\right)}^{m} b^{3} c m^{3} x^{5} e^{8} + 143160 \, {\left(x e + d\right)}^{m} a b c^{2} m^{3} x^{5} e^{8} + 151470 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{2} x^{6} e^{8} + 100980 \, {\left(x e + d\right)}^{m} a c^{3} m^{2} x^{6} e^{8} + 103824 \, {\left(x e + d\right)}^{m} b c^{3} m x^{7} e^{8} + 10080 \, {\left(x e + d\right)}^{m} c^{4} x^{8} e^{8} + {\left(x e + d\right)}^{m} a^{3} b d m^{7} e^{7} + 99 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{6} x e^{7} + 66 \, {\left(x e + d\right)}^{m} a^{3} c d m^{6} x e^{7} + 1155 \, {\left(x e + d\right)}^{m} a b^{3} d m^{5} x^{2} e^{7} + 3465 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{5} x^{2} e^{7} + 1871 \, {\left(x e + d\right)}^{m} b^{4} d m^{4} x^{3} e^{7} + 22452 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{4} x^{3} e^{7} + 11226 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{4} x^{3} e^{7} + 18740 \, {\left(x e + d\right)}^{m} b^{3} c d m^{3} x^{4} e^{7} + 56220 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{3} x^{4} e^{7} + 28440 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{2} x^{5} e^{7} + 18960 \, {\left(x e + d\right)}^{m} a c^{3} d m^{2} x^{5} e^{7} + 6720 \, {\left(x e + d\right)}^{m} b c^{3} d m x^{6} e^{7} - 3 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{6} e^{6} - 2 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{6} e^{6} - 180 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{5} x e^{6} - 540 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{5} x e^{6} - 831 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{4} x^{2} e^{6} - 9972 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{4} x^{2} e^{6} - 4986 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{4} x^{2} e^{6} - 16320 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{3} x^{3} e^{6} - 48960 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{3} x^{3} e^{6} - 31770 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{2} x^{4} e^{6} - 21180 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{2} x^{4} e^{6} - 8064 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m x^{5} e^{6} + 6 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{5} e^{5} + 18 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m^{5} e^{5} + 156 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{4} x e^{5} + 1872 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m^{4} x e^{5} + 936 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m^{4} x e^{5} + 10020 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m^{3} x^{2} e^{5} + 30060 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m^{3} x^{2} e^{5} + 35640 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{2} x^{3} e^{5} + 23760 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{2} x^{3} e^{5} + 10080 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m x^{4} e^{5} - 6 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m^{4} e^{4} - 72 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} m^{4} e^{4} - 36 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} m^{4} e^{4} - 2520 \, {\left(x e + d\right)}^{m} b^{3} c d^{4} m^{3} x e^{4} - 7560 \, {\left(x e + d\right)}^{m} a b c^{2} d^{4} m^{3} x e^{4} - 38340 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{4} m^{2} x^{2} e^{4} - 25560 \, {\left(x e + d\right)}^{m} a c^{3} d^{4} m^{2} x^{2} e^{4} - 13440 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m x^{3} e^{4} + 120 \, {\left(x e + d\right)}^{m} b^{3} c d^{5} m^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} a b c^{2} d^{5} m^{3} e^{3} + 16200 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{5} m^{2} x e^{3} + 10800 \, {\left(x e + d\right)}^{m} a c^{3} d^{5} m^{2} x e^{3} + 20160 \, {\left(x e + d\right)}^{m} b c^{3} d^{5} m x^{2} e^{3} - 1080 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{6} m^{2} e^{2} - 720 \, {\left(x e + d\right)}^{m} a c^{3} d^{6} m^{2} e^{2} - 40320 \, {\left(x e + d\right)}^{m} b c^{3} d^{6} m x e^{2} + 5040 \, {\left(x e + d\right)}^{m} b c^{3} d^{7} m e - 10080 \, {\left(x e + d\right)}^{m} c^{4} d^{8} + 35 \, {\left(x e + d\right)}^{m} a^{3} b m^{6} x e^{8} + 1434 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{5} x^{2} e^{8} + 956 \, {\left(x e + d\right)}^{m} a^{3} c m^{5} x^{2} e^{8} + 9585 \, {\left(x e + d\right)}^{m} a b^{3} m^{4} x^{3} e^{8} + 28755 \, {\left(x e + d\right)}^{m} a^{2} b c m^{4} x^{3} e^{8} + 10993 \, {\left(x e + d\right)}^{m} b^{4} m^{3} x^{4} e^{8} + 131916 \, {\left(x e + d\right)}^{m} a b^{2} c m^{3} x^{4} e^{8} + 65958 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{3} x^{4} e^{8} + 97820 \, {\left(x e + d\right)}^{m} b^{3} c m^{2} x^{5} e^{8} + 293460 \, {\left(x e + d\right)}^{m} a b c^{2} m^{2} x^{5} e^{8} + 154296 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m x^{6} e^{8} + 102864 \, {\left(x e + d\right)}^{m} a c^{3} m x^{6} e^{8} + 40320 \, {\left(x e + d\right)}^{m} b c^{3} x^{7} e^{8} + 35 \, {\left(x e + d\right)}^{m} a^{3} b d m^{6} e^{7} + 1335 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{5} x e^{7} + 890 \, {\left(x e + d\right)}^{m} a^{3} c d m^{5} x e^{7} + 7275 \, {\left(x e + d\right)}^{m} a b^{3} d m^{4} x^{2} e^{7} + 21825 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{4} x^{2} e^{7} + 5380 \, {\left(x e + d\right)}^{m} b^{4} d m^{3} x^{3} e^{7} + 64560 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{3} x^{3} e^{7} + 32280 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{3} x^{3} e^{7} + 22860 \, {\left(x e + d\right)}^{m} b^{3} c d m^{2} x^{4} e^{7} + 68580 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{2} x^{4} e^{7} + 12096 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m x^{5} e^{7} + 8064 \, {\left(x e + d\right)}^{m} a c^{3} d m x^{5} e^{7} - 99 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{5} e^{6} - 66 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{5} e^{6} - 2130 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{4} x e^{6} - 6390 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{4} x e^{6} - 3951 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{3} x^{2} e^{6} - 47412 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{3} x^{2} e^{6} - 23706 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{3} x^{2} e^{6} - 26000 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{2} x^{3} e^{6} - 78000 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{2} x^{3} e^{6} - 15120 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m x^{4} e^{6} - 10080 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m x^{4} e^{6} + 180 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{4} e^{5} + 540 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m^{4} e^{5} + 1506 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{3} x e^{5} + 18072 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m^{3} x e^{5} + 9036 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m^{3} x e^{5} + 28920 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m^{2} x^{2} e^{5} + 86760 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m^{2} x^{2} e^{5} + 20160 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m x^{3} e^{5} + 13440 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m x^{3} e^{5} - 156 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m^{3} e^{4} - 1872 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} m^{3} e^{4} - 936 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} m^{3} e^{4} - 17520 \, {\left(x e + d\right)}^{m} b^{3} c d^{4} m^{2} x e^{4} - 52560 \, {\left(x e + d\right)}^{m} a b c^{2} d^{4} m^{2} x e^{4} - 30240 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{4} m x^{2} e^{4} - 20160 \, {\left(x e + d\right)}^{m} a c^{3} d^{4} m x^{2} e^{4} + 2520 \, {\left(x e + d\right)}^{m} b^{3} c d^{5} m^{2} e^{3} + 7560 \, {\left(x e + d\right)}^{m} a b c^{2} d^{5} m^{2} e^{3} + 60480 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{5} m x e^{3} + 40320 \, {\left(x e + d\right)}^{m} a c^{3} d^{5} m x e^{3} - 16200 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{6} m e^{2} - 10800 \, {\left(x e + d\right)}^{m} a c^{3} d^{6} m e^{2} + 40320 \, {\left(x e + d\right)}^{m} b c^{3} d^{7} e + 511 \, {\left(x e + d\right)}^{m} a^{3} b m^{5} x e^{8} + 10740 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{4} x^{2} e^{8} + 7160 \, {\left(x e + d\right)}^{m} a^{3} c m^{4} x^{2} e^{8} + 38592 \, {\left(x e + d\right)}^{m} a b^{3} m^{3} x^{3} e^{8} + 115776 \, {\left(x e + d\right)}^{m} a^{2} b c m^{3} x^{3} e^{8} + 23312 \, {\left(x e + d\right)}^{m} b^{4} m^{2} x^{4} e^{8} + 279744 \, {\left(x e + d\right)}^{m} a b^{2} c m^{2} x^{4} e^{8} + 139872 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{2} x^{4} e^{8} + 101520 \, {\left(x e + d\right)}^{m} b^{3} c m x^{5} e^{8} + 304560 \, {\left(x e + d\right)}^{m} a b c^{2} m x^{5} e^{8} + 60480 \, {\left(x e + d\right)}^{m} b^{2} c^{2} x^{6} e^{8} + 40320 \, {\left(x e + d\right)}^{m} a c^{3} x^{6} e^{8} + 511 \, {\left(x e + d\right)}^{m} a^{3} b d m^{5} e^{7} + 9405 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{4} x e^{7} + 6270 \, {\left(x e + d\right)}^{m} a^{3} c d m^{4} x e^{7} + 24042 \, {\left(x e + d\right)}^{m} a b^{3} d m^{3} x^{2} e^{7} + 72126 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{3} x^{2} e^{7} + 7172 \, {\left(x e + d\right)}^{m} b^{4} d m^{2} x^{3} e^{7} + 86064 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{2} x^{3} e^{7} + 43032 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{2} x^{3} e^{7} + 10080 \, {\left(x e + d\right)}^{m} b^{3} c d m x^{4} e^{7} + 30240 \, {\left(x e + d\right)}^{m} a b c^{2} d m x^{4} e^{7} - 1335 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{4} e^{6} - 890 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{4} e^{6} - 12420 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{3} x e^{6} - 37260 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{3} x e^{6} - 8238 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{2} x^{2} e^{6} - 98856 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{2} x^{2} e^{6} - 49428 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{2} x^{2} e^{6} - 13440 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m x^{3} e^{6} - 40320 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m x^{3} e^{6} + 2130 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{3} e^{5} + 6390 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m^{3} e^{5} + 6396 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{2} x e^{5} + 76752 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m^{2} x e^{5} + 38376 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m^{2} x e^{5} + 20160 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m x^{2} e^{5} + 60480 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m x^{2} e^{5} - 1506 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m^{2} e^{4} - 18072 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} m^{2} e^{4} - 9036 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} m^{2} e^{4} - 40320 \, {\left(x e + d\right)}^{m} b^{3} c d^{4} m x e^{4} - 120960 \, {\left(x e + d\right)}^{m} a b c^{2} d^{4} m x e^{4} + 17520 \, {\left(x e + d\right)}^{m} b^{3} c d^{5} m e^{3} + 52560 \, {\left(x e + d\right)}^{m} a b c^{2} d^{5} m e^{3} - 60480 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{6} e^{2} - 40320 \, {\left(x e + d\right)}^{m} a c^{3} d^{6} e^{2} + 4025 \, {\left(x e + d\right)}^{m} a^{3} b m^{4} x e^{8} + 45867 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{3} x^{2} e^{8} + 30578 \, {\left(x e + d\right)}^{m} a^{3} c m^{3} x^{2} e^{8} + 86076 \, {\left(x e + d\right)}^{m} a b^{3} m^{2} x^{3} e^{8} + 258228 \, {\left(x e + d\right)}^{m} a^{2} b c m^{2} x^{3} e^{8} + 24876 \, {\left(x e + d\right)}^{m} b^{4} m x^{4} e^{8} + 298512 \, {\left(x e + d\right)}^{m} a b^{2} c m x^{4} e^{8} + 149256 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m x^{4} e^{8} + 40320 \, {\left(x e + d\right)}^{m} b^{3} c x^{5} e^{8} + 120960 \, {\left(x e + d\right)}^{m} a b c^{2} x^{5} e^{8} + 4025 \, {\left(x e + d\right)}^{m} a^{3} b d m^{4} e^{7} + 36462 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{3} x e^{7} + 24308 \, {\left(x e + d\right)}^{m} a^{3} c d m^{3} x e^{7} + 37992 \, {\left(x e + d\right)}^{m} a b^{3} d m^{2} x^{2} e^{7} + 113976 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{2} x^{2} e^{7} + 3360 \, {\left(x e + d\right)}^{m} b^{4} d m x^{3} e^{7} + 40320 \, {\left(x e + d\right)}^{m} a b^{2} c d m x^{3} e^{7} + 20160 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m x^{3} e^{7} - 9405 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{3} e^{6} - 6270 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{3} e^{6} - 35664 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{2} x e^{6} - 106992 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{2} x e^{6} - 5040 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m x^{2} e^{6} - 60480 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m x^{2} e^{6} - 30240 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m x^{2} e^{6} + 12420 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{2} e^{5} + 37260 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m^{2} e^{5} + 10080 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m x e^{5} + 120960 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m x e^{5} + 60480 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m x e^{5} - 6396 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m e^{4} - 76752 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} m e^{4} - 38376 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} m e^{4} + 40320 \, {\left(x e + d\right)}^{m} b^{3} c d^{5} e^{3} + 120960 \, {\left(x e + d\right)}^{m} a b c^{2} d^{5} e^{3} + 18424 \, {\left(x e + d\right)}^{m} a^{3} b m^{3} x e^{8} + 110118 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{2} x^{2} e^{8} + 73412 \, {\left(x e + d\right)}^{m} a^{3} c m^{2} x^{2} e^{8} + 96144 \, {\left(x e + d\right)}^{m} a b^{3} m x^{3} e^{8} + 288432 \, {\left(x e + d\right)}^{m} a^{2} b c m x^{3} e^{8} + 10080 \, {\left(x e + d\right)}^{m} b^{4} x^{4} e^{8} + 120960 \, {\left(x e + d\right)}^{m} a b^{2} c x^{4} e^{8} + 60480 \, {\left(x e + d\right)}^{m} a^{2} c^{2} x^{4} e^{8} + 18424 \, {\left(x e + d\right)}^{m} a^{3} b d m^{3} e^{7} + 73656 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{2} x e^{7} + 49104 \, {\left(x e + d\right)}^{m} a^{3} c d m^{2} x e^{7} + 20160 \, {\left(x e + d\right)}^{m} a b^{3} d m x^{2} e^{7} + 60480 \, {\left(x e + d\right)}^{m} a^{2} b c d m x^{2} e^{7} - 36462 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{2} e^{6} - 24308 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{2} e^{6} - 40320 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m x e^{6} - 120960 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m x e^{6} + 35664 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m e^{5} + 106992 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m e^{5} - 10080 \, {\left(x e + d\right)}^{m} b^{4} d^{4} e^{4} - 120960 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} e^{4} - 60480 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} e^{4} + 48860 \, {\left(x e + d\right)}^{m} a^{3} b m^{2} x e^{8} + 134136 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m x^{2} e^{8} + 89424 \, {\left(x e + d\right)}^{m} a^{3} c m x^{2} e^{8} + 40320 \, {\left(x e + d\right)}^{m} a b^{3} x^{3} e^{8} + 120960 \, {\left(x e + d\right)}^{m} a^{2} b c x^{3} e^{8} + 48860 \, {\left(x e + d\right)}^{m} a^{3} b d m^{2} e^{7} + 60480 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m x e^{7} + 40320 \, {\left(x e + d\right)}^{m} a^{3} c d m x e^{7} - 73656 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m e^{6} - 49104 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m e^{6} + 40320 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} e^{5} + 120960 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} e^{5} + 69264 \, {\left(x e + d\right)}^{m} a^{3} b m x e^{8} + 60480 \, {\left(x e + d\right)}^{m} a^{2} b^{2} x^{2} e^{8} + 40320 \, {\left(x e + d\right)}^{m} a^{3} c x^{2} e^{8} + 69264 \, {\left(x e + d\right)}^{m} a^{3} b d m e^{7} - 60480 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} e^{6} - 40320 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} e^{6} + 40320 \, {\left(x e + d\right)}^{m} a^{3} b x e^{8} + 40320 \, {\left(x e + d\right)}^{m} a^{3} b d e^{7}}{m^{8} e^{8} + 36 \, m^{7} e^{8} + 546 \, m^{6} e^{8} + 4536 \, m^{5} e^{8} + 22449 \, m^{4} e^{8} + 67284 \, m^{3} e^{8} + 118124 \, m^{2} e^{8} + 109584 \, m e^{8} + 40320 \, e^{8}}"," ",0,"(2*(x*e + d)^m*c^4*m^7*x^8*e^8 + 2*(x*e + d)^m*c^4*d*m^7*x^7*e^7 + 7*(x*e + d)^m*b*c^3*m^7*x^7*e^8 + 56*(x*e + d)^m*c^4*m^6*x^8*e^8 + 7*(x*e + d)^m*b*c^3*d*m^7*x^6*e^7 + 42*(x*e + d)^m*c^4*d*m^6*x^7*e^7 - 14*(x*e + d)^m*c^4*d^2*m^6*x^6*e^6 + 9*(x*e + d)^m*b^2*c^2*m^7*x^6*e^8 + 6*(x*e + d)^m*a*c^3*m^7*x^6*e^8 + 203*(x*e + d)^m*b*c^3*m^6*x^7*e^8 + 644*(x*e + d)^m*c^4*m^5*x^8*e^8 + 9*(x*e + d)^m*b^2*c^2*d*m^7*x^5*e^7 + 6*(x*e + d)^m*a*c^3*d*m^7*x^5*e^7 + 161*(x*e + d)^m*b*c^3*d*m^6*x^6*e^7 + 350*(x*e + d)^m*c^4*d*m^5*x^7*e^7 - 42*(x*e + d)^m*b*c^3*d^2*m^6*x^5*e^6 - 210*(x*e + d)^m*c^4*d^2*m^5*x^6*e^6 + 84*(x*e + d)^m*c^4*d^3*m^5*x^5*e^5 + 5*(x*e + d)^m*b^3*c*m^7*x^5*e^8 + 15*(x*e + d)^m*a*b*c^2*m^7*x^5*e^8 + 270*(x*e + d)^m*b^2*c^2*m^6*x^6*e^8 + 180*(x*e + d)^m*a*c^3*m^6*x^6*e^8 + 2401*(x*e + d)^m*b*c^3*m^5*x^7*e^8 + 3920*(x*e + d)^m*c^4*m^4*x^8*e^8 + 5*(x*e + d)^m*b^3*c*d*m^7*x^4*e^7 + 15*(x*e + d)^m*a*b*c^2*d*m^7*x^4*e^7 + 225*(x*e + d)^m*b^2*c^2*d*m^6*x^5*e^7 + 150*(x*e + d)^m*a*c^3*d*m^6*x^5*e^7 + 1435*(x*e + d)^m*b*c^3*d*m^5*x^6*e^7 + 1470*(x*e + d)^m*c^4*d*m^4*x^7*e^7 - 45*(x*e + d)^m*b^2*c^2*d^2*m^6*x^4*e^6 - 30*(x*e + d)^m*a*c^3*d^2*m^6*x^4*e^6 - 756*(x*e + d)^m*b*c^3*d^2*m^5*x^5*e^6 - 1190*(x*e + d)^m*c^4*d^2*m^4*x^6*e^6 + 210*(x*e + d)^m*b*c^3*d^3*m^5*x^4*e^5 + 840*(x*e + d)^m*c^4*d^3*m^4*x^5*e^5 - 420*(x*e + d)^m*c^4*d^4*m^4*x^4*e^4 + (x*e + d)^m*b^4*m^7*x^4*e^8 + 12*(x*e + d)^m*a*b^2*c*m^7*x^4*e^8 + 6*(x*e + d)^m*a^2*c^2*m^7*x^4*e^8 + 155*(x*e + d)^m*b^3*c*m^6*x^5*e^8 + 465*(x*e + d)^m*a*b*c^2*m^6*x^5*e^8 + 3294*(x*e + d)^m*b^2*c^2*m^5*x^6*e^8 + 2196*(x*e + d)^m*a*c^3*m^5*x^6*e^8 + 14945*(x*e + d)^m*b*c^3*m^4*x^7*e^8 + 13538*(x*e + d)^m*c^4*m^3*x^8*e^8 + (x*e + d)^m*b^4*d*m^7*x^3*e^7 + 12*(x*e + d)^m*a*b^2*c*d*m^7*x^3*e^7 + 6*(x*e + d)^m*a^2*c^2*d*m^7*x^3*e^7 + 135*(x*e + d)^m*b^3*c*d*m^6*x^4*e^7 + 405*(x*e + d)^m*a*b*c^2*d*m^6*x^4*e^7 + 2169*(x*e + d)^m*b^2*c^2*d*m^5*x^5*e^7 + 1446*(x*e + d)^m*a*c^3*d*m^5*x^5*e^7 + 6335*(x*e + d)^m*b*c^3*d*m^4*x^6*e^7 + 3248*(x*e + d)^m*c^4*d*m^3*x^7*e^7 - 20*(x*e + d)^m*b^3*c*d^2*m^6*x^3*e^6 - 60*(x*e + d)^m*a*b*c^2*d^2*m^6*x^3*e^6 - 945*(x*e + d)^m*b^2*c^2*d^2*m^5*x^4*e^6 - 630*(x*e + d)^m*a*c^3*d^2*m^5*x^4*e^6 - 4830*(x*e + d)^m*b*c^3*d^2*m^4*x^5*e^6 - 3150*(x*e + d)^m*c^4*d^2*m^3*x^6*e^6 + 180*(x*e + d)^m*b^2*c^2*d^3*m^5*x^3*e^5 + 120*(x*e + d)^m*a*c^3*d^3*m^5*x^3*e^5 + 2940*(x*e + d)^m*b*c^3*d^3*m^4*x^4*e^5 + 2940*(x*e + d)^m*c^4*d^3*m^3*x^5*e^5 - 840*(x*e + d)^m*b*c^3*d^4*m^4*x^3*e^4 - 2520*(x*e + d)^m*c^4*d^4*m^3*x^4*e^4 + 1680*(x*e + d)^m*c^4*d^5*m^3*x^3*e^3 + 3*(x*e + d)^m*a*b^3*m^7*x^3*e^8 + 9*(x*e + d)^m*a^2*b*c*m^7*x^3*e^8 + 32*(x*e + d)^m*b^4*m^6*x^4*e^8 + 384*(x*e + d)^m*a*b^2*c*m^6*x^4*e^8 + 192*(x*e + d)^m*a^2*c^2*m^6*x^4*e^8 + 1955*(x*e + d)^m*b^3*c*m^5*x^5*e^8 + 5865*(x*e + d)^m*a*b*c^2*m^5*x^5*e^8 + 21060*(x*e + d)^m*b^2*c^2*m^4*x^6*e^8 + 14040*(x*e + d)^m*a*c^3*m^4*x^6*e^8 + 52528*(x*e + d)^m*b*c^3*m^3*x^7*e^8 + 26264*(x*e + d)^m*c^4*m^2*x^8*e^8 + 3*(x*e + d)^m*a*b^3*d*m^7*x^2*e^7 + 9*(x*e + d)^m*a^2*b*c*d*m^7*x^2*e^7 + 29*(x*e + d)^m*b^4*d*m^6*x^3*e^7 + 348*(x*e + d)^m*a*b^2*c*d*m^6*x^3*e^7 + 174*(x*e + d)^m*a^2*c^2*d*m^6*x^3*e^7 + 1415*(x*e + d)^m*b^3*c*d*m^5*x^4*e^7 + 4245*(x*e + d)^m*a*b*c^2*d*m^5*x^4*e^7 + 10215*(x*e + d)^m*b^2*c^2*d*m^4*x^5*e^7 + 6810*(x*e + d)^m*a*c^3*d*m^4*x^5*e^7 + 14518*(x*e + d)^m*b*c^3*d*m^3*x^6*e^7 + 3528*(x*e + d)^m*c^4*d*m^2*x^7*e^7 - 3*(x*e + d)^m*b^4*d^2*m^6*x^2*e^6 - 36*(x*e + d)^m*a*b^2*c*d^2*m^6*x^2*e^6 - 18*(x*e + d)^m*a^2*c^2*d^2*m^6*x^2*e^6 - 480*(x*e + d)^m*b^3*c*d^2*m^5*x^3*e^6 - 1440*(x*e + d)^m*a*b*c^2*d^2*m^5*x^3*e^6 - 7065*(x*e + d)^m*b^2*c^2*d^2*m^4*x^4*e^6 - 4710*(x*e + d)^m*a*c^3*d^2*m^4*x^4*e^6 - 13860*(x*e + d)^m*b*c^3*d^2*m^3*x^5*e^6 - 3836*(x*e + d)^m*c^4*d^2*m^2*x^6*e^6 + 60*(x*e + d)^m*b^3*c*d^3*m^5*x^2*e^5 + 180*(x*e + d)^m*a*b*c^2*d^3*m^5*x^2*e^5 + 3240*(x*e + d)^m*b^2*c^2*d^3*m^4*x^3*e^5 + 2160*(x*e + d)^m*a*c^3*d^3*m^4*x^3*e^5 + 12390*(x*e + d)^m*b*c^3*d^3*m^3*x^4*e^5 + 4200*(x*e + d)^m*c^4*d^3*m^2*x^5*e^5 - 540*(x*e + d)^m*b^2*c^2*d^4*m^4*x^2*e^4 - 360*(x*e + d)^m*a*c^3*d^4*m^4*x^2*e^4 - 9240*(x*e + d)^m*b*c^3*d^4*m^3*x^3*e^4 - 4620*(x*e + d)^m*c^4*d^4*m^2*x^4*e^4 + 2520*(x*e + d)^m*b*c^3*d^5*m^3*x^2*e^3 + 5040*(x*e + d)^m*c^4*d^5*m^2*x^3*e^3 - 5040*(x*e + d)^m*c^4*d^6*m^2*x^2*e^2 + 3*(x*e + d)^m*a^2*b^2*m^7*x^2*e^8 + 2*(x*e + d)^m*a^3*c*m^7*x^2*e^8 + 99*(x*e + d)^m*a*b^3*m^6*x^3*e^8 + 297*(x*e + d)^m*a^2*b*c*m^6*x^3*e^8 + 418*(x*e + d)^m*b^4*m^5*x^4*e^8 + 5016*(x*e + d)^m*a*b^2*c*m^5*x^4*e^8 + 2508*(x*e + d)^m*a^2*c^2*m^5*x^4*e^8 + 12905*(x*e + d)^m*b^3*c*m^4*x^5*e^8 + 38715*(x*e + d)^m*a*b*c^2*m^4*x^5*e^8 + 75681*(x*e + d)^m*b^2*c^2*m^3*x^6*e^8 + 50454*(x*e + d)^m*a*c^3*m^3*x^6*e^8 + 103292*(x*e + d)^m*b*c^3*m^2*x^7*e^8 + 26136*(x*e + d)^m*c^4*m*x^8*e^8 + 3*(x*e + d)^m*a^2*b^2*d*m^7*x*e^7 + 2*(x*e + d)^m*a^3*c*d*m^7*x*e^7 + 93*(x*e + d)^m*a*b^3*d*m^6*x^2*e^7 + 279*(x*e + d)^m*a^2*b*c*d*m^6*x^2*e^7 + 331*(x*e + d)^m*b^4*d*m^5*x^3*e^7 + 3972*(x*e + d)^m*a*b^2*c*d*m^5*x^3*e^7 + 1986*(x*e + d)^m*a^2*c^2*d*m^5*x^3*e^7 + 7245*(x*e + d)^m*b^3*c*d*m^4*x^4*e^7 + 21735*(x*e + d)^m*a*b*c^2*d*m^4*x^4*e^7 + 24606*(x*e + d)^m*b^2*c^2*d*m^3*x^5*e^7 + 16404*(x*e + d)^m*a*c^3*d*m^3*x^5*e^7 + 16184*(x*e + d)^m*b*c^3*d*m^2*x^6*e^7 + 1440*(x*e + d)^m*c^4*d*m*x^7*e^7 - 6*(x*e + d)^m*a*b^3*d^2*m^6*x*e^6 - 18*(x*e + d)^m*a^2*b*c*d^2*m^6*x*e^6 - 81*(x*e + d)^m*b^4*d^2*m^5*x^2*e^6 - 972*(x*e + d)^m*a*b^2*c*d^2*m^5*x^2*e^6 - 486*(x*e + d)^m*a^2*c^2*d^2*m^5*x^2*e^6 - 4220*(x*e + d)^m*b^3*c*d^2*m^4*x^3*e^6 - 12660*(x*e + d)^m*a*b*c^2*d^2*m^4*x^3*e^6 - 22815*(x*e + d)^m*b^2*c^2*d^2*m^3*x^4*e^6 - 15210*(x*e + d)^m*a*c^3*d^2*m^3*x^4*e^6 - 17808*(x*e + d)^m*b*c^3*d^2*m^2*x^5*e^6 - 1680*(x*e + d)^m*c^4*d^2*m*x^6*e^6 + 6*(x*e + d)^m*b^4*d^3*m^5*x*e^5 + 72*(x*e + d)^m*a*b^2*c*d^3*m^5*x*e^5 + 36*(x*e + d)^m*a^2*c^2*d^3*m^5*x*e^5 + 1320*(x*e + d)^m*b^3*c*d^3*m^4*x^2*e^5 + 3960*(x*e + d)^m*a*b*c^2*d^3*m^4*x^2*e^5 + 18540*(x*e + d)^m*b^2*c^2*d^3*m^3*x^3*e^5 + 12360*(x*e + d)^m*a*c^3*d^3*m^3*x^3*e^5 + 19740*(x*e + d)^m*b*c^3*d^3*m^2*x^4*e^5 + 2016*(x*e + d)^m*c^4*d^3*m*x^5*e^5 - 120*(x*e + d)^m*b^3*c*d^4*m^4*x*e^4 - 360*(x*e + d)^m*a*b*c^2*d^4*m^4*x*e^4 - 8640*(x*e + d)^m*b^2*c^2*d^4*m^3*x^2*e^4 - 5760*(x*e + d)^m*a*c^3*d^4*m^3*x^2*e^4 - 21840*(x*e + d)^m*b*c^3*d^4*m^2*x^3*e^4 - 2520*(x*e + d)^m*c^4*d^4*m*x^4*e^4 + 1080*(x*e + d)^m*b^2*c^2*d^5*m^3*x*e^3 + 720*(x*e + d)^m*a*c^3*d^5*m^3*x*e^3 + 22680*(x*e + d)^m*b*c^3*d^5*m^2*x^2*e^3 + 3360*(x*e + d)^m*c^4*d^5*m*x^3*e^3 - 5040*(x*e + d)^m*b*c^3*d^6*m^2*x*e^2 - 5040*(x*e + d)^m*c^4*d^6*m*x^2*e^2 + 10080*(x*e + d)^m*c^4*d^7*m*x*e + (x*e + d)^m*a^3*b*m^7*x*e^8 + 102*(x*e + d)^m*a^2*b^2*m^6*x^2*e^8 + 68*(x*e + d)^m*a^3*c*m^6*x^2*e^8 + 1341*(x*e + d)^m*a*b^3*m^5*x^3*e^8 + 4023*(x*e + d)^m*a^2*b*c*m^5*x^3*e^8 + 2864*(x*e + d)^m*b^4*m^4*x^4*e^8 + 34368*(x*e + d)^m*a*b^2*c*m^4*x^4*e^8 + 17184*(x*e + d)^m*a^2*c^2*m^4*x^4*e^8 + 47720*(x*e + d)^m*b^3*c*m^3*x^5*e^8 + 143160*(x*e + d)^m*a*b*c^2*m^3*x^5*e^8 + 151470*(x*e + d)^m*b^2*c^2*m^2*x^6*e^8 + 100980*(x*e + d)^m*a*c^3*m^2*x^6*e^8 + 103824*(x*e + d)^m*b*c^3*m*x^7*e^8 + 10080*(x*e + d)^m*c^4*x^8*e^8 + (x*e + d)^m*a^3*b*d*m^7*e^7 + 99*(x*e + d)^m*a^2*b^2*d*m^6*x*e^7 + 66*(x*e + d)^m*a^3*c*d*m^6*x*e^7 + 1155*(x*e + d)^m*a*b^3*d*m^5*x^2*e^7 + 3465*(x*e + d)^m*a^2*b*c*d*m^5*x^2*e^7 + 1871*(x*e + d)^m*b^4*d*m^4*x^3*e^7 + 22452*(x*e + d)^m*a*b^2*c*d*m^4*x^3*e^7 + 11226*(x*e + d)^m*a^2*c^2*d*m^4*x^3*e^7 + 18740*(x*e + d)^m*b^3*c*d*m^3*x^4*e^7 + 56220*(x*e + d)^m*a*b*c^2*d*m^3*x^4*e^7 + 28440*(x*e + d)^m*b^2*c^2*d*m^2*x^5*e^7 + 18960*(x*e + d)^m*a*c^3*d*m^2*x^5*e^7 + 6720*(x*e + d)^m*b*c^3*d*m*x^6*e^7 - 3*(x*e + d)^m*a^2*b^2*d^2*m^6*e^6 - 2*(x*e + d)^m*a^3*c*d^2*m^6*e^6 - 180*(x*e + d)^m*a*b^3*d^2*m^5*x*e^6 - 540*(x*e + d)^m*a^2*b*c*d^2*m^5*x*e^6 - 831*(x*e + d)^m*b^4*d^2*m^4*x^2*e^6 - 9972*(x*e + d)^m*a*b^2*c*d^2*m^4*x^2*e^6 - 4986*(x*e + d)^m*a^2*c^2*d^2*m^4*x^2*e^6 - 16320*(x*e + d)^m*b^3*c*d^2*m^3*x^3*e^6 - 48960*(x*e + d)^m*a*b*c^2*d^2*m^3*x^3*e^6 - 31770*(x*e + d)^m*b^2*c^2*d^2*m^2*x^4*e^6 - 21180*(x*e + d)^m*a*c^3*d^2*m^2*x^4*e^6 - 8064*(x*e + d)^m*b*c^3*d^2*m*x^5*e^6 + 6*(x*e + d)^m*a*b^3*d^3*m^5*e^5 + 18*(x*e + d)^m*a^2*b*c*d^3*m^5*e^5 + 156*(x*e + d)^m*b^4*d^3*m^4*x*e^5 + 1872*(x*e + d)^m*a*b^2*c*d^3*m^4*x*e^5 + 936*(x*e + d)^m*a^2*c^2*d^3*m^4*x*e^5 + 10020*(x*e + d)^m*b^3*c*d^3*m^3*x^2*e^5 + 30060*(x*e + d)^m*a*b*c^2*d^3*m^3*x^2*e^5 + 35640*(x*e + d)^m*b^2*c^2*d^3*m^2*x^3*e^5 + 23760*(x*e + d)^m*a*c^3*d^3*m^2*x^3*e^5 + 10080*(x*e + d)^m*b*c^3*d^3*m*x^4*e^5 - 6*(x*e + d)^m*b^4*d^4*m^4*e^4 - 72*(x*e + d)^m*a*b^2*c*d^4*m^4*e^4 - 36*(x*e + d)^m*a^2*c^2*d^4*m^4*e^4 - 2520*(x*e + d)^m*b^3*c*d^4*m^3*x*e^4 - 7560*(x*e + d)^m*a*b*c^2*d^4*m^3*x*e^4 - 38340*(x*e + d)^m*b^2*c^2*d^4*m^2*x^2*e^4 - 25560*(x*e + d)^m*a*c^3*d^4*m^2*x^2*e^4 - 13440*(x*e + d)^m*b*c^3*d^4*m*x^3*e^4 + 120*(x*e + d)^m*b^3*c*d^5*m^3*e^3 + 360*(x*e + d)^m*a*b*c^2*d^5*m^3*e^3 + 16200*(x*e + d)^m*b^2*c^2*d^5*m^2*x*e^3 + 10800*(x*e + d)^m*a*c^3*d^5*m^2*x*e^3 + 20160*(x*e + d)^m*b*c^3*d^5*m*x^2*e^3 - 1080*(x*e + d)^m*b^2*c^2*d^6*m^2*e^2 - 720*(x*e + d)^m*a*c^3*d^6*m^2*e^2 - 40320*(x*e + d)^m*b*c^3*d^6*m*x*e^2 + 5040*(x*e + d)^m*b*c^3*d^7*m*e - 10080*(x*e + d)^m*c^4*d^8 + 35*(x*e + d)^m*a^3*b*m^6*x*e^8 + 1434*(x*e + d)^m*a^2*b^2*m^5*x^2*e^8 + 956*(x*e + d)^m*a^3*c*m^5*x^2*e^8 + 9585*(x*e + d)^m*a*b^3*m^4*x^3*e^8 + 28755*(x*e + d)^m*a^2*b*c*m^4*x^3*e^8 + 10993*(x*e + d)^m*b^4*m^3*x^4*e^8 + 131916*(x*e + d)^m*a*b^2*c*m^3*x^4*e^8 + 65958*(x*e + d)^m*a^2*c^2*m^3*x^4*e^8 + 97820*(x*e + d)^m*b^3*c*m^2*x^5*e^8 + 293460*(x*e + d)^m*a*b*c^2*m^2*x^5*e^8 + 154296*(x*e + d)^m*b^2*c^2*m*x^6*e^8 + 102864*(x*e + d)^m*a*c^3*m*x^6*e^8 + 40320*(x*e + d)^m*b*c^3*x^7*e^8 + 35*(x*e + d)^m*a^3*b*d*m^6*e^7 + 1335*(x*e + d)^m*a^2*b^2*d*m^5*x*e^7 + 890*(x*e + d)^m*a^3*c*d*m^5*x*e^7 + 7275*(x*e + d)^m*a*b^3*d*m^4*x^2*e^7 + 21825*(x*e + d)^m*a^2*b*c*d*m^4*x^2*e^7 + 5380*(x*e + d)^m*b^4*d*m^3*x^3*e^7 + 64560*(x*e + d)^m*a*b^2*c*d*m^3*x^3*e^7 + 32280*(x*e + d)^m*a^2*c^2*d*m^3*x^3*e^7 + 22860*(x*e + d)^m*b^3*c*d*m^2*x^4*e^7 + 68580*(x*e + d)^m*a*b*c^2*d*m^2*x^4*e^7 + 12096*(x*e + d)^m*b^2*c^2*d*m*x^5*e^7 + 8064*(x*e + d)^m*a*c^3*d*m*x^5*e^7 - 99*(x*e + d)^m*a^2*b^2*d^2*m^5*e^6 - 66*(x*e + d)^m*a^3*c*d^2*m^5*e^6 - 2130*(x*e + d)^m*a*b^3*d^2*m^4*x*e^6 - 6390*(x*e + d)^m*a^2*b*c*d^2*m^4*x*e^6 - 3951*(x*e + d)^m*b^4*d^2*m^3*x^2*e^6 - 47412*(x*e + d)^m*a*b^2*c*d^2*m^3*x^2*e^6 - 23706*(x*e + d)^m*a^2*c^2*d^2*m^3*x^2*e^6 - 26000*(x*e + d)^m*b^3*c*d^2*m^2*x^3*e^6 - 78000*(x*e + d)^m*a*b*c^2*d^2*m^2*x^3*e^6 - 15120*(x*e + d)^m*b^2*c^2*d^2*m*x^4*e^6 - 10080*(x*e + d)^m*a*c^3*d^2*m*x^4*e^6 + 180*(x*e + d)^m*a*b^3*d^3*m^4*e^5 + 540*(x*e + d)^m*a^2*b*c*d^3*m^4*e^5 + 1506*(x*e + d)^m*b^4*d^3*m^3*x*e^5 + 18072*(x*e + d)^m*a*b^2*c*d^3*m^3*x*e^5 + 9036*(x*e + d)^m*a^2*c^2*d^3*m^3*x*e^5 + 28920*(x*e + d)^m*b^3*c*d^3*m^2*x^2*e^5 + 86760*(x*e + d)^m*a*b*c^2*d^3*m^2*x^2*e^5 + 20160*(x*e + d)^m*b^2*c^2*d^3*m*x^3*e^5 + 13440*(x*e + d)^m*a*c^3*d^3*m*x^3*e^5 - 156*(x*e + d)^m*b^4*d^4*m^3*e^4 - 1872*(x*e + d)^m*a*b^2*c*d^4*m^3*e^4 - 936*(x*e + d)^m*a^2*c^2*d^4*m^3*e^4 - 17520*(x*e + d)^m*b^3*c*d^4*m^2*x*e^4 - 52560*(x*e + d)^m*a*b*c^2*d^4*m^2*x*e^4 - 30240*(x*e + d)^m*b^2*c^2*d^4*m*x^2*e^4 - 20160*(x*e + d)^m*a*c^3*d^4*m*x^2*e^4 + 2520*(x*e + d)^m*b^3*c*d^5*m^2*e^3 + 7560*(x*e + d)^m*a*b*c^2*d^5*m^2*e^3 + 60480*(x*e + d)^m*b^2*c^2*d^5*m*x*e^3 + 40320*(x*e + d)^m*a*c^3*d^5*m*x*e^3 - 16200*(x*e + d)^m*b^2*c^2*d^6*m*e^2 - 10800*(x*e + d)^m*a*c^3*d^6*m*e^2 + 40320*(x*e + d)^m*b*c^3*d^7*e + 511*(x*e + d)^m*a^3*b*m^5*x*e^8 + 10740*(x*e + d)^m*a^2*b^2*m^4*x^2*e^8 + 7160*(x*e + d)^m*a^3*c*m^4*x^2*e^8 + 38592*(x*e + d)^m*a*b^3*m^3*x^3*e^8 + 115776*(x*e + d)^m*a^2*b*c*m^3*x^3*e^8 + 23312*(x*e + d)^m*b^4*m^2*x^4*e^8 + 279744*(x*e + d)^m*a*b^2*c*m^2*x^4*e^8 + 139872*(x*e + d)^m*a^2*c^2*m^2*x^4*e^8 + 101520*(x*e + d)^m*b^3*c*m*x^5*e^8 + 304560*(x*e + d)^m*a*b*c^2*m*x^5*e^8 + 60480*(x*e + d)^m*b^2*c^2*x^6*e^8 + 40320*(x*e + d)^m*a*c^3*x^6*e^8 + 511*(x*e + d)^m*a^3*b*d*m^5*e^7 + 9405*(x*e + d)^m*a^2*b^2*d*m^4*x*e^7 + 6270*(x*e + d)^m*a^3*c*d*m^4*x*e^7 + 24042*(x*e + d)^m*a*b^3*d*m^3*x^2*e^7 + 72126*(x*e + d)^m*a^2*b*c*d*m^3*x^2*e^7 + 7172*(x*e + d)^m*b^4*d*m^2*x^3*e^7 + 86064*(x*e + d)^m*a*b^2*c*d*m^2*x^3*e^7 + 43032*(x*e + d)^m*a^2*c^2*d*m^2*x^3*e^7 + 10080*(x*e + d)^m*b^3*c*d*m*x^4*e^7 + 30240*(x*e + d)^m*a*b*c^2*d*m*x^4*e^7 - 1335*(x*e + d)^m*a^2*b^2*d^2*m^4*e^6 - 890*(x*e + d)^m*a^3*c*d^2*m^4*e^6 - 12420*(x*e + d)^m*a*b^3*d^2*m^3*x*e^6 - 37260*(x*e + d)^m*a^2*b*c*d^2*m^3*x*e^6 - 8238*(x*e + d)^m*b^4*d^2*m^2*x^2*e^6 - 98856*(x*e + d)^m*a*b^2*c*d^2*m^2*x^2*e^6 - 49428*(x*e + d)^m*a^2*c^2*d^2*m^2*x^2*e^6 - 13440*(x*e + d)^m*b^3*c*d^2*m*x^3*e^6 - 40320*(x*e + d)^m*a*b*c^2*d^2*m*x^3*e^6 + 2130*(x*e + d)^m*a*b^3*d^3*m^3*e^5 + 6390*(x*e + d)^m*a^2*b*c*d^3*m^3*e^5 + 6396*(x*e + d)^m*b^4*d^3*m^2*x*e^5 + 76752*(x*e + d)^m*a*b^2*c*d^3*m^2*x*e^5 + 38376*(x*e + d)^m*a^2*c^2*d^3*m^2*x*e^5 + 20160*(x*e + d)^m*b^3*c*d^3*m*x^2*e^5 + 60480*(x*e + d)^m*a*b*c^2*d^3*m*x^2*e^5 - 1506*(x*e + d)^m*b^4*d^4*m^2*e^4 - 18072*(x*e + d)^m*a*b^2*c*d^4*m^2*e^4 - 9036*(x*e + d)^m*a^2*c^2*d^4*m^2*e^4 - 40320*(x*e + d)^m*b^3*c*d^4*m*x*e^4 - 120960*(x*e + d)^m*a*b*c^2*d^4*m*x*e^4 + 17520*(x*e + d)^m*b^3*c*d^5*m*e^3 + 52560*(x*e + d)^m*a*b*c^2*d^5*m*e^3 - 60480*(x*e + d)^m*b^2*c^2*d^6*e^2 - 40320*(x*e + d)^m*a*c^3*d^6*e^2 + 4025*(x*e + d)^m*a^3*b*m^4*x*e^8 + 45867*(x*e + d)^m*a^2*b^2*m^3*x^2*e^8 + 30578*(x*e + d)^m*a^3*c*m^3*x^2*e^8 + 86076*(x*e + d)^m*a*b^3*m^2*x^3*e^8 + 258228*(x*e + d)^m*a^2*b*c*m^2*x^3*e^8 + 24876*(x*e + d)^m*b^4*m*x^4*e^8 + 298512*(x*e + d)^m*a*b^2*c*m*x^4*e^8 + 149256*(x*e + d)^m*a^2*c^2*m*x^4*e^8 + 40320*(x*e + d)^m*b^3*c*x^5*e^8 + 120960*(x*e + d)^m*a*b*c^2*x^5*e^8 + 4025*(x*e + d)^m*a^3*b*d*m^4*e^7 + 36462*(x*e + d)^m*a^2*b^2*d*m^3*x*e^7 + 24308*(x*e + d)^m*a^3*c*d*m^3*x*e^7 + 37992*(x*e + d)^m*a*b^3*d*m^2*x^2*e^7 + 113976*(x*e + d)^m*a^2*b*c*d*m^2*x^2*e^7 + 3360*(x*e + d)^m*b^4*d*m*x^3*e^7 + 40320*(x*e + d)^m*a*b^2*c*d*m*x^3*e^7 + 20160*(x*e + d)^m*a^2*c^2*d*m*x^3*e^7 - 9405*(x*e + d)^m*a^2*b^2*d^2*m^3*e^6 - 6270*(x*e + d)^m*a^3*c*d^2*m^3*e^6 - 35664*(x*e + d)^m*a*b^3*d^2*m^2*x*e^6 - 106992*(x*e + d)^m*a^2*b*c*d^2*m^2*x*e^6 - 5040*(x*e + d)^m*b^4*d^2*m*x^2*e^6 - 60480*(x*e + d)^m*a*b^2*c*d^2*m*x^2*e^6 - 30240*(x*e + d)^m*a^2*c^2*d^2*m*x^2*e^6 + 12420*(x*e + d)^m*a*b^3*d^3*m^2*e^5 + 37260*(x*e + d)^m*a^2*b*c*d^3*m^2*e^5 + 10080*(x*e + d)^m*b^4*d^3*m*x*e^5 + 120960*(x*e + d)^m*a*b^2*c*d^3*m*x*e^5 + 60480*(x*e + d)^m*a^2*c^2*d^3*m*x*e^5 - 6396*(x*e + d)^m*b^4*d^4*m*e^4 - 76752*(x*e + d)^m*a*b^2*c*d^4*m*e^4 - 38376*(x*e + d)^m*a^2*c^2*d^4*m*e^4 + 40320*(x*e + d)^m*b^3*c*d^5*e^3 + 120960*(x*e + d)^m*a*b*c^2*d^5*e^3 + 18424*(x*e + d)^m*a^3*b*m^3*x*e^8 + 110118*(x*e + d)^m*a^2*b^2*m^2*x^2*e^8 + 73412*(x*e + d)^m*a^3*c*m^2*x^2*e^8 + 96144*(x*e + d)^m*a*b^3*m*x^3*e^8 + 288432*(x*e + d)^m*a^2*b*c*m*x^3*e^8 + 10080*(x*e + d)^m*b^4*x^4*e^8 + 120960*(x*e + d)^m*a*b^2*c*x^4*e^8 + 60480*(x*e + d)^m*a^2*c^2*x^4*e^8 + 18424*(x*e + d)^m*a^3*b*d*m^3*e^7 + 73656*(x*e + d)^m*a^2*b^2*d*m^2*x*e^7 + 49104*(x*e + d)^m*a^3*c*d*m^2*x*e^7 + 20160*(x*e + d)^m*a*b^3*d*m*x^2*e^7 + 60480*(x*e + d)^m*a^2*b*c*d*m*x^2*e^7 - 36462*(x*e + d)^m*a^2*b^2*d^2*m^2*e^6 - 24308*(x*e + d)^m*a^3*c*d^2*m^2*e^6 - 40320*(x*e + d)^m*a*b^3*d^2*m*x*e^6 - 120960*(x*e + d)^m*a^2*b*c*d^2*m*x*e^6 + 35664*(x*e + d)^m*a*b^3*d^3*m*e^5 + 106992*(x*e + d)^m*a^2*b*c*d^3*m*e^5 - 10080*(x*e + d)^m*b^4*d^4*e^4 - 120960*(x*e + d)^m*a*b^2*c*d^4*e^4 - 60480*(x*e + d)^m*a^2*c^2*d^4*e^4 + 48860*(x*e + d)^m*a^3*b*m^2*x*e^8 + 134136*(x*e + d)^m*a^2*b^2*m*x^2*e^8 + 89424*(x*e + d)^m*a^3*c*m*x^2*e^8 + 40320*(x*e + d)^m*a*b^3*x^3*e^8 + 120960*(x*e + d)^m*a^2*b*c*x^3*e^8 + 48860*(x*e + d)^m*a^3*b*d*m^2*e^7 + 60480*(x*e + d)^m*a^2*b^2*d*m*x*e^7 + 40320*(x*e + d)^m*a^3*c*d*m*x*e^7 - 73656*(x*e + d)^m*a^2*b^2*d^2*m*e^6 - 49104*(x*e + d)^m*a^3*c*d^2*m*e^6 + 40320*(x*e + d)^m*a*b^3*d^3*e^5 + 120960*(x*e + d)^m*a^2*b*c*d^3*e^5 + 69264*(x*e + d)^m*a^3*b*m*x*e^8 + 60480*(x*e + d)^m*a^2*b^2*x^2*e^8 + 40320*(x*e + d)^m*a^3*c*x^2*e^8 + 69264*(x*e + d)^m*a^3*b*d*m*e^7 - 60480*(x*e + d)^m*a^2*b^2*d^2*e^6 - 40320*(x*e + d)^m*a^3*c*d^2*e^6 + 40320*(x*e + d)^m*a^3*b*x*e^8 + 40320*(x*e + d)^m*a^3*b*d*e^7)/(m^8*e^8 + 36*m^7*e^8 + 546*m^6*e^8 + 4536*m^5*e^8 + 22449*m^4*e^8 + 67284*m^3*e^8 + 118124*m^2*e^8 + 109584*m*e^8 + 40320*e^8)","B",0
1655,1,3633,0,0.315143," ","integrate((2*c*x+b)*(e*x+d)^m*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2 \, {\left(x e + d\right)}^{m} c^{3} m^{5} x^{6} e^{6} + 2 \, {\left(x e + d\right)}^{m} c^{3} d m^{5} x^{5} e^{5} + 5 \, {\left(x e + d\right)}^{m} b c^{2} m^{5} x^{5} e^{6} + 30 \, {\left(x e + d\right)}^{m} c^{3} m^{4} x^{6} e^{6} + 5 \, {\left(x e + d\right)}^{m} b c^{2} d m^{5} x^{4} e^{5} + 20 \, {\left(x e + d\right)}^{m} c^{3} d m^{4} x^{5} e^{5} - 10 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{4} x^{4} e^{4} + 4 \, {\left(x e + d\right)}^{m} b^{2} c m^{5} x^{4} e^{6} + 4 \, {\left(x e + d\right)}^{m} a c^{2} m^{5} x^{4} e^{6} + 80 \, {\left(x e + d\right)}^{m} b c^{2} m^{4} x^{5} e^{6} + 170 \, {\left(x e + d\right)}^{m} c^{3} m^{3} x^{6} e^{6} + 4 \, {\left(x e + d\right)}^{m} b^{2} c d m^{5} x^{3} e^{5} + 4 \, {\left(x e + d\right)}^{m} a c^{2} d m^{5} x^{3} e^{5} + 60 \, {\left(x e + d\right)}^{m} b c^{2} d m^{4} x^{4} e^{5} + 70 \, {\left(x e + d\right)}^{m} c^{3} d m^{3} x^{5} e^{5} - 20 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{4} x^{3} e^{4} - 60 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{3} x^{4} e^{4} + 40 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} b^{3} m^{5} x^{3} e^{6} + 6 \, {\left(x e + d\right)}^{m} a b c m^{5} x^{3} e^{6} + 68 \, {\left(x e + d\right)}^{m} b^{2} c m^{4} x^{4} e^{6} + 68 \, {\left(x e + d\right)}^{m} a c^{2} m^{4} x^{4} e^{6} + 475 \, {\left(x e + d\right)}^{m} b c^{2} m^{3} x^{5} e^{6} + 450 \, {\left(x e + d\right)}^{m} c^{3} m^{2} x^{6} e^{6} + {\left(x e + d\right)}^{m} b^{3} d m^{5} x^{2} e^{5} + 6 \, {\left(x e + d\right)}^{m} a b c d m^{5} x^{2} e^{5} + 56 \, {\left(x e + d\right)}^{m} b^{2} c d m^{4} x^{3} e^{5} + 56 \, {\left(x e + d\right)}^{m} a c^{2} d m^{4} x^{3} e^{5} + 235 \, {\left(x e + d\right)}^{m} b c^{2} d m^{3} x^{4} e^{5} + 100 \, {\left(x e + d\right)}^{m} c^{3} d m^{2} x^{5} e^{5} - 12 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{4} x^{2} e^{4} - 12 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{4} x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{3} x^{3} e^{4} - 110 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{2} x^{4} e^{4} + 60 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{3} x^{2} e^{3} + 120 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{2} x^{3} e^{3} - 120 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{2} x^{2} e^{2} + 2 \, {\left(x e + d\right)}^{m} a b^{2} m^{5} x^{2} e^{6} + 2 \, {\left(x e + d\right)}^{m} a^{2} c m^{5} x^{2} e^{6} + 18 \, {\left(x e + d\right)}^{m} b^{3} m^{4} x^{3} e^{6} + 108 \, {\left(x e + d\right)}^{m} a b c m^{4} x^{3} e^{6} + 428 \, {\left(x e + d\right)}^{m} b^{2} c m^{3} x^{4} e^{6} + 428 \, {\left(x e + d\right)}^{m} a c^{2} m^{3} x^{4} e^{6} + 1300 \, {\left(x e + d\right)}^{m} b c^{2} m^{2} x^{5} e^{6} + 548 \, {\left(x e + d\right)}^{m} c^{3} m x^{6} e^{6} + 2 \, {\left(x e + d\right)}^{m} a b^{2} d m^{5} x e^{5} + 2 \, {\left(x e + d\right)}^{m} a^{2} c d m^{5} x e^{5} + 16 \, {\left(x e + d\right)}^{m} b^{3} d m^{4} x^{2} e^{5} + 96 \, {\left(x e + d\right)}^{m} a b c d m^{4} x^{2} e^{5} + 260 \, {\left(x e + d\right)}^{m} b^{2} c d m^{3} x^{3} e^{5} + 260 \, {\left(x e + d\right)}^{m} a c^{2} d m^{3} x^{3} e^{5} + 360 \, {\left(x e + d\right)}^{m} b c^{2} d m^{2} x^{4} e^{5} + 48 \, {\left(x e + d\right)}^{m} c^{3} d m x^{5} e^{5} - 2 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{4} x e^{4} - 12 \, {\left(x e + d\right)}^{m} a b c d^{2} m^{4} x e^{4} - 144 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{3} x^{2} e^{4} - 144 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{3} x^{2} e^{4} - 400 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{2} x^{3} e^{4} - 60 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m x^{4} e^{4} + 24 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{3} x e^{3} + 24 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{3} x e^{3} + 420 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{2} x^{2} e^{3} + 80 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m x^{3} e^{3} - 120 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m^{2} x e^{2} - 120 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m x^{2} e^{2} + 240 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m x e + {\left(x e + d\right)}^{m} a^{2} b m^{5} x e^{6} + 38 \, {\left(x e + d\right)}^{m} a b^{2} m^{4} x^{2} e^{6} + 38 \, {\left(x e + d\right)}^{m} a^{2} c m^{4} x^{2} e^{6} + 121 \, {\left(x e + d\right)}^{m} b^{3} m^{3} x^{3} e^{6} + 726 \, {\left(x e + d\right)}^{m} a b c m^{3} x^{3} e^{6} + 1228 \, {\left(x e + d\right)}^{m} b^{2} c m^{2} x^{4} e^{6} + 1228 \, {\left(x e + d\right)}^{m} a c^{2} m^{2} x^{4} e^{6} + 1620 \, {\left(x e + d\right)}^{m} b c^{2} m x^{5} e^{6} + 240 \, {\left(x e + d\right)}^{m} c^{3} x^{6} e^{6} + {\left(x e + d\right)}^{m} a^{2} b d m^{5} e^{5} + 36 \, {\left(x e + d\right)}^{m} a b^{2} d m^{4} x e^{5} + 36 \, {\left(x e + d\right)}^{m} a^{2} c d m^{4} x e^{5} + 89 \, {\left(x e + d\right)}^{m} b^{3} d m^{3} x^{2} e^{5} + 534 \, {\left(x e + d\right)}^{m} a b c d m^{3} x^{2} e^{5} + 448 \, {\left(x e + d\right)}^{m} b^{2} c d m^{2} x^{3} e^{5} + 448 \, {\left(x e + d\right)}^{m} a c^{2} d m^{2} x^{3} e^{5} + 180 \, {\left(x e + d\right)}^{m} b c^{2} d m x^{4} e^{5} - 2 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{4} e^{4} - 2 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{4} e^{4} - 30 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{3} x e^{4} - 180 \, {\left(x e + d\right)}^{m} a b c d^{2} m^{3} x e^{4} - 492 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{2} x^{2} e^{4} - 492 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{2} x^{2} e^{4} - 240 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m x^{3} e^{4} + 2 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} a b c d^{3} m^{3} e^{3} + 264 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{2} x e^{3} + 264 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{2} x e^{3} + 360 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m x^{2} e^{3} - 24 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m^{2} e^{2} - 720 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m x e^{2} + 120 \, {\left(x e + d\right)}^{m} b c^{2} d^{5} m e - 240 \, {\left(x e + d\right)}^{m} c^{3} d^{6} + 20 \, {\left(x e + d\right)}^{m} a^{2} b m^{4} x e^{6} + 274 \, {\left(x e + d\right)}^{m} a b^{2} m^{3} x^{2} e^{6} + 274 \, {\left(x e + d\right)}^{m} a^{2} c m^{3} x^{2} e^{6} + 372 \, {\left(x e + d\right)}^{m} b^{3} m^{2} x^{3} e^{6} + 2232 \, {\left(x e + d\right)}^{m} a b c m^{2} x^{3} e^{6} + 1584 \, {\left(x e + d\right)}^{m} b^{2} c m x^{4} e^{6} + 1584 \, {\left(x e + d\right)}^{m} a c^{2} m x^{4} e^{6} + 720 \, {\left(x e + d\right)}^{m} b c^{2} x^{5} e^{6} + 20 \, {\left(x e + d\right)}^{m} a^{2} b d m^{4} e^{5} + 238 \, {\left(x e + d\right)}^{m} a b^{2} d m^{3} x e^{5} + 238 \, {\left(x e + d\right)}^{m} a^{2} c d m^{3} x e^{5} + 194 \, {\left(x e + d\right)}^{m} b^{3} d m^{2} x^{2} e^{5} + 1164 \, {\left(x e + d\right)}^{m} a b c d m^{2} x^{2} e^{5} + 240 \, {\left(x e + d\right)}^{m} b^{2} c d m x^{3} e^{5} + 240 \, {\left(x e + d\right)}^{m} a c^{2} d m x^{3} e^{5} - 36 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{3} e^{4} - 36 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{3} e^{4} - 148 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{2} x e^{4} - 888 \, {\left(x e + d\right)}^{m} a b c d^{2} m^{2} x e^{4} - 360 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m x^{2} e^{4} - 360 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m x^{2} e^{4} + 30 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{2} e^{3} + 180 \, {\left(x e + d\right)}^{m} a b c d^{3} m^{2} e^{3} + 720 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m x e^{3} + 720 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m x e^{3} - 264 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m e^{2} - 264 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m e^{2} + 720 \, {\left(x e + d\right)}^{m} b c^{2} d^{5} e + 155 \, {\left(x e + d\right)}^{m} a^{2} b m^{3} x e^{6} + 922 \, {\left(x e + d\right)}^{m} a b^{2} m^{2} x^{2} e^{6} + 922 \, {\left(x e + d\right)}^{m} a^{2} c m^{2} x^{2} e^{6} + 508 \, {\left(x e + d\right)}^{m} b^{3} m x^{3} e^{6} + 3048 \, {\left(x e + d\right)}^{m} a b c m x^{3} e^{6} + 720 \, {\left(x e + d\right)}^{m} b^{2} c x^{4} e^{6} + 720 \, {\left(x e + d\right)}^{m} a c^{2} x^{4} e^{6} + 155 \, {\left(x e + d\right)}^{m} a^{2} b d m^{3} e^{5} + 684 \, {\left(x e + d\right)}^{m} a b^{2} d m^{2} x e^{5} + 684 \, {\left(x e + d\right)}^{m} a^{2} c d m^{2} x e^{5} + 120 \, {\left(x e + d\right)}^{m} b^{3} d m x^{2} e^{5} + 720 \, {\left(x e + d\right)}^{m} a b c d m x^{2} e^{5} - 238 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{2} e^{4} - 238 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{2} e^{4} - 240 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m x e^{4} - 1440 \, {\left(x e + d\right)}^{m} a b c d^{2} m x e^{4} + 148 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m e^{3} + 888 \, {\left(x e + d\right)}^{m} a b c d^{3} m e^{3} - 720 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} e^{2} - 720 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} e^{2} + 580 \, {\left(x e + d\right)}^{m} a^{2} b m^{2} x e^{6} + 1404 \, {\left(x e + d\right)}^{m} a b^{2} m x^{2} e^{6} + 1404 \, {\left(x e + d\right)}^{m} a^{2} c m x^{2} e^{6} + 240 \, {\left(x e + d\right)}^{m} b^{3} x^{3} e^{6} + 1440 \, {\left(x e + d\right)}^{m} a b c x^{3} e^{6} + 580 \, {\left(x e + d\right)}^{m} a^{2} b d m^{2} e^{5} + 720 \, {\left(x e + d\right)}^{m} a b^{2} d m x e^{5} + 720 \, {\left(x e + d\right)}^{m} a^{2} c d m x e^{5} - 684 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m e^{4} - 684 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m e^{4} + 240 \, {\left(x e + d\right)}^{m} b^{3} d^{3} e^{3} + 1440 \, {\left(x e + d\right)}^{m} a b c d^{3} e^{3} + 1044 \, {\left(x e + d\right)}^{m} a^{2} b m x e^{6} + 720 \, {\left(x e + d\right)}^{m} a b^{2} x^{2} e^{6} + 720 \, {\left(x e + d\right)}^{m} a^{2} c x^{2} e^{6} + 1044 \, {\left(x e + d\right)}^{m} a^{2} b d m e^{5} - 720 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} e^{4} - 720 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} e^{4} + 720 \, {\left(x e + d\right)}^{m} a^{2} b x e^{6} + 720 \, {\left(x e + d\right)}^{m} a^{2} b d e^{5}}{m^{6} e^{6} + 21 \, m^{5} e^{6} + 175 \, m^{4} e^{6} + 735 \, m^{3} e^{6} + 1624 \, m^{2} e^{6} + 1764 \, m e^{6} + 720 \, e^{6}}"," ",0,"(2*(x*e + d)^m*c^3*m^5*x^6*e^6 + 2*(x*e + d)^m*c^3*d*m^5*x^5*e^5 + 5*(x*e + d)^m*b*c^2*m^5*x^5*e^6 + 30*(x*e + d)^m*c^3*m^4*x^6*e^6 + 5*(x*e + d)^m*b*c^2*d*m^5*x^4*e^5 + 20*(x*e + d)^m*c^3*d*m^4*x^5*e^5 - 10*(x*e + d)^m*c^3*d^2*m^4*x^4*e^4 + 4*(x*e + d)^m*b^2*c*m^5*x^4*e^6 + 4*(x*e + d)^m*a*c^2*m^5*x^4*e^6 + 80*(x*e + d)^m*b*c^2*m^4*x^5*e^6 + 170*(x*e + d)^m*c^3*m^3*x^6*e^6 + 4*(x*e + d)^m*b^2*c*d*m^5*x^3*e^5 + 4*(x*e + d)^m*a*c^2*d*m^5*x^3*e^5 + 60*(x*e + d)^m*b*c^2*d*m^4*x^4*e^5 + 70*(x*e + d)^m*c^3*d*m^3*x^5*e^5 - 20*(x*e + d)^m*b*c^2*d^2*m^4*x^3*e^4 - 60*(x*e + d)^m*c^3*d^2*m^3*x^4*e^4 + 40*(x*e + d)^m*c^3*d^3*m^3*x^3*e^3 + (x*e + d)^m*b^3*m^5*x^3*e^6 + 6*(x*e + d)^m*a*b*c*m^5*x^3*e^6 + 68*(x*e + d)^m*b^2*c*m^4*x^4*e^6 + 68*(x*e + d)^m*a*c^2*m^4*x^4*e^6 + 475*(x*e + d)^m*b*c^2*m^3*x^5*e^6 + 450*(x*e + d)^m*c^3*m^2*x^6*e^6 + (x*e + d)^m*b^3*d*m^5*x^2*e^5 + 6*(x*e + d)^m*a*b*c*d*m^5*x^2*e^5 + 56*(x*e + d)^m*b^2*c*d*m^4*x^3*e^5 + 56*(x*e + d)^m*a*c^2*d*m^4*x^3*e^5 + 235*(x*e + d)^m*b*c^2*d*m^3*x^4*e^5 + 100*(x*e + d)^m*c^3*d*m^2*x^5*e^5 - 12*(x*e + d)^m*b^2*c*d^2*m^4*x^2*e^4 - 12*(x*e + d)^m*a*c^2*d^2*m^4*x^2*e^4 - 180*(x*e + d)^m*b*c^2*d^2*m^3*x^3*e^4 - 110*(x*e + d)^m*c^3*d^2*m^2*x^4*e^4 + 60*(x*e + d)^m*b*c^2*d^3*m^3*x^2*e^3 + 120*(x*e + d)^m*c^3*d^3*m^2*x^3*e^3 - 120*(x*e + d)^m*c^3*d^4*m^2*x^2*e^2 + 2*(x*e + d)^m*a*b^2*m^5*x^2*e^6 + 2*(x*e + d)^m*a^2*c*m^5*x^2*e^6 + 18*(x*e + d)^m*b^3*m^4*x^3*e^6 + 108*(x*e + d)^m*a*b*c*m^4*x^3*e^6 + 428*(x*e + d)^m*b^2*c*m^3*x^4*e^6 + 428*(x*e + d)^m*a*c^2*m^3*x^4*e^6 + 1300*(x*e + d)^m*b*c^2*m^2*x^5*e^6 + 548*(x*e + d)^m*c^3*m*x^6*e^6 + 2*(x*e + d)^m*a*b^2*d*m^5*x*e^5 + 2*(x*e + d)^m*a^2*c*d*m^5*x*e^5 + 16*(x*e + d)^m*b^3*d*m^4*x^2*e^5 + 96*(x*e + d)^m*a*b*c*d*m^4*x^2*e^5 + 260*(x*e + d)^m*b^2*c*d*m^3*x^3*e^5 + 260*(x*e + d)^m*a*c^2*d*m^3*x^3*e^5 + 360*(x*e + d)^m*b*c^2*d*m^2*x^4*e^5 + 48*(x*e + d)^m*c^3*d*m*x^5*e^5 - 2*(x*e + d)^m*b^3*d^2*m^4*x*e^4 - 12*(x*e + d)^m*a*b*c*d^2*m^4*x*e^4 - 144*(x*e + d)^m*b^2*c*d^2*m^3*x^2*e^4 - 144*(x*e + d)^m*a*c^2*d^2*m^3*x^2*e^4 - 400*(x*e + d)^m*b*c^2*d^2*m^2*x^3*e^4 - 60*(x*e + d)^m*c^3*d^2*m*x^4*e^4 + 24*(x*e + d)^m*b^2*c*d^3*m^3*x*e^3 + 24*(x*e + d)^m*a*c^2*d^3*m^3*x*e^3 + 420*(x*e + d)^m*b*c^2*d^3*m^2*x^2*e^3 + 80*(x*e + d)^m*c^3*d^3*m*x^3*e^3 - 120*(x*e + d)^m*b*c^2*d^4*m^2*x*e^2 - 120*(x*e + d)^m*c^3*d^4*m*x^2*e^2 + 240*(x*e + d)^m*c^3*d^5*m*x*e + (x*e + d)^m*a^2*b*m^5*x*e^6 + 38*(x*e + d)^m*a*b^2*m^4*x^2*e^6 + 38*(x*e + d)^m*a^2*c*m^4*x^2*e^6 + 121*(x*e + d)^m*b^3*m^3*x^3*e^6 + 726*(x*e + d)^m*a*b*c*m^3*x^3*e^6 + 1228*(x*e + d)^m*b^2*c*m^2*x^4*e^6 + 1228*(x*e + d)^m*a*c^2*m^2*x^4*e^6 + 1620*(x*e + d)^m*b*c^2*m*x^5*e^6 + 240*(x*e + d)^m*c^3*x^6*e^6 + (x*e + d)^m*a^2*b*d*m^5*e^5 + 36*(x*e + d)^m*a*b^2*d*m^4*x*e^5 + 36*(x*e + d)^m*a^2*c*d*m^4*x*e^5 + 89*(x*e + d)^m*b^3*d*m^3*x^2*e^5 + 534*(x*e + d)^m*a*b*c*d*m^3*x^2*e^5 + 448*(x*e + d)^m*b^2*c*d*m^2*x^3*e^5 + 448*(x*e + d)^m*a*c^2*d*m^2*x^3*e^5 + 180*(x*e + d)^m*b*c^2*d*m*x^4*e^5 - 2*(x*e + d)^m*a*b^2*d^2*m^4*e^4 - 2*(x*e + d)^m*a^2*c*d^2*m^4*e^4 - 30*(x*e + d)^m*b^3*d^2*m^3*x*e^4 - 180*(x*e + d)^m*a*b*c*d^2*m^3*x*e^4 - 492*(x*e + d)^m*b^2*c*d^2*m^2*x^2*e^4 - 492*(x*e + d)^m*a*c^2*d^2*m^2*x^2*e^4 - 240*(x*e + d)^m*b*c^2*d^2*m*x^3*e^4 + 2*(x*e + d)^m*b^3*d^3*m^3*e^3 + 12*(x*e + d)^m*a*b*c*d^3*m^3*e^3 + 264*(x*e + d)^m*b^2*c*d^3*m^2*x*e^3 + 264*(x*e + d)^m*a*c^2*d^3*m^2*x*e^3 + 360*(x*e + d)^m*b*c^2*d^3*m*x^2*e^3 - 24*(x*e + d)^m*b^2*c*d^4*m^2*e^2 - 24*(x*e + d)^m*a*c^2*d^4*m^2*e^2 - 720*(x*e + d)^m*b*c^2*d^4*m*x*e^2 + 120*(x*e + d)^m*b*c^2*d^5*m*e - 240*(x*e + d)^m*c^3*d^6 + 20*(x*e + d)^m*a^2*b*m^4*x*e^6 + 274*(x*e + d)^m*a*b^2*m^3*x^2*e^6 + 274*(x*e + d)^m*a^2*c*m^3*x^2*e^6 + 372*(x*e + d)^m*b^3*m^2*x^3*e^6 + 2232*(x*e + d)^m*a*b*c*m^2*x^3*e^6 + 1584*(x*e + d)^m*b^2*c*m*x^4*e^6 + 1584*(x*e + d)^m*a*c^2*m*x^4*e^6 + 720*(x*e + d)^m*b*c^2*x^5*e^6 + 20*(x*e + d)^m*a^2*b*d*m^4*e^5 + 238*(x*e + d)^m*a*b^2*d*m^3*x*e^5 + 238*(x*e + d)^m*a^2*c*d*m^3*x*e^5 + 194*(x*e + d)^m*b^3*d*m^2*x^2*e^5 + 1164*(x*e + d)^m*a*b*c*d*m^2*x^2*e^5 + 240*(x*e + d)^m*b^2*c*d*m*x^3*e^5 + 240*(x*e + d)^m*a*c^2*d*m*x^3*e^5 - 36*(x*e + d)^m*a*b^2*d^2*m^3*e^4 - 36*(x*e + d)^m*a^2*c*d^2*m^3*e^4 - 148*(x*e + d)^m*b^3*d^2*m^2*x*e^4 - 888*(x*e + d)^m*a*b*c*d^2*m^2*x*e^4 - 360*(x*e + d)^m*b^2*c*d^2*m*x^2*e^4 - 360*(x*e + d)^m*a*c^2*d^2*m*x^2*e^4 + 30*(x*e + d)^m*b^3*d^3*m^2*e^3 + 180*(x*e + d)^m*a*b*c*d^3*m^2*e^3 + 720*(x*e + d)^m*b^2*c*d^3*m*x*e^3 + 720*(x*e + d)^m*a*c^2*d^3*m*x*e^3 - 264*(x*e + d)^m*b^2*c*d^4*m*e^2 - 264*(x*e + d)^m*a*c^2*d^4*m*e^2 + 720*(x*e + d)^m*b*c^2*d^5*e + 155*(x*e + d)^m*a^2*b*m^3*x*e^6 + 922*(x*e + d)^m*a*b^2*m^2*x^2*e^6 + 922*(x*e + d)^m*a^2*c*m^2*x^2*e^6 + 508*(x*e + d)^m*b^3*m*x^3*e^6 + 3048*(x*e + d)^m*a*b*c*m*x^3*e^6 + 720*(x*e + d)^m*b^2*c*x^4*e^6 + 720*(x*e + d)^m*a*c^2*x^4*e^6 + 155*(x*e + d)^m*a^2*b*d*m^3*e^5 + 684*(x*e + d)^m*a*b^2*d*m^2*x*e^5 + 684*(x*e + d)^m*a^2*c*d*m^2*x*e^5 + 120*(x*e + d)^m*b^3*d*m*x^2*e^5 + 720*(x*e + d)^m*a*b*c*d*m*x^2*e^5 - 238*(x*e + d)^m*a*b^2*d^2*m^2*e^4 - 238*(x*e + d)^m*a^2*c*d^2*m^2*e^4 - 240*(x*e + d)^m*b^3*d^2*m*x*e^4 - 1440*(x*e + d)^m*a*b*c*d^2*m*x*e^4 + 148*(x*e + d)^m*b^3*d^3*m*e^3 + 888*(x*e + d)^m*a*b*c*d^3*m*e^3 - 720*(x*e + d)^m*b^2*c*d^4*e^2 - 720*(x*e + d)^m*a*c^2*d^4*e^2 + 580*(x*e + d)^m*a^2*b*m^2*x*e^6 + 1404*(x*e + d)^m*a*b^2*m*x^2*e^6 + 1404*(x*e + d)^m*a^2*c*m*x^2*e^6 + 240*(x*e + d)^m*b^3*x^3*e^6 + 1440*(x*e + d)^m*a*b*c*x^3*e^6 + 580*(x*e + d)^m*a^2*b*d*m^2*e^5 + 720*(x*e + d)^m*a*b^2*d*m*x*e^5 + 720*(x*e + d)^m*a^2*c*d*m*x*e^5 - 684*(x*e + d)^m*a*b^2*d^2*m*e^4 - 684*(x*e + d)^m*a^2*c*d^2*m*e^4 + 240*(x*e + d)^m*b^3*d^3*e^3 + 1440*(x*e + d)^m*a*b*c*d^3*e^3 + 1044*(x*e + d)^m*a^2*b*m*x*e^6 + 720*(x*e + d)^m*a*b^2*x^2*e^6 + 720*(x*e + d)^m*a^2*c*x^2*e^6 + 1044*(x*e + d)^m*a^2*b*d*m*e^5 - 720*(x*e + d)^m*a*b^2*d^2*e^4 - 720*(x*e + d)^m*a^2*c*d^2*e^4 + 720*(x*e + d)^m*a^2*b*x*e^6 + 720*(x*e + d)^m*a^2*b*d*e^5)/(m^6*e^6 + 21*m^5*e^6 + 175*m^4*e^6 + 735*m^3*e^6 + 1624*m^2*e^6 + 1764*m*e^6 + 720*e^6)","B",0
1656,1,980,0,0.194195," ","integrate((2*c*x+b)*(e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, {\left(x e + d\right)}^{m} c^{2} m^{3} x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} c^{2} d m^{3} x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} b c m^{3} x^{3} e^{4} + 12 \, {\left(x e + d\right)}^{m} c^{2} m^{2} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} b c d m^{3} x^{2} e^{3} + 6 \, {\left(x e + d\right)}^{m} c^{2} d m^{2} x^{3} e^{3} - 6 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} b^{2} m^{3} x^{2} e^{4} + 2 \, {\left(x e + d\right)}^{m} a c m^{3} x^{2} e^{4} + 21 \, {\left(x e + d\right)}^{m} b c m^{2} x^{3} e^{4} + 22 \, {\left(x e + d\right)}^{m} c^{2} m x^{4} e^{4} + {\left(x e + d\right)}^{m} b^{2} d m^{3} x e^{3} + 2 \, {\left(x e + d\right)}^{m} a c d m^{3} x e^{3} + 15 \, {\left(x e + d\right)}^{m} b c d m^{2} x^{2} e^{3} + 4 \, {\left(x e + d\right)}^{m} c^{2} d m x^{3} e^{3} - 6 \, {\left(x e + d\right)}^{m} b c d^{2} m^{2} x e^{2} - 6 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m x^{2} e^{2} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m x e + {\left(x e + d\right)}^{m} a b m^{3} x e^{4} + 8 \, {\left(x e + d\right)}^{m} b^{2} m^{2} x^{2} e^{4} + 16 \, {\left(x e + d\right)}^{m} a c m^{2} x^{2} e^{4} + 42 \, {\left(x e + d\right)}^{m} b c m x^{3} e^{4} + 12 \, {\left(x e + d\right)}^{m} c^{2} x^{4} e^{4} + {\left(x e + d\right)}^{m} a b d m^{3} e^{3} + 7 \, {\left(x e + d\right)}^{m} b^{2} d m^{2} x e^{3} + 14 \, {\left(x e + d\right)}^{m} a c d m^{2} x e^{3} + 12 \, {\left(x e + d\right)}^{m} b c d m x^{2} e^{3} - {\left(x e + d\right)}^{m} b^{2} d^{2} m^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} a c d^{2} m^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} b c d^{2} m x e^{2} + 6 \, {\left(x e + d\right)}^{m} b c d^{3} m e - 12 \, {\left(x e + d\right)}^{m} c^{2} d^{4} + 9 \, {\left(x e + d\right)}^{m} a b m^{2} x e^{4} + 19 \, {\left(x e + d\right)}^{m} b^{2} m x^{2} e^{4} + 38 \, {\left(x e + d\right)}^{m} a c m x^{2} e^{4} + 24 \, {\left(x e + d\right)}^{m} b c x^{3} e^{4} + 9 \, {\left(x e + d\right)}^{m} a b d m^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} b^{2} d m x e^{3} + 24 \, {\left(x e + d\right)}^{m} a c d m x e^{3} - 7 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m e^{2} - 14 \, {\left(x e + d\right)}^{m} a c d^{2} m e^{2} + 24 \, {\left(x e + d\right)}^{m} b c d^{3} e + 26 \, {\left(x e + d\right)}^{m} a b m x e^{4} + 12 \, {\left(x e + d\right)}^{m} b^{2} x^{2} e^{4} + 24 \, {\left(x e + d\right)}^{m} a c x^{2} e^{4} + 26 \, {\left(x e + d\right)}^{m} a b d m e^{3} - 12 \, {\left(x e + d\right)}^{m} b^{2} d^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} a c d^{2} e^{2} + 24 \, {\left(x e + d\right)}^{m} a b x e^{4} + 24 \, {\left(x e + d\right)}^{m} a b d e^{3}}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"(2*(x*e + d)^m*c^2*m^3*x^4*e^4 + 2*(x*e + d)^m*c^2*d*m^3*x^3*e^3 + 3*(x*e + d)^m*b*c*m^3*x^3*e^4 + 12*(x*e + d)^m*c^2*m^2*x^4*e^4 + 3*(x*e + d)^m*b*c*d*m^3*x^2*e^3 + 6*(x*e + d)^m*c^2*d*m^2*x^3*e^3 - 6*(x*e + d)^m*c^2*d^2*m^2*x^2*e^2 + (x*e + d)^m*b^2*m^3*x^2*e^4 + 2*(x*e + d)^m*a*c*m^3*x^2*e^4 + 21*(x*e + d)^m*b*c*m^2*x^3*e^4 + 22*(x*e + d)^m*c^2*m*x^4*e^4 + (x*e + d)^m*b^2*d*m^3*x*e^3 + 2*(x*e + d)^m*a*c*d*m^3*x*e^3 + 15*(x*e + d)^m*b*c*d*m^2*x^2*e^3 + 4*(x*e + d)^m*c^2*d*m*x^3*e^3 - 6*(x*e + d)^m*b*c*d^2*m^2*x*e^2 - 6*(x*e + d)^m*c^2*d^2*m*x^2*e^2 + 12*(x*e + d)^m*c^2*d^3*m*x*e + (x*e + d)^m*a*b*m^3*x*e^4 + 8*(x*e + d)^m*b^2*m^2*x^2*e^4 + 16*(x*e + d)^m*a*c*m^2*x^2*e^4 + 42*(x*e + d)^m*b*c*m*x^3*e^4 + 12*(x*e + d)^m*c^2*x^4*e^4 + (x*e + d)^m*a*b*d*m^3*e^3 + 7*(x*e + d)^m*b^2*d*m^2*x*e^3 + 14*(x*e + d)^m*a*c*d*m^2*x*e^3 + 12*(x*e + d)^m*b*c*d*m*x^2*e^3 - (x*e + d)^m*b^2*d^2*m^2*e^2 - 2*(x*e + d)^m*a*c*d^2*m^2*e^2 - 24*(x*e + d)^m*b*c*d^2*m*x*e^2 + 6*(x*e + d)^m*b*c*d^3*m*e - 12*(x*e + d)^m*c^2*d^4 + 9*(x*e + d)^m*a*b*m^2*x*e^4 + 19*(x*e + d)^m*b^2*m*x^2*e^4 + 38*(x*e + d)^m*a*c*m*x^2*e^4 + 24*(x*e + d)^m*b*c*x^3*e^4 + 9*(x*e + d)^m*a*b*d*m^2*e^3 + 12*(x*e + d)^m*b^2*d*m*x*e^3 + 24*(x*e + d)^m*a*c*d*m*x*e^3 - 7*(x*e + d)^m*b^2*d^2*m*e^2 - 14*(x*e + d)^m*a*c*d^2*m*e^2 + 24*(x*e + d)^m*b*c*d^3*e + 26*(x*e + d)^m*a*b*m*x*e^4 + 12*(x*e + d)^m*b^2*x^2*e^4 + 24*(x*e + d)^m*a*c*x^2*e^4 + 26*(x*e + d)^m*a*b*d*m*e^3 - 12*(x*e + d)^m*b^2*d^2*e^2 - 24*(x*e + d)^m*a*c*d^2*e^2 + 24*(x*e + d)^m*a*b*x*e^4 + 24*(x*e + d)^m*a*b*d*e^3)/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
1657,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^m/(c*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{m}}{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^m/(c*x^2 + b*x + a), x)","F",0
1658,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^m/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\int \frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{2}}\,{d x}"," ",0,"integrate((2*c*x + b)*(e*x + d)^m/(c*x^2 + b*x + a)^2, x)","F",0
1659,1,445,0,0.154151," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{9} \, B b^{2} x^{9} e^{5} + \frac{5}{8} \, B b^{2} d x^{8} e^{4} + \frac{10}{7} \, B b^{2} d^{2} x^{7} e^{3} + \frac{5}{3} \, B b^{2} d^{3} x^{6} e^{2} + B b^{2} d^{4} x^{5} e + \frac{1}{4} \, B b^{2} d^{5} x^{4} + \frac{1}{4} \, B a b x^{8} e^{5} + \frac{1}{8} \, A b^{2} x^{8} e^{5} + \frac{10}{7} \, B a b d x^{7} e^{4} + \frac{5}{7} \, A b^{2} d x^{7} e^{4} + \frac{10}{3} \, B a b d^{2} x^{6} e^{3} + \frac{5}{3} \, A b^{2} d^{2} x^{6} e^{3} + 4 \, B a b d^{3} x^{5} e^{2} + 2 \, A b^{2} d^{3} x^{5} e^{2} + \frac{5}{2} \, B a b d^{4} x^{4} e + \frac{5}{4} \, A b^{2} d^{4} x^{4} e + \frac{2}{3} \, B a b d^{5} x^{3} + \frac{1}{3} \, A b^{2} d^{5} x^{3} + \frac{1}{7} \, B a^{2} x^{7} e^{5} + \frac{2}{7} \, A a b x^{7} e^{5} + \frac{5}{6} \, B a^{2} d x^{6} e^{4} + \frac{5}{3} \, A a b d x^{6} e^{4} + 2 \, B a^{2} d^{2} x^{5} e^{3} + 4 \, A a b d^{2} x^{5} e^{3} + \frac{5}{2} \, B a^{2} d^{3} x^{4} e^{2} + 5 \, A a b d^{3} x^{4} e^{2} + \frac{5}{3} \, B a^{2} d^{4} x^{3} e + \frac{10}{3} \, A a b d^{4} x^{3} e + \frac{1}{2} \, B a^{2} d^{5} x^{2} + A a b d^{5} x^{2} + \frac{1}{6} \, A a^{2} x^{6} e^{5} + A a^{2} d x^{5} e^{4} + \frac{5}{2} \, A a^{2} d^{2} x^{4} e^{3} + \frac{10}{3} \, A a^{2} d^{3} x^{3} e^{2} + \frac{5}{2} \, A a^{2} d^{4} x^{2} e + A a^{2} d^{5} x"," ",0,"1/9*B*b^2*x^9*e^5 + 5/8*B*b^2*d*x^8*e^4 + 10/7*B*b^2*d^2*x^7*e^3 + 5/3*B*b^2*d^3*x^6*e^2 + B*b^2*d^4*x^5*e + 1/4*B*b^2*d^5*x^4 + 1/4*B*a*b*x^8*e^5 + 1/8*A*b^2*x^8*e^5 + 10/7*B*a*b*d*x^7*e^4 + 5/7*A*b^2*d*x^7*e^4 + 10/3*B*a*b*d^2*x^6*e^3 + 5/3*A*b^2*d^2*x^6*e^3 + 4*B*a*b*d^3*x^5*e^2 + 2*A*b^2*d^3*x^5*e^2 + 5/2*B*a*b*d^4*x^4*e + 5/4*A*b^2*d^4*x^4*e + 2/3*B*a*b*d^5*x^3 + 1/3*A*b^2*d^5*x^3 + 1/7*B*a^2*x^7*e^5 + 2/7*A*a*b*x^7*e^5 + 5/6*B*a^2*d*x^6*e^4 + 5/3*A*a*b*d*x^6*e^4 + 2*B*a^2*d^2*x^5*e^3 + 4*A*a*b*d^2*x^5*e^3 + 5/2*B*a^2*d^3*x^4*e^2 + 5*A*a*b*d^3*x^4*e^2 + 5/3*B*a^2*d^4*x^3*e + 10/3*A*a*b*d^4*x^3*e + 1/2*B*a^2*d^5*x^2 + A*a*b*d^5*x^2 + 1/6*A*a^2*x^6*e^5 + A*a^2*d*x^5*e^4 + 5/2*A*a^2*d^2*x^4*e^3 + 10/3*A*a^2*d^3*x^3*e^2 + 5/2*A*a^2*d^4*x^2*e + A*a^2*d^5*x","B",0
1660,1,362,0,0.157523," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{8} \, B b^{2} x^{8} e^{4} + \frac{4}{7} \, B b^{2} d x^{7} e^{3} + B b^{2} d^{2} x^{6} e^{2} + \frac{4}{5} \, B b^{2} d^{3} x^{5} e + \frac{1}{4} \, B b^{2} d^{4} x^{4} + \frac{2}{7} \, B a b x^{7} e^{4} + \frac{1}{7} \, A b^{2} x^{7} e^{4} + \frac{4}{3} \, B a b d x^{6} e^{3} + \frac{2}{3} \, A b^{2} d x^{6} e^{3} + \frac{12}{5} \, B a b d^{2} x^{5} e^{2} + \frac{6}{5} \, A b^{2} d^{2} x^{5} e^{2} + 2 \, B a b d^{3} x^{4} e + A b^{2} d^{3} x^{4} e + \frac{2}{3} \, B a b d^{4} x^{3} + \frac{1}{3} \, A b^{2} d^{4} x^{3} + \frac{1}{6} \, B a^{2} x^{6} e^{4} + \frac{1}{3} \, A a b x^{6} e^{4} + \frac{4}{5} \, B a^{2} d x^{5} e^{3} + \frac{8}{5} \, A a b d x^{5} e^{3} + \frac{3}{2} \, B a^{2} d^{2} x^{4} e^{2} + 3 \, A a b d^{2} x^{4} e^{2} + \frac{4}{3} \, B a^{2} d^{3} x^{3} e + \frac{8}{3} \, A a b d^{3} x^{3} e + \frac{1}{2} \, B a^{2} d^{4} x^{2} + A a b d^{4} x^{2} + \frac{1}{5} \, A a^{2} x^{5} e^{4} + A a^{2} d x^{4} e^{3} + 2 \, A a^{2} d^{2} x^{3} e^{2} + 2 \, A a^{2} d^{3} x^{2} e + A a^{2} d^{4} x"," ",0,"1/8*B*b^2*x^8*e^4 + 4/7*B*b^2*d*x^7*e^3 + B*b^2*d^2*x^6*e^2 + 4/5*B*b^2*d^3*x^5*e + 1/4*B*b^2*d^4*x^4 + 2/7*B*a*b*x^7*e^4 + 1/7*A*b^2*x^7*e^4 + 4/3*B*a*b*d*x^6*e^3 + 2/3*A*b^2*d*x^6*e^3 + 12/5*B*a*b*d^2*x^5*e^2 + 6/5*A*b^2*d^2*x^5*e^2 + 2*B*a*b*d^3*x^4*e + A*b^2*d^3*x^4*e + 2/3*B*a*b*d^4*x^3 + 1/3*A*b^2*d^4*x^3 + 1/6*B*a^2*x^6*e^4 + 1/3*A*a*b*x^6*e^4 + 4/5*B*a^2*d*x^5*e^3 + 8/5*A*a*b*d*x^5*e^3 + 3/2*B*a^2*d^2*x^4*e^2 + 3*A*a*b*d^2*x^4*e^2 + 4/3*B*a^2*d^3*x^3*e + 8/3*A*a*b*d^3*x^3*e + 1/2*B*a^2*d^4*x^2 + A*a*b*d^4*x^2 + 1/5*A*a^2*x^5*e^4 + A*a^2*d*x^4*e^3 + 2*A*a^2*d^2*x^3*e^2 + 2*A*a^2*d^3*x^2*e + A*a^2*d^4*x","B",0
1661,1,281,0,0.167407," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{7} \, B b^{2} x^{7} e^{3} + \frac{1}{2} \, B b^{2} d x^{6} e^{2} + \frac{3}{5} \, B b^{2} d^{2} x^{5} e + \frac{1}{4} \, B b^{2} d^{3} x^{4} + \frac{1}{3} \, B a b x^{6} e^{3} + \frac{1}{6} \, A b^{2} x^{6} e^{3} + \frac{6}{5} \, B a b d x^{5} e^{2} + \frac{3}{5} \, A b^{2} d x^{5} e^{2} + \frac{3}{2} \, B a b d^{2} x^{4} e + \frac{3}{4} \, A b^{2} d^{2} x^{4} e + \frac{2}{3} \, B a b d^{3} x^{3} + \frac{1}{3} \, A b^{2} d^{3} x^{3} + \frac{1}{5} \, B a^{2} x^{5} e^{3} + \frac{2}{5} \, A a b x^{5} e^{3} + \frac{3}{4} \, B a^{2} d x^{4} e^{2} + \frac{3}{2} \, A a b d x^{4} e^{2} + B a^{2} d^{2} x^{3} e + 2 \, A a b d^{2} x^{3} e + \frac{1}{2} \, B a^{2} d^{3} x^{2} + A a b d^{3} x^{2} + \frac{1}{4} \, A a^{2} x^{4} e^{3} + A a^{2} d x^{3} e^{2} + \frac{3}{2} \, A a^{2} d^{2} x^{2} e + A a^{2} d^{3} x"," ",0,"1/7*B*b^2*x^7*e^3 + 1/2*B*b^2*d*x^6*e^2 + 3/5*B*b^2*d^2*x^5*e + 1/4*B*b^2*d^3*x^4 + 1/3*B*a*b*x^6*e^3 + 1/6*A*b^2*x^6*e^3 + 6/5*B*a*b*d*x^5*e^2 + 3/5*A*b^2*d*x^5*e^2 + 3/2*B*a*b*d^2*x^4*e + 3/4*A*b^2*d^2*x^4*e + 2/3*B*a*b*d^3*x^3 + 1/3*A*b^2*d^3*x^3 + 1/5*B*a^2*x^5*e^3 + 2/5*A*a*b*x^5*e^3 + 3/4*B*a^2*d*x^4*e^2 + 3/2*A*a*b*d*x^4*e^2 + B*a^2*d^2*x^3*e + 2*A*a*b*d^2*x^3*e + 1/2*B*a^2*d^3*x^2 + A*a*b*d^3*x^2 + 1/4*A*a^2*x^4*e^3 + A*a^2*d*x^3*e^2 + 3/2*A*a^2*d^2*x^2*e + A*a^2*d^3*x","B",0
1662,1,199,0,0.157213," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{6} \, B b^{2} x^{6} e^{2} + \frac{2}{5} \, B b^{2} d x^{5} e + \frac{1}{4} \, B b^{2} d^{2} x^{4} + \frac{2}{5} \, B a b x^{5} e^{2} + \frac{1}{5} \, A b^{2} x^{5} e^{2} + B a b d x^{4} e + \frac{1}{2} \, A b^{2} d x^{4} e + \frac{2}{3} \, B a b d^{2} x^{3} + \frac{1}{3} \, A b^{2} d^{2} x^{3} + \frac{1}{4} \, B a^{2} x^{4} e^{2} + \frac{1}{2} \, A a b x^{4} e^{2} + \frac{2}{3} \, B a^{2} d x^{3} e + \frac{4}{3} \, A a b d x^{3} e + \frac{1}{2} \, B a^{2} d^{2} x^{2} + A a b d^{2} x^{2} + \frac{1}{3} \, A a^{2} x^{3} e^{2} + A a^{2} d x^{2} e + A a^{2} d^{2} x"," ",0,"1/6*B*b^2*x^6*e^2 + 2/5*B*b^2*d*x^5*e + 1/4*B*b^2*d^2*x^4 + 2/5*B*a*b*x^5*e^2 + 1/5*A*b^2*x^5*e^2 + B*a*b*d*x^4*e + 1/2*A*b^2*d*x^4*e + 2/3*B*a*b*d^2*x^3 + 1/3*A*b^2*d^2*x^3 + 1/4*B*a^2*x^4*e^2 + 1/2*A*a*b*x^4*e^2 + 2/3*B*a^2*d*x^3*e + 4/3*A*a*b*d*x^3*e + 1/2*B*a^2*d^2*x^2 + A*a*b*d^2*x^2 + 1/3*A*a^2*x^3*e^2 + A*a^2*d*x^2*e + A*a^2*d^2*x","A",0
1663,1,119,0,0.170433," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{5} \, B b^{2} x^{5} e + \frac{1}{4} \, B b^{2} d x^{4} + \frac{1}{2} \, B a b x^{4} e + \frac{1}{4} \, A b^{2} x^{4} e + \frac{2}{3} \, B a b d x^{3} + \frac{1}{3} \, A b^{2} d x^{3} + \frac{1}{3} \, B a^{2} x^{3} e + \frac{2}{3} \, A a b x^{3} e + \frac{1}{2} \, B a^{2} d x^{2} + A a b d x^{2} + \frac{1}{2} \, A a^{2} x^{2} e + A a^{2} d x"," ",0,"1/5*B*b^2*x^5*e + 1/4*B*b^2*d*x^4 + 1/2*B*a*b*x^4*e + 1/4*A*b^2*x^4*e + 2/3*B*a*b*d*x^3 + 1/3*A*b^2*d*x^3 + 1/3*B*a^2*x^3*e + 2/3*A*a*b*x^3*e + 1/2*B*a^2*d*x^2 + A*a*b*d*x^2 + 1/2*A*a^2*x^2*e + A*a^2*d*x","A",0
1664,1,49,0,0.151369," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{4} \, B b^{2} x^{4} + \frac{2}{3} \, B a b x^{3} + \frac{1}{3} \, A b^{2} x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a b x^{2} + A a^{2} x"," ",0,"1/4*B*b^2*x^4 + 2/3*B*a*b*x^3 + 1/3*A*b^2*x^3 + 1/2*B*a^2*x^2 + A*a*b*x^2 + A*a^2*x","A",0
1665,1,162,0,0.187041," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d),x, algorithm=""giac"")","-{\left(B b^{2} d^{3} - 2 \, B a b d^{2} e - A b^{2} d^{2} e + B a^{2} d e^{2} + 2 \, A a b d e^{2} - A a^{2} e^{3}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B b^{2} x^{3} e^{2} - 3 \, B b^{2} d x^{2} e + 6 \, B b^{2} d^{2} x + 6 \, B a b x^{2} e^{2} + 3 \, A b^{2} x^{2} e^{2} - 12 \, B a b d x e - 6 \, A b^{2} d x e + 6 \, B a^{2} x e^{2} + 12 \, A a b x e^{2}\right)} e^{\left(-3\right)}"," ",0,"-(B*b^2*d^3 - 2*B*a*b*d^2*e - A*b^2*d^2*e + B*a^2*d*e^2 + 2*A*a*b*d*e^2 - A*a^2*e^3)*e^(-4)*log(abs(x*e + d)) + 1/6*(2*B*b^2*x^3*e^2 - 3*B*b^2*d*x^2*e + 6*B*b^2*d^2*x + 6*B*a*b*x^2*e^2 + 3*A*b^2*x^2*e^2 - 12*B*a*b*d*x*e - 6*A*b^2*d*x*e + 6*B*a^2*x*e^2 + 12*A*a*b*x*e^2)*e^(-3)","A",0
1666,1,227,0,0.159068," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(B b^{2} - \frac{2 \, {\left(3 \, B b^{2} d e - 2 \, B a b e^{2} - A b^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)} - {\left(3 \, B b^{2} d^{2} - 4 \, B a b d e - 2 \, A b^{2} d e + B a^{2} e^{2} + 2 \, A a b e^{2}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B b^{2} d^{3} e^{2}}{x e + d} - \frac{2 \, B a b d^{2} e^{3}}{x e + d} - \frac{A b^{2} d^{2} e^{3}}{x e + d} + \frac{B a^{2} d e^{4}}{x e + d} + \frac{2 \, A a b d e^{4}}{x e + d} - \frac{A a^{2} e^{5}}{x e + d}\right)} e^{\left(-6\right)}"," ",0,"1/2*(B*b^2 - 2*(3*B*b^2*d*e - 2*B*a*b*e^2 - A*b^2*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4) - (3*B*b^2*d^2 - 4*B*a*b*d*e - 2*A*b^2*d*e + B*a^2*e^2 + 2*A*a*b*e^2)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*b^2*d^3*e^2/(x*e + d) - 2*B*a*b*d^2*e^3/(x*e + d) - A*b^2*d^2*e^3/(x*e + d) + B*a^2*d*e^4/(x*e + d) + 2*A*a*b*d*e^4/(x*e + d) - A*a^2*e^5/(x*e + d))*e^(-6)","B",0
1667,1,156,0,0.152173," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^3,x, algorithm=""giac"")","B b^{2} x e^{\left(-3\right)} - {\left(3 \, B b^{2} d - 2 \, B a b e - A b^{2} e\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, B b^{2} d^{3} - 6 \, B a b d^{2} e - 3 \, A b^{2} d^{2} e + B a^{2} d e^{2} + 2 \, A a b d e^{2} + A a^{2} e^{3} + 2 \, {\left(3 \, B b^{2} d^{2} e - 4 \, B a b d e^{2} - 2 \, A b^{2} d e^{2} + B a^{2} e^{3} + 2 \, A a b e^{3}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"B*b^2*x*e^(-3) - (3*B*b^2*d - 2*B*a*b*e - A*b^2*e)*e^(-4)*log(abs(x*e + d)) - 1/2*(5*B*b^2*d^3 - 6*B*a*b*d^2*e - 3*A*b^2*d^2*e + B*a^2*d*e^2 + 2*A*a*b*d*e^2 + A*a^2*e^3 + 2*(3*B*b^2*d^2*e - 4*B*a*b*d*e^2 - 2*A*b^2*d*e^2 + B*a^2*e^3 + 2*A*a*b*e^3)*x)*e^(-4)/(x*e + d)^2","A",0
1668,1,163,0,0.155963," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^4,x, algorithm=""giac"")","B b^{2} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(6 \, {\left(3 \, B b^{2} d e - 2 \, B a b e^{2} - A b^{2} e^{2}\right)} x^{2} + 3 \, {\left(9 \, B b^{2} d^{2} - 4 \, B a b d e - 2 \, A b^{2} d e - B a^{2} e^{2} - 2 \, A a b e^{2}\right)} x + {\left(11 \, B b^{2} d^{3} - 4 \, B a b d^{2} e - 2 \, A b^{2} d^{2} e - B a^{2} d e^{2} - 2 \, A a b d e^{2} - 2 \, A a^{2} e^{3}\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"B*b^2*e^(-4)*log(abs(x*e + d)) + 1/6*(6*(3*B*b^2*d*e - 2*B*a*b*e^2 - A*b^2*e^2)*x^2 + 3*(9*B*b^2*d^2 - 4*B*a*b*d*e - 2*A*b^2*d*e - B*a^2*e^2 - 2*A*a*b*e^2)*x + (11*B*b^2*d^3 - 4*B*a*b*d^2*e - 2*A*b^2*d^2*e - B*a^2*d*e^2 - 2*A*a*b*d*e^2 - 2*A*a^2*e^3)*e^(-1))*e^(-3)/(x*e + d)^3","A",0
1669,1,245,0,0.201214," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{12 \, B b^{2} e^{\left(-1\right)}}{x e + d} - \frac{18 \, B b^{2} d e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}} + \frac{12 \, B b^{2} d^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B b^{2} d^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{12 \, B a b}{{\left(x e + d\right)}^{2}} + \frac{6 \, A b^{2}}{{\left(x e + d\right)}^{2}} - \frac{16 \, B a b d}{{\left(x e + d\right)}^{3}} - \frac{8 \, A b^{2} d}{{\left(x e + d\right)}^{3}} + \frac{6 \, B a b d^{2}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A b^{2} d^{2}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a^{2} e}{{\left(x e + d\right)}^{3}} + \frac{8 \, A a b e}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a^{2} d e}{{\left(x e + d\right)}^{4}} - \frac{6 \, A a b d e}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a^{2} e^{2}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-3\right)}"," ",0,"-1/12*(12*B*b^2*e^(-1)/(x*e + d) - 18*B*b^2*d*e^(-1)/(x*e + d)^2 + 12*B*b^2*d^2*e^(-1)/(x*e + d)^3 - 3*B*b^2*d^3*e^(-1)/(x*e + d)^4 + 12*B*a*b/(x*e + d)^2 + 6*A*b^2/(x*e + d)^2 - 16*B*a*b*d/(x*e + d)^3 - 8*A*b^2*d/(x*e + d)^3 + 6*B*a*b*d^2/(x*e + d)^4 + 3*A*b^2*d^2/(x*e + d)^4 + 4*B*a^2*e/(x*e + d)^3 + 8*A*a*b*e/(x*e + d)^3 - 3*B*a^2*d*e/(x*e + d)^4 - 6*A*a*b*d*e/(x*e + d)^4 + 3*A*a^2*e^2/(x*e + d)^4)*e^(-3)","B",0
1670,1,160,0,0.153610," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(30 \, B b^{2} x^{3} e^{3} + 30 \, B b^{2} d x^{2} e^{2} + 15 \, B b^{2} d^{2} x e + 3 \, B b^{2} d^{3} + 40 \, B a b x^{2} e^{3} + 20 \, A b^{2} x^{2} e^{3} + 20 \, B a b d x e^{2} + 10 \, A b^{2} d x e^{2} + 4 \, B a b d^{2} e + 2 \, A b^{2} d^{2} e + 15 \, B a^{2} x e^{3} + 30 \, A a b x e^{3} + 3 \, B a^{2} d e^{2} + 6 \, A a b d e^{2} + 12 \, A a^{2} e^{3}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/60*(30*B*b^2*x^3*e^3 + 30*B*b^2*d*x^2*e^2 + 15*B*b^2*d^2*x*e + 3*B*b^2*d^3 + 40*B*a*b*x^2*e^3 + 20*A*b^2*x^2*e^3 + 20*B*a*b*d*x*e^2 + 10*A*b^2*d*x*e^2 + 4*B*a*b*d^2*e + 2*A*b^2*d^2*e + 15*B*a^2*x*e^3 + 30*A*a*b*x*e^3 + 3*B*a^2*d*e^2 + 6*A*a*b*d*e^2 + 12*A*a^2*e^3)*e^(-4)/(x*e + d)^5","A",0
1671,1,158,0,0.152763," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(20 \, B b^{2} x^{3} e^{3} + 15 \, B b^{2} d x^{2} e^{2} + 6 \, B b^{2} d^{2} x e + B b^{2} d^{3} + 30 \, B a b x^{2} e^{3} + 15 \, A b^{2} x^{2} e^{3} + 12 \, B a b d x e^{2} + 6 \, A b^{2} d x e^{2} + 2 \, B a b d^{2} e + A b^{2} d^{2} e + 12 \, B a^{2} x e^{3} + 24 \, A a b x e^{3} + 2 \, B a^{2} d e^{2} + 4 \, A a b d e^{2} + 10 \, A a^{2} e^{3}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(20*B*b^2*x^3*e^3 + 15*B*b^2*d*x^2*e^2 + 6*B*b^2*d^2*x*e + B*b^2*d^3 + 30*B*a*b*x^2*e^3 + 15*A*b^2*x^2*e^3 + 12*B*a*b*d*x*e^2 + 6*A*b^2*d*x*e^2 + 2*B*a*b*d^2*e + A*b^2*d^2*e + 12*B*a^2*x*e^3 + 24*A*a*b*x*e^3 + 2*B*a^2*d*e^2 + 4*A*a*b*d*e^2 + 10*A*a^2*e^3)*e^(-4)/(x*e + d)^6","A",0
1672,1,160,0,0.154005," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(105 \, B b^{2} x^{3} e^{3} + 63 \, B b^{2} d x^{2} e^{2} + 21 \, B b^{2} d^{2} x e + 3 \, B b^{2} d^{3} + 168 \, B a b x^{2} e^{3} + 84 \, A b^{2} x^{2} e^{3} + 56 \, B a b d x e^{2} + 28 \, A b^{2} d x e^{2} + 8 \, B a b d^{2} e + 4 \, A b^{2} d^{2} e + 70 \, B a^{2} x e^{3} + 140 \, A a b x e^{3} + 10 \, B a^{2} d e^{2} + 20 \, A a b d e^{2} + 60 \, A a^{2} e^{3}\right)} e^{\left(-4\right)}}{420 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/420*(105*B*b^2*x^3*e^3 + 63*B*b^2*d*x^2*e^2 + 21*B*b^2*d^2*x*e + 3*B*b^2*d^3 + 168*B*a*b*x^2*e^3 + 84*A*b^2*x^2*e^3 + 56*B*a*b*d*x*e^2 + 28*A*b^2*d*x*e^2 + 8*B*a*b*d^2*e + 4*A*b^2*d^2*e + 70*B*a^2*x*e^3 + 140*A*a*b*x*e^3 + 10*B*a^2*d*e^2 + 20*A*a*b*d*e^2 + 60*A*a^2*e^3)*e^(-4)/(x*e + d)^7","A",0
1673,1,1125,0,0.166871," ","integrate((B*x+A)*(e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{13} \, B b^{4} x^{13} e^{7} + \frac{7}{12} \, B b^{4} d x^{12} e^{6} + \frac{21}{11} \, B b^{4} d^{2} x^{11} e^{5} + \frac{7}{2} \, B b^{4} d^{3} x^{10} e^{4} + \frac{35}{9} \, B b^{4} d^{4} x^{9} e^{3} + \frac{21}{8} \, B b^{4} d^{5} x^{8} e^{2} + B b^{4} d^{6} x^{7} e + \frac{1}{6} \, B b^{4} d^{7} x^{6} + \frac{1}{3} \, B a b^{3} x^{12} e^{7} + \frac{1}{12} \, A b^{4} x^{12} e^{7} + \frac{28}{11} \, B a b^{3} d x^{11} e^{6} + \frac{7}{11} \, A b^{4} d x^{11} e^{6} + \frac{42}{5} \, B a b^{3} d^{2} x^{10} e^{5} + \frac{21}{10} \, A b^{4} d^{2} x^{10} e^{5} + \frac{140}{9} \, B a b^{3} d^{3} x^{9} e^{4} + \frac{35}{9} \, A b^{4} d^{3} x^{9} e^{4} + \frac{35}{2} \, B a b^{3} d^{4} x^{8} e^{3} + \frac{35}{8} \, A b^{4} d^{4} x^{8} e^{3} + 12 \, B a b^{3} d^{5} x^{7} e^{2} + 3 \, A b^{4} d^{5} x^{7} e^{2} + \frac{14}{3} \, B a b^{3} d^{6} x^{6} e + \frac{7}{6} \, A b^{4} d^{6} x^{6} e + \frac{4}{5} \, B a b^{3} d^{7} x^{5} + \frac{1}{5} \, A b^{4} d^{7} x^{5} + \frac{6}{11} \, B a^{2} b^{2} x^{11} e^{7} + \frac{4}{11} \, A a b^{3} x^{11} e^{7} + \frac{21}{5} \, B a^{2} b^{2} d x^{10} e^{6} + \frac{14}{5} \, A a b^{3} d x^{10} e^{6} + 14 \, B a^{2} b^{2} d^{2} x^{9} e^{5} + \frac{28}{3} \, A a b^{3} d^{2} x^{9} e^{5} + \frac{105}{4} \, B a^{2} b^{2} d^{3} x^{8} e^{4} + \frac{35}{2} \, A a b^{3} d^{3} x^{8} e^{4} + 30 \, B a^{2} b^{2} d^{4} x^{7} e^{3} + 20 \, A a b^{3} d^{4} x^{7} e^{3} + 21 \, B a^{2} b^{2} d^{5} x^{6} e^{2} + 14 \, A a b^{3} d^{5} x^{6} e^{2} + \frac{42}{5} \, B a^{2} b^{2} d^{6} x^{5} e + \frac{28}{5} \, A a b^{3} d^{6} x^{5} e + \frac{3}{2} \, B a^{2} b^{2} d^{7} x^{4} + A a b^{3} d^{7} x^{4} + \frac{2}{5} \, B a^{3} b x^{10} e^{7} + \frac{3}{5} \, A a^{2} b^{2} x^{10} e^{7} + \frac{28}{9} \, B a^{3} b d x^{9} e^{6} + \frac{14}{3} \, A a^{2} b^{2} d x^{9} e^{6} + \frac{21}{2} \, B a^{3} b d^{2} x^{8} e^{5} + \frac{63}{4} \, A a^{2} b^{2} d^{2} x^{8} e^{5} + 20 \, B a^{3} b d^{3} x^{7} e^{4} + 30 \, A a^{2} b^{2} d^{3} x^{7} e^{4} + \frac{70}{3} \, B a^{3} b d^{4} x^{6} e^{3} + 35 \, A a^{2} b^{2} d^{4} x^{6} e^{3} + \frac{84}{5} \, B a^{3} b d^{5} x^{5} e^{2} + \frac{126}{5} \, A a^{2} b^{2} d^{5} x^{5} e^{2} + 7 \, B a^{3} b d^{6} x^{4} e + \frac{21}{2} \, A a^{2} b^{2} d^{6} x^{4} e + \frac{4}{3} \, B a^{3} b d^{7} x^{3} + 2 \, A a^{2} b^{2} d^{7} x^{3} + \frac{1}{9} \, B a^{4} x^{9} e^{7} + \frac{4}{9} \, A a^{3} b x^{9} e^{7} + \frac{7}{8} \, B a^{4} d x^{8} e^{6} + \frac{7}{2} \, A a^{3} b d x^{8} e^{6} + 3 \, B a^{4} d^{2} x^{7} e^{5} + 12 \, A a^{3} b d^{2} x^{7} e^{5} + \frac{35}{6} \, B a^{4} d^{3} x^{6} e^{4} + \frac{70}{3} \, A a^{3} b d^{3} x^{6} e^{4} + 7 \, B a^{4} d^{4} x^{5} e^{3} + 28 \, A a^{3} b d^{4} x^{5} e^{3} + \frac{21}{4} \, B a^{4} d^{5} x^{4} e^{2} + 21 \, A a^{3} b d^{5} x^{4} e^{2} + \frac{7}{3} \, B a^{4} d^{6} x^{3} e + \frac{28}{3} \, A a^{3} b d^{6} x^{3} e + \frac{1}{2} \, B a^{4} d^{7} x^{2} + 2 \, A a^{3} b d^{7} x^{2} + \frac{1}{8} \, A a^{4} x^{8} e^{7} + A a^{4} d x^{7} e^{6} + \frac{7}{2} \, A a^{4} d^{2} x^{6} e^{5} + 7 \, A a^{4} d^{3} x^{5} e^{4} + \frac{35}{4} \, A a^{4} d^{4} x^{4} e^{3} + 7 \, A a^{4} d^{5} x^{3} e^{2} + \frac{7}{2} \, A a^{4} d^{6} x^{2} e + A a^{4} d^{7} x"," ",0,"1/13*B*b^4*x^13*e^7 + 7/12*B*b^4*d*x^12*e^6 + 21/11*B*b^4*d^2*x^11*e^5 + 7/2*B*b^4*d^3*x^10*e^4 + 35/9*B*b^4*d^4*x^9*e^3 + 21/8*B*b^4*d^5*x^8*e^2 + B*b^4*d^6*x^7*e + 1/6*B*b^4*d^7*x^6 + 1/3*B*a*b^3*x^12*e^7 + 1/12*A*b^4*x^12*e^7 + 28/11*B*a*b^3*d*x^11*e^6 + 7/11*A*b^4*d*x^11*e^6 + 42/5*B*a*b^3*d^2*x^10*e^5 + 21/10*A*b^4*d^2*x^10*e^5 + 140/9*B*a*b^3*d^3*x^9*e^4 + 35/9*A*b^4*d^3*x^9*e^4 + 35/2*B*a*b^3*d^4*x^8*e^3 + 35/8*A*b^4*d^4*x^8*e^3 + 12*B*a*b^3*d^5*x^7*e^2 + 3*A*b^4*d^5*x^7*e^2 + 14/3*B*a*b^3*d^6*x^6*e + 7/6*A*b^4*d^6*x^6*e + 4/5*B*a*b^3*d^7*x^5 + 1/5*A*b^4*d^7*x^5 + 6/11*B*a^2*b^2*x^11*e^7 + 4/11*A*a*b^3*x^11*e^7 + 21/5*B*a^2*b^2*d*x^10*e^6 + 14/5*A*a*b^3*d*x^10*e^6 + 14*B*a^2*b^2*d^2*x^9*e^5 + 28/3*A*a*b^3*d^2*x^9*e^5 + 105/4*B*a^2*b^2*d^3*x^8*e^4 + 35/2*A*a*b^3*d^3*x^8*e^4 + 30*B*a^2*b^2*d^4*x^7*e^3 + 20*A*a*b^3*d^4*x^7*e^3 + 21*B*a^2*b^2*d^5*x^6*e^2 + 14*A*a*b^3*d^5*x^6*e^2 + 42/5*B*a^2*b^2*d^6*x^5*e + 28/5*A*a*b^3*d^6*x^5*e + 3/2*B*a^2*b^2*d^7*x^4 + A*a*b^3*d^7*x^4 + 2/5*B*a^3*b*x^10*e^7 + 3/5*A*a^2*b^2*x^10*e^7 + 28/9*B*a^3*b*d*x^9*e^6 + 14/3*A*a^2*b^2*d*x^9*e^6 + 21/2*B*a^3*b*d^2*x^8*e^5 + 63/4*A*a^2*b^2*d^2*x^8*e^5 + 20*B*a^3*b*d^3*x^7*e^4 + 30*A*a^2*b^2*d^3*x^7*e^4 + 70/3*B*a^3*b*d^4*x^6*e^3 + 35*A*a^2*b^2*d^4*x^6*e^3 + 84/5*B*a^3*b*d^5*x^5*e^2 + 126/5*A*a^2*b^2*d^5*x^5*e^2 + 7*B*a^3*b*d^6*x^4*e + 21/2*A*a^2*b^2*d^6*x^4*e + 4/3*B*a^3*b*d^7*x^3 + 2*A*a^2*b^2*d^7*x^3 + 1/9*B*a^4*x^9*e^7 + 4/9*A*a^3*b*x^9*e^7 + 7/8*B*a^4*d*x^8*e^6 + 7/2*A*a^3*b*d*x^8*e^6 + 3*B*a^4*d^2*x^7*e^5 + 12*A*a^3*b*d^2*x^7*e^5 + 35/6*B*a^4*d^3*x^6*e^4 + 70/3*A*a^3*b*d^3*x^6*e^4 + 7*B*a^4*d^4*x^5*e^3 + 28*A*a^3*b*d^4*x^5*e^3 + 21/4*B*a^4*d^5*x^4*e^2 + 21*A*a^3*b*d^5*x^4*e^2 + 7/3*B*a^4*d^6*x^3*e + 28/3*A*a^3*b*d^6*x^3*e + 1/2*B*a^4*d^7*x^2 + 2*A*a^3*b*d^7*x^2 + 1/8*A*a^4*x^8*e^7 + A*a^4*d*x^7*e^6 + 7/2*A*a^4*d^2*x^6*e^5 + 7*A*a^4*d^3*x^5*e^4 + 35/4*A*a^4*d^4*x^4*e^3 + 7*A*a^4*d^5*x^3*e^2 + 7/2*A*a^4*d^6*x^2*e + A*a^4*d^7*x","B",0
1674,1,975,0,0.163634," ","integrate((B*x+A)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{12} \, B b^{4} x^{12} e^{6} + \frac{6}{11} \, B b^{4} d x^{11} e^{5} + \frac{3}{2} \, B b^{4} d^{2} x^{10} e^{4} + \frac{20}{9} \, B b^{4} d^{3} x^{9} e^{3} + \frac{15}{8} \, B b^{4} d^{4} x^{8} e^{2} + \frac{6}{7} \, B b^{4} d^{5} x^{7} e + \frac{1}{6} \, B b^{4} d^{6} x^{6} + \frac{4}{11} \, B a b^{3} x^{11} e^{6} + \frac{1}{11} \, A b^{4} x^{11} e^{6} + \frac{12}{5} \, B a b^{3} d x^{10} e^{5} + \frac{3}{5} \, A b^{4} d x^{10} e^{5} + \frac{20}{3} \, B a b^{3} d^{2} x^{9} e^{4} + \frac{5}{3} \, A b^{4} d^{2} x^{9} e^{4} + 10 \, B a b^{3} d^{3} x^{8} e^{3} + \frac{5}{2} \, A b^{4} d^{3} x^{8} e^{3} + \frac{60}{7} \, B a b^{3} d^{4} x^{7} e^{2} + \frac{15}{7} \, A b^{4} d^{4} x^{7} e^{2} + 4 \, B a b^{3} d^{5} x^{6} e + A b^{4} d^{5} x^{6} e + \frac{4}{5} \, B a b^{3} d^{6} x^{5} + \frac{1}{5} \, A b^{4} d^{6} x^{5} + \frac{3}{5} \, B a^{2} b^{2} x^{10} e^{6} + \frac{2}{5} \, A a b^{3} x^{10} e^{6} + 4 \, B a^{2} b^{2} d x^{9} e^{5} + \frac{8}{3} \, A a b^{3} d x^{9} e^{5} + \frac{45}{4} \, B a^{2} b^{2} d^{2} x^{8} e^{4} + \frac{15}{2} \, A a b^{3} d^{2} x^{8} e^{4} + \frac{120}{7} \, B a^{2} b^{2} d^{3} x^{7} e^{3} + \frac{80}{7} \, A a b^{3} d^{3} x^{7} e^{3} + 15 \, B a^{2} b^{2} d^{4} x^{6} e^{2} + 10 \, A a b^{3} d^{4} x^{6} e^{2} + \frac{36}{5} \, B a^{2} b^{2} d^{5} x^{5} e + \frac{24}{5} \, A a b^{3} d^{5} x^{5} e + \frac{3}{2} \, B a^{2} b^{2} d^{6} x^{4} + A a b^{3} d^{6} x^{4} + \frac{4}{9} \, B a^{3} b x^{9} e^{6} + \frac{2}{3} \, A a^{2} b^{2} x^{9} e^{6} + 3 \, B a^{3} b d x^{8} e^{5} + \frac{9}{2} \, A a^{2} b^{2} d x^{8} e^{5} + \frac{60}{7} \, B a^{3} b d^{2} x^{7} e^{4} + \frac{90}{7} \, A a^{2} b^{2} d^{2} x^{7} e^{4} + \frac{40}{3} \, B a^{3} b d^{3} x^{6} e^{3} + 20 \, A a^{2} b^{2} d^{3} x^{6} e^{3} + 12 \, B a^{3} b d^{4} x^{5} e^{2} + 18 \, A a^{2} b^{2} d^{4} x^{5} e^{2} + 6 \, B a^{3} b d^{5} x^{4} e + 9 \, A a^{2} b^{2} d^{5} x^{4} e + \frac{4}{3} \, B a^{3} b d^{6} x^{3} + 2 \, A a^{2} b^{2} d^{6} x^{3} + \frac{1}{8} \, B a^{4} x^{8} e^{6} + \frac{1}{2} \, A a^{3} b x^{8} e^{6} + \frac{6}{7} \, B a^{4} d x^{7} e^{5} + \frac{24}{7} \, A a^{3} b d x^{7} e^{5} + \frac{5}{2} \, B a^{4} d^{2} x^{6} e^{4} + 10 \, A a^{3} b d^{2} x^{6} e^{4} + 4 \, B a^{4} d^{3} x^{5} e^{3} + 16 \, A a^{3} b d^{3} x^{5} e^{3} + \frac{15}{4} \, B a^{4} d^{4} x^{4} e^{2} + 15 \, A a^{3} b d^{4} x^{4} e^{2} + 2 \, B a^{4} d^{5} x^{3} e + 8 \, A a^{3} b d^{5} x^{3} e + \frac{1}{2} \, B a^{4} d^{6} x^{2} + 2 \, A a^{3} b d^{6} x^{2} + \frac{1}{7} \, A a^{4} x^{7} e^{6} + A a^{4} d x^{6} e^{5} + 3 \, A a^{4} d^{2} x^{5} e^{4} + 5 \, A a^{4} d^{3} x^{4} e^{3} + 5 \, A a^{4} d^{4} x^{3} e^{2} + 3 \, A a^{4} d^{5} x^{2} e + A a^{4} d^{6} x"," ",0,"1/12*B*b^4*x^12*e^6 + 6/11*B*b^4*d*x^11*e^5 + 3/2*B*b^4*d^2*x^10*e^4 + 20/9*B*b^4*d^3*x^9*e^3 + 15/8*B*b^4*d^4*x^8*e^2 + 6/7*B*b^4*d^5*x^7*e + 1/6*B*b^4*d^6*x^6 + 4/11*B*a*b^3*x^11*e^6 + 1/11*A*b^4*x^11*e^6 + 12/5*B*a*b^3*d*x^10*e^5 + 3/5*A*b^4*d*x^10*e^5 + 20/3*B*a*b^3*d^2*x^9*e^4 + 5/3*A*b^4*d^2*x^9*e^4 + 10*B*a*b^3*d^3*x^8*e^3 + 5/2*A*b^4*d^3*x^8*e^3 + 60/7*B*a*b^3*d^4*x^7*e^2 + 15/7*A*b^4*d^4*x^7*e^2 + 4*B*a*b^3*d^5*x^6*e + A*b^4*d^5*x^6*e + 4/5*B*a*b^3*d^6*x^5 + 1/5*A*b^4*d^6*x^5 + 3/5*B*a^2*b^2*x^10*e^6 + 2/5*A*a*b^3*x^10*e^6 + 4*B*a^2*b^2*d*x^9*e^5 + 8/3*A*a*b^3*d*x^9*e^5 + 45/4*B*a^2*b^2*d^2*x^8*e^4 + 15/2*A*a*b^3*d^2*x^8*e^4 + 120/7*B*a^2*b^2*d^3*x^7*e^3 + 80/7*A*a*b^3*d^3*x^7*e^3 + 15*B*a^2*b^2*d^4*x^6*e^2 + 10*A*a*b^3*d^4*x^6*e^2 + 36/5*B*a^2*b^2*d^5*x^5*e + 24/5*A*a*b^3*d^5*x^5*e + 3/2*B*a^2*b^2*d^6*x^4 + A*a*b^3*d^6*x^4 + 4/9*B*a^3*b*x^9*e^6 + 2/3*A*a^2*b^2*x^9*e^6 + 3*B*a^3*b*d*x^8*e^5 + 9/2*A*a^2*b^2*d*x^8*e^5 + 60/7*B*a^3*b*d^2*x^7*e^4 + 90/7*A*a^2*b^2*d^2*x^7*e^4 + 40/3*B*a^3*b*d^3*x^6*e^3 + 20*A*a^2*b^2*d^3*x^6*e^3 + 12*B*a^3*b*d^4*x^5*e^2 + 18*A*a^2*b^2*d^4*x^5*e^2 + 6*B*a^3*b*d^5*x^4*e + 9*A*a^2*b^2*d^5*x^4*e + 4/3*B*a^3*b*d^6*x^3 + 2*A*a^2*b^2*d^6*x^3 + 1/8*B*a^4*x^8*e^6 + 1/2*A*a^3*b*x^8*e^6 + 6/7*B*a^4*d*x^7*e^5 + 24/7*A*a^3*b*d*x^7*e^5 + 5/2*B*a^4*d^2*x^6*e^4 + 10*A*a^3*b*d^2*x^6*e^4 + 4*B*a^4*d^3*x^5*e^3 + 16*A*a^3*b*d^3*x^5*e^3 + 15/4*B*a^4*d^4*x^4*e^2 + 15*A*a^3*b*d^4*x^4*e^2 + 2*B*a^4*d^5*x^3*e + 8*A*a^3*b*d^5*x^3*e + 1/2*B*a^4*d^6*x^2 + 2*A*a^3*b*d^6*x^2 + 1/7*A*a^4*x^7*e^6 + A*a^4*d*x^6*e^5 + 3*A*a^4*d^2*x^5*e^4 + 5*A*a^4*d^3*x^4*e^3 + 5*A*a^4*d^4*x^3*e^2 + 3*A*a^4*d^5*x^2*e + A*a^4*d^6*x","B",0
1675,1,826,0,0.199909," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{11} \, B b^{4} x^{11} e^{5} + \frac{1}{2} \, B b^{4} d x^{10} e^{4} + \frac{10}{9} \, B b^{4} d^{2} x^{9} e^{3} + \frac{5}{4} \, B b^{4} d^{3} x^{8} e^{2} + \frac{5}{7} \, B b^{4} d^{4} x^{7} e + \frac{1}{6} \, B b^{4} d^{5} x^{6} + \frac{2}{5} \, B a b^{3} x^{10} e^{5} + \frac{1}{10} \, A b^{4} x^{10} e^{5} + \frac{20}{9} \, B a b^{3} d x^{9} e^{4} + \frac{5}{9} \, A b^{4} d x^{9} e^{4} + 5 \, B a b^{3} d^{2} x^{8} e^{3} + \frac{5}{4} \, A b^{4} d^{2} x^{8} e^{3} + \frac{40}{7} \, B a b^{3} d^{3} x^{7} e^{2} + \frac{10}{7} \, A b^{4} d^{3} x^{7} e^{2} + \frac{10}{3} \, B a b^{3} d^{4} x^{6} e + \frac{5}{6} \, A b^{4} d^{4} x^{6} e + \frac{4}{5} \, B a b^{3} d^{5} x^{5} + \frac{1}{5} \, A b^{4} d^{5} x^{5} + \frac{2}{3} \, B a^{2} b^{2} x^{9} e^{5} + \frac{4}{9} \, A a b^{3} x^{9} e^{5} + \frac{15}{4} \, B a^{2} b^{2} d x^{8} e^{4} + \frac{5}{2} \, A a b^{3} d x^{8} e^{4} + \frac{60}{7} \, B a^{2} b^{2} d^{2} x^{7} e^{3} + \frac{40}{7} \, A a b^{3} d^{2} x^{7} e^{3} + 10 \, B a^{2} b^{2} d^{3} x^{6} e^{2} + \frac{20}{3} \, A a b^{3} d^{3} x^{6} e^{2} + 6 \, B a^{2} b^{2} d^{4} x^{5} e + 4 \, A a b^{3} d^{4} x^{5} e + \frac{3}{2} \, B a^{2} b^{2} d^{5} x^{4} + A a b^{3} d^{5} x^{4} + \frac{1}{2} \, B a^{3} b x^{8} e^{5} + \frac{3}{4} \, A a^{2} b^{2} x^{8} e^{5} + \frac{20}{7} \, B a^{3} b d x^{7} e^{4} + \frac{30}{7} \, A a^{2} b^{2} d x^{7} e^{4} + \frac{20}{3} \, B a^{3} b d^{2} x^{6} e^{3} + 10 \, A a^{2} b^{2} d^{2} x^{6} e^{3} + 8 \, B a^{3} b d^{3} x^{5} e^{2} + 12 \, A a^{2} b^{2} d^{3} x^{5} e^{2} + 5 \, B a^{3} b d^{4} x^{4} e + \frac{15}{2} \, A a^{2} b^{2} d^{4} x^{4} e + \frac{4}{3} \, B a^{3} b d^{5} x^{3} + 2 \, A a^{2} b^{2} d^{5} x^{3} + \frac{1}{7} \, B a^{4} x^{7} e^{5} + \frac{4}{7} \, A a^{3} b x^{7} e^{5} + \frac{5}{6} \, B a^{4} d x^{6} e^{4} + \frac{10}{3} \, A a^{3} b d x^{6} e^{4} + 2 \, B a^{4} d^{2} x^{5} e^{3} + 8 \, A a^{3} b d^{2} x^{5} e^{3} + \frac{5}{2} \, B a^{4} d^{3} x^{4} e^{2} + 10 \, A a^{3} b d^{3} x^{4} e^{2} + \frac{5}{3} \, B a^{4} d^{4} x^{3} e + \frac{20}{3} \, A a^{3} b d^{4} x^{3} e + \frac{1}{2} \, B a^{4} d^{5} x^{2} + 2 \, A a^{3} b d^{5} x^{2} + \frac{1}{6} \, A a^{4} x^{6} e^{5} + A a^{4} d x^{5} e^{4} + \frac{5}{2} \, A a^{4} d^{2} x^{4} e^{3} + \frac{10}{3} \, A a^{4} d^{3} x^{3} e^{2} + \frac{5}{2} \, A a^{4} d^{4} x^{2} e + A a^{4} d^{5} x"," ",0,"1/11*B*b^4*x^11*e^5 + 1/2*B*b^4*d*x^10*e^4 + 10/9*B*b^4*d^2*x^9*e^3 + 5/4*B*b^4*d^3*x^8*e^2 + 5/7*B*b^4*d^4*x^7*e + 1/6*B*b^4*d^5*x^6 + 2/5*B*a*b^3*x^10*e^5 + 1/10*A*b^4*x^10*e^5 + 20/9*B*a*b^3*d*x^9*e^4 + 5/9*A*b^4*d*x^9*e^4 + 5*B*a*b^3*d^2*x^8*e^3 + 5/4*A*b^4*d^2*x^8*e^3 + 40/7*B*a*b^3*d^3*x^7*e^2 + 10/7*A*b^4*d^3*x^7*e^2 + 10/3*B*a*b^3*d^4*x^6*e + 5/6*A*b^4*d^4*x^6*e + 4/5*B*a*b^3*d^5*x^5 + 1/5*A*b^4*d^5*x^5 + 2/3*B*a^2*b^2*x^9*e^5 + 4/9*A*a*b^3*x^9*e^5 + 15/4*B*a^2*b^2*d*x^8*e^4 + 5/2*A*a*b^3*d*x^8*e^4 + 60/7*B*a^2*b^2*d^2*x^7*e^3 + 40/7*A*a*b^3*d^2*x^7*e^3 + 10*B*a^2*b^2*d^3*x^6*e^2 + 20/3*A*a*b^3*d^3*x^6*e^2 + 6*B*a^2*b^2*d^4*x^5*e + 4*A*a*b^3*d^4*x^5*e + 3/2*B*a^2*b^2*d^5*x^4 + A*a*b^3*d^5*x^4 + 1/2*B*a^3*b*x^8*e^5 + 3/4*A*a^2*b^2*x^8*e^5 + 20/7*B*a^3*b*d*x^7*e^4 + 30/7*A*a^2*b^2*d*x^7*e^4 + 20/3*B*a^3*b*d^2*x^6*e^3 + 10*A*a^2*b^2*d^2*x^6*e^3 + 8*B*a^3*b*d^3*x^5*e^2 + 12*A*a^2*b^2*d^3*x^5*e^2 + 5*B*a^3*b*d^4*x^4*e + 15/2*A*a^2*b^2*d^4*x^4*e + 4/3*B*a^3*b*d^5*x^3 + 2*A*a^2*b^2*d^5*x^3 + 1/7*B*a^4*x^7*e^5 + 4/7*A*a^3*b*x^7*e^5 + 5/6*B*a^4*d*x^6*e^4 + 10/3*A*a^3*b*d*x^6*e^4 + 2*B*a^4*d^2*x^5*e^3 + 8*A*a^3*b*d^2*x^5*e^3 + 5/2*B*a^4*d^3*x^4*e^2 + 10*A*a^3*b*d^3*x^4*e^2 + 5/3*B*a^4*d^4*x^3*e + 20/3*A*a^3*b*d^4*x^3*e + 1/2*B*a^4*d^5*x^2 + 2*A*a^3*b*d^5*x^2 + 1/6*A*a^4*x^6*e^5 + A*a^4*d*x^5*e^4 + 5/2*A*a^4*d^2*x^4*e^3 + 10/3*A*a^4*d^3*x^3*e^2 + 5/2*A*a^4*d^4*x^2*e + A*a^4*d^5*x","B",0
1676,1,676,0,0.161818," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{10} \, B b^{4} x^{10} e^{4} + \frac{4}{9} \, B b^{4} d x^{9} e^{3} + \frac{3}{4} \, B b^{4} d^{2} x^{8} e^{2} + \frac{4}{7} \, B b^{4} d^{3} x^{7} e + \frac{1}{6} \, B b^{4} d^{4} x^{6} + \frac{4}{9} \, B a b^{3} x^{9} e^{4} + \frac{1}{9} \, A b^{4} x^{9} e^{4} + 2 \, B a b^{3} d x^{8} e^{3} + \frac{1}{2} \, A b^{4} d x^{8} e^{3} + \frac{24}{7} \, B a b^{3} d^{2} x^{7} e^{2} + \frac{6}{7} \, A b^{4} d^{2} x^{7} e^{2} + \frac{8}{3} \, B a b^{3} d^{3} x^{6} e + \frac{2}{3} \, A b^{4} d^{3} x^{6} e + \frac{4}{5} \, B a b^{3} d^{4} x^{5} + \frac{1}{5} \, A b^{4} d^{4} x^{5} + \frac{3}{4} \, B a^{2} b^{2} x^{8} e^{4} + \frac{1}{2} \, A a b^{3} x^{8} e^{4} + \frac{24}{7} \, B a^{2} b^{2} d x^{7} e^{3} + \frac{16}{7} \, A a b^{3} d x^{7} e^{3} + 6 \, B a^{2} b^{2} d^{2} x^{6} e^{2} + 4 \, A a b^{3} d^{2} x^{6} e^{2} + \frac{24}{5} \, B a^{2} b^{2} d^{3} x^{5} e + \frac{16}{5} \, A a b^{3} d^{3} x^{5} e + \frac{3}{2} \, B a^{2} b^{2} d^{4} x^{4} + A a b^{3} d^{4} x^{4} + \frac{4}{7} \, B a^{3} b x^{7} e^{4} + \frac{6}{7} \, A a^{2} b^{2} x^{7} e^{4} + \frac{8}{3} \, B a^{3} b d x^{6} e^{3} + 4 \, A a^{2} b^{2} d x^{6} e^{3} + \frac{24}{5} \, B a^{3} b d^{2} x^{5} e^{2} + \frac{36}{5} \, A a^{2} b^{2} d^{2} x^{5} e^{2} + 4 \, B a^{3} b d^{3} x^{4} e + 6 \, A a^{2} b^{2} d^{3} x^{4} e + \frac{4}{3} \, B a^{3} b d^{4} x^{3} + 2 \, A a^{2} b^{2} d^{4} x^{3} + \frac{1}{6} \, B a^{4} x^{6} e^{4} + \frac{2}{3} \, A a^{3} b x^{6} e^{4} + \frac{4}{5} \, B a^{4} d x^{5} e^{3} + \frac{16}{5} \, A a^{3} b d x^{5} e^{3} + \frac{3}{2} \, B a^{4} d^{2} x^{4} e^{2} + 6 \, A a^{3} b d^{2} x^{4} e^{2} + \frac{4}{3} \, B a^{4} d^{3} x^{3} e + \frac{16}{3} \, A a^{3} b d^{3} x^{3} e + \frac{1}{2} \, B a^{4} d^{4} x^{2} + 2 \, A a^{3} b d^{4} x^{2} + \frac{1}{5} \, A a^{4} x^{5} e^{4} + A a^{4} d x^{4} e^{3} + 2 \, A a^{4} d^{2} x^{3} e^{2} + 2 \, A a^{4} d^{3} x^{2} e + A a^{4} d^{4} x"," ",0,"1/10*B*b^4*x^10*e^4 + 4/9*B*b^4*d*x^9*e^3 + 3/4*B*b^4*d^2*x^8*e^2 + 4/7*B*b^4*d^3*x^7*e + 1/6*B*b^4*d^4*x^6 + 4/9*B*a*b^3*x^9*e^4 + 1/9*A*b^4*x^9*e^4 + 2*B*a*b^3*d*x^8*e^3 + 1/2*A*b^4*d*x^8*e^3 + 24/7*B*a*b^3*d^2*x^7*e^2 + 6/7*A*b^4*d^2*x^7*e^2 + 8/3*B*a*b^3*d^3*x^6*e + 2/3*A*b^4*d^3*x^6*e + 4/5*B*a*b^3*d^4*x^5 + 1/5*A*b^4*d^4*x^5 + 3/4*B*a^2*b^2*x^8*e^4 + 1/2*A*a*b^3*x^8*e^4 + 24/7*B*a^2*b^2*d*x^7*e^3 + 16/7*A*a*b^3*d*x^7*e^3 + 6*B*a^2*b^2*d^2*x^6*e^2 + 4*A*a*b^3*d^2*x^6*e^2 + 24/5*B*a^2*b^2*d^3*x^5*e + 16/5*A*a*b^3*d^3*x^5*e + 3/2*B*a^2*b^2*d^4*x^4 + A*a*b^3*d^4*x^4 + 4/7*B*a^3*b*x^7*e^4 + 6/7*A*a^2*b^2*x^7*e^4 + 8/3*B*a^3*b*d*x^6*e^3 + 4*A*a^2*b^2*d*x^6*e^3 + 24/5*B*a^3*b*d^2*x^5*e^2 + 36/5*A*a^2*b^2*d^2*x^5*e^2 + 4*B*a^3*b*d^3*x^4*e + 6*A*a^2*b^2*d^3*x^4*e + 4/3*B*a^3*b*d^4*x^3 + 2*A*a^2*b^2*d^4*x^3 + 1/6*B*a^4*x^6*e^4 + 2/3*A*a^3*b*x^6*e^4 + 4/5*B*a^4*d*x^5*e^3 + 16/5*A*a^3*b*d*x^5*e^3 + 3/2*B*a^4*d^2*x^4*e^2 + 6*A*a^3*b*d^2*x^4*e^2 + 4/3*B*a^4*d^3*x^3*e + 16/3*A*a^3*b*d^3*x^3*e + 1/2*B*a^4*d^4*x^2 + 2*A*a^3*b*d^4*x^2 + 1/5*A*a^4*x^5*e^4 + A*a^4*d*x^4*e^3 + 2*A*a^4*d^2*x^3*e^2 + 2*A*a^4*d^3*x^2*e + A*a^4*d^4*x","B",0
1677,1,524,0,0.174122," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{9} \, B b^{4} x^{9} e^{3} + \frac{3}{8} \, B b^{4} d x^{8} e^{2} + \frac{3}{7} \, B b^{4} d^{2} x^{7} e + \frac{1}{6} \, B b^{4} d^{3} x^{6} + \frac{1}{2} \, B a b^{3} x^{8} e^{3} + \frac{1}{8} \, A b^{4} x^{8} e^{3} + \frac{12}{7} \, B a b^{3} d x^{7} e^{2} + \frac{3}{7} \, A b^{4} d x^{7} e^{2} + 2 \, B a b^{3} d^{2} x^{6} e + \frac{1}{2} \, A b^{4} d^{2} x^{6} e + \frac{4}{5} \, B a b^{3} d^{3} x^{5} + \frac{1}{5} \, A b^{4} d^{3} x^{5} + \frac{6}{7} \, B a^{2} b^{2} x^{7} e^{3} + \frac{4}{7} \, A a b^{3} x^{7} e^{3} + 3 \, B a^{2} b^{2} d x^{6} e^{2} + 2 \, A a b^{3} d x^{6} e^{2} + \frac{18}{5} \, B a^{2} b^{2} d^{2} x^{5} e + \frac{12}{5} \, A a b^{3} d^{2} x^{5} e + \frac{3}{2} \, B a^{2} b^{2} d^{3} x^{4} + A a b^{3} d^{3} x^{4} + \frac{2}{3} \, B a^{3} b x^{6} e^{3} + A a^{2} b^{2} x^{6} e^{3} + \frac{12}{5} \, B a^{3} b d x^{5} e^{2} + \frac{18}{5} \, A a^{2} b^{2} d x^{5} e^{2} + 3 \, B a^{3} b d^{2} x^{4} e + \frac{9}{2} \, A a^{2} b^{2} d^{2} x^{4} e + \frac{4}{3} \, B a^{3} b d^{3} x^{3} + 2 \, A a^{2} b^{2} d^{3} x^{3} + \frac{1}{5} \, B a^{4} x^{5} e^{3} + \frac{4}{5} \, A a^{3} b x^{5} e^{3} + \frac{3}{4} \, B a^{4} d x^{4} e^{2} + 3 \, A a^{3} b d x^{4} e^{2} + B a^{4} d^{2} x^{3} e + 4 \, A a^{3} b d^{2} x^{3} e + \frac{1}{2} \, B a^{4} d^{3} x^{2} + 2 \, A a^{3} b d^{3} x^{2} + \frac{1}{4} \, A a^{4} x^{4} e^{3} + A a^{4} d x^{3} e^{2} + \frac{3}{2} \, A a^{4} d^{2} x^{2} e + A a^{4} d^{3} x"," ",0,"1/9*B*b^4*x^9*e^3 + 3/8*B*b^4*d*x^8*e^2 + 3/7*B*b^4*d^2*x^7*e + 1/6*B*b^4*d^3*x^6 + 1/2*B*a*b^3*x^8*e^3 + 1/8*A*b^4*x^8*e^3 + 12/7*B*a*b^3*d*x^7*e^2 + 3/7*A*b^4*d*x^7*e^2 + 2*B*a*b^3*d^2*x^6*e + 1/2*A*b^4*d^2*x^6*e + 4/5*B*a*b^3*d^3*x^5 + 1/5*A*b^4*d^3*x^5 + 6/7*B*a^2*b^2*x^7*e^3 + 4/7*A*a*b^3*x^7*e^3 + 3*B*a^2*b^2*d*x^6*e^2 + 2*A*a*b^3*d*x^6*e^2 + 18/5*B*a^2*b^2*d^2*x^5*e + 12/5*A*a*b^3*d^2*x^5*e + 3/2*B*a^2*b^2*d^3*x^4 + A*a*b^3*d^3*x^4 + 2/3*B*a^3*b*x^6*e^3 + A*a^2*b^2*x^6*e^3 + 12/5*B*a^3*b*d*x^5*e^2 + 18/5*A*a^2*b^2*d*x^5*e^2 + 3*B*a^3*b*d^2*x^4*e + 9/2*A*a^2*b^2*d^2*x^4*e + 4/3*B*a^3*b*d^3*x^3 + 2*A*a^2*b^2*d^3*x^3 + 1/5*B*a^4*x^5*e^3 + 4/5*A*a^3*b*x^5*e^3 + 3/4*B*a^4*d*x^4*e^2 + 3*A*a^3*b*d*x^4*e^2 + B*a^4*d^2*x^3*e + 4*A*a^3*b*d^2*x^3*e + 1/2*B*a^4*d^3*x^2 + 2*A*a^3*b*d^3*x^2 + 1/4*A*a^4*x^4*e^3 + A*a^4*d*x^3*e^2 + 3/2*A*a^4*d^2*x^2*e + A*a^4*d^3*x","B",0
1678,1,374,0,0.168421," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{8} \, B b^{4} x^{8} e^{2} + \frac{2}{7} \, B b^{4} d x^{7} e + \frac{1}{6} \, B b^{4} d^{2} x^{6} + \frac{4}{7} \, B a b^{3} x^{7} e^{2} + \frac{1}{7} \, A b^{4} x^{7} e^{2} + \frac{4}{3} \, B a b^{3} d x^{6} e + \frac{1}{3} \, A b^{4} d x^{6} e + \frac{4}{5} \, B a b^{3} d^{2} x^{5} + \frac{1}{5} \, A b^{4} d^{2} x^{5} + B a^{2} b^{2} x^{6} e^{2} + \frac{2}{3} \, A a b^{3} x^{6} e^{2} + \frac{12}{5} \, B a^{2} b^{2} d x^{5} e + \frac{8}{5} \, A a b^{3} d x^{5} e + \frac{3}{2} \, B a^{2} b^{2} d^{2} x^{4} + A a b^{3} d^{2} x^{4} + \frac{4}{5} \, B a^{3} b x^{5} e^{2} + \frac{6}{5} \, A a^{2} b^{2} x^{5} e^{2} + 2 \, B a^{3} b d x^{4} e + 3 \, A a^{2} b^{2} d x^{4} e + \frac{4}{3} \, B a^{3} b d^{2} x^{3} + 2 \, A a^{2} b^{2} d^{2} x^{3} + \frac{1}{4} \, B a^{4} x^{4} e^{2} + A a^{3} b x^{4} e^{2} + \frac{2}{3} \, B a^{4} d x^{3} e + \frac{8}{3} \, A a^{3} b d x^{3} e + \frac{1}{2} \, B a^{4} d^{2} x^{2} + 2 \, A a^{3} b d^{2} x^{2} + \frac{1}{3} \, A a^{4} x^{3} e^{2} + A a^{4} d x^{2} e + A a^{4} d^{2} x"," ",0,"1/8*B*b^4*x^8*e^2 + 2/7*B*b^4*d*x^7*e + 1/6*B*b^4*d^2*x^6 + 4/7*B*a*b^3*x^7*e^2 + 1/7*A*b^4*x^7*e^2 + 4/3*B*a*b^3*d*x^6*e + 1/3*A*b^4*d*x^6*e + 4/5*B*a*b^3*d^2*x^5 + 1/5*A*b^4*d^2*x^5 + B*a^2*b^2*x^6*e^2 + 2/3*A*a*b^3*x^6*e^2 + 12/5*B*a^2*b^2*d*x^5*e + 8/5*A*a*b^3*d*x^5*e + 3/2*B*a^2*b^2*d^2*x^4 + A*a*b^3*d^2*x^4 + 4/5*B*a^3*b*x^5*e^2 + 6/5*A*a^2*b^2*x^5*e^2 + 2*B*a^3*b*d*x^4*e + 3*A*a^2*b^2*d*x^4*e + 4/3*B*a^3*b*d^2*x^3 + 2*A*a^2*b^2*d^2*x^3 + 1/4*B*a^4*x^4*e^2 + A*a^3*b*x^4*e^2 + 2/3*B*a^4*d*x^3*e + 8/3*A*a^3*b*d*x^3*e + 1/2*B*a^4*d^2*x^2 + 2*A*a^3*b*d^2*x^2 + 1/3*A*a^4*x^3*e^2 + A*a^4*d*x^2*e + A*a^4*d^2*x","B",0
1679,1,226,0,0.190167," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{7} \, B b^{4} x^{7} e + \frac{1}{6} \, B b^{4} d x^{6} + \frac{2}{3} \, B a b^{3} x^{6} e + \frac{1}{6} \, A b^{4} x^{6} e + \frac{4}{5} \, B a b^{3} d x^{5} + \frac{1}{5} \, A b^{4} d x^{5} + \frac{6}{5} \, B a^{2} b^{2} x^{5} e + \frac{4}{5} \, A a b^{3} x^{5} e + \frac{3}{2} \, B a^{2} b^{2} d x^{4} + A a b^{3} d x^{4} + B a^{3} b x^{4} e + \frac{3}{2} \, A a^{2} b^{2} x^{4} e + \frac{4}{3} \, B a^{3} b d x^{3} + 2 \, A a^{2} b^{2} d x^{3} + \frac{1}{3} \, B a^{4} x^{3} e + \frac{4}{3} \, A a^{3} b x^{3} e + \frac{1}{2} \, B a^{4} d x^{2} + 2 \, A a^{3} b d x^{2} + \frac{1}{2} \, A a^{4} x^{2} e + A a^{4} d x"," ",0,"1/7*B*b^4*x^7*e + 1/6*B*b^4*d*x^6 + 2/3*B*a*b^3*x^6*e + 1/6*A*b^4*x^6*e + 4/5*B*a*b^3*d*x^5 + 1/5*A*b^4*d*x^5 + 6/5*B*a^2*b^2*x^5*e + 4/5*A*a*b^3*x^5*e + 3/2*B*a^2*b^2*d*x^4 + A*a*b^3*d*x^4 + B*a^3*b*x^4*e + 3/2*A*a^2*b^2*x^4*e + 4/3*B*a^3*b*d*x^3 + 2*A*a^2*b^2*d*x^3 + 1/3*B*a^4*x^3*e + 4/3*A*a^3*b*x^3*e + 1/2*B*a^4*d*x^2 + 2*A*a^3*b*d*x^2 + 1/2*A*a^4*x^2*e + A*a^4*d*x","B",0
1680,1,97,0,0.166789," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, B b^{4} x^{6} + \frac{4}{5} \, B a b^{3} x^{5} + \frac{1}{5} \, A b^{4} x^{5} + \frac{3}{2} \, B a^{2} b^{2} x^{4} + A a b^{3} x^{4} + \frac{4}{3} \, B a^{3} b x^{3} + 2 \, A a^{2} b^{2} x^{3} + \frac{1}{2} \, B a^{4} x^{2} + 2 \, A a^{3} b x^{2} + A a^{4} x"," ",0,"1/6*B*b^4*x^6 + 4/5*B*a*b^3*x^5 + 1/5*A*b^4*x^5 + 3/2*B*a^2*b^2*x^4 + A*a*b^3*x^4 + 4/3*B*a^3*b*x^3 + 2*A*a^2*b^2*x^3 + 1/2*B*a^4*x^2 + 2*A*a^3*b*x^2 + A*a^4*x","B",0
1681,1,442,0,0.199386," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d),x, algorithm=""giac"")","-{\left(B b^{4} d^{5} - 4 \, B a b^{3} d^{4} e - A b^{4} d^{4} e + 6 \, B a^{2} b^{2} d^{3} e^{2} + 4 \, A a b^{3} d^{3} e^{2} - 4 \, B a^{3} b d^{2} e^{3} - 6 \, A a^{2} b^{2} d^{2} e^{3} + B a^{4} d e^{4} + 4 \, A a^{3} b d e^{4} - A a^{4} e^{5}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(12 \, B b^{4} x^{5} e^{4} - 15 \, B b^{4} d x^{4} e^{3} + 20 \, B b^{4} d^{2} x^{3} e^{2} - 30 \, B b^{4} d^{3} x^{2} e + 60 \, B b^{4} d^{4} x + 60 \, B a b^{3} x^{4} e^{4} + 15 \, A b^{4} x^{4} e^{4} - 80 \, B a b^{3} d x^{3} e^{3} - 20 \, A b^{4} d x^{3} e^{3} + 120 \, B a b^{3} d^{2} x^{2} e^{2} + 30 \, A b^{4} d^{2} x^{2} e^{2} - 240 \, B a b^{3} d^{3} x e - 60 \, A b^{4} d^{3} x e + 120 \, B a^{2} b^{2} x^{3} e^{4} + 80 \, A a b^{3} x^{3} e^{4} - 180 \, B a^{2} b^{2} d x^{2} e^{3} - 120 \, A a b^{3} d x^{2} e^{3} + 360 \, B a^{2} b^{2} d^{2} x e^{2} + 240 \, A a b^{3} d^{2} x e^{2} + 120 \, B a^{3} b x^{2} e^{4} + 180 \, A a^{2} b^{2} x^{2} e^{4} - 240 \, B a^{3} b d x e^{3} - 360 \, A a^{2} b^{2} d x e^{3} + 60 \, B a^{4} x e^{4} + 240 \, A a^{3} b x e^{4}\right)} e^{\left(-5\right)}"," ",0,"-(B*b^4*d^5 - 4*B*a*b^3*d^4*e - A*b^4*d^4*e + 6*B*a^2*b^2*d^3*e^2 + 4*A*a*b^3*d^3*e^2 - 4*B*a^3*b*d^2*e^3 - 6*A*a^2*b^2*d^2*e^3 + B*a^4*d*e^4 + 4*A*a^3*b*d*e^4 - A*a^4*e^5)*e^(-6)*log(abs(x*e + d)) + 1/60*(12*B*b^4*x^5*e^4 - 15*B*b^4*d*x^4*e^3 + 20*B*b^4*d^2*x^3*e^2 - 30*B*b^4*d^3*x^2*e + 60*B*b^4*d^4*x + 60*B*a*b^3*x^4*e^4 + 15*A*b^4*x^4*e^4 - 80*B*a*b^3*d*x^3*e^3 - 20*A*b^4*d*x^3*e^3 + 120*B*a*b^3*d^2*x^2*e^2 + 30*A*b^4*d^2*x^2*e^2 - 240*B*a*b^3*d^3*x*e - 60*A*b^4*d^3*x*e + 120*B*a^2*b^2*x^3*e^4 + 80*A*a*b^3*x^3*e^4 - 180*B*a^2*b^2*d*x^2*e^3 - 120*A*a*b^3*d*x^2*e^3 + 360*B*a^2*b^2*d^2*x*e^2 + 240*A*a*b^3*d^2*x*e^2 + 120*B*a^3*b*x^2*e^4 + 180*A*a^2*b^2*x^2*e^4 - 240*B*a^3*b*d*x*e^3 - 360*A*a^2*b^2*d*x*e^3 + 60*B*a^4*x*e^4 + 240*A*a^3*b*x*e^4)*e^(-5)","B",0
1682,1,526,0,0.192067," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, B b^{4} - \frac{4 \, {\left(5 \, B b^{4} d e - 4 \, B a b^{3} e^{2} - A b^{4} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{12 \, {\left(5 \, B b^{4} d^{2} e^{2} - 8 \, B a b^{3} d e^{3} - 2 \, A b^{4} d e^{3} + 3 \, B a^{2} b^{2} e^{4} + 2 \, A a b^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{24 \, {\left(5 \, B b^{4} d^{3} e^{3} - 12 \, B a b^{3} d^{2} e^{4} - 3 \, A b^{4} d^{2} e^{4} + 9 \, B a^{2} b^{2} d e^{5} + 6 \, A a b^{3} d e^{5} - 2 \, B a^{3} b e^{6} - 3 \, A a^{2} b^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{4} e^{\left(-6\right)} - {\left(5 \, B b^{4} d^{4} - 16 \, B a b^{3} d^{3} e - 4 \, A b^{4} d^{3} e + 18 \, B a^{2} b^{2} d^{2} e^{2} + 12 \, A a b^{3} d^{2} e^{2} - 8 \, B a^{3} b d e^{3} - 12 \, A a^{2} b^{2} d e^{3} + B a^{4} e^{4} + 4 \, A a^{3} b e^{4}\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B b^{4} d^{5} e^{4}}{x e + d} - \frac{4 \, B a b^{3} d^{4} e^{5}}{x e + d} - \frac{A b^{4} d^{4} e^{5}}{x e + d} + \frac{6 \, B a^{2} b^{2} d^{3} e^{6}}{x e + d} + \frac{4 \, A a b^{3} d^{3} e^{6}}{x e + d} - \frac{4 \, B a^{3} b d^{2} e^{7}}{x e + d} - \frac{6 \, A a^{2} b^{2} d^{2} e^{7}}{x e + d} + \frac{B a^{4} d e^{8}}{x e + d} + \frac{4 \, A a^{3} b d e^{8}}{x e + d} - \frac{A a^{4} e^{9}}{x e + d}\right)} e^{\left(-10\right)}"," ",0,"1/12*(3*B*b^4 - 4*(5*B*b^4*d*e - 4*B*a*b^3*e^2 - A*b^4*e^2)*e^(-1)/(x*e + d) + 12*(5*B*b^4*d^2*e^2 - 8*B*a*b^3*d*e^3 - 2*A*b^4*d*e^3 + 3*B*a^2*b^2*e^4 + 2*A*a*b^3*e^4)*e^(-2)/(x*e + d)^2 - 24*(5*B*b^4*d^3*e^3 - 12*B*a*b^3*d^2*e^4 - 3*A*b^4*d^2*e^4 + 9*B*a^2*b^2*d*e^5 + 6*A*a*b^3*d*e^5 - 2*B*a^3*b*e^6 - 3*A*a^2*b^2*e^6)*e^(-3)/(x*e + d)^3)*(x*e + d)^4*e^(-6) - (5*B*b^4*d^4 - 16*B*a*b^3*d^3*e - 4*A*b^4*d^3*e + 18*B*a^2*b^2*d^2*e^2 + 12*A*a*b^3*d^2*e^2 - 8*B*a^3*b*d*e^3 - 12*A*a^2*b^2*d*e^3 + B*a^4*e^4 + 4*A*a^3*b*e^4)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*b^4*d^5*e^4/(x*e + d) - 4*B*a*b^3*d^4*e^5/(x*e + d) - A*b^4*d^4*e^5/(x*e + d) + 6*B*a^2*b^2*d^3*e^6/(x*e + d) + 4*A*a*b^3*d^3*e^6/(x*e + d) - 4*B*a^3*b*d^2*e^7/(x*e + d) - 6*A*a^2*b^2*d^2*e^7/(x*e + d) + B*a^4*d*e^8/(x*e + d) + 4*A*a^3*b*d*e^8/(x*e + d) - A*a^4*e^9/(x*e + d))*e^(-10)","B",0
1683,1,418,0,0.166284," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^3,x, algorithm=""giac"")","-2 \, {\left(5 \, B b^{4} d^{3} - 12 \, B a b^{3} d^{2} e - 3 \, A b^{4} d^{2} e + 9 \, B a^{2} b^{2} d e^{2} + 6 \, A a b^{3} d e^{2} - 2 \, B a^{3} b e^{3} - 3 \, A a^{2} b^{2} e^{3}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B b^{4} x^{3} e^{6} - 9 \, B b^{4} d x^{2} e^{5} + 36 \, B b^{4} d^{2} x e^{4} + 12 \, B a b^{3} x^{2} e^{6} + 3 \, A b^{4} x^{2} e^{6} - 72 \, B a b^{3} d x e^{5} - 18 \, A b^{4} d x e^{5} + 36 \, B a^{2} b^{2} x e^{6} + 24 \, A a b^{3} x e^{6}\right)} e^{\left(-9\right)} - \frac{{\left(9 \, B b^{4} d^{5} - 28 \, B a b^{3} d^{4} e - 7 \, A b^{4} d^{4} e + 30 \, B a^{2} b^{2} d^{3} e^{2} + 20 \, A a b^{3} d^{3} e^{2} - 12 \, B a^{3} b d^{2} e^{3} - 18 \, A a^{2} b^{2} d^{2} e^{3} + B a^{4} d e^{4} + 4 \, A a^{3} b d e^{4} + A a^{4} e^{5} + 2 \, {\left(5 \, B b^{4} d^{4} e - 16 \, B a b^{3} d^{3} e^{2} - 4 \, A b^{4} d^{3} e^{2} + 18 \, B a^{2} b^{2} d^{2} e^{3} + 12 \, A a b^{3} d^{2} e^{3} - 8 \, B a^{3} b d e^{4} - 12 \, A a^{2} b^{2} d e^{4} + B a^{4} e^{5} + 4 \, A a^{3} b e^{5}\right)} x\right)} e^{\left(-6\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-2*(5*B*b^4*d^3 - 12*B*a*b^3*d^2*e - 3*A*b^4*d^2*e + 9*B*a^2*b^2*d*e^2 + 6*A*a*b^3*d*e^2 - 2*B*a^3*b*e^3 - 3*A*a^2*b^2*e^3)*e^(-6)*log(abs(x*e + d)) + 1/6*(2*B*b^4*x^3*e^6 - 9*B*b^4*d*x^2*e^5 + 36*B*b^4*d^2*x*e^4 + 12*B*a*b^3*x^2*e^6 + 3*A*b^4*x^2*e^6 - 72*B*a*b^3*d*x*e^5 - 18*A*b^4*d*x*e^5 + 36*B*a^2*b^2*x*e^6 + 24*A*a*b^3*x*e^6)*e^(-9) - 1/2*(9*B*b^4*d^5 - 28*B*a*b^3*d^4*e - 7*A*b^4*d^4*e + 30*B*a^2*b^2*d^3*e^2 + 20*A*a*b^3*d^3*e^2 - 12*B*a^3*b*d^2*e^3 - 18*A*a^2*b^2*d^2*e^3 + B*a^4*d*e^4 + 4*A*a^3*b*d*e^4 + A*a^4*e^5 + 2*(5*B*b^4*d^4*e - 16*B*a*b^3*d^3*e^2 - 4*A*b^4*d^3*e^2 + 18*B*a^2*b^2*d^2*e^3 + 12*A*a*b^3*d^2*e^3 - 8*B*a^3*b*d*e^4 - 12*A*a^2*b^2*d*e^4 + B*a^4*e^5 + 4*A*a^3*b*e^5)*x)*e^(-6)/(x*e + d)^2","B",0
1684,1,415,0,0.159952," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^4,x, algorithm=""giac"")","2 \, {\left(5 \, B b^{4} d^{2} - 8 \, B a b^{3} d e - 2 \, A b^{4} d e + 3 \, B a^{2} b^{2} e^{2} + 2 \, A a b^{3} e^{2}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B b^{4} x^{2} e^{4} - 8 \, B b^{4} d x e^{3} + 8 \, B a b^{3} x e^{4} + 2 \, A b^{4} x e^{4}\right)} e^{\left(-8\right)} + \frac{{\left(47 \, B b^{4} d^{5} - 104 \, B a b^{3} d^{4} e - 26 \, A b^{4} d^{4} e + 66 \, B a^{2} b^{2} d^{3} e^{2} + 44 \, A a b^{3} d^{3} e^{2} - 8 \, B a^{3} b d^{2} e^{3} - 12 \, A a^{2} b^{2} d^{2} e^{3} - B a^{4} d e^{4} - 4 \, A a^{3} b d e^{4} - 2 \, A a^{4} e^{5} + 12 \, {\left(5 \, B b^{4} d^{3} e^{2} - 12 \, B a b^{3} d^{2} e^{3} - 3 \, A b^{4} d^{2} e^{3} + 9 \, B a^{2} b^{2} d e^{4} + 6 \, A a b^{3} d e^{4} - 2 \, B a^{3} b e^{5} - 3 \, A a^{2} b^{2} e^{5}\right)} x^{2} + 3 \, {\left(35 \, B b^{4} d^{4} e - 80 \, B a b^{3} d^{3} e^{2} - 20 \, A b^{4} d^{3} e^{2} + 54 \, B a^{2} b^{2} d^{2} e^{3} + 36 \, A a b^{3} d^{2} e^{3} - 8 \, B a^{3} b d e^{4} - 12 \, A a^{2} b^{2} d e^{4} - B a^{4} e^{5} - 4 \, A a^{3} b e^{5}\right)} x\right)} e^{\left(-6\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"2*(5*B*b^4*d^2 - 8*B*a*b^3*d*e - 2*A*b^4*d*e + 3*B*a^2*b^2*e^2 + 2*A*a*b^3*e^2)*e^(-6)*log(abs(x*e + d)) + 1/2*(B*b^4*x^2*e^4 - 8*B*b^4*d*x*e^3 + 8*B*a*b^3*x*e^4 + 2*A*b^4*x*e^4)*e^(-8) + 1/6*(47*B*b^4*d^5 - 104*B*a*b^3*d^4*e - 26*A*b^4*d^4*e + 66*B*a^2*b^2*d^3*e^2 + 44*A*a*b^3*d^3*e^2 - 8*B*a^3*b*d^2*e^3 - 12*A*a^2*b^2*d^2*e^3 - B*a^4*d*e^4 - 4*A*a^3*b*d*e^4 - 2*A*a^4*e^5 + 12*(5*B*b^4*d^3*e^2 - 12*B*a*b^3*d^2*e^3 - 3*A*b^4*d^2*e^3 + 9*B*a^2*b^2*d*e^4 + 6*A*a*b^3*d*e^4 - 2*B*a^3*b*e^5 - 3*A*a^2*b^2*e^5)*x^2 + 3*(35*B*b^4*d^4*e - 80*B*a*b^3*d^3*e^2 - 20*A*b^4*d^3*e^2 + 54*B*a^2*b^2*d^2*e^3 + 36*A*a*b^3*d^2*e^3 - 8*B*a^3*b*d*e^4 - 12*A*a^2*b^2*d*e^4 - B*a^4*e^5 - 4*A*a^3*b*e^5)*x)*e^(-6)/(x*e + d)^3","B",0
1685,1,652,0,0.180593," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^5,x, algorithm=""giac"")","{\left(x e + d\right)} B b^{4} e^{\left(-6\right)} + {\left(5 \, B b^{4} d - 4 \, B a b^{3} e - A b^{4} e\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{120 \, B b^{4} d^{2} e^{22}}{x e + d} - \frac{60 \, B b^{4} d^{3} e^{22}}{{\left(x e + d\right)}^{2}} + \frac{20 \, B b^{4} d^{4} e^{22}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B b^{4} d^{5} e^{22}}{{\left(x e + d\right)}^{4}} - \frac{192 \, B a b^{3} d e^{23}}{x e + d} - \frac{48 \, A b^{4} d e^{23}}{x e + d} + \frac{144 \, B a b^{3} d^{2} e^{23}}{{\left(x e + d\right)}^{2}} + \frac{36 \, A b^{4} d^{2} e^{23}}{{\left(x e + d\right)}^{2}} - \frac{64 \, B a b^{3} d^{3} e^{23}}{{\left(x e + d\right)}^{3}} - \frac{16 \, A b^{4} d^{3} e^{23}}{{\left(x e + d\right)}^{3}} + \frac{12 \, B a b^{3} d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A b^{4} d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{72 \, B a^{2} b^{2} e^{24}}{x e + d} + \frac{48 \, A a b^{3} e^{24}}{x e + d} - \frac{108 \, B a^{2} b^{2} d e^{24}}{{\left(x e + d\right)}^{2}} - \frac{72 \, A a b^{3} d e^{24}}{{\left(x e + d\right)}^{2}} + \frac{72 \, B a^{2} b^{2} d^{2} e^{24}}{{\left(x e + d\right)}^{3}} + \frac{48 \, A a b^{3} d^{2} e^{24}}{{\left(x e + d\right)}^{3}} - \frac{18 \, B a^{2} b^{2} d^{3} e^{24}}{{\left(x e + d\right)}^{4}} - \frac{12 \, A a b^{3} d^{3} e^{24}}{{\left(x e + d\right)}^{4}} + \frac{24 \, B a^{3} b e^{25}}{{\left(x e + d\right)}^{2}} + \frac{36 \, A a^{2} b^{2} e^{25}}{{\left(x e + d\right)}^{2}} - \frac{32 \, B a^{3} b d e^{25}}{{\left(x e + d\right)}^{3}} - \frac{48 \, A a^{2} b^{2} d e^{25}}{{\left(x e + d\right)}^{3}} + \frac{12 \, B a^{3} b d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{18 \, A a^{2} b^{2} d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a^{4} e^{26}}{{\left(x e + d\right)}^{3}} + \frac{16 \, A a^{3} b e^{26}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a^{4} d e^{26}}{{\left(x e + d\right)}^{4}} - \frac{12 \, A a^{3} b d e^{26}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a^{4} e^{27}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-28\right)}"," ",0,"(x*e + d)*B*b^4*e^(-6) + (5*B*b^4*d - 4*B*a*b^3*e - A*b^4*e)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(120*B*b^4*d^2*e^22/(x*e + d) - 60*B*b^4*d^3*e^22/(x*e + d)^2 + 20*B*b^4*d^4*e^22/(x*e + d)^3 - 3*B*b^4*d^5*e^22/(x*e + d)^4 - 192*B*a*b^3*d*e^23/(x*e + d) - 48*A*b^4*d*e^23/(x*e + d) + 144*B*a*b^3*d^2*e^23/(x*e + d)^2 + 36*A*b^4*d^2*e^23/(x*e + d)^2 - 64*B*a*b^3*d^3*e^23/(x*e + d)^3 - 16*A*b^4*d^3*e^23/(x*e + d)^3 + 12*B*a*b^3*d^4*e^23/(x*e + d)^4 + 3*A*b^4*d^4*e^23/(x*e + d)^4 + 72*B*a^2*b^2*e^24/(x*e + d) + 48*A*a*b^3*e^24/(x*e + d) - 108*B*a^2*b^2*d*e^24/(x*e + d)^2 - 72*A*a*b^3*d*e^24/(x*e + d)^2 + 72*B*a^2*b^2*d^2*e^24/(x*e + d)^3 + 48*A*a*b^3*d^2*e^24/(x*e + d)^3 - 18*B*a^2*b^2*d^3*e^24/(x*e + d)^4 - 12*A*a*b^3*d^3*e^24/(x*e + d)^4 + 24*B*a^3*b*e^25/(x*e + d)^2 + 36*A*a^2*b^2*e^25/(x*e + d)^2 - 32*B*a^3*b*d*e^25/(x*e + d)^3 - 48*A*a^2*b^2*d*e^25/(x*e + d)^3 + 12*B*a^3*b*d^2*e^25/(x*e + d)^4 + 18*A*a^2*b^2*d^2*e^25/(x*e + d)^4 + 4*B*a^4*e^26/(x*e + d)^3 + 16*A*a^3*b*e^26/(x*e + d)^3 - 3*B*a^4*d*e^26/(x*e + d)^4 - 12*A*a^3*b*d*e^26/(x*e + d)^4 + 3*A*a^4*e^27/(x*e + d)^4)*e^(-28)","B",0
1686,1,415,0,0.163874," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^6,x, algorithm=""giac"")","B b^{4} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(60 \, {\left(5 \, B b^{4} d e^{3} - 4 \, B a b^{3} e^{4} - A b^{4} e^{4}\right)} x^{4} + 60 \, {\left(15 \, B b^{4} d^{2} e^{2} - 8 \, B a b^{3} d e^{3} - 2 \, A b^{4} d e^{3} - 3 \, B a^{2} b^{2} e^{4} - 2 \, A a b^{3} e^{4}\right)} x^{3} + 20 \, {\left(55 \, B b^{4} d^{3} e - 24 \, B a b^{3} d^{2} e^{2} - 6 \, A b^{4} d^{2} e^{2} - 9 \, B a^{2} b^{2} d e^{3} - 6 \, A a b^{3} d e^{3} - 4 \, B a^{3} b e^{4} - 6 \, A a^{2} b^{2} e^{4}\right)} x^{2} + 5 \, {\left(125 \, B b^{4} d^{4} - 48 \, B a b^{3} d^{3} e - 12 \, A b^{4} d^{3} e - 18 \, B a^{2} b^{2} d^{2} e^{2} - 12 \, A a b^{3} d^{2} e^{2} - 8 \, B a^{3} b d e^{3} - 12 \, A a^{2} b^{2} d e^{3} - 3 \, B a^{4} e^{4} - 12 \, A a^{3} b e^{4}\right)} x + {\left(137 \, B b^{4} d^{5} - 48 \, B a b^{3} d^{4} e - 12 \, A b^{4} d^{4} e - 18 \, B a^{2} b^{2} d^{3} e^{2} - 12 \, A a b^{3} d^{3} e^{2} - 8 \, B a^{3} b d^{2} e^{3} - 12 \, A a^{2} b^{2} d^{2} e^{3} - 3 \, B a^{4} d e^{4} - 12 \, A a^{3} b d e^{4} - 12 \, A a^{4} e^{5}\right)} e^{\left(-1\right)}\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"B*b^4*e^(-6)*log(abs(x*e + d)) + 1/60*(60*(5*B*b^4*d*e^3 - 4*B*a*b^3*e^4 - A*b^4*e^4)*x^4 + 60*(15*B*b^4*d^2*e^2 - 8*B*a*b^3*d*e^3 - 2*A*b^4*d*e^3 - 3*B*a^2*b^2*e^4 - 2*A*a*b^3*e^4)*x^3 + 20*(55*B*b^4*d^3*e - 24*B*a*b^3*d^2*e^2 - 6*A*b^4*d^2*e^2 - 9*B*a^2*b^2*d*e^3 - 6*A*a*b^3*d*e^3 - 4*B*a^3*b*e^4 - 6*A*a^2*b^2*e^4)*x^2 + 5*(125*B*b^4*d^4 - 48*B*a*b^3*d^3*e - 12*A*b^4*d^3*e - 18*B*a^2*b^2*d^2*e^2 - 12*A*a*b^3*d^2*e^2 - 8*B*a^3*b*d*e^3 - 12*A*a^2*b^2*d*e^3 - 3*B*a^4*e^4 - 12*A*a^3*b*e^4)*x + (137*B*b^4*d^5 - 48*B*a*b^3*d^4*e - 12*A*b^4*d^4*e - 18*B*a^2*b^2*d^3*e^2 - 12*A*a*b^3*d^3*e^2 - 8*B*a^3*b*d^2*e^3 - 12*A*a^2*b^2*d^2*e^3 - 3*B*a^4*d*e^4 - 12*A*a^3*b*d*e^4 - 12*A*a^4*e^5)*e^(-1))*e^(-5)/(x*e + d)^5","B",0
1687,1,438,0,0.161296," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(30 \, B b^{4} x^{5} e^{5} + 75 \, B b^{4} d x^{4} e^{4} + 100 \, B b^{4} d^{2} x^{3} e^{3} + 75 \, B b^{4} d^{3} x^{2} e^{2} + 30 \, B b^{4} d^{4} x e + 5 \, B b^{4} d^{5} + 60 \, B a b^{3} x^{4} e^{5} + 15 \, A b^{4} x^{4} e^{5} + 80 \, B a b^{3} d x^{3} e^{4} + 20 \, A b^{4} d x^{3} e^{4} + 60 \, B a b^{3} d^{2} x^{2} e^{3} + 15 \, A b^{4} d^{2} x^{2} e^{3} + 24 \, B a b^{3} d^{3} x e^{2} + 6 \, A b^{4} d^{3} x e^{2} + 4 \, B a b^{3} d^{4} e + A b^{4} d^{4} e + 60 \, B a^{2} b^{2} x^{3} e^{5} + 40 \, A a b^{3} x^{3} e^{5} + 45 \, B a^{2} b^{2} d x^{2} e^{4} + 30 \, A a b^{3} d x^{2} e^{4} + 18 \, B a^{2} b^{2} d^{2} x e^{3} + 12 \, A a b^{3} d^{2} x e^{3} + 3 \, B a^{2} b^{2} d^{3} e^{2} + 2 \, A a b^{3} d^{3} e^{2} + 30 \, B a^{3} b x^{2} e^{5} + 45 \, A a^{2} b^{2} x^{2} e^{5} + 12 \, B a^{3} b d x e^{4} + 18 \, A a^{2} b^{2} d x e^{4} + 2 \, B a^{3} b d^{2} e^{3} + 3 \, A a^{2} b^{2} d^{2} e^{3} + 6 \, B a^{4} x e^{5} + 24 \, A a^{3} b x e^{5} + B a^{4} d e^{4} + 4 \, A a^{3} b d e^{4} + 5 \, A a^{4} e^{5}\right)} e^{\left(-6\right)}}{30 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/30*(30*B*b^4*x^5*e^5 + 75*B*b^4*d*x^4*e^4 + 100*B*b^4*d^2*x^3*e^3 + 75*B*b^4*d^3*x^2*e^2 + 30*B*b^4*d^4*x*e + 5*B*b^4*d^5 + 60*B*a*b^3*x^4*e^5 + 15*A*b^4*x^4*e^5 + 80*B*a*b^3*d*x^3*e^4 + 20*A*b^4*d*x^3*e^4 + 60*B*a*b^3*d^2*x^2*e^3 + 15*A*b^4*d^2*x^2*e^3 + 24*B*a*b^3*d^3*x*e^2 + 6*A*b^4*d^3*x*e^2 + 4*B*a*b^3*d^4*e + A*b^4*d^4*e + 60*B*a^2*b^2*x^3*e^5 + 40*A*a*b^3*x^3*e^5 + 45*B*a^2*b^2*d*x^2*e^4 + 30*A*a*b^3*d*x^2*e^4 + 18*B*a^2*b^2*d^2*x*e^3 + 12*A*a*b^3*d^2*x*e^3 + 3*B*a^2*b^2*d^3*e^2 + 2*A*a*b^3*d^3*e^2 + 30*B*a^3*b*x^2*e^5 + 45*A*a^2*b^2*x^2*e^5 + 12*B*a^3*b*d*x*e^4 + 18*A*a^2*b^2*d*x*e^4 + 2*B*a^3*b*d^2*e^3 + 3*A*a^2*b^2*d^2*e^3 + 6*B*a^4*x*e^5 + 24*A*a^3*b*x*e^5 + B*a^4*d*e^4 + 4*A*a^3*b*d*e^4 + 5*A*a^4*e^5)*e^(-6)/(x*e + d)^6","B",0
1688,1,440,0,0.159481," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(105 \, B b^{4} x^{5} e^{5} + 175 \, B b^{4} d x^{4} e^{4} + 175 \, B b^{4} d^{2} x^{3} e^{3} + 105 \, B b^{4} d^{3} x^{2} e^{2} + 35 \, B b^{4} d^{4} x e + 5 \, B b^{4} d^{5} + 280 \, B a b^{3} x^{4} e^{5} + 70 \, A b^{4} x^{4} e^{5} + 280 \, B a b^{3} d x^{3} e^{4} + 70 \, A b^{4} d x^{3} e^{4} + 168 \, B a b^{3} d^{2} x^{2} e^{3} + 42 \, A b^{4} d^{2} x^{2} e^{3} + 56 \, B a b^{3} d^{3} x e^{2} + 14 \, A b^{4} d^{3} x e^{2} + 8 \, B a b^{3} d^{4} e + 2 \, A b^{4} d^{4} e + 315 \, B a^{2} b^{2} x^{3} e^{5} + 210 \, A a b^{3} x^{3} e^{5} + 189 \, B a^{2} b^{2} d x^{2} e^{4} + 126 \, A a b^{3} d x^{2} e^{4} + 63 \, B a^{2} b^{2} d^{2} x e^{3} + 42 \, A a b^{3} d^{2} x e^{3} + 9 \, B a^{2} b^{2} d^{3} e^{2} + 6 \, A a b^{3} d^{3} e^{2} + 168 \, B a^{3} b x^{2} e^{5} + 252 \, A a^{2} b^{2} x^{2} e^{5} + 56 \, B a^{3} b d x e^{4} + 84 \, A a^{2} b^{2} d x e^{4} + 8 \, B a^{3} b d^{2} e^{3} + 12 \, A a^{2} b^{2} d^{2} e^{3} + 35 \, B a^{4} x e^{5} + 140 \, A a^{3} b x e^{5} + 5 \, B a^{4} d e^{4} + 20 \, A a^{3} b d e^{4} + 30 \, A a^{4} e^{5}\right)} e^{\left(-6\right)}}{210 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/210*(105*B*b^4*x^5*e^5 + 175*B*b^4*d*x^4*e^4 + 175*B*b^4*d^2*x^3*e^3 + 105*B*b^4*d^3*x^2*e^2 + 35*B*b^4*d^4*x*e + 5*B*b^4*d^5 + 280*B*a*b^3*x^4*e^5 + 70*A*b^4*x^4*e^5 + 280*B*a*b^3*d*x^3*e^4 + 70*A*b^4*d*x^3*e^4 + 168*B*a*b^3*d^2*x^2*e^3 + 42*A*b^4*d^2*x^2*e^3 + 56*B*a*b^3*d^3*x*e^2 + 14*A*b^4*d^3*x*e^2 + 8*B*a*b^3*d^4*e + 2*A*b^4*d^4*e + 315*B*a^2*b^2*x^3*e^5 + 210*A*a*b^3*x^3*e^5 + 189*B*a^2*b^2*d*x^2*e^4 + 126*A*a*b^3*d*x^2*e^4 + 63*B*a^2*b^2*d^2*x*e^3 + 42*A*a*b^3*d^2*x*e^3 + 9*B*a^2*b^2*d^3*e^2 + 6*A*a*b^3*d^3*e^2 + 168*B*a^3*b*x^2*e^5 + 252*A*a^2*b^2*x^2*e^5 + 56*B*a^3*b*d*x*e^4 + 84*A*a^2*b^2*d*x*e^4 + 8*B*a^3*b*d^2*e^3 + 12*A*a^2*b^2*d^2*e^3 + 35*B*a^4*x*e^5 + 140*A*a^3*b*x*e^5 + 5*B*a^4*d*e^4 + 20*A*a^3*b*d*e^4 + 30*A*a^4*e^5)*e^(-6)/(x*e + d)^7","B",0
1689,1,440,0,0.162558," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(280 \, B b^{4} x^{5} e^{5} + 350 \, B b^{4} d x^{4} e^{4} + 280 \, B b^{4} d^{2} x^{3} e^{3} + 140 \, B b^{4} d^{3} x^{2} e^{2} + 40 \, B b^{4} d^{4} x e + 5 \, B b^{4} d^{5} + 840 \, B a b^{3} x^{4} e^{5} + 210 \, A b^{4} x^{4} e^{5} + 672 \, B a b^{3} d x^{3} e^{4} + 168 \, A b^{4} d x^{3} e^{4} + 336 \, B a b^{3} d^{2} x^{2} e^{3} + 84 \, A b^{4} d^{2} x^{2} e^{3} + 96 \, B a b^{3} d^{3} x e^{2} + 24 \, A b^{4} d^{3} x e^{2} + 12 \, B a b^{3} d^{4} e + 3 \, A b^{4} d^{4} e + 1008 \, B a^{2} b^{2} x^{3} e^{5} + 672 \, A a b^{3} x^{3} e^{5} + 504 \, B a^{2} b^{2} d x^{2} e^{4} + 336 \, A a b^{3} d x^{2} e^{4} + 144 \, B a^{2} b^{2} d^{2} x e^{3} + 96 \, A a b^{3} d^{2} x e^{3} + 18 \, B a^{2} b^{2} d^{3} e^{2} + 12 \, A a b^{3} d^{3} e^{2} + 560 \, B a^{3} b x^{2} e^{5} + 840 \, A a^{2} b^{2} x^{2} e^{5} + 160 \, B a^{3} b d x e^{4} + 240 \, A a^{2} b^{2} d x e^{4} + 20 \, B a^{3} b d^{2} e^{3} + 30 \, A a^{2} b^{2} d^{2} e^{3} + 120 \, B a^{4} x e^{5} + 480 \, A a^{3} b x e^{5} + 15 \, B a^{4} d e^{4} + 60 \, A a^{3} b d e^{4} + 105 \, A a^{4} e^{5}\right)} e^{\left(-6\right)}}{840 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/840*(280*B*b^4*x^5*e^5 + 350*B*b^4*d*x^4*e^4 + 280*B*b^4*d^2*x^3*e^3 + 140*B*b^4*d^3*x^2*e^2 + 40*B*b^4*d^4*x*e + 5*B*b^4*d^5 + 840*B*a*b^3*x^4*e^5 + 210*A*b^4*x^4*e^5 + 672*B*a*b^3*d*x^3*e^4 + 168*A*b^4*d*x^3*e^4 + 336*B*a*b^3*d^2*x^2*e^3 + 84*A*b^4*d^2*x^2*e^3 + 96*B*a*b^3*d^3*x*e^2 + 24*A*b^4*d^3*x*e^2 + 12*B*a*b^3*d^4*e + 3*A*b^4*d^4*e + 1008*B*a^2*b^2*x^3*e^5 + 672*A*a*b^3*x^3*e^5 + 504*B*a^2*b^2*d*x^2*e^4 + 336*A*a*b^3*d*x^2*e^4 + 144*B*a^2*b^2*d^2*x*e^3 + 96*A*a*b^3*d^2*x*e^3 + 18*B*a^2*b^2*d^3*e^2 + 12*A*a*b^3*d^3*e^2 + 560*B*a^3*b*x^2*e^5 + 840*A*a^2*b^2*x^2*e^5 + 160*B*a^3*b*d*x*e^4 + 240*A*a^2*b^2*d*x*e^4 + 20*B*a^3*b*d^2*e^3 + 30*A*a^2*b^2*d^2*e^3 + 120*B*a^4*x*e^5 + 480*A*a^3*b*x*e^5 + 15*B*a^4*d*e^4 + 60*A*a^3*b*d*e^4 + 105*A*a^4*e^5)*e^(-6)/(x*e + d)^8","B",0
1690,1,440,0,0.161361," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(630 \, B b^{4} x^{5} e^{5} + 630 \, B b^{4} d x^{4} e^{4} + 420 \, B b^{4} d^{2} x^{3} e^{3} + 180 \, B b^{4} d^{3} x^{2} e^{2} + 45 \, B b^{4} d^{4} x e + 5 \, B b^{4} d^{5} + 2016 \, B a b^{3} x^{4} e^{5} + 504 \, A b^{4} x^{4} e^{5} + 1344 \, B a b^{3} d x^{3} e^{4} + 336 \, A b^{4} d x^{3} e^{4} + 576 \, B a b^{3} d^{2} x^{2} e^{3} + 144 \, A b^{4} d^{2} x^{2} e^{3} + 144 \, B a b^{3} d^{3} x e^{2} + 36 \, A b^{4} d^{3} x e^{2} + 16 \, B a b^{3} d^{4} e + 4 \, A b^{4} d^{4} e + 2520 \, B a^{2} b^{2} x^{3} e^{5} + 1680 \, A a b^{3} x^{3} e^{5} + 1080 \, B a^{2} b^{2} d x^{2} e^{4} + 720 \, A a b^{3} d x^{2} e^{4} + 270 \, B a^{2} b^{2} d^{2} x e^{3} + 180 \, A a b^{3} d^{2} x e^{3} + 30 \, B a^{2} b^{2} d^{3} e^{2} + 20 \, A a b^{3} d^{3} e^{2} + 1440 \, B a^{3} b x^{2} e^{5} + 2160 \, A a^{2} b^{2} x^{2} e^{5} + 360 \, B a^{3} b d x e^{4} + 540 \, A a^{2} b^{2} d x e^{4} + 40 \, B a^{3} b d^{2} e^{3} + 60 \, A a^{2} b^{2} d^{2} e^{3} + 315 \, B a^{4} x e^{5} + 1260 \, A a^{3} b x e^{5} + 35 \, B a^{4} d e^{4} + 140 \, A a^{3} b d e^{4} + 280 \, A a^{4} e^{5}\right)} e^{\left(-6\right)}}{2520 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/2520*(630*B*b^4*x^5*e^5 + 630*B*b^4*d*x^4*e^4 + 420*B*b^4*d^2*x^3*e^3 + 180*B*b^4*d^3*x^2*e^2 + 45*B*b^4*d^4*x*e + 5*B*b^4*d^5 + 2016*B*a*b^3*x^4*e^5 + 504*A*b^4*x^4*e^5 + 1344*B*a*b^3*d*x^3*e^4 + 336*A*b^4*d*x^3*e^4 + 576*B*a*b^3*d^2*x^2*e^3 + 144*A*b^4*d^2*x^2*e^3 + 144*B*a*b^3*d^3*x*e^2 + 36*A*b^4*d^3*x*e^2 + 16*B*a*b^3*d^4*e + 4*A*b^4*d^4*e + 2520*B*a^2*b^2*x^3*e^5 + 1680*A*a*b^3*x^3*e^5 + 1080*B*a^2*b^2*d*x^2*e^4 + 720*A*a*b^3*d*x^2*e^4 + 270*B*a^2*b^2*d^2*x*e^3 + 180*A*a*b^3*d^2*x*e^3 + 30*B*a^2*b^2*d^3*e^2 + 20*A*a*b^3*d^3*e^2 + 1440*B*a^3*b*x^2*e^5 + 2160*A*a^2*b^2*x^2*e^5 + 360*B*a^3*b*d*x*e^4 + 540*A*a^2*b^2*d*x*e^4 + 40*B*a^3*b*d^2*e^3 + 60*A*a^2*b^2*d^2*e^3 + 315*B*a^4*x*e^5 + 1260*A*a^3*b*x*e^5 + 35*B*a^4*d*e^4 + 140*A*a^3*b*d*e^4 + 280*A*a^4*e^5)*e^(-6)/(x*e + d)^9","B",0
1691,1,438,0,0.166751," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(252 \, B b^{4} x^{5} e^{5} + 210 \, B b^{4} d x^{4} e^{4} + 120 \, B b^{4} d^{2} x^{3} e^{3} + 45 \, B b^{4} d^{3} x^{2} e^{2} + 10 \, B b^{4} d^{4} x e + B b^{4} d^{5} + 840 \, B a b^{3} x^{4} e^{5} + 210 \, A b^{4} x^{4} e^{5} + 480 \, B a b^{3} d x^{3} e^{4} + 120 \, A b^{4} d x^{3} e^{4} + 180 \, B a b^{3} d^{2} x^{2} e^{3} + 45 \, A b^{4} d^{2} x^{2} e^{3} + 40 \, B a b^{3} d^{3} x e^{2} + 10 \, A b^{4} d^{3} x e^{2} + 4 \, B a b^{3} d^{4} e + A b^{4} d^{4} e + 1080 \, B a^{2} b^{2} x^{3} e^{5} + 720 \, A a b^{3} x^{3} e^{5} + 405 \, B a^{2} b^{2} d x^{2} e^{4} + 270 \, A a b^{3} d x^{2} e^{4} + 90 \, B a^{2} b^{2} d^{2} x e^{3} + 60 \, A a b^{3} d^{2} x e^{3} + 9 \, B a^{2} b^{2} d^{3} e^{2} + 6 \, A a b^{3} d^{3} e^{2} + 630 \, B a^{3} b x^{2} e^{5} + 945 \, A a^{2} b^{2} x^{2} e^{5} + 140 \, B a^{3} b d x e^{4} + 210 \, A a^{2} b^{2} d x e^{4} + 14 \, B a^{3} b d^{2} e^{3} + 21 \, A a^{2} b^{2} d^{2} e^{3} + 140 \, B a^{4} x e^{5} + 560 \, A a^{3} b x e^{5} + 14 \, B a^{4} d e^{4} + 56 \, A a^{3} b d e^{4} + 126 \, A a^{4} e^{5}\right)} e^{\left(-6\right)}}{1260 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/1260*(252*B*b^4*x^5*e^5 + 210*B*b^4*d*x^4*e^4 + 120*B*b^4*d^2*x^3*e^3 + 45*B*b^4*d^3*x^2*e^2 + 10*B*b^4*d^4*x*e + B*b^4*d^5 + 840*B*a*b^3*x^4*e^5 + 210*A*b^4*x^4*e^5 + 480*B*a*b^3*d*x^3*e^4 + 120*A*b^4*d*x^3*e^4 + 180*B*a*b^3*d^2*x^2*e^3 + 45*A*b^4*d^2*x^2*e^3 + 40*B*a*b^3*d^3*x*e^2 + 10*A*b^4*d^3*x*e^2 + 4*B*a*b^3*d^4*e + A*b^4*d^4*e + 1080*B*a^2*b^2*x^3*e^5 + 720*A*a*b^3*x^3*e^5 + 405*B*a^2*b^2*d*x^2*e^4 + 270*A*a*b^3*d*x^2*e^4 + 90*B*a^2*b^2*d^2*x*e^3 + 60*A*a*b^3*d^2*x*e^3 + 9*B*a^2*b^2*d^3*e^2 + 6*A*a*b^3*d^3*e^2 + 630*B*a^3*b*x^2*e^5 + 945*A*a^2*b^2*x^2*e^5 + 140*B*a^3*b*d*x*e^4 + 210*A*a^2*b^2*d*x*e^4 + 14*B*a^3*b*d^2*e^3 + 21*A*a^2*b^2*d^2*e^3 + 140*B*a^4*x*e^5 + 560*A*a^3*b*x*e^5 + 14*B*a^4*d*e^4 + 56*A*a^3*b*d*e^4 + 126*A*a^4*e^5)*e^(-6)/(x*e + d)^10","B",0
1692,1,440,0,0.159980," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(2310 \, B b^{4} x^{5} e^{5} + 1650 \, B b^{4} d x^{4} e^{4} + 825 \, B b^{4} d^{2} x^{3} e^{3} + 275 \, B b^{4} d^{3} x^{2} e^{2} + 55 \, B b^{4} d^{4} x e + 5 \, B b^{4} d^{5} + 7920 \, B a b^{3} x^{4} e^{5} + 1980 \, A b^{4} x^{4} e^{5} + 3960 \, B a b^{3} d x^{3} e^{4} + 990 \, A b^{4} d x^{3} e^{4} + 1320 \, B a b^{3} d^{2} x^{2} e^{3} + 330 \, A b^{4} d^{2} x^{2} e^{3} + 264 \, B a b^{3} d^{3} x e^{2} + 66 \, A b^{4} d^{3} x e^{2} + 24 \, B a b^{3} d^{4} e + 6 \, A b^{4} d^{4} e + 10395 \, B a^{2} b^{2} x^{3} e^{5} + 6930 \, A a b^{3} x^{3} e^{5} + 3465 \, B a^{2} b^{2} d x^{2} e^{4} + 2310 \, A a b^{3} d x^{2} e^{4} + 693 \, B a^{2} b^{2} d^{2} x e^{3} + 462 \, A a b^{3} d^{2} x e^{3} + 63 \, B a^{2} b^{2} d^{3} e^{2} + 42 \, A a b^{3} d^{3} e^{2} + 6160 \, B a^{3} b x^{2} e^{5} + 9240 \, A a^{2} b^{2} x^{2} e^{5} + 1232 \, B a^{3} b d x e^{4} + 1848 \, A a^{2} b^{2} d x e^{4} + 112 \, B a^{3} b d^{2} e^{3} + 168 \, A a^{2} b^{2} d^{2} e^{3} + 1386 \, B a^{4} x e^{5} + 5544 \, A a^{3} b x e^{5} + 126 \, B a^{4} d e^{4} + 504 \, A a^{3} b d e^{4} + 1260 \, A a^{4} e^{5}\right)} e^{\left(-6\right)}}{13860 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/13860*(2310*B*b^4*x^5*e^5 + 1650*B*b^4*d*x^4*e^4 + 825*B*b^4*d^2*x^3*e^3 + 275*B*b^4*d^3*x^2*e^2 + 55*B*b^4*d^4*x*e + 5*B*b^4*d^5 + 7920*B*a*b^3*x^4*e^5 + 1980*A*b^4*x^4*e^5 + 3960*B*a*b^3*d*x^3*e^4 + 990*A*b^4*d*x^3*e^4 + 1320*B*a*b^3*d^2*x^2*e^3 + 330*A*b^4*d^2*x^2*e^3 + 264*B*a*b^3*d^3*x*e^2 + 66*A*b^4*d^3*x*e^2 + 24*B*a*b^3*d^4*e + 6*A*b^4*d^4*e + 10395*B*a^2*b^2*x^3*e^5 + 6930*A*a*b^3*x^3*e^5 + 3465*B*a^2*b^2*d*x^2*e^4 + 2310*A*a*b^3*d*x^2*e^4 + 693*B*a^2*b^2*d^2*x*e^3 + 462*A*a*b^3*d^2*x*e^3 + 63*B*a^2*b^2*d^3*e^2 + 42*A*a*b^3*d^3*e^2 + 6160*B*a^3*b*x^2*e^5 + 9240*A*a^2*b^2*x^2*e^5 + 1232*B*a^3*b*d*x*e^4 + 1848*A*a^2*b^2*d*x*e^4 + 112*B*a^3*b*d^2*e^3 + 168*A*a^2*b^2*d^2*e^3 + 1386*B*a^4*x*e^5 + 5544*A*a^3*b*x*e^5 + 126*B*a^4*d*e^4 + 504*A*a^3*b*d*e^4 + 1260*A*a^4*e^5)*e^(-6)/(x*e + d)^11","B",0
1693,1,433,0,0.165147," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B b^{4} d^{4} - 8 \, B a b^{3} d^{3} e + 4 \, A b^{4} d^{3} e + 18 \, B a^{2} b^{2} d^{2} e^{2} - 12 \, A a b^{3} d^{2} e^{2} - 16 \, B a^{3} b d e^{3} + 12 \, A a^{2} b^{2} d e^{3} + 5 \, B a^{4} e^{4} - 4 \, A a^{3} b e^{4}\right)} \log\left({\left| b x + a \right|}\right)}{b^{6}} + \frac{B a b^{4} d^{4} - A b^{5} d^{4} - 4 \, B a^{2} b^{3} d^{3} e + 4 \, A a b^{4} d^{3} e + 6 \, B a^{3} b^{2} d^{2} e^{2} - 6 \, A a^{2} b^{3} d^{2} e^{2} - 4 \, B a^{4} b d e^{3} + 4 \, A a^{3} b^{2} d e^{3} + B a^{5} e^{4} - A a^{4} b e^{4}}{{\left(b x + a\right)} b^{6}} + \frac{3 \, B b^{6} x^{4} e^{4} + 16 \, B b^{6} d x^{3} e^{3} + 36 \, B b^{6} d^{2} x^{2} e^{2} + 48 \, B b^{6} d^{3} x e - 8 \, B a b^{5} x^{3} e^{4} + 4 \, A b^{6} x^{3} e^{4} - 48 \, B a b^{5} d x^{2} e^{3} + 24 \, A b^{6} d x^{2} e^{3} - 144 \, B a b^{5} d^{2} x e^{2} + 72 \, A b^{6} d^{2} x e^{2} + 18 \, B a^{2} b^{4} x^{2} e^{4} - 12 \, A a b^{5} x^{2} e^{4} + 144 \, B a^{2} b^{4} d x e^{3} - 96 \, A a b^{5} d x e^{3} - 48 \, B a^{3} b^{3} x e^{4} + 36 \, A a^{2} b^{4} x e^{4}}{12 \, b^{8}}"," ",0,"(B*b^4*d^4 - 8*B*a*b^3*d^3*e + 4*A*b^4*d^3*e + 18*B*a^2*b^2*d^2*e^2 - 12*A*a*b^3*d^2*e^2 - 16*B*a^3*b*d*e^3 + 12*A*a^2*b^2*d*e^3 + 5*B*a^4*e^4 - 4*A*a^3*b*e^4)*log(abs(b*x + a))/b^6 + (B*a*b^4*d^4 - A*b^5*d^4 - 4*B*a^2*b^3*d^3*e + 4*A*a*b^4*d^3*e + 6*B*a^3*b^2*d^2*e^2 - 6*A*a^2*b^3*d^2*e^2 - 4*B*a^4*b*d*e^3 + 4*A*a^3*b^2*d*e^3 + B*a^5*e^4 - A*a^4*b*e^4)/((b*x + a)*b^6) + 1/12*(3*B*b^6*x^4*e^4 + 16*B*b^6*d*x^3*e^3 + 36*B*b^6*d^2*x^2*e^2 + 48*B*b^6*d^3*x*e - 8*B*a*b^5*x^3*e^4 + 4*A*b^6*x^3*e^4 - 48*B*a*b^5*d*x^2*e^3 + 24*A*b^6*d*x^2*e^3 - 144*B*a*b^5*d^2*x*e^2 + 72*A*b^6*d^2*x*e^2 + 18*B*a^2*b^4*x^2*e^4 - 12*A*a*b^5*x^2*e^4 + 144*B*a^2*b^4*d*x*e^3 - 96*A*a*b^5*d*x*e^3 - 48*B*a^3*b^3*x*e^4 + 36*A*a^2*b^4*x*e^4)/b^8","B",0
1694,1,282,0,0.164670," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B b^{3} d^{3} - 6 \, B a b^{2} d^{2} e + 3 \, A b^{3} d^{2} e + 9 \, B a^{2} b d e^{2} - 6 \, A a b^{2} d e^{2} - 4 \, B a^{3} e^{3} + 3 \, A a^{2} b e^{3}\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}} + \frac{2 \, B b^{4} x^{3} e^{3} + 9 \, B b^{4} d x^{2} e^{2} + 18 \, B b^{4} d^{2} x e - 6 \, B a b^{3} x^{2} e^{3} + 3 \, A b^{4} x^{2} e^{3} - 36 \, B a b^{3} d x e^{2} + 18 \, A b^{4} d x e^{2} + 18 \, B a^{2} b^{2} x e^{3} - 12 \, A a b^{3} x e^{3}}{6 \, b^{6}} + \frac{B a b^{3} d^{3} - A b^{4} d^{3} - 3 \, B a^{2} b^{2} d^{2} e + 3 \, A a b^{3} d^{2} e + 3 \, B a^{3} b d e^{2} - 3 \, A a^{2} b^{2} d e^{2} - B a^{4} e^{3} + A a^{3} b e^{3}}{{\left(b x + a\right)} b^{5}}"," ",0,"(B*b^3*d^3 - 6*B*a*b^2*d^2*e + 3*A*b^3*d^2*e + 9*B*a^2*b*d*e^2 - 6*A*a*b^2*d*e^2 - 4*B*a^3*e^3 + 3*A*a^2*b*e^3)*log(abs(b*x + a))/b^5 + 1/6*(2*B*b^4*x^3*e^3 + 9*B*b^4*d*x^2*e^2 + 18*B*b^4*d^2*x*e - 6*B*a*b^3*x^2*e^3 + 3*A*b^4*x^2*e^3 - 36*B*a*b^3*d*x*e^2 + 18*A*b^4*d*x*e^2 + 18*B*a^2*b^2*x*e^3 - 12*A*a*b^3*x*e^3)/b^6 + (B*a*b^3*d^3 - A*b^4*d^3 - 3*B*a^2*b^2*d^2*e + 3*A*a*b^3*d^2*e + 3*B*a^3*b*d*e^2 - 3*A*a^2*b^2*d*e^2 - B*a^4*e^3 + A*a^3*b*e^3)/((b*x + a)*b^5)","B",0
1695,1,162,0,0.154929," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B b^{2} d^{2} - 4 \, B a b d e + 2 \, A b^{2} d e + 3 \, B a^{2} e^{2} - 2 \, A a b e^{2}\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}} + \frac{B b^{2} x^{2} e^{2} + 4 \, B b^{2} d x e - 4 \, B a b x e^{2} + 2 \, A b^{2} x e^{2}}{2 \, b^{4}} + \frac{B a b^{2} d^{2} - A b^{3} d^{2} - 2 \, B a^{2} b d e + 2 \, A a b^{2} d e + B a^{3} e^{2} - A a^{2} b e^{2}}{{\left(b x + a\right)} b^{4}}"," ",0,"(B*b^2*d^2 - 4*B*a*b*d*e + 2*A*b^2*d*e + 3*B*a^2*e^2 - 2*A*a*b*e^2)*log(abs(b*x + a))/b^4 + 1/2*(B*b^2*x^2*e^2 + 4*B*b^2*d*x*e - 4*B*a*b*x*e^2 + 2*A*b^2*x*e^2)/b^4 + (B*a*b^2*d^2 - A*b^3*d^2 - 2*B*a^2*b*d*e + 2*A*a*b^2*d*e + B*a^3*e^2 - A*a^2*b*e^2)/((b*x + a)*b^4)","A",0
1696,1,74,0,0.158308," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{B x e}{b^{2}} + \frac{{\left(B b d - 2 \, B a e + A b e\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}} + \frac{B a b d - A b^{2} d - B a^{2} e + A a b e}{{\left(b x + a\right)} b^{3}}"," ",0,"B*x*e/b^2 + (B*b*d - 2*B*a*e + A*b*e)*log(abs(b*x + a))/b^3 + (B*a*b*d - A*b^2*d - B*a^2*e + A*a*b*e)/((b*x + a)*b^3)","A",0
1697,1,32,0,0.151785," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{B \log\left({\left| b x + a \right|}\right)}{b^{2}} + \frac{B a - A b}{{\left(b x + a\right)} b^{2}}"," ",0,"B*log(abs(b*x + a))/b^2 + (B*a - A*b)/((b*x + a)*b^2)","A",0
1698,1,141,0,0.155092," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B b d - A b e\right)} \log\left({\left| b x + a \right|}\right)}{b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}} - \frac{{\left(B d e - A e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}} + \frac{B a b d - A b^{2} d - B a^{2} e + A a b e}{{\left(b d - a e\right)}^{2} {\left(b x + a\right)} b}"," ",0,"(B*b*d - A*b*e)*log(abs(b*x + a))/(b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2) - (B*d*e - A*e^2)*log(abs(x*e + d))/(b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3) + (B*a*b*d - A*b^2*d - B*a^2*e + A*a*b*e)/((b*d - a*e)^2*(b*x + a)*b)","A",0
1699,1,195,0,0.221227," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B b d e + B a e^{2} - 2 \, A b e^{2}\right)} \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}} + \frac{\frac{B d e^{2}}{x e + d} - \frac{A e^{3}}{x e + d}}{b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}} + \frac{B a b e - A b^{2} e}{{\left(b d - a e\right)}^{3} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}}"," ",0,"(B*b*d*e + B*a*e^2 - 2*A*b*e^2)*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4) + (B*d*e^2/(x*e + d) - A*e^3/(x*e + d))/(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) + (B*a*b*e - A*b^2*e)/((b*d - a*e)^3*(b - b*d/(x*e + d) + a*e/(x*e + d)))","A",0
1700,1,393,0,0.162689," ","integrate((B*x+A)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(B b^{3} d + 2 \, B a b^{2} e - 3 \, A b^{3} e\right)} \log\left({\left| b x + a \right|}\right)}{b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}} - \frac{{\left(B b^{2} d e + 2 \, B a b e^{2} - 3 \, A b^{2} e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} + \frac{5 \, B a b^{2} d^{3} - 2 \, A b^{3} d^{3} - 4 \, B a^{2} b d^{2} e - 3 \, A a b^{2} d^{2} e - B a^{3} d e^{2} + 6 \, A a^{2} b d e^{2} - A a^{3} e^{3} + 2 \, {\left(B b^{3} d^{2} e + B a b^{2} d e^{2} - 3 \, A b^{3} d e^{2} - 2 \, B a^{2} b e^{3} + 3 \, A a b^{2} e^{3}\right)} x^{2} + {\left(3 \, B b^{3} d^{3} + 4 \, B a b^{2} d^{2} e - 9 \, A b^{3} d^{2} e - 5 \, B a^{2} b d e^{2} + 6 \, A a b^{2} d e^{2} - 2 \, B a^{3} e^{3} + 3 \, A a^{2} b e^{3}\right)} x}{2 \, {\left(b d - a e\right)}^{4} {\left(b x + a\right)} {\left(x e + d\right)}^{2}}"," ",0,"(B*b^3*d + 2*B*a*b^2*e - 3*A*b^3*e)*log(abs(b*x + a))/(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4) - (B*b^2*d*e + 2*B*a*b*e^2 - 3*A*b^2*e^2)*log(abs(x*e + d))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) + 1/2*(5*B*a*b^2*d^3 - 2*A*b^3*d^3 - 4*B*a^2*b*d^2*e - 3*A*a*b^2*d^2*e - B*a^3*d*e^2 + 6*A*a^2*b*d*e^2 - A*a^3*e^3 + 2*(B*b^3*d^2*e + B*a*b^2*d*e^2 - 3*A*b^3*d*e^2 - 2*B*a^2*b*e^3 + 3*A*a*b^2*e^3)*x^2 + (3*B*b^3*d^3 + 4*B*a*b^2*d^2*e - 9*A*b^3*d^2*e - 5*B*a^2*b*d*e^2 + 6*A*a*b^2*d*e^2 - 2*B*a^3*e^3 + 3*A*a^2*b*e^3)*x)/((b*d - a*e)^4*(b*x + a)*(x*e + d)^2)","B",0
1701,1,415,0,0.179761," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, B b^{2} d^{2} e^{2} - 8 \, B a b d e^{3} + 2 \, A b^{2} d e^{3} + 5 \, B a^{2} e^{4} - 2 \, A a b e^{4}\right)} \log\left({\left| b x + a \right|}\right)}{b^{6}} + \frac{B b^{4} x^{2} e^{4} + 8 \, B b^{4} d x e^{3} - 8 \, B a b^{3} x e^{4} + 2 \, A b^{4} x e^{4}}{2 \, b^{8}} - \frac{B a b^{4} d^{4} + 2 \, A b^{5} d^{4} + 8 \, B a^{2} b^{3} d^{3} e + 4 \, A a b^{4} d^{3} e - 66 \, B a^{3} b^{2} d^{2} e^{2} + 12 \, A a^{2} b^{3} d^{2} e^{2} + 104 \, B a^{4} b d e^{3} - 44 \, A a^{3} b^{2} d e^{3} - 47 \, B a^{5} e^{4} + 26 \, A a^{4} b e^{4} + 12 \, {\left(2 \, B b^{5} d^{3} e - 9 \, B a b^{4} d^{2} e^{2} + 3 \, A b^{5} d^{2} e^{2} + 12 \, B a^{2} b^{3} d e^{3} - 6 \, A a b^{4} d e^{3} - 5 \, B a^{3} b^{2} e^{4} + 3 \, A a^{2} b^{3} e^{4}\right)} x^{2} + 3 \, {\left(B b^{5} d^{4} + 8 \, B a b^{4} d^{3} e + 4 \, A b^{5} d^{3} e - 54 \, B a^{2} b^{3} d^{2} e^{2} + 12 \, A a b^{4} d^{2} e^{2} + 80 \, B a^{3} b^{2} d e^{3} - 36 \, A a^{2} b^{3} d e^{3} - 35 \, B a^{4} b e^{4} + 20 \, A a^{3} b^{2} e^{4}\right)} x}{6 \, {\left(b x + a\right)}^{3} b^{6}}"," ",0,"2*(3*B*b^2*d^2*e^2 - 8*B*a*b*d*e^3 + 2*A*b^2*d*e^3 + 5*B*a^2*e^4 - 2*A*a*b*e^4)*log(abs(b*x + a))/b^6 + 1/2*(B*b^4*x^2*e^4 + 8*B*b^4*d*x*e^3 - 8*B*a*b^3*x*e^4 + 2*A*b^4*x*e^4)/b^8 - 1/6*(B*a*b^4*d^4 + 2*A*b^5*d^4 + 8*B*a^2*b^3*d^3*e + 4*A*a*b^4*d^3*e - 66*B*a^3*b^2*d^2*e^2 + 12*A*a^2*b^3*d^2*e^2 + 104*B*a^4*b*d*e^3 - 44*A*a^3*b^2*d*e^3 - 47*B*a^5*e^4 + 26*A*a^4*b*e^4 + 12*(2*B*b^5*d^3*e - 9*B*a*b^4*d^2*e^2 + 3*A*b^5*d^2*e^2 + 12*B*a^2*b^3*d*e^3 - 6*A*a*b^4*d*e^3 - 5*B*a^3*b^2*e^4 + 3*A*a^2*b^3*e^4)*x^2 + 3*(B*b^5*d^4 + 8*B*a*b^4*d^3*e + 4*A*b^5*d^3*e - 54*B*a^2*b^3*d^2*e^2 + 12*A*a*b^4*d^2*e^2 + 80*B*a^3*b^2*d*e^3 - 36*A*a^2*b^3*d*e^3 - 35*B*a^4*b*e^4 + 20*A*a^3*b^2*e^4)*x)/((b*x + a)^3*b^6)","B",0
1702,1,266,0,0.190750," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{B x e^{3}}{b^{4}} + \frac{{\left(3 \, B b d e^{2} - 4 \, B a e^{3} + A b e^{3}\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}} - \frac{B a b^{3} d^{3} + 2 \, A b^{4} d^{3} + 6 \, B a^{2} b^{2} d^{2} e + 3 \, A a b^{3} d^{2} e - 33 \, B a^{3} b d e^{2} + 6 \, A a^{2} b^{2} d e^{2} + 26 \, B a^{4} e^{3} - 11 \, A a^{3} b e^{3} + 18 \, {\left(B b^{4} d^{2} e - 3 \, B a b^{3} d e^{2} + A b^{4} d e^{2} + 2 \, B a^{2} b^{2} e^{3} - A a b^{3} e^{3}\right)} x^{2} + 3 \, {\left(B b^{4} d^{3} + 6 \, B a b^{3} d^{2} e + 3 \, A b^{4} d^{2} e - 27 \, B a^{2} b^{2} d e^{2} + 6 \, A a b^{3} d e^{2} + 20 \, B a^{3} b e^{3} - 9 \, A a^{2} b^{2} e^{3}\right)} x}{6 \, {\left(b x + a\right)}^{3} b^{5}}"," ",0,"B*x*e^3/b^4 + (3*B*b*d*e^2 - 4*B*a*e^3 + A*b*e^3)*log(abs(b*x + a))/b^5 - 1/6*(B*a*b^3*d^3 + 2*A*b^4*d^3 + 6*B*a^2*b^2*d^2*e + 3*A*a*b^3*d^2*e - 33*B*a^3*b*d*e^2 + 6*A*a^2*b^2*d*e^2 + 26*B*a^4*e^3 - 11*A*a^3*b*e^3 + 18*(B*b^4*d^2*e - 3*B*a*b^3*d*e^2 + A*b^4*d*e^2 + 2*B*a^2*b^2*e^3 - A*a*b^3*e^3)*x^2 + 3*(B*b^4*d^3 + 6*B*a*b^3*d^2*e + 3*A*b^4*d^2*e - 27*B*a^2*b^2*d*e^2 + 6*A*a*b^3*d*e^2 + 20*B*a^3*b*e^3 - 9*A*a^2*b^2*e^3)*x)/((b*x + a)^3*b^5)","A",0
1703,1,161,0,0.158033," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{B e^{2} \log\left({\left| b x + a \right|}\right)}{b^{4}} - \frac{6 \, {\left(2 \, B b^{2} d e - 3 \, B a b e^{2} + A b^{2} e^{2}\right)} x^{2} + 3 \, {\left(B b^{2} d^{2} + 4 \, B a b d e + 2 \, A b^{2} d e - 9 \, B a^{2} e^{2} + 2 \, A a b e^{2}\right)} x + \frac{B a b^{2} d^{2} + 2 \, A b^{3} d^{2} + 4 \, B a^{2} b d e + 2 \, A a b^{2} d e - 11 \, B a^{3} e^{2} + 2 \, A a^{2} b e^{2}}{b}}{6 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"B*e^2*log(abs(b*x + a))/b^4 - 1/6*(6*(2*B*b^2*d*e - 3*B*a*b*e^2 + A*b^2*e^2)*x^2 + 3*(B*b^2*d^2 + 4*B*a*b*d*e + 2*A*b^2*d*e - 9*B*a^2*e^2 + 2*A*a*b*e^2)*x + (B*a*b^2*d^2 + 2*A*b^3*d^2 + 4*B*a^2*b*d*e + 2*A*a*b^2*d*e - 11*B*a^3*e^2 + 2*A*a^2*b*e^2)/b)/((b*x + a)^3*b^3)","A",0
1704,1,75,0,0.162297," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{6 \, B b^{2} x^{2} e + 3 \, B b^{2} d x + 6 \, B a b x e + 3 \, A b^{2} x e + B a b d + 2 \, A b^{2} d + 2 \, B a^{2} e + A a b e}{6 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"-1/6*(6*B*b^2*x^2*e + 3*B*b^2*d*x + 6*B*a*b*x*e + 3*A*b^2*x*e + B*a*b*d + 2*A*b^2*d + 2*B*a^2*e + A*a*b*e)/((b*x + a)^3*b^3)","A",0
1705,1,25,0,0.150538," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{3 \, B b x + B a + 2 \, A b}{6 \, {\left(b x + a\right)}^{3} b^{2}}"," ",0,"-1/6*(3*B*b*x + B*a + 2*A*b)/((b*x + a)^3*b^2)","A",0
1706,1,364,0,0.185833," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(B b d e^{2} - A b e^{3}\right)} \log\left({\left| b x + a \right|}\right)}{b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}} - \frac{{\left(B d e^{3} - A e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} - \frac{B a b^{3} d^{3} + 2 \, A b^{4} d^{3} - 6 \, B a^{2} b^{2} d^{2} e - 9 \, A a b^{3} d^{2} e + 3 \, B a^{3} b d e^{2} + 18 \, A a^{2} b^{2} d e^{2} + 2 \, B a^{4} e^{3} - 11 \, A a^{3} b e^{3} - 6 \, {\left(B b^{4} d^{2} e - B a b^{3} d e^{2} - A b^{4} d e^{2} + A a b^{3} e^{3}\right)} x^{2} + 3 \, {\left(B b^{4} d^{3} - 6 \, B a b^{3} d^{2} e - A b^{4} d^{2} e + 5 \, B a^{2} b^{2} d e^{2} + 6 \, A a b^{3} d e^{2} - 5 \, A a^{2} b^{2} e^{3}\right)} x}{6 \, {\left(b d - a e\right)}^{4} {\left(b x + a\right)}^{3} b}"," ",0,"(B*b*d*e^2 - A*b*e^3)*log(abs(b*x + a))/(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4) - (B*d*e^3 - A*e^4)*log(abs(x*e + d))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) - 1/6*(B*a*b^3*d^3 + 2*A*b^4*d^3 - 6*B*a^2*b^2*d^2*e - 9*A*a*b^3*d^2*e + 3*B*a^3*b*d*e^2 + 18*A*a^2*b^2*d*e^2 + 2*B*a^4*e^3 - 11*A*a^3*b*e^3 - 6*(B*b^4*d^2*e - B*a*b^3*d*e^2 - A*b^4*d*e^2 + A*a*b^3*e^3)*x^2 + 3*(B*b^4*d^3 - 6*B*a*b^3*d^2*e - A*b^4*d^2*e + 5*B*a^2*b^2*d*e^2 + 6*A*a*b^3*d*e^2 - 5*A*a^2*b^2*e^3)*x)/((b*d - a*e)^4*(b*x + a)^3*b)","B",0
1707,1,411,0,0.224528," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(3 \, B b d e^{3} + B a e^{4} - 4 \, A b e^{4}\right)} \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{5} d^{5} e - 5 \, a b^{4} d^{4} e^{2} + 10 \, a^{2} b^{3} d^{3} e^{3} - 10 \, a^{3} b^{2} d^{2} e^{4} + 5 \, a^{4} b d e^{5} - a^{5} e^{6}} + \frac{\frac{B d e^{6}}{x e + d} - \frac{A e^{7}}{x e + d}}{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}} + \frac{15 \, B b^{4} d e^{2} + 11 \, B a b^{3} e^{3} - 26 \, A b^{4} e^{3} - \frac{3 \, {\left(11 \, B b^{4} d^{2} e^{3} - 2 \, B a b^{3} d e^{4} - 20 \, A b^{4} d e^{4} - 9 \, B a^{2} b^{2} e^{5} + 20 \, A a b^{3} e^{5}\right)} e^{\left(-1\right)}}{x e + d} + \frac{18 \, {\left(B b^{4} d^{3} e^{4} - B a b^{3} d^{2} e^{5} - 2 \, A b^{4} d^{2} e^{5} - B a^{2} b^{2} d e^{6} + 4 \, A a b^{3} d e^{6} + B a^{3} b e^{7} - 2 \, A a^{2} b^{2} e^{7}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}}{6 \, {\left(b d - a e\right)}^{5} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{3}}"," ",0,"(3*B*b*d*e^3 + B*a*e^4 - 4*A*b*e^4)*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^5*d^5*e - 5*a*b^4*d^4*e^2 + 10*a^2*b^3*d^3*e^3 - 10*a^3*b^2*d^2*e^4 + 5*a^4*b*d*e^5 - a^5*e^6) + (B*d*e^6/(x*e + d) - A*e^7/(x*e + d))/(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) + 1/6*(15*B*b^4*d*e^2 + 11*B*a*b^3*e^3 - 26*A*b^4*e^3 - 3*(11*B*b^4*d^2*e^3 - 2*B*a*b^3*d*e^4 - 20*A*b^4*d*e^4 - 9*B*a^2*b^2*e^5 + 20*A*a*b^3*e^5)*e^(-1)/(x*e + d) + 18*(B*b^4*d^3*e^4 - B*a*b^3*d^2*e^5 - 2*A*b^4*d^2*e^5 - B*a^2*b^2*d*e^6 + 4*A*a*b^3*d*e^6 + B*a^3*b*e^7 - 2*A*a^2*b^2*e^7)*e^(-2)/(x*e + d)^2)/((b*d - a*e)^5*(b - b*d/(x*e + d) + a*e/(x*e + d))^3)","B",0
1708,1,328,0,0.171352," ","integrate((B*x+A)*(e*x+d)^4*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{7} \, B b x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B b d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, B b d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + B b d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B b d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, B a x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, B a d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, A b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, B a d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, B a d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, A b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A a x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + A a d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, A a d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, A a d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/7*B*b*x^7*e^4*sgn(b*x + a) + 2/3*B*b*d*x^6*e^3*sgn(b*x + a) + 6/5*B*b*d^2*x^5*e^2*sgn(b*x + a) + B*b*d^3*x^4*e*sgn(b*x + a) + 1/3*B*b*d^4*x^3*sgn(b*x + a) + 1/6*B*a*x^6*e^4*sgn(b*x + a) + 1/6*A*b*x^6*e^4*sgn(b*x + a) + 4/5*B*a*d*x^5*e^3*sgn(b*x + a) + 4/5*A*b*d*x^5*e^3*sgn(b*x + a) + 3/2*B*a*d^2*x^4*e^2*sgn(b*x + a) + 3/2*A*b*d^2*x^4*e^2*sgn(b*x + a) + 4/3*B*a*d^3*x^3*e*sgn(b*x + a) + 4/3*A*b*d^3*x^3*e*sgn(b*x + a) + 1/2*B*a*d^4*x^2*sgn(b*x + a) + 1/2*A*b*d^4*x^2*sgn(b*x + a) + 1/5*A*a*x^5*e^4*sgn(b*x + a) + A*a*d*x^4*e^3*sgn(b*x + a) + 2*A*a*d^2*x^3*e^2*sgn(b*x + a) + 2*A*a*d^3*x^2*e*sgn(b*x + a) + A*a*d^4*x*sgn(b*x + a)","B",0
1709,1,255,0,0.178456," ","integrate((B*x+A)*(e*x+d)^3*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, B b x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, B b d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B b d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B b d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B a x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, A b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + B a d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + A b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A a x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + A a d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*B*b*x^6*e^3*sgn(b*x + a) + 3/5*B*b*d*x^5*e^2*sgn(b*x + a) + 3/4*B*b*d^2*x^4*e*sgn(b*x + a) + 1/3*B*b*d^3*x^3*sgn(b*x + a) + 1/5*B*a*x^5*e^3*sgn(b*x + a) + 1/5*A*b*x^5*e^3*sgn(b*x + a) + 3/4*B*a*d*x^4*e^2*sgn(b*x + a) + 3/4*A*b*d*x^4*e^2*sgn(b*x + a) + B*a*d^2*x^3*e*sgn(b*x + a) + A*b*d^2*x^3*e*sgn(b*x + a) + 1/2*B*a*d^3*x^2*sgn(b*x + a) + 1/2*A*b*d^3*x^2*sgn(b*x + a) + 1/4*A*a*x^4*e^3*sgn(b*x + a) + A*a*d*x^3*e^2*sgn(b*x + a) + 3/2*A*a*d^2*x^2*e*sgn(b*x + a) + A*a*d^3*x*sgn(b*x + a)","B",0
1710,1,185,0,0.161321," ","integrate((B*x+A)*(e*x+d)^2*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, B b x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B b d x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B b d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, B a x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, A b d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A a x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + A a d x^{2} e \mathrm{sgn}\left(b x + a\right) + A a d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/5*B*b*x^5*e^2*sgn(b*x + a) + 1/2*B*b*d*x^4*e*sgn(b*x + a) + 1/3*B*b*d^2*x^3*sgn(b*x + a) + 1/4*B*a*x^4*e^2*sgn(b*x + a) + 1/4*A*b*x^4*e^2*sgn(b*x + a) + 2/3*B*a*d*x^3*e*sgn(b*x + a) + 2/3*A*b*d*x^3*e*sgn(b*x + a) + 1/2*B*a*d^2*x^2*sgn(b*x + a) + 1/2*A*b*d^2*x^2*sgn(b*x + a) + 1/3*A*a*x^3*e^2*sgn(b*x + a) + A*a*d*x^2*e*sgn(b*x + a) + A*a*d^2*x*sgn(b*x + a)","A",0
1711,1,114,0,0.159833," ","integrate((B*x+A)*(e*x+d)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, B b x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B b d x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A b x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a x^{2} e \mathrm{sgn}\left(b x + a\right) + A a d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/4*B*b*x^4*e*sgn(b*x + a) + 1/3*B*b*d*x^3*sgn(b*x + a) + 1/3*B*a*x^3*e*sgn(b*x + a) + 1/3*A*b*x^3*e*sgn(b*x + a) + 1/2*B*a*d*x^2*sgn(b*x + a) + 1/2*A*b*d*x^2*sgn(b*x + a) + 1/2*A*a*x^2*e*sgn(b*x + a) + A*a*d*x*sgn(b*x + a)","A",0
1712,1,74,0,0.210740," ","integrate((B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, B b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b x^{2} \mathrm{sgn}\left(b x + a\right) + A a x \mathrm{sgn}\left(b x + a\right) - \frac{{\left(B a^{3} - 3 \, A a^{2} b\right)} \mathrm{sgn}\left(b x + a\right)}{6 \, b^{2}}"," ",0,"1/3*B*b*x^3*sgn(b*x + a) + 1/2*B*a*x^2*sgn(b*x + a) + 1/2*A*b*x^2*sgn(b*x + a) + A*a*x*sgn(b*x + a) - 1/6*(B*a^3 - 3*A*a^2*b)*sgn(b*x + a)/b^2","A",0
1713,1,119,0,0.164981," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","{\left(B b d^{2} \mathrm{sgn}\left(b x + a\right) - B a d e \mathrm{sgn}\left(b x + a\right) - A b d e \mathrm{sgn}\left(b x + a\right) + A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B b x^{2} e \mathrm{sgn}\left(b x + a\right) - 2 \, B b d x \mathrm{sgn}\left(b x + a\right) + 2 \, B a x e \mathrm{sgn}\left(b x + a\right) + 2 \, A b x e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}"," ",0,"(B*b*d^2*sgn(b*x + a) - B*a*d*e*sgn(b*x + a) - A*b*d*e*sgn(b*x + a) + A*a*e^2*sgn(b*x + a))*e^(-3)*log(abs(x*e + d)) + 1/2*(B*b*x^2*e*sgn(b*x + a) - 2*B*b*d*x*sgn(b*x + a) + 2*B*a*x*e*sgn(b*x + a) + 2*A*b*x*e*sgn(b*x + a))*e^(-2)","A",0
1714,1,123,0,0.181825," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","B b x e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) - {\left(2 \, B b d \mathrm{sgn}\left(b x + a\right) - B a e \mathrm{sgn}\left(b x + a\right) - A b e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(B b d^{2} \mathrm{sgn}\left(b x + a\right) - B a d e \mathrm{sgn}\left(b x + a\right) - A b d e \mathrm{sgn}\left(b x + a\right) + A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{x e + d}"," ",0,"B*b*x*e^(-2)*sgn(b*x + a) - (2*B*b*d*sgn(b*x + a) - B*a*e*sgn(b*x + a) - A*b*e*sgn(b*x + a))*e^(-3)*log(abs(x*e + d)) - (B*b*d^2*sgn(b*x + a) - B*a*d*e*sgn(b*x + a) - A*b*d*e*sgn(b*x + a) + A*a*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)","A",0
1715,1,127,0,0.182772," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","B b e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(2 \, {\left(2 \, B b d \mathrm{sgn}\left(b x + a\right) - B a e \mathrm{sgn}\left(b x + a\right) - A b e \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(3 \, B b d^{2} \mathrm{sgn}\left(b x + a\right) - B a d e \mathrm{sgn}\left(b x + a\right) - A b d e \mathrm{sgn}\left(b x + a\right) - A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"B*b*e^(-3)*log(abs(x*e + d))*sgn(b*x + a) + 1/2*(2*(2*B*b*d*sgn(b*x + a) - B*a*e*sgn(b*x + a) - A*b*e*sgn(b*x + a))*x + (3*B*b*d^2*sgn(b*x + a) - B*a*d*e*sgn(b*x + a) - A*b*d*e*sgn(b*x + a) - A*a*e^2*sgn(b*x + a))*e^(-1))*e^(-2)/(x*e + d)^2","A",0
1716,1,117,0,0.164174," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(6 \, B b x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B b d x e \mathrm{sgn}\left(b x + a\right) + 2 \, B b d^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A b x e^{2} \mathrm{sgn}\left(b x + a\right) + B a d e \mathrm{sgn}\left(b x + a\right) + A b d e \mathrm{sgn}\left(b x + a\right) + 2 \, A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/6*(6*B*b*x^2*e^2*sgn(b*x + a) + 6*B*b*d*x*e*sgn(b*x + a) + 2*B*b*d^2*sgn(b*x + a) + 3*B*a*x*e^2*sgn(b*x + a) + 3*A*b*x*e^2*sgn(b*x + a) + B*a*d*e*sgn(b*x + a) + A*b*d*e*sgn(b*x + a) + 2*A*a*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^3","A",0
1717,1,116,0,0.201291," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{{\left(6 \, B b x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, B b d x e \mathrm{sgn}\left(b x + a\right) + B b d^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, B a x e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, A b x e^{2} \mathrm{sgn}\left(b x + a\right) + B a d e \mathrm{sgn}\left(b x + a\right) + A b d e \mathrm{sgn}\left(b x + a\right) + 3 \, A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{12 \, {\left(x e + d\right)}^{4}}"," ",0,"-1/12*(6*B*b*x^2*e^2*sgn(b*x + a) + 4*B*b*d*x*e*sgn(b*x + a) + B*b*d^2*sgn(b*x + a) + 4*B*a*x*e^2*sgn(b*x + a) + 4*A*b*x*e^2*sgn(b*x + a) + B*a*d*e*sgn(b*x + a) + A*b*d*e*sgn(b*x + a) + 3*A*a*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^4","A",0
1718,1,119,0,0.160165," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(20 \, B b x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, B b d x e \mathrm{sgn}\left(b x + a\right) + 2 \, B b d^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, B a x e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, A b x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a d e \mathrm{sgn}\left(b x + a\right) + 3 \, A b d e \mathrm{sgn}\left(b x + a\right) + 12 \, A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/60*(20*B*b*x^2*e^2*sgn(b*x + a) + 10*B*b*d*x*e*sgn(b*x + a) + 2*B*b*d^2*sgn(b*x + a) + 15*B*a*x*e^2*sgn(b*x + a) + 15*A*b*x*e^2*sgn(b*x + a) + 3*B*a*d*e*sgn(b*x + a) + 3*A*b*d*e*sgn(b*x + a) + 12*A*a*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^5","A",0
1719,1,118,0,0.158569," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(15 \, B b x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B b d x e \mathrm{sgn}\left(b x + a\right) + B b d^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B a x e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, A b x e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, B a d e \mathrm{sgn}\left(b x + a\right) + 2 \, A b d e \mathrm{sgn}\left(b x + a\right) + 10 \, A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(15*B*b*x^2*e^2*sgn(b*x + a) + 6*B*b*d*x*e*sgn(b*x + a) + B*b*d^2*sgn(b*x + a) + 12*B*a*x*e^2*sgn(b*x + a) + 12*A*b*x*e^2*sgn(b*x + a) + 2*B*a*d*e*sgn(b*x + a) + 2*A*b*d*e*sgn(b*x + a) + 10*A*a*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^6","A",0
1720,1,922,0,0.219315," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{10} \, B b^{3} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, B b^{3} d x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B b^{3} d^{2} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B b^{3} d^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B b^{3} d^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B b^{3} d^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a b^{2} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{9} \, A b^{3} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{8} \, B a b^{2} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, A b^{3} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, B a b^{2} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, A b^{3} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a b^{2} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A b^{3} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + A b^{3} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a b^{2} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{3} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, B a^{2} b x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, A a b^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, B a^{2} b d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, A a b^{2} d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{2} b d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, A a b^{2} d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{2} d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, B a^{2} b d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, A a b^{2} d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + B a^{2} b d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{2} d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B a^{3} x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, A a^{2} b x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a^{3} d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{3} d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{2} b d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, A a^{2} b d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{3} d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{2} b d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{3} d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{2} b d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A a^{3} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + A a^{3} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{3} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{3} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{3} d^{5} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/10*B*b^3*x^10*e^5*sgn(b*x + a) + 5/9*B*b^3*d*x^9*e^4*sgn(b*x + a) + 5/4*B*b^3*d^2*x^8*e^3*sgn(b*x + a) + 10/7*B*b^3*d^3*x^7*e^2*sgn(b*x + a) + 5/6*B*b^3*d^4*x^6*e*sgn(b*x + a) + 1/5*B*b^3*d^5*x^5*sgn(b*x + a) + 1/3*B*a*b^2*x^9*e^5*sgn(b*x + a) + 1/9*A*b^3*x^9*e^5*sgn(b*x + a) + 15/8*B*a*b^2*d*x^8*e^4*sgn(b*x + a) + 5/8*A*b^3*d*x^8*e^4*sgn(b*x + a) + 30/7*B*a*b^2*d^2*x^7*e^3*sgn(b*x + a) + 10/7*A*b^3*d^2*x^7*e^3*sgn(b*x + a) + 5*B*a*b^2*d^3*x^6*e^2*sgn(b*x + a) + 5/3*A*b^3*d^3*x^6*e^2*sgn(b*x + a) + 3*B*a*b^2*d^4*x^5*e*sgn(b*x + a) + A*b^3*d^4*x^5*e*sgn(b*x + a) + 3/4*B*a*b^2*d^5*x^4*sgn(b*x + a) + 1/4*A*b^3*d^5*x^4*sgn(b*x + a) + 3/8*B*a^2*b*x^8*e^5*sgn(b*x + a) + 3/8*A*a*b^2*x^8*e^5*sgn(b*x + a) + 15/7*B*a^2*b*d*x^7*e^4*sgn(b*x + a) + 15/7*A*a*b^2*d*x^7*e^4*sgn(b*x + a) + 5*B*a^2*b*d^2*x^6*e^3*sgn(b*x + a) + 5*A*a*b^2*d^2*x^6*e^3*sgn(b*x + a) + 6*B*a^2*b*d^3*x^5*e^2*sgn(b*x + a) + 6*A*a*b^2*d^3*x^5*e^2*sgn(b*x + a) + 15/4*B*a^2*b*d^4*x^4*e*sgn(b*x + a) + 15/4*A*a*b^2*d^4*x^4*e*sgn(b*x + a) + B*a^2*b*d^5*x^3*sgn(b*x + a) + A*a*b^2*d^5*x^3*sgn(b*x + a) + 1/7*B*a^3*x^7*e^5*sgn(b*x + a) + 3/7*A*a^2*b*x^7*e^5*sgn(b*x + a) + 5/6*B*a^3*d*x^6*e^4*sgn(b*x + a) + 5/2*A*a^2*b*d*x^6*e^4*sgn(b*x + a) + 2*B*a^3*d^2*x^5*e^3*sgn(b*x + a) + 6*A*a^2*b*d^2*x^5*e^3*sgn(b*x + a) + 5/2*B*a^3*d^3*x^4*e^2*sgn(b*x + a) + 15/2*A*a^2*b*d^3*x^4*e^2*sgn(b*x + a) + 5/3*B*a^3*d^4*x^3*e*sgn(b*x + a) + 5*A*a^2*b*d^4*x^3*e*sgn(b*x + a) + 1/2*B*a^3*d^5*x^2*sgn(b*x + a) + 3/2*A*a^2*b*d^5*x^2*sgn(b*x + a) + 1/6*A*a^3*x^6*e^5*sgn(b*x + a) + A*a^3*d*x^5*e^4*sgn(b*x + a) + 5/2*A*a^3*d^2*x^4*e^3*sgn(b*x + a) + 10/3*A*a^3*d^3*x^3*e^2*sgn(b*x + a) + 5/2*A*a^3*d^4*x^2*e*sgn(b*x + a) + A*a^3*d^5*x*sgn(b*x + a)","B",0
1721,1,758,0,0.198219," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, B b^{3} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B b^{3} d x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, B b^{3} d^{2} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B b^{3} d^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B b^{3} d^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, B a b^{2} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, A b^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{12}{7} \, B a b^{2} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{4}{7} \, A b^{3} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + A b^{3} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{12}{5} \, B a b^{2} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, A b^{3} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a b^{2} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{3} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, B a^{2} b x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, A a b^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{2} d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{18}{5} \, B a^{2} b d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{18}{5} \, A a b^{2} d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{2} b d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{2} d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + B a^{2} b d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{2} d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, B a^{3} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a^{2} b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, B a^{3} d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{12}{5} \, A a^{2} b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, B a^{3} d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, A a^{2} b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, B a^{3} d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{2} b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{3} d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{2} b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A a^{3} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + A a^{3} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{3} d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/9*B*b^3*x^9*e^4*sgn(b*x + a) + 1/2*B*b^3*d*x^8*e^3*sgn(b*x + a) + 6/7*B*b^3*d^2*x^7*e^2*sgn(b*x + a) + 2/3*B*b^3*d^3*x^6*e*sgn(b*x + a) + 1/5*B*b^3*d^4*x^5*sgn(b*x + a) + 3/8*B*a*b^2*x^8*e^4*sgn(b*x + a) + 1/8*A*b^3*x^8*e^4*sgn(b*x + a) + 12/7*B*a*b^2*d*x^7*e^3*sgn(b*x + a) + 4/7*A*b^3*d*x^7*e^3*sgn(b*x + a) + 3*B*a*b^2*d^2*x^6*e^2*sgn(b*x + a) + A*b^3*d^2*x^6*e^2*sgn(b*x + a) + 12/5*B*a*b^2*d^3*x^5*e*sgn(b*x + a) + 4/5*A*b^3*d^3*x^5*e*sgn(b*x + a) + 3/4*B*a*b^2*d^4*x^4*sgn(b*x + a) + 1/4*A*b^3*d^4*x^4*sgn(b*x + a) + 3/7*B*a^2*b*x^7*e^4*sgn(b*x + a) + 3/7*A*a*b^2*x^7*e^4*sgn(b*x + a) + 2*B*a^2*b*d*x^6*e^3*sgn(b*x + a) + 2*A*a*b^2*d*x^6*e^3*sgn(b*x + a) + 18/5*B*a^2*b*d^2*x^5*e^2*sgn(b*x + a) + 18/5*A*a*b^2*d^2*x^5*e^2*sgn(b*x + a) + 3*B*a^2*b*d^3*x^4*e*sgn(b*x + a) + 3*A*a*b^2*d^3*x^4*e*sgn(b*x + a) + B*a^2*b*d^4*x^3*sgn(b*x + a) + A*a*b^2*d^4*x^3*sgn(b*x + a) + 1/6*B*a^3*x^6*e^4*sgn(b*x + a) + 1/2*A*a^2*b*x^6*e^4*sgn(b*x + a) + 4/5*B*a^3*d*x^5*e^3*sgn(b*x + a) + 12/5*A*a^2*b*d*x^5*e^3*sgn(b*x + a) + 3/2*B*a^3*d^2*x^4*e^2*sgn(b*x + a) + 9/2*A*a^2*b*d^2*x^4*e^2*sgn(b*x + a) + 4/3*B*a^3*d^3*x^3*e*sgn(b*x + a) + 4*A*a^2*b*d^3*x^3*e*sgn(b*x + a) + 1/2*B*a^3*d^4*x^2*sgn(b*x + a) + 3/2*A*a^2*b*d^4*x^2*sgn(b*x + a) + 1/5*A*a^3*x^5*e^4*sgn(b*x + a) + A*a^3*d*x^4*e^3*sgn(b*x + a) + 2*A*a^3*d^2*x^3*e^2*sgn(b*x + a) + 2*A*a^3*d^3*x^2*e*sgn(b*x + a) + A*a^3*d^4*x*sgn(b*x + a)","B",0
1722,1,594,0,0.205894," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, B b^{3} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, B b^{3} d x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B b^{3} d^{2} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B b^{3} d^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, B a b^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, A b^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, B a b^{2} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b^{3} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{5} \, B a b^{2} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, A b^{3} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a b^{2} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{3} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{2} b x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a b^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{9}{5} \, B a^{2} b d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{5} \, A a b^{2} d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{4} \, B a^{2} b d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{9}{4} \, A a b^{2} d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + B a^{2} b d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{2} d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B a^{3} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, A a^{2} b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a^{3} d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{4} \, A a^{2} b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + B a^{3} d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{3} d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{2} b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A a^{3} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{3} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{3} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{3} d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/8*B*b^3*x^8*e^3*sgn(b*x + a) + 3/7*B*b^3*d*x^7*e^2*sgn(b*x + a) + 1/2*B*b^3*d^2*x^6*e*sgn(b*x + a) + 1/5*B*b^3*d^3*x^5*sgn(b*x + a) + 3/7*B*a*b^2*x^7*e^3*sgn(b*x + a) + 1/7*A*b^3*x^7*e^3*sgn(b*x + a) + 3/2*B*a*b^2*d*x^6*e^2*sgn(b*x + a) + 1/2*A*b^3*d*x^6*e^2*sgn(b*x + a) + 9/5*B*a*b^2*d^2*x^5*e*sgn(b*x + a) + 3/5*A*b^3*d^2*x^5*e*sgn(b*x + a) + 3/4*B*a*b^2*d^3*x^4*sgn(b*x + a) + 1/4*A*b^3*d^3*x^4*sgn(b*x + a) + 1/2*B*a^2*b*x^6*e^3*sgn(b*x + a) + 1/2*A*a*b^2*x^6*e^3*sgn(b*x + a) + 9/5*B*a^2*b*d*x^5*e^2*sgn(b*x + a) + 9/5*A*a*b^2*d*x^5*e^2*sgn(b*x + a) + 9/4*B*a^2*b*d^2*x^4*e*sgn(b*x + a) + 9/4*A*a*b^2*d^2*x^4*e*sgn(b*x + a) + B*a^2*b*d^3*x^3*sgn(b*x + a) + A*a*b^2*d^3*x^3*sgn(b*x + a) + 1/5*B*a^3*x^5*e^3*sgn(b*x + a) + 3/5*A*a^2*b*x^5*e^3*sgn(b*x + a) + 3/4*B*a^3*d*x^4*e^2*sgn(b*x + a) + 9/4*A*a^2*b*d*x^4*e^2*sgn(b*x + a) + B*a^3*d^2*x^3*e*sgn(b*x + a) + 3*A*a^2*b*d^2*x^3*e*sgn(b*x + a) + 1/2*B*a^3*d^3*x^2*sgn(b*x + a) + 3/2*A*a^2*b*d^3*x^2*sgn(b*x + a) + 1/4*A*a^3*x^4*e^3*sgn(b*x + a) + A*a^3*d*x^3*e^2*sgn(b*x + a) + 3/2*A*a^3*d^2*x^2*e*sgn(b*x + a) + A*a^3*d^3*x*sgn(b*x + a)","B",0
1723,1,431,0,0.177438," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7} \, B b^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B b^{3} d x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B b^{3} d^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a b^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, B a b^{2} d x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, A b^{3} d x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a b^{2} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{3} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, B a^{2} b x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, A a b^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, B a^{2} b d x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a b^{2} d x^{4} e \mathrm{sgn}\left(b x + a\right) + B a^{2} b d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{2} d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, B a^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, A a^{2} b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a^{3} d x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{2} b d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{3} d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{2} b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A a^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + A a^{3} d x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{3} d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/7*B*b^3*x^7*e^2*sgn(b*x + a) + 1/3*B*b^3*d*x^6*e*sgn(b*x + a) + 1/5*B*b^3*d^2*x^5*sgn(b*x + a) + 1/2*B*a*b^2*x^6*e^2*sgn(b*x + a) + 1/6*A*b^3*x^6*e^2*sgn(b*x + a) + 6/5*B*a*b^2*d*x^5*e*sgn(b*x + a) + 2/5*A*b^3*d*x^5*e*sgn(b*x + a) + 3/4*B*a*b^2*d^2*x^4*sgn(b*x + a) + 1/4*A*b^3*d^2*x^4*sgn(b*x + a) + 3/5*B*a^2*b*x^5*e^2*sgn(b*x + a) + 3/5*A*a*b^2*x^5*e^2*sgn(b*x + a) + 3/2*B*a^2*b*d*x^4*e*sgn(b*x + a) + 3/2*A*a*b^2*d*x^4*e*sgn(b*x + a) + B*a^2*b*d^2*x^3*sgn(b*x + a) + A*a*b^2*d^2*x^3*sgn(b*x + a) + 1/4*B*a^3*x^4*e^2*sgn(b*x + a) + 3/4*A*a^2*b*x^4*e^2*sgn(b*x + a) + 2/3*B*a^3*d*x^3*e*sgn(b*x + a) + 2*A*a^2*b*d*x^3*e*sgn(b*x + a) + 1/2*B*a^3*d^2*x^2*sgn(b*x + a) + 3/2*A*a^2*b*d^2*x^2*sgn(b*x + a) + 1/3*A*a^3*x^3*e^2*sgn(b*x + a) + A*a^3*d*x^2*e*sgn(b*x + a) + A*a^3*d^2*x*sgn(b*x + a)","B",0
1724,1,267,0,0.168931," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, B b^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B b^{3} d x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, B a b^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A b^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a b^{2} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{3} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a^{2} b x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, A a b^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + B a^{2} b d x^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{2} d x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + A a^{2} b x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{3} d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{2} b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{3} d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*B*b^3*x^6*e*sgn(b*x + a) + 1/5*B*b^3*d*x^5*sgn(b*x + a) + 3/5*B*a*b^2*x^5*e*sgn(b*x + a) + 1/5*A*b^3*x^5*e*sgn(b*x + a) + 3/4*B*a*b^2*d*x^4*sgn(b*x + a) + 1/4*A*b^3*d*x^4*sgn(b*x + a) + 3/4*B*a^2*b*x^4*e*sgn(b*x + a) + 3/4*A*a*b^2*x^4*e*sgn(b*x + a) + B*a^2*b*d*x^3*sgn(b*x + a) + A*a*b^2*d*x^3*sgn(b*x + a) + 1/3*B*a^3*x^3*e*sgn(b*x + a) + A*a^2*b*x^3*e*sgn(b*x + a) + 1/2*B*a^3*d*x^2*sgn(b*x + a) + 3/2*A*a^2*b*d*x^2*sgn(b*x + a) + 1/2*A*a^3*x^2*e*sgn(b*x + a) + A*a^3*d*x*sgn(b*x + a)","B",0
1725,1,144,0,0.188201," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{5} \, B b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + B a^{2} b x^{3} \mathrm{sgn}\left(b x + a\right) + A a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) + A a^{3} x \mathrm{sgn}\left(b x + a\right) - \frac{{\left(B a^{5} - 5 \, A a^{4} b\right)} \mathrm{sgn}\left(b x + a\right)}{20 \, b^{2}}"," ",0,"1/5*B*b^3*x^5*sgn(b*x + a) + 3/4*B*a*b^2*x^4*sgn(b*x + a) + 1/4*A*b^3*x^4*sgn(b*x + a) + B*a^2*b*x^3*sgn(b*x + a) + A*a*b^2*x^3*sgn(b*x + a) + 1/2*B*a^3*x^2*sgn(b*x + a) + 3/2*A*a^2*b*x^2*sgn(b*x + a) + A*a^3*x*sgn(b*x + a) - 1/20*(B*a^5 - 5*A*a^4*b)*sgn(b*x + a)/b^2","B",0
1726,1,428,0,0.178497," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d),x, algorithm=""giac"")","{\left(B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, B b^{3} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) - 4 \, B b^{3} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B b^{3} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) - 12 \, B b^{3} d^{3} x \mathrm{sgn}\left(b x + a\right) + 12 \, B a b^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, A b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 18 \, B a b^{2} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, A b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 36 \, B a b^{2} d^{2} x e \mathrm{sgn}\left(b x + a\right) + 12 \, A b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + 18 \, B a^{2} b x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, A a b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 36 \, B a^{2} b d x e^{2} \mathrm{sgn}\left(b x + a\right) - 36 \, A a b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, A a^{2} b x e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}"," ",0,"(B*b^3*d^4*sgn(b*x + a) - 3*B*a*b^2*d^3*e*sgn(b*x + a) - A*b^3*d^3*e*sgn(b*x + a) + 3*B*a^2*b*d^2*e^2*sgn(b*x + a) + 3*A*a*b^2*d^2*e^2*sgn(b*x + a) - B*a^3*d*e^3*sgn(b*x + a) - 3*A*a^2*b*d*e^3*sgn(b*x + a) + A*a^3*e^4*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) + 1/12*(3*B*b^3*x^4*e^3*sgn(b*x + a) - 4*B*b^3*d*x^3*e^2*sgn(b*x + a) + 6*B*b^3*d^2*x^2*e*sgn(b*x + a) - 12*B*b^3*d^3*x*sgn(b*x + a) + 12*B*a*b^2*x^3*e^3*sgn(b*x + a) + 4*A*b^3*x^3*e^3*sgn(b*x + a) - 18*B*a*b^2*d*x^2*e^2*sgn(b*x + a) - 6*A*b^3*d*x^2*e^2*sgn(b*x + a) + 36*B*a*b^2*d^2*x*e*sgn(b*x + a) + 12*A*b^3*d^2*x*e*sgn(b*x + a) + 18*B*a^2*b*x^2*e^3*sgn(b*x + a) + 18*A*a*b^2*x^2*e^3*sgn(b*x + a) - 36*B*a^2*b*d*x*e^2*sgn(b*x + a) - 36*A*a*b^2*d*x*e^2*sgn(b*x + a) + 12*B*a^3*x*e^3*sgn(b*x + a) + 36*A*a^2*b*x*e^3*sgn(b*x + a))*e^(-4)","B",0
1727,1,425,0,0.193847," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","-{\left(4 \, B b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 9 \, B a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, B b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, B b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, B a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, A b^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 36 \, B a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) - 12 \, A b^{3} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, B a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 18 \, A a b^{2} x e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} - \frac{{\left(B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{x e + d}"," ",0,"-(4*B*b^3*d^3*sgn(b*x + a) - 9*B*a*b^2*d^2*e*sgn(b*x + a) - 3*A*b^3*d^2*e*sgn(b*x + a) + 6*B*a^2*b*d*e^2*sgn(b*x + a) + 6*A*a*b^2*d*e^2*sgn(b*x + a) - B*a^3*e^3*sgn(b*x + a) - 3*A*a^2*b*e^3*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) + 1/6*(2*B*b^3*x^3*e^4*sgn(b*x + a) - 6*B*b^3*d*x^2*e^3*sgn(b*x + a) + 18*B*b^3*d^2*x*e^2*sgn(b*x + a) + 9*B*a*b^2*x^2*e^4*sgn(b*x + a) + 3*A*b^3*x^2*e^4*sgn(b*x + a) - 36*B*a*b^2*d*x*e^3*sgn(b*x + a) - 12*A*b^3*d*x*e^3*sgn(b*x + a) + 18*B*a^2*b*x*e^4*sgn(b*x + a) + 18*A*a*b^2*x*e^4*sgn(b*x + a))*e^(-6) - (B*b^3*d^4*sgn(b*x + a) - 3*B*a*b^2*d^3*e*sgn(b*x + a) - A*b^3*d^3*e*sgn(b*x + a) + 3*B*a^2*b*d^2*e^2*sgn(b*x + a) + 3*A*a*b^2*d^2*e^2*sgn(b*x + a) - B*a^3*d*e^3*sgn(b*x + a) - 3*A*a^2*b*d*e^3*sgn(b*x + a) + A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)","A",0
1728,1,417,0,0.241540," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","3 \, {\left(2 \, B b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} d e \mathrm{sgn}\left(b x + a\right) - A b^{3} d e \mathrm{sgn}\left(b x + a\right) + B a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right) + A a b^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B b^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, B b^{3} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B a b^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, A b^{3} x e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} + \frac{{\left(7 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 15 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - 5 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 9 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) - A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(4 \, B b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) - 9 \, B a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - B a^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"3*(2*B*b^3*d^2*sgn(b*x + a) - 3*B*a*b^2*d*e*sgn(b*x + a) - A*b^3*d*e*sgn(b*x + a) + B*a^2*b*e^2*sgn(b*x + a) + A*a*b^2*e^2*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) + 1/2*(B*b^3*x^2*e^3*sgn(b*x + a) - 6*B*b^3*d*x*e^2*sgn(b*x + a) + 6*B*a*b^2*x*e^3*sgn(b*x + a) + 2*A*b^3*x*e^3*sgn(b*x + a))*e^(-6) + 1/2*(7*B*b^3*d^4*sgn(b*x + a) - 15*B*a*b^2*d^3*e*sgn(b*x + a) - 5*A*b^3*d^3*e*sgn(b*x + a) + 9*B*a^2*b*d^2*e^2*sgn(b*x + a) + 9*A*a*b^2*d^2*e^2*sgn(b*x + a) - B*a^3*d*e^3*sgn(b*x + a) - 3*A*a^2*b*d*e^3*sgn(b*x + a) - A*a^3*e^4*sgn(b*x + a) + 2*(4*B*b^3*d^3*e*sgn(b*x + a) - 9*B*a*b^2*d^2*e^2*sgn(b*x + a) - 3*A*b^3*d^2*e^2*sgn(b*x + a) + 6*B*a^2*b*d*e^3*sgn(b*x + a) + 6*A*a*b^2*d*e^3*sgn(b*x + a) - B*a^3*e^4*sgn(b*x + a) - 3*A*a^2*b*e^4*sgn(b*x + a))*x)*e^(-5)/(x*e + d)^2","A",0
1729,1,411,0,0.188548," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","B b^{3} x e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) - {\left(4 \, B b^{3} d \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} e \mathrm{sgn}\left(b x + a\right) - A b^{3} e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(26 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 33 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - 11 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(2 \, B b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - A b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + B a^{2} b e^{4} \mathrm{sgn}\left(b x + a\right) + A a b^{2} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 3 \, {\left(20 \, B b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) - 27 \, B a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 9 \, A b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + B a^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-5\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"B*b^3*x*e^(-4)*sgn(b*x + a) - (4*B*b^3*d*sgn(b*x + a) - 3*B*a*b^2*e*sgn(b*x + a) - A*b^3*e*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) - 1/6*(26*B*b^3*d^4*sgn(b*x + a) - 33*B*a*b^2*d^3*e*sgn(b*x + a) - 11*A*b^3*d^3*e*sgn(b*x + a) + 6*B*a^2*b*d^2*e^2*sgn(b*x + a) + 6*A*a*b^2*d^2*e^2*sgn(b*x + a) + B*a^3*d*e^3*sgn(b*x + a) + 3*A*a^2*b*d*e^3*sgn(b*x + a) + 2*A*a^3*e^4*sgn(b*x + a) + 18*(2*B*b^3*d^2*e^2*sgn(b*x + a) - 3*B*a*b^2*d*e^3*sgn(b*x + a) - A*b^3*d*e^3*sgn(b*x + a) + B*a^2*b*e^4*sgn(b*x + a) + A*a*b^2*e^4*sgn(b*x + a))*x^2 + 3*(20*B*b^3*d^3*e*sgn(b*x + a) - 27*B*a*b^2*d^2*e^2*sgn(b*x + a) - 9*A*b^3*d^2*e^2*sgn(b*x + a) + 6*B*a^2*b*d*e^3*sgn(b*x + a) + 6*A*a*b^2*d*e^3*sgn(b*x + a) + B*a^3*e^4*sgn(b*x + a) + 3*A*a^2*b*e^4*sgn(b*x + a))*x)*e^(-5)/(x*e + d)^3","A",0
1730,1,419,0,0.231532," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","B b^{3} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(12 \, {\left(4 \, B b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - A b^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 18 \, {\left(6 \, B b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{2} b e^{3} \mathrm{sgn}\left(b x + a\right) - A a b^{2} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 4 \, {\left(22 \, B b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 9 \, B a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, B a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, A a b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(25 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 9 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) - 3 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-4\right)}}{12 \, {\left(x e + d\right)}^{4}}"," ",0,"B*b^3*e^(-5)*log(abs(x*e + d))*sgn(b*x + a) + 1/12*(12*(4*B*b^3*d*e^2*sgn(b*x + a) - 3*B*a*b^2*e^3*sgn(b*x + a) - A*b^3*e^3*sgn(b*x + a))*x^3 + 18*(6*B*b^3*d^2*e*sgn(b*x + a) - 3*B*a*b^2*d*e^2*sgn(b*x + a) - A*b^3*d*e^2*sgn(b*x + a) - B*a^2*b*e^3*sgn(b*x + a) - A*a*b^2*e^3*sgn(b*x + a))*x^2 + 4*(22*B*b^3*d^3*sgn(b*x + a) - 9*B*a*b^2*d^2*e*sgn(b*x + a) - 3*A*b^3*d^2*e*sgn(b*x + a) - 3*B*a^2*b*d*e^2*sgn(b*x + a) - 3*A*a*b^2*d*e^2*sgn(b*x + a) - B*a^3*e^3*sgn(b*x + a) - 3*A*a^2*b*e^3*sgn(b*x + a))*x + (25*B*b^3*d^4*sgn(b*x + a) - 9*B*a*b^2*d^3*e*sgn(b*x + a) - 3*A*b^3*d^3*e*sgn(b*x + a) - 3*B*a^2*b*d^2*e^2*sgn(b*x + a) - 3*A*a*b^2*d^2*e^2*sgn(b*x + a) - B*a^3*d*e^3*sgn(b*x + a) - 3*A*a^2*b*d*e^3*sgn(b*x + a) - 3*A*a^3*e^4*sgn(b*x + a))*e^(-1))*e^(-4)/(x*e + d)^4","B",0
1731,1,425,0,0.185344," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(20 \, B b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 40 \, B b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 40 \, B b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, B b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) + 4 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, B a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, A b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, B a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, A b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, B a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 20 \, B a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, A a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, A a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{20 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/20*(20*B*b^3*x^4*e^4*sgn(b*x + a) + 40*B*b^3*d*x^3*e^3*sgn(b*x + a) + 40*B*b^3*d^2*x^2*e^2*sgn(b*x + a) + 20*B*b^3*d^3*x*e*sgn(b*x + a) + 4*B*b^3*d^4*sgn(b*x + a) + 30*B*a*b^2*x^3*e^4*sgn(b*x + a) + 10*A*b^3*x^3*e^4*sgn(b*x + a) + 30*B*a*b^2*d*x^2*e^3*sgn(b*x + a) + 10*A*b^3*d*x^2*e^3*sgn(b*x + a) + 15*B*a*b^2*d^2*x*e^2*sgn(b*x + a) + 5*A*b^3*d^2*x*e^2*sgn(b*x + a) + 3*B*a*b^2*d^3*e*sgn(b*x + a) + A*b^3*d^3*e*sgn(b*x + a) + 20*B*a^2*b*x^2*e^4*sgn(b*x + a) + 20*A*a*b^2*x^2*e^4*sgn(b*x + a) + 10*B*a^2*b*d*x*e^3*sgn(b*x + a) + 10*A*a*b^2*d*x*e^3*sgn(b*x + a) + 2*B*a^2*b*d^2*e^2*sgn(b*x + a) + 2*A*a*b^2*d^2*e^2*sgn(b*x + a) + 5*B*a^3*x*e^4*sgn(b*x + a) + 15*A*a^2*b*x*e^4*sgn(b*x + a) + B*a^3*d*e^3*sgn(b*x + a) + 3*A*a^2*b*d*e^3*sgn(b*x + a) + 4*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^5","B",0
1732,1,426,0,0.182713," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(30 \, B b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 40 \, B b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, B b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) + 2 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, B a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, A b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 45 \, B a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, A b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, B a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, A b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 45 \, B a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 45 \, A a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 18 \, B a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, A a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 36 \, A a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(30*B*b^3*x^4*e^4*sgn(b*x + a) + 40*B*b^3*d*x^3*e^3*sgn(b*x + a) + 30*B*b^3*d^2*x^2*e^2*sgn(b*x + a) + 12*B*b^3*d^3*x*e*sgn(b*x + a) + 2*B*b^3*d^4*sgn(b*x + a) + 60*B*a*b^2*x^3*e^4*sgn(b*x + a) + 20*A*b^3*x^3*e^4*sgn(b*x + a) + 45*B*a*b^2*d*x^2*e^3*sgn(b*x + a) + 15*A*b^3*d*x^2*e^3*sgn(b*x + a) + 18*B*a*b^2*d^2*x*e^2*sgn(b*x + a) + 6*A*b^3*d^2*x*e^2*sgn(b*x + a) + 3*B*a*b^2*d^3*e*sgn(b*x + a) + A*b^3*d^3*e*sgn(b*x + a) + 45*B*a^2*b*x^2*e^4*sgn(b*x + a) + 45*A*a*b^2*x^2*e^4*sgn(b*x + a) + 18*B*a^2*b*d*x*e^3*sgn(b*x + a) + 18*A*a*b^2*d*x*e^3*sgn(b*x + a) + 3*B*a^2*b*d^2*e^2*sgn(b*x + a) + 3*A*a*b^2*d^2*e^2*sgn(b*x + a) + 12*B*a^3*x*e^4*sgn(b*x + a) + 36*A*a^2*b*x*e^4*sgn(b*x + a) + 2*B*a^3*d*e^3*sgn(b*x + a) + 6*A*a^2*b*d*e^3*sgn(b*x + a) + 10*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^6","B",0
1733,1,427,0,0.230046," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(140 \, B b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 140 \, B b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, B b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 28 \, B b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) + 4 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 315 \, B a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, A b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 189 \, B a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 63 \, A b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 63 \, B a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 21 \, A b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 252 \, B a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 252 \, A a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, B a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, A a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 70 \, B a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 210 \, A a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{420 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/420*(140*B*b^3*x^4*e^4*sgn(b*x + a) + 140*B*b^3*d*x^3*e^3*sgn(b*x + a) + 84*B*b^3*d^2*x^2*e^2*sgn(b*x + a) + 28*B*b^3*d^3*x*e*sgn(b*x + a) + 4*B*b^3*d^4*sgn(b*x + a) + 315*B*a*b^2*x^3*e^4*sgn(b*x + a) + 105*A*b^3*x^3*e^4*sgn(b*x + a) + 189*B*a*b^2*d*x^2*e^3*sgn(b*x + a) + 63*A*b^3*d*x^2*e^3*sgn(b*x + a) + 63*B*a*b^2*d^2*x*e^2*sgn(b*x + a) + 21*A*b^3*d^2*x*e^2*sgn(b*x + a) + 9*B*a*b^2*d^3*e*sgn(b*x + a) + 3*A*b^3*d^3*e*sgn(b*x + a) + 252*B*a^2*b*x^2*e^4*sgn(b*x + a) + 252*A*a*b^2*x^2*e^4*sgn(b*x + a) + 84*B*a^2*b*d*x*e^3*sgn(b*x + a) + 84*A*a*b^2*d*x*e^3*sgn(b*x + a) + 12*B*a^2*b*d^2*e^2*sgn(b*x + a) + 12*A*a*b^2*d^2*e^2*sgn(b*x + a) + 70*B*a^3*x*e^4*sgn(b*x + a) + 210*A*a^2*b*x*e^4*sgn(b*x + a) + 10*B*a^3*d*e^3*sgn(b*x + a) + 30*A*a^2*b*d*e^3*sgn(b*x + a) + 60*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^7","A",0
1734,1,425,0,0.192011," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(70 \, B b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, B b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, B b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, B b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) + B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 168 \, B a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, A b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, B a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, A b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 24 \, B a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, A b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 140 \, A a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 40 \, B a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) + 40 \, A a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 40 \, B a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 120 \, A a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(70*B*b^3*x^4*e^4*sgn(b*x + a) + 56*B*b^3*d*x^3*e^3*sgn(b*x + a) + 28*B*b^3*d^2*x^2*e^2*sgn(b*x + a) + 8*B*b^3*d^3*x*e*sgn(b*x + a) + B*b^3*d^4*sgn(b*x + a) + 168*B*a*b^2*x^3*e^4*sgn(b*x + a) + 56*A*b^3*x^3*e^4*sgn(b*x + a) + 84*B*a*b^2*d*x^2*e^3*sgn(b*x + a) + 28*A*b^3*d*x^2*e^3*sgn(b*x + a) + 24*B*a*b^2*d^2*x*e^2*sgn(b*x + a) + 8*A*b^3*d^2*x*e^2*sgn(b*x + a) + 3*B*a*b^2*d^3*e*sgn(b*x + a) + A*b^3*d^3*e*sgn(b*x + a) + 140*B*a^2*b*x^2*e^4*sgn(b*x + a) + 140*A*a*b^2*x^2*e^4*sgn(b*x + a) + 40*B*a^2*b*d*x*e^3*sgn(b*x + a) + 40*A*a*b^2*d*x*e^3*sgn(b*x + a) + 5*B*a^2*b*d^2*e^2*sgn(b*x + a) + 5*A*a*b^2*d^2*e^2*sgn(b*x + a) + 40*B*a^3*x*e^4*sgn(b*x + a) + 120*A*a^2*b*x*e^4*sgn(b*x + a) + 5*B*a^3*d*e^3*sgn(b*x + a) + 15*A*a^2*b*d*e^3*sgn(b*x + a) + 35*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^8","A",0
1735,1,427,0,0.194557," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(504 \, B b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 336 \, B b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 144 \, B b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 36 \, B b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) + 4 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 1260 \, B a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 420 \, A b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 540 \, B a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 180 \, A b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 135 \, B a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 45 \, A b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + 5 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 1080 \, B a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1080 \, A a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 270 \, B a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) + 270 \, A a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 315 \, B a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 945 \, A a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 105 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 280 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{2520 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/2520*(504*B*b^3*x^4*e^4*sgn(b*x + a) + 336*B*b^3*d*x^3*e^3*sgn(b*x + a) + 144*B*b^3*d^2*x^2*e^2*sgn(b*x + a) + 36*B*b^3*d^3*x*e*sgn(b*x + a) + 4*B*b^3*d^4*sgn(b*x + a) + 1260*B*a*b^2*x^3*e^4*sgn(b*x + a) + 420*A*b^3*x^3*e^4*sgn(b*x + a) + 540*B*a*b^2*d*x^2*e^3*sgn(b*x + a) + 180*A*b^3*d*x^2*e^3*sgn(b*x + a) + 135*B*a*b^2*d^2*x*e^2*sgn(b*x + a) + 45*A*b^3*d^2*x*e^2*sgn(b*x + a) + 15*B*a*b^2*d^3*e*sgn(b*x + a) + 5*A*b^3*d^3*e*sgn(b*x + a) + 1080*B*a^2*b*x^2*e^4*sgn(b*x + a) + 1080*A*a*b^2*x^2*e^4*sgn(b*x + a) + 270*B*a^2*b*d*x*e^3*sgn(b*x + a) + 270*A*a*b^2*d*x*e^3*sgn(b*x + a) + 30*B*a^2*b*d^2*e^2*sgn(b*x + a) + 30*A*a*b^2*d^2*e^2*sgn(b*x + a) + 315*B*a^3*x*e^4*sgn(b*x + a) + 945*A*a^2*b*x*e^4*sgn(b*x + a) + 35*B*a^3*d*e^3*sgn(b*x + a) + 105*A*a^2*b*d*e^3*sgn(b*x + a) + 280*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^9","A",0
1736,1,427,0,0.241305," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(420 \, B b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 240 \, B b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 90 \, B b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, B b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) + 2 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 1080 \, B a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 360 \, A b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 405 \, B a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 135 \, A b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 90 \, B a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, A b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 945 \, B a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 945 \, A a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 210 \, B a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) + 210 \, A a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 21 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 280 \, B a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 840 \, A a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 28 \, B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 252 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{2520 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/2520*(420*B*b^3*x^4*e^4*sgn(b*x + a) + 240*B*b^3*d*x^3*e^3*sgn(b*x + a) + 90*B*b^3*d^2*x^2*e^2*sgn(b*x + a) + 20*B*b^3*d^3*x*e*sgn(b*x + a) + 2*B*b^3*d^4*sgn(b*x + a) + 1080*B*a*b^2*x^3*e^4*sgn(b*x + a) + 360*A*b^3*x^3*e^4*sgn(b*x + a) + 405*B*a*b^2*d*x^2*e^3*sgn(b*x + a) + 135*A*b^3*d*x^2*e^3*sgn(b*x + a) + 90*B*a*b^2*d^2*x*e^2*sgn(b*x + a) + 30*A*b^3*d^2*x*e^2*sgn(b*x + a) + 9*B*a*b^2*d^3*e*sgn(b*x + a) + 3*A*b^3*d^3*e*sgn(b*x + a) + 945*B*a^2*b*x^2*e^4*sgn(b*x + a) + 945*A*a*b^2*x^2*e^4*sgn(b*x + a) + 210*B*a^2*b*d*x*e^3*sgn(b*x + a) + 210*A*a*b^2*d*x*e^3*sgn(b*x + a) + 21*B*a^2*b*d^2*e^2*sgn(b*x + a) + 21*A*a*b^2*d^2*e^2*sgn(b*x + a) + 280*B*a^3*x*e^4*sgn(b*x + a) + 840*A*a^2*b*x*e^4*sgn(b*x + a) + 28*B*a^3*d*e^3*sgn(b*x + a) + 84*A*a^2*b*d*e^3*sgn(b*x + a) + 252*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^10","A",0
1737,1,427,0,0.196553," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(1320 \, B b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 660 \, B b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 220 \, B b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 44 \, B b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) + 4 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 3465 \, B a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 1155 \, A b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 1155 \, B a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 385 \, A b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 231 \, B a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 77 \, A b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 21 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + 7 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 3080 \, B a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3080 \, A a b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 616 \, B a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) + 616 \, A a b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 56 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 56 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 924 \, B a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 2772 \, A a^{2} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 252 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 840 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{9240 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/9240*(1320*B*b^3*x^4*e^4*sgn(b*x + a) + 660*B*b^3*d*x^3*e^3*sgn(b*x + a) + 220*B*b^3*d^2*x^2*e^2*sgn(b*x + a) + 44*B*b^3*d^3*x*e*sgn(b*x + a) + 4*B*b^3*d^4*sgn(b*x + a) + 3465*B*a*b^2*x^3*e^4*sgn(b*x + a) + 1155*A*b^3*x^3*e^4*sgn(b*x + a) + 1155*B*a*b^2*d*x^2*e^3*sgn(b*x + a) + 385*A*b^3*d*x^2*e^3*sgn(b*x + a) + 231*B*a*b^2*d^2*x*e^2*sgn(b*x + a) + 77*A*b^3*d^2*x*e^2*sgn(b*x + a) + 21*B*a*b^2*d^3*e*sgn(b*x + a) + 7*A*b^3*d^3*e*sgn(b*x + a) + 3080*B*a^2*b*x^2*e^4*sgn(b*x + a) + 3080*A*a*b^2*x^2*e^4*sgn(b*x + a) + 616*B*a^2*b*d*x*e^3*sgn(b*x + a) + 616*A*a*b^2*d*x*e^3*sgn(b*x + a) + 56*B*a^2*b*d^2*e^2*sgn(b*x + a) + 56*A*a*b^2*d^2*e^2*sgn(b*x + a) + 924*B*a^3*x*e^4*sgn(b*x + a) + 2772*A*a^2*b*x*e^4*sgn(b*x + a) + 84*B*a^3*d*e^3*sgn(b*x + a) + 252*A*a^2*b*d*e^3*sgn(b*x + a) + 840*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^11","A",0
1738,1,1702,0,0.268608," ","integrate((B*x+A)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{13} \, B b^{5} x^{13} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B b^{5} d x^{12} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{11} \, B b^{5} d^{2} x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, B b^{5} d^{3} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B b^{5} d^{4} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B b^{5} d^{5} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B b^{5} d^{6} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{12} \, B a b^{4} x^{12} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{12} \, A b^{5} x^{12} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{30}{11} \, B a b^{4} d x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{6}{11} \, A b^{5} d x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, B a b^{4} d^{2} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A b^{5} d^{2} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{100}{9} \, B a b^{4} d^{3} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{20}{9} \, A b^{5} d^{3} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{75}{8} \, B a b^{4} d^{4} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{8} \, A b^{5} d^{4} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, B a b^{4} d^{5} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, A b^{5} d^{5} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} d^{6} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} d^{6} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{10}{11} \, B a^{2} b^{3} x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{11} \, A a b^{4} x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b^{3} d x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{4} d x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{50}{3} \, B a^{2} b^{3} d^{2} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{3} \, A a b^{4} d^{2} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + 25 \, B a^{2} b^{3} d^{3} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, A a b^{4} d^{3} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{150}{7} \, B a^{2} b^{3} d^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{75}{7} \, A a b^{4} d^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{2} b^{3} d^{5} x^{6} e \mathrm{sgn}\left(b x + a\right) + 5 \, A a b^{4} d^{5} x^{6} e \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} d^{6} x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} d^{6} x^{5} \mathrm{sgn}\left(b x + a\right) + B a^{3} b^{2} x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + A a^{2} b^{3} x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, B a^{3} b^{2} d x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, A a^{2} b^{3} d x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{75}{4} \, B a^{3} b^{2} d^{2} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{75}{4} \, A a^{2} b^{3} d^{2} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{200}{7} \, B a^{3} b^{2} d^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{200}{7} \, A a^{2} b^{3} d^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 25 \, B a^{3} b^{2} d^{4} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 25 \, A a^{2} b^{3} d^{4} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{3} b^{2} d^{5} x^{5} e \mathrm{sgn}\left(b x + a\right) + 12 \, A a^{2} b^{3} d^{5} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} d^{6} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} d^{6} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, B a^{4} b x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, A a^{3} b^{2} x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, B a^{4} b d x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, A a^{3} b^{2} d x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{75}{7} \, B a^{4} b d^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{150}{7} \, A a^{3} b^{2} d^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{50}{3} \, B a^{4} b d^{3} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{100}{3} \, A a^{3} b^{2} d^{3} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, B a^{4} b d^{4} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{3} b^{2} d^{4} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, B a^{4} b d^{5} x^{4} e \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{3} b^{2} d^{5} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b d^{6} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} d^{6} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, B a^{5} x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, A a^{4} b x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, B a^{5} d x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, A a^{4} b d x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{5} d^{2} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, A a^{4} b d^{2} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{5} d^{3} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{4} b d^{3} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, B a^{5} d^{4} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{75}{4} \, A a^{4} b d^{4} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{5} d^{5} x^{3} e \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{4} b d^{5} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} d^{6} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b d^{6} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, A a^{5} x^{7} e^{6} \mathrm{sgn}\left(b x + a\right) + A a^{5} d x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{5} d^{2} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{5} d^{3} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{5} d^{4} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{5} d^{5} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{5} d^{6} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/13*B*b^5*x^13*e^6*sgn(b*x + a) + 1/2*B*b^5*d*x^12*e^5*sgn(b*x + a) + 15/11*B*b^5*d^2*x^11*e^4*sgn(b*x + a) + 2*B*b^5*d^3*x^10*e^3*sgn(b*x + a) + 5/3*B*b^5*d^4*x^9*e^2*sgn(b*x + a) + 3/4*B*b^5*d^5*x^8*e*sgn(b*x + a) + 1/7*B*b^5*d^6*x^7*sgn(b*x + a) + 5/12*B*a*b^4*x^12*e^6*sgn(b*x + a) + 1/12*A*b^5*x^12*e^6*sgn(b*x + a) + 30/11*B*a*b^4*d*x^11*e^5*sgn(b*x + a) + 6/11*A*b^5*d*x^11*e^5*sgn(b*x + a) + 15/2*B*a*b^4*d^2*x^10*e^4*sgn(b*x + a) + 3/2*A*b^5*d^2*x^10*e^4*sgn(b*x + a) + 100/9*B*a*b^4*d^3*x^9*e^3*sgn(b*x + a) + 20/9*A*b^5*d^3*x^9*e^3*sgn(b*x + a) + 75/8*B*a*b^4*d^4*x^8*e^2*sgn(b*x + a) + 15/8*A*b^5*d^4*x^8*e^2*sgn(b*x + a) + 30/7*B*a*b^4*d^5*x^7*e*sgn(b*x + a) + 6/7*A*b^5*d^5*x^7*e*sgn(b*x + a) + 5/6*B*a*b^4*d^6*x^6*sgn(b*x + a) + 1/6*A*b^5*d^6*x^6*sgn(b*x + a) + 10/11*B*a^2*b^3*x^11*e^6*sgn(b*x + a) + 5/11*A*a*b^4*x^11*e^6*sgn(b*x + a) + 6*B*a^2*b^3*d*x^10*e^5*sgn(b*x + a) + 3*A*a*b^4*d*x^10*e^5*sgn(b*x + a) + 50/3*B*a^2*b^3*d^2*x^9*e^4*sgn(b*x + a) + 25/3*A*a*b^4*d^2*x^9*e^4*sgn(b*x + a) + 25*B*a^2*b^3*d^3*x^8*e^3*sgn(b*x + a) + 25/2*A*a*b^4*d^3*x^8*e^3*sgn(b*x + a) + 150/7*B*a^2*b^3*d^4*x^7*e^2*sgn(b*x + a) + 75/7*A*a*b^4*d^4*x^7*e^2*sgn(b*x + a) + 10*B*a^2*b^3*d^5*x^6*e*sgn(b*x + a) + 5*A*a*b^4*d^5*x^6*e*sgn(b*x + a) + 2*B*a^2*b^3*d^6*x^5*sgn(b*x + a) + A*a*b^4*d^6*x^5*sgn(b*x + a) + B*a^3*b^2*x^10*e^6*sgn(b*x + a) + A*a^2*b^3*x^10*e^6*sgn(b*x + a) + 20/3*B*a^3*b^2*d*x^9*e^5*sgn(b*x + a) + 20/3*A*a^2*b^3*d*x^9*e^5*sgn(b*x + a) + 75/4*B*a^3*b^2*d^2*x^8*e^4*sgn(b*x + a) + 75/4*A*a^2*b^3*d^2*x^8*e^4*sgn(b*x + a) + 200/7*B*a^3*b^2*d^3*x^7*e^3*sgn(b*x + a) + 200/7*A*a^2*b^3*d^3*x^7*e^3*sgn(b*x + a) + 25*B*a^3*b^2*d^4*x^6*e^2*sgn(b*x + a) + 25*A*a^2*b^3*d^4*x^6*e^2*sgn(b*x + a) + 12*B*a^3*b^2*d^5*x^5*e*sgn(b*x + a) + 12*A*a^2*b^3*d^5*x^5*e*sgn(b*x + a) + 5/2*B*a^3*b^2*d^6*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*d^6*x^4*sgn(b*x + a) + 5/9*B*a^4*b*x^9*e^6*sgn(b*x + a) + 10/9*A*a^3*b^2*x^9*e^6*sgn(b*x + a) + 15/4*B*a^4*b*d*x^8*e^5*sgn(b*x + a) + 15/2*A*a^3*b^2*d*x^8*e^5*sgn(b*x + a) + 75/7*B*a^4*b*d^2*x^7*e^4*sgn(b*x + a) + 150/7*A*a^3*b^2*d^2*x^7*e^4*sgn(b*x + a) + 50/3*B*a^4*b*d^3*x^6*e^3*sgn(b*x + a) + 100/3*A*a^3*b^2*d^3*x^6*e^3*sgn(b*x + a) + 15*B*a^4*b*d^4*x^5*e^2*sgn(b*x + a) + 30*A*a^3*b^2*d^4*x^5*e^2*sgn(b*x + a) + 15/2*B*a^4*b*d^5*x^4*e*sgn(b*x + a) + 15*A*a^3*b^2*d^5*x^4*e*sgn(b*x + a) + 5/3*B*a^4*b*d^6*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*d^6*x^3*sgn(b*x + a) + 1/8*B*a^5*x^8*e^6*sgn(b*x + a) + 5/8*A*a^4*b*x^8*e^6*sgn(b*x + a) + 6/7*B*a^5*d*x^7*e^5*sgn(b*x + a) + 30/7*A*a^4*b*d*x^7*e^5*sgn(b*x + a) + 5/2*B*a^5*d^2*x^6*e^4*sgn(b*x + a) + 25/2*A*a^4*b*d^2*x^6*e^4*sgn(b*x + a) + 4*B*a^5*d^3*x^5*e^3*sgn(b*x + a) + 20*A*a^4*b*d^3*x^5*e^3*sgn(b*x + a) + 15/4*B*a^5*d^4*x^4*e^2*sgn(b*x + a) + 75/4*A*a^4*b*d^4*x^4*e^2*sgn(b*x + a) + 2*B*a^5*d^5*x^3*e*sgn(b*x + a) + 10*A*a^4*b*d^5*x^3*e*sgn(b*x + a) + 1/2*B*a^5*d^6*x^2*sgn(b*x + a) + 5/2*A*a^4*b*d^6*x^2*sgn(b*x + a) + 1/7*A*a^5*x^7*e^6*sgn(b*x + a) + A*a^5*d*x^6*e^5*sgn(b*x + a) + 3*A*a^5*d^2*x^5*e^4*sgn(b*x + a) + 5*A*a^5*d^3*x^4*e^3*sgn(b*x + a) + 5*A*a^5*d^4*x^3*e^2*sgn(b*x + a) + 3*A*a^5*d^5*x^2*e*sgn(b*x + a) + A*a^5*d^6*x*sgn(b*x + a)","B",0
1739,1,1446,0,0.279804," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{12} \, B b^{5} x^{12} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{11} \, B b^{5} d x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + B b^{5} d^{2} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, B b^{5} d^{3} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, B b^{5} d^{4} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B b^{5} d^{5} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{11} \, B a b^{4} x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{11} \, A b^{5} x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a b^{4} d x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A b^{5} d x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{50}{9} \, B a b^{4} d^{2} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, A b^{5} d^{2} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{25}{4} \, B a b^{4} d^{3} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A b^{5} d^{3} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{7} \, B a b^{4} d^{4} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, A b^{5} d^{4} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} d^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} d^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + B a^{2} b^{3} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a b^{4} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{50}{9} \, B a^{2} b^{3} d x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{9} \, A a b^{4} d x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, B a^{2} b^{3} d^{2} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{25}{4} \, A a b^{4} d^{2} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{100}{7} \, B a^{2} b^{3} d^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{50}{7} \, A a b^{4} d^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{3} \, B a^{2} b^{3} d^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{25}{6} \, A a b^{4} d^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} d^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} d^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, B a^{3} b^{2} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, A a^{2} b^{3} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{25}{4} \, B a^{3} b^{2} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{4} \, A a^{2} b^{3} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{100}{7} \, B a^{3} b^{2} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{100}{7} \, A a^{2} b^{3} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{50}{3} \, B a^{3} b^{2} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{50}{3} \, A a^{2} b^{3} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{3} b^{2} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{2} b^{3} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, B a^{4} b x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A a^{3} b^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{25}{7} \, B a^{4} b d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{50}{7} \, A a^{3} b^{2} d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{3} \, B a^{4} b d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{50}{3} \, A a^{3} b^{2} d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{4} \, B a^{4} b d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, A a^{3} b^{2} d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B a^{5} x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, A a^{4} b x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a^{5} d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{6} \, A a^{4} b d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{5} d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{4} b d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{5} d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, A a^{4} b d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{5} d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{25}{3} \, A a^{4} b d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A a^{5} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + A a^{5} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{5} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{5} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{5} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{5} d^{5} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/12*B*b^5*x^12*e^5*sgn(b*x + a) + 5/11*B*b^5*d*x^11*e^4*sgn(b*x + a) + B*b^5*d^2*x^10*e^3*sgn(b*x + a) + 10/9*B*b^5*d^3*x^9*e^2*sgn(b*x + a) + 5/8*B*b^5*d^4*x^8*e*sgn(b*x + a) + 1/7*B*b^5*d^5*x^7*sgn(b*x + a) + 5/11*B*a*b^4*x^11*e^5*sgn(b*x + a) + 1/11*A*b^5*x^11*e^5*sgn(b*x + a) + 5/2*B*a*b^4*d*x^10*e^4*sgn(b*x + a) + 1/2*A*b^5*d*x^10*e^4*sgn(b*x + a) + 50/9*B*a*b^4*d^2*x^9*e^3*sgn(b*x + a) + 10/9*A*b^5*d^2*x^9*e^3*sgn(b*x + a) + 25/4*B*a*b^4*d^3*x^8*e^2*sgn(b*x + a) + 5/4*A*b^5*d^3*x^8*e^2*sgn(b*x + a) + 25/7*B*a*b^4*d^4*x^7*e*sgn(b*x + a) + 5/7*A*b^5*d^4*x^7*e*sgn(b*x + a) + 5/6*B*a*b^4*d^5*x^6*sgn(b*x + a) + 1/6*A*b^5*d^5*x^6*sgn(b*x + a) + B*a^2*b^3*x^10*e^5*sgn(b*x + a) + 1/2*A*a*b^4*x^10*e^5*sgn(b*x + a) + 50/9*B*a^2*b^3*d*x^9*e^4*sgn(b*x + a) + 25/9*A*a*b^4*d*x^9*e^4*sgn(b*x + a) + 25/2*B*a^2*b^3*d^2*x^8*e^3*sgn(b*x + a) + 25/4*A*a*b^4*d^2*x^8*e^3*sgn(b*x + a) + 100/7*B*a^2*b^3*d^3*x^7*e^2*sgn(b*x + a) + 50/7*A*a*b^4*d^3*x^7*e^2*sgn(b*x + a) + 25/3*B*a^2*b^3*d^4*x^6*e*sgn(b*x + a) + 25/6*A*a*b^4*d^4*x^6*e*sgn(b*x + a) + 2*B*a^2*b^3*d^5*x^5*sgn(b*x + a) + A*a*b^4*d^5*x^5*sgn(b*x + a) + 10/9*B*a^3*b^2*x^9*e^5*sgn(b*x + a) + 10/9*A*a^2*b^3*x^9*e^5*sgn(b*x + a) + 25/4*B*a^3*b^2*d*x^8*e^4*sgn(b*x + a) + 25/4*A*a^2*b^3*d*x^8*e^4*sgn(b*x + a) + 100/7*B*a^3*b^2*d^2*x^7*e^3*sgn(b*x + a) + 100/7*A*a^2*b^3*d^2*x^7*e^3*sgn(b*x + a) + 50/3*B*a^3*b^2*d^3*x^6*e^2*sgn(b*x + a) + 50/3*A*a^2*b^3*d^3*x^6*e^2*sgn(b*x + a) + 10*B*a^3*b^2*d^4*x^5*e*sgn(b*x + a) + 10*A*a^2*b^3*d^4*x^5*e*sgn(b*x + a) + 5/2*B*a^3*b^2*d^5*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*d^5*x^4*sgn(b*x + a) + 5/8*B*a^4*b*x^8*e^5*sgn(b*x + a) + 5/4*A*a^3*b^2*x^8*e^5*sgn(b*x + a) + 25/7*B*a^4*b*d*x^7*e^4*sgn(b*x + a) + 50/7*A*a^3*b^2*d*x^7*e^4*sgn(b*x + a) + 25/3*B*a^4*b*d^2*x^6*e^3*sgn(b*x + a) + 50/3*A*a^3*b^2*d^2*x^6*e^3*sgn(b*x + a) + 10*B*a^4*b*d^3*x^5*e^2*sgn(b*x + a) + 20*A*a^3*b^2*d^3*x^5*e^2*sgn(b*x + a) + 25/4*B*a^4*b*d^4*x^4*e*sgn(b*x + a) + 25/2*A*a^3*b^2*d^4*x^4*e*sgn(b*x + a) + 5/3*B*a^4*b*d^5*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*d^5*x^3*sgn(b*x + a) + 1/7*B*a^5*x^7*e^5*sgn(b*x + a) + 5/7*A*a^4*b*x^7*e^5*sgn(b*x + a) + 5/6*B*a^5*d*x^6*e^4*sgn(b*x + a) + 25/6*A*a^4*b*d*x^6*e^4*sgn(b*x + a) + 2*B*a^5*d^2*x^5*e^3*sgn(b*x + a) + 10*A*a^4*b*d^2*x^5*e^3*sgn(b*x + a) + 5/2*B*a^5*d^3*x^4*e^2*sgn(b*x + a) + 25/2*A*a^4*b*d^3*x^4*e^2*sgn(b*x + a) + 5/3*B*a^5*d^4*x^3*e*sgn(b*x + a) + 25/3*A*a^4*b*d^4*x^3*e*sgn(b*x + a) + 1/2*B*a^5*d^5*x^2*sgn(b*x + a) + 5/2*A*a^4*b*d^5*x^2*sgn(b*x + a) + 1/6*A*a^5*x^6*e^5*sgn(b*x + a) + A*a^5*d*x^5*e^4*sgn(b*x + a) + 5/2*A*a^5*d^2*x^4*e^3*sgn(b*x + a) + 10/3*A*a^5*d^3*x^3*e^2*sgn(b*x + a) + 5/2*A*a^5*d^4*x^2*e*sgn(b*x + a) + A*a^5*d^5*x*sgn(b*x + a)","B",0
1740,1,1192,0,0.253302," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{11} \, B b^{5} x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, B b^{5} d x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B b^{5} d^{2} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B b^{5} d^{3} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B b^{5} d^{4} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a b^{4} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{10} \, A b^{5} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{20}{9} \, B a b^{4} d x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{4}{9} \, A b^{5} d x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, B a b^{4} d^{2} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, A b^{5} d^{2} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{20}{7} \, B a b^{4} d^{3} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{4}{7} \, A b^{5} d^{3} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} d^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} d^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, B a^{2} b^{3} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, A a b^{4} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{2} b^{3} d x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a b^{4} d x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{60}{7} \, B a^{2} b^{3} d^{2} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, A a b^{4} d^{2} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, B a^{2} b^{3} d^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a b^{4} d^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} d^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} d^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B a^{3} b^{2} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A a^{2} b^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{40}{7} \, B a^{3} b^{2} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{40}{7} \, A a^{2} b^{3} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{3} b^{2} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{2} b^{3} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, B a^{3} b^{2} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + 8 \, A a^{2} b^{3} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, B a^{4} b x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, A a^{3} b^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, B a^{4} b d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, A a^{3} b^{2} d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{4} b d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, A a^{3} b^{2} d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{4} b d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} b^{2} d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, B a^{5} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, A a^{4} b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, B a^{5} d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{4} b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, B a^{5} d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, A a^{4} b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, B a^{5} d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, A a^{4} b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, A a^{5} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + A a^{5} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{5} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{5} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{5} d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/11*B*b^5*x^11*e^4*sgn(b*x + a) + 2/5*B*b^5*d*x^10*e^3*sgn(b*x + a) + 2/3*B*b^5*d^2*x^9*e^2*sgn(b*x + a) + 1/2*B*b^5*d^3*x^8*e*sgn(b*x + a) + 1/7*B*b^5*d^4*x^7*sgn(b*x + a) + 1/2*B*a*b^4*x^10*e^4*sgn(b*x + a) + 1/10*A*b^5*x^10*e^4*sgn(b*x + a) + 20/9*B*a*b^4*d*x^9*e^3*sgn(b*x + a) + 4/9*A*b^5*d*x^9*e^3*sgn(b*x + a) + 15/4*B*a*b^4*d^2*x^8*e^2*sgn(b*x + a) + 3/4*A*b^5*d^2*x^8*e^2*sgn(b*x + a) + 20/7*B*a*b^4*d^3*x^7*e*sgn(b*x + a) + 4/7*A*b^5*d^3*x^7*e*sgn(b*x + a) + 5/6*B*a*b^4*d^4*x^6*sgn(b*x + a) + 1/6*A*b^5*d^4*x^6*sgn(b*x + a) + 10/9*B*a^2*b^3*x^9*e^4*sgn(b*x + a) + 5/9*A*a*b^4*x^9*e^4*sgn(b*x + a) + 5*B*a^2*b^3*d*x^8*e^3*sgn(b*x + a) + 5/2*A*a*b^4*d*x^8*e^3*sgn(b*x + a) + 60/7*B*a^2*b^3*d^2*x^7*e^2*sgn(b*x + a) + 30/7*A*a*b^4*d^2*x^7*e^2*sgn(b*x + a) + 20/3*B*a^2*b^3*d^3*x^6*e*sgn(b*x + a) + 10/3*A*a*b^4*d^3*x^6*e*sgn(b*x + a) + 2*B*a^2*b^3*d^4*x^5*sgn(b*x + a) + A*a*b^4*d^4*x^5*sgn(b*x + a) + 5/4*B*a^3*b^2*x^8*e^4*sgn(b*x + a) + 5/4*A*a^2*b^3*x^8*e^4*sgn(b*x + a) + 40/7*B*a^3*b^2*d*x^7*e^3*sgn(b*x + a) + 40/7*A*a^2*b^3*d*x^7*e^3*sgn(b*x + a) + 10*B*a^3*b^2*d^2*x^6*e^2*sgn(b*x + a) + 10*A*a^2*b^3*d^2*x^6*e^2*sgn(b*x + a) + 8*B*a^3*b^2*d^3*x^5*e*sgn(b*x + a) + 8*A*a^2*b^3*d^3*x^5*e*sgn(b*x + a) + 5/2*B*a^3*b^2*d^4*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*d^4*x^4*sgn(b*x + a) + 5/7*B*a^4*b*x^7*e^4*sgn(b*x + a) + 10/7*A*a^3*b^2*x^7*e^4*sgn(b*x + a) + 10/3*B*a^4*b*d*x^6*e^3*sgn(b*x + a) + 20/3*A*a^3*b^2*d*x^6*e^3*sgn(b*x + a) + 6*B*a^4*b*d^2*x^5*e^2*sgn(b*x + a) + 12*A*a^3*b^2*d^2*x^5*e^2*sgn(b*x + a) + 5*B*a^4*b*d^3*x^4*e*sgn(b*x + a) + 10*A*a^3*b^2*d^3*x^4*e*sgn(b*x + a) + 5/3*B*a^4*b*d^4*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*d^4*x^3*sgn(b*x + a) + 1/6*B*a^5*x^6*e^4*sgn(b*x + a) + 5/6*A*a^4*b*x^6*e^4*sgn(b*x + a) + 4/5*B*a^5*d*x^5*e^3*sgn(b*x + a) + 4*A*a^4*b*d*x^5*e^3*sgn(b*x + a) + 3/2*B*a^5*d^2*x^4*e^2*sgn(b*x + a) + 15/2*A*a^4*b*d^2*x^4*e^2*sgn(b*x + a) + 4/3*B*a^5*d^3*x^3*e*sgn(b*x + a) + 20/3*A*a^4*b*d^3*x^3*e*sgn(b*x + a) + 1/2*B*a^5*d^4*x^2*sgn(b*x + a) + 5/2*A*a^4*b*d^4*x^2*sgn(b*x + a) + 1/5*A*a^5*x^5*e^4*sgn(b*x + a) + A*a^5*d*x^4*e^3*sgn(b*x + a) + 2*A*a^5*d^2*x^3*e^2*sgn(b*x + a) + 2*A*a^5*d^3*x^2*e*sgn(b*x + a) + A*a^5*d^4*x*sgn(b*x + a)","B",0
1741,1,934,0,0.224231," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{10} \, B b^{5} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B b^{5} d x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, B b^{5} d^{2} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B b^{5} d^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, B a b^{4} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{9} \, A b^{5} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{8} \, B a b^{4} d x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, A b^{5} d x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, B a b^{4} d^{2} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, A b^{5} d^{2} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} d^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} d^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B a^{2} b^{3} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, A a b^{4} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, B a^{2} b^{3} d x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, A a b^{4} d x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{2} b^{3} d^{2} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a b^{4} d^{2} x^{6} e \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} d^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} d^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B a^{3} b^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, A a^{2} b^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{3} b^{2} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{2} b^{3} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{3} b^{2} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{2} b^{3} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a^{4} b x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a^{3} b^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{4} b d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{3} b^{2} d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, B a^{4} b d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, A a^{3} b^{2} d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, B a^{5} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{4} b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, B a^{5} d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, A a^{4} b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + B a^{5} d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, A a^{5} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{5} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, A a^{5} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{5} d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/10*B*b^5*x^10*e^3*sgn(b*x + a) + 1/3*B*b^5*d*x^9*e^2*sgn(b*x + a) + 3/8*B*b^5*d^2*x^8*e*sgn(b*x + a) + 1/7*B*b^5*d^3*x^7*sgn(b*x + a) + 5/9*B*a*b^4*x^9*e^3*sgn(b*x + a) + 1/9*A*b^5*x^9*e^3*sgn(b*x + a) + 15/8*B*a*b^4*d*x^8*e^2*sgn(b*x + a) + 3/8*A*b^5*d*x^8*e^2*sgn(b*x + a) + 15/7*B*a*b^4*d^2*x^7*e*sgn(b*x + a) + 3/7*A*b^5*d^2*x^7*e*sgn(b*x + a) + 5/6*B*a*b^4*d^3*x^6*sgn(b*x + a) + 1/6*A*b^5*d^3*x^6*sgn(b*x + a) + 5/4*B*a^2*b^3*x^8*e^3*sgn(b*x + a) + 5/8*A*a*b^4*x^8*e^3*sgn(b*x + a) + 30/7*B*a^2*b^3*d*x^7*e^2*sgn(b*x + a) + 15/7*A*a*b^4*d*x^7*e^2*sgn(b*x + a) + 5*B*a^2*b^3*d^2*x^6*e*sgn(b*x + a) + 5/2*A*a*b^4*d^2*x^6*e*sgn(b*x + a) + 2*B*a^2*b^3*d^3*x^5*sgn(b*x + a) + A*a*b^4*d^3*x^5*sgn(b*x + a) + 10/7*B*a^3*b^2*x^7*e^3*sgn(b*x + a) + 10/7*A*a^2*b^3*x^7*e^3*sgn(b*x + a) + 5*B*a^3*b^2*d*x^6*e^2*sgn(b*x + a) + 5*A*a^2*b^3*d*x^6*e^2*sgn(b*x + a) + 6*B*a^3*b^2*d^2*x^5*e*sgn(b*x + a) + 6*A*a^2*b^3*d^2*x^5*e*sgn(b*x + a) + 5/2*B*a^3*b^2*d^3*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*d^3*x^4*sgn(b*x + a) + 5/6*B*a^4*b*x^6*e^3*sgn(b*x + a) + 5/3*A*a^3*b^2*x^6*e^3*sgn(b*x + a) + 3*B*a^4*b*d*x^5*e^2*sgn(b*x + a) + 6*A*a^3*b^2*d*x^5*e^2*sgn(b*x + a) + 15/4*B*a^4*b*d^2*x^4*e*sgn(b*x + a) + 15/2*A*a^3*b^2*d^2*x^4*e*sgn(b*x + a) + 5/3*B*a^4*b*d^3*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*d^3*x^3*sgn(b*x + a) + 1/5*B*a^5*x^5*e^3*sgn(b*x + a) + A*a^4*b*x^5*e^3*sgn(b*x + a) + 3/4*B*a^5*d*x^4*e^2*sgn(b*x + a) + 15/4*A*a^4*b*d*x^4*e^2*sgn(b*x + a) + B*a^5*d^2*x^3*e*sgn(b*x + a) + 5*A*a^4*b*d^2*x^3*e*sgn(b*x + a) + 1/2*B*a^5*d^3*x^2*sgn(b*x + a) + 5/2*A*a^4*b*d^3*x^2*sgn(b*x + a) + 1/4*A*a^5*x^4*e^3*sgn(b*x + a) + A*a^5*d*x^3*e^2*sgn(b*x + a) + 3/2*A*a^5*d^2*x^2*e*sgn(b*x + a) + A*a^5*d^3*x*sgn(b*x + a)","B",0
1742,1,679,0,0.196139," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{9} \, B b^{5} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, B b^{5} d x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B b^{5} d^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, B a b^{4} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, A b^{5} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B a b^{4} d x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, A b^{5} d x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} d^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} d^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, B a^{2} b^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, A a b^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, B a^{2} b^{3} d x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a b^{4} d x^{6} e \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} d^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} d^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{3} b^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a^{2} b^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{3} b^{2} d x^{5} e \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{2} b^{3} d x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + B a^{4} b x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{4} b d x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{3} b^{2} d x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, B a^{5} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, A a^{4} b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, B a^{5} d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{4} b d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, A a^{5} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + A a^{5} d x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{5} d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/9*B*b^5*x^9*e^2*sgn(b*x + a) + 1/4*B*b^5*d*x^8*e*sgn(b*x + a) + 1/7*B*b^5*d^2*x^7*sgn(b*x + a) + 5/8*B*a*b^4*x^8*e^2*sgn(b*x + a) + 1/8*A*b^5*x^8*e^2*sgn(b*x + a) + 10/7*B*a*b^4*d*x^7*e*sgn(b*x + a) + 2/7*A*b^5*d*x^7*e*sgn(b*x + a) + 5/6*B*a*b^4*d^2*x^6*sgn(b*x + a) + 1/6*A*b^5*d^2*x^6*sgn(b*x + a) + 10/7*B*a^2*b^3*x^7*e^2*sgn(b*x + a) + 5/7*A*a*b^4*x^7*e^2*sgn(b*x + a) + 10/3*B*a^2*b^3*d*x^6*e*sgn(b*x + a) + 5/3*A*a*b^4*d*x^6*e*sgn(b*x + a) + 2*B*a^2*b^3*d^2*x^5*sgn(b*x + a) + A*a*b^4*d^2*x^5*sgn(b*x + a) + 5/3*B*a^3*b^2*x^6*e^2*sgn(b*x + a) + 5/3*A*a^2*b^3*x^6*e^2*sgn(b*x + a) + 4*B*a^3*b^2*d*x^5*e*sgn(b*x + a) + 4*A*a^2*b^3*d*x^5*e*sgn(b*x + a) + 5/2*B*a^3*b^2*d^2*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*d^2*x^4*sgn(b*x + a) + B*a^4*b*x^5*e^2*sgn(b*x + a) + 2*A*a^3*b^2*x^5*e^2*sgn(b*x + a) + 5/2*B*a^4*b*d*x^4*e*sgn(b*x + a) + 5*A*a^3*b^2*d*x^4*e*sgn(b*x + a) + 5/3*B*a^4*b*d^2*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*d^2*x^3*sgn(b*x + a) + 1/4*B*a^5*x^4*e^2*sgn(b*x + a) + 5/4*A*a^4*b*x^4*e^2*sgn(b*x + a) + 2/3*B*a^5*d*x^3*e*sgn(b*x + a) + 10/3*A*a^4*b*d*x^3*e*sgn(b*x + a) + 1/2*B*a^5*d^2*x^2*sgn(b*x + a) + 5/2*A*a^4*b*d^2*x^2*sgn(b*x + a) + 1/3*A*a^5*x^3*e^2*sgn(b*x + a) + A*a^5*d*x^2*e*sgn(b*x + a) + A*a^5*d^2*x*sgn(b*x + a)","B",0
1743,1,425,0,0.183268," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, B b^{5} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, B b^{5} d x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, B a b^{4} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, A b^{5} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} d x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} d x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{2} b^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, A a b^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} d x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} d x^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{3} b^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{2} b^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, B a^{4} b x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{3} b^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b d x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} d x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, B a^{5} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, A a^{4} b x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, A a^{5} x^{2} e \mathrm{sgn}\left(b x + a\right) + A a^{5} d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/8*B*b^5*x^8*e*sgn(b*x + a) + 1/7*B*b^5*d*x^7*sgn(b*x + a) + 5/7*B*a*b^4*x^7*e*sgn(b*x + a) + 1/7*A*b^5*x^7*e*sgn(b*x + a) + 5/6*B*a*b^4*d*x^6*sgn(b*x + a) + 1/6*A*b^5*d*x^6*sgn(b*x + a) + 5/3*B*a^2*b^3*x^6*e*sgn(b*x + a) + 5/6*A*a*b^4*x^6*e*sgn(b*x + a) + 2*B*a^2*b^3*d*x^5*sgn(b*x + a) + A*a*b^4*d*x^5*sgn(b*x + a) + 2*B*a^3*b^2*x^5*e*sgn(b*x + a) + 2*A*a^2*b^3*x^5*e*sgn(b*x + a) + 5/2*B*a^3*b^2*d*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*d*x^4*sgn(b*x + a) + 5/4*B*a^4*b*x^4*e*sgn(b*x + a) + 5/2*A*a^3*b^2*x^4*e*sgn(b*x + a) + 5/3*B*a^4*b*d*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*d*x^3*sgn(b*x + a) + 1/3*B*a^5*x^3*e*sgn(b*x + a) + 5/3*A*a^4*b*x^3*e*sgn(b*x + a) + 1/2*B*a^5*d*x^2*sgn(b*x + a) + 5/2*A*a^4*b*d*x^2*sgn(b*x + a) + 1/2*A*a^5*x^2*e*sgn(b*x + a) + A*a^5*d*x*sgn(b*x + a)","B",0
1744,1,217,0,0.209906," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{7} \, B b^{5} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, B a b^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, A b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + A a b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, B a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, B a^{4} b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, A a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, B a^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, A a^{4} b x^{2} \mathrm{sgn}\left(b x + a\right) + A a^{5} x \mathrm{sgn}\left(b x + a\right) - \frac{{\left(B a^{7} - 7 \, A a^{6} b\right)} \mathrm{sgn}\left(b x + a\right)}{42 \, b^{2}}"," ",0,"1/7*B*b^5*x^7*sgn(b*x + a) + 5/6*B*a*b^4*x^6*sgn(b*x + a) + 1/6*A*b^5*x^6*sgn(b*x + a) + 2*B*a^2*b^3*x^5*sgn(b*x + a) + A*a*b^4*x^5*sgn(b*x + a) + 5/2*B*a^3*b^2*x^4*sgn(b*x + a) + 5/2*A*a^2*b^3*x^4*sgn(b*x + a) + 5/3*B*a^4*b*x^3*sgn(b*x + a) + 10/3*A*a^3*b^2*x^3*sgn(b*x + a) + 1/2*B*a^5*x^2*sgn(b*x + a) + 5/2*A*a^4*b*x^2*sgn(b*x + a) + A*a^5*x*sgn(b*x + a) - 1/42*(B*a^7 - 7*A*a^6*b)*sgn(b*x + a)/b^2","B",0
1745,1,920,0,0.236649," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d),x, algorithm=""giac"")","{\left(B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, B b^{5} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) - 12 \, B b^{5} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, B b^{5} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) - 20 \, B b^{5} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, B b^{5} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) - 60 \, B b^{5} d^{5} x \mathrm{sgn}\left(b x + a\right) + 60 \, B a b^{4} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 12 \, A b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 75 \, B a b^{4} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 15 \, A b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 100 \, B a b^{4} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, A b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 150 \, B a b^{4} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, A b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 300 \, B a b^{4} d^{4} x e \mathrm{sgn}\left(b x + a\right) + 60 \, A b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + 150 \, B a^{2} b^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 75 \, A a b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 200 \, B a^{2} b^{3} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 100 \, A a b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 300 \, B a^{2} b^{3} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 150 \, A a b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 600 \, B a^{2} b^{3} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) - 300 \, A a b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + 200 \, B a^{3} b^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 200 \, A a^{2} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 300 \, B a^{3} b^{2} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 300 \, A a^{2} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 600 \, B a^{3} b^{2} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 600 \, A a^{2} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 150 \, B a^{4} b x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 300 \, A a^{3} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 300 \, B a^{4} b d x e^{4} \mathrm{sgn}\left(b x + a\right) - 600 \, A a^{3} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, B a^{5} x e^{5} \mathrm{sgn}\left(b x + a\right) + 300 \, A a^{4} b x e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}"," ",0,"(B*b^5*d^6*sgn(b*x + a) - 5*B*a*b^4*d^5*e*sgn(b*x + a) - A*b^5*d^5*e*sgn(b*x + a) + 10*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 5*A*a*b^4*d^4*e^2*sgn(b*x + a) - 10*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 10*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 5*B*a^4*b*d^2*e^4*sgn(b*x + a) + 10*A*a^3*b^2*d^2*e^4*sgn(b*x + a) - B*a^5*d*e^5*sgn(b*x + a) - 5*A*a^4*b*d*e^5*sgn(b*x + a) + A*a^5*e^6*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/60*(10*B*b^5*x^6*e^5*sgn(b*x + a) - 12*B*b^5*d*x^5*e^4*sgn(b*x + a) + 15*B*b^5*d^2*x^4*e^3*sgn(b*x + a) - 20*B*b^5*d^3*x^3*e^2*sgn(b*x + a) + 30*B*b^5*d^4*x^2*e*sgn(b*x + a) - 60*B*b^5*d^5*x*sgn(b*x + a) + 60*B*a*b^4*x^5*e^5*sgn(b*x + a) + 12*A*b^5*x^5*e^5*sgn(b*x + a) - 75*B*a*b^4*d*x^4*e^4*sgn(b*x + a) - 15*A*b^5*d*x^4*e^4*sgn(b*x + a) + 100*B*a*b^4*d^2*x^3*e^3*sgn(b*x + a) + 20*A*b^5*d^2*x^3*e^3*sgn(b*x + a) - 150*B*a*b^4*d^3*x^2*e^2*sgn(b*x + a) - 30*A*b^5*d^3*x^2*e^2*sgn(b*x + a) + 300*B*a*b^4*d^4*x*e*sgn(b*x + a) + 60*A*b^5*d^4*x*e*sgn(b*x + a) + 150*B*a^2*b^3*x^4*e^5*sgn(b*x + a) + 75*A*a*b^4*x^4*e^5*sgn(b*x + a) - 200*B*a^2*b^3*d*x^3*e^4*sgn(b*x + a) - 100*A*a*b^4*d*x^3*e^4*sgn(b*x + a) + 300*B*a^2*b^3*d^2*x^2*e^3*sgn(b*x + a) + 150*A*a*b^4*d^2*x^2*e^3*sgn(b*x + a) - 600*B*a^2*b^3*d^3*x*e^2*sgn(b*x + a) - 300*A*a*b^4*d^3*x*e^2*sgn(b*x + a) + 200*B*a^3*b^2*x^3*e^5*sgn(b*x + a) + 200*A*a^2*b^3*x^3*e^5*sgn(b*x + a) - 300*B*a^3*b^2*d*x^2*e^4*sgn(b*x + a) - 300*A*a^2*b^3*d*x^2*e^4*sgn(b*x + a) + 600*B*a^3*b^2*d^2*x*e^3*sgn(b*x + a) + 600*A*a^2*b^3*d^2*x*e^3*sgn(b*x + a) + 150*B*a^4*b*x^2*e^5*sgn(b*x + a) + 300*A*a^3*b^2*x^2*e^5*sgn(b*x + a) - 300*B*a^4*b*d*x*e^4*sgn(b*x + a) - 600*A*a^3*b^2*d*x*e^4*sgn(b*x + a) + 60*B*a^5*x*e^5*sgn(b*x + a) + 300*A*a^4*b*x*e^5*sgn(b*x + a))*e^(-6)","B",0
1746,1,905,0,0.223138," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","-{\left(6 \, B b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 25 \, B a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) - 5 \, A b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) + 40 \, B a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, A a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, B a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, A a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(12 \, B b^{5} x^{5} e^{8} \mathrm{sgn}\left(b x + a\right) - 30 \, B b^{5} d x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 60 \, B b^{5} d^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) - 120 \, B b^{5} d^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 300 \, B b^{5} d^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 75 \, B a b^{4} x^{4} e^{8} \mathrm{sgn}\left(b x + a\right) + 15 \, A b^{5} x^{4} e^{8} \mathrm{sgn}\left(b x + a\right) - 200 \, B a b^{4} d x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) - 40 \, A b^{5} d x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 450 \, B a b^{4} d^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 90 \, A b^{5} d^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 1200 \, B a b^{4} d^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) - 240 \, A b^{5} d^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) + 200 \, B a^{2} b^{3} x^{3} e^{8} \mathrm{sgn}\left(b x + a\right) + 100 \, A a b^{4} x^{3} e^{8} \mathrm{sgn}\left(b x + a\right) - 600 \, B a^{2} b^{3} d x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) - 300 \, A a b^{4} d x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 1800 \, B a^{2} b^{3} d^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 900 \, A a b^{4} d^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 300 \, B a^{3} b^{2} x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) + 300 \, A a^{2} b^{3} x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) - 1200 \, B a^{3} b^{2} d x e^{7} \mathrm{sgn}\left(b x + a\right) - 1200 \, A a^{2} b^{3} d x e^{7} \mathrm{sgn}\left(b x + a\right) + 300 \, B a^{4} b x e^{8} \mathrm{sgn}\left(b x + a\right) + 600 \, A a^{3} b^{2} x e^{8} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-10\right)} - \frac{{\left(B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{x e + d}"," ",0,"-(6*B*b^5*d^5*sgn(b*x + a) - 25*B*a*b^4*d^4*e*sgn(b*x + a) - 5*A*b^5*d^4*e*sgn(b*x + a) + 40*B*a^2*b^3*d^3*e^2*sgn(b*x + a) + 20*A*a*b^4*d^3*e^2*sgn(b*x + a) - 30*B*a^3*b^2*d^2*e^3*sgn(b*x + a) - 30*A*a^2*b^3*d^2*e^3*sgn(b*x + a) + 10*B*a^4*b*d*e^4*sgn(b*x + a) + 20*A*a^3*b^2*d*e^4*sgn(b*x + a) - B*a^5*e^5*sgn(b*x + a) - 5*A*a^4*b*e^5*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/60*(12*B*b^5*x^5*e^8*sgn(b*x + a) - 30*B*b^5*d*x^4*e^7*sgn(b*x + a) + 60*B*b^5*d^2*x^3*e^6*sgn(b*x + a) - 120*B*b^5*d^3*x^2*e^5*sgn(b*x + a) + 300*B*b^5*d^4*x*e^4*sgn(b*x + a) + 75*B*a*b^4*x^4*e^8*sgn(b*x + a) + 15*A*b^5*x^4*e^8*sgn(b*x + a) - 200*B*a*b^4*d*x^3*e^7*sgn(b*x + a) - 40*A*b^5*d*x^3*e^7*sgn(b*x + a) + 450*B*a*b^4*d^2*x^2*e^6*sgn(b*x + a) + 90*A*b^5*d^2*x^2*e^6*sgn(b*x + a) - 1200*B*a*b^4*d^3*x*e^5*sgn(b*x + a) - 240*A*b^5*d^3*x*e^5*sgn(b*x + a) + 200*B*a^2*b^3*x^3*e^8*sgn(b*x + a) + 100*A*a*b^4*x^3*e^8*sgn(b*x + a) - 600*B*a^2*b^3*d*x^2*e^7*sgn(b*x + a) - 300*A*a*b^4*d*x^2*e^7*sgn(b*x + a) + 1800*B*a^2*b^3*d^2*x*e^6*sgn(b*x + a) + 900*A*a*b^4*d^2*x*e^6*sgn(b*x + a) + 300*B*a^3*b^2*x^2*e^8*sgn(b*x + a) + 300*A*a^2*b^3*x^2*e^8*sgn(b*x + a) - 1200*B*a^3*b^2*d*x*e^7*sgn(b*x + a) - 1200*A*a^2*b^3*d*x*e^7*sgn(b*x + a) + 300*B*a^4*b*x*e^8*sgn(b*x + a) + 600*A*a^3*b^2*x*e^8*sgn(b*x + a))*e^(-10) - (B*b^5*d^6*sgn(b*x + a) - 5*B*a*b^4*d^5*e*sgn(b*x + a) - A*b^5*d^5*e*sgn(b*x + a) + 10*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 5*A*a*b^4*d^4*e^2*sgn(b*x + a) - 10*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 10*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 5*B*a^4*b*d^2*e^4*sgn(b*x + a) + 10*A*a^3*b^2*d^2*e^4*sgn(b*x + a) - B*a^5*d*e^5*sgn(b*x + a) - 5*A*a^4*b*d*e^5*sgn(b*x + a) + A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)","B",0
1747,1,887,0,0.262192," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","5 \, {\left(3 \, B b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - 10 \, B a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) - 2 \, A b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, B a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, A a^{2} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + B a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, B b^{5} x^{4} e^{9} \mathrm{sgn}\left(b x + a\right) - 12 \, B b^{5} d x^{3} e^{8} \mathrm{sgn}\left(b x + a\right) + 36 \, B b^{5} d^{2} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) - 120 \, B b^{5} d^{3} x e^{6} \mathrm{sgn}\left(b x + a\right) + 20 \, B a b^{4} x^{3} e^{9} \mathrm{sgn}\left(b x + a\right) + 4 \, A b^{5} x^{3} e^{9} \mathrm{sgn}\left(b x + a\right) - 90 \, B a b^{4} d x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) - 18 \, A b^{5} d x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) + 360 \, B a b^{4} d^{2} x e^{7} \mathrm{sgn}\left(b x + a\right) + 72 \, A b^{5} d^{2} x e^{7} \mathrm{sgn}\left(b x + a\right) + 60 \, B a^{2} b^{3} x^{2} e^{9} \mathrm{sgn}\left(b x + a\right) + 30 \, A a b^{4} x^{2} e^{9} \mathrm{sgn}\left(b x + a\right) - 360 \, B a^{2} b^{3} d x e^{8} \mathrm{sgn}\left(b x + a\right) - 180 \, A a b^{4} d x e^{8} \mathrm{sgn}\left(b x + a\right) + 120 \, B a^{3} b^{2} x e^{9} \mathrm{sgn}\left(b x + a\right) + 120 \, A a^{2} b^{3} x e^{9} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-12\right)} + \frac{{\left(11 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 45 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - 9 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 70 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 50 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 50 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) - A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(6 \, B b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) - 25 \, B a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, A b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 40 \, B a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, A a b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, B a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 30 \, A a^{2} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) - B a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"5*(3*B*b^5*d^4*sgn(b*x + a) - 10*B*a*b^4*d^3*e*sgn(b*x + a) - 2*A*b^5*d^3*e*sgn(b*x + a) + 12*B*a^2*b^3*d^2*e^2*sgn(b*x + a) + 6*A*a*b^4*d^2*e^2*sgn(b*x + a) - 6*B*a^3*b^2*d*e^3*sgn(b*x + a) - 6*A*a^2*b^3*d*e^3*sgn(b*x + a) + B*a^4*b*e^4*sgn(b*x + a) + 2*A*a^3*b^2*e^4*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/12*(3*B*b^5*x^4*e^9*sgn(b*x + a) - 12*B*b^5*d*x^3*e^8*sgn(b*x + a) + 36*B*b^5*d^2*x^2*e^7*sgn(b*x + a) - 120*B*b^5*d^3*x*e^6*sgn(b*x + a) + 20*B*a*b^4*x^3*e^9*sgn(b*x + a) + 4*A*b^5*x^3*e^9*sgn(b*x + a) - 90*B*a*b^4*d*x^2*e^8*sgn(b*x + a) - 18*A*b^5*d*x^2*e^8*sgn(b*x + a) + 360*B*a*b^4*d^2*x*e^7*sgn(b*x + a) + 72*A*b^5*d^2*x*e^7*sgn(b*x + a) + 60*B*a^2*b^3*x^2*e^9*sgn(b*x + a) + 30*A*a*b^4*x^2*e^9*sgn(b*x + a) - 360*B*a^2*b^3*d*x*e^8*sgn(b*x + a) - 180*A*a*b^4*d*x*e^8*sgn(b*x + a) + 120*B*a^3*b^2*x*e^9*sgn(b*x + a) + 120*A*a^2*b^3*x*e^9*sgn(b*x + a))*e^(-12) + 1/2*(11*B*b^5*d^6*sgn(b*x + a) - 45*B*a*b^4*d^5*e*sgn(b*x + a) - 9*A*b^5*d^5*e*sgn(b*x + a) + 70*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 35*A*a*b^4*d^4*e^2*sgn(b*x + a) - 50*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 50*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 15*B*a^4*b*d^2*e^4*sgn(b*x + a) + 30*A*a^3*b^2*d^2*e^4*sgn(b*x + a) - B*a^5*d*e^5*sgn(b*x + a) - 5*A*a^4*b*d*e^5*sgn(b*x + a) - A*a^5*e^6*sgn(b*x + a) + 2*(6*B*b^5*d^5*e*sgn(b*x + a) - 25*B*a*b^4*d^4*e^2*sgn(b*x + a) - 5*A*b^5*d^4*e^2*sgn(b*x + a) + 40*B*a^2*b^3*d^3*e^3*sgn(b*x + a) + 20*A*a*b^4*d^3*e^3*sgn(b*x + a) - 30*B*a^3*b^2*d^2*e^4*sgn(b*x + a) - 30*A*a^2*b^3*d^2*e^4*sgn(b*x + a) + 10*B*a^4*b*d*e^5*sgn(b*x + a) + 20*A*a^3*b^2*d*e^5*sgn(b*x + a) - B*a^5*e^6*sgn(b*x + a) - 5*A*a^4*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^2","B",0
1748,1,874,0,0.222950," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","-10 \, {\left(2 \, B b^{5} d^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) - A b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{2} b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - A a^{2} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B b^{5} x^{3} e^{8} \mathrm{sgn}\left(b x + a\right) - 12 \, B b^{5} d x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 60 \, B b^{5} d^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 15 \, B a b^{4} x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) + 3 \, A b^{5} x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) - 120 \, B a b^{4} d x e^{7} \mathrm{sgn}\left(b x + a\right) - 24 \, A b^{5} d x e^{7} \mathrm{sgn}\left(b x + a\right) + 60 \, B a^{2} b^{3} x e^{8} \mathrm{sgn}\left(b x + a\right) + 30 \, A a b^{4} x e^{8} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-12\right)} - \frac{{\left(74 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 235 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - 47 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 260 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 130 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 110 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 110 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(3 \, B b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, B a b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 2 \, A b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{2} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, B a^{3} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) - 6 \, A a^{2} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) + B a^{4} b e^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 3 \, {\left(54 \, B b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) - 175 \, B a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 35 \, A b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 200 \, B a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 100 \, A a b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 90 \, B a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 90 \, A a^{2} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) + B a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-10*(2*B*b^5*d^3*sgn(b*x + a) - 5*B*a*b^4*d^2*e*sgn(b*x + a) - A*b^5*d^2*e*sgn(b*x + a) + 4*B*a^2*b^3*d*e^2*sgn(b*x + a) + 2*A*a*b^4*d*e^2*sgn(b*x + a) - B*a^3*b^2*e^3*sgn(b*x + a) - A*a^2*b^3*e^3*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/6*(2*B*b^5*x^3*e^8*sgn(b*x + a) - 12*B*b^5*d*x^2*e^7*sgn(b*x + a) + 60*B*b^5*d^2*x*e^6*sgn(b*x + a) + 15*B*a*b^4*x^2*e^8*sgn(b*x + a) + 3*A*b^5*x^2*e^8*sgn(b*x + a) - 120*B*a*b^4*d*x*e^7*sgn(b*x + a) - 24*A*b^5*d*x*e^7*sgn(b*x + a) + 60*B*a^2*b^3*x*e^8*sgn(b*x + a) + 30*A*a*b^4*x*e^8*sgn(b*x + a))*e^(-12) - 1/6*(74*B*b^5*d^6*sgn(b*x + a) - 235*B*a*b^4*d^5*e*sgn(b*x + a) - 47*A*b^5*d^5*e*sgn(b*x + a) + 260*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 130*A*a*b^4*d^4*e^2*sgn(b*x + a) - 110*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 110*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 10*B*a^4*b*d^2*e^4*sgn(b*x + a) + 20*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + B*a^5*d*e^5*sgn(b*x + a) + 5*A*a^4*b*d*e^5*sgn(b*x + a) + 2*A*a^5*e^6*sgn(b*x + a) + 30*(3*B*b^5*d^4*e^2*sgn(b*x + a) - 10*B*a*b^4*d^3*e^3*sgn(b*x + a) - 2*A*b^5*d^3*e^3*sgn(b*x + a) + 12*B*a^2*b^3*d^2*e^4*sgn(b*x + a) + 6*A*a*b^4*d^2*e^4*sgn(b*x + a) - 6*B*a^3*b^2*d*e^5*sgn(b*x + a) - 6*A*a^2*b^3*d*e^5*sgn(b*x + a) + B*a^4*b*e^6*sgn(b*x + a) + 2*A*a^3*b^2*e^6*sgn(b*x + a))*x^2 + 3*(54*B*b^5*d^5*e*sgn(b*x + a) - 175*B*a*b^4*d^4*e^2*sgn(b*x + a) - 35*A*b^5*d^4*e^2*sgn(b*x + a) + 200*B*a^2*b^3*d^3*e^3*sgn(b*x + a) + 100*A*a*b^4*d^3*e^3*sgn(b*x + a) - 90*B*a^3*b^2*d^2*e^4*sgn(b*x + a) - 90*A*a^2*b^3*d^2*e^4*sgn(b*x + a) + 10*B*a^4*b*d*e^5*sgn(b*x + a) + 20*A*a^3*b^2*d*e^5*sgn(b*x + a) + B*a^5*e^6*sgn(b*x + a) + 5*A*a^4*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^3","B",0
1749,1,870,0,0.225902," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","5 \, {\left(3 \, B b^{5} d^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d e \mathrm{sgn}\left(b x + a\right) - A b^{5} d e \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + A a b^{4} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B b^{5} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 10 \, B b^{5} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, B a b^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, A b^{5} x e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-10\right)} + \frac{{\left(171 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 385 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - 77 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 250 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 125 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(2 \, B b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - A b^{5} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{2} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{4} d e^{5} \mathrm{sgn}\left(b x + a\right) - B a^{3} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - A a^{2} b^{3} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 30 \, {\left(21 \, B b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 50 \, B a b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 10 \, A b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, B a^{2} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 18 \, A a b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, B a^{3} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) - 6 \, A a^{2} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) - B a^{4} b e^{6} \mathrm{sgn}\left(b x + a\right) - 2 \, A a^{3} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 4 \, {\left(141 \, B b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) - 325 \, B a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 65 \, A b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 220 \, B a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 110 \, A a b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, B a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 30 \, A a^{2} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 5 \, B a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{3} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) - B a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{12 \, {\left(x e + d\right)}^{4}}"," ",0,"5*(3*B*b^5*d^2*sgn(b*x + a) - 5*B*a*b^4*d*e*sgn(b*x + a) - A*b^5*d*e*sgn(b*x + a) + 2*B*a^2*b^3*e^2*sgn(b*x + a) + A*a*b^4*e^2*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/2*(B*b^5*x^2*e^5*sgn(b*x + a) - 10*B*b^5*d*x*e^4*sgn(b*x + a) + 10*B*a*b^4*x*e^5*sgn(b*x + a) + 2*A*b^5*x*e^5*sgn(b*x + a))*e^(-10) + 1/12*(171*B*b^5*d^6*sgn(b*x + a) - 385*B*a*b^4*d^5*e*sgn(b*x + a) - 77*A*b^5*d^5*e*sgn(b*x + a) + 250*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 125*A*a*b^4*d^4*e^2*sgn(b*x + a) - 30*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 30*A*a^2*b^3*d^3*e^3*sgn(b*x + a) - 5*B*a^4*b*d^2*e^4*sgn(b*x + a) - 10*A*a^3*b^2*d^2*e^4*sgn(b*x + a) - B*a^5*d*e^5*sgn(b*x + a) - 5*A*a^4*b*d*e^5*sgn(b*x + a) - 3*A*a^5*e^6*sgn(b*x + a) + 120*(2*B*b^5*d^3*e^3*sgn(b*x + a) - 5*B*a*b^4*d^2*e^4*sgn(b*x + a) - A*b^5*d^2*e^4*sgn(b*x + a) + 4*B*a^2*b^3*d*e^5*sgn(b*x + a) + 2*A*a*b^4*d*e^5*sgn(b*x + a) - B*a^3*b^2*e^6*sgn(b*x + a) - A*a^2*b^3*e^6*sgn(b*x + a))*x^3 + 30*(21*B*b^5*d^4*e^2*sgn(b*x + a) - 50*B*a*b^4*d^3*e^3*sgn(b*x + a) - 10*A*b^5*d^3*e^3*sgn(b*x + a) + 36*B*a^2*b^3*d^2*e^4*sgn(b*x + a) + 18*A*a*b^4*d^2*e^4*sgn(b*x + a) - 6*B*a^3*b^2*d*e^5*sgn(b*x + a) - 6*A*a^2*b^3*d*e^5*sgn(b*x + a) - B*a^4*b*e^6*sgn(b*x + a) - 2*A*a^3*b^2*e^6*sgn(b*x + a))*x^2 + 4*(141*B*b^5*d^5*e*sgn(b*x + a) - 325*B*a*b^4*d^4*e^2*sgn(b*x + a) - 65*A*b^5*d^4*e^2*sgn(b*x + a) + 220*B*a^2*b^3*d^3*e^3*sgn(b*x + a) + 110*A*a*b^4*d^3*e^3*sgn(b*x + a) - 30*B*a^3*b^2*d^2*e^4*sgn(b*x + a) - 30*A*a^2*b^3*d^2*e^4*sgn(b*x + a) - 5*B*a^4*b*d*e^5*sgn(b*x + a) - 10*A*a^3*b^2*d*e^5*sgn(b*x + a) - B*a^5*e^6*sgn(b*x + a) - 5*A*a^4*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^4","B",0
1750,1,863,0,0.271440," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^6,x, algorithm=""giac"")","B b^{5} x e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) - {\left(6 \, B b^{5} d \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} e \mathrm{sgn}\left(b x + a\right) - A b^{5} e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(522 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 685 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - 137 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 120 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 60 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 12 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 300 \, {\left(3 \, B b^{5} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d e^{5} \mathrm{sgn}\left(b x + a\right) - A b^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{2} b^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + A a b^{4} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{4} + 300 \, {\left(10 \, B b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 15 \, B a b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{5} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{2} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{4} d e^{5} \mathrm{sgn}\left(b x + a\right) + B a^{3} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + A a^{2} b^{3} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 100 \, {\left(39 \, B b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 55 \, B a b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 11 \, A b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, B a^{2} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{3} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) + B a^{4} b e^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 5 \, {\left(462 \, B b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) - 625 \, B a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 125 \, A b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, B a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, A a b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, B a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{2} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{4} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"B*b^5*x*e^(-6)*sgn(b*x + a) - (6*B*b^5*d*sgn(b*x + a) - 5*B*a*b^4*e*sgn(b*x + a) - A*b^5*e*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) - 1/60*(522*B*b^5*d^6*sgn(b*x + a) - 685*B*a*b^4*d^5*e*sgn(b*x + a) - 137*A*b^5*d^5*e*sgn(b*x + a) + 120*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 60*A*a*b^4*d^4*e^2*sgn(b*x + a) + 30*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 30*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 10*B*a^4*b*d^2*e^4*sgn(b*x + a) + 20*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 3*B*a^5*d*e^5*sgn(b*x + a) + 15*A*a^4*b*d*e^5*sgn(b*x + a) + 12*A*a^5*e^6*sgn(b*x + a) + 300*(3*B*b^5*d^2*e^4*sgn(b*x + a) - 5*B*a*b^4*d*e^5*sgn(b*x + a) - A*b^5*d*e^5*sgn(b*x + a) + 2*B*a^2*b^3*e^6*sgn(b*x + a) + A*a*b^4*e^6*sgn(b*x + a))*x^4 + 300*(10*B*b^5*d^3*e^3*sgn(b*x + a) - 15*B*a*b^4*d^2*e^4*sgn(b*x + a) - 3*A*b^5*d^2*e^4*sgn(b*x + a) + 4*B*a^2*b^3*d*e^5*sgn(b*x + a) + 2*A*a*b^4*d*e^5*sgn(b*x + a) + B*a^3*b^2*e^6*sgn(b*x + a) + A*a^2*b^3*e^6*sgn(b*x + a))*x^3 + 100*(39*B*b^5*d^4*e^2*sgn(b*x + a) - 55*B*a*b^4*d^3*e^3*sgn(b*x + a) - 11*A*b^5*d^3*e^3*sgn(b*x + a) + 12*B*a^2*b^3*d^2*e^4*sgn(b*x + a) + 6*A*a*b^4*d^2*e^4*sgn(b*x + a) + 3*B*a^3*b^2*d*e^5*sgn(b*x + a) + 3*A*a^2*b^3*d*e^5*sgn(b*x + a) + B*a^4*b*e^6*sgn(b*x + a) + 2*A*a^3*b^2*e^6*sgn(b*x + a))*x^2 + 5*(462*B*b^5*d^5*e*sgn(b*x + a) - 625*B*a*b^4*d^4*e^2*sgn(b*x + a) - 125*A*b^5*d^4*e^2*sgn(b*x + a) + 120*B*a^2*b^3*d^3*e^3*sgn(b*x + a) + 60*A*a*b^4*d^3*e^3*sgn(b*x + a) + 30*B*a^3*b^2*d^2*e^4*sgn(b*x + a) + 30*A*a^2*b^3*d^2*e^4*sgn(b*x + a) + 10*B*a^4*b*d*e^5*sgn(b*x + a) + 20*A*a^3*b^2*d*e^5*sgn(b*x + a) + 3*B*a^5*e^6*sgn(b*x + a) + 15*A*a^4*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^5","B",0
1751,1,871,0,0.298308," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^7,x, algorithm=""giac"")","B b^{5} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(60 \, {\left(6 \, B b^{5} d e^{4} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - A b^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{5} + 150 \, {\left(9 \, B b^{5} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d e^{4} \mathrm{sgn}\left(b x + a\right) - A b^{5} d e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, B a^{2} b^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - A a b^{4} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{4} + 200 \, {\left(11 \, B b^{5} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - A b^{5} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 2 \, B a^{2} b^{3} d e^{4} \mathrm{sgn}\left(b x + a\right) - A a b^{4} d e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{3} b^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - A a^{2} b^{3} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 75 \, {\left(25 \, B b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 10 \, B a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, A b^{5} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, B a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 2 \, A a b^{4} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 2 \, B a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, A a^{2} b^{3} d e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right) - 2 \, A a^{3} b^{2} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 6 \, {\left(137 \, B b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 50 \, B a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) - 10 \, A b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 20 \, B a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, A a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, B a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, B a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, B a^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(147 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 50 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - 10 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) - 20 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"B*b^5*e^(-7)*log(abs(x*e + d))*sgn(b*x + a) + 1/60*(60*(6*B*b^5*d*e^4*sgn(b*x + a) - 5*B*a*b^4*e^5*sgn(b*x + a) - A*b^5*e^5*sgn(b*x + a))*x^5 + 150*(9*B*b^5*d^2*e^3*sgn(b*x + a) - 5*B*a*b^4*d*e^4*sgn(b*x + a) - A*b^5*d*e^4*sgn(b*x + a) - 2*B*a^2*b^3*e^5*sgn(b*x + a) - A*a*b^4*e^5*sgn(b*x + a))*x^4 + 200*(11*B*b^5*d^3*e^2*sgn(b*x + a) - 5*B*a*b^4*d^2*e^3*sgn(b*x + a) - A*b^5*d^2*e^3*sgn(b*x + a) - 2*B*a^2*b^3*d*e^4*sgn(b*x + a) - A*a*b^4*d*e^4*sgn(b*x + a) - B*a^3*b^2*e^5*sgn(b*x + a) - A*a^2*b^3*e^5*sgn(b*x + a))*x^3 + 75*(25*B*b^5*d^4*e*sgn(b*x + a) - 10*B*a*b^4*d^3*e^2*sgn(b*x + a) - 2*A*b^5*d^3*e^2*sgn(b*x + a) - 4*B*a^2*b^3*d^2*e^3*sgn(b*x + a) - 2*A*a*b^4*d^2*e^3*sgn(b*x + a) - 2*B*a^3*b^2*d*e^4*sgn(b*x + a) - 2*A*a^2*b^3*d*e^4*sgn(b*x + a) - B*a^4*b*e^5*sgn(b*x + a) - 2*A*a^3*b^2*e^5*sgn(b*x + a))*x^2 + 6*(137*B*b^5*d^5*sgn(b*x + a) - 50*B*a*b^4*d^4*e*sgn(b*x + a) - 10*A*b^5*d^4*e*sgn(b*x + a) - 20*B*a^2*b^3*d^3*e^2*sgn(b*x + a) - 10*A*a*b^4*d^3*e^2*sgn(b*x + a) - 10*B*a^3*b^2*d^2*e^3*sgn(b*x + a) - 10*A*a^2*b^3*d^2*e^3*sgn(b*x + a) - 5*B*a^4*b*d*e^4*sgn(b*x + a) - 10*A*a^3*b^2*d*e^4*sgn(b*x + a) - 2*B*a^5*e^5*sgn(b*x + a) - 10*A*a^4*b*e^5*sgn(b*x + a))*x + (147*B*b^5*d^6*sgn(b*x + a) - 50*B*a*b^4*d^5*e*sgn(b*x + a) - 10*A*b^5*d^5*e*sgn(b*x + a) - 20*B*a^2*b^3*d^4*e^2*sgn(b*x + a) - 10*A*a*b^4*d^4*e^2*sgn(b*x + a) - 10*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 10*A*a^2*b^3*d^3*e^3*sgn(b*x + a) - 5*B*a^4*b*d^2*e^4*sgn(b*x + a) - 10*A*a^3*b^2*d^2*e^4*sgn(b*x + a) - 2*B*a^5*d*e^5*sgn(b*x + a) - 10*A*a^4*b*d*e^5*sgn(b*x + a) - 10*A*a^5*e^6*sgn(b*x + a))*e^(-1))*e^(-6)/(x*e + d)^6","B",0
1752,1,917,0,0.218544," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(42 \, B b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 126 \, B b^{5} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, B b^{5} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 210 \, B b^{5} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 126 \, B b^{5} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 42 \, B b^{5} d^{5} x e \mathrm{sgn}\left(b x + a\right) + 6 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 105 \, B a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 21 \, A b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 175 \, B a b^{4} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, A b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 175 \, B a b^{4} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, A b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, B a b^{4} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, A b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, B a b^{4} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, A b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 70 \, A a b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{2} b^{3} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, A a b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 84 \, B a^{2} b^{3} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 42 \, A a b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 28 \, B a^{2} b^{3} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 14 \, A a b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 105 \, B a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 105 \, A a^{2} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 63 \, B a^{3} b^{2} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 63 \, A a^{2} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 21 \, B a^{3} b^{2} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 21 \, A a^{2} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 42 \, B a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 84 \, A a^{3} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 14 \, B a^{4} b d x e^{5} \mathrm{sgn}\left(b x + a\right) + 28 \, A a^{3} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 7 \, B a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 35 \, A a^{4} b x e^{6} \mathrm{sgn}\left(b x + a\right) + B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{42 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/42*(42*B*b^5*x^6*e^6*sgn(b*x + a) + 126*B*b^5*d*x^5*e^5*sgn(b*x + a) + 210*B*b^5*d^2*x^4*e^4*sgn(b*x + a) + 210*B*b^5*d^3*x^3*e^3*sgn(b*x + a) + 126*B*b^5*d^4*x^2*e^2*sgn(b*x + a) + 42*B*b^5*d^5*x*e*sgn(b*x + a) + 6*B*b^5*d^6*sgn(b*x + a) + 105*B*a*b^4*x^5*e^6*sgn(b*x + a) + 21*A*b^5*x^5*e^6*sgn(b*x + a) + 175*B*a*b^4*d*x^4*e^5*sgn(b*x + a) + 35*A*b^5*d*x^4*e^5*sgn(b*x + a) + 175*B*a*b^4*d^2*x^3*e^4*sgn(b*x + a) + 35*A*b^5*d^2*x^3*e^4*sgn(b*x + a) + 105*B*a*b^4*d^3*x^2*e^3*sgn(b*x + a) + 21*A*b^5*d^3*x^2*e^3*sgn(b*x + a) + 35*B*a*b^4*d^4*x*e^2*sgn(b*x + a) + 7*A*b^5*d^4*x*e^2*sgn(b*x + a) + 5*B*a*b^4*d^5*e*sgn(b*x + a) + A*b^5*d^5*e*sgn(b*x + a) + 140*B*a^2*b^3*x^4*e^6*sgn(b*x + a) + 70*A*a*b^4*x^4*e^6*sgn(b*x + a) + 140*B*a^2*b^3*d*x^3*e^5*sgn(b*x + a) + 70*A*a*b^4*d*x^3*e^5*sgn(b*x + a) + 84*B*a^2*b^3*d^2*x^2*e^4*sgn(b*x + a) + 42*A*a*b^4*d^2*x^2*e^4*sgn(b*x + a) + 28*B*a^2*b^3*d^3*x*e^3*sgn(b*x + a) + 14*A*a*b^4*d^3*x*e^3*sgn(b*x + a) + 4*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 2*A*a*b^4*d^4*e^2*sgn(b*x + a) + 105*B*a^3*b^2*x^3*e^6*sgn(b*x + a) + 105*A*a^2*b^3*x^3*e^6*sgn(b*x + a) + 63*B*a^3*b^2*d*x^2*e^5*sgn(b*x + a) + 63*A*a^2*b^3*d*x^2*e^5*sgn(b*x + a) + 21*B*a^3*b^2*d^2*x*e^4*sgn(b*x + a) + 21*A*a^2*b^3*d^2*x*e^4*sgn(b*x + a) + 3*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 3*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 42*B*a^4*b*x^2*e^6*sgn(b*x + a) + 84*A*a^3*b^2*x^2*e^6*sgn(b*x + a) + 14*B*a^4*b*d*x*e^5*sgn(b*x + a) + 28*A*a^3*b^2*d*x*e^5*sgn(b*x + a) + 2*B*a^4*b*d^2*e^4*sgn(b*x + a) + 4*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 7*B*a^5*x*e^6*sgn(b*x + a) + 35*A*a^4*b*x*e^6*sgn(b*x + a) + B*a^5*d*e^5*sgn(b*x + a) + 5*A*a^4*b*d*e^5*sgn(b*x + a) + 6*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^7","B",0
1753,1,918,0,0.219628," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(84 \, B b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 168 \, B b^{5} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, B b^{5} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 168 \, B b^{5} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, B b^{5} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 24 \, B b^{5} d^{5} x e \mathrm{sgn}\left(b x + a\right) + 3 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 280 \, B a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 56 \, A b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 350 \, B a b^{4} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, A b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 280 \, B a b^{4} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, A b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 140 \, B a b^{4} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, A b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 40 \, B a b^{4} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, A b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 420 \, B a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 210 \, A a b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 336 \, B a^{2} b^{3} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 168 \, A a b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 168 \, B a^{2} b^{3} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, A a b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 48 \, B a^{2} b^{3} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 24 \, A a b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 336 \, B a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 336 \, A a^{2} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 168 \, B a^{3} b^{2} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 168 \, A a^{2} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 48 \, B a^{3} b^{2} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 48 \, A a^{2} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 280 \, A a^{3} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 40 \, B a^{4} b d x e^{5} \mathrm{sgn}\left(b x + a\right) + 80 \, A a^{3} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 24 \, B a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 120 \, A a^{4} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 21 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{168 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/168*(84*B*b^5*x^6*e^6*sgn(b*x + a) + 168*B*b^5*d*x^5*e^5*sgn(b*x + a) + 210*B*b^5*d^2*x^4*e^4*sgn(b*x + a) + 168*B*b^5*d^3*x^3*e^3*sgn(b*x + a) + 84*B*b^5*d^4*x^2*e^2*sgn(b*x + a) + 24*B*b^5*d^5*x*e*sgn(b*x + a) + 3*B*b^5*d^6*sgn(b*x + a) + 280*B*a*b^4*x^5*e^6*sgn(b*x + a) + 56*A*b^5*x^5*e^6*sgn(b*x + a) + 350*B*a*b^4*d*x^4*e^5*sgn(b*x + a) + 70*A*b^5*d*x^4*e^5*sgn(b*x + a) + 280*B*a*b^4*d^2*x^3*e^4*sgn(b*x + a) + 56*A*b^5*d^2*x^3*e^4*sgn(b*x + a) + 140*B*a*b^4*d^3*x^2*e^3*sgn(b*x + a) + 28*A*b^5*d^3*x^2*e^3*sgn(b*x + a) + 40*B*a*b^4*d^4*x*e^2*sgn(b*x + a) + 8*A*b^5*d^4*x*e^2*sgn(b*x + a) + 5*B*a*b^4*d^5*e*sgn(b*x + a) + A*b^5*d^5*e*sgn(b*x + a) + 420*B*a^2*b^3*x^4*e^6*sgn(b*x + a) + 210*A*a*b^4*x^4*e^6*sgn(b*x + a) + 336*B*a^2*b^3*d*x^3*e^5*sgn(b*x + a) + 168*A*a*b^4*d*x^3*e^5*sgn(b*x + a) + 168*B*a^2*b^3*d^2*x^2*e^4*sgn(b*x + a) + 84*A*a*b^4*d^2*x^2*e^4*sgn(b*x + a) + 48*B*a^2*b^3*d^3*x*e^3*sgn(b*x + a) + 24*A*a*b^4*d^3*x*e^3*sgn(b*x + a) + 6*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 3*A*a*b^4*d^4*e^2*sgn(b*x + a) + 336*B*a^3*b^2*x^3*e^6*sgn(b*x + a) + 336*A*a^2*b^3*x^3*e^6*sgn(b*x + a) + 168*B*a^3*b^2*d*x^2*e^5*sgn(b*x + a) + 168*A*a^2*b^3*d*x^2*e^5*sgn(b*x + a) + 48*B*a^3*b^2*d^2*x*e^4*sgn(b*x + a) + 48*A*a^2*b^3*d^2*x*e^4*sgn(b*x + a) + 6*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 6*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 140*B*a^4*b*x^2*e^6*sgn(b*x + a) + 280*A*a^3*b^2*x^2*e^6*sgn(b*x + a) + 40*B*a^4*b*d*x*e^5*sgn(b*x + a) + 80*A*a^3*b^2*d*x*e^5*sgn(b*x + a) + 5*B*a^4*b*d^2*e^4*sgn(b*x + a) + 10*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 24*B*a^5*x*e^6*sgn(b*x + a) + 120*A*a^4*b*x*e^6*sgn(b*x + a) + 3*B*a^5*d*e^5*sgn(b*x + a) + 15*A*a^4*b*d*e^5*sgn(b*x + a) + 21*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^8","B",0
1754,1,918,0,0.240966," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(168 \, B b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 252 \, B b^{5} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 252 \, B b^{5} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 168 \, B b^{5} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 72 \, B b^{5} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, B b^{5} d^{5} x e \mathrm{sgn}\left(b x + a\right) + 2 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 630 \, B a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 126 \, A b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 630 \, B a b^{4} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, A b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 420 \, B a b^{4} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, A b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, B a b^{4} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, A b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, B a b^{4} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, A b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 1008 \, B a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 504 \, A a b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 672 \, B a^{2} b^{3} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 336 \, A a b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 288 \, B a^{2} b^{3} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 144 \, A a b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 72 \, B a^{2} b^{3} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, A a b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 8 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 840 \, B a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 840 \, A a^{2} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 360 \, B a^{3} b^{2} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 360 \, A a^{2} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 90 \, B a^{3} b^{2} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 90 \, A a^{2} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 360 \, B a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 720 \, A a^{3} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 90 \, B a^{4} b d x e^{5} \mathrm{sgn}\left(b x + a\right) + 180 \, A a^{3} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 63 \, B a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 315 \, A a^{4} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 7 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 56 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{504 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/504*(168*B*b^5*x^6*e^6*sgn(b*x + a) + 252*B*b^5*d*x^5*e^5*sgn(b*x + a) + 252*B*b^5*d^2*x^4*e^4*sgn(b*x + a) + 168*B*b^5*d^3*x^3*e^3*sgn(b*x + a) + 72*B*b^5*d^4*x^2*e^2*sgn(b*x + a) + 18*B*b^5*d^5*x*e*sgn(b*x + a) + 2*B*b^5*d^6*sgn(b*x + a) + 630*B*a*b^4*x^5*e^6*sgn(b*x + a) + 126*A*b^5*x^5*e^6*sgn(b*x + a) + 630*B*a*b^4*d*x^4*e^5*sgn(b*x + a) + 126*A*b^5*d*x^4*e^5*sgn(b*x + a) + 420*B*a*b^4*d^2*x^3*e^4*sgn(b*x + a) + 84*A*b^5*d^2*x^3*e^4*sgn(b*x + a) + 180*B*a*b^4*d^3*x^2*e^3*sgn(b*x + a) + 36*A*b^5*d^3*x^2*e^3*sgn(b*x + a) + 45*B*a*b^4*d^4*x*e^2*sgn(b*x + a) + 9*A*b^5*d^4*x*e^2*sgn(b*x + a) + 5*B*a*b^4*d^5*e*sgn(b*x + a) + A*b^5*d^5*e*sgn(b*x + a) + 1008*B*a^2*b^3*x^4*e^6*sgn(b*x + a) + 504*A*a*b^4*x^4*e^6*sgn(b*x + a) + 672*B*a^2*b^3*d*x^3*e^5*sgn(b*x + a) + 336*A*a*b^4*d*x^3*e^5*sgn(b*x + a) + 288*B*a^2*b^3*d^2*x^2*e^4*sgn(b*x + a) + 144*A*a*b^4*d^2*x^2*e^4*sgn(b*x + a) + 72*B*a^2*b^3*d^3*x*e^3*sgn(b*x + a) + 36*A*a*b^4*d^3*x*e^3*sgn(b*x + a) + 8*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 4*A*a*b^4*d^4*e^2*sgn(b*x + a) + 840*B*a^3*b^2*x^3*e^6*sgn(b*x + a) + 840*A*a^2*b^3*x^3*e^6*sgn(b*x + a) + 360*B*a^3*b^2*d*x^2*e^5*sgn(b*x + a) + 360*A*a^2*b^3*d*x^2*e^5*sgn(b*x + a) + 90*B*a^3*b^2*d^2*x*e^4*sgn(b*x + a) + 90*A*a^2*b^3*d^2*x*e^4*sgn(b*x + a) + 10*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 10*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 360*B*a^4*b*x^2*e^6*sgn(b*x + a) + 720*A*a^3*b^2*x^2*e^6*sgn(b*x + a) + 90*B*a^4*b*d*x*e^5*sgn(b*x + a) + 180*A*a^3*b^2*d*x*e^5*sgn(b*x + a) + 10*B*a^4*b*d^2*e^4*sgn(b*x + a) + 20*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 63*B*a^5*x*e^6*sgn(b*x + a) + 315*A*a^4*b*x*e^6*sgn(b*x + a) + 7*B*a^5*d*e^5*sgn(b*x + a) + 35*A*a^4*b*d*e^5*sgn(b*x + a) + 56*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^9","B",0
1755,1,919,0,0.224825," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(630 \, B b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 756 \, B b^{5} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 630 \, B b^{5} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 360 \, B b^{5} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 135 \, B b^{5} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, B b^{5} d^{5} x e \mathrm{sgn}\left(b x + a\right) + 3 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 2520 \, B a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 504 \, A b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 2100 \, B a b^{4} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 420 \, A b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 1200 \, B a b^{4} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 240 \, A b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 450 \, B a b^{4} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 90 \, A b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 100 \, B a b^{4} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, A b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + 2 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 4200 \, B a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 2100 \, A a b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 2400 \, B a^{2} b^{3} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 1200 \, A a b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 900 \, B a^{2} b^{3} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 450 \, A a b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 200 \, B a^{2} b^{3} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 100 \, A a b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 3600 \, B a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 3600 \, A a^{2} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1350 \, B a^{3} b^{2} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1350 \, A a^{2} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 300 \, B a^{3} b^{2} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 300 \, A a^{2} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 1575 \, B a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 3150 \, A a^{3} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 350 \, B a^{4} b d x e^{5} \mathrm{sgn}\left(b x + a\right) + 700 \, A a^{3} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 70 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 280 \, B a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 1400 \, A a^{4} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 28 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 140 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 252 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{2520 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/2520*(630*B*b^5*x^6*e^6*sgn(b*x + a) + 756*B*b^5*d*x^5*e^5*sgn(b*x + a) + 630*B*b^5*d^2*x^4*e^4*sgn(b*x + a) + 360*B*b^5*d^3*x^3*e^3*sgn(b*x + a) + 135*B*b^5*d^4*x^2*e^2*sgn(b*x + a) + 30*B*b^5*d^5*x*e*sgn(b*x + a) + 3*B*b^5*d^6*sgn(b*x + a) + 2520*B*a*b^4*x^5*e^6*sgn(b*x + a) + 504*A*b^5*x^5*e^6*sgn(b*x + a) + 2100*B*a*b^4*d*x^4*e^5*sgn(b*x + a) + 420*A*b^5*d*x^4*e^5*sgn(b*x + a) + 1200*B*a*b^4*d^2*x^3*e^4*sgn(b*x + a) + 240*A*b^5*d^2*x^3*e^4*sgn(b*x + a) + 450*B*a*b^4*d^3*x^2*e^3*sgn(b*x + a) + 90*A*b^5*d^3*x^2*e^3*sgn(b*x + a) + 100*B*a*b^4*d^4*x*e^2*sgn(b*x + a) + 20*A*b^5*d^4*x*e^2*sgn(b*x + a) + 10*B*a*b^4*d^5*e*sgn(b*x + a) + 2*A*b^5*d^5*e*sgn(b*x + a) + 4200*B*a^2*b^3*x^4*e^6*sgn(b*x + a) + 2100*A*a*b^4*x^4*e^6*sgn(b*x + a) + 2400*B*a^2*b^3*d*x^3*e^5*sgn(b*x + a) + 1200*A*a*b^4*d*x^3*e^5*sgn(b*x + a) + 900*B*a^2*b^3*d^2*x^2*e^4*sgn(b*x + a) + 450*A*a*b^4*d^2*x^2*e^4*sgn(b*x + a) + 200*B*a^2*b^3*d^3*x*e^3*sgn(b*x + a) + 100*A*a*b^4*d^3*x*e^3*sgn(b*x + a) + 20*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 10*A*a*b^4*d^4*e^2*sgn(b*x + a) + 3600*B*a^3*b^2*x^3*e^6*sgn(b*x + a) + 3600*A*a^2*b^3*x^3*e^6*sgn(b*x + a) + 1350*B*a^3*b^2*d*x^2*e^5*sgn(b*x + a) + 1350*A*a^2*b^3*d*x^2*e^5*sgn(b*x + a) + 300*B*a^3*b^2*d^2*x*e^4*sgn(b*x + a) + 300*A*a^2*b^3*d^2*x*e^4*sgn(b*x + a) + 30*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 30*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 1575*B*a^4*b*x^2*e^6*sgn(b*x + a) + 3150*A*a^3*b^2*x^2*e^6*sgn(b*x + a) + 350*B*a^4*b*d*x*e^5*sgn(b*x + a) + 700*A*a^3*b^2*d*x*e^5*sgn(b*x + a) + 35*B*a^4*b*d^2*e^4*sgn(b*x + a) + 70*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 280*B*a^5*x*e^6*sgn(b*x + a) + 1400*A*a^4*b*x*e^6*sgn(b*x + a) + 28*B*a^5*d*e^5*sgn(b*x + a) + 140*A*a^4*b*d*e^5*sgn(b*x + a) + 252*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^10","B",0
1756,1,919,0,0.364436," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(2772 \, B b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 2772 \, B b^{5} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 1980 \, B b^{5} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 990 \, B b^{5} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 330 \, B b^{5} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 66 \, B b^{5} d^{5} x e \mathrm{sgn}\left(b x + a\right) + 6 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 11550 \, B a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 2310 \, A b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 8250 \, B a b^{4} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 1650 \, A b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 4125 \, B a b^{4} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 825 \, A b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 1375 \, B a b^{4} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 275 \, A b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 275 \, B a b^{4} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 55 \, A b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 25 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 19800 \, B a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 9900 \, A a b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 9900 \, B a^{2} b^{3} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 4950 \, A a b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 3300 \, B a^{2} b^{3} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1650 \, A a b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 660 \, B a^{2} b^{3} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 330 \, A a b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 17325 \, B a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 17325 \, A a^{2} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 5775 \, B a^{3} b^{2} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 5775 \, A a^{2} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1155 \, B a^{3} b^{2} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 1155 \, A a^{2} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 105 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 7700 \, B a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 15400 \, A a^{3} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 1540 \, B a^{4} b d x e^{5} \mathrm{sgn}\left(b x + a\right) + 3080 \, A a^{3} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 140 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 280 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1386 \, B a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 6930 \, A a^{4} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 126 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 630 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 1260 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{13860 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/13860*(2772*B*b^5*x^6*e^6*sgn(b*x + a) + 2772*B*b^5*d*x^5*e^5*sgn(b*x + a) + 1980*B*b^5*d^2*x^4*e^4*sgn(b*x + a) + 990*B*b^5*d^3*x^3*e^3*sgn(b*x + a) + 330*B*b^5*d^4*x^2*e^2*sgn(b*x + a) + 66*B*b^5*d^5*x*e*sgn(b*x + a) + 6*B*b^5*d^6*sgn(b*x + a) + 11550*B*a*b^4*x^5*e^6*sgn(b*x + a) + 2310*A*b^5*x^5*e^6*sgn(b*x + a) + 8250*B*a*b^4*d*x^4*e^5*sgn(b*x + a) + 1650*A*b^5*d*x^4*e^5*sgn(b*x + a) + 4125*B*a*b^4*d^2*x^3*e^4*sgn(b*x + a) + 825*A*b^5*d^2*x^3*e^4*sgn(b*x + a) + 1375*B*a*b^4*d^3*x^2*e^3*sgn(b*x + a) + 275*A*b^5*d^3*x^2*e^3*sgn(b*x + a) + 275*B*a*b^4*d^4*x*e^2*sgn(b*x + a) + 55*A*b^5*d^4*x*e^2*sgn(b*x + a) + 25*B*a*b^4*d^5*e*sgn(b*x + a) + 5*A*b^5*d^5*e*sgn(b*x + a) + 19800*B*a^2*b^3*x^4*e^6*sgn(b*x + a) + 9900*A*a*b^4*x^4*e^6*sgn(b*x + a) + 9900*B*a^2*b^3*d*x^3*e^5*sgn(b*x + a) + 4950*A*a*b^4*d*x^3*e^5*sgn(b*x + a) + 3300*B*a^2*b^3*d^2*x^2*e^4*sgn(b*x + a) + 1650*A*a*b^4*d^2*x^2*e^4*sgn(b*x + a) + 660*B*a^2*b^3*d^3*x*e^3*sgn(b*x + a) + 330*A*a*b^4*d^3*x*e^3*sgn(b*x + a) + 60*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 30*A*a*b^4*d^4*e^2*sgn(b*x + a) + 17325*B*a^3*b^2*x^3*e^6*sgn(b*x + a) + 17325*A*a^2*b^3*x^3*e^6*sgn(b*x + a) + 5775*B*a^3*b^2*d*x^2*e^5*sgn(b*x + a) + 5775*A*a^2*b^3*d*x^2*e^5*sgn(b*x + a) + 1155*B*a^3*b^2*d^2*x*e^4*sgn(b*x + a) + 1155*A*a^2*b^3*d^2*x*e^4*sgn(b*x + a) + 105*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 105*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 7700*B*a^4*b*x^2*e^6*sgn(b*x + a) + 15400*A*a^3*b^2*x^2*e^6*sgn(b*x + a) + 1540*B*a^4*b*d*x*e^5*sgn(b*x + a) + 3080*A*a^3*b^2*d*x*e^5*sgn(b*x + a) + 140*B*a^4*b*d^2*e^4*sgn(b*x + a) + 280*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 1386*B*a^5*x*e^6*sgn(b*x + a) + 6930*A*a^4*b*x*e^6*sgn(b*x + a) + 126*B*a^5*d*e^5*sgn(b*x + a) + 630*A*a^4*b*d*e^5*sgn(b*x + a) + 1260*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^11","B",0
1757,1,917,0,0.224521," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^13,x, algorithm=""giac"")","-\frac{{\left(924 \, B b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 792 \, B b^{5} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 495 \, B b^{5} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 220 \, B b^{5} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 66 \, B b^{5} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, B b^{5} d^{5} x e \mathrm{sgn}\left(b x + a\right) + B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 3960 \, B a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 792 \, A b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 2475 \, B a b^{4} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 495 \, A b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 1100 \, B a b^{4} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 220 \, A b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 330 \, B a b^{4} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 66 \, A b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, B a b^{4} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, A b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 6930 \, B a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 3465 \, A a b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 3080 \, B a^{2} b^{3} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 1540 \, A a b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 924 \, B a^{2} b^{3} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 462 \, A a b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 168 \, B a^{2} b^{3} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, A a b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 14 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 6160 \, B a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 6160 \, A a^{2} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1848 \, B a^{3} b^{2} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1848 \, A a^{2} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 336 \, B a^{3} b^{2} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 336 \, A a^{2} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 28 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 2772 \, B a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 5544 \, A a^{3} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 504 \, B a^{4} b d x e^{5} \mathrm{sgn}\left(b x + a\right) + 1008 \, A a^{3} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 42 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 504 \, B a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 2520 \, A a^{4} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 42 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 462 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{5544 \, {\left(x e + d\right)}^{12}}"," ",0,"-1/5544*(924*B*b^5*x^6*e^6*sgn(b*x + a) + 792*B*b^5*d*x^5*e^5*sgn(b*x + a) + 495*B*b^5*d^2*x^4*e^4*sgn(b*x + a) + 220*B*b^5*d^3*x^3*e^3*sgn(b*x + a) + 66*B*b^5*d^4*x^2*e^2*sgn(b*x + a) + 12*B*b^5*d^5*x*e*sgn(b*x + a) + B*b^5*d^6*sgn(b*x + a) + 3960*B*a*b^4*x^5*e^6*sgn(b*x + a) + 792*A*b^5*x^5*e^6*sgn(b*x + a) + 2475*B*a*b^4*d*x^4*e^5*sgn(b*x + a) + 495*A*b^5*d*x^4*e^5*sgn(b*x + a) + 1100*B*a*b^4*d^2*x^3*e^4*sgn(b*x + a) + 220*A*b^5*d^2*x^3*e^4*sgn(b*x + a) + 330*B*a*b^4*d^3*x^2*e^3*sgn(b*x + a) + 66*A*b^5*d^3*x^2*e^3*sgn(b*x + a) + 60*B*a*b^4*d^4*x*e^2*sgn(b*x + a) + 12*A*b^5*d^4*x*e^2*sgn(b*x + a) + 5*B*a*b^4*d^5*e*sgn(b*x + a) + A*b^5*d^5*e*sgn(b*x + a) + 6930*B*a^2*b^3*x^4*e^6*sgn(b*x + a) + 3465*A*a*b^4*x^4*e^6*sgn(b*x + a) + 3080*B*a^2*b^3*d*x^3*e^5*sgn(b*x + a) + 1540*A*a*b^4*d*x^3*e^5*sgn(b*x + a) + 924*B*a^2*b^3*d^2*x^2*e^4*sgn(b*x + a) + 462*A*a*b^4*d^2*x^2*e^4*sgn(b*x + a) + 168*B*a^2*b^3*d^3*x*e^3*sgn(b*x + a) + 84*A*a*b^4*d^3*x*e^3*sgn(b*x + a) + 14*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 7*A*a*b^4*d^4*e^2*sgn(b*x + a) + 6160*B*a^3*b^2*x^3*e^6*sgn(b*x + a) + 6160*A*a^2*b^3*x^3*e^6*sgn(b*x + a) + 1848*B*a^3*b^2*d*x^2*e^5*sgn(b*x + a) + 1848*A*a^2*b^3*d*x^2*e^5*sgn(b*x + a) + 336*B*a^3*b^2*d^2*x*e^4*sgn(b*x + a) + 336*A*a^2*b^3*d^2*x*e^4*sgn(b*x + a) + 28*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 28*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 2772*B*a^4*b*x^2*e^6*sgn(b*x + a) + 5544*A*a^3*b^2*x^2*e^6*sgn(b*x + a) + 504*B*a^4*b*d*x*e^5*sgn(b*x + a) + 1008*A*a^3*b^2*d*x*e^5*sgn(b*x + a) + 42*B*a^4*b*d^2*e^4*sgn(b*x + a) + 84*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 504*B*a^5*x*e^6*sgn(b*x + a) + 2520*A*a^4*b*x*e^6*sgn(b*x + a) + 42*B*a^5*d*e^5*sgn(b*x + a) + 210*A*a^4*b*d*e^5*sgn(b*x + a) + 462*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^12","B",0
1758,1,919,0,0.219388," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^14,x, algorithm=""giac"")","-\frac{{\left(10296 \, B b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 7722 \, B b^{5} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 4290 \, B b^{5} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 1716 \, B b^{5} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 468 \, B b^{5} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 78 \, B b^{5} d^{5} x e \mathrm{sgn}\left(b x + a\right) + 6 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 45045 \, B a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 9009 \, A b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 25025 \, B a b^{4} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 5005 \, A b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 10010 \, B a b^{4} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 2002 \, A b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 2730 \, B a b^{4} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 546 \, A b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 455 \, B a b^{4} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 91 \, A b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + 7 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 80080 \, B a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 40040 \, A a b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 32032 \, B a^{2} b^{3} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 16016 \, A a b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 8736 \, B a^{2} b^{3} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 4368 \, A a b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1456 \, B a^{2} b^{3} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 728 \, A a b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 112 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 56 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 72072 \, B a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 72072 \, A a^{2} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 19656 \, B a^{3} b^{2} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 19656 \, A a^{2} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 3276 \, B a^{3} b^{2} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 3276 \, A a^{2} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 252 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 252 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 32760 \, B a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 65520 \, A a^{3} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 5460 \, B a^{4} b d x e^{5} \mathrm{sgn}\left(b x + a\right) + 10920 \, A a^{3} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 420 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 840 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 6006 \, B a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 30030 \, A a^{4} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 462 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 2310 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 5544 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{72072 \, {\left(x e + d\right)}^{13}}"," ",0,"-1/72072*(10296*B*b^5*x^6*e^6*sgn(b*x + a) + 7722*B*b^5*d*x^5*e^5*sgn(b*x + a) + 4290*B*b^5*d^2*x^4*e^4*sgn(b*x + a) + 1716*B*b^5*d^3*x^3*e^3*sgn(b*x + a) + 468*B*b^5*d^4*x^2*e^2*sgn(b*x + a) + 78*B*b^5*d^5*x*e*sgn(b*x + a) + 6*B*b^5*d^6*sgn(b*x + a) + 45045*B*a*b^4*x^5*e^6*sgn(b*x + a) + 9009*A*b^5*x^5*e^6*sgn(b*x + a) + 25025*B*a*b^4*d*x^4*e^5*sgn(b*x + a) + 5005*A*b^5*d*x^4*e^5*sgn(b*x + a) + 10010*B*a*b^4*d^2*x^3*e^4*sgn(b*x + a) + 2002*A*b^5*d^2*x^3*e^4*sgn(b*x + a) + 2730*B*a*b^4*d^3*x^2*e^3*sgn(b*x + a) + 546*A*b^5*d^3*x^2*e^3*sgn(b*x + a) + 455*B*a*b^4*d^4*x*e^2*sgn(b*x + a) + 91*A*b^5*d^4*x*e^2*sgn(b*x + a) + 35*B*a*b^4*d^5*e*sgn(b*x + a) + 7*A*b^5*d^5*e*sgn(b*x + a) + 80080*B*a^2*b^3*x^4*e^6*sgn(b*x + a) + 40040*A*a*b^4*x^4*e^6*sgn(b*x + a) + 32032*B*a^2*b^3*d*x^3*e^5*sgn(b*x + a) + 16016*A*a*b^4*d*x^3*e^5*sgn(b*x + a) + 8736*B*a^2*b^3*d^2*x^2*e^4*sgn(b*x + a) + 4368*A*a*b^4*d^2*x^2*e^4*sgn(b*x + a) + 1456*B*a^2*b^3*d^3*x*e^3*sgn(b*x + a) + 728*A*a*b^4*d^3*x*e^3*sgn(b*x + a) + 112*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 56*A*a*b^4*d^4*e^2*sgn(b*x + a) + 72072*B*a^3*b^2*x^3*e^6*sgn(b*x + a) + 72072*A*a^2*b^3*x^3*e^6*sgn(b*x + a) + 19656*B*a^3*b^2*d*x^2*e^5*sgn(b*x + a) + 19656*A*a^2*b^3*d*x^2*e^5*sgn(b*x + a) + 3276*B*a^3*b^2*d^2*x*e^4*sgn(b*x + a) + 3276*A*a^2*b^3*d^2*x*e^4*sgn(b*x + a) + 252*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 252*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 32760*B*a^4*b*x^2*e^6*sgn(b*x + a) + 65520*A*a^3*b^2*x^2*e^6*sgn(b*x + a) + 5460*B*a^4*b*d*x*e^5*sgn(b*x + a) + 10920*A*a^3*b^2*d*x*e^5*sgn(b*x + a) + 420*B*a^4*b*d^2*e^4*sgn(b*x + a) + 840*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 6006*B*a^5*x*e^6*sgn(b*x + a) + 30030*A*a^4*b*x*e^6*sgn(b*x + a) + 462*B*a^5*d*e^5*sgn(b*x + a) + 2310*A*a^4*b*d*e^5*sgn(b*x + a) + 5544*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^13","B",0
1759,1,431,0,0.188924," ","integrate((B*x+A)*(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{3 \, B b^{3} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, B b^{3} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, B b^{3} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + 12 \, B b^{3} d^{3} x \mathrm{sgn}\left(b x + a\right) - 4 \, B a b^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, A b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 18 \, B a b^{2} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, A b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 36 \, B a b^{2} d^{2} x e \mathrm{sgn}\left(b x + a\right) + 36 \, A b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} b x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, A a b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, B a^{2} b d x e^{2} \mathrm{sgn}\left(b x + a\right) - 36 \, A a b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) - 12 \, B a^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, A a^{2} b x e^{3} \mathrm{sgn}\left(b x + a\right)}{12 \, b^{4}} - \frac{{\left(B a b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - A b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, B a^{2} b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{3} b d e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}}"," ",0,"1/12*(3*B*b^3*x^4*e^3*sgn(b*x + a) + 12*B*b^3*d*x^3*e^2*sgn(b*x + a) + 18*B*b^3*d^2*x^2*e*sgn(b*x + a) + 12*B*b^3*d^3*x*sgn(b*x + a) - 4*B*a*b^2*x^3*e^3*sgn(b*x + a) + 4*A*b^3*x^3*e^3*sgn(b*x + a) - 18*B*a*b^2*d*x^2*e^2*sgn(b*x + a) + 18*A*b^3*d*x^2*e^2*sgn(b*x + a) - 36*B*a*b^2*d^2*x*e*sgn(b*x + a) + 36*A*b^3*d^2*x*e*sgn(b*x + a) + 6*B*a^2*b*x^2*e^3*sgn(b*x + a) - 6*A*a*b^2*x^2*e^3*sgn(b*x + a) + 36*B*a^2*b*d*x*e^2*sgn(b*x + a) - 36*A*a*b^2*d*x*e^2*sgn(b*x + a) - 12*B*a^3*x*e^3*sgn(b*x + a) + 12*A*a^2*b*x*e^3*sgn(b*x + a))/b^4 - (B*a*b^3*d^3*sgn(b*x + a) - A*b^4*d^3*sgn(b*x + a) - 3*B*a^2*b^2*d^2*e*sgn(b*x + a) + 3*A*a*b^3*d^2*e*sgn(b*x + a) + 3*B*a^3*b*d*e^2*sgn(b*x + a) - 3*A*a^2*b^2*d*e^2*sgn(b*x + a) - B*a^4*e^3*sgn(b*x + a) + A*a^3*b*e^3*sgn(b*x + a))*log(abs(b*x + a))/b^5","B",0
1760,1,254,0,0.219580," ","integrate((B*x+A)*(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, B b^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, B b^{2} d x^{2} e \mathrm{sgn}\left(b x + a\right) + 6 \, B b^{2} d^{2} x \mathrm{sgn}\left(b x + a\right) - 3 \, B a b x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A b^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 12 \, B a b d x e \mathrm{sgn}\left(b x + a\right) + 12 \, A b^{2} d x e \mathrm{sgn}\left(b x + a\right) + 6 \, B a^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, A a b x e^{2} \mathrm{sgn}\left(b x + a\right)}{6 \, b^{3}} - \frac{{\left(B a b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, B a^{2} b d e \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{2} d e \mathrm{sgn}\left(b x + a\right) + B a^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - A a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}}"," ",0,"1/6*(2*B*b^2*x^3*e^2*sgn(b*x + a) + 6*B*b^2*d*x^2*e*sgn(b*x + a) + 6*B*b^2*d^2*x*sgn(b*x + a) - 3*B*a*b*x^2*e^2*sgn(b*x + a) + 3*A*b^2*x^2*e^2*sgn(b*x + a) - 12*B*a*b*d*x*e*sgn(b*x + a) + 12*A*b^2*d*x*e*sgn(b*x + a) + 6*B*a^2*x*e^2*sgn(b*x + a) - 6*A*a*b*x*e^2*sgn(b*x + a))/b^3 - (B*a*b^2*d^2*sgn(b*x + a) - A*b^3*d^2*sgn(b*x + a) - 2*B*a^2*b*d*e*sgn(b*x + a) + 2*A*a*b^2*d*e*sgn(b*x + a) + B*a^3*e^2*sgn(b*x + a) - A*a^2*b*e^2*sgn(b*x + a))*log(abs(b*x + a))/b^4","A",0
1761,1,122,0,0.167374," ","integrate((B*x+A)*(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{B b x^{2} e \mathrm{sgn}\left(b x + a\right) + 2 \, B b d x \mathrm{sgn}\left(b x + a\right) - 2 \, B a x e \mathrm{sgn}\left(b x + a\right) + 2 \, A b x e \mathrm{sgn}\left(b x + a\right)}{2 \, b^{2}} - \frac{{\left(B a b d \mathrm{sgn}\left(b x + a\right) - A b^{2} d \mathrm{sgn}\left(b x + a\right) - B a^{2} e \mathrm{sgn}\left(b x + a\right) + A a b e \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}}"," ",0,"1/2*(B*b*x^2*e*sgn(b*x + a) + 2*B*b*d*x*sgn(b*x + a) - 2*B*a*x*e*sgn(b*x + a) + 2*A*b*x*e*sgn(b*x + a))/b^2 - (B*a*b*d*sgn(b*x + a) - A*b^2*d*sgn(b*x + a) - B*a^2*e*sgn(b*x + a) + A*a*b*e*sgn(b*x + a))*log(abs(b*x + a))/b^3","A",0
1762,1,45,0,0.154212," ","integrate((B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{B x \mathrm{sgn}\left(b x + a\right)}{b} - \frac{{\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{2}}"," ",0,"B*x*sgn(b*x + a)/b - (B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*log(abs(b*x + a))/b^2","A",0
1763,1,87,0,0.166596," ","integrate((B*x+A)/(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{2} d - a b e} + \frac{{\left(B d \mathrm{sgn}\left(b x + a\right) - A e \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x e + d \right|}\right)}{b d e - a e^{2}}"," ",0,"-(B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*log(abs(b*x + a))/(b^2*d - a*b*e) + (B*d*sgn(b*x + a) - A*e*sgn(b*x + a))*log(abs(x*e + d))/(b*d*e - a*e^2)","A",0
1764,1,190,0,0.173548," ","integrate((B*x+A)/(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(B a b \mathrm{sgn}\left(b x + a\right) - A b^{2} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}} + \frac{{\left(B a e \mathrm{sgn}\left(b x + a\right) - A b e \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x e + d \right|}\right)}{b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}} - \frac{{\left(B b d^{2} \mathrm{sgn}\left(b x + a\right) - B a d e \mathrm{sgn}\left(b x + a\right) - A b d e \mathrm{sgn}\left(b x + a\right) + A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}}{{\left(b d - a e\right)}^{2} {\left(x e + d\right)}}"," ",0,"-(B*a*b*sgn(b*x + a) - A*b^2*sgn(b*x + a))*log(abs(b*x + a))/(b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2) + (B*a*e*sgn(b*x + a) - A*b*e*sgn(b*x + a))*log(abs(x*e + d))/(b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3) - (B*b*d^2*sgn(b*x + a) - B*a*d*e*sgn(b*x + a) - A*b*d*e*sgn(b*x + a) + A*a*e^2*sgn(b*x + a))*e^(-1)/((b*d - a*e)^2*(x*e + d))","A",0
1765,1,306,0,0.183423," ","integrate((B*x+A)/(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(B a b^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}} + \frac{{\left(B a b e \mathrm{sgn}\left(b x + a\right) - A b^{2} e \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x e + d \right|}\right)}{b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}} - \frac{{\left(B b^{2} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - B a^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, A a b d e^{2} \mathrm{sgn}\left(b x + a\right) - A a^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(B a b d e^{2} \mathrm{sgn}\left(b x + a\right) - A b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + A a b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-1\right)}}{2 \, {\left(b d - a e\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"-(B*a*b^2*sgn(b*x + a) - A*b^3*sgn(b*x + a))*log(abs(b*x + a))/(b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3) + (B*a*b*e*sgn(b*x + a) - A*b^2*e*sgn(b*x + a))*log(abs(x*e + d))/(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4) - 1/2*(B*b^2*d^3*sgn(b*x + a) - 3*A*b^2*d^2*e*sgn(b*x + a) - B*a^2*d*e^2*sgn(b*x + a) + 4*A*a*b*d*e^2*sgn(b*x + a) - A*a^2*e^3*sgn(b*x + a) + 2*(B*a*b*d*e^2*sgn(b*x + a) - A*b^2*d*e^2*sgn(b*x + a) - B*a^2*e^3*sgn(b*x + a) + A*a*b*e^3*sgn(b*x + a))*x)*e^(-1)/((b*d - a*e)^3*(x*e + d)^2)","A",0
1766,1,494,0,0.230547," ","integrate((B*x+A)/(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(B a b^{3} \mathrm{sgn}\left(b x + a\right) - A b^{4} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}} + \frac{{\left(B a b^{2} e \mathrm{sgn}\left(b x + a\right) - A b^{3} e \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| x e + d \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} - \frac{{\left(2 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - 11 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) - 6 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 9 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(B a b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - A b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - B a^{2} b e^{4} \mathrm{sgn}\left(b x + a\right) + A a b^{2} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 3 \, {\left(5 \, B a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, A b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, B a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + B a^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - A a^{2} b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-1\right)}}{6 \, {\left(b d - a e\right)}^{4} {\left(x e + d\right)}^{3}}"," ",0,"-(B*a*b^3*sgn(b*x + a) - A*b^4*sgn(b*x + a))*log(abs(b*x + a))/(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4) + (B*a*b^2*e*sgn(b*x + a) - A*b^3*e*sgn(b*x + a))*log(abs(x*e + d))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) - 1/6*(2*B*b^3*d^4*sgn(b*x + a) + 3*B*a*b^2*d^3*e*sgn(b*x + a) - 11*A*b^3*d^3*e*sgn(b*x + a) - 6*B*a^2*b*d^2*e^2*sgn(b*x + a) + 18*A*a*b^2*d^2*e^2*sgn(b*x + a) + B*a^3*d*e^3*sgn(b*x + a) - 9*A*a^2*b*d*e^3*sgn(b*x + a) + 2*A*a^3*e^4*sgn(b*x + a) + 6*(B*a*b^2*d*e^3*sgn(b*x + a) - A*b^3*d*e^3*sgn(b*x + a) - B*a^2*b*e^4*sgn(b*x + a) + A*a*b^2*e^4*sgn(b*x + a))*x^2 + 3*(5*B*a*b^2*d^2*e^2*sgn(b*x + a) - 5*A*b^3*d^2*e^2*sgn(b*x + a) - 6*B*a^2*b*d*e^3*sgn(b*x + a) + 6*A*a*b^2*d*e^3*sgn(b*x + a) + B*a^3*e^4*sgn(b*x + a) - A*a^2*b*e^4*sgn(b*x + a))*x)*e^(-1)/((b*d - a*e)^4*(x*e + d)^3)","B",0
1767,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1768,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1769,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1770,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1771,0,0,0,0.000000," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1772,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1773,1,708,0,0.530783," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(2 \, B b d e^{2} + B a e^{3} - 3 \, A b e^{3}\right)} \log\left({\left| -b + \frac{b d}{x e + d} - \frac{a e}{x e + d} \right|}\right)}{b^{4} d^{4} e \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + a^{4} e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} + \frac{\frac{B d e^{4}}{x e + d} - \frac{A e^{5}}{x e + d}}{b^{3} d^{3} e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 3 \, a b^{2} d^{2} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 3 \, a^{2} b d e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - a^{3} e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} + \frac{2 \, B b^{3} d e + 3 \, B a b^{2} e^{2} - 5 \, A b^{3} e^{2} - \frac{2 \, {\left(B b^{3} d^{2} e^{2} + B a b^{2} d e^{3} - 3 \, A b^{3} d e^{3} - 2 \, B a^{2} b e^{4} + 3 \, A a b^{2} e^{4}\right)} e^{\left(-1\right)}}{x e + d}}{2 \, {\left(b d - a e\right)}^{4} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}"," ",0,"(2*B*b*d*e^2 + B*a*e^3 - 3*A*b*e^3)*log(abs(-b + b*d/(x*e + d) - a*e/(x*e + d)))/(b^4*d^4*e*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 4*a*b^3*d^3*e^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 6*a^2*b^2*d^2*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 4*a^3*b*d*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + a^4*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) + (B*d*e^4/(x*e + d) - A*e^5/(x*e + d))/(b^3*d^3*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 3*a*b^2*d^2*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 3*a^2*b*d*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - a^3*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) + 1/2*(2*B*b^3*d*e + 3*B*a*b^2*e^2 - 5*A*b^3*e^2 - 2*(B*b^3*d^2*e^2 + B*a*b^2*d*e^3 - 3*A*b^3*d*e^3 - 2*B*a^2*b*e^4 + 3*A*a*b^2*e^4)*e^(-1)/(x*e + d))/((b*d - a*e)^4*(b - b*d/(x*e + d) + a*e/(x*e + d))^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))","B",0
1774,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1775,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1776,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1777,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1778,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1779,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1780,0,0,0,0.000000," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1781,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1782,1,1136,0,0.596238," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(4 \, B b d e^{4} + B a e^{5} - 5 \, A b e^{5}\right)} \log\left({\left| -b + \frac{b d}{x e + d} - \frac{a e}{x e + d} \right|}\right)}{b^{6} d^{6} e \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 6 \, a b^{5} d^{5} e^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 15 \, a^{2} b^{4} d^{4} e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 20 \, a^{3} b^{3} d^{3} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 15 \, a^{4} b^{2} d^{2} e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 6 \, a^{5} b d e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + a^{6} e^{7} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} + \frac{\frac{B d e^{8}}{x e + d} - \frac{A e^{9}}{x e + d}}{b^{5} d^{5} e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 5 \, a b^{4} d^{4} e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 10 \, a^{2} b^{3} d^{3} e^{7} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 10 \, a^{3} b^{2} d^{2} e^{8} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 5 \, a^{4} b d e^{9} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - a^{5} e^{10} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} + \frac{52 \, B b^{5} d e^{3} + 25 \, B a b^{4} e^{4} - 77 \, A b^{5} e^{4} - \frac{4 \, {\left(43 \, B b^{5} d^{2} e^{4} - 21 \, B a b^{4} d e^{5} - 65 \, A b^{5} d e^{5} - 22 \, B a^{2} b^{3} e^{6} + 65 \, A a b^{4} e^{6}\right)} e^{\left(-1\right)}}{x e + d} + \frac{12 \, {\left(16 \, B b^{5} d^{3} e^{5} - 23 \, B a b^{4} d^{2} e^{6} - 25 \, A b^{5} d^{2} e^{6} - 2 \, B a^{2} b^{3} d e^{7} + 50 \, A a b^{4} d e^{7} + 9 \, B a^{3} b^{2} e^{8} - 25 \, A a^{2} b^{3} e^{8}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{24 \, {\left(3 \, B b^{5} d^{4} e^{6} - 7 \, B a b^{4} d^{3} e^{7} - 5 \, A b^{5} d^{3} e^{7} + 3 \, B a^{2} b^{3} d^{2} e^{8} + 15 \, A a b^{4} d^{2} e^{8} + 3 \, B a^{3} b^{2} d e^{9} - 15 \, A a^{2} b^{3} d e^{9} - 2 \, B a^{4} b e^{10} + 5 \, A a^{3} b^{2} e^{10}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{12 \, {\left(b d - a e\right)}^{6} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}"," ",0,"(4*B*b*d*e^4 + B*a*e^5 - 5*A*b*e^5)*log(abs(-b + b*d/(x*e + d) - a*e/(x*e + d)))/(b^6*d^6*e*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 6*a*b^5*d^5*e^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 15*a^2*b^4*d^4*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 20*a^3*b^3*d^3*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 15*a^4*b^2*d^2*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 6*a^5*b*d*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + a^6*e^7*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) + (B*d*e^8/(x*e + d) - A*e^9/(x*e + d))/(b^5*d^5*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 5*a*b^4*d^4*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 10*a^2*b^3*d^3*e^7*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 10*a^3*b^2*d^2*e^8*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 5*a^4*b*d*e^9*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - a^5*e^10*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) + 1/12*(52*B*b^5*d*e^3 + 25*B*a*b^4*e^4 - 77*A*b^5*e^4 - 4*(43*B*b^5*d^2*e^4 - 21*B*a*b^4*d*e^5 - 65*A*b^5*d*e^5 - 22*B*a^2*b^3*e^6 + 65*A*a*b^4*e^6)*e^(-1)/(x*e + d) + 12*(16*B*b^5*d^3*e^5 - 23*B*a*b^4*d^2*e^6 - 25*A*b^5*d^2*e^6 - 2*B*a^2*b^3*d*e^7 + 50*A*a*b^4*d*e^7 + 9*B*a^3*b^2*e^8 - 25*A*a^2*b^3*e^8)*e^(-2)/(x*e + d)^2 - 24*(3*B*b^5*d^4*e^6 - 7*B*a*b^4*d^3*e^7 - 5*A*b^5*d^3*e^7 + 3*B*a^2*b^3*d^2*e^8 + 15*A*a*b^4*d^2*e^8 + 3*B*a^3*b^2*d*e^9 - 15*A*a^2*b^3*d*e^9 - 2*B*a^4*b*e^10 + 5*A*a^3*b^2*e^10)*e^(-3)/(x*e + d)^3)/((b*d - a*e)^6*(b - b*d/(x*e + d) + a*e/(x*e + d))^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))","B",0
1783,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1784,1,1913,0,0.293141," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{2} d^{4} e^{\left(-1\right)} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a b d^{4} e^{\left(-1\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a b d^{4} e^{\left(-2\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d^{4} e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d^{4} e^{\left(-3\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} d^{3} e^{\left(-1\right)} + 24024 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b d^{3} e^{\left(-1\right)} + 10296 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b d^{3} e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} d^{3} e^{\left(-2\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} d^{3} e^{\left(-3\right)} + 45045 \, \sqrt{x e + d} A a^{2} d^{4} + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} d^{3} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} d^{2} e^{\left(-1\right)} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b d^{2} e^{\left(-1\right)} + 1716 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b d^{2} e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{2} d^{2} e^{\left(-2\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{2} d^{2} e^{\left(-3\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} d^{2} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} d e^{\left(-1\right)} + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b d e^{\left(-1\right)} + 520 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b d e^{\left(-2\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{2} d e^{\left(-2\right)} + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{2} d e^{\left(-3\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} d + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} e^{\left(-1\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b e^{\left(-1\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b e^{\left(-2\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{2} e^{\left(-2\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{2} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^2*d^4*e^(-1) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*b*d^4*e^(-1) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*b*d^4*e^(-2) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d^4*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d^4*e^(-3) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*d^3*e^(-1) + 24024*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b*d^3*e^(-1) + 10296*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b*d^3*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*d^3*e^(-2) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*d^3*e^(-3) + 45045*sqrt(x*e + d)*A*a^2*d^4 + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*d^3 + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*d^2*e^(-1) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b*d^2*e^(-1) + 1716*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b*d^2*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^2*d^2*e^(-2) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^2*d^2*e^(-3) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*d^2 + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*d*e^(-1) + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b*d*e^(-1) + 520*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b*d*e^(-2) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^2*d*e^(-2) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^2*d*e^(-3) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*d + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*e^(-1) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b*e^(-1) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b*e^(-2) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^2*e^(-2) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^2*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2)*e^(-1)","B",0
1785,1,1368,0,0.258036," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{2} d^{3} e^{\left(-1\right)} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a b d^{3} e^{\left(-1\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a b d^{3} e^{\left(-2\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d^{3} e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d^{3} e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} d^{2} e^{\left(-1\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b d^{2} e^{\left(-1\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b d^{2} e^{\left(-2\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} d^{2} e^{\left(-2\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} d^{2} e^{\left(-3\right)} + 45045 \, \sqrt{x e + d} A a^{2} d^{3} + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} d^{2} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} d e^{\left(-1\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b d e^{\left(-1\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b d e^{\left(-2\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{2} d e^{\left(-2\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{2} d e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} d + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} e^{\left(-1\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b e^{\left(-1\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b e^{\left(-2\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{2} e^{\left(-2\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{2} e^{\left(-3\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^2*d^3*e^(-1) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*b*d^3*e^(-1) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*b*d^3*e^(-2) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d^3*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d^3*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*d^2*e^(-1) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b*d^2*e^(-1) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b*d^2*e^(-2) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*d^2*e^(-2) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*d^2*e^(-3) + 45045*sqrt(x*e + d)*A*a^2*d^3 + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*d^2 + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*d*e^(-1) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b*d*e^(-1) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b*d*e^(-2) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^2*d*e^(-2) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^2*d*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*d + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*e^(-1) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b*e^(-1) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b*e^(-2) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^2*e^(-2) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^2*e^(-3) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2)*e^(-1)","B",0
1786,1,901,0,0.232825," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{2} d^{2} e^{\left(-1\right)} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a b d^{2} e^{\left(-1\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a b d^{2} e^{\left(-2\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d^{2} e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d^{2} e^{\left(-3\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} d e^{\left(-1\right)} + 924 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b d e^{\left(-1\right)} + 396 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b d e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} d e^{\left(-2\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} d e^{\left(-3\right)} + 3465 \, \sqrt{x e + d} A a^{2} d^{2} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} d + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} e^{\left(-1\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b e^{\left(-1\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b e^{\left(-2\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{2} e^{\left(-2\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{2} e^{\left(-3\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^2*d^2*e^(-1) + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*b*d^2*e^(-1) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*b*d^2*e^(-2) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d^2*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d^2*e^(-3) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*d*e^(-1) + 924*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b*d*e^(-1) + 396*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b*d*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*d*e^(-2) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*d*e^(-3) + 3465*sqrt(x*e + d)*A*a^2*d^2 + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*d + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*e^(-1) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b*e^(-1) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b*e^(-2) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^2*e^(-2) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^2*e^(-3) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2)*e^(-1)","B",0
1787,1,511,0,0.184009," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{2} d e^{\left(-1\right)} + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a b d e^{\left(-1\right)} + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a b d e^{\left(-2\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} d e^{\left(-2\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} d e^{\left(-3\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} e^{\left(-1\right)} + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b e^{\left(-1\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b e^{\left(-2\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{2} e^{\left(-2\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{2} e^{\left(-3\right)} + 315 \, \sqrt{x e + d} A a^{2} d + 105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^2*d*e^(-1) + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*b*d*e^(-1) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*b*d*e^(-2) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*d*e^(-2) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*d*e^(-3) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*e^(-1) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b*e^(-1) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b*e^(-2) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^2*e^(-2) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^2*e^(-3) + 315*sqrt(x*e + d)*A*a^2*d + 105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2)*e^(-1)","B",0
1788,1,215,0,0.169621," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{2} e^{\left(-1\right)} + 70 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a b e^{\left(-1\right)} + 14 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a b e^{\left(-2\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b^{2} e^{\left(-2\right)} + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b^{2} e^{\left(-3\right)} + 105 \, \sqrt{x e + d} A a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^2*e^(-1) + 70*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*b*e^(-1) + 14*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*b*e^(-2) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b^2*e^(-2) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b^2*e^(-3) + 105*sqrt(x*e + d)*A*a^2)*e^(-1)","A",0
1789,1,219,0,0.205259," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{2} e^{16} - 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} d e^{16} + 45 \, \sqrt{x e + d} B b^{2} d^{2} e^{16} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b e^{17} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} e^{17} - 60 \, \sqrt{x e + d} B a b d e^{17} - 30 \, \sqrt{x e + d} A b^{2} d e^{17} + 15 \, \sqrt{x e + d} B a^{2} e^{18} + 30 \, \sqrt{x e + d} A a b e^{18}\right)} e^{\left(-20\right)} + \frac{2 \, {\left(B b^{2} d^{3} - 2 \, B a b d^{2} e - A b^{2} d^{2} e + B a^{2} d e^{2} + 2 \, A a b d e^{2} - A a^{2} e^{3}\right)} e^{\left(-4\right)}}{\sqrt{x e + d}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*b^2*e^16 - 15*(x*e + d)^(3/2)*B*b^2*d*e^16 + 45*sqrt(x*e + d)*B*b^2*d^2*e^16 + 10*(x*e + d)^(3/2)*B*a*b*e^17 + 5*(x*e + d)^(3/2)*A*b^2*e^17 - 60*sqrt(x*e + d)*B*a*b*d*e^17 - 30*sqrt(x*e + d)*A*b^2*d*e^17 + 15*sqrt(x*e + d)*B*a^2*e^18 + 30*sqrt(x*e + d)*A*a*b*e^18)*e^(-20) + 2*(B*b^2*d^3 - 2*B*a*b*d^2*e - A*b^2*d^2*e + B*a^2*d*e^2 + 2*A*a*b*d*e^2 - A*a^2*e^3)*e^(-4)/sqrt(x*e + d)","A",0
1790,1,206,0,0.210505," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{2} e^{8} - 9 \, \sqrt{x e + d} B b^{2} d e^{8} + 6 \, \sqrt{x e + d} B a b e^{9} + 3 \, \sqrt{x e + d} A b^{2} e^{9}\right)} e^{\left(-12\right)} - \frac{2 \, {\left(9 \, {\left(x e + d\right)} B b^{2} d^{2} - B b^{2} d^{3} - 12 \, {\left(x e + d\right)} B a b d e - 6 \, {\left(x e + d\right)} A b^{2} d e + 2 \, B a b d^{2} e + A b^{2} d^{2} e + 3 \, {\left(x e + d\right)} B a^{2} e^{2} + 6 \, {\left(x e + d\right)} A a b e^{2} - B a^{2} d e^{2} - 2 \, A a b d e^{2} + A a^{2} e^{3}\right)} e^{\left(-4\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*B*b^2*e^8 - 9*sqrt(x*e + d)*B*b^2*d*e^8 + 6*sqrt(x*e + d)*B*a*b*e^9 + 3*sqrt(x*e + d)*A*b^2*e^9)*e^(-12) - 2/3*(9*(x*e + d)*B*b^2*d^2 - B*b^2*d^3 - 12*(x*e + d)*B*a*b*d*e - 6*(x*e + d)*A*b^2*d*e + 2*B*a*b*d^2*e + A*b^2*d^2*e + 3*(x*e + d)*B*a^2*e^2 + 6*(x*e + d)*A*a*b*e^2 - B*a^2*d*e^2 - 2*A*a*b*d*e^2 + A*a^2*e^3)*e^(-4)/(x*e + d)^(3/2)","A",0
1791,1,202,0,0.207530," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(7/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} B b^{2} e^{\left(-4\right)} + \frac{2 \, {\left(45 \, {\left(x e + d\right)}^{2} B b^{2} d - 15 \, {\left(x e + d\right)} B b^{2} d^{2} + 3 \, B b^{2} d^{3} - 30 \, {\left(x e + d\right)}^{2} B a b e - 15 \, {\left(x e + d\right)}^{2} A b^{2} e + 20 \, {\left(x e + d\right)} B a b d e + 10 \, {\left(x e + d\right)} A b^{2} d e - 6 \, B a b d^{2} e - 3 \, A b^{2} d^{2} e - 5 \, {\left(x e + d\right)} B a^{2} e^{2} - 10 \, {\left(x e + d\right)} A a b e^{2} + 3 \, B a^{2} d e^{2} + 6 \, A a b d e^{2} - 3 \, A a^{2} e^{3}\right)} e^{\left(-4\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2*sqrt(x*e + d)*B*b^2*e^(-4) + 2/15*(45*(x*e + d)^2*B*b^2*d - 15*(x*e + d)*B*b^2*d^2 + 3*B*b^2*d^3 - 30*(x*e + d)^2*B*a*b*e - 15*(x*e + d)^2*A*b^2*e + 20*(x*e + d)*B*a*b*d*e + 10*(x*e + d)*A*b^2*d*e - 6*B*a*b*d^2*e - 3*A*b^2*d^2*e - 5*(x*e + d)*B*a^2*e^2 - 10*(x*e + d)*A*a*b*e^2 + 3*B*a^2*d*e^2 + 6*A*a*b*d*e^2 - 3*A*a^2*e^3)*e^(-4)/(x*e + d)^(5/2)","A",0
1792,1,3913,0,0.461344," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{4} d^{4} e^{\left(-1\right)} + 19399380 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} b d^{4} e^{\left(-1\right)} + 3879876 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} b d^{4} e^{\left(-2\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b^{2} d^{4} e^{\left(-2\right)} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b^{2} d^{4} e^{\left(-3\right)} + 1662804 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{3} d^{4} e^{\left(-3\right)} + 184756 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{3} d^{4} e^{\left(-4\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{4} d^{4} e^{\left(-4\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{4} d^{4} e^{\left(-5\right)} + 3879876 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} d^{3} e^{\left(-1\right)} + 15519504 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b d^{3} e^{\left(-1\right)} + 6651216 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b d^{3} e^{\left(-2\right)} + 9976824 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{2} d^{3} e^{\left(-2\right)} + 1108536 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{2} d^{3} e^{\left(-3\right)} + 739024 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{3} d^{3} e^{\left(-3\right)} + 335920 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{3} d^{3} e^{\left(-4\right)} + 83980 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{4} d^{3} e^{\left(-4\right)} + 19380 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{4} d^{3} e^{\left(-5\right)} + 14549535 \, \sqrt{x e + d} A a^{4} d^{4} + 19399380 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} d^{3} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} d^{2} e^{\left(-1\right)} + 9976824 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b d^{2} e^{\left(-1\right)} + 1108536 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b d^{2} e^{\left(-2\right)} + 1662804 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{2} d^{2} e^{\left(-2\right)} + 755820 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{2} d^{2} e^{\left(-3\right)} + 503880 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{3} d^{2} e^{\left(-3\right)} + 116280 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{3} d^{2} e^{\left(-4\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{4} d^{2} e^{\left(-4\right)} + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{4} d^{2} e^{\left(-5\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} d^{2} + 184756 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} d e^{\left(-1\right)} + 739024 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b d e^{\left(-1\right)} + 335920 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b d e^{\left(-2\right)} + 503880 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{2} d e^{\left(-2\right)} + 116280 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{2} d e^{\left(-3\right)} + 77520 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{3} d e^{\left(-3\right)} + 36176 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{3} d e^{\left(-4\right)} + 9044 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{4} d e^{\left(-4\right)} + 532 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{4} d e^{\left(-5\right)} + 1662804 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} d + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{4} e^{\left(-1\right)} + 83980 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{3} b e^{\left(-1\right)} + 19380 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{3} b e^{\left(-2\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{2} b^{2} e^{\left(-2\right)} + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{2} b^{2} e^{\left(-3\right)} + 9044 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a b^{3} e^{\left(-3\right)} + 532 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a b^{3} e^{\left(-4\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A b^{4} e^{\left(-4\right)} + 63 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B b^{4} e^{\left(-5\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^4*d^4*e^(-1) + 19399380*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*b*d^4*e^(-1) + 3879876*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*b*d^4*e^(-2) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b^2*d^4*e^(-2) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b^2*d^4*e^(-3) + 1662804*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^3*d^4*e^(-3) + 184756*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^3*d^4*e^(-4) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^4*d^4*e^(-4) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^4*d^4*e^(-5) + 3879876*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*d^3*e^(-1) + 15519504*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b*d^3*e^(-1) + 6651216*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b*d^3*e^(-2) + 9976824*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^2*d^3*e^(-2) + 1108536*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^2*d^3*e^(-3) + 739024*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^3*d^3*e^(-3) + 335920*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^3*d^3*e^(-4) + 83980*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^4*d^3*e^(-4) + 19380*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^4*d^3*e^(-5) + 14549535*sqrt(x*e + d)*A*a^4*d^4 + 19399380*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*d^3 + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*d^2*e^(-1) + 9976824*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b*d^2*e^(-1) + 1108536*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b*d^2*e^(-2) + 1662804*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^2*d^2*e^(-2) + 755820*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^2*d^2*e^(-3) + 503880*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^3*d^2*e^(-3) + 116280*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^3*d^2*e^(-4) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^4*d^2*e^(-4) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^4*d^2*e^(-5) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*d^2 + 184756*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*d*e^(-1) + 739024*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b*d*e^(-1) + 335920*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b*d*e^(-2) + 503880*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^2*d*e^(-2) + 116280*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^2*d*e^(-3) + 77520*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^3*d*e^(-3) + 36176*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^3*d*e^(-4) + 9044*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^4*d*e^(-4) + 532*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^4*d*e^(-5) + 1662804*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*d + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^4*e^(-1) + 83980*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^3*b*e^(-1) + 19380*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^3*b*e^(-2) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^2*b^2*e^(-2) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^2*b^2*e^(-3) + 9044*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a*b^3*e^(-3) + 532*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a*b^3*e^(-4) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*b^4*e^(-4) + 63*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*b^4*e^(-5) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^4)*e^(-1)","B",0
1793,1,2860,0,0.515710," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(255255 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{4} d^{3} e^{\left(-1\right)} + 1021020 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} b d^{3} e^{\left(-1\right)} + 204204 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} b d^{3} e^{\left(-2\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b^{2} d^{3} e^{\left(-2\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b^{2} d^{3} e^{\left(-3\right)} + 87516 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{3} d^{3} e^{\left(-3\right)} + 9724 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{3} d^{3} e^{\left(-4\right)} + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{4} d^{3} e^{\left(-4\right)} + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{4} d^{3} e^{\left(-5\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} d^{2} e^{\left(-1\right)} + 612612 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b d^{2} e^{\left(-1\right)} + 262548 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b d^{2} e^{\left(-2\right)} + 393822 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{2} d^{2} e^{\left(-2\right)} + 43758 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{2} d^{2} e^{\left(-3\right)} + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{3} d^{2} e^{\left(-3\right)} + 13260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{3} d^{2} e^{\left(-4\right)} + 3315 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{4} d^{2} e^{\left(-4\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{4} d^{2} e^{\left(-5\right)} + 765765 \, \sqrt{x e + d} A a^{4} d^{3} + 765765 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} d^{2} + 65637 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} d e^{\left(-1\right)} + 262548 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b d e^{\left(-1\right)} + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b d e^{\left(-2\right)} + 43758 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{2} d e^{\left(-2\right)} + 19890 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{2} d e^{\left(-3\right)} + 13260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{3} d e^{\left(-3\right)} + 3060 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{3} d e^{\left(-4\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{4} d e^{\left(-4\right)} + 357 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{4} d e^{\left(-5\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} d + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} e^{\left(-1\right)} + 9724 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b e^{\left(-1\right)} + 4420 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b e^{\left(-2\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{2} e^{\left(-2\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{2} e^{\left(-3\right)} + 1020 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{3} e^{\left(-3\right)} + 476 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{3} e^{\left(-4\right)} + 119 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{4} e^{\left(-4\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{4} e^{\left(-5\right)} + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(255255*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^4*d^3*e^(-1) + 1021020*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*b*d^3*e^(-1) + 204204*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*b*d^3*e^(-2) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b^2*d^3*e^(-2) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b^2*d^3*e^(-3) + 87516*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^3*d^3*e^(-3) + 9724*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^3*d^3*e^(-4) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^4*d^3*e^(-4) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^4*d^3*e^(-5) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*d^2*e^(-1) + 612612*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b*d^2*e^(-1) + 262548*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b*d^2*e^(-2) + 393822*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^2*d^2*e^(-2) + 43758*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^2*d^2*e^(-3) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^3*d^2*e^(-3) + 13260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^3*d^2*e^(-4) + 3315*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^4*d^2*e^(-4) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^4*d^2*e^(-5) + 765765*sqrt(x*e + d)*A*a^4*d^3 + 765765*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*d^2 + 65637*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*d*e^(-1) + 262548*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b*d*e^(-1) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b*d*e^(-2) + 43758*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^2*d*e^(-2) + 19890*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^2*d*e^(-3) + 13260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^3*d*e^(-3) + 3060*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^3*d*e^(-4) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^4*d*e^(-4) + 357*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^4*d*e^(-5) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*d + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*e^(-1) + 9724*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b*e^(-1) + 4420*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b*e^(-2) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^2*e^(-2) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^2*e^(-3) + 1020*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^3*e^(-3) + 476*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^3*e^(-4) + 119*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^4*e^(-4) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^4*e^(-5) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4)*e^(-1)","B",0
1794,1,1937,0,0.314959," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{4} d^{2} e^{\left(-1\right)} + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} b d^{2} e^{\left(-1\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} b d^{2} e^{\left(-2\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b^{2} d^{2} e^{\left(-2\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b^{2} d^{2} e^{\left(-3\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{3} d^{2} e^{\left(-3\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{3} d^{2} e^{\left(-4\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{4} d^{2} e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{4} d^{2} e^{\left(-5\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} d e^{\left(-1\right)} + 24024 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b d e^{\left(-1\right)} + 10296 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b d e^{\left(-2\right)} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{2} d e^{\left(-2\right)} + 1716 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{2} d e^{\left(-3\right)} + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{3} d e^{\left(-3\right)} + 520 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{3} d e^{\left(-4\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{4} d e^{\left(-4\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{4} d e^{\left(-5\right)} + 45045 \, \sqrt{x e + d} A a^{4} d^{2} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} d + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} e^{\left(-1\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b e^{\left(-1\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{2} e^{\left(-2\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{2} e^{\left(-3\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{3} e^{\left(-3\right)} + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{3} e^{\left(-4\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{4} e^{\left(-4\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{4} e^{\left(-5\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^4*d^2*e^(-1) + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*b*d^2*e^(-1) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*b*d^2*e^(-2) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b^2*d^2*e^(-2) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b^2*d^2*e^(-3) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^3*d^2*e^(-3) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^3*d^2*e^(-4) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^4*d^2*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^4*d^2*e^(-5) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*d*e^(-1) + 24024*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b*d*e^(-1) + 10296*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b*d*e^(-2) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^2*d*e^(-2) + 1716*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^2*d*e^(-3) + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^3*d*e^(-3) + 520*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^3*d*e^(-4) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^4*d*e^(-4) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^4*d*e^(-5) + 45045*sqrt(x*e + d)*A*a^4*d^2 + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*d + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*e^(-1) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b*e^(-1) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^2*e^(-2) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^2*e^(-3) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^3*e^(-3) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^3*e^(-4) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^4*e^(-4) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^4*e^(-5) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4)*e^(-1)","B",0
1795,1,1144,0,0.234822," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{4} d e^{\left(-1\right)} + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} b d e^{\left(-1\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} b d e^{\left(-2\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b^{2} d e^{\left(-2\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b^{2} d e^{\left(-3\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{3} d e^{\left(-3\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{3} d e^{\left(-4\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{4} d e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{4} d e^{\left(-5\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} e^{\left(-1\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b e^{\left(-1\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b e^{\left(-2\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{2} e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{2} e^{\left(-3\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{3} e^{\left(-3\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{3} e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{4} e^{\left(-4\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{4} e^{\left(-5\right)} + 45045 \, \sqrt{x e + d} A a^{4} d + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^4*d*e^(-1) + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*b*d*e^(-1) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*b*d*e^(-2) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b^2*d*e^(-2) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b^2*d*e^(-3) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^3*d*e^(-3) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^3*d*e^(-4) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^4*d*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^4*d*e^(-5) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*e^(-1) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b*e^(-1) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b*e^(-2) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^2*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^2*e^(-3) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^3*e^(-3) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^3*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^4*e^(-4) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^4*e^(-5) + 45045*sqrt(x*e + d)*A*a^4*d + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4)*e^(-1)","B",0
1796,1,503,0,0.195855," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{4} e^{\left(-1\right)} + 4620 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} b e^{\left(-1\right)} + 924 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} b e^{\left(-2\right)} + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b^{2} e^{\left(-2\right)} + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b^{2} e^{\left(-3\right)} + 396 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{3} e^{\left(-3\right)} + 44 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{3} e^{\left(-4\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{4} e^{\left(-4\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{4} e^{\left(-5\right)} + 3465 \, \sqrt{x e + d} A a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^4*e^(-1) + 4620*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*b*e^(-1) + 924*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*b*e^(-2) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b^2*e^(-2) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b^2*e^(-3) + 396*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^3*e^(-3) + 44*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^3*e^(-4) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^4*e^(-4) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^4*e^(-5) + 3465*sqrt(x*e + d)*A*a^4)*e^(-1)","B",0
1797,1,587,0,0.248494," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{4} e^{48} - 225 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} d e^{48} + 630 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{48} - 1050 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{48} + 1575 \, \sqrt{x e + d} B b^{4} d^{4} e^{48} + 180 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{3} e^{49} + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} e^{49} - 1008 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{49} - 252 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{49} + 2520 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{49} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{49} - 5040 \, \sqrt{x e + d} B a b^{3} d^{3} e^{49} - 1260 \, \sqrt{x e + d} A b^{4} d^{3} e^{49} + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{50} + 252 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{50} - 1890 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{50} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{50} + 5670 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{50} + 3780 \, \sqrt{x e + d} A a b^{3} d^{2} e^{50} + 420 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{51} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{51} - 2520 \, \sqrt{x e + d} B a^{3} b d e^{51} - 3780 \, \sqrt{x e + d} A a^{2} b^{2} d e^{51} + 315 \, \sqrt{x e + d} B a^{4} e^{52} + 1260 \, \sqrt{x e + d} A a^{3} b e^{52}\right)} e^{\left(-54\right)} + \frac{2 \, {\left(B b^{4} d^{5} - 4 \, B a b^{3} d^{4} e - A b^{4} d^{4} e + 6 \, B a^{2} b^{2} d^{3} e^{2} + 4 \, A a b^{3} d^{3} e^{2} - 4 \, B a^{3} b d^{2} e^{3} - 6 \, A a^{2} b^{2} d^{2} e^{3} + B a^{4} d e^{4} + 4 \, A a^{3} b d e^{4} - A a^{4} e^{5}\right)} e^{\left(-6\right)}}{\sqrt{x e + d}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*B*b^4*e^48 - 225*(x*e + d)^(7/2)*B*b^4*d*e^48 + 630*(x*e + d)^(5/2)*B*b^4*d^2*e^48 - 1050*(x*e + d)^(3/2)*B*b^4*d^3*e^48 + 1575*sqrt(x*e + d)*B*b^4*d^4*e^48 + 180*(x*e + d)^(7/2)*B*a*b^3*e^49 + 45*(x*e + d)^(7/2)*A*b^4*e^49 - 1008*(x*e + d)^(5/2)*B*a*b^3*d*e^49 - 252*(x*e + d)^(5/2)*A*b^4*d*e^49 + 2520*(x*e + d)^(3/2)*B*a*b^3*d^2*e^49 + 630*(x*e + d)^(3/2)*A*b^4*d^2*e^49 - 5040*sqrt(x*e + d)*B*a*b^3*d^3*e^49 - 1260*sqrt(x*e + d)*A*b^4*d^3*e^49 + 378*(x*e + d)^(5/2)*B*a^2*b^2*e^50 + 252*(x*e + d)^(5/2)*A*a*b^3*e^50 - 1890*(x*e + d)^(3/2)*B*a^2*b^2*d*e^50 - 1260*(x*e + d)^(3/2)*A*a*b^3*d*e^50 + 5670*sqrt(x*e + d)*B*a^2*b^2*d^2*e^50 + 3780*sqrt(x*e + d)*A*a*b^3*d^2*e^50 + 420*(x*e + d)^(3/2)*B*a^3*b*e^51 + 630*(x*e + d)^(3/2)*A*a^2*b^2*e^51 - 2520*sqrt(x*e + d)*B*a^3*b*d*e^51 - 3780*sqrt(x*e + d)*A*a^2*b^2*d*e^51 + 315*sqrt(x*e + d)*B*a^4*e^52 + 1260*sqrt(x*e + d)*A*a^3*b*e^52)*e^(-54) + 2*(B*b^4*d^5 - 4*B*a*b^3*d^4*e - A*b^4*d^4*e + 6*B*a^2*b^2*d^3*e^2 + 4*A*a*b^3*d^3*e^2 - 4*B*a^3*b*d^2*e^3 - 6*A*a^2*b^2*d^2*e^3 + B*a^4*d*e^4 + 4*A*a^3*b*d*e^4 - A*a^4*e^5)*e^(-6)/sqrt(x*e + d)","B",0
1798,1,567,0,0.241222," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} e^{36} - 105 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d e^{36} + 350 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{2} e^{36} - 1050 \, \sqrt{x e + d} B b^{4} d^{3} e^{36} + 84 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} e^{37} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} e^{37} - 560 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d e^{37} - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d e^{37} + 2520 \, \sqrt{x e + d} B a b^{3} d^{2} e^{37} + 630 \, \sqrt{x e + d} A b^{4} d^{2} e^{37} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} e^{38} + 140 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} e^{38} - 1890 \, \sqrt{x e + d} B a^{2} b^{2} d e^{38} - 1260 \, \sqrt{x e + d} A a b^{3} d e^{38} + 420 \, \sqrt{x e + d} B a^{3} b e^{39} + 630 \, \sqrt{x e + d} A a^{2} b^{2} e^{39}\right)} e^{\left(-42\right)} - \frac{2 \, {\left(15 \, {\left(x e + d\right)} B b^{4} d^{4} - B b^{4} d^{5} - 48 \, {\left(x e + d\right)} B a b^{3} d^{3} e - 12 \, {\left(x e + d\right)} A b^{4} d^{3} e + 4 \, B a b^{3} d^{4} e + A b^{4} d^{4} e + 54 \, {\left(x e + d\right)} B a^{2} b^{2} d^{2} e^{2} + 36 \, {\left(x e + d\right)} A a b^{3} d^{2} e^{2} - 6 \, B a^{2} b^{2} d^{3} e^{2} - 4 \, A a b^{3} d^{3} e^{2} - 24 \, {\left(x e + d\right)} B a^{3} b d e^{3} - 36 \, {\left(x e + d\right)} A a^{2} b^{2} d e^{3} + 4 \, B a^{3} b d^{2} e^{3} + 6 \, A a^{2} b^{2} d^{2} e^{3} + 3 \, {\left(x e + d\right)} B a^{4} e^{4} + 12 \, {\left(x e + d\right)} A a^{3} b e^{4} - B a^{4} d e^{4} - 4 \, A a^{3} b d e^{4} + A a^{4} e^{5}\right)} e^{\left(-6\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/105*(15*(x*e + d)^(7/2)*B*b^4*e^36 - 105*(x*e + d)^(5/2)*B*b^4*d*e^36 + 350*(x*e + d)^(3/2)*B*b^4*d^2*e^36 - 1050*sqrt(x*e + d)*B*b^4*d^3*e^36 + 84*(x*e + d)^(5/2)*B*a*b^3*e^37 + 21*(x*e + d)^(5/2)*A*b^4*e^37 - 560*(x*e + d)^(3/2)*B*a*b^3*d*e^37 - 140*(x*e + d)^(3/2)*A*b^4*d*e^37 + 2520*sqrt(x*e + d)*B*a*b^3*d^2*e^37 + 630*sqrt(x*e + d)*A*b^4*d^2*e^37 + 210*(x*e + d)^(3/2)*B*a^2*b^2*e^38 + 140*(x*e + d)^(3/2)*A*a*b^3*e^38 - 1890*sqrt(x*e + d)*B*a^2*b^2*d*e^38 - 1260*sqrt(x*e + d)*A*a*b^3*d*e^38 + 420*sqrt(x*e + d)*B*a^3*b*e^39 + 630*sqrt(x*e + d)*A*a^2*b^2*e^39)*e^(-42) - 2/3*(15*(x*e + d)*B*b^4*d^4 - B*b^4*d^5 - 48*(x*e + d)*B*a*b^3*d^3*e - 12*(x*e + d)*A*b^4*d^3*e + 4*B*a*b^3*d^4*e + A*b^4*d^4*e + 54*(x*e + d)*B*a^2*b^2*d^2*e^2 + 36*(x*e + d)*A*a*b^3*d^2*e^2 - 6*B*a^2*b^2*d^3*e^2 - 4*A*a*b^3*d^3*e^2 - 24*(x*e + d)*B*a^3*b*d*e^3 - 36*(x*e + d)*A*a^2*b^2*d*e^3 + 4*B*a^3*b*d^2*e^3 + 6*A*a^2*b^2*d^2*e^3 + 3*(x*e + d)*B*a^4*e^4 + 12*(x*e + d)*A*a^3*b*e^4 - B*a^4*d*e^4 - 4*A*a^3*b*d*e^4 + A*a^4*e^5)*e^(-6)/(x*e + d)^(3/2)","B",0
1799,1,567,0,0.250310," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} e^{24} - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d e^{24} + 150 \, \sqrt{x e + d} B b^{4} d^{2} e^{24} + 20 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} e^{25} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} e^{25} - 240 \, \sqrt{x e + d} B a b^{3} d e^{25} - 60 \, \sqrt{x e + d} A b^{4} d e^{25} + 90 \, \sqrt{x e + d} B a^{2} b^{2} e^{26} + 60 \, \sqrt{x e + d} A a b^{3} e^{26}\right)} e^{\left(-30\right)} + \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} B b^{4} d^{3} - 25 \, {\left(x e + d\right)} B b^{4} d^{4} + 3 \, B b^{4} d^{5} - 360 \, {\left(x e + d\right)}^{2} B a b^{3} d^{2} e - 90 \, {\left(x e + d\right)}^{2} A b^{4} d^{2} e + 80 \, {\left(x e + d\right)} B a b^{3} d^{3} e + 20 \, {\left(x e + d\right)} A b^{4} d^{3} e - 12 \, B a b^{3} d^{4} e - 3 \, A b^{4} d^{4} e + 270 \, {\left(x e + d\right)}^{2} B a^{2} b^{2} d e^{2} + 180 \, {\left(x e + d\right)}^{2} A a b^{3} d e^{2} - 90 \, {\left(x e + d\right)} B a^{2} b^{2} d^{2} e^{2} - 60 \, {\left(x e + d\right)} A a b^{3} d^{2} e^{2} + 18 \, B a^{2} b^{2} d^{3} e^{2} + 12 \, A a b^{3} d^{3} e^{2} - 60 \, {\left(x e + d\right)}^{2} B a^{3} b e^{3} - 90 \, {\left(x e + d\right)}^{2} A a^{2} b^{2} e^{3} + 40 \, {\left(x e + d\right)} B a^{3} b d e^{3} + 60 \, {\left(x e + d\right)} A a^{2} b^{2} d e^{3} - 12 \, B a^{3} b d^{2} e^{3} - 18 \, A a^{2} b^{2} d^{2} e^{3} - 5 \, {\left(x e + d\right)} B a^{4} e^{4} - 20 \, {\left(x e + d\right)} A a^{3} b e^{4} + 3 \, B a^{4} d e^{4} + 12 \, A a^{3} b d e^{4} - 3 \, A a^{4} e^{5}\right)} e^{\left(-6\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*b^4*e^24 - 25*(x*e + d)^(3/2)*B*b^4*d*e^24 + 150*sqrt(x*e + d)*B*b^4*d^2*e^24 + 20*(x*e + d)^(3/2)*B*a*b^3*e^25 + 5*(x*e + d)^(3/2)*A*b^4*e^25 - 240*sqrt(x*e + d)*B*a*b^3*d*e^25 - 60*sqrt(x*e + d)*A*b^4*d*e^25 + 90*sqrt(x*e + d)*B*a^2*b^2*e^26 + 60*sqrt(x*e + d)*A*a*b^3*e^26)*e^(-30) + 2/15*(150*(x*e + d)^2*B*b^4*d^3 - 25*(x*e + d)*B*b^4*d^4 + 3*B*b^4*d^5 - 360*(x*e + d)^2*B*a*b^3*d^2*e - 90*(x*e + d)^2*A*b^4*d^2*e + 80*(x*e + d)*B*a*b^3*d^3*e + 20*(x*e + d)*A*b^4*d^3*e - 12*B*a*b^3*d^4*e - 3*A*b^4*d^4*e + 270*(x*e + d)^2*B*a^2*b^2*d*e^2 + 180*(x*e + d)^2*A*a*b^3*d*e^2 - 90*(x*e + d)*B*a^2*b^2*d^2*e^2 - 60*(x*e + d)*A*a*b^3*d^2*e^2 + 18*B*a^2*b^2*d^3*e^2 + 12*A*a*b^3*d^3*e^2 - 60*(x*e + d)^2*B*a^3*b*e^3 - 90*(x*e + d)^2*A*a^2*b^2*e^3 + 40*(x*e + d)*B*a^3*b*d*e^3 + 60*(x*e + d)*A*a^2*b^2*d*e^3 - 12*B*a^3*b*d^2*e^3 - 18*A*a^2*b^2*d^2*e^3 - 5*(x*e + d)*B*a^4*e^4 - 20*(x*e + d)*A*a^3*b*e^4 + 3*B*a^4*d*e^4 + 12*A*a^3*b*d*e^4 - 3*A*a^4*e^5)*e^(-6)/(x*e + d)^(5/2)","B",0
1800,1,6433,0,0.739080," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{334639305} \, {\left(111546435 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{6} d^{4} e^{\left(-1\right)} + 669278610 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} b d^{4} e^{\left(-1\right)} + 133855722 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} b d^{4} e^{\left(-2\right)} + 334639305 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b^{2} d^{4} e^{\left(-2\right)} + 143416845 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b^{2} d^{4} e^{\left(-3\right)} + 191222460 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{3} d^{4} e^{\left(-3\right)} + 21246940 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{3} d^{4} e^{\left(-4\right)} + 15935205 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{4} d^{4} e^{\left(-4\right)} + 7243275 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{4} d^{4} e^{\left(-5\right)} + 2897310 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{5} d^{4} e^{\left(-5\right)} + 668610 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{5} d^{4} e^{\left(-6\right)} + 111435 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{6} d^{4} e^{\left(-6\right)} + 52003 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{6} d^{4} e^{\left(-7\right)} + 89237148 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{6} d^{3} e^{\left(-1\right)} + 535422888 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{5} b d^{3} e^{\left(-1\right)} + 229466952 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{5} b d^{3} e^{\left(-2\right)} + 573667380 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} b^{2} d^{3} e^{\left(-2\right)} + 63740820 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} b^{2} d^{3} e^{\left(-3\right)} + 84987760 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b^{3} d^{3} e^{\left(-3\right)} + 38630800 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b^{3} d^{3} e^{\left(-4\right)} + 28973100 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{4} d^{3} e^{\left(-4\right)} + 6686100 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{4} d^{3} e^{\left(-5\right)} + 2674440 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{5} d^{3} e^{\left(-5\right)} + 1248072 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{5} d^{3} e^{\left(-6\right)} + 208012 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{6} d^{3} e^{\left(-6\right)} + 12236 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{6} d^{3} e^{\left(-7\right)} + 334639305 \, \sqrt{x e + d} A a^{6} d^{4} + 446185740 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{6} d^{3} + 57366738 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{6} d^{2} e^{\left(-1\right)} + 344200428 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{5} b d^{2} e^{\left(-1\right)} + 38244492 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{5} b d^{2} e^{\left(-2\right)} + 95611230 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{4} b^{2} d^{2} e^{\left(-2\right)} + 43459650 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{4} b^{2} d^{2} e^{\left(-3\right)} + 57946200 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{3} b^{3} d^{2} e^{\left(-3\right)} + 13372200 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{3} b^{3} d^{2} e^{\left(-4\right)} + 10029150 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{2} b^{4} d^{2} e^{\left(-4\right)} + 4680270 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{2} b^{4} d^{2} e^{\left(-5\right)} + 1872108 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a b^{5} d^{2} e^{\left(-5\right)} + 110124 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a b^{5} d^{2} e^{\left(-6\right)} + 18354 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A b^{6} d^{2} e^{\left(-6\right)} + 8694 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B b^{6} d^{2} e^{\left(-7\right)} + 133855722 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{6} d^{2} + 4249388 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{6} d e^{\left(-1\right)} + 25496328 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{5} b d e^{\left(-1\right)} + 11589240 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{5} b d e^{\left(-2\right)} + 28973100 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{4} b^{2} d e^{\left(-2\right)} + 6686100 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{4} b^{2} d e^{\left(-3\right)} + 8914800 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{3} b^{3} d e^{\left(-3\right)} + 4160240 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{3} b^{3} d e^{\left(-4\right)} + 3120180 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a^{2} b^{4} d e^{\left(-4\right)} + 183540 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a^{2} b^{4} d e^{\left(-5\right)} + 73416 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A a b^{5} d e^{\left(-5\right)} + 34776 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B a b^{5} d e^{\left(-6\right)} + 5796 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} A b^{6} d e^{\left(-6\right)} + 1380 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} B b^{6} d e^{\left(-7\right)} + 38244492 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{6} d + 482885 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{6} e^{\left(-1\right)} + 2897310 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{5} b e^{\left(-1\right)} + 668610 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{5} b e^{\left(-2\right)} + 1671525 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{4} b^{2} e^{\left(-2\right)} + 780045 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{4} b^{2} e^{\left(-3\right)} + 1040060 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a^{3} b^{3} e^{\left(-3\right)} + 61180 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a^{3} b^{3} e^{\left(-4\right)} + 45885 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A a^{2} b^{4} e^{\left(-4\right)} + 21735 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B a^{2} b^{4} e^{\left(-5\right)} + 8694 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} A a b^{5} e^{\left(-5\right)} + 2070 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} B a b^{5} e^{\left(-6\right)} + 345 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} A b^{6} e^{\left(-6\right)} + 165 \, {\left(88179 \, {\left(x e + d\right)}^{\frac{23}{2}} - 1062347 \, {\left(x e + d\right)}^{\frac{21}{2}} d + 5870865 \, {\left(x e + d\right)}^{\frac{19}{2}} d^{2} - 19684665 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{3} + 44618574 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{4} - 72076158 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{5} + 85180914 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{6} - 74364290 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{7} + 47805615 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{8} - 22309287 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{9} + 7436429 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{10} - 2028117 \, \sqrt{x e + d} d^{11}\right)} B b^{6} e^{\left(-7\right)} + 1062347 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/334639305*(111546435*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^6*d^4*e^(-1) + 669278610*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*b*d^4*e^(-1) + 133855722*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*b*d^4*e^(-2) + 334639305*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b^2*d^4*e^(-2) + 143416845*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b^2*d^4*e^(-3) + 191222460*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^3*d^4*e^(-3) + 21246940*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^3*d^4*e^(-4) + 15935205*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^4*d^4*e^(-4) + 7243275*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^4*d^4*e^(-5) + 2897310*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^5*d^4*e^(-5) + 668610*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^5*d^4*e^(-6) + 111435*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^6*d^4*e^(-6) + 52003*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^6*d^4*e^(-7) + 89237148*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^6*d^3*e^(-1) + 535422888*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^5*b*d^3*e^(-1) + 229466952*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^5*b*d^3*e^(-2) + 573667380*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*b^2*d^3*e^(-2) + 63740820*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b^2*d^3*e^(-3) + 84987760*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b^3*d^3*e^(-3) + 38630800*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^3*d^3*e^(-4) + 28973100*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^4*d^3*e^(-4) + 6686100*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^4*d^3*e^(-5) + 2674440*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^5*d^3*e^(-5) + 1248072*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^5*d^3*e^(-6) + 208012*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^6*d^3*e^(-6) + 12236*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^6*d^3*e^(-7) + 334639305*sqrt(x*e + d)*A*a^6*d^4 + 446185740*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^6*d^3 + 57366738*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^6*d^2*e^(-1) + 344200428*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^5*b*d^2*e^(-1) + 38244492*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^5*b*d^2*e^(-2) + 95611230*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^4*b^2*d^2*e^(-2) + 43459650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^4*b^2*d^2*e^(-3) + 57946200*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^3*b^3*d^2*e^(-3) + 13372200*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^3*b^3*d^2*e^(-4) + 10029150*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^2*b^4*d^2*e^(-4) + 4680270*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^2*b^4*d^2*e^(-5) + 1872108*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a*b^5*d^2*e^(-5) + 110124*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a*b^5*d^2*e^(-6) + 18354*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*b^6*d^2*e^(-6) + 8694*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*b^6*d^2*e^(-7) + 133855722*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^6*d^2 + 4249388*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^6*d*e^(-1) + 25496328*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^5*b*d*e^(-1) + 11589240*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^5*b*d*e^(-2) + 28973100*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^4*b^2*d*e^(-2) + 6686100*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^4*b^2*d*e^(-3) + 8914800*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^3*b^3*d*e^(-3) + 4160240*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^3*b^3*d*e^(-4) + 3120180*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a^2*b^4*d*e^(-4) + 183540*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a^2*b^4*d*e^(-5) + 73416*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*a*b^5*d*e^(-5) + 34776*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*a*b^5*d*e^(-6) + 5796*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*A*b^6*d*e^(-6) + 1380*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*B*b^6*d*e^(-7) + 38244492*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^6*d + 482885*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^6*e^(-1) + 2897310*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^5*b*e^(-1) + 668610*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^5*b*e^(-2) + 1671525*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^4*b^2*e^(-2) + 780045*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^4*b^2*e^(-3) + 1040060*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a^3*b^3*e^(-3) + 61180*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a^3*b^3*e^(-4) + 45885*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*a^2*b^4*e^(-4) + 21735*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*a^2*b^4*e^(-5) + 8694*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*A*a*b^5*e^(-5) + 2070*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*B*a*b^5*e^(-6) + 345*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*A*b^6*e^(-6) + 165*(88179*(x*e + d)^(23/2) - 1062347*(x*e + d)^(21/2)*d + 5870865*(x*e + d)^(19/2)*d^2 - 19684665*(x*e + d)^(17/2)*d^3 + 44618574*(x*e + d)^(15/2)*d^4 - 72076158*(x*e + d)^(13/2)*d^5 + 85180914*(x*e + d)^(11/2)*d^6 - 74364290*(x*e + d)^(9/2)*d^7 + 47805615*(x*e + d)^(7/2)*d^8 - 22309287*(x*e + d)^(5/2)*d^9 + 7436429*(x*e + d)^(3/2)*d^10 - 2028117*sqrt(x*e + d)*d^11)*B*b^6*e^(-7) + 1062347*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^6)*e^(-1)","B",0
1801,1,4768,0,0.505717," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{6} d^{3} e^{\left(-1\right)} + 29099070 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} b d^{3} e^{\left(-1\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} b d^{3} e^{\left(-2\right)} + 14549535 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b^{2} d^{3} e^{\left(-2\right)} + 6235515 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b^{2} d^{3} e^{\left(-3\right)} + 8314020 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{3} d^{3} e^{\left(-3\right)} + 923780 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{3} d^{3} e^{\left(-4\right)} + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{4} d^{3} e^{\left(-4\right)} + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{4} d^{3} e^{\left(-5\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{5} d^{3} e^{\left(-5\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{5} d^{3} e^{\left(-6\right)} + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{6} d^{3} e^{\left(-6\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{6} d^{3} e^{\left(-7\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{6} d^{2} e^{\left(-1\right)} + 17459442 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{5} b d^{2} e^{\left(-1\right)} + 7482618 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{5} b d^{2} e^{\left(-2\right)} + 18706545 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} b^{2} d^{2} e^{\left(-2\right)} + 2078505 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} b^{2} d^{2} e^{\left(-3\right)} + 2771340 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b^{3} d^{2} e^{\left(-3\right)} + 1259700 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b^{3} d^{2} e^{\left(-4\right)} + 944775 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{4} d^{2} e^{\left(-4\right)} + 218025 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{4} d^{2} e^{\left(-5\right)} + 87210 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{5} d^{2} e^{\left(-5\right)} + 40698 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{5} d^{2} e^{\left(-6\right)} + 6783 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{6} d^{2} e^{\left(-6\right)} + 399 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{6} d^{2} e^{\left(-7\right)} + 14549535 \, \sqrt{x e + d} A a^{6} d^{3} + 14549535 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{6} d^{2} + 1247103 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{6} d e^{\left(-1\right)} + 7482618 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{5} b d e^{\left(-1\right)} + 831402 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{5} b d e^{\left(-2\right)} + 2078505 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{4} b^{2} d e^{\left(-2\right)} + 944775 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{4} b^{2} d e^{\left(-3\right)} + 1259700 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{3} b^{3} d e^{\left(-3\right)} + 290700 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{3} b^{3} d e^{\left(-4\right)} + 218025 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{2} b^{4} d e^{\left(-4\right)} + 101745 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{2} b^{4} d e^{\left(-5\right)} + 40698 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a b^{5} d e^{\left(-5\right)} + 2394 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a b^{5} d e^{\left(-6\right)} + 399 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A b^{6} d e^{\left(-6\right)} + 189 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B b^{6} d e^{\left(-7\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{6} d + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{6} e^{\left(-1\right)} + 277134 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{5} b e^{\left(-1\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{5} b e^{\left(-2\right)} + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{4} b^{2} e^{\left(-2\right)} + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{4} b^{2} e^{\left(-3\right)} + 96900 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{3} b^{3} e^{\left(-3\right)} + 45220 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{3} b^{3} e^{\left(-4\right)} + 33915 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a^{2} b^{4} e^{\left(-4\right)} + 1995 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a^{2} b^{4} e^{\left(-5\right)} + 798 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A a b^{5} e^{\left(-5\right)} + 378 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B a b^{5} e^{\left(-6\right)} + 63 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} A b^{6} e^{\left(-6\right)} + 15 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} B b^{6} e^{\left(-7\right)} + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^6*d^3*e^(-1) + 29099070*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*b*d^3*e^(-1) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*b*d^3*e^(-2) + 14549535*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b^2*d^3*e^(-2) + 6235515*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b^2*d^3*e^(-3) + 8314020*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^3*d^3*e^(-3) + 923780*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^3*d^3*e^(-4) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^4*d^3*e^(-4) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^4*d^3*e^(-5) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^5*d^3*e^(-5) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^5*d^3*e^(-6) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^6*d^3*e^(-6) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^6*d^3*e^(-7) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^6*d^2*e^(-1) + 17459442*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^5*b*d^2*e^(-1) + 7482618*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^5*b*d^2*e^(-2) + 18706545*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*b^2*d^2*e^(-2) + 2078505*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b^2*d^2*e^(-3) + 2771340*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b^3*d^2*e^(-3) + 1259700*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^3*d^2*e^(-4) + 944775*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^4*d^2*e^(-4) + 218025*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^4*d^2*e^(-5) + 87210*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^5*d^2*e^(-5) + 40698*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^5*d^2*e^(-6) + 6783*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^6*d^2*e^(-6) + 399*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^6*d^2*e^(-7) + 14549535*sqrt(x*e + d)*A*a^6*d^3 + 14549535*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^6*d^2 + 1247103*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^6*d*e^(-1) + 7482618*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^5*b*d*e^(-1) + 831402*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^5*b*d*e^(-2) + 2078505*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^4*b^2*d*e^(-2) + 944775*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^4*b^2*d*e^(-3) + 1259700*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^3*b^3*d*e^(-3) + 290700*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^3*b^3*d*e^(-4) + 218025*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^2*b^4*d*e^(-4) + 101745*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^2*b^4*d*e^(-5) + 40698*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a*b^5*d*e^(-5) + 2394*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a*b^5*d*e^(-6) + 399*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*b^6*d*e^(-6) + 189*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*b^6*d*e^(-7) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^6*d + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^6*e^(-1) + 277134*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^5*b*e^(-1) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^5*b*e^(-2) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^4*b^2*e^(-2) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^4*b^2*e^(-3) + 96900*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^3*b^3*e^(-3) + 45220*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^3*b^3*e^(-4) + 33915*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a^2*b^4*e^(-4) + 1995*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a^2*b^4*e^(-5) + 798*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*a*b^5*e^(-5) + 378*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*a*b^5*e^(-6) + 63*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*A*b^6*e^(-6) + 15*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*B*b^6*e^(-7) + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^6)*e^(-1)","B",0
1802,1,3285,0,0.407274," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{6} d^{2} e^{\left(-1\right)} + 29099070 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} b d^{2} e^{\left(-1\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} b d^{2} e^{\left(-2\right)} + 14549535 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b^{2} d^{2} e^{\left(-2\right)} + 6235515 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b^{2} d^{2} e^{\left(-3\right)} + 8314020 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{3} d^{2} e^{\left(-3\right)} + 923780 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{3} d^{2} e^{\left(-4\right)} + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{4} d^{2} e^{\left(-4\right)} + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{4} d^{2} e^{\left(-5\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{5} d^{2} e^{\left(-5\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{5} d^{2} e^{\left(-6\right)} + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{6} d^{2} e^{\left(-6\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{6} d^{2} e^{\left(-7\right)} + 1939938 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{6} d e^{\left(-1\right)} + 11639628 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{5} b d e^{\left(-1\right)} + 4988412 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{5} b d e^{\left(-2\right)} + 12471030 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} b^{2} d e^{\left(-2\right)} + 1385670 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} b^{2} d e^{\left(-3\right)} + 1847560 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b^{3} d e^{\left(-3\right)} + 839800 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b^{3} d e^{\left(-4\right)} + 629850 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{4} d e^{\left(-4\right)} + 145350 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{4} d e^{\left(-5\right)} + 58140 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{5} d e^{\left(-5\right)} + 27132 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{5} d e^{\left(-6\right)} + 4522 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{6} d e^{\left(-6\right)} + 266 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{6} d e^{\left(-7\right)} + 14549535 \, \sqrt{x e + d} A a^{6} d^{2} + 9699690 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{6} d + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{6} e^{\left(-1\right)} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{5} b e^{\left(-1\right)} + 277134 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{5} b e^{\left(-2\right)} + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{4} b^{2} e^{\left(-2\right)} + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{4} b^{2} e^{\left(-3\right)} + 419900 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{3} b^{3} e^{\left(-3\right)} + 96900 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{3} b^{3} e^{\left(-4\right)} + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{2} b^{4} e^{\left(-4\right)} + 33915 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{2} b^{4} e^{\left(-5\right)} + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a b^{5} e^{\left(-5\right)} + 798 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a b^{5} e^{\left(-6\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A b^{6} e^{\left(-6\right)} + 63 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B b^{6} e^{\left(-7\right)} + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^6*d^2*e^(-1) + 29099070*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*b*d^2*e^(-1) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*b*d^2*e^(-2) + 14549535*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b^2*d^2*e^(-2) + 6235515*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b^2*d^2*e^(-3) + 8314020*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^3*d^2*e^(-3) + 923780*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^3*d^2*e^(-4) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^4*d^2*e^(-4) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^4*d^2*e^(-5) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^5*d^2*e^(-5) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^5*d^2*e^(-6) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^6*d^2*e^(-6) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^6*d^2*e^(-7) + 1939938*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^6*d*e^(-1) + 11639628*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^5*b*d*e^(-1) + 4988412*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^5*b*d*e^(-2) + 12471030*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*b^2*d*e^(-2) + 1385670*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b^2*d*e^(-3) + 1847560*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b^3*d*e^(-3) + 839800*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^3*d*e^(-4) + 629850*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^4*d*e^(-4) + 145350*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^4*d*e^(-5) + 58140*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^5*d*e^(-5) + 27132*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^5*d*e^(-6) + 4522*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^6*d*e^(-6) + 266*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^6*d*e^(-7) + 14549535*sqrt(x*e + d)*A*a^6*d^2 + 9699690*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^6*d + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^6*e^(-1) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^5*b*e^(-1) + 277134*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^5*b*e^(-2) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^4*b^2*e^(-2) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^4*b^2*e^(-3) + 419900*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^3*b^3*e^(-3) + 96900*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^3*b^3*e^(-4) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^2*b^4*e^(-4) + 33915*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^2*b^4*e^(-5) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a*b^5*e^(-5) + 798*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a*b^5*e^(-6) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*b^6*e^(-6) + 63*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*b^6*e^(-7) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^6)*e^(-1)","B",0
1803,1,1984,0,0.285817," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{765765} \, {\left(255255 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{6} d e^{\left(-1\right)} + 1531530 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} b d e^{\left(-1\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} b d e^{\left(-2\right)} + 765765 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b^{2} d e^{\left(-2\right)} + 328185 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b^{2} d e^{\left(-3\right)} + 437580 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{3} d e^{\left(-3\right)} + 48620 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{3} d e^{\left(-4\right)} + 36465 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{4} d e^{\left(-4\right)} + 16575 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{4} d e^{\left(-5\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{5} d e^{\left(-5\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{5} d e^{\left(-6\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{6} d e^{\left(-6\right)} + 119 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{6} d e^{\left(-7\right)} + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{6} e^{\left(-1\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{5} b e^{\left(-1\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{5} b e^{\left(-2\right)} + 328185 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} b^{2} e^{\left(-2\right)} + 36465 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} b^{2} e^{\left(-3\right)} + 48620 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b^{3} e^{\left(-3\right)} + 22100 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b^{3} e^{\left(-4\right)} + 16575 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{4} e^{\left(-4\right)} + 3825 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{4} e^{\left(-5\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{5} e^{\left(-5\right)} + 714 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{5} e^{\left(-6\right)} + 119 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{6} e^{\left(-6\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{6} e^{\left(-7\right)} + 765765 \, \sqrt{x e + d} A a^{6} d + 255255 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(255255*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^6*d*e^(-1) + 1531530*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*b*d*e^(-1) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*b*d*e^(-2) + 765765*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b^2*d*e^(-2) + 328185*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b^2*d*e^(-3) + 437580*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^3*d*e^(-3) + 48620*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^3*d*e^(-4) + 36465*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^4*d*e^(-4) + 16575*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^4*d*e^(-5) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^5*d*e^(-5) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^5*d*e^(-6) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^6*d*e^(-6) + 119*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^6*d*e^(-7) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^6*e^(-1) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^5*b*e^(-1) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^5*b*e^(-2) + 328185*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*b^2*e^(-2) + 36465*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b^2*e^(-3) + 48620*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b^3*e^(-3) + 22100*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^3*e^(-4) + 16575*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^4*e^(-4) + 3825*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^4*e^(-5) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^5*e^(-5) + 714*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^5*e^(-6) + 119*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^6*e^(-6) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^6*e^(-7) + 765765*sqrt(x*e + d)*A*a^6*d + 255255*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^6)*e^(-1)","B",0
1804,1,895,0,0.243199," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{6} e^{\left(-1\right)} + 90090 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} b e^{\left(-1\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} b e^{\left(-2\right)} + 45045 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b^{2} e^{\left(-2\right)} + 19305 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b^{2} e^{\left(-3\right)} + 25740 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{3} e^{\left(-3\right)} + 2860 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{3} e^{\left(-4\right)} + 2145 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{4} e^{\left(-4\right)} + 975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{4} e^{\left(-5\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{5} e^{\left(-5\right)} + 90 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{5} e^{\left(-6\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{6} e^{\left(-6\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{6} e^{\left(-7\right)} + 45045 \, \sqrt{x e + d} A a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^6*e^(-1) + 90090*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*b*e^(-1) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*b*e^(-2) + 45045*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b^2*e^(-2) + 19305*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b^2*e^(-3) + 25740*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^3*e^(-3) + 2860*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^3*e^(-4) + 2145*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^4*e^(-4) + 975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^4*e^(-5) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^5*e^(-5) + 90*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^5*e^(-6) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^6*e^(-6) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^6*e^(-7) + 45045*sqrt(x*e + d)*A*a^6)*e^(-1)","B",0
1805,1,1131,0,0.322553," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3003} \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} B b^{6} e^{96} - 1911 \, {\left(x e + d\right)}^{\frac{11}{2}} B b^{6} d e^{96} + 7007 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{6} d^{2} e^{96} - 15015 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} d^{3} e^{96} + 21021 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} d^{4} e^{96} - 21021 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d^{5} e^{96} + 21021 \, \sqrt{x e + d} B b^{6} d^{6} e^{96} + 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} B a b^{5} e^{97} + 273 \, {\left(x e + d\right)}^{\frac{11}{2}} A b^{6} e^{97} - 12012 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{5} d e^{97} - 2002 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{6} d e^{97} + 38610 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{5} d^{2} e^{97} + 6435 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{6} d^{2} e^{97} - 72072 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} d^{3} e^{97} - 12012 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} d^{3} e^{97} + 90090 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d^{4} e^{97} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d^{4} e^{97} - 108108 \, \sqrt{x e + d} B a b^{5} d^{5} e^{97} - 18018 \, \sqrt{x e + d} A b^{6} d^{5} e^{97} + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} B a^{2} b^{4} e^{98} + 2002 \, {\left(x e + d\right)}^{\frac{9}{2}} A a b^{5} e^{98} - 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{4} d e^{98} - 12870 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{5} d e^{98} + 90090 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{4} d^{2} e^{98} + 36036 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{5} d^{2} e^{98} - 150150 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} d^{3} e^{98} - 60060 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} d^{3} e^{98} + 225225 \, \sqrt{x e + d} B a^{2} b^{4} d^{4} e^{98} + 90090 \, \sqrt{x e + d} A a b^{5} d^{4} e^{98} + 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{3} b^{3} e^{99} + 6435 \, {\left(x e + d\right)}^{\frac{7}{2}} A a^{2} b^{4} e^{99} - 48048 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{3} d e^{99} - 36036 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{4} d e^{99} + 120120 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{3} d^{2} e^{99} + 90090 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{4} d^{2} e^{99} - 240240 \, \sqrt{x e + d} B a^{3} b^{3} d^{3} e^{99} - 180180 \, \sqrt{x e + d} A a^{2} b^{4} d^{3} e^{99} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{4} b^{2} e^{100} + 12012 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{3} b^{3} e^{100} - 45045 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b^{2} d e^{100} - 60060 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{3} d e^{100} + 135135 \, \sqrt{x e + d} B a^{4} b^{2} d^{2} e^{100} + 180180 \, \sqrt{x e + d} A a^{3} b^{3} d^{2} e^{100} + 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{5} b e^{101} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{4} b^{2} e^{101} - 36036 \, \sqrt{x e + d} B a^{5} b d e^{101} - 90090 \, \sqrt{x e + d} A a^{4} b^{2} d e^{101} + 3003 \, \sqrt{x e + d} B a^{6} e^{102} + 18018 \, \sqrt{x e + d} A a^{5} b e^{102}\right)} e^{\left(-104\right)} + \frac{2 \, {\left(B b^{6} d^{7} - 6 \, B a b^{5} d^{6} e - A b^{6} d^{6} e + 15 \, B a^{2} b^{4} d^{5} e^{2} + 6 \, A a b^{5} d^{5} e^{2} - 20 \, B a^{3} b^{3} d^{4} e^{3} - 15 \, A a^{2} b^{4} d^{4} e^{3} + 15 \, B a^{4} b^{2} d^{3} e^{4} + 20 \, A a^{3} b^{3} d^{3} e^{4} - 6 \, B a^{5} b d^{2} e^{5} - 15 \, A a^{4} b^{2} d^{2} e^{5} + B a^{6} d e^{6} + 6 \, A a^{5} b d e^{6} - A a^{6} e^{7}\right)} e^{\left(-8\right)}}{\sqrt{x e + d}}"," ",0,"2/3003*(231*(x*e + d)^(13/2)*B*b^6*e^96 - 1911*(x*e + d)^(11/2)*B*b^6*d*e^96 + 7007*(x*e + d)^(9/2)*B*b^6*d^2*e^96 - 15015*(x*e + d)^(7/2)*B*b^6*d^3*e^96 + 21021*(x*e + d)^(5/2)*B*b^6*d^4*e^96 - 21021*(x*e + d)^(3/2)*B*b^6*d^5*e^96 + 21021*sqrt(x*e + d)*B*b^6*d^6*e^96 + 1638*(x*e + d)^(11/2)*B*a*b^5*e^97 + 273*(x*e + d)^(11/2)*A*b^6*e^97 - 12012*(x*e + d)^(9/2)*B*a*b^5*d*e^97 - 2002*(x*e + d)^(9/2)*A*b^6*d*e^97 + 38610*(x*e + d)^(7/2)*B*a*b^5*d^2*e^97 + 6435*(x*e + d)^(7/2)*A*b^6*d^2*e^97 - 72072*(x*e + d)^(5/2)*B*a*b^5*d^3*e^97 - 12012*(x*e + d)^(5/2)*A*b^6*d^3*e^97 + 90090*(x*e + d)^(3/2)*B*a*b^5*d^4*e^97 + 15015*(x*e + d)^(3/2)*A*b^6*d^4*e^97 - 108108*sqrt(x*e + d)*B*a*b^5*d^5*e^97 - 18018*sqrt(x*e + d)*A*b^6*d^5*e^97 + 5005*(x*e + d)^(9/2)*B*a^2*b^4*e^98 + 2002*(x*e + d)^(9/2)*A*a*b^5*e^98 - 32175*(x*e + d)^(7/2)*B*a^2*b^4*d*e^98 - 12870*(x*e + d)^(7/2)*A*a*b^5*d*e^98 + 90090*(x*e + d)^(5/2)*B*a^2*b^4*d^2*e^98 + 36036*(x*e + d)^(5/2)*A*a*b^5*d^2*e^98 - 150150*(x*e + d)^(3/2)*B*a^2*b^4*d^3*e^98 - 60060*(x*e + d)^(3/2)*A*a*b^5*d^3*e^98 + 225225*sqrt(x*e + d)*B*a^2*b^4*d^4*e^98 + 90090*sqrt(x*e + d)*A*a*b^5*d^4*e^98 + 8580*(x*e + d)^(7/2)*B*a^3*b^3*e^99 + 6435*(x*e + d)^(7/2)*A*a^2*b^4*e^99 - 48048*(x*e + d)^(5/2)*B*a^3*b^3*d*e^99 - 36036*(x*e + d)^(5/2)*A*a^2*b^4*d*e^99 + 120120*(x*e + d)^(3/2)*B*a^3*b^3*d^2*e^99 + 90090*(x*e + d)^(3/2)*A*a^2*b^4*d^2*e^99 - 240240*sqrt(x*e + d)*B*a^3*b^3*d^3*e^99 - 180180*sqrt(x*e + d)*A*a^2*b^4*d^3*e^99 + 9009*(x*e + d)^(5/2)*B*a^4*b^2*e^100 + 12012*(x*e + d)^(5/2)*A*a^3*b^3*e^100 - 45045*(x*e + d)^(3/2)*B*a^4*b^2*d*e^100 - 60060*(x*e + d)^(3/2)*A*a^3*b^3*d*e^100 + 135135*sqrt(x*e + d)*B*a^4*b^2*d^2*e^100 + 180180*sqrt(x*e + d)*A*a^3*b^3*d^2*e^100 + 6006*(x*e + d)^(3/2)*B*a^5*b*e^101 + 15015*(x*e + d)^(3/2)*A*a^4*b^2*e^101 - 36036*sqrt(x*e + d)*B*a^5*b*d*e^101 - 90090*sqrt(x*e + d)*A*a^4*b^2*d*e^101 + 3003*sqrt(x*e + d)*B*a^6*e^102 + 18018*sqrt(x*e + d)*A*a^5*b*e^102)*e^(-104) + 2*(B*b^6*d^7 - 6*B*a*b^5*d^6*e - A*b^6*d^6*e + 15*B*a^2*b^4*d^5*e^2 + 6*A*a*b^5*d^5*e^2 - 20*B*a^3*b^3*d^4*e^3 - 15*A*a^2*b^4*d^4*e^3 + 15*B*a^4*b^2*d^3*e^4 + 20*A*a^3*b^3*d^3*e^4 - 6*B*a^5*b*d^2*e^5 - 15*A*a^4*b^2*d^2*e^5 + B*a^6*d*e^6 + 6*A*a^5*b*d*e^6 - A*a^6*e^7)*e^(-8)/sqrt(x*e + d)","B",0
1806,1,1103,0,0.308386," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{693} \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} B b^{6} e^{80} - 539 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{6} d e^{80} + 2079 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} d^{2} e^{80} - 4851 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} d^{3} e^{80} + 8085 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d^{4} e^{80} - 14553 \, \sqrt{x e + d} B b^{6} d^{5} e^{80} + 462 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{5} e^{81} + 77 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{6} e^{81} - 3564 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{5} d e^{81} - 594 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{6} d e^{81} + 12474 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} d^{2} e^{81} + 2079 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} d^{2} e^{81} - 27720 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d^{3} e^{81} - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d^{3} e^{81} + 62370 \, \sqrt{x e + d} B a b^{5} d^{4} e^{81} + 10395 \, \sqrt{x e + d} A b^{6} d^{4} e^{81} + 1485 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{4} e^{82} + 594 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{5} e^{82} - 10395 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{4} d e^{82} - 4158 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{5} d e^{82} + 34650 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} d^{2} e^{82} + 13860 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} d^{2} e^{82} - 103950 \, \sqrt{x e + d} B a^{2} b^{4} d^{3} e^{82} - 41580 \, \sqrt{x e + d} A a b^{5} d^{3} e^{82} + 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{3} e^{83} + 2079 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{4} e^{83} - 18480 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{3} d e^{83} - 13860 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{4} d e^{83} + 83160 \, \sqrt{x e + d} B a^{3} b^{3} d^{2} e^{83} + 62370 \, \sqrt{x e + d} A a^{2} b^{4} d^{2} e^{83} + 3465 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b^{2} e^{84} + 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{3} e^{84} - 31185 \, \sqrt{x e + d} B a^{4} b^{2} d e^{84} - 41580 \, \sqrt{x e + d} A a^{3} b^{3} d e^{84} + 4158 \, \sqrt{x e + d} B a^{5} b e^{85} + 10395 \, \sqrt{x e + d} A a^{4} b^{2} e^{85}\right)} e^{\left(-88\right)} - \frac{2 \, {\left(21 \, {\left(x e + d\right)} B b^{6} d^{6} - B b^{6} d^{7} - 108 \, {\left(x e + d\right)} B a b^{5} d^{5} e - 18 \, {\left(x e + d\right)} A b^{6} d^{5} e + 6 \, B a b^{5} d^{6} e + A b^{6} d^{6} e + 225 \, {\left(x e + d\right)} B a^{2} b^{4} d^{4} e^{2} + 90 \, {\left(x e + d\right)} A a b^{5} d^{4} e^{2} - 15 \, B a^{2} b^{4} d^{5} e^{2} - 6 \, A a b^{5} d^{5} e^{2} - 240 \, {\left(x e + d\right)} B a^{3} b^{3} d^{3} e^{3} - 180 \, {\left(x e + d\right)} A a^{2} b^{4} d^{3} e^{3} + 20 \, B a^{3} b^{3} d^{4} e^{3} + 15 \, A a^{2} b^{4} d^{4} e^{3} + 135 \, {\left(x e + d\right)} B a^{4} b^{2} d^{2} e^{4} + 180 \, {\left(x e + d\right)} A a^{3} b^{3} d^{2} e^{4} - 15 \, B a^{4} b^{2} d^{3} e^{4} - 20 \, A a^{3} b^{3} d^{3} e^{4} - 36 \, {\left(x e + d\right)} B a^{5} b d e^{5} - 90 \, {\left(x e + d\right)} A a^{4} b^{2} d e^{5} + 6 \, B a^{5} b d^{2} e^{5} + 15 \, A a^{4} b^{2} d^{2} e^{5} + 3 \, {\left(x e + d\right)} B a^{6} e^{6} + 18 \, {\left(x e + d\right)} A a^{5} b e^{6} - B a^{6} d e^{6} - 6 \, A a^{5} b d e^{6} + A a^{6} e^{7}\right)} e^{\left(-8\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/693*(63*(x*e + d)^(11/2)*B*b^6*e^80 - 539*(x*e + d)^(9/2)*B*b^6*d*e^80 + 2079*(x*e + d)^(7/2)*B*b^6*d^2*e^80 - 4851*(x*e + d)^(5/2)*B*b^6*d^3*e^80 + 8085*(x*e + d)^(3/2)*B*b^6*d^4*e^80 - 14553*sqrt(x*e + d)*B*b^6*d^5*e^80 + 462*(x*e + d)^(9/2)*B*a*b^5*e^81 + 77*(x*e + d)^(9/2)*A*b^6*e^81 - 3564*(x*e + d)^(7/2)*B*a*b^5*d*e^81 - 594*(x*e + d)^(7/2)*A*b^6*d*e^81 + 12474*(x*e + d)^(5/2)*B*a*b^5*d^2*e^81 + 2079*(x*e + d)^(5/2)*A*b^6*d^2*e^81 - 27720*(x*e + d)^(3/2)*B*a*b^5*d^3*e^81 - 4620*(x*e + d)^(3/2)*A*b^6*d^3*e^81 + 62370*sqrt(x*e + d)*B*a*b^5*d^4*e^81 + 10395*sqrt(x*e + d)*A*b^6*d^4*e^81 + 1485*(x*e + d)^(7/2)*B*a^2*b^4*e^82 + 594*(x*e + d)^(7/2)*A*a*b^5*e^82 - 10395*(x*e + d)^(5/2)*B*a^2*b^4*d*e^82 - 4158*(x*e + d)^(5/2)*A*a*b^5*d*e^82 + 34650*(x*e + d)^(3/2)*B*a^2*b^4*d^2*e^82 + 13860*(x*e + d)^(3/2)*A*a*b^5*d^2*e^82 - 103950*sqrt(x*e + d)*B*a^2*b^4*d^3*e^82 - 41580*sqrt(x*e + d)*A*a*b^5*d^3*e^82 + 2772*(x*e + d)^(5/2)*B*a^3*b^3*e^83 + 2079*(x*e + d)^(5/2)*A*a^2*b^4*e^83 - 18480*(x*e + d)^(3/2)*B*a^3*b^3*d*e^83 - 13860*(x*e + d)^(3/2)*A*a^2*b^4*d*e^83 + 83160*sqrt(x*e + d)*B*a^3*b^3*d^2*e^83 + 62370*sqrt(x*e + d)*A*a^2*b^4*d^2*e^83 + 3465*(x*e + d)^(3/2)*B*a^4*b^2*e^84 + 4620*(x*e + d)^(3/2)*A*a^3*b^3*e^84 - 31185*sqrt(x*e + d)*B*a^4*b^2*d*e^84 - 41580*sqrt(x*e + d)*A*a^3*b^3*d*e^84 + 4158*sqrt(x*e + d)*B*a^5*b*e^85 + 10395*sqrt(x*e + d)*A*a^4*b^2*e^85)*e^(-88) - 2/3*(21*(x*e + d)*B*b^6*d^6 - B*b^6*d^7 - 108*(x*e + d)*B*a*b^5*d^5*e - 18*(x*e + d)*A*b^6*d^5*e + 6*B*a*b^5*d^6*e + A*b^6*d^6*e + 225*(x*e + d)*B*a^2*b^4*d^4*e^2 + 90*(x*e + d)*A*a*b^5*d^4*e^2 - 15*B*a^2*b^4*d^5*e^2 - 6*A*a*b^5*d^5*e^2 - 240*(x*e + d)*B*a^3*b^3*d^3*e^3 - 180*(x*e + d)*A*a^2*b^4*d^3*e^3 + 20*B*a^3*b^3*d^4*e^3 + 15*A*a^2*b^4*d^4*e^3 + 135*(x*e + d)*B*a^4*b^2*d^2*e^4 + 180*(x*e + d)*A*a^3*b^3*d^2*e^4 - 15*B*a^4*b^2*d^3*e^4 - 20*A*a^3*b^3*d^3*e^4 - 36*(x*e + d)*B*a^5*b*d*e^5 - 90*(x*e + d)*A*a^4*b^2*d*e^5 + 6*B*a^5*b*d^2*e^5 + 15*A*a^4*b^2*d^2*e^5 + 3*(x*e + d)*B*a^6*e^6 + 18*(x*e + d)*A*a^5*b*e^6 - B*a^6*d*e^6 - 6*A*a^5*b*d*e^6 + A*a^6*e^7)*e^(-8)/(x*e + d)^(3/2)","B",0
1807,1,1103,0,0.328493," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{6} e^{64} - 315 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} d e^{64} + 1323 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} d^{2} e^{64} - 3675 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d^{3} e^{64} + 11025 \, \sqrt{x e + d} B b^{6} d^{4} e^{64} + 270 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{5} e^{65} + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{6} e^{65} - 2268 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} d e^{65} - 378 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} d e^{65} + 9450 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d^{2} e^{65} + 1575 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d^{2} e^{65} - 37800 \, \sqrt{x e + d} B a b^{5} d^{3} e^{65} - 6300 \, \sqrt{x e + d} A b^{6} d^{3} e^{65} + 945 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{4} e^{66} + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{5} e^{66} - 7875 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} d e^{66} - 3150 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} d e^{66} + 47250 \, \sqrt{x e + d} B a^{2} b^{4} d^{2} e^{66} + 18900 \, \sqrt{x e + d} A a b^{5} d^{2} e^{66} + 2100 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{3} e^{67} + 1575 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{4} e^{67} - 25200 \, \sqrt{x e + d} B a^{3} b^{3} d e^{67} - 18900 \, \sqrt{x e + d} A a^{2} b^{4} d e^{67} + 4725 \, \sqrt{x e + d} B a^{4} b^{2} e^{68} + 6300 \, \sqrt{x e + d} A a^{3} b^{3} e^{68}\right)} e^{\left(-72\right)} + \frac{2 \, {\left(315 \, {\left(x e + d\right)}^{2} B b^{6} d^{5} - 35 \, {\left(x e + d\right)} B b^{6} d^{6} + 3 \, B b^{6} d^{7} - 1350 \, {\left(x e + d\right)}^{2} B a b^{5} d^{4} e - 225 \, {\left(x e + d\right)}^{2} A b^{6} d^{4} e + 180 \, {\left(x e + d\right)} B a b^{5} d^{5} e + 30 \, {\left(x e + d\right)} A b^{6} d^{5} e - 18 \, B a b^{5} d^{6} e - 3 \, A b^{6} d^{6} e + 2250 \, {\left(x e + d\right)}^{2} B a^{2} b^{4} d^{3} e^{2} + 900 \, {\left(x e + d\right)}^{2} A a b^{5} d^{3} e^{2} - 375 \, {\left(x e + d\right)} B a^{2} b^{4} d^{4} e^{2} - 150 \, {\left(x e + d\right)} A a b^{5} d^{4} e^{2} + 45 \, B a^{2} b^{4} d^{5} e^{2} + 18 \, A a b^{5} d^{5} e^{2} - 1800 \, {\left(x e + d\right)}^{2} B a^{3} b^{3} d^{2} e^{3} - 1350 \, {\left(x e + d\right)}^{2} A a^{2} b^{4} d^{2} e^{3} + 400 \, {\left(x e + d\right)} B a^{3} b^{3} d^{3} e^{3} + 300 \, {\left(x e + d\right)} A a^{2} b^{4} d^{3} e^{3} - 60 \, B a^{3} b^{3} d^{4} e^{3} - 45 \, A a^{2} b^{4} d^{4} e^{3} + 675 \, {\left(x e + d\right)}^{2} B a^{4} b^{2} d e^{4} + 900 \, {\left(x e + d\right)}^{2} A a^{3} b^{3} d e^{4} - 225 \, {\left(x e + d\right)} B a^{4} b^{2} d^{2} e^{4} - 300 \, {\left(x e + d\right)} A a^{3} b^{3} d^{2} e^{4} + 45 \, B a^{4} b^{2} d^{3} e^{4} + 60 \, A a^{3} b^{3} d^{3} e^{4} - 90 \, {\left(x e + d\right)}^{2} B a^{5} b e^{5} - 225 \, {\left(x e + d\right)}^{2} A a^{4} b^{2} e^{5} + 60 \, {\left(x e + d\right)} B a^{5} b d e^{5} + 150 \, {\left(x e + d\right)} A a^{4} b^{2} d e^{5} - 18 \, B a^{5} b d^{2} e^{5} - 45 \, A a^{4} b^{2} d^{2} e^{5} - 5 \, {\left(x e + d\right)} B a^{6} e^{6} - 30 \, {\left(x e + d\right)} A a^{5} b e^{6} + 3 \, B a^{6} d e^{6} + 18 \, A a^{5} b d e^{6} - 3 \, A a^{6} e^{7}\right)} e^{\left(-8\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*B*b^6*e^64 - 315*(x*e + d)^(7/2)*B*b^6*d*e^64 + 1323*(x*e + d)^(5/2)*B*b^6*d^2*e^64 - 3675*(x*e + d)^(3/2)*B*b^6*d^3*e^64 + 11025*sqrt(x*e + d)*B*b^6*d^4*e^64 + 270*(x*e + d)^(7/2)*B*a*b^5*e^65 + 45*(x*e + d)^(7/2)*A*b^6*e^65 - 2268*(x*e + d)^(5/2)*B*a*b^5*d*e^65 - 378*(x*e + d)^(5/2)*A*b^6*d*e^65 + 9450*(x*e + d)^(3/2)*B*a*b^5*d^2*e^65 + 1575*(x*e + d)^(3/2)*A*b^6*d^2*e^65 - 37800*sqrt(x*e + d)*B*a*b^5*d^3*e^65 - 6300*sqrt(x*e + d)*A*b^6*d^3*e^65 + 945*(x*e + d)^(5/2)*B*a^2*b^4*e^66 + 378*(x*e + d)^(5/2)*A*a*b^5*e^66 - 7875*(x*e + d)^(3/2)*B*a^2*b^4*d*e^66 - 3150*(x*e + d)^(3/2)*A*a*b^5*d*e^66 + 47250*sqrt(x*e + d)*B*a^2*b^4*d^2*e^66 + 18900*sqrt(x*e + d)*A*a*b^5*d^2*e^66 + 2100*(x*e + d)^(3/2)*B*a^3*b^3*e^67 + 1575*(x*e + d)^(3/2)*A*a^2*b^4*e^67 - 25200*sqrt(x*e + d)*B*a^3*b^3*d*e^67 - 18900*sqrt(x*e + d)*A*a^2*b^4*d*e^67 + 4725*sqrt(x*e + d)*B*a^4*b^2*e^68 + 6300*sqrt(x*e + d)*A*a^3*b^3*e^68)*e^(-72) + 2/15*(315*(x*e + d)^2*B*b^6*d^5 - 35*(x*e + d)*B*b^6*d^6 + 3*B*b^6*d^7 - 1350*(x*e + d)^2*B*a*b^5*d^4*e - 225*(x*e + d)^2*A*b^6*d^4*e + 180*(x*e + d)*B*a*b^5*d^5*e + 30*(x*e + d)*A*b^6*d^5*e - 18*B*a*b^5*d^6*e - 3*A*b^6*d^6*e + 2250*(x*e + d)^2*B*a^2*b^4*d^3*e^2 + 900*(x*e + d)^2*A*a*b^5*d^3*e^2 - 375*(x*e + d)*B*a^2*b^4*d^4*e^2 - 150*(x*e + d)*A*a*b^5*d^4*e^2 + 45*B*a^2*b^4*d^5*e^2 + 18*A*a*b^5*d^5*e^2 - 1800*(x*e + d)^2*B*a^3*b^3*d^2*e^3 - 1350*(x*e + d)^2*A*a^2*b^4*d^2*e^3 + 400*(x*e + d)*B*a^3*b^3*d^3*e^3 + 300*(x*e + d)*A*a^2*b^4*d^3*e^3 - 60*B*a^3*b^3*d^4*e^3 - 45*A*a^2*b^4*d^4*e^3 + 675*(x*e + d)^2*B*a^4*b^2*d*e^4 + 900*(x*e + d)^2*A*a^3*b^3*d*e^4 - 225*(x*e + d)*B*a^4*b^2*d^2*e^4 - 300*(x*e + d)*A*a^3*b^3*d^2*e^4 + 45*B*a^4*b^2*d^3*e^4 + 60*A*a^3*b^3*d^3*e^4 - 90*(x*e + d)^2*B*a^5*b*e^5 - 225*(x*e + d)^2*A*a^4*b^2*e^5 + 60*(x*e + d)*B*a^5*b*d*e^5 + 150*(x*e + d)*A*a^4*b^2*d*e^5 - 18*B*a^5*b*d^2*e^5 - 45*A*a^4*b^2*d^2*e^5 - 5*(x*e + d)*B*a^6*e^6 - 30*(x*e + d)*A*a^5*b*e^6 + 3*B*a^6*d*e^6 + 18*A*a^5*b*d*e^6 - 3*A*a^6*e^7)*e^(-8)/(x*e + d)^(5/2)","B",0
1808,1,604,0,0.252443," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(2 \, B b^{4} d^{4} - 15 \, B a b^{3} d^{3} e + 7 \, A b^{4} d^{3} e + 33 \, B a^{2} b^{2} d^{2} e^{2} - 21 \, A a b^{3} d^{2} e^{2} - 29 \, B a^{3} b d e^{3} + 21 \, A a^{2} b^{2} d e^{3} + 9 \, B a^{4} e^{4} - 7 \, A a^{3} b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{5}} + \frac{\sqrt{x e + d} B a b^{3} d^{3} e - \sqrt{x e + d} A b^{4} d^{3} e - 3 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{2} + 3 \, \sqrt{x e + d} A a b^{3} d^{2} e^{2} + 3 \, \sqrt{x e + d} B a^{3} b d e^{3} - 3 \, \sqrt{x e + d} A a^{2} b^{2} d e^{3} - \sqrt{x e + d} B a^{4} e^{4} + \sqrt{x e + d} A a^{3} b e^{4}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{5}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{12} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{12} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{12} d^{2} + 105 \, \sqrt{x e + d} B b^{12} d^{3} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{11} e + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{12} e - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{11} d e + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{12} d e - 630 \, \sqrt{x e + d} B a b^{11} d^{2} e + 315 \, \sqrt{x e + d} A b^{12} d^{2} e + 105 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{10} e^{2} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{11} e^{2} + 945 \, \sqrt{x e + d} B a^{2} b^{10} d e^{2} - 630 \, \sqrt{x e + d} A a b^{11} d e^{2} - 420 \, \sqrt{x e + d} B a^{3} b^{9} e^{3} + 315 \, \sqrt{x e + d} A a^{2} b^{10} e^{3}\right)}}{105 \, b^{14}}"," ",0,"(2*B*b^4*d^4 - 15*B*a*b^3*d^3*e + 7*A*b^4*d^3*e + 33*B*a^2*b^2*d^2*e^2 - 21*A*a*b^3*d^2*e^2 - 29*B*a^3*b*d*e^3 + 21*A*a^2*b^2*d*e^3 + 9*B*a^4*e^4 - 7*A*a^3*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5) + (sqrt(x*e + d)*B*a*b^3*d^3*e - sqrt(x*e + d)*A*b^4*d^3*e - 3*sqrt(x*e + d)*B*a^2*b^2*d^2*e^2 + 3*sqrt(x*e + d)*A*a*b^3*d^2*e^2 + 3*sqrt(x*e + d)*B*a^3*b*d*e^3 - 3*sqrt(x*e + d)*A*a^2*b^2*d*e^3 - sqrt(x*e + d)*B*a^4*e^4 + sqrt(x*e + d)*A*a^3*b*e^4)/(((x*e + d)*b - b*d + a*e)*b^5) + 2/105*(15*(x*e + d)^(7/2)*B*b^12 + 21*(x*e + d)^(5/2)*B*b^12*d + 35*(x*e + d)^(3/2)*B*b^12*d^2 + 105*sqrt(x*e + d)*B*b^12*d^3 - 42*(x*e + d)^(5/2)*B*a*b^11*e + 21*(x*e + d)^(5/2)*A*b^12*e - 140*(x*e + d)^(3/2)*B*a*b^11*d*e + 70*(x*e + d)^(3/2)*A*b^12*d*e - 630*sqrt(x*e + d)*B*a*b^11*d^2*e + 315*sqrt(x*e + d)*A*b^12*d^2*e + 105*(x*e + d)^(3/2)*B*a^2*b^10*e^2 - 70*(x*e + d)^(3/2)*A*a*b^11*e^2 + 945*sqrt(x*e + d)*B*a^2*b^10*d*e^2 - 630*sqrt(x*e + d)*A*a*b^11*d*e^2 - 420*sqrt(x*e + d)*B*a^3*b^9*e^3 + 315*sqrt(x*e + d)*A*a^2*b^10*e^3)/b^14","B",0
1809,1,400,0,0.199383," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(2 \, B b^{3} d^{3} - 11 \, B a b^{2} d^{2} e + 5 \, A b^{3} d^{2} e + 16 \, B a^{2} b d e^{2} - 10 \, A a b^{2} d e^{2} - 7 \, B a^{3} e^{3} + 5 \, A a^{2} b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{4}} + \frac{\sqrt{x e + d} B a b^{2} d^{2} e - \sqrt{x e + d} A b^{3} d^{2} e - 2 \, \sqrt{x e + d} B a^{2} b d e^{2} + 2 \, \sqrt{x e + d} A a b^{2} d e^{2} + \sqrt{x e + d} B a^{3} e^{3} - \sqrt{x e + d} A a^{2} b e^{3}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{4}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{8} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{8} d + 15 \, \sqrt{x e + d} B b^{8} d^{2} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{7} e + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{8} e - 60 \, \sqrt{x e + d} B a b^{7} d e + 30 \, \sqrt{x e + d} A b^{8} d e + 45 \, \sqrt{x e + d} B a^{2} b^{6} e^{2} - 30 \, \sqrt{x e + d} A a b^{7} e^{2}\right)}}{15 \, b^{10}}"," ",0,"(2*B*b^3*d^3 - 11*B*a*b^2*d^2*e + 5*A*b^3*d^2*e + 16*B*a^2*b*d*e^2 - 10*A*a*b^2*d*e^2 - 7*B*a^3*e^3 + 5*A*a^2*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) + (sqrt(x*e + d)*B*a*b^2*d^2*e - sqrt(x*e + d)*A*b^3*d^2*e - 2*sqrt(x*e + d)*B*a^2*b*d*e^2 + 2*sqrt(x*e + d)*A*a*b^2*d*e^2 + sqrt(x*e + d)*B*a^3*e^3 - sqrt(x*e + d)*A*a^2*b*e^3)/(((x*e + d)*b - b*d + a*e)*b^4) + 2/15*(3*(x*e + d)^(5/2)*B*b^8 + 5*(x*e + d)^(3/2)*B*b^8*d + 15*sqrt(x*e + d)*B*b^8*d^2 - 10*(x*e + d)^(3/2)*B*a*b^7*e + 5*(x*e + d)^(3/2)*A*b^8*e - 60*sqrt(x*e + d)*B*a*b^7*d*e + 30*sqrt(x*e + d)*A*b^8*d*e + 45*sqrt(x*e + d)*B*a^2*b^6*e^2 - 30*sqrt(x*e + d)*A*a*b^7*e^2)/b^10","B",0
1810,1,239,0,0.189735," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(2 \, B b^{2} d^{2} - 7 \, B a b d e + 3 \, A b^{2} d e + 5 \, B a^{2} e^{2} - 3 \, A a b e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{3}} + \frac{\sqrt{x e + d} B a b d e - \sqrt{x e + d} A b^{2} d e - \sqrt{x e + d} B a^{2} e^{2} + \sqrt{x e + d} A a b e^{2}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{3}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{4} + 3 \, \sqrt{x e + d} B b^{4} d - 6 \, \sqrt{x e + d} B a b^{3} e + 3 \, \sqrt{x e + d} A b^{4} e\right)}}{3 \, b^{6}}"," ",0,"(2*B*b^2*d^2 - 7*B*a*b*d*e + 3*A*b^2*d*e + 5*B*a^2*e^2 - 3*A*a*b*e^2)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^3) + (sqrt(x*e + d)*B*a*b*d*e - sqrt(x*e + d)*A*b^2*d*e - sqrt(x*e + d)*B*a^2*e^2 + sqrt(x*e + d)*A*a*b*e^2)/(((x*e + d)*b - b*d + a*e)*b^3) + 2/3*((x*e + d)^(3/2)*B*b^4 + 3*sqrt(x*e + d)*B*b^4*d - 6*sqrt(x*e + d)*B*a*b^3*e + 3*sqrt(x*e + d)*A*b^4*e)/b^6","A",0
1811,1,126,0,0.221729," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B}{b^{2}} + \frac{{\left(2 \, B b d - 3 \, B a e + A b e\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{2}} + \frac{\sqrt{x e + d} B a e - \sqrt{x e + d} A b e}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{2}}"," ",0,"2*sqrt(x*e + d)*B/b^2 + (2*B*b*d - 3*B*a*e + A*b*e)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^2) + (sqrt(x*e + d)*B*a*e - sqrt(x*e + d)*A*b*e)/(((x*e + d)*b - b*d + a*e)*b^2)","A",0
1812,1,135,0,0.173857," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, B b d - B a e - A b e\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\left(b^{2} d - a b e\right)} \sqrt{-b^{2} d + a b e}} + \frac{\sqrt{x e + d} B a e - \sqrt{x e + d} A b e}{{\left(b^{2} d - a b e\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}}"," ",0,"(2*B*b*d - B*a*e - A*b*e)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^2*d - a*b*e)*sqrt(-b^2*d + a*b*e)) + (sqrt(x*e + d)*B*a*e - sqrt(x*e + d)*A*b*e)/((b^2*d - a*b*e)*((x*e + d)*b - b*d + a*e))","A",0
1813,1,204,0,0.189314," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(2 \, B b d + B a e - 3 \, A b e\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(x e + d\right)} B b d - 2 \, B b d^{2} + {\left(x e + d\right)} B a e - 3 \, {\left(x e + d\right)} A b e + 2 \, B a d e + 2 \, A b d e - 2 \, A a e^{2}}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}}"," ",0,"(2*B*b*d + B*a*e - 3*A*b*e)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-b^2*d + a*b*e)) + (2*(x*e + d)*B*b*d - 2*B*b*d^2 + (x*e + d)*B*a*e - 3*(x*e + d)*A*b*e + 2*B*a*d*e + 2*A*b*d*e - 2*A*a*e^2)/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e))","A",0
1814,1,297,0,0.220859," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(2 \, B b^{2} d + 3 \, B a b e - 5 \, A b^{2} e\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\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{-b^{2} d + a b e}} + \frac{\sqrt{x e + d} B a b e - \sqrt{x e + d} A b^{2} e}{{\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)} B b d + B b d^{2} + 3 \, {\left(x e + d\right)} B a e - 6 \, {\left(x e + d\right)} A b e - B a d e - A b d e + A a e^{2}\right)}}{3 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"(2*B*b^2*d + 3*B*a*b*e - 5*A*b^2*e)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-b^2*d + a*b*e)) + (sqrt(x*e + d)*B*a*b*e - sqrt(x*e + d)*A*b^2*e)/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*((x*e + d)*b - b*d + a*e)) + 2/3*(3*(x*e + d)*B*b*d + B*b*d^2 + 3*(x*e + d)*B*a*e - 6*(x*e + d)*A*b*e - B*a*d*e - A*b*d*e + A*a*e^2)/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*(x*e + d)^(3/2))","A",0
1815,1,435,0,0.228419," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(2 \, B b^{3} d + 5 \, B a b^{2} e - 7 \, A b^{3} e\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\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)} \sqrt{-b^{2} d + a b e}} + \frac{\sqrt{x e + d} B a b^{2} e - \sqrt{x e + d} A b^{3} e}{{\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} B b^{2} d + 5 \, {\left(x e + d\right)} B b^{2} d^{2} + 3 \, B b^{2} d^{3} + 30 \, {\left(x e + d\right)}^{2} B a b e - 45 \, {\left(x e + d\right)}^{2} A b^{2} e - 10 \, {\left(x e + d\right)} A b^{2} d e - 6 \, B a b d^{2} e - 3 \, A b^{2} d^{2} e - 5 \, {\left(x e + d\right)} B a^{2} e^{2} + 10 \, {\left(x e + d\right)} A a b e^{2} + 3 \, B a^{2} d e^{2} + 6 \, A a b d e^{2} - 3 \, A a^{2} e^{3}\right)}}{15 \, {\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)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"(2*B*b^3*d + 5*B*a*b^2*e - 7*A*b^3*e)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((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)*sqrt(-b^2*d + a*b*e)) + (sqrt(x*e + d)*B*a*b^2*e - sqrt(x*e + d)*A*b^3*e)/((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)*((x*e + d)*b - b*d + a*e)) + 2/15*(15*(x*e + d)^2*B*b^2*d + 5*(x*e + d)*B*b^2*d^2 + 3*B*b^2*d^3 + 30*(x*e + d)^2*B*a*b*e - 45*(x*e + d)^2*A*b^2*e - 10*(x*e + d)*A*b^2*d*e - 6*B*a*b*d^2*e - 3*A*b^2*d^2*e - 5*(x*e + d)*B*a^2*e^2 + 10*(x*e + d)*A*a*b*e^2 + 3*B*a^2*d*e^2 + 6*A*a*b*d*e^2 - 3*A*a^2*e^3)/((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)*(x*e + d)^(5/2))","B",0
1816,1,829,0,0.295049," ","integrate((B*x+A)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{21 \, {\left(6 \, B b^{3} d^{3} e^{2} - 23 \, B a b^{2} d^{2} e^{3} + 5 \, A b^{3} d^{2} e^{3} + 28 \, B a^{2} b d e^{4} - 10 \, A a b^{2} d e^{4} - 11 \, B a^{3} e^{5} + 5 \, A a^{2} b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, \sqrt{-b^{2} d + a b e} b^{6}} - \frac{102 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{2} - 192 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{2} + 90 \, \sqrt{x e + d} B b^{5} d^{5} e^{2} - 471 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{3} + 165 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{3} + 1048 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{3} - 280 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{3} - 573 \, \sqrt{x e + d} B a b^{4} d^{4} e^{3} + 123 \, \sqrt{x e + d} A b^{5} d^{4} e^{3} + 636 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{4} - 330 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{4} - 1992 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{4} + 840 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{4} + 1392 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{4} - 492 \, \sqrt{x e + d} A a b^{4} d^{3} e^{4} - 267 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{5} + 165 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{5} + 1608 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{5} - 840 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{5} - 1638 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{5} + 738 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{5} - 472 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{6} + 280 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{6} + 942 \, \sqrt{x e + d} B a^{4} b d e^{6} - 492 \, \sqrt{x e + d} A a^{3} b^{2} d e^{6} - 213 \, \sqrt{x e + d} B a^{5} e^{7} + 123 \, \sqrt{x e + d} A a^{4} b e^{7}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{6}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{16} e^{2} + 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{16} d e^{2} + 90 \, \sqrt{x e + d} B b^{16} d^{2} e^{2} - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{15} e^{3} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{16} e^{3} - 240 \, \sqrt{x e + d} B a b^{15} d e^{3} + 60 \, \sqrt{x e + d} A b^{16} d e^{3} + 150 \, \sqrt{x e + d} B a^{2} b^{14} e^{4} - 60 \, \sqrt{x e + d} A a b^{15} e^{4}\right)}}{15 \, b^{20}}"," ",0,"21/8*(6*B*b^3*d^3*e^2 - 23*B*a*b^2*d^2*e^3 + 5*A*b^3*d^2*e^3 + 28*B*a^2*b*d*e^4 - 10*A*a*b^2*d*e^4 - 11*B*a^3*e^5 + 5*A*a^2*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^6) - 1/24*(102*(x*e + d)^(5/2)*B*b^5*d^3*e^2 - 192*(x*e + d)^(3/2)*B*b^5*d^4*e^2 + 90*sqrt(x*e + d)*B*b^5*d^5*e^2 - 471*(x*e + d)^(5/2)*B*a*b^4*d^2*e^3 + 165*(x*e + d)^(5/2)*A*b^5*d^2*e^3 + 1048*(x*e + d)^(3/2)*B*a*b^4*d^3*e^3 - 280*(x*e + d)^(3/2)*A*b^5*d^3*e^3 - 573*sqrt(x*e + d)*B*a*b^4*d^4*e^3 + 123*sqrt(x*e + d)*A*b^5*d^4*e^3 + 636*(x*e + d)^(5/2)*B*a^2*b^3*d*e^4 - 330*(x*e + d)^(5/2)*A*a*b^4*d*e^4 - 1992*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^4 + 840*(x*e + d)^(3/2)*A*a*b^4*d^2*e^4 + 1392*sqrt(x*e + d)*B*a^2*b^3*d^3*e^4 - 492*sqrt(x*e + d)*A*a*b^4*d^3*e^4 - 267*(x*e + d)^(5/2)*B*a^3*b^2*e^5 + 165*(x*e + d)^(5/2)*A*a^2*b^3*e^5 + 1608*(x*e + d)^(3/2)*B*a^3*b^2*d*e^5 - 840*(x*e + d)^(3/2)*A*a^2*b^3*d*e^5 - 1638*sqrt(x*e + d)*B*a^3*b^2*d^2*e^5 + 738*sqrt(x*e + d)*A*a^2*b^3*d^2*e^5 - 472*(x*e + d)^(3/2)*B*a^4*b*e^6 + 280*(x*e + d)^(3/2)*A*a^3*b^2*e^6 + 942*sqrt(x*e + d)*B*a^4*b*d*e^6 - 492*sqrt(x*e + d)*A*a^3*b^2*d*e^6 - 213*sqrt(x*e + d)*B*a^5*e^7 + 123*sqrt(x*e + d)*A*a^4*b*e^7)/(((x*e + d)*b - b*d + a*e)^3*b^6) + 2/15*(3*(x*e + d)^(5/2)*B*b^16*e^2 + 15*(x*e + d)^(3/2)*B*b^16*d*e^2 + 90*sqrt(x*e + d)*B*b^16*d^2*e^2 - 20*(x*e + d)^(3/2)*B*a*b^15*e^3 + 5*(x*e + d)^(3/2)*A*b^16*e^3 - 240*sqrt(x*e + d)*B*a*b^15*d*e^3 + 60*sqrt(x*e + d)*A*b^16*d*e^3 + 150*sqrt(x*e + d)*B*a^2*b^14*e^4 - 60*sqrt(x*e + d)*A*a*b^15*e^4)/b^20","B",0
1817,1,577,0,0.247626," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{35 \, {\left(2 \, B b^{2} d^{2} e^{2} - 5 \, B a b d e^{3} + A b^{2} d e^{3} + 3 \, B a^{2} e^{4} - A a b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, \sqrt{-b^{2} d + a b e} b^{5}} - \frac{78 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{2} - 144 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{2} + 66 \, \sqrt{x e + d} B b^{4} d^{4} e^{2} - 243 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{3} + 87 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{3} + 568 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{3} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{3} - 321 \, \sqrt{x e + d} B a b^{3} d^{3} e^{3} + 57 \, \sqrt{x e + d} A b^{4} d^{3} e^{3} + 165 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{4} - 87 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{4} - 704 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{4} + 272 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{4} + 567 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{4} - 171 \, \sqrt{x e + d} A a b^{3} d^{2} e^{4} + 280 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{5} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{5} - 435 \, \sqrt{x e + d} B a^{3} b d e^{5} + 171 \, \sqrt{x e + d} A a^{2} b^{2} d e^{5} + 123 \, \sqrt{x e + d} B a^{4} e^{6} - 57 \, \sqrt{x e + d} A a^{3} b e^{6}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{5}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{8} e^{2} + 9 \, \sqrt{x e + d} B b^{8} d e^{2} - 12 \, \sqrt{x e + d} B a b^{7} e^{3} + 3 \, \sqrt{x e + d} A b^{8} e^{3}\right)}}{3 \, b^{12}}"," ",0,"35/8*(2*B*b^2*d^2*e^2 - 5*B*a*b*d*e^3 + A*b^2*d*e^3 + 3*B*a^2*e^4 - A*a*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5) - 1/24*(78*(x*e + d)^(5/2)*B*b^4*d^2*e^2 - 144*(x*e + d)^(3/2)*B*b^4*d^3*e^2 + 66*sqrt(x*e + d)*B*b^4*d^4*e^2 - 243*(x*e + d)^(5/2)*B*a*b^3*d*e^3 + 87*(x*e + d)^(5/2)*A*b^4*d*e^3 + 568*(x*e + d)^(3/2)*B*a*b^3*d^2*e^3 - 136*(x*e + d)^(3/2)*A*b^4*d^2*e^3 - 321*sqrt(x*e + d)*B*a*b^3*d^3*e^3 + 57*sqrt(x*e + d)*A*b^4*d^3*e^3 + 165*(x*e + d)^(5/2)*B*a^2*b^2*e^4 - 87*(x*e + d)^(5/2)*A*a*b^3*e^4 - 704*(x*e + d)^(3/2)*B*a^2*b^2*d*e^4 + 272*(x*e + d)^(3/2)*A*a*b^3*d*e^4 + 567*sqrt(x*e + d)*B*a^2*b^2*d^2*e^4 - 171*sqrt(x*e + d)*A*a*b^3*d^2*e^4 + 280*(x*e + d)^(3/2)*B*a^3*b*e^5 - 136*(x*e + d)^(3/2)*A*a^2*b^2*e^5 - 435*sqrt(x*e + d)*B*a^3*b*d*e^5 + 171*sqrt(x*e + d)*A*a^2*b^2*d*e^5 + 123*sqrt(x*e + d)*B*a^4*e^6 - 57*sqrt(x*e + d)*A*a^3*b*e^6)/(((x*e + d)*b - b*d + a*e)^3*b^5) + 2/3*((x*e + d)^(3/2)*B*b^8*e^2 + 9*sqrt(x*e + d)*B*b^8*d*e^2 - 12*sqrt(x*e + d)*B*a*b^7*e^3 + 3*sqrt(x*e + d)*A*b^8*e^3)/b^12","B",0
1818,1,370,0,0.273682," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e^{2}}{b^{4}} + \frac{5 \, {\left(6 \, B b d e^{2} - 7 \, B a e^{3} + A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, \sqrt{-b^{2} d + a b e} b^{4}} - \frac{54 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} d e^{2} - 96 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d^{2} e^{2} + 42 \, \sqrt{x e + d} B b^{3} d^{3} e^{2} - 87 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{2} e^{3} + 33 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} e^{3} + 232 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} d e^{3} - 40 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} d e^{3} - 141 \, \sqrt{x e + d} B a b^{2} d^{2} e^{3} + 15 \, \sqrt{x e + d} A b^{3} d^{2} e^{3} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b e^{4} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{2} e^{4} + 156 \, \sqrt{x e + d} B a^{2} b d e^{4} - 30 \, \sqrt{x e + d} A a b^{2} d e^{4} - 57 \, \sqrt{x e + d} B a^{3} e^{5} + 15 \, \sqrt{x e + d} A a^{2} b e^{5}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{4}}"," ",0,"2*sqrt(x*e + d)*B*e^2/b^4 + 5/8*(6*B*b*d*e^2 - 7*B*a*e^3 + A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) - 1/24*(54*(x*e + d)^(5/2)*B*b^3*d*e^2 - 96*(x*e + d)^(3/2)*B*b^3*d^2*e^2 + 42*sqrt(x*e + d)*B*b^3*d^3*e^2 - 87*(x*e + d)^(5/2)*B*a*b^2*e^3 + 33*(x*e + d)^(5/2)*A*b^3*e^3 + 232*(x*e + d)^(3/2)*B*a*b^2*d*e^3 - 40*(x*e + d)^(3/2)*A*b^3*d*e^3 - 141*sqrt(x*e + d)*B*a*b^2*d^2*e^3 + 15*sqrt(x*e + d)*A*b^3*d^2*e^3 - 136*(x*e + d)^(3/2)*B*a^2*b*e^4 + 40*(x*e + d)^(3/2)*A*a*b^2*e^4 + 156*sqrt(x*e + d)*B*a^2*b*d*e^4 - 30*sqrt(x*e + d)*A*a*b^2*d*e^4 - 57*sqrt(x*e + d)*B*a^3*e^5 + 15*sqrt(x*e + d)*A*a^2*b*e^5)/(((x*e + d)*b - b*d + a*e)^3*b^4)","A",0
1819,1,381,0,0.230561," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(6 \, B b d e^{2} - 5 \, B a e^{3} - A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, {\left(b^{4} d - a b^{3} e\right)} \sqrt{-b^{2} d + a b e}} - \frac{30 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} d e^{2} - 48 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d^{2} e^{2} + 18 \, \sqrt{x e + d} B b^{3} d^{3} e^{2} - 33 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{2} e^{3} + 3 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} e^{3} + 88 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} d e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} d e^{3} - 51 \, \sqrt{x e + d} B a b^{2} d^{2} e^{3} - 3 \, \sqrt{x e + d} A b^{3} d^{2} e^{3} - 40 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b e^{4} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{2} e^{4} + 48 \, \sqrt{x e + d} B a^{2} b d e^{4} + 6 \, \sqrt{x e + d} A a b^{2} d e^{4} - 15 \, \sqrt{x e + d} B a^{3} e^{5} - 3 \, \sqrt{x e + d} A a^{2} b e^{5}}{24 \, {\left(b^{4} d - a b^{3} e\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"1/8*(6*B*b*d*e^2 - 5*B*a*e^3 - A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^4*d - a*b^3*e)*sqrt(-b^2*d + a*b*e)) - 1/24*(30*(x*e + d)^(5/2)*B*b^3*d*e^2 - 48*(x*e + d)^(3/2)*B*b^3*d^2*e^2 + 18*sqrt(x*e + d)*B*b^3*d^3*e^2 - 33*(x*e + d)^(5/2)*B*a*b^2*e^3 + 3*(x*e + d)^(5/2)*A*b^3*e^3 + 88*(x*e + d)^(3/2)*B*a*b^2*d*e^3 + 8*(x*e + d)^(3/2)*A*b^3*d*e^3 - 51*sqrt(x*e + d)*B*a*b^2*d^2*e^3 - 3*sqrt(x*e + d)*A*b^3*d^2*e^3 - 40*(x*e + d)^(3/2)*B*a^2*b*e^4 - 8*(x*e + d)^(3/2)*A*a*b^2*e^4 + 48*sqrt(x*e + d)*B*a^2*b*d*e^4 + 6*sqrt(x*e + d)*A*a*b^2*d*e^4 - 15*sqrt(x*e + d)*B*a^3*e^5 - 3*sqrt(x*e + d)*A*a^2*b*e^5)/((b^4*d - a*b^3*e)*((x*e + d)*b - b*d + a*e)^3)","B",0
1820,1,386,0,0.250013," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B b d e^{2} - B a e^{3} - A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} - \frac{6 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} d e^{2} - 6 \, \sqrt{x e + d} B b^{3} d^{3} e^{2} - 3 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{2} e^{3} - 3 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} d e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} d e^{3} + 15 \, \sqrt{x e + d} B a b^{2} d^{2} e^{3} + 3 \, \sqrt{x e + d} A b^{3} d^{2} e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b e^{4} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{2} e^{4} - 12 \, \sqrt{x e + d} B a^{2} b d e^{4} - 6 \, \sqrt{x e + d} A a b^{2} d e^{4} + 3 \, \sqrt{x e + d} B a^{3} e^{5} + 3 \, \sqrt{x e + d} A a^{2} b e^{5}}{24 \, {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-1/8*(2*B*b*d*e^2 - B*a*e^3 - A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*sqrt(-b^2*d + a*b*e)) - 1/24*(6*(x*e + d)^(5/2)*B*b^3*d*e^2 - 6*sqrt(x*e + d)*B*b^3*d^3*e^2 - 3*(x*e + d)^(5/2)*B*a*b^2*e^3 - 3*(x*e + d)^(5/2)*A*b^3*e^3 - 8*(x*e + d)^(3/2)*B*a*b^2*d*e^3 + 8*(x*e + d)^(3/2)*A*b^3*d*e^3 + 15*sqrt(x*e + d)*B*a*b^2*d^2*e^3 + 3*sqrt(x*e + d)*A*b^3*d^2*e^3 + 8*(x*e + d)^(3/2)*B*a^2*b*e^4 - 8*(x*e + d)^(3/2)*A*a*b^2*e^4 - 12*sqrt(x*e + d)*B*a^2*b*d*e^4 - 6*sqrt(x*e + d)*A*a*b^2*d*e^4 + 3*sqrt(x*e + d)*B*a^3*e^5 + 3*sqrt(x*e + d)*A*a^2*b*e^5)/((b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*((x*e + d)*b - b*d + a*e)^3)","B",0
1821,1,429,0,0.208702," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{{\left(6 \, B b d e^{2} - B a e^{3} - 5 \, A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, {\left(b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}\right)} \sqrt{-b^{2} d + a b e}} + \frac{18 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} d e^{2} - 48 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d^{2} e^{2} + 30 \, \sqrt{x e + d} B b^{3} d^{3} e^{2} - 3 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{2} e^{3} - 15 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} e^{3} + 56 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} d e^{3} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} d e^{3} - 57 \, \sqrt{x e + d} B a b^{2} d^{2} e^{3} - 33 \, \sqrt{x e + d} A b^{3} d^{2} e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b e^{4} - 40 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{2} e^{4} + 24 \, \sqrt{x e + d} B a^{2} b d e^{4} + 66 \, \sqrt{x e + d} A a b^{2} d e^{4} + 3 \, \sqrt{x e + d} B a^{3} e^{5} - 33 \, \sqrt{x e + d} A a^{2} b e^{5}}{24 \, {\left(b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"1/8*(6*B*b*d*e^2 - B*a*e^3 - 5*A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3)*sqrt(-b^2*d + a*b*e)) + 1/24*(18*(x*e + d)^(5/2)*B*b^3*d*e^2 - 48*(x*e + d)^(3/2)*B*b^3*d^2*e^2 + 30*sqrt(x*e + d)*B*b^3*d^3*e^2 - 3*(x*e + d)^(5/2)*B*a*b^2*e^3 - 15*(x*e + d)^(5/2)*A*b^3*e^3 + 56*(x*e + d)^(3/2)*B*a*b^2*d*e^3 + 40*(x*e + d)^(3/2)*A*b^3*d*e^3 - 57*sqrt(x*e + d)*B*a*b^2*d^2*e^3 - 33*sqrt(x*e + d)*A*b^3*d^2*e^3 - 8*(x*e + d)^(3/2)*B*a^2*b*e^4 - 40*(x*e + d)^(3/2)*A*a*b^2*e^4 + 24*sqrt(x*e + d)*B*a^2*b*d*e^4 + 66*sqrt(x*e + d)*A*a*b^2*d*e^4 + 3*sqrt(x*e + d)*B*a^3*e^5 - 33*sqrt(x*e + d)*A*a^2*b*e^5)/((b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3)*((x*e + d)*b - b*d + a*e)^3)","B",0
1822,1,516,0,0.256148," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{5 \, {\left(6 \, B b d e^{2} + B a e^{3} - 7 \, A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(B d e^{2} - A e^{3}\right)}}{{\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)} \sqrt{x e + d}} + \frac{42 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} d e^{2} - 96 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d^{2} e^{2} + 54 \, \sqrt{x e + d} B b^{3} d^{3} e^{2} + 15 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{2} e^{3} - 57 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} e^{3} + 56 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} d e^{3} + 136 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} d e^{3} - 75 \, \sqrt{x e + d} B a b^{2} d^{2} e^{3} - 87 \, \sqrt{x e + d} A b^{3} d^{2} e^{3} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b e^{4} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{2} e^{4} - 12 \, \sqrt{x e + d} B a^{2} b d e^{4} + 174 \, \sqrt{x e + d} A a b^{2} d e^{4} + 33 \, \sqrt{x e + d} B a^{3} e^{5} - 87 \, \sqrt{x e + d} A a^{2} b e^{5}}{24 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"5/8*(6*B*b*d*e^2 + B*a*e^3 - 7*A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((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)*sqrt(-b^2*d + a*b*e)) + 2*(B*d*e^2 - A*e^3)/((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)*sqrt(x*e + d)) + 1/24*(42*(x*e + d)^(5/2)*B*b^3*d*e^2 - 96*(x*e + d)^(3/2)*B*b^3*d^2*e^2 + 54*sqrt(x*e + d)*B*b^3*d^3*e^2 + 15*(x*e + d)^(5/2)*B*a*b^2*e^3 - 57*(x*e + d)^(5/2)*A*b^3*e^3 + 56*(x*e + d)^(3/2)*B*a*b^2*d*e^3 + 136*(x*e + d)^(3/2)*A*b^3*d*e^3 - 75*sqrt(x*e + d)*B*a*b^2*d^2*e^3 - 87*sqrt(x*e + d)*A*b^3*d^2*e^3 + 40*(x*e + d)^(3/2)*B*a^2*b*e^4 - 136*(x*e + d)^(3/2)*A*a*b^2*e^4 - 12*sqrt(x*e + d)*B*a^2*b*d*e^4 + 174*sqrt(x*e + d)*A*a*b^2*d*e^4 + 33*sqrt(x*e + d)*B*a^3*e^5 - 87*sqrt(x*e + d)*A*a^2*b*e^5)/((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)*((x*e + d)*b - b*d + a*e)^3)","B",0
1823,1,750,0,0.287633," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{35 \, {\left(2 \, B b^{2} d e^{2} + B a b e^{3} - 3 \, A b^{2} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{210 \, {\left(x e + d\right)}^{4} B b^{4} d e^{2} - 560 \, {\left(x e + d\right)}^{3} B b^{4} d^{2} e^{2} + 462 \, {\left(x e + d\right)}^{2} B b^{4} d^{3} e^{2} - 96 \, {\left(x e + d\right)} B b^{4} d^{4} e^{2} - 16 \, B b^{4} d^{5} e^{2} + 105 \, {\left(x e + d\right)}^{4} B a b^{3} e^{3} - 315 \, {\left(x e + d\right)}^{4} A b^{4} e^{3} + 280 \, {\left(x e + d\right)}^{3} B a b^{3} d e^{3} + 840 \, {\left(x e + d\right)}^{3} A b^{4} d e^{3} - 693 \, {\left(x e + d\right)}^{2} B a b^{3} d^{2} e^{3} - 693 \, {\left(x e + d\right)}^{2} A b^{4} d^{2} e^{3} + 240 \, {\left(x e + d\right)} B a b^{3} d^{3} e^{3} + 144 \, {\left(x e + d\right)} A b^{4} d^{3} e^{3} + 64 \, B a b^{3} d^{4} e^{3} + 16 \, A b^{4} d^{4} e^{3} + 280 \, {\left(x e + d\right)}^{3} B a^{2} b^{2} e^{4} - 840 \, {\left(x e + d\right)}^{3} A a b^{3} e^{4} + 1386 \, {\left(x e + d\right)}^{2} A a b^{3} d e^{4} - 144 \, {\left(x e + d\right)} B a^{2} b^{2} d^{2} e^{4} - 432 \, {\left(x e + d\right)} A a b^{3} d^{2} e^{4} - 96 \, B a^{2} b^{2} d^{3} e^{4} - 64 \, A a b^{3} d^{3} e^{4} + 231 \, {\left(x e + d\right)}^{2} B a^{3} b e^{5} - 693 \, {\left(x e + d\right)}^{2} A a^{2} b^{2} e^{5} - 48 \, {\left(x e + d\right)} B a^{3} b d e^{5} + 432 \, {\left(x e + d\right)} A a^{2} b^{2} d e^{5} + 64 \, B a^{3} b d^{2} e^{5} + 96 \, A a^{2} b^{2} d^{2} e^{5} + 48 \, {\left(x e + d\right)} B a^{4} e^{6} - 144 \, {\left(x e + d\right)} A a^{3} b e^{6} - 16 \, B a^{4} d e^{6} - 64 \, A a^{3} b d e^{6} + 16 \, A a^{4} e^{7}}{24 \, {\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)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}^{3}}"," ",0,"35/8*(2*B*b^2*d*e^2 + B*a*b*e^3 - 3*A*b^2*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((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)*sqrt(-b^2*d + a*b*e)) + 1/24*(210*(x*e + d)^4*B*b^4*d*e^2 - 560*(x*e + d)^3*B*b^4*d^2*e^2 + 462*(x*e + d)^2*B*b^4*d^3*e^2 - 96*(x*e + d)*B*b^4*d^4*e^2 - 16*B*b^4*d^5*e^2 + 105*(x*e + d)^4*B*a*b^3*e^3 - 315*(x*e + d)^4*A*b^4*e^3 + 280*(x*e + d)^3*B*a*b^3*d*e^3 + 840*(x*e + d)^3*A*b^4*d*e^3 - 693*(x*e + d)^2*B*a*b^3*d^2*e^3 - 693*(x*e + d)^2*A*b^4*d^2*e^3 + 240*(x*e + d)*B*a*b^3*d^3*e^3 + 144*(x*e + d)*A*b^4*d^3*e^3 + 64*B*a*b^3*d^4*e^3 + 16*A*b^4*d^4*e^3 + 280*(x*e + d)^3*B*a^2*b^2*e^4 - 840*(x*e + d)^3*A*a*b^3*e^4 + 1386*(x*e + d)^2*A*a*b^3*d*e^4 - 144*(x*e + d)*B*a^2*b^2*d^2*e^4 - 432*(x*e + d)*A*a*b^3*d^2*e^4 - 96*B*a^2*b^2*d^3*e^4 - 64*A*a*b^3*d^3*e^4 + 231*(x*e + d)^2*B*a^3*b*e^5 - 693*(x*e + d)^2*A*a^2*b^2*e^5 - 48*(x*e + d)*B*a^3*b*d*e^5 + 432*(x*e + d)*A*a^2*b^2*d*e^5 + 64*B*a^3*b*d^2*e^5 + 96*A*a^2*b^2*d^2*e^5 + 48*(x*e + d)*B*a^4*e^6 - 144*(x*e + d)*A*a^3*b*e^6 - 16*B*a^4*d*e^6 - 64*A*a^3*b*d*e^6 + 16*A*a^4*e^7)/((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)*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e)^3)","B",0
1824,1,779,0,0.340277," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{21 \, {\left(6 \, B b^{3} d e^{2} + 5 \, B a b^{2} e^{3} - 11 \, A b^{3} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} B b^{2} d e^{2} + 15 \, {\left(x e + d\right)} B b^{2} d^{2} e^{2} + 3 \, B b^{2} d^{3} e^{2} + 60 \, {\left(x e + d\right)}^{2} B a b e^{3} - 150 \, {\left(x e + d\right)}^{2} A b^{2} e^{3} - 10 \, {\left(x e + d\right)} B a b d e^{3} - 20 \, {\left(x e + d\right)} A b^{2} d e^{3} - 6 \, B a b d^{2} e^{3} - 3 \, A b^{2} d^{2} e^{3} - 5 \, {\left(x e + d\right)} B a^{2} e^{4} + 20 \, {\left(x e + d\right)} A a b e^{4} + 3 \, B a^{2} d e^{4} + 6 \, A a b d e^{4} - 3 \, A a^{2} e^{5}\right)}}{15 \, {\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)} {\left(x e + d\right)}^{\frac{5}{2}}} + \frac{90 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d e^{2} - 192 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{2} e^{2} + 102 \, \sqrt{x e + d} B b^{5} d^{3} e^{2} + 123 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} e^{3} - 213 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} e^{3} - 88 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d e^{3} + 472 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d e^{3} - 39 \, \sqrt{x e + d} B a b^{4} d^{2} e^{3} - 267 \, \sqrt{x e + d} A b^{5} d^{2} e^{3} + 280 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} e^{4} - 472 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} e^{4} - 228 \, \sqrt{x e + d} B a^{2} b^{3} d e^{4} + 534 \, \sqrt{x e + d} A a b^{4} d e^{4} + 165 \, \sqrt{x e + d} B a^{3} b^{2} e^{5} - 267 \, \sqrt{x e + d} A a^{2} b^{3} e^{5}}{24 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"21/8*(6*B*b^3*d*e^2 + 5*B*a*b^2*e^3 - 11*A*b^3*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((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)*sqrt(-b^2*d + a*b*e)) + 2/15*(90*(x*e + d)^2*B*b^2*d*e^2 + 15*(x*e + d)*B*b^2*d^2*e^2 + 3*B*b^2*d^3*e^2 + 60*(x*e + d)^2*B*a*b*e^3 - 150*(x*e + d)^2*A*b^2*e^3 - 10*(x*e + d)*B*a*b*d*e^3 - 20*(x*e + d)*A*b^2*d*e^3 - 6*B*a*b*d^2*e^3 - 3*A*b^2*d^2*e^3 - 5*(x*e + d)*B*a^2*e^4 + 20*(x*e + d)*A*a*b*e^4 + 3*B*a^2*d*e^4 + 6*A*a*b*d*e^4 - 3*A*a^2*e^5)/((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)*(x*e + d)^(5/2)) + 1/24*(90*(x*e + d)^(5/2)*B*b^5*d*e^2 - 192*(x*e + d)^(3/2)*B*b^5*d^2*e^2 + 102*sqrt(x*e + d)*B*b^5*d^3*e^2 + 123*(x*e + d)^(5/2)*B*a*b^4*e^3 - 213*(x*e + d)^(5/2)*A*b^5*e^3 - 88*(x*e + d)^(3/2)*B*a*b^4*d*e^3 + 472*(x*e + d)^(3/2)*A*b^5*d*e^3 - 39*sqrt(x*e + d)*B*a*b^4*d^2*e^3 - 267*sqrt(x*e + d)*A*b^5*d^2*e^3 + 280*(x*e + d)^(3/2)*B*a^2*b^3*e^4 - 472*(x*e + d)^(3/2)*A*a*b^4*e^4 - 228*sqrt(x*e + d)*B*a^2*b^3*d*e^4 + 534*sqrt(x*e + d)*A*a*b^4*d*e^4 + 165*sqrt(x*e + d)*B*a^3*b^2*e^5 - 267*sqrt(x*e + d)*A*a^2*b^3*e^5)/((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)*((x*e + d)*b - b*d + a*e)^3)","B",0
1825,1,1066,0,0.359539," ","integrate((B*x+A)*(e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{231 \, {\left(10 \, B b^{2} d^{2} e^{4} - 23 \, B a b d e^{5} + 3 \, A b^{2} d e^{5} + 13 \, B a^{2} e^{6} - 3 \, A a b e^{6}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, \sqrt{-b^{2} d + a b e} b^{7}} - \frac{22950 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{6} d^{2} e^{4} - 81500 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} d^{3} e^{4} + 110080 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} d^{4} e^{4} - 66980 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d^{5} e^{4} + 15450 \, \sqrt{x e + d} B b^{6} d^{6} e^{4} - 58545 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{5} d e^{5} + 12645 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{6} d e^{5} + 284310 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{5} d^{2} e^{5} - 39810 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{6} d^{2} e^{5} - 490624 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} d^{3} e^{5} + 50304 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} d^{3} e^{5} + 364210 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d^{4} e^{5} - 29310 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d^{4} e^{5} - 99255 \, \sqrt{x e + d} B a b^{5} d^{5} e^{5} + 6555 \, \sqrt{x e + d} A b^{6} d^{5} e^{5} + 35595 \, {\left(x e + d\right)}^{\frac{9}{2}} B a^{2} b^{4} e^{6} - 12645 \, {\left(x e + d\right)}^{\frac{9}{2}} A a b^{5} e^{6} - 324120 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{4} d e^{6} + 79620 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{5} d e^{6} + 811392 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{4} d^{2} e^{6} - 150912 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{5} d^{2} e^{6} - 787040 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} d^{3} e^{6} + 117240 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} d^{3} e^{6} + 264525 \, \sqrt{x e + d} B a^{2} b^{4} d^{4} e^{6} - 32775 \, \sqrt{x e + d} A a b^{5} d^{4} e^{6} + 121310 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{3} b^{3} e^{7} - 39810 \, {\left(x e + d\right)}^{\frac{7}{2}} A a^{2} b^{4} e^{7} - 591232 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{3} d e^{7} + 150912 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{4} d e^{7} + 845660 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{3} d^{2} e^{7} - 175860 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{4} d^{2} e^{7} - 374550 \, \sqrt{x e + d} B a^{3} b^{3} d^{3} e^{7} + 65550 \, \sqrt{x e + d} A a^{2} b^{4} d^{3} e^{7} + 160384 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{4} b^{2} e^{8} - 50304 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{3} b^{3} e^{8} - 452140 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b^{2} d e^{8} + 117240 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{3} d e^{8} + 297300 \, \sqrt{x e + d} B a^{4} b^{2} d^{2} e^{8} - 65550 \, \sqrt{x e + d} A a^{3} b^{3} d^{2} e^{8} + 96290 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{5} b e^{9} - 29310 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{4} b^{2} e^{9} - 125475 \, \sqrt{x e + d} B a^{5} b d e^{9} + 32775 \, \sqrt{x e + d} A a^{4} b^{2} d e^{9} + 22005 \, \sqrt{x e + d} B a^{6} e^{10} - 6555 \, \sqrt{x e + d} A a^{5} b e^{10}}{1920 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{5} b^{7}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{12} e^{4} + 15 \, \sqrt{x e + d} B b^{12} d e^{4} - 18 \, \sqrt{x e + d} B a b^{11} e^{5} + 3 \, \sqrt{x e + d} A b^{12} e^{5}\right)}}{3 \, b^{18}}"," ",0,"231/128*(10*B*b^2*d^2*e^4 - 23*B*a*b*d*e^5 + 3*A*b^2*d*e^5 + 13*B*a^2*e^6 - 3*A*a*b*e^6)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^7) - 1/1920*(22950*(x*e + d)^(9/2)*B*b^6*d^2*e^4 - 81500*(x*e + d)^(7/2)*B*b^6*d^3*e^4 + 110080*(x*e + d)^(5/2)*B*b^6*d^4*e^4 - 66980*(x*e + d)^(3/2)*B*b^6*d^5*e^4 + 15450*sqrt(x*e + d)*B*b^6*d^6*e^4 - 58545*(x*e + d)^(9/2)*B*a*b^5*d*e^5 + 12645*(x*e + d)^(9/2)*A*b^6*d*e^5 + 284310*(x*e + d)^(7/2)*B*a*b^5*d^2*e^5 - 39810*(x*e + d)^(7/2)*A*b^6*d^2*e^5 - 490624*(x*e + d)^(5/2)*B*a*b^5*d^3*e^5 + 50304*(x*e + d)^(5/2)*A*b^6*d^3*e^5 + 364210*(x*e + d)^(3/2)*B*a*b^5*d^4*e^5 - 29310*(x*e + d)^(3/2)*A*b^6*d^4*e^5 - 99255*sqrt(x*e + d)*B*a*b^5*d^5*e^5 + 6555*sqrt(x*e + d)*A*b^6*d^5*e^5 + 35595*(x*e + d)^(9/2)*B*a^2*b^4*e^6 - 12645*(x*e + d)^(9/2)*A*a*b^5*e^6 - 324120*(x*e + d)^(7/2)*B*a^2*b^4*d*e^6 + 79620*(x*e + d)^(7/2)*A*a*b^5*d*e^6 + 811392*(x*e + d)^(5/2)*B*a^2*b^4*d^2*e^6 - 150912*(x*e + d)^(5/2)*A*a*b^5*d^2*e^6 - 787040*(x*e + d)^(3/2)*B*a^2*b^4*d^3*e^6 + 117240*(x*e + d)^(3/2)*A*a*b^5*d^3*e^6 + 264525*sqrt(x*e + d)*B*a^2*b^4*d^4*e^6 - 32775*sqrt(x*e + d)*A*a*b^5*d^4*e^6 + 121310*(x*e + d)^(7/2)*B*a^3*b^3*e^7 - 39810*(x*e + d)^(7/2)*A*a^2*b^4*e^7 - 591232*(x*e + d)^(5/2)*B*a^3*b^3*d*e^7 + 150912*(x*e + d)^(5/2)*A*a^2*b^4*d*e^7 + 845660*(x*e + d)^(3/2)*B*a^3*b^3*d^2*e^7 - 175860*(x*e + d)^(3/2)*A*a^2*b^4*d^2*e^7 - 374550*sqrt(x*e + d)*B*a^3*b^3*d^3*e^7 + 65550*sqrt(x*e + d)*A*a^2*b^4*d^3*e^7 + 160384*(x*e + d)^(5/2)*B*a^4*b^2*e^8 - 50304*(x*e + d)^(5/2)*A*a^3*b^3*e^8 - 452140*(x*e + d)^(3/2)*B*a^4*b^2*d*e^8 + 117240*(x*e + d)^(3/2)*A*a^3*b^3*d*e^8 + 297300*sqrt(x*e + d)*B*a^4*b^2*d^2*e^8 - 65550*sqrt(x*e + d)*A*a^3*b^3*d^2*e^8 + 96290*(x*e + d)^(3/2)*B*a^5*b*e^9 - 29310*(x*e + d)^(3/2)*A*a^4*b^2*e^9 - 125475*sqrt(x*e + d)*B*a^5*b*d*e^9 + 32775*sqrt(x*e + d)*A*a^4*b^2*d*e^9 + 22005*sqrt(x*e + d)*B*a^6*e^10 - 6555*sqrt(x*e + d)*A*a^5*b*e^10)/(((x*e + d)*b - b*d + a*e)^5*b^7) + 2/3*((x*e + d)^(3/2)*B*b^12*e^4 + 15*sqrt(x*e + d)*B*b^12*d*e^4 - 18*sqrt(x*e + d)*B*a*b^11*e^5 + 3*sqrt(x*e + d)*A*b^12*e^5)/b^18","B",0
1826,1,770,0,0.303442," ","integrate((B*x+A)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e^{4}}{b^{6}} + \frac{63 \, {\left(10 \, B b d e^{4} - 11 \, B a e^{5} + A b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, \sqrt{-b^{2} d + a b e} b^{6}} - \frac{3250 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{4} - 10900 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{4} + 14080 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{4} - 8300 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{4} + 1870 \, \sqrt{x e + d} B b^{5} d^{5} e^{4} - 4215 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{5} + 965 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{5} + 24170 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{5} - 2370 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{5} - 44928 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{5} + 2688 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{5} + 34670 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{5} - 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{5} - 9665 \, \sqrt{x e + d} B a b^{4} d^{4} e^{5} + 315 \, \sqrt{x e + d} A b^{5} d^{4} e^{5} - 13270 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{6} + 2370 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{6} + 47616 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{6} - 5376 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{6} - 54210 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{6} + 4410 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{6} + 19960 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{6} - 1260 \, \sqrt{x e + d} A a b^{4} d^{3} e^{6} - 16768 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{7} + 2688 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{7} + 37610 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{7} - 4410 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{7} - 20590 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{7} + 1890 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{7} - 9770 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{8} + 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{8} + 10610 \, \sqrt{x e + d} B a^{4} b d e^{8} - 1260 \, \sqrt{x e + d} A a^{3} b^{2} d e^{8} - 2185 \, \sqrt{x e + d} B a^{5} e^{9} + 315 \, \sqrt{x e + d} A a^{4} b e^{9}}{640 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{5} b^{6}}"," ",0,"2*sqrt(x*e + d)*B*e^4/b^6 + 63/128*(10*B*b*d*e^4 - 11*B*a*e^5 + A*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^6) - 1/640*(3250*(x*e + d)^(9/2)*B*b^5*d*e^4 - 10900*(x*e + d)^(7/2)*B*b^5*d^2*e^4 + 14080*(x*e + d)^(5/2)*B*b^5*d^3*e^4 - 8300*(x*e + d)^(3/2)*B*b^5*d^4*e^4 + 1870*sqrt(x*e + d)*B*b^5*d^5*e^4 - 4215*(x*e + d)^(9/2)*B*a*b^4*e^5 + 965*(x*e + d)^(9/2)*A*b^5*e^5 + 24170*(x*e + d)^(7/2)*B*a*b^4*d*e^5 - 2370*(x*e + d)^(7/2)*A*b^5*d*e^5 - 44928*(x*e + d)^(5/2)*B*a*b^4*d^2*e^5 + 2688*(x*e + d)^(5/2)*A*b^5*d^2*e^5 + 34670*(x*e + d)^(3/2)*B*a*b^4*d^3*e^5 - 1470*(x*e + d)^(3/2)*A*b^5*d^3*e^5 - 9665*sqrt(x*e + d)*B*a*b^4*d^4*e^5 + 315*sqrt(x*e + d)*A*b^5*d^4*e^5 - 13270*(x*e + d)^(7/2)*B*a^2*b^3*e^6 + 2370*(x*e + d)^(7/2)*A*a*b^4*e^6 + 47616*(x*e + d)^(5/2)*B*a^2*b^3*d*e^6 - 5376*(x*e + d)^(5/2)*A*a*b^4*d*e^6 - 54210*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^6 + 4410*(x*e + d)^(3/2)*A*a*b^4*d^2*e^6 + 19960*sqrt(x*e + d)*B*a^2*b^3*d^3*e^6 - 1260*sqrt(x*e + d)*A*a*b^4*d^3*e^6 - 16768*(x*e + d)^(5/2)*B*a^3*b^2*e^7 + 2688*(x*e + d)^(5/2)*A*a^2*b^3*e^7 + 37610*(x*e + d)^(3/2)*B*a^3*b^2*d*e^7 - 4410*(x*e + d)^(3/2)*A*a^2*b^3*d*e^7 - 20590*sqrt(x*e + d)*B*a^3*b^2*d^2*e^7 + 1890*sqrt(x*e + d)*A*a^2*b^3*d^2*e^7 - 9770*(x*e + d)^(3/2)*B*a^4*b*e^8 + 1470*(x*e + d)^(3/2)*A*a^3*b^2*e^8 + 10610*sqrt(x*e + d)*B*a^4*b*d*e^8 - 1260*sqrt(x*e + d)*A*a^3*b^2*d*e^8 - 2185*sqrt(x*e + d)*B*a^5*e^9 + 315*sqrt(x*e + d)*A*a^4*b*e^9)/(((x*e + d)*b - b*d + a*e)^5*b^6)","B",0
1827,1,781,0,0.295759," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{7 \, {\left(10 \, B b d e^{4} - 9 \, B a e^{5} - A b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\left(b^{6} d - a b^{5} e\right)} \sqrt{-b^{2} d + a b e}} - \frac{2790 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{4} - 7900 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{4} + 8960 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{4} - 4900 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{4} + 1050 \, \sqrt{x e + d} B b^{5} d^{5} e^{4} - 2895 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{5} + 105 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{5} + 15010 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{5} + 790 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{5} - 25984 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{5} - 896 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{5} + 19110 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{5} + 490 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{5} - 5145 \, \sqrt{x e + d} B a b^{4} d^{4} e^{5} - 105 \, \sqrt{x e + d} A b^{5} d^{4} e^{5} - 7110 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{6} - 790 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{6} + 25088 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{6} + 1792 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{6} - 27930 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{6} - 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{6} + 10080 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{6} + 420 \, \sqrt{x e + d} A a b^{4} d^{3} e^{6} - 8064 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{7} - 896 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{7} + 18130 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{7} + 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{7} - 9870 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{7} - 630 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{7} - 4410 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{8} - 490 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{8} + 4830 \, \sqrt{x e + d} B a^{4} b d e^{8} + 420 \, \sqrt{x e + d} A a^{3} b^{2} d e^{8} - 945 \, \sqrt{x e + d} B a^{5} e^{9} - 105 \, \sqrt{x e + d} A a^{4} b e^{9}}{1920 \, {\left(b^{6} d - a b^{5} e\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"7/128*(10*B*b*d*e^4 - 9*B*a*e^5 - A*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^6*d - a*b^5*e)*sqrt(-b^2*d + a*b*e)) - 1/1920*(2790*(x*e + d)^(9/2)*B*b^5*d*e^4 - 7900*(x*e + d)^(7/2)*B*b^5*d^2*e^4 + 8960*(x*e + d)^(5/2)*B*b^5*d^3*e^4 - 4900*(x*e + d)^(3/2)*B*b^5*d^4*e^4 + 1050*sqrt(x*e + d)*B*b^5*d^5*e^4 - 2895*(x*e + d)^(9/2)*B*a*b^4*e^5 + 105*(x*e + d)^(9/2)*A*b^5*e^5 + 15010*(x*e + d)^(7/2)*B*a*b^4*d*e^5 + 790*(x*e + d)^(7/2)*A*b^5*d*e^5 - 25984*(x*e + d)^(5/2)*B*a*b^4*d^2*e^5 - 896*(x*e + d)^(5/2)*A*b^5*d^2*e^5 + 19110*(x*e + d)^(3/2)*B*a*b^4*d^3*e^5 + 490*(x*e + d)^(3/2)*A*b^5*d^3*e^5 - 5145*sqrt(x*e + d)*B*a*b^4*d^4*e^5 - 105*sqrt(x*e + d)*A*b^5*d^4*e^5 - 7110*(x*e + d)^(7/2)*B*a^2*b^3*e^6 - 790*(x*e + d)^(7/2)*A*a*b^4*e^6 + 25088*(x*e + d)^(5/2)*B*a^2*b^3*d*e^6 + 1792*(x*e + d)^(5/2)*A*a*b^4*d*e^6 - 27930*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^6 - 1470*(x*e + d)^(3/2)*A*a*b^4*d^2*e^6 + 10080*sqrt(x*e + d)*B*a^2*b^3*d^3*e^6 + 420*sqrt(x*e + d)*A*a*b^4*d^3*e^6 - 8064*(x*e + d)^(5/2)*B*a^3*b^2*e^7 - 896*(x*e + d)^(5/2)*A*a^2*b^3*e^7 + 18130*(x*e + d)^(3/2)*B*a^3*b^2*d*e^7 + 1470*(x*e + d)^(3/2)*A*a^2*b^3*d*e^7 - 9870*sqrt(x*e + d)*B*a^3*b^2*d^2*e^7 - 630*sqrt(x*e + d)*A*a^2*b^3*d^2*e^7 - 4410*(x*e + d)^(3/2)*B*a^4*b*e^8 - 490*(x*e + d)^(3/2)*A*a^3*b^2*e^8 + 4830*sqrt(x*e + d)*B*a^4*b*d*e^8 + 420*sqrt(x*e + d)*A*a^3*b^2*d*e^8 - 945*sqrt(x*e + d)*B*a^5*e^9 - 105*sqrt(x*e + d)*A*a^4*b*e^9)/((b^6*d - a*b^5*e)*((x*e + d)*b - b*d + a*e)^5)","B",0
1828,1,805,0,0.304870," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{{\left(10 \, B b d e^{4} - 7 \, B a e^{5} - 3 \, A b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\left(b^{6} d^{2} - 2 \, a b^{5} d e + a^{2} b^{4} e^{2}\right)} \sqrt{-b^{2} d + a b e}} - \frac{150 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{4} + 580 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{4} - 1280 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{4} + 700 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{4} - 150 \, \sqrt{x e + d} B b^{5} d^{5} e^{4} - 105 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{5} - 45 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{5} - 1370 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{5} + 210 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{5} + 3456 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{5} + 384 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{5} - 2590 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{5} - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{5} + 705 \, \sqrt{x e + d} B a b^{4} d^{4} e^{5} + 45 \, \sqrt{x e + d} A b^{5} d^{4} e^{5} + 790 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{6} - 210 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{6} - 3072 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{6} - 768 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{6} + 3570 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{6} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{6} - 1320 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{6} - 180 \, \sqrt{x e + d} A a b^{4} d^{3} e^{6} + 896 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{7} + 384 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{7} - 2170 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{7} - 630 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{7} + 1230 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{7} + 270 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{7} + 490 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{8} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{8} - 570 \, \sqrt{x e + d} B a^{4} b d e^{8} - 180 \, \sqrt{x e + d} A a^{3} b^{2} d e^{8} + 105 \, \sqrt{x e + d} B a^{5} e^{9} + 45 \, \sqrt{x e + d} A a^{4} b e^{9}}{1920 \, {\left(b^{6} d^{2} - 2 \, a b^{5} d e + a^{2} b^{4} e^{2}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"-1/128*(10*B*b*d*e^4 - 7*B*a*e^5 - 3*A*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^6*d^2 - 2*a*b^5*d*e + a^2*b^4*e^2)*sqrt(-b^2*d + a*b*e)) - 1/1920*(150*(x*e + d)^(9/2)*B*b^5*d*e^4 + 580*(x*e + d)^(7/2)*B*b^5*d^2*e^4 - 1280*(x*e + d)^(5/2)*B*b^5*d^3*e^4 + 700*(x*e + d)^(3/2)*B*b^5*d^4*e^4 - 150*sqrt(x*e + d)*B*b^5*d^5*e^4 - 105*(x*e + d)^(9/2)*B*a*b^4*e^5 - 45*(x*e + d)^(9/2)*A*b^5*e^5 - 1370*(x*e + d)^(7/2)*B*a*b^4*d*e^5 + 210*(x*e + d)^(7/2)*A*b^5*d*e^5 + 3456*(x*e + d)^(5/2)*B*a*b^4*d^2*e^5 + 384*(x*e + d)^(5/2)*A*b^5*d^2*e^5 - 2590*(x*e + d)^(3/2)*B*a*b^4*d^3*e^5 - 210*(x*e + d)^(3/2)*A*b^5*d^3*e^5 + 705*sqrt(x*e + d)*B*a*b^4*d^4*e^5 + 45*sqrt(x*e + d)*A*b^5*d^4*e^5 + 790*(x*e + d)^(7/2)*B*a^2*b^3*e^6 - 210*(x*e + d)^(7/2)*A*a*b^4*e^6 - 3072*(x*e + d)^(5/2)*B*a^2*b^3*d*e^6 - 768*(x*e + d)^(5/2)*A*a*b^4*d*e^6 + 3570*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^6 + 630*(x*e + d)^(3/2)*A*a*b^4*d^2*e^6 - 1320*sqrt(x*e + d)*B*a^2*b^3*d^3*e^6 - 180*sqrt(x*e + d)*A*a*b^4*d^3*e^6 + 896*(x*e + d)^(5/2)*B*a^3*b^2*e^7 + 384*(x*e + d)^(5/2)*A*a^2*b^3*e^7 - 2170*(x*e + d)^(3/2)*B*a^3*b^2*d*e^7 - 630*(x*e + d)^(3/2)*A*a^2*b^3*d*e^7 + 1230*sqrt(x*e + d)*B*a^3*b^2*d^2*e^7 + 270*sqrt(x*e + d)*A*a^2*b^3*d^2*e^7 + 490*(x*e + d)^(3/2)*B*a^4*b*e^8 + 210*(x*e + d)^(3/2)*A*a^3*b^2*e^8 - 570*sqrt(x*e + d)*B*a^4*b*d*e^8 - 180*sqrt(x*e + d)*A*a^3*b^2*d*e^8 + 105*sqrt(x*e + d)*B*a^5*e^9 + 45*sqrt(x*e + d)*A*a^4*b*e^9)/((b^6*d^2 - 2*a*b^5*d*e + a^2*b^4*e^2)*((x*e + d)*b - b*d + a*e)^5)","B",0
1829,1,814,0,0.267829," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B b d e^{4} - B a e^{5} - A b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{30 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{4} - 140 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{4} + 140 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{4} - 30 \, \sqrt{x e + d} B b^{5} d^{5} e^{4} - 15 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{5} - 15 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{5} + 210 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{5} + 70 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{5} + 128 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{5} - 128 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{5} - 490 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{5} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{5} + 135 \, \sqrt{x e + d} B a b^{4} d^{4} e^{5} + 15 \, \sqrt{x e + d} A b^{5} d^{4} e^{5} - 70 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{6} - 70 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{6} - 256 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{6} + 256 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{6} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{6} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{6} - 240 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{6} - 60 \, \sqrt{x e + d} A a b^{4} d^{3} e^{6} + 128 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{7} - 128 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{7} - 350 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{7} - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{7} + 210 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{7} + 90 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{7} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{8} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{8} - 90 \, \sqrt{x e + d} B a^{4} b d e^{8} - 60 \, \sqrt{x e + d} A a^{3} b^{2} d e^{8} + 15 \, \sqrt{x e + d} B a^{5} e^{9} + 15 \, \sqrt{x e + d} A a^{4} b e^{9}}{640 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"3/128*(2*B*b*d*e^4 - B*a*e^5 - A*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((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)*sqrt(-b^2*d + a*b*e)) + 1/640*(30*(x*e + d)^(9/2)*B*b^5*d*e^4 - 140*(x*e + d)^(7/2)*B*b^5*d^2*e^4 + 140*(x*e + d)^(3/2)*B*b^5*d^4*e^4 - 30*sqrt(x*e + d)*B*b^5*d^5*e^4 - 15*(x*e + d)^(9/2)*B*a*b^4*e^5 - 15*(x*e + d)^(9/2)*A*b^5*e^5 + 210*(x*e + d)^(7/2)*B*a*b^4*d*e^5 + 70*(x*e + d)^(7/2)*A*b^5*d*e^5 + 128*(x*e + d)^(5/2)*B*a*b^4*d^2*e^5 - 128*(x*e + d)^(5/2)*A*b^5*d^2*e^5 - 490*(x*e + d)^(3/2)*B*a*b^4*d^3*e^5 - 70*(x*e + d)^(3/2)*A*b^5*d^3*e^5 + 135*sqrt(x*e + d)*B*a*b^4*d^4*e^5 + 15*sqrt(x*e + d)*A*b^5*d^4*e^5 - 70*(x*e + d)^(7/2)*B*a^2*b^3*e^6 - 70*(x*e + d)^(7/2)*A*a*b^4*e^6 - 256*(x*e + d)^(5/2)*B*a^2*b^3*d*e^6 + 256*(x*e + d)^(5/2)*A*a*b^4*d*e^6 + 630*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^6 + 210*(x*e + d)^(3/2)*A*a*b^4*d^2*e^6 - 240*sqrt(x*e + d)*B*a^2*b^3*d^3*e^6 - 60*sqrt(x*e + d)*A*a*b^4*d^3*e^6 + 128*(x*e + d)^(5/2)*B*a^3*b^2*e^7 - 128*(x*e + d)^(5/2)*A*a^2*b^3*e^7 - 350*(x*e + d)^(3/2)*B*a^3*b^2*d*e^7 - 210*(x*e + d)^(3/2)*A*a^2*b^3*d*e^7 + 210*sqrt(x*e + d)*B*a^3*b^2*d^2*e^7 + 90*sqrt(x*e + d)*A*a^2*b^3*d^2*e^7 + 70*(x*e + d)^(3/2)*B*a^4*b*e^8 + 70*(x*e + d)^(3/2)*A*a^3*b^2*e^8 - 90*sqrt(x*e + d)*B*a^4*b*d*e^8 - 60*sqrt(x*e + d)*A*a^3*b^2*d*e^8 + 15*sqrt(x*e + d)*B*a^5*e^9 + 15*sqrt(x*e + d)*A*a^4*b*e^9)/((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*e + d)*b - b*d + a*e)^5)","B",0
1830,1,857,0,0.272311," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{{\left(10 \, B b d e^{4} - 3 \, B a e^{5} - 7 \, A b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\left(b^{6} d^{4} - 4 \, a b^{5} d^{3} e + 6 \, a^{2} b^{4} d^{2} e^{2} - 4 \, a^{3} b^{3} d e^{3} + a^{4} b^{2} e^{4}\right)} \sqrt{-b^{2} d + a b e}} - \frac{150 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{4} - 700 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{4} + 1280 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{4} - 580 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{4} - 150 \, \sqrt{x e + d} B b^{5} d^{5} e^{4} - 45 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{5} - 105 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{5} + 910 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{5} + 490 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{5} - 2944 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{5} - 896 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{5} + 1530 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{5} + 790 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{5} + 645 \, \sqrt{x e + d} B a b^{4} d^{4} e^{5} + 105 \, \sqrt{x e + d} A b^{5} d^{4} e^{5} - 210 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{6} - 490 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{6} + 2048 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{6} + 1792 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{6} - 1110 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{6} - 2370 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{6} - 1080 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{6} - 420 \, \sqrt{x e + d} A a b^{4} d^{3} e^{6} - 384 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{7} - 896 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{7} - 50 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{7} + 2370 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{7} + 870 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{7} + 630 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{7} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{8} - 790 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{8} - 330 \, \sqrt{x e + d} B a^{4} b d e^{8} - 420 \, \sqrt{x e + d} A a^{3} b^{2} d e^{8} + 45 \, \sqrt{x e + d} B a^{5} e^{9} + 105 \, \sqrt{x e + d} A a^{4} b e^{9}}{1920 \, {\left(b^{6} d^{4} - 4 \, a b^{5} d^{3} e + 6 \, a^{2} b^{4} d^{2} e^{2} - 4 \, a^{3} b^{3} d e^{3} + a^{4} b^{2} e^{4}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"-1/128*(10*B*b*d*e^4 - 3*B*a*e^5 - 7*A*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^6*d^4 - 4*a*b^5*d^3*e + 6*a^2*b^4*d^2*e^2 - 4*a^3*b^3*d*e^3 + a^4*b^2*e^4)*sqrt(-b^2*d + a*b*e)) - 1/1920*(150*(x*e + d)^(9/2)*B*b^5*d*e^4 - 700*(x*e + d)^(7/2)*B*b^5*d^2*e^4 + 1280*(x*e + d)^(5/2)*B*b^5*d^3*e^4 - 580*(x*e + d)^(3/2)*B*b^5*d^4*e^4 - 150*sqrt(x*e + d)*B*b^5*d^5*e^4 - 45*(x*e + d)^(9/2)*B*a*b^4*e^5 - 105*(x*e + d)^(9/2)*A*b^5*e^5 + 910*(x*e + d)^(7/2)*B*a*b^4*d*e^5 + 490*(x*e + d)^(7/2)*A*b^5*d*e^5 - 2944*(x*e + d)^(5/2)*B*a*b^4*d^2*e^5 - 896*(x*e + d)^(5/2)*A*b^5*d^2*e^5 + 1530*(x*e + d)^(3/2)*B*a*b^4*d^3*e^5 + 790*(x*e + d)^(3/2)*A*b^5*d^3*e^5 + 645*sqrt(x*e + d)*B*a*b^4*d^4*e^5 + 105*sqrt(x*e + d)*A*b^5*d^4*e^5 - 210*(x*e + d)^(7/2)*B*a^2*b^3*e^6 - 490*(x*e + d)^(7/2)*A*a*b^4*e^6 + 2048*(x*e + d)^(5/2)*B*a^2*b^3*d*e^6 + 1792*(x*e + d)^(5/2)*A*a*b^4*d*e^6 - 1110*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^6 - 2370*(x*e + d)^(3/2)*A*a*b^4*d^2*e^6 - 1080*sqrt(x*e + d)*B*a^2*b^3*d^3*e^6 - 420*sqrt(x*e + d)*A*a*b^4*d^3*e^6 - 384*(x*e + d)^(5/2)*B*a^3*b^2*e^7 - 896*(x*e + d)^(5/2)*A*a^2*b^3*e^7 - 50*(x*e + d)^(3/2)*B*a^3*b^2*d*e^7 + 2370*(x*e + d)^(3/2)*A*a^2*b^3*d*e^7 + 870*sqrt(x*e + d)*B*a^3*b^2*d^2*e^7 + 630*sqrt(x*e + d)*A*a^2*b^3*d^2*e^7 + 210*(x*e + d)^(3/2)*B*a^4*b*e^8 - 790*(x*e + d)^(3/2)*A*a^3*b^2*e^8 - 330*sqrt(x*e + d)*B*a^4*b*d*e^8 - 420*sqrt(x*e + d)*A*a^3*b^2*d*e^8 + 45*sqrt(x*e + d)*B*a^5*e^9 + 105*sqrt(x*e + d)*A*a^4*b*e^9)/((b^6*d^4 - 4*a*b^5*d^3*e + 6*a^2*b^4*d^2*e^2 - 4*a^3*b^3*d*e^3 + a^4*b^2*e^4)*((x*e + d)*b - b*d + a*e)^5)","B",0
1831,1,881,0,0.300147," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{7 \, {\left(10 \, B b d e^{4} - B a e^{5} - 9 \, A b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\left(b^{6} d^{5} - 5 \, a b^{5} d^{4} e + 10 \, a^{2} b^{4} d^{3} e^{2} - 10 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - a^{5} b e^{5}\right)} \sqrt{-b^{2} d + a b e}} + \frac{1050 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{4} - 4900 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{4} + 8960 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{4} - 7900 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{4} + 2790 \, \sqrt{x e + d} B b^{5} d^{5} e^{4} - 105 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{5} - 945 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{5} + 5390 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{5} + 4410 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{5} - 18816 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{5} - 8064 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{5} + 24490 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{5} + 7110 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{5} - 11055 \, \sqrt{x e + d} B a b^{4} d^{4} e^{5} - 2895 \, \sqrt{x e + d} A b^{5} d^{4} e^{5} - 490 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{6} - 4410 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{6} + 10752 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{6} + 16128 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{6} - 26070 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{6} - 21330 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{6} + 16320 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{6} + 11580 \, \sqrt{x e + d} A a b^{4} d^{3} e^{6} - 896 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{7} - 8064 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{7} + 10270 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{7} + 21330 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{7} - 10530 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{7} - 17370 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{7} - 790 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{8} - 7110 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{8} + 2370 \, \sqrt{x e + d} B a^{4} b d e^{8} + 11580 \, \sqrt{x e + d} A a^{3} b^{2} d e^{8} + 105 \, \sqrt{x e + d} B a^{5} e^{9} - 2895 \, \sqrt{x e + d} A a^{4} b e^{9}}{1920 \, {\left(b^{6} d^{5} - 5 \, a b^{5} d^{4} e + 10 \, a^{2} b^{4} d^{3} e^{2} - 10 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - a^{5} b e^{5}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"7/128*(10*B*b*d*e^4 - B*a*e^5 - 9*A*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^6*d^5 - 5*a*b^5*d^4*e + 10*a^2*b^4*d^3*e^2 - 10*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - a^5*b*e^5)*sqrt(-b^2*d + a*b*e)) + 1/1920*(1050*(x*e + d)^(9/2)*B*b^5*d*e^4 - 4900*(x*e + d)^(7/2)*B*b^5*d^2*e^4 + 8960*(x*e + d)^(5/2)*B*b^5*d^3*e^4 - 7900*(x*e + d)^(3/2)*B*b^5*d^4*e^4 + 2790*sqrt(x*e + d)*B*b^5*d^5*e^4 - 105*(x*e + d)^(9/2)*B*a*b^4*e^5 - 945*(x*e + d)^(9/2)*A*b^5*e^5 + 5390*(x*e + d)^(7/2)*B*a*b^4*d*e^5 + 4410*(x*e + d)^(7/2)*A*b^5*d*e^5 - 18816*(x*e + d)^(5/2)*B*a*b^4*d^2*e^5 - 8064*(x*e + d)^(5/2)*A*b^5*d^2*e^5 + 24490*(x*e + d)^(3/2)*B*a*b^4*d^3*e^5 + 7110*(x*e + d)^(3/2)*A*b^5*d^3*e^5 - 11055*sqrt(x*e + d)*B*a*b^4*d^4*e^5 - 2895*sqrt(x*e + d)*A*b^5*d^4*e^5 - 490*(x*e + d)^(7/2)*B*a^2*b^3*e^6 - 4410*(x*e + d)^(7/2)*A*a*b^4*e^6 + 10752*(x*e + d)^(5/2)*B*a^2*b^3*d*e^6 + 16128*(x*e + d)^(5/2)*A*a*b^4*d*e^6 - 26070*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^6 - 21330*(x*e + d)^(3/2)*A*a*b^4*d^2*e^6 + 16320*sqrt(x*e + d)*B*a^2*b^3*d^3*e^6 + 11580*sqrt(x*e + d)*A*a*b^4*d^3*e^6 - 896*(x*e + d)^(5/2)*B*a^3*b^2*e^7 - 8064*(x*e + d)^(5/2)*A*a^2*b^3*e^7 + 10270*(x*e + d)^(3/2)*B*a^3*b^2*d*e^7 + 21330*(x*e + d)^(3/2)*A*a^2*b^3*d*e^7 - 10530*sqrt(x*e + d)*B*a^3*b^2*d^2*e^7 - 17370*sqrt(x*e + d)*A*a^2*b^3*d^2*e^7 - 790*(x*e + d)^(3/2)*B*a^4*b*e^8 - 7110*(x*e + d)^(3/2)*A*a^3*b^2*e^8 + 2370*sqrt(x*e + d)*B*a^4*b*d*e^8 + 11580*sqrt(x*e + d)*A*a^3*b^2*d*e^8 + 105*sqrt(x*e + d)*B*a^5*e^9 - 2895*sqrt(x*e + d)*A*a^4*b*e^9)/((b^6*d^5 - 5*a*b^5*d^4*e + 10*a^2*b^4*d^3*e^2 - 10*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - a^5*b*e^5)*((x*e + d)*b - b*d + a*e)^5)","B",0
1832,1,994,0,0.365775," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{63 \, {\left(10 \, B b d e^{4} + B a e^{5} - 11 \, A b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(B d e^{4} - A e^{5}\right)}}{{\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)} \sqrt{x e + d}} + \frac{1870 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{4} - 8300 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{4} + 14080 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{4} - 10900 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{4} + 3250 \, \sqrt{x e + d} B b^{5} d^{5} e^{4} + 315 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{5} - 2185 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{5} + 6830 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{5} + 9770 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{5} - 25472 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{5} - 16768 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{5} + 30330 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{5} + 13270 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{5} - 12035 \, \sqrt{x e + d} B a b^{4} d^{4} e^{5} - 4215 \, \sqrt{x e + d} A b^{5} d^{4} e^{5} + 1470 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{6} - 9770 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{6} + 8704 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{6} + 33536 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{6} - 25590 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{6} - 39810 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{6} + 15640 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{6} + 16860 \, \sqrt{x e + d} A a b^{4} d^{3} e^{6} + 2688 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{7} - 16768 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{7} + 3790 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{7} + 39810 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{7} - 7210 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{7} - 25290 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{7} + 2370 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{8} - 13270 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{8} - 610 \, \sqrt{x e + d} B a^{4} b d e^{8} + 16860 \, \sqrt{x e + d} A a^{3} b^{2} d e^{8} + 965 \, \sqrt{x e + d} B a^{5} e^{9} - 4215 \, \sqrt{x e + d} A a^{4} b e^{9}}{640 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"63/128*(10*B*b*d*e^4 + B*a*e^5 - 11*A*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((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)*sqrt(-b^2*d + a*b*e)) + 2*(B*d*e^4 - A*e^5)/((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)*sqrt(x*e + d)) + 1/640*(1870*(x*e + d)^(9/2)*B*b^5*d*e^4 - 8300*(x*e + d)^(7/2)*B*b^5*d^2*e^4 + 14080*(x*e + d)^(5/2)*B*b^5*d^3*e^4 - 10900*(x*e + d)^(3/2)*B*b^5*d^4*e^4 + 3250*sqrt(x*e + d)*B*b^5*d^5*e^4 + 315*(x*e + d)^(9/2)*B*a*b^4*e^5 - 2185*(x*e + d)^(9/2)*A*b^5*e^5 + 6830*(x*e + d)^(7/2)*B*a*b^4*d*e^5 + 9770*(x*e + d)^(7/2)*A*b^5*d*e^5 - 25472*(x*e + d)^(5/2)*B*a*b^4*d^2*e^5 - 16768*(x*e + d)^(5/2)*A*b^5*d^2*e^5 + 30330*(x*e + d)^(3/2)*B*a*b^4*d^3*e^5 + 13270*(x*e + d)^(3/2)*A*b^5*d^3*e^5 - 12035*sqrt(x*e + d)*B*a*b^4*d^4*e^5 - 4215*sqrt(x*e + d)*A*b^5*d^4*e^5 + 1470*(x*e + d)^(7/2)*B*a^2*b^3*e^6 - 9770*(x*e + d)^(7/2)*A*a*b^4*e^6 + 8704*(x*e + d)^(5/2)*B*a^2*b^3*d*e^6 + 33536*(x*e + d)^(5/2)*A*a*b^4*d*e^6 - 25590*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^6 - 39810*(x*e + d)^(3/2)*A*a*b^4*d^2*e^6 + 15640*sqrt(x*e + d)*B*a^2*b^3*d^3*e^6 + 16860*sqrt(x*e + d)*A*a*b^4*d^3*e^6 + 2688*(x*e + d)^(5/2)*B*a^3*b^2*e^7 - 16768*(x*e + d)^(5/2)*A*a^2*b^3*e^7 + 3790*(x*e + d)^(3/2)*B*a^3*b^2*d*e^7 + 39810*(x*e + d)^(3/2)*A*a^2*b^3*d*e^7 - 7210*sqrt(x*e + d)*B*a^3*b^2*d^2*e^7 - 25290*sqrt(x*e + d)*A*a^2*b^3*d^2*e^7 + 2370*(x*e + d)^(3/2)*B*a^4*b*e^8 - 13270*(x*e + d)^(3/2)*A*a^3*b^2*e^8 - 610*sqrt(x*e + d)*B*a^4*b*d*e^8 + 16860*sqrt(x*e + d)*A*a^3*b^2*d*e^8 + 965*sqrt(x*e + d)*B*a^5*e^9 - 4215*sqrt(x*e + d)*A*a^4*b*e^9)/((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)*((x*e + d)*b - b*d + a*e)^5)","B",0
1833,1,1103,0,0.417417," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{231 \, {\left(10 \, B b^{2} d e^{4} + 3 \, B a b e^{5} - 13 \, A b^{2} e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)} B b d e^{4} + B b d^{2} e^{4} + 3 \, {\left(x e + d\right)} B a e^{5} - 18 \, {\left(x e + d\right)} A b e^{5} - B a d e^{5} - A b d e^{5} + A a e^{6}\right)}}{3 \, {\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)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{15450 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{6} d e^{4} - 66980 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} d^{2} e^{4} + 110080 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} d^{3} e^{4} - 81500 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d^{4} e^{4} + 22950 \, \sqrt{x e + d} B b^{6} d^{5} e^{4} + 6555 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{5} e^{5} - 22005 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{6} e^{5} + 37670 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{5} d e^{5} + 96290 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{6} d e^{5} - 169856 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} d^{2} e^{5} - 160384 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} d^{2} e^{5} + 204690 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d^{3} e^{5} + 121310 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d^{3} e^{5} - 79155 \, \sqrt{x e + d} B a b^{5} d^{4} e^{5} - 35595 \, \sqrt{x e + d} A b^{6} d^{4} e^{5} + 29310 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{4} e^{6} - 96290 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{5} e^{6} + 9472 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{4} d e^{6} + 320768 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{5} d e^{6} - 125070 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} d^{2} e^{6} - 363930 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} d^{2} e^{6} + 87120 \, \sqrt{x e + d} B a^{2} b^{4} d^{3} e^{6} + 142380 \, \sqrt{x e + d} A a b^{5} d^{3} e^{6} + 50304 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{3} e^{7} - 160384 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{4} e^{7} - 37930 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{3} d e^{7} + 363930 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{4} d e^{7} - 15930 \, \sqrt{x e + d} B a^{3} b^{3} d^{2} e^{7} - 213570 \, \sqrt{x e + d} A a^{2} b^{4} d^{2} e^{7} + 39810 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b^{2} e^{8} - 121310 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{3} e^{8} - 27630 \, \sqrt{x e + d} B a^{4} b^{2} d e^{8} + 142380 \, \sqrt{x e + d} A a^{3} b^{3} d e^{8} + 12645 \, \sqrt{x e + d} B a^{5} b e^{9} - 35595 \, \sqrt{x e + d} A a^{4} b^{2} e^{9}}{1920 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"231/128*(10*B*b^2*d*e^4 + 3*B*a*b*e^5 - 13*A*b^2*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((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)*sqrt(-b^2*d + a*b*e)) + 2/3*(15*(x*e + d)*B*b*d*e^4 + B*b*d^2*e^4 + 3*(x*e + d)*B*a*e^5 - 18*(x*e + d)*A*b*e^5 - B*a*d*e^5 - A*b*d*e^5 + A*a*e^6)/((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)*(x*e + d)^(3/2)) + 1/1920*(15450*(x*e + d)^(9/2)*B*b^6*d*e^4 - 66980*(x*e + d)^(7/2)*B*b^6*d^2*e^4 + 110080*(x*e + d)^(5/2)*B*b^6*d^3*e^4 - 81500*(x*e + d)^(3/2)*B*b^6*d^4*e^4 + 22950*sqrt(x*e + d)*B*b^6*d^5*e^4 + 6555*(x*e + d)^(9/2)*B*a*b^5*e^5 - 22005*(x*e + d)^(9/2)*A*b^6*e^5 + 37670*(x*e + d)^(7/2)*B*a*b^5*d*e^5 + 96290*(x*e + d)^(7/2)*A*b^6*d*e^5 - 169856*(x*e + d)^(5/2)*B*a*b^5*d^2*e^5 - 160384*(x*e + d)^(5/2)*A*b^6*d^2*e^5 + 204690*(x*e + d)^(3/2)*B*a*b^5*d^3*e^5 + 121310*(x*e + d)^(3/2)*A*b^6*d^3*e^5 - 79155*sqrt(x*e + d)*B*a*b^5*d^4*e^5 - 35595*sqrt(x*e + d)*A*b^6*d^4*e^5 + 29310*(x*e + d)^(7/2)*B*a^2*b^4*e^6 - 96290*(x*e + d)^(7/2)*A*a*b^5*e^6 + 9472*(x*e + d)^(5/2)*B*a^2*b^4*d*e^6 + 320768*(x*e + d)^(5/2)*A*a*b^5*d*e^6 - 125070*(x*e + d)^(3/2)*B*a^2*b^4*d^2*e^6 - 363930*(x*e + d)^(3/2)*A*a*b^5*d^2*e^6 + 87120*sqrt(x*e + d)*B*a^2*b^4*d^3*e^6 + 142380*sqrt(x*e + d)*A*a*b^5*d^3*e^6 + 50304*(x*e + d)^(5/2)*B*a^3*b^3*e^7 - 160384*(x*e + d)^(5/2)*A*a^2*b^4*e^7 - 37930*(x*e + d)^(3/2)*B*a^3*b^3*d*e^7 + 363930*(x*e + d)^(3/2)*A*a^2*b^4*d*e^7 - 15930*sqrt(x*e + d)*B*a^3*b^3*d^2*e^7 - 213570*sqrt(x*e + d)*A*a^2*b^4*d^2*e^7 + 39810*(x*e + d)^(3/2)*B*a^4*b^2*e^8 - 121310*(x*e + d)^(3/2)*A*a^3*b^3*e^8 - 27630*sqrt(x*e + d)*B*a^4*b^2*d*e^8 + 142380*sqrt(x*e + d)*A*a^3*b^3*d*e^8 + 12645*sqrt(x*e + d)*B*a^5*b*e^9 - 35595*sqrt(x*e + d)*A*a^4*b^2*e^9)/((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)*((x*e + d)*b - b*d + a*e)^5)","B",0
1834,1,1676,0,0.436725," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{3003 \, {\left(2 \, B b^{3} d e^{4} + B a b^{2} e^{5} - 3 \, A b^{3} e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, {\left(b^{8} d^{8} - 8 \, a b^{7} d^{7} e + 28 \, a^{2} b^{6} d^{6} e^{2} - 56 \, a^{3} b^{5} d^{5} e^{3} + 70 \, a^{4} b^{4} d^{4} e^{4} - 56 \, a^{5} b^{3} d^{3} e^{5} + 28 \, a^{6} b^{2} d^{2} e^{6} - 8 \, a^{7} b d e^{7} + a^{8} e^{8}\right)} \sqrt{-b^{2} d + a b e}} + \frac{90090 \, {\left(x e + d\right)}^{7} B b^{7} d e^{4} - 420420 \, {\left(x e + d\right)}^{6} B b^{7} d^{2} e^{4} + 768768 \, {\left(x e + d\right)}^{5} B b^{7} d^{3} e^{4} - 677820 \, {\left(x e + d\right)}^{4} B b^{7} d^{4} e^{4} + 275990 \, {\left(x e + d\right)}^{3} B b^{7} d^{5} e^{4} - 33280 \, {\left(x e + d\right)}^{2} B b^{7} d^{6} e^{4} - 2560 \, {\left(x e + d\right)} B b^{7} d^{7} e^{4} - 768 \, B b^{7} d^{8} e^{4} + 45045 \, {\left(x e + d\right)}^{7} B a b^{6} e^{5} - 135135 \, {\left(x e + d\right)}^{7} A b^{7} e^{5} + 210210 \, {\left(x e + d\right)}^{6} B a b^{6} d e^{5} + 630630 \, {\left(x e + d\right)}^{6} A b^{7} d e^{5} - 1153152 \, {\left(x e + d\right)}^{5} B a b^{6} d^{2} e^{5} - 1153152 \, {\left(x e + d\right)}^{5} A b^{7} d^{2} e^{5} + 1694550 \, {\left(x e + d\right)}^{4} B a b^{6} d^{3} e^{5} + 1016730 \, {\left(x e + d\right)}^{4} A b^{7} d^{3} e^{5} - 965965 \, {\left(x e + d\right)}^{3} B a b^{6} d^{4} e^{5} - 413985 \, {\left(x e + d\right)}^{3} A b^{7} d^{4} e^{5} + 149760 \, {\left(x e + d\right)}^{2} B a b^{6} d^{5} e^{5} + 49920 \, {\left(x e + d\right)}^{2} A b^{7} d^{5} e^{5} + 14080 \, {\left(x e + d\right)} B a b^{6} d^{6} e^{5} + 3840 \, {\left(x e + d\right)} A b^{7} d^{6} e^{5} + 5376 \, B a b^{6} d^{7} e^{5} + 768 \, A b^{7} d^{7} e^{5} + 210210 \, {\left(x e + d\right)}^{6} B a^{2} b^{5} e^{6} - 630630 \, {\left(x e + d\right)}^{6} A a b^{6} e^{6} + 2306304 \, {\left(x e + d\right)}^{5} A a b^{6} d e^{6} - 1016730 \, {\left(x e + d\right)}^{4} B a^{2} b^{5} d^{2} e^{6} - 3050190 \, {\left(x e + d\right)}^{4} A a b^{6} d^{2} e^{6} + 1103960 \, {\left(x e + d\right)}^{3} B a^{2} b^{5} d^{3} e^{6} + 1655940 \, {\left(x e + d\right)}^{3} A a b^{6} d^{3} e^{6} - 249600 \, {\left(x e + d\right)}^{2} B a^{2} b^{5} d^{4} e^{6} - 249600 \, {\left(x e + d\right)}^{2} A a b^{6} d^{4} e^{6} - 30720 \, {\left(x e + d\right)} B a^{2} b^{5} d^{5} e^{6} - 23040 \, {\left(x e + d\right)} A a b^{6} d^{5} e^{6} - 16128 \, B a^{2} b^{5} d^{6} e^{6} - 5376 \, A a b^{6} d^{6} e^{6} + 384384 \, {\left(x e + d\right)}^{5} B a^{3} b^{4} e^{7} - 1153152 \, {\left(x e + d\right)}^{5} A a^{2} b^{5} e^{7} - 338910 \, {\left(x e + d\right)}^{4} B a^{3} b^{4} d e^{7} + 3050190 \, {\left(x e + d\right)}^{4} A a^{2} b^{5} d e^{7} - 275990 \, {\left(x e + d\right)}^{3} B a^{3} b^{4} d^{2} e^{7} - 2483910 \, {\left(x e + d\right)}^{3} A a^{2} b^{5} d^{2} e^{7} + 166400 \, {\left(x e + d\right)}^{2} B a^{3} b^{4} d^{3} e^{7} + 499200 \, {\left(x e + d\right)}^{2} A a^{2} b^{5} d^{3} e^{7} + 32000 \, {\left(x e + d\right)} B a^{3} b^{4} d^{4} e^{7} + 57600 \, {\left(x e + d\right)} A a^{2} b^{5} d^{4} e^{7} + 26880 \, B a^{3} b^{4} d^{5} e^{7} + 16128 \, A a^{2} b^{5} d^{5} e^{7} + 338910 \, {\left(x e + d\right)}^{4} B a^{4} b^{3} e^{8} - 1016730 \, {\left(x e + d\right)}^{4} A a^{3} b^{4} e^{8} - 275990 \, {\left(x e + d\right)}^{3} B a^{4} b^{3} d e^{8} + 1655940 \, {\left(x e + d\right)}^{3} A a^{3} b^{4} d e^{8} - 499200 \, {\left(x e + d\right)}^{2} A a^{3} b^{4} d^{2} e^{8} - 12800 \, {\left(x e + d\right)} B a^{4} b^{3} d^{3} e^{8} - 76800 \, {\left(x e + d\right)} A a^{3} b^{4} d^{3} e^{8} - 26880 \, B a^{4} b^{3} d^{4} e^{8} - 26880 \, A a^{3} b^{4} d^{4} e^{8} + 137995 \, {\left(x e + d\right)}^{3} B a^{5} b^{2} e^{9} - 413985 \, {\left(x e + d\right)}^{3} A a^{4} b^{3} e^{9} - 49920 \, {\left(x e + d\right)}^{2} B a^{5} b^{2} d e^{9} + 249600 \, {\left(x e + d\right)}^{2} A a^{4} b^{3} d e^{9} - 3840 \, {\left(x e + d\right)} B a^{5} b^{2} d^{2} e^{9} + 57600 \, {\left(x e + d\right)} A a^{4} b^{3} d^{2} e^{9} + 16128 \, B a^{5} b^{2} d^{3} e^{9} + 26880 \, A a^{4} b^{3} d^{3} e^{9} + 16640 \, {\left(x e + d\right)}^{2} B a^{6} b e^{10} - 49920 \, {\left(x e + d\right)}^{2} A a^{5} b^{2} e^{10} + 5120 \, {\left(x e + d\right)} B a^{6} b d e^{10} - 23040 \, {\left(x e + d\right)} A a^{5} b^{2} d e^{10} - 5376 \, B a^{6} b d^{2} e^{10} - 16128 \, A a^{5} b^{2} d^{2} e^{10} - 1280 \, {\left(x e + d\right)} B a^{7} e^{11} + 3840 \, {\left(x e + d\right)} A a^{6} b e^{11} + 768 \, B a^{7} d e^{11} + 5376 \, A a^{6} b d e^{11} - 768 \, A a^{7} e^{12}}{1920 \, {\left(b^{8} d^{8} - 8 \, a b^{7} d^{7} e + 28 \, a^{2} b^{6} d^{6} e^{2} - 56 \, a^{3} b^{5} d^{5} e^{3} + 70 \, a^{4} b^{4} d^{4} e^{4} - 56 \, a^{5} b^{3} d^{3} e^{5} + 28 \, a^{6} b^{2} d^{2} e^{6} - 8 \, a^{7} b d e^{7} + a^{8} e^{8}\right)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}^{5}}"," ",0,"3003/128*(2*B*b^3*d*e^4 + B*a*b^2*e^5 - 3*A*b^3*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^8*d^8 - 8*a*b^7*d^7*e + 28*a^2*b^6*d^6*e^2 - 56*a^3*b^5*d^5*e^3 + 70*a^4*b^4*d^4*e^4 - 56*a^5*b^3*d^3*e^5 + 28*a^6*b^2*d^2*e^6 - 8*a^7*b*d*e^7 + a^8*e^8)*sqrt(-b^2*d + a*b*e)) + 1/1920*(90090*(x*e + d)^7*B*b^7*d*e^4 - 420420*(x*e + d)^6*B*b^7*d^2*e^4 + 768768*(x*e + d)^5*B*b^7*d^3*e^4 - 677820*(x*e + d)^4*B*b^7*d^4*e^4 + 275990*(x*e + d)^3*B*b^7*d^5*e^4 - 33280*(x*e + d)^2*B*b^7*d^6*e^4 - 2560*(x*e + d)*B*b^7*d^7*e^4 - 768*B*b^7*d^8*e^4 + 45045*(x*e + d)^7*B*a*b^6*e^5 - 135135*(x*e + d)^7*A*b^7*e^5 + 210210*(x*e + d)^6*B*a*b^6*d*e^5 + 630630*(x*e + d)^6*A*b^7*d*e^5 - 1153152*(x*e + d)^5*B*a*b^6*d^2*e^5 - 1153152*(x*e + d)^5*A*b^7*d^2*e^5 + 1694550*(x*e + d)^4*B*a*b^6*d^3*e^5 + 1016730*(x*e + d)^4*A*b^7*d^3*e^5 - 965965*(x*e + d)^3*B*a*b^6*d^4*e^5 - 413985*(x*e + d)^3*A*b^7*d^4*e^5 + 149760*(x*e + d)^2*B*a*b^6*d^5*e^5 + 49920*(x*e + d)^2*A*b^7*d^5*e^5 + 14080*(x*e + d)*B*a*b^6*d^6*e^5 + 3840*(x*e + d)*A*b^7*d^6*e^5 + 5376*B*a*b^6*d^7*e^5 + 768*A*b^7*d^7*e^5 + 210210*(x*e + d)^6*B*a^2*b^5*e^6 - 630630*(x*e + d)^6*A*a*b^6*e^6 + 2306304*(x*e + d)^5*A*a*b^6*d*e^6 - 1016730*(x*e + d)^4*B*a^2*b^5*d^2*e^6 - 3050190*(x*e + d)^4*A*a*b^6*d^2*e^6 + 1103960*(x*e + d)^3*B*a^2*b^5*d^3*e^6 + 1655940*(x*e + d)^3*A*a*b^6*d^3*e^6 - 249600*(x*e + d)^2*B*a^2*b^5*d^4*e^6 - 249600*(x*e + d)^2*A*a*b^6*d^4*e^6 - 30720*(x*e + d)*B*a^2*b^5*d^5*e^6 - 23040*(x*e + d)*A*a*b^6*d^5*e^6 - 16128*B*a^2*b^5*d^6*e^6 - 5376*A*a*b^6*d^6*e^6 + 384384*(x*e + d)^5*B*a^3*b^4*e^7 - 1153152*(x*e + d)^5*A*a^2*b^5*e^7 - 338910*(x*e + d)^4*B*a^3*b^4*d*e^7 + 3050190*(x*e + d)^4*A*a^2*b^5*d*e^7 - 275990*(x*e + d)^3*B*a^3*b^4*d^2*e^7 - 2483910*(x*e + d)^3*A*a^2*b^5*d^2*e^7 + 166400*(x*e + d)^2*B*a^3*b^4*d^3*e^7 + 499200*(x*e + d)^2*A*a^2*b^5*d^3*e^7 + 32000*(x*e + d)*B*a^3*b^4*d^4*e^7 + 57600*(x*e + d)*A*a^2*b^5*d^4*e^7 + 26880*B*a^3*b^4*d^5*e^7 + 16128*A*a^2*b^5*d^5*e^7 + 338910*(x*e + d)^4*B*a^4*b^3*e^8 - 1016730*(x*e + d)^4*A*a^3*b^4*e^8 - 275990*(x*e + d)^3*B*a^4*b^3*d*e^8 + 1655940*(x*e + d)^3*A*a^3*b^4*d*e^8 - 499200*(x*e + d)^2*A*a^3*b^4*d^2*e^8 - 12800*(x*e + d)*B*a^4*b^3*d^3*e^8 - 76800*(x*e + d)*A*a^3*b^4*d^3*e^8 - 26880*B*a^4*b^3*d^4*e^8 - 26880*A*a^3*b^4*d^4*e^8 + 137995*(x*e + d)^3*B*a^5*b^2*e^9 - 413985*(x*e + d)^3*A*a^4*b^3*e^9 - 49920*(x*e + d)^2*B*a^5*b^2*d*e^9 + 249600*(x*e + d)^2*A*a^4*b^3*d*e^9 - 3840*(x*e + d)*B*a^5*b^2*d^2*e^9 + 57600*(x*e + d)*A*a^4*b^3*d^2*e^9 + 16128*B*a^5*b^2*d^3*e^9 + 26880*A*a^4*b^3*d^3*e^9 + 16640*(x*e + d)^2*B*a^6*b*e^10 - 49920*(x*e + d)^2*A*a^5*b^2*e^10 + 5120*(x*e + d)*B*a^6*b*d*e^10 - 23040*(x*e + d)*A*a^5*b^2*d*e^10 - 5376*B*a^6*b*d^2*e^10 - 16128*A*a^5*b^2*d^2*e^10 - 1280*(x*e + d)*B*a^7*e^11 + 3840*(x*e + d)*A*a^6*b*e^11 + 768*B*a^7*d*e^11 + 5376*A*a^6*b*d*e^11 - 768*A*a^7*e^12)/((b^8*d^8 - 8*a*b^7*d^7*e + 28*a^2*b^6*d^6*e^2 - 56*a^3*b^5*d^5*e^3 + 70*a^4*b^4*d^4*e^4 - 56*a^5*b^3*d^3*e^5 + 28*a^6*b^2*d^2*e^6 - 8*a^7*b*d*e^7 + a^8*e^8)*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e)^5)","B",0
1835,1,1228,0,0.290173," ","integrate((B*x+A)*(e*x+d)^(7/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a d^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d^{4} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} A a d^{4} \mathrm{sgn}\left(b x + a\right) + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a d^{3} \mathrm{sgn}\left(b x + a\right) + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a d^{2} \mathrm{sgn}\left(b x + a\right) + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a d \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*d^4*e^(-1)*sgn(b*x + a) + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d^4*e^(-1)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d^4*e^(-2)*sgn(b*x + a) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*d^3*e^(-1)*sgn(b*x + a) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*d^3*e^(-1)*sgn(b*x + a) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*d^3*e^(-2)*sgn(b*x + a) + 45045*sqrt(x*e + d)*A*a*d^4*sgn(b*x + a) + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*d^3*sgn(b*x + a) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*d^2*e^(-1)*sgn(b*x + a) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*d^2*e^(-1)*sgn(b*x + a) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*d^2*e^(-2)*sgn(b*x + a) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*d^2*sgn(b*x + a) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*d*e^(-1)*sgn(b*x + a) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*d*e^(-1)*sgn(b*x + a) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*d*e^(-2)*sgn(b*x + a) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*d*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*e^(-1)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b*e^(-1)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b*e^(-2)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*sgn(b*x + a))*e^(-1)","B",0
1836,1,874,0,0.254972," ","integrate((B*x+A)*(e*x+d)^(5/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 3465 \, \sqrt{x e + d} A a d^{3} \mathrm{sgn}\left(b x + a\right) + 3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a d^{2} \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a d \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*d^3*e^(-1)*sgn(b*x + a) + 1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d^3*e^(-1)*sgn(b*x + a) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d^3*e^(-2)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*d^2*e^(-1)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*d^2*e^(-1)*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*d^2*e^(-2)*sgn(b*x + a) + 3465*sqrt(x*e + d)*A*a*d^3*sgn(b*x + a) + 3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*d^2*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*d*e^(-1)*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*d*e^(-1)*sgn(b*x + a) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*d*e^(-2)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*d*sgn(b*x + a) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*e^(-1)*sgn(b*x + a) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b*e^(-1)*sgn(b*x + a) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b*e^(-2)*sgn(b*x + a) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*sgn(b*x + a))*e^(-1)","B",0
1837,1,571,0,0.268405," ","integrate((B*x+A)*(e*x+d)^(3/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} A a d^{2} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a d \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*d^2*e^(-1)*sgn(b*x + a) + 105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d^2*e^(-1)*sgn(b*x + a) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d^2*e^(-2)*sgn(b*x + a) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*d*e^(-1)*sgn(b*x + a) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*d*e^(-1)*sgn(b*x + a) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*d*e^(-2)*sgn(b*x + a) + 315*sqrt(x*e + d)*A*a*d^2*sgn(b*x + a) + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*d*sgn(b*x + a) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*e^(-1)*sgn(b*x + a) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b*e^(-1)*sgn(b*x + a) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b*e^(-2)*sgn(b*x + a) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*sgn(b*x + a))*e^(-1)","B",0
1838,1,322,0,0.241220," ","integrate((B*x+A)*(e*x+d)^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} A a d \mathrm{sgn}\left(b x + a\right) + 35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*d*e^(-1)*sgn(b*x + a) + 35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*d*e^(-1)*sgn(b*x + a) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*d*e^(-2)*sgn(b*x + a) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a*e^(-1)*sgn(b*x + a) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*b*e^(-1)*sgn(b*x + a) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*b*e^(-2)*sgn(b*x + a) + 105*sqrt(x*e + d)*A*a*d*sgn(b*x + a) + 35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a*sgn(b*x + a))*e^(-1)","B",0
1839,1,133,0,0.169379," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} A a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/15*(5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a*e^(-1)*sgn(b*x + a) + 5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*b*e^(-1)*sgn(b*x + a) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*b*e^(-2)*sgn(b*x + a) + 15*sqrt(x*e + d)*A*a*sgn(b*x + a))*e^(-1)","A",0
1840,1,148,0,0.180388," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b e^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, \sqrt{x e + d} B b d e^{6} \mathrm{sgn}\left(b x + a\right) + 3 \, \sqrt{x e + d} B a e^{7} \mathrm{sgn}\left(b x + a\right) + 3 \, \sqrt{x e + d} A b e^{7} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-9\right)} - \frac{2 \, {\left(B b d^{2} \mathrm{sgn}\left(b x + a\right) - B a d e \mathrm{sgn}\left(b x + a\right) - A b d e \mathrm{sgn}\left(b x + a\right) + A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{\sqrt{x e + d}}"," ",0,"2/3*((x*e + d)^(3/2)*B*b*e^6*sgn(b*x + a) - 6*sqrt(x*e + d)*B*b*d*e^6*sgn(b*x + a) + 3*sqrt(x*e + d)*B*a*e^7*sgn(b*x + a) + 3*sqrt(x*e + d)*A*b*e^7*sgn(b*x + a))*e^(-9) - 2*(B*b*d^2*sgn(b*x + a) - B*a*d*e*sgn(b*x + a) - A*b*d*e*sgn(b*x + a) + A*a*e^2*sgn(b*x + a))*e^(-3)/sqrt(x*e + d)","A",0
1841,1,136,0,0.215333," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} B b e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + \frac{2 \, {\left(6 \, {\left(x e + d\right)} B b d \mathrm{sgn}\left(b x + a\right) - B b d^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)} B a e \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)} A b e \mathrm{sgn}\left(b x + a\right) + B a d e \mathrm{sgn}\left(b x + a\right) + A b d e \mathrm{sgn}\left(b x + a\right) - A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*sqrt(x*e + d)*B*b*e^(-3)*sgn(b*x + a) + 2/3*(6*(x*e + d)*B*b*d*sgn(b*x + a) - B*b*d^2*sgn(b*x + a) - 3*(x*e + d)*B*a*e*sgn(b*x + a) - 3*(x*e + d)*A*b*e*sgn(b*x + a) + B*a*d*e*sgn(b*x + a) + A*b*d*e*sgn(b*x + a) - A*a*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^(3/2)","A",0
1842,1,135,0,0.294066," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} B b \mathrm{sgn}\left(b x + a\right) - 10 \, {\left(x e + d\right)} B b d \mathrm{sgn}\left(b x + a\right) + 3 \, B b d^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)} B a e \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)} A b e \mathrm{sgn}\left(b x + a\right) - 3 \, B a d e \mathrm{sgn}\left(b x + a\right) - 3 \, A b d e \mathrm{sgn}\left(b x + a\right) + 3 \, A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(15*(x*e + d)^2*B*b*sgn(b*x + a) - 10*(x*e + d)*B*b*d*sgn(b*x + a) + 3*B*b*d^2*sgn(b*x + a) + 5*(x*e + d)*B*a*e*sgn(b*x + a) + 5*(x*e + d)*A*b*e*sgn(b*x + a) - 3*B*a*d*e*sgn(b*x + a) - 3*A*b*d*e*sgn(b*x + a) + 3*A*a*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^(5/2)","A",0
1843,1,3088,0,0.536291," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{765765} \, {\left(255255 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{3} d^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 765765 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} b d^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} b d^{4} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b^{2} d^{4} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 65637 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b^{2} d^{4} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{3} d^{4} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{3} d^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 204204 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 612612 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 262548 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 262548 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{2} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 9724 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 4420 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{3} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 765765 \, \sqrt{x e + d} A a^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 1021020 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 393822 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 43758 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 43758 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 19890 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{2} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{3} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} d^{2} \mathrm{sgn}\left(b x + a\right) + 9724 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 13260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 13260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 3060 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1020 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 476 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 87516 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} d \mathrm{sgn}\left(b x + a\right) + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3315 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 357 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 119 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/765765*(255255*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^3*d^4*e^(-1)*sgn(b*x + a) + 765765*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*b*d^4*e^(-1)*sgn(b*x + a) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*b*d^4*e^(-2)*sgn(b*x + a) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b^2*d^4*e^(-2)*sgn(b*x + a) + 65637*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b^2*d^4*e^(-3)*sgn(b*x + a) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^3*d^4*e^(-3)*sgn(b*x + a) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^3*d^4*e^(-4)*sgn(b*x + a) + 204204*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*d^3*e^(-1)*sgn(b*x + a) + 612612*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b*d^3*e^(-1)*sgn(b*x + a) + 262548*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b*d^3*e^(-2)*sgn(b*x + a) + 262548*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^2*d^3*e^(-2)*sgn(b*x + a) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^2*d^3*e^(-3)*sgn(b*x + a) + 9724*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^3*d^3*e^(-3)*sgn(b*x + a) + 4420*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^3*d^3*e^(-4)*sgn(b*x + a) + 765765*sqrt(x*e + d)*A*a^3*d^4*sgn(b*x + a) + 1021020*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*d^3*sgn(b*x + a) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*d^2*e^(-1)*sgn(b*x + a) + 393822*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b*d^2*e^(-1)*sgn(b*x + a) + 43758*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b*d^2*e^(-2)*sgn(b*x + a) + 43758*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^2*d^2*e^(-2)*sgn(b*x + a) + 19890*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^2*d^2*e^(-3)*sgn(b*x + a) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^3*d^2*e^(-3)*sgn(b*x + a) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^3*d^2*e^(-4)*sgn(b*x + a) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*d^2*sgn(b*x + a) + 9724*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*d*e^(-1)*sgn(b*x + a) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b*d*e^(-1)*sgn(b*x + a) + 13260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b*d*e^(-2)*sgn(b*x + a) + 13260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^2*d*e^(-2)*sgn(b*x + a) + 3060*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^2*d*e^(-3)*sgn(b*x + a) + 1020*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^3*d*e^(-3)*sgn(b*x + a) + 476*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^3*d*e^(-4)*sgn(b*x + a) + 87516*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*d*sgn(b*x + a) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*e^(-1)*sgn(b*x + a) + 3315*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b*e^(-1)*sgn(b*x + a) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b*e^(-2)*sgn(b*x + a) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^2*e^(-2)*sgn(b*x + a) + 357*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^2*e^(-3)*sgn(b*x + a) + 119*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^3*e^(-3)*sgn(b*x + a) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^3*e^(-4)*sgn(b*x + a) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*sgn(b*x + a))*e^(-1)","B",0
1844,1,2254,0,0.416292," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{3} d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} b d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b^{2} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{3} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 27027 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 11583 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 11583 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{2} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{3} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} A a^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} d^{2} \mathrm{sgn}\left(b x + a\right) + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 11583 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 585 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} d \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^3*d^3*e^(-1)*sgn(b*x + a) + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*b*d^3*e^(-1)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*b*d^3*e^(-2)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b^2*d^3*e^(-2)*sgn(b*x + a) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b^2*d^3*e^(-3)*sgn(b*x + a) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^3*d^3*e^(-3)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^3*d^3*e^(-4)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*d^2*e^(-1)*sgn(b*x + a) + 27027*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b*d^2*e^(-1)*sgn(b*x + a) + 11583*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b*d^2*e^(-2)*sgn(b*x + a) + 11583*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^2*d^2*e^(-2)*sgn(b*x + a) + 1287*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^2*d^2*e^(-3)*sgn(b*x + a) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^3*d^2*e^(-3)*sgn(b*x + a) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^3*d^2*e^(-4)*sgn(b*x + a) + 45045*sqrt(x*e + d)*A*a^3*d^3*sgn(b*x + a) + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*d^2*sgn(b*x + a) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*d*e^(-1)*sgn(b*x + a) + 11583*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b*d*e^(-1)*sgn(b*x + a) + 1287*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b*d*e^(-2)*sgn(b*x + a) + 1287*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^2*d*e^(-2)*sgn(b*x + a) + 585*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^2*d*e^(-3)*sgn(b*x + a) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^3*d*e^(-3)*sgn(b*x + a) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^3*d*e^(-4)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*d*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*e^(-1)*sgn(b*x + a) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b*e^(-1)*sgn(b*x + a) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b*e^(-2)*sgn(b*x + a) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^2*e^(-2)*sgn(b*x + a) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^2*e^(-3)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^3*e^(-3)*sgn(b*x + a) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^3*e^(-4)*sgn(b*x + a) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*sgn(b*x + a))*e^(-1)","B",0
1845,1,1524,0,0.343694," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{3} d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b^{2} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{3} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} A a^{3} d^{2} \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} d \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^3*d^2*e^(-1)*sgn(b*x + a) + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*b*d^2*e^(-1)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*b*d^2*e^(-2)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b^2*d^2*e^(-2)*sgn(b*x + a) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b^2*d^2*e^(-3)*sgn(b*x + a) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^3*d^2*e^(-3)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^3*d^2*e^(-4)*sgn(b*x + a) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*d*e^(-1)*sgn(b*x + a) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b*d*e^(-1)*sgn(b*x + a) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b*d*e^(-2)*sgn(b*x + a) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^2*d*e^(-2)*sgn(b*x + a) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^2*d*e^(-3)*sgn(b*x + a) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^3*d*e^(-3)*sgn(b*x + a) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^3*d*e^(-4)*sgn(b*x + a) + 45045*sqrt(x*e + d)*A*a^3*d^2*sgn(b*x + a) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*d*sgn(b*x + a) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*e^(-1)*sgn(b*x + a) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b*e^(-1)*sgn(b*x + a) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b*e^(-2)*sgn(b*x + a) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^2*e^(-2)*sgn(b*x + a) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^2*e^(-3)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^3*e^(-3)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^3*e^(-4)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*sgn(b*x + a))*e^(-1)","B",0
1846,1,898,0,0.272577," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{3} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{2} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 3465 \, \sqrt{x e + d} A a^{3} d \mathrm{sgn}\left(b x + a\right) + 1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^3*d*e^(-1)*sgn(b*x + a) + 3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*b*d*e^(-1)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*b*d*e^(-2)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b^2*d*e^(-2)*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b^2*d*e^(-3)*sgn(b*x + a) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^3*d*e^(-3)*sgn(b*x + a) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^3*d*e^(-4)*sgn(b*x + a) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^3*e^(-1)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^2*b*e^(-1)*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^2*b*e^(-2)*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a*b^2*e^(-2)*sgn(b*x + a) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a*b^2*e^(-3)*sgn(b*x + a) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*b^3*e^(-3)*sgn(b*x + a) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*b^3*e^(-4)*sgn(b*x + a) + 3465*sqrt(x*e + d)*A*a^3*d*sgn(b*x + a) + 1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^3*sgn(b*x + a))*e^(-1)","B",0
1847,1,393,0,0.234494," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{2} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 27 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} A a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^3*e^(-1)*sgn(b*x + a) + 315*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^2*b*e^(-1)*sgn(b*x + a) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^2*b*e^(-2)*sgn(b*x + a) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a*b^2*e^(-2)*sgn(b*x + a) + 27*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a*b^2*e^(-3)*sgn(b*x + a) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*b^3*e^(-3)*sgn(b*x + a) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*b^3*e^(-4)*sgn(b*x + a) + 315*sqrt(x*e + d)*A*a^3*sgn(b*x + a))*e^(-1)","A",0
1848,1,525,0,0.305470," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{3} e^{30} \mathrm{sgn}\left(b x + a\right) - 28 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} d e^{30} \mathrm{sgn}\left(b x + a\right) + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d^{2} e^{30} \mathrm{sgn}\left(b x + a\right) - 140 \, \sqrt{x e + d} B b^{3} d^{3} e^{30} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{2} e^{31} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{3} e^{31} \mathrm{sgn}\left(b x + a\right) - 105 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} d e^{31} \mathrm{sgn}\left(b x + a\right) - 35 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} d e^{31} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} B a b^{2} d^{2} e^{31} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} A b^{3} d^{2} e^{31} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b e^{32} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{2} e^{32} \mathrm{sgn}\left(b x + a\right) - 210 \, \sqrt{x e + d} B a^{2} b d e^{32} \mathrm{sgn}\left(b x + a\right) - 210 \, \sqrt{x e + d} A a b^{2} d e^{32} \mathrm{sgn}\left(b x + a\right) + 35 \, \sqrt{x e + d} B a^{3} e^{33} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} A a^{2} b e^{33} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-35\right)} - \frac{2 \, {\left(B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{\sqrt{x e + d}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*B*b^3*e^30*sgn(b*x + a) - 28*(x*e + d)^(5/2)*B*b^3*d*e^30*sgn(b*x + a) + 70*(x*e + d)^(3/2)*B*b^3*d^2*e^30*sgn(b*x + a) - 140*sqrt(x*e + d)*B*b^3*d^3*e^30*sgn(b*x + a) + 21*(x*e + d)^(5/2)*B*a*b^2*e^31*sgn(b*x + a) + 7*(x*e + d)^(5/2)*A*b^3*e^31*sgn(b*x + a) - 105*(x*e + d)^(3/2)*B*a*b^2*d*e^31*sgn(b*x + a) - 35*(x*e + d)^(3/2)*A*b^3*d*e^31*sgn(b*x + a) + 315*sqrt(x*e + d)*B*a*b^2*d^2*e^31*sgn(b*x + a) + 105*sqrt(x*e + d)*A*b^3*d^2*e^31*sgn(b*x + a) + 35*(x*e + d)^(3/2)*B*a^2*b*e^32*sgn(b*x + a) + 35*(x*e + d)^(3/2)*A*a*b^2*e^32*sgn(b*x + a) - 210*sqrt(x*e + d)*B*a^2*b*d*e^32*sgn(b*x + a) - 210*sqrt(x*e + d)*A*a*b^2*d*e^32*sgn(b*x + a) + 35*sqrt(x*e + d)*B*a^3*e^33*sgn(b*x + a) + 105*sqrt(x*e + d)*A*a^2*b*e^33*sgn(b*x + a))*e^(-35) - 2*(B*b^3*d^4*sgn(b*x + a) - 3*B*a*b^2*d^3*e*sgn(b*x + a) - A*b^3*d^3*e*sgn(b*x + a) + 3*B*a^2*b*d^2*e^2*sgn(b*x + a) + 3*A*a*b^2*d^2*e^2*sgn(b*x + a) - B*a^3*d*e^3*sgn(b*x + a) - 3*A*a^2*b*d*e^3*sgn(b*x + a) + A*a^3*e^4*sgn(b*x + a))*e^(-5)/sqrt(x*e + d)","B",0
1849,1,509,0,0.254430," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{3} e^{20} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d e^{20} \mathrm{sgn}\left(b x + a\right) + 90 \, \sqrt{x e + d} B b^{3} d^{2} e^{20} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} e^{21} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} e^{21} \mathrm{sgn}\left(b x + a\right) - 135 \, \sqrt{x e + d} B a b^{2} d e^{21} \mathrm{sgn}\left(b x + a\right) - 45 \, \sqrt{x e + d} A b^{3} d e^{21} \mathrm{sgn}\left(b x + a\right) + 45 \, \sqrt{x e + d} B a^{2} b e^{22} \mathrm{sgn}\left(b x + a\right) + 45 \, \sqrt{x e + d} A a b^{2} e^{22} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-25\right)} + \frac{2 \, {\left(12 \, {\left(x e + d\right)} B b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 27 \, {\left(x e + d\right)} B a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - 9 \, {\left(x e + d\right)} A b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(x e + d\right)} B a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(x e + d\right)} A a b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)} B a^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 9 \, {\left(x e + d\right)} A a^{2} b e^{3} \mathrm{sgn}\left(b x + a\right) + B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) - A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*B*b^3*e^20*sgn(b*x + a) - 20*(x*e + d)^(3/2)*B*b^3*d*e^20*sgn(b*x + a) + 90*sqrt(x*e + d)*B*b^3*d^2*e^20*sgn(b*x + a) + 15*(x*e + d)^(3/2)*B*a*b^2*e^21*sgn(b*x + a) + 5*(x*e + d)^(3/2)*A*b^3*e^21*sgn(b*x + a) - 135*sqrt(x*e + d)*B*a*b^2*d*e^21*sgn(b*x + a) - 45*sqrt(x*e + d)*A*b^3*d*e^21*sgn(b*x + a) + 45*sqrt(x*e + d)*B*a^2*b*e^22*sgn(b*x + a) + 45*sqrt(x*e + d)*A*a*b^2*e^22*sgn(b*x + a))*e^(-25) + 2/3*(12*(x*e + d)*B*b^3*d^3*sgn(b*x + a) - B*b^3*d^4*sgn(b*x + a) - 27*(x*e + d)*B*a*b^2*d^2*e*sgn(b*x + a) - 9*(x*e + d)*A*b^3*d^2*e*sgn(b*x + a) + 3*B*a*b^2*d^3*e*sgn(b*x + a) + A*b^3*d^3*e*sgn(b*x + a) + 18*(x*e + d)*B*a^2*b*d*e^2*sgn(b*x + a) + 18*(x*e + d)*A*a*b^2*d*e^2*sgn(b*x + a) - 3*B*a^2*b*d^2*e^2*sgn(b*x + a) - 3*A*a*b^2*d^2*e^2*sgn(b*x + a) - 3*(x*e + d)*B*a^3*e^3*sgn(b*x + a) - 9*(x*e + d)*A*a^2*b*e^3*sgn(b*x + a) + B*a^3*d*e^3*sgn(b*x + a) + 3*A*a^2*b*d*e^3*sgn(b*x + a) - A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^(3/2)","B",0
1850,1,508,0,0.256215," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{3} e^{10} \mathrm{sgn}\left(b x + a\right) - 12 \, \sqrt{x e + d} B b^{3} d e^{10} \mathrm{sgn}\left(b x + a\right) + 9 \, \sqrt{x e + d} B a b^{2} e^{11} \mathrm{sgn}\left(b x + a\right) + 3 \, \sqrt{x e + d} A b^{3} e^{11} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-15\right)} - \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} B b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)} B b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, B b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) - 135 \, {\left(x e + d\right)}^{2} B a b^{2} d e \mathrm{sgn}\left(b x + a\right) - 45 \, {\left(x e + d\right)}^{2} A b^{3} d e \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(x e + d\right)} B a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)} A b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 9 \, B a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(x e + d\right)}^{2} B a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(x e + d\right)}^{2} A a b^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)} B a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)} A a b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, B a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, A a b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)} B a^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)} A a^{2} b e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, B a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 9 \, A a^{2} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*B*b^3*e^10*sgn(b*x + a) - 12*sqrt(x*e + d)*B*b^3*d*e^10*sgn(b*x + a) + 9*sqrt(x*e + d)*B*a*b^2*e^11*sgn(b*x + a) + 3*sqrt(x*e + d)*A*b^3*e^11*sgn(b*x + a))*e^(-15) - 2/15*(90*(x*e + d)^2*B*b^3*d^2*sgn(b*x + a) - 20*(x*e + d)*B*b^3*d^3*sgn(b*x + a) + 3*B*b^3*d^4*sgn(b*x + a) - 135*(x*e + d)^2*B*a*b^2*d*e*sgn(b*x + a) - 45*(x*e + d)^2*A*b^3*d*e*sgn(b*x + a) + 45*(x*e + d)*B*a*b^2*d^2*e*sgn(b*x + a) + 15*(x*e + d)*A*b^3*d^2*e*sgn(b*x + a) - 9*B*a*b^2*d^3*e*sgn(b*x + a) - 3*A*b^3*d^3*e*sgn(b*x + a) + 45*(x*e + d)^2*B*a^2*b*e^2*sgn(b*x + a) + 45*(x*e + d)^2*A*a*b^2*e^2*sgn(b*x + a) - 30*(x*e + d)*B*a^2*b*d*e^2*sgn(b*x + a) - 30*(x*e + d)*A*a*b^2*d*e^2*sgn(b*x + a) + 9*B*a^2*b*d^2*e^2*sgn(b*x + a) + 9*A*a*b^2*d^2*e^2*sgn(b*x + a) + 5*(x*e + d)*B*a^3*e^3*sgn(b*x + a) + 15*(x*e + d)*A*a^2*b*e^3*sgn(b*x + a) - 3*B*a^3*d*e^3*sgn(b*x + a) - 9*A*a^2*b*d*e^3*sgn(b*x + a) + 3*A*a^3*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^(5/2)","B",0
1851,1,5468,0,0.775089," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{5} d^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 24249225 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} b d^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 4849845 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} b d^{4} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 9699690 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b^{2} d^{4} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 4157010 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b^{2} d^{4} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 4157010 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{3} d^{4} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 461890 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{3} d^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{4} d^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{4} d^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{5} d^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{5} d^{4} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 3879876 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 19399380 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 8314020 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 16628040 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1847560 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{2} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1847560 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 839800 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{3} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 419900 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{4} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 96900 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{4} d^{3} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 19380 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{5} d^{3} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 9044 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{5} d^{3} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 14549535 \, \sqrt{x e + d} A a^{5} d^{4} \mathrm{sgn}\left(b x + a\right) + 19399380 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} d^{3} \mathrm{sgn}\left(b x + a\right) + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{5} d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 12471030 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 1385670 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 2771340 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1259700 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b^{2} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1259700 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 290700 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{3} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 145350 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 67830 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{4} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{5} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 798 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{5} d^{2} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{5} d^{2} \mathrm{sgn}\left(b x + a\right) + 184756 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{5} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 923780 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{4} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 419900 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{4} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 839800 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{3} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 193800 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{3} b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 193800 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{2} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 90440 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{2} b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 45220 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 2660 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a b^{4} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 532 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 252 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B b^{5} d e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 1662804 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{5} d \mathrm{sgn}\left(b x + a\right) + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{5} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 24225 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{4} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 48450 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 22610 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{3} b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 22610 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1330 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a^{2} b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 665 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B a b^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} A b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} B b^{5} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^5*d^4*e^(-1)*sgn(b*x + a) + 24249225*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*b*d^4*e^(-1)*sgn(b*x + a) + 4849845*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*b*d^4*e^(-2)*sgn(b*x + a) + 9699690*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b^2*d^4*e^(-2)*sgn(b*x + a) + 4157010*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b^2*d^4*e^(-3)*sgn(b*x + a) + 4157010*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^3*d^4*e^(-3)*sgn(b*x + a) + 461890*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^3*d^4*e^(-4)*sgn(b*x + a) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^4*d^4*e^(-4)*sgn(b*x + a) + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^4*d^4*e^(-5)*sgn(b*x + a) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^5*d^4*e^(-5)*sgn(b*x + a) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^5*d^4*e^(-6)*sgn(b*x + a) + 3879876*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*d^3*e^(-1)*sgn(b*x + a) + 19399380*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b*d^3*e^(-1)*sgn(b*x + a) + 8314020*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b*d^3*e^(-2)*sgn(b*x + a) + 16628040*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^2*d^3*e^(-2)*sgn(b*x + a) + 1847560*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^2*d^3*e^(-3)*sgn(b*x + a) + 1847560*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^3*d^3*e^(-3)*sgn(b*x + a) + 839800*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^3*d^3*e^(-4)*sgn(b*x + a) + 419900*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^4*d^3*e^(-4)*sgn(b*x + a) + 96900*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^4*d^3*e^(-5)*sgn(b*x + a) + 19380*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^5*d^3*e^(-5)*sgn(b*x + a) + 9044*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^5*d^3*e^(-6)*sgn(b*x + a) + 14549535*sqrt(x*e + d)*A*a^5*d^4*sgn(b*x + a) + 19399380*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*d^3*sgn(b*x + a) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^5*d^2*e^(-1)*sgn(b*x + a) + 12471030*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*b*d^2*e^(-1)*sgn(b*x + a) + 1385670*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b*d^2*e^(-2)*sgn(b*x + a) + 2771340*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b^2*d^2*e^(-2)*sgn(b*x + a) + 1259700*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^2*d^2*e^(-3)*sgn(b*x + a) + 1259700*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^3*d^2*e^(-3)*sgn(b*x + a) + 290700*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^3*d^2*e^(-4)*sgn(b*x + a) + 145350*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^4*d^2*e^(-4)*sgn(b*x + a) + 67830*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^4*d^2*e^(-5)*sgn(b*x + a) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^5*d^2*e^(-5)*sgn(b*x + a) + 798*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^5*d^2*e^(-6)*sgn(b*x + a) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^5*d^2*sgn(b*x + a) + 184756*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^5*d*e^(-1)*sgn(b*x + a) + 923780*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^4*b*d*e^(-1)*sgn(b*x + a) + 419900*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^4*b*d*e^(-2)*sgn(b*x + a) + 839800*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^3*b^2*d*e^(-2)*sgn(b*x + a) + 193800*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^3*b^2*d*e^(-3)*sgn(b*x + a) + 193800*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^2*b^3*d*e^(-3)*sgn(b*x + a) + 90440*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^2*b^3*d*e^(-4)*sgn(b*x + a) + 45220*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a*b^4*d*e^(-4)*sgn(b*x + a) + 2660*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a*b^4*d*e^(-5)*sgn(b*x + a) + 532*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*b^5*d*e^(-5)*sgn(b*x + a) + 252*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*b^5*d*e^(-6)*sgn(b*x + a) + 1662804*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^5*d*sgn(b*x + a) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^5*e^(-1)*sgn(b*x + a) + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^4*b*e^(-1)*sgn(b*x + a) + 24225*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^4*b*e^(-2)*sgn(b*x + a) + 48450*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^3*b^2*e^(-2)*sgn(b*x + a) + 22610*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^3*b^2*e^(-3)*sgn(b*x + a) + 22610*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a^2*b^3*e^(-3)*sgn(b*x + a) + 1330*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a^2*b^3*e^(-4)*sgn(b*x + a) + 665*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*a*b^4*e^(-4)*sgn(b*x + a) + 315*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*a*b^4*e^(-5)*sgn(b*x + a) + 63*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*A*b^5*e^(-5)*sgn(b*x + a) + 15*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*B*b^5*e^(-6)*sgn(b*x + a) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^5*sgn(b*x + a))*e^(-1)","B",0
1852,1,4050,0,0.615018," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{5} d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 24249225 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 4849845 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} b d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 9699690 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 4157010 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b^{2} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 4157010 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 461890 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{3} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{4} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{4} d^{3} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{5} d^{3} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{5} d^{3} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 14549535 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 6235515 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 12471030 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1385670 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{2} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1385670 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 629850 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{3} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{4} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 14535 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{5} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 6783 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{5} d^{2} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 14549535 \, \sqrt{x e + d} A a^{5} d^{3} \mathrm{sgn}\left(b x + a\right) + 14549535 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} d^{2} \mathrm{sgn}\left(b x + a\right) + 1247103 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{5} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 6235515 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1385670 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 629850 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 629850 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 145350 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 33915 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{4} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 6783 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 399 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{5} d e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{5} d \mathrm{sgn}\left(b x + a\right) + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{5} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{4} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 209950 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 48450 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{3} b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 48450 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 22610 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a^{2} b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 11305 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 665 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B a b^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} A b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} B b^{5} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^5*d^3*e^(-1)*sgn(b*x + a) + 24249225*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*b*d^3*e^(-1)*sgn(b*x + a) + 4849845*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*b*d^3*e^(-2)*sgn(b*x + a) + 9699690*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b^2*d^3*e^(-2)*sgn(b*x + a) + 4157010*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b^2*d^3*e^(-3)*sgn(b*x + a) + 4157010*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^3*d^3*e^(-3)*sgn(b*x + a) + 461890*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^3*d^3*e^(-4)*sgn(b*x + a) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^4*d^3*e^(-4)*sgn(b*x + a) + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^4*d^3*e^(-5)*sgn(b*x + a) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^5*d^3*e^(-5)*sgn(b*x + a) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^5*d^3*e^(-6)*sgn(b*x + a) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*d^2*e^(-1)*sgn(b*x + a) + 14549535*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b*d^2*e^(-1)*sgn(b*x + a) + 6235515*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b*d^2*e^(-2)*sgn(b*x + a) + 12471030*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^2*d^2*e^(-2)*sgn(b*x + a) + 1385670*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^2*d^2*e^(-3)*sgn(b*x + a) + 1385670*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^3*d^2*e^(-3)*sgn(b*x + a) + 629850*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^3*d^2*e^(-4)*sgn(b*x + a) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^4*d^2*e^(-4)*sgn(b*x + a) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^4*d^2*e^(-5)*sgn(b*x + a) + 14535*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^5*d^2*e^(-5)*sgn(b*x + a) + 6783*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^5*d^2*e^(-6)*sgn(b*x + a) + 14549535*sqrt(x*e + d)*A*a^5*d^3*sgn(b*x + a) + 14549535*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*d^2*sgn(b*x + a) + 1247103*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^5*d*e^(-1)*sgn(b*x + a) + 6235515*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*b*d*e^(-1)*sgn(b*x + a) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b*d*e^(-2)*sgn(b*x + a) + 1385670*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b^2*d*e^(-2)*sgn(b*x + a) + 629850*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^2*d*e^(-3)*sgn(b*x + a) + 629850*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^3*d*e^(-3)*sgn(b*x + a) + 145350*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^3*d*e^(-4)*sgn(b*x + a) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^4*d*e^(-4)*sgn(b*x + a) + 33915*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^4*d*e^(-5)*sgn(b*x + a) + 6783*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^5*d*e^(-5)*sgn(b*x + a) + 399*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^5*d*e^(-6)*sgn(b*x + a) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^5*d*sgn(b*x + a) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^5*e^(-1)*sgn(b*x + a) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^4*b*e^(-1)*sgn(b*x + a) + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^4*b*e^(-2)*sgn(b*x + a) + 209950*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^3*b^2*e^(-2)*sgn(b*x + a) + 48450*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^3*b^2*e^(-3)*sgn(b*x + a) + 48450*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^2*b^3*e^(-3)*sgn(b*x + a) + 22610*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^2*b^3*e^(-4)*sgn(b*x + a) + 11305*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a*b^4*e^(-4)*sgn(b*x + a) + 665*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a*b^4*e^(-5)*sgn(b*x + a) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*b^5*e^(-5)*sgn(b*x + a) + 63*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*b^5*e^(-6)*sgn(b*x + a) + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^5*sgn(b*x + a))*e^(-1)","B",0
1853,1,2788,0,0.479332," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{765765} \, {\left(255255 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{5} d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 1276275 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 255255 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} b d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 510510 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 218790 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b^{2} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 218790 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 24310 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{3} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 5525 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{4} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{5} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{5} d^{2} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 102102 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 510510 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 218790 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 437580 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 48620 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 48620 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 22100 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 11050 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 2550 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{4} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 510 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{5} d e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 765765 \, \sqrt{x e + d} A a^{5} d^{2} \mathrm{sgn}\left(b x + a\right) + 510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} d \mathrm{sgn}\left(b x + a\right) + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{5} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 109395 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{4} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 24310 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 11050 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{3} b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 11050 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 2550 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a^{2} b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 1275 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 595 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B a b^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 119 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} A b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} B b^{5} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/765765*(255255*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^5*d^2*e^(-1)*sgn(b*x + a) + 1276275*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*b*d^2*e^(-1)*sgn(b*x + a) + 255255*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*b*d^2*e^(-2)*sgn(b*x + a) + 510510*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b^2*d^2*e^(-2)*sgn(b*x + a) + 218790*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b^2*d^2*e^(-3)*sgn(b*x + a) + 218790*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^3*d^2*e^(-3)*sgn(b*x + a) + 24310*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^3*d^2*e^(-4)*sgn(b*x + a) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^4*d^2*e^(-4)*sgn(b*x + a) + 5525*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^4*d^2*e^(-5)*sgn(b*x + a) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^5*d^2*e^(-5)*sgn(b*x + a) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^5*d^2*e^(-6)*sgn(b*x + a) + 102102*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*d*e^(-1)*sgn(b*x + a) + 510510*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b*d*e^(-1)*sgn(b*x + a) + 218790*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b*d*e^(-2)*sgn(b*x + a) + 437580*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^2*d*e^(-2)*sgn(b*x + a) + 48620*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^2*d*e^(-3)*sgn(b*x + a) + 48620*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^3*d*e^(-3)*sgn(b*x + a) + 22100*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^3*d*e^(-4)*sgn(b*x + a) + 11050*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^4*d*e^(-4)*sgn(b*x + a) + 2550*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^4*d*e^(-5)*sgn(b*x + a) + 510*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^5*d*e^(-5)*sgn(b*x + a) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^5*d*e^(-6)*sgn(b*x + a) + 765765*sqrt(x*e + d)*A*a^5*d^2*sgn(b*x + a) + 510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*d*sgn(b*x + a) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^5*e^(-1)*sgn(b*x + a) + 109395*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^4*b*e^(-1)*sgn(b*x + a) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b*e^(-2)*sgn(b*x + a) + 24310*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^3*b^2*e^(-2)*sgn(b*x + a) + 11050*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^2*e^(-3)*sgn(b*x + a) + 11050*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^3*e^(-3)*sgn(b*x + a) + 2550*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^2*b^3*e^(-4)*sgn(b*x + a) + 1275*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a*b^4*e^(-4)*sgn(b*x + a) + 595*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^4*e^(-5)*sgn(b*x + a) + 119*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^5*e^(-5)*sgn(b*x + a) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*b^5*e^(-6)*sgn(b*x + a) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^5*sgn(b*x + a))*e^(-1)","B",0
1854,1,1682,0,0.394041," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{5} d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 75075 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15015 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} b d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 12870 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b^{2} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 12870 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1430 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{3} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 715 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 325 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{4} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{5} d e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{5} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15015 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 6435 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{4} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 12870 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1430 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{3} b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1430 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 650 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a^{2} b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 325 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 75 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B a b^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} A b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} B b^{5} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} A a^{5} d \mathrm{sgn}\left(b x + a\right) + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^5*d*e^(-1)*sgn(b*x + a) + 75075*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*b*d*e^(-1)*sgn(b*x + a) + 15015*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*b*d*e^(-2)*sgn(b*x + a) + 30030*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b^2*d*e^(-2)*sgn(b*x + a) + 12870*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b^2*d*e^(-3)*sgn(b*x + a) + 12870*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^3*d*e^(-3)*sgn(b*x + a) + 1430*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^3*d*e^(-4)*sgn(b*x + a) + 715*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^4*d*e^(-4)*sgn(b*x + a) + 325*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^4*d*e^(-5)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^5*d*e^(-5)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^5*d*e^(-6)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^5*e^(-1)*sgn(b*x + a) + 15015*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b*e^(-1)*sgn(b*x + a) + 6435*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^4*b*e^(-2)*sgn(b*x + a) + 12870*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^3*b^2*e^(-2)*sgn(b*x + a) + 1430*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^2*e^(-3)*sgn(b*x + a) + 1430*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^2*b^3*e^(-3)*sgn(b*x + a) + 650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^3*e^(-4)*sgn(b*x + a) + 325*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^4*e^(-4)*sgn(b*x + a) + 75*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a*b^4*e^(-5)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*b^5*e^(-5)*sgn(b*x + a) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*b^5*e^(-6)*sgn(b*x + a) + 45045*sqrt(x*e + d)*A*a^5*d*sgn(b*x + a) + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^5*sgn(b*x + a))*e^(-1)","B",0
1855,1,758,0,0.246951," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{9009} \, {\left(3003 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} B a^{5} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} A a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} B a^{4} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} A a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} B a^{3} b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} A a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} B a^{2} b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} A a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} B a b^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 13 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} A b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} B b^{5} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, \sqrt{x e + d} A a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/9009*(3003*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^5*e^(-1)*sgn(b*x + a) + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*A*a^4*b*e^(-1)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*B*a^4*b*e^(-2)*sgn(b*x + a) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^3*b^2*e^(-2)*sgn(b*x + a) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*B*a^3*b^2*e^(-3)*sgn(b*x + a) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^2*b^3*e^(-3)*sgn(b*x + a) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^2*b^3*e^(-4)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a*b^4*e^(-4)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a*b^4*e^(-5)*sgn(b*x + a) + 13*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*b^5*e^(-5)*sgn(b*x + a) + 3*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*b^5*e^(-6)*sgn(b*x + a) + 9009*sqrt(x*e + d)*A*a^5*sgn(b*x + a))*e^(-1)","B",0
1856,1,1125,0,0.334611," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{693} \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} B b^{5} e^{70} \mathrm{sgn}\left(b x + a\right) - 462 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} d e^{70} \mathrm{sgn}\left(b x + a\right) + 1485 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{70} \mathrm{sgn}\left(b x + a\right) - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{70} \mathrm{sgn}\left(b x + a\right) + 3465 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{70} \mathrm{sgn}\left(b x + a\right) - 4158 \, \sqrt{x e + d} B b^{5} d^{5} e^{70} \mathrm{sgn}\left(b x + a\right) + 385 \, {\left(x e + d\right)}^{\frac{9}{2}} B a b^{4} e^{71} \mathrm{sgn}\left(b x + a\right) + 77 \, {\left(x e + d\right)}^{\frac{9}{2}} A b^{5} e^{71} \mathrm{sgn}\left(b x + a\right) - 2475 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{71} \mathrm{sgn}\left(b x + a\right) - 495 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{71} \mathrm{sgn}\left(b x + a\right) + 6930 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{71} \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{71} \mathrm{sgn}\left(b x + a\right) - 11550 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{71} \mathrm{sgn}\left(b x + a\right) - 2310 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{71} \mathrm{sgn}\left(b x + a\right) + 17325 \, \sqrt{x e + d} B a b^{4} d^{4} e^{71} \mathrm{sgn}\left(b x + a\right) + 3465 \, \sqrt{x e + d} A b^{5} d^{4} e^{71} \mathrm{sgn}\left(b x + a\right) + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{72} \mathrm{sgn}\left(b x + a\right) + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{72} \mathrm{sgn}\left(b x + a\right) - 5544 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{72} \mathrm{sgn}\left(b x + a\right) - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{72} \mathrm{sgn}\left(b x + a\right) + 13860 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{72} \mathrm{sgn}\left(b x + a\right) + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{72} \mathrm{sgn}\left(b x + a\right) - 27720 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{72} \mathrm{sgn}\left(b x + a\right) - 13860 \, \sqrt{x e + d} A a b^{4} d^{3} e^{72} \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{73} \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{73} \mathrm{sgn}\left(b x + a\right) - 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{73} \mathrm{sgn}\left(b x + a\right) - 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{73} \mathrm{sgn}\left(b x + a\right) + 20790 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{73} \mathrm{sgn}\left(b x + a\right) + 20790 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{73} \mathrm{sgn}\left(b x + a\right) + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{74} \mathrm{sgn}\left(b x + a\right) + 2310 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{74} \mathrm{sgn}\left(b x + a\right) - 6930 \, \sqrt{x e + d} B a^{4} b d e^{74} \mathrm{sgn}\left(b x + a\right) - 13860 \, \sqrt{x e + d} A a^{3} b^{2} d e^{74} \mathrm{sgn}\left(b x + a\right) + 693 \, \sqrt{x e + d} B a^{5} e^{75} \mathrm{sgn}\left(b x + a\right) + 3465 \, \sqrt{x e + d} A a^{4} b e^{75} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-77\right)} - \frac{2 \, {\left(B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{\sqrt{x e + d}}"," ",0,"2/693*(63*(x*e + d)^(11/2)*B*b^5*e^70*sgn(b*x + a) - 462*(x*e + d)^(9/2)*B*b^5*d*e^70*sgn(b*x + a) + 1485*(x*e + d)^(7/2)*B*b^5*d^2*e^70*sgn(b*x + a) - 2772*(x*e + d)^(5/2)*B*b^5*d^3*e^70*sgn(b*x + a) + 3465*(x*e + d)^(3/2)*B*b^5*d^4*e^70*sgn(b*x + a) - 4158*sqrt(x*e + d)*B*b^5*d^5*e^70*sgn(b*x + a) + 385*(x*e + d)^(9/2)*B*a*b^4*e^71*sgn(b*x + a) + 77*(x*e + d)^(9/2)*A*b^5*e^71*sgn(b*x + a) - 2475*(x*e + d)^(7/2)*B*a*b^4*d*e^71*sgn(b*x + a) - 495*(x*e + d)^(7/2)*A*b^5*d*e^71*sgn(b*x + a) + 6930*(x*e + d)^(5/2)*B*a*b^4*d^2*e^71*sgn(b*x + a) + 1386*(x*e + d)^(5/2)*A*b^5*d^2*e^71*sgn(b*x + a) - 11550*(x*e + d)^(3/2)*B*a*b^4*d^3*e^71*sgn(b*x + a) - 2310*(x*e + d)^(3/2)*A*b^5*d^3*e^71*sgn(b*x + a) + 17325*sqrt(x*e + d)*B*a*b^4*d^4*e^71*sgn(b*x + a) + 3465*sqrt(x*e + d)*A*b^5*d^4*e^71*sgn(b*x + a) + 990*(x*e + d)^(7/2)*B*a^2*b^3*e^72*sgn(b*x + a) + 495*(x*e + d)^(7/2)*A*a*b^4*e^72*sgn(b*x + a) - 5544*(x*e + d)^(5/2)*B*a^2*b^3*d*e^72*sgn(b*x + a) - 2772*(x*e + d)^(5/2)*A*a*b^4*d*e^72*sgn(b*x + a) + 13860*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^72*sgn(b*x + a) + 6930*(x*e + d)^(3/2)*A*a*b^4*d^2*e^72*sgn(b*x + a) - 27720*sqrt(x*e + d)*B*a^2*b^3*d^3*e^72*sgn(b*x + a) - 13860*sqrt(x*e + d)*A*a*b^4*d^3*e^72*sgn(b*x + a) + 1386*(x*e + d)^(5/2)*B*a^3*b^2*e^73*sgn(b*x + a) + 1386*(x*e + d)^(5/2)*A*a^2*b^3*e^73*sgn(b*x + a) - 6930*(x*e + d)^(3/2)*B*a^3*b^2*d*e^73*sgn(b*x + a) - 6930*(x*e + d)^(3/2)*A*a^2*b^3*d*e^73*sgn(b*x + a) + 20790*sqrt(x*e + d)*B*a^3*b^2*d^2*e^73*sgn(b*x + a) + 20790*sqrt(x*e + d)*A*a^2*b^3*d^2*e^73*sgn(b*x + a) + 1155*(x*e + d)^(3/2)*B*a^4*b*e^74*sgn(b*x + a) + 2310*(x*e + d)^(3/2)*A*a^3*b^2*e^74*sgn(b*x + a) - 6930*sqrt(x*e + d)*B*a^4*b*d*e^74*sgn(b*x + a) - 13860*sqrt(x*e + d)*A*a^3*b^2*d*e^74*sgn(b*x + a) + 693*sqrt(x*e + d)*B*a^5*e^75*sgn(b*x + a) + 3465*sqrt(x*e + d)*A*a^4*b*e^75*sgn(b*x + a))*e^(-77) - 2*(B*b^5*d^6*sgn(b*x + a) - 5*B*a*b^4*d^5*e*sgn(b*x + a) - A*b^5*d^5*e*sgn(b*x + a) + 10*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 5*A*a*b^4*d^4*e^2*sgn(b*x + a) - 10*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 10*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 5*B*a^4*b*d^2*e^4*sgn(b*x + a) + 10*A*a^3*b^2*d^2*e^4*sgn(b*x + a) - B*a^5*d*e^5*sgn(b*x + a) - 5*A*a^4*b*d*e^5*sgn(b*x + a) + A*a^5*e^6*sgn(b*x + a))*e^(-7)/sqrt(x*e + d)","B",0
1857,1,1101,0,0.396557," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{63} \, {\left(7 \, {\left(x e + d\right)}^{\frac{9}{2}} B b^{5} e^{56} \mathrm{sgn}\left(b x + a\right) - 54 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d e^{56} \mathrm{sgn}\left(b x + a\right) + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{2} e^{56} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{3} e^{56} \mathrm{sgn}\left(b x + a\right) + 945 \, \sqrt{x e + d} B b^{5} d^{4} e^{56} \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} e^{57} \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} e^{57} \mathrm{sgn}\left(b x + a\right) - 315 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d e^{57} \mathrm{sgn}\left(b x + a\right) - 63 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d e^{57} \mathrm{sgn}\left(b x + a\right) + 1050 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{2} e^{57} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{2} e^{57} \mathrm{sgn}\left(b x + a\right) - 3150 \, \sqrt{x e + d} B a b^{4} d^{3} e^{57} \mathrm{sgn}\left(b x + a\right) - 630 \, \sqrt{x e + d} A b^{5} d^{3} e^{57} \mathrm{sgn}\left(b x + a\right) + 126 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} e^{58} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} e^{58} \mathrm{sgn}\left(b x + a\right) - 840 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d e^{58} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d e^{58} \mathrm{sgn}\left(b x + a\right) + 3780 \, \sqrt{x e + d} B a^{2} b^{3} d^{2} e^{58} \mathrm{sgn}\left(b x + a\right) + 1890 \, \sqrt{x e + d} A a b^{4} d^{2} e^{58} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} e^{59} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} e^{59} \mathrm{sgn}\left(b x + a\right) - 1890 \, \sqrt{x e + d} B a^{3} b^{2} d e^{59} \mathrm{sgn}\left(b x + a\right) - 1890 \, \sqrt{x e + d} A a^{2} b^{3} d e^{59} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} B a^{4} b e^{60} \mathrm{sgn}\left(b x + a\right) + 630 \, \sqrt{x e + d} A a^{3} b^{2} e^{60} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-63\right)} + \frac{2 \, {\left(18 \, {\left(x e + d\right)} B b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 75 \, {\left(x e + d\right)} B a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) - 15 \, {\left(x e + d\right)} A b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)} B a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)} A a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 90 \, {\left(x e + d\right)} B a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 90 \, {\left(x e + d\right)} A a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)} B a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)} A a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - 5 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 10 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)} B a^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 15 \, {\left(x e + d\right)} A a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right) + B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) - A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/63*(7*(x*e + d)^(9/2)*B*b^5*e^56*sgn(b*x + a) - 54*(x*e + d)^(7/2)*B*b^5*d*e^56*sgn(b*x + a) + 189*(x*e + d)^(5/2)*B*b^5*d^2*e^56*sgn(b*x + a) - 420*(x*e + d)^(3/2)*B*b^5*d^3*e^56*sgn(b*x + a) + 945*sqrt(x*e + d)*B*b^5*d^4*e^56*sgn(b*x + a) + 45*(x*e + d)^(7/2)*B*a*b^4*e^57*sgn(b*x + a) + 9*(x*e + d)^(7/2)*A*b^5*e^57*sgn(b*x + a) - 315*(x*e + d)^(5/2)*B*a*b^4*d*e^57*sgn(b*x + a) - 63*(x*e + d)^(5/2)*A*b^5*d*e^57*sgn(b*x + a) + 1050*(x*e + d)^(3/2)*B*a*b^4*d^2*e^57*sgn(b*x + a) + 210*(x*e + d)^(3/2)*A*b^5*d^2*e^57*sgn(b*x + a) - 3150*sqrt(x*e + d)*B*a*b^4*d^3*e^57*sgn(b*x + a) - 630*sqrt(x*e + d)*A*b^5*d^3*e^57*sgn(b*x + a) + 126*(x*e + d)^(5/2)*B*a^2*b^3*e^58*sgn(b*x + a) + 63*(x*e + d)^(5/2)*A*a*b^4*e^58*sgn(b*x + a) - 840*(x*e + d)^(3/2)*B*a^2*b^3*d*e^58*sgn(b*x + a) - 420*(x*e + d)^(3/2)*A*a*b^4*d*e^58*sgn(b*x + a) + 3780*sqrt(x*e + d)*B*a^2*b^3*d^2*e^58*sgn(b*x + a) + 1890*sqrt(x*e + d)*A*a*b^4*d^2*e^58*sgn(b*x + a) + 210*(x*e + d)^(3/2)*B*a^3*b^2*e^59*sgn(b*x + a) + 210*(x*e + d)^(3/2)*A*a^2*b^3*e^59*sgn(b*x + a) - 1890*sqrt(x*e + d)*B*a^3*b^2*d*e^59*sgn(b*x + a) - 1890*sqrt(x*e + d)*A*a^2*b^3*d*e^59*sgn(b*x + a) + 315*sqrt(x*e + d)*B*a^4*b*e^60*sgn(b*x + a) + 630*sqrt(x*e + d)*A*a^3*b^2*e^60*sgn(b*x + a))*e^(-63) + 2/3*(18*(x*e + d)*B*b^5*d^5*sgn(b*x + a) - B*b^5*d^6*sgn(b*x + a) - 75*(x*e + d)*B*a*b^4*d^4*e*sgn(b*x + a) - 15*(x*e + d)*A*b^5*d^4*e*sgn(b*x + a) + 5*B*a*b^4*d^5*e*sgn(b*x + a) + A*b^5*d^5*e*sgn(b*x + a) + 120*(x*e + d)*B*a^2*b^3*d^3*e^2*sgn(b*x + a) + 60*(x*e + d)*A*a*b^4*d^3*e^2*sgn(b*x + a) - 10*B*a^2*b^3*d^4*e^2*sgn(b*x + a) - 5*A*a*b^4*d^4*e^2*sgn(b*x + a) - 90*(x*e + d)*B*a^3*b^2*d^2*e^3*sgn(b*x + a) - 90*(x*e + d)*A*a^2*b^3*d^2*e^3*sgn(b*x + a) + 10*B*a^3*b^2*d^3*e^3*sgn(b*x + a) + 10*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 30*(x*e + d)*B*a^4*b*d*e^4*sgn(b*x + a) + 60*(x*e + d)*A*a^3*b^2*d*e^4*sgn(b*x + a) - 5*B*a^4*b*d^2*e^4*sgn(b*x + a) - 10*A*a^3*b^2*d^2*e^4*sgn(b*x + a) - 3*(x*e + d)*B*a^5*e^5*sgn(b*x + a) - 15*(x*e + d)*A*a^4*b*e^5*sgn(b*x + a) + B*a^5*d*e^5*sgn(b*x + a) + 5*A*a^4*b*d*e^5*sgn(b*x + a) - A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(3/2)","B",0
1858,1,1101,0,0.354890," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} e^{42} \mathrm{sgn}\left(b x + a\right) - 126 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d e^{42} \mathrm{sgn}\left(b x + a\right) + 525 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{2} e^{42} \mathrm{sgn}\left(b x + a\right) - 2100 \, \sqrt{x e + d} B b^{5} d^{3} e^{42} \mathrm{sgn}\left(b x + a\right) + 105 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} e^{43} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} e^{43} \mathrm{sgn}\left(b x + a\right) - 875 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d e^{43} \mathrm{sgn}\left(b x + a\right) - 175 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d e^{43} \mathrm{sgn}\left(b x + a\right) + 5250 \, \sqrt{x e + d} B a b^{4} d^{2} e^{43} \mathrm{sgn}\left(b x + a\right) + 1050 \, \sqrt{x e + d} A b^{5} d^{2} e^{43} \mathrm{sgn}\left(b x + a\right) + 350 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} e^{44} \mathrm{sgn}\left(b x + a\right) + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} e^{44} \mathrm{sgn}\left(b x + a\right) - 4200 \, \sqrt{x e + d} B a^{2} b^{3} d e^{44} \mathrm{sgn}\left(b x + a\right) - 2100 \, \sqrt{x e + d} A a b^{4} d e^{44} \mathrm{sgn}\left(b x + a\right) + 1050 \, \sqrt{x e + d} B a^{3} b^{2} e^{45} \mathrm{sgn}\left(b x + a\right) + 1050 \, \sqrt{x e + d} A a^{2} b^{3} e^{45} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-49\right)} - \frac{2 \, {\left(225 \, {\left(x e + d\right)}^{2} B b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)} B b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, B b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) - 750 \, {\left(x e + d\right)}^{2} B a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) - 150 \, {\left(x e + d\right)}^{2} A b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) + 125 \, {\left(x e + d\right)} B a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 25 \, {\left(x e + d\right)} A b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 15 \, B a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 900 \, {\left(x e + d\right)}^{2} B a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 450 \, {\left(x e + d\right)}^{2} A a b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 200 \, {\left(x e + d\right)} B a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 100 \, {\left(x e + d\right)} A a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, B a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, A a b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 450 \, {\left(x e + d\right)}^{2} B a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - 450 \, {\left(x e + d\right)}^{2} A a^{2} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 150 \, {\left(x e + d\right)} B a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 150 \, {\left(x e + d\right)} A a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, B a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, A a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 75 \, {\left(x e + d\right)}^{2} B a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) + 150 \, {\left(x e + d\right)}^{2} A a^{3} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 50 \, {\left(x e + d\right)} B a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - 100 \, {\left(x e + d\right)} A a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, B a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, A a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)} B a^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 25 \, {\left(x e + d\right)} A a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right) - 3 \, B a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) - 15 \, A a^{4} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, A a^{5} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/105*(15*(x*e + d)^(7/2)*B*b^5*e^42*sgn(b*x + a) - 126*(x*e + d)^(5/2)*B*b^5*d*e^42*sgn(b*x + a) + 525*(x*e + d)^(3/2)*B*b^5*d^2*e^42*sgn(b*x + a) - 2100*sqrt(x*e + d)*B*b^5*d^3*e^42*sgn(b*x + a) + 105*(x*e + d)^(5/2)*B*a*b^4*e^43*sgn(b*x + a) + 21*(x*e + d)^(5/2)*A*b^5*e^43*sgn(b*x + a) - 875*(x*e + d)^(3/2)*B*a*b^4*d*e^43*sgn(b*x + a) - 175*(x*e + d)^(3/2)*A*b^5*d*e^43*sgn(b*x + a) + 5250*sqrt(x*e + d)*B*a*b^4*d^2*e^43*sgn(b*x + a) + 1050*sqrt(x*e + d)*A*b^5*d^2*e^43*sgn(b*x + a) + 350*(x*e + d)^(3/2)*B*a^2*b^3*e^44*sgn(b*x + a) + 175*(x*e + d)^(3/2)*A*a*b^4*e^44*sgn(b*x + a) - 4200*sqrt(x*e + d)*B*a^2*b^3*d*e^44*sgn(b*x + a) - 2100*sqrt(x*e + d)*A*a*b^4*d*e^44*sgn(b*x + a) + 1050*sqrt(x*e + d)*B*a^3*b^2*e^45*sgn(b*x + a) + 1050*sqrt(x*e + d)*A*a^2*b^3*e^45*sgn(b*x + a))*e^(-49) - 2/15*(225*(x*e + d)^2*B*b^5*d^4*sgn(b*x + a) - 30*(x*e + d)*B*b^5*d^5*sgn(b*x + a) + 3*B*b^5*d^6*sgn(b*x + a) - 750*(x*e + d)^2*B*a*b^4*d^3*e*sgn(b*x + a) - 150*(x*e + d)^2*A*b^5*d^3*e*sgn(b*x + a) + 125*(x*e + d)*B*a*b^4*d^4*e*sgn(b*x + a) + 25*(x*e + d)*A*b^5*d^4*e*sgn(b*x + a) - 15*B*a*b^4*d^5*e*sgn(b*x + a) - 3*A*b^5*d^5*e*sgn(b*x + a) + 900*(x*e + d)^2*B*a^2*b^3*d^2*e^2*sgn(b*x + a) + 450*(x*e + d)^2*A*a*b^4*d^2*e^2*sgn(b*x + a) - 200*(x*e + d)*B*a^2*b^3*d^3*e^2*sgn(b*x + a) - 100*(x*e + d)*A*a*b^4*d^3*e^2*sgn(b*x + a) + 30*B*a^2*b^3*d^4*e^2*sgn(b*x + a) + 15*A*a*b^4*d^4*e^2*sgn(b*x + a) - 450*(x*e + d)^2*B*a^3*b^2*d*e^3*sgn(b*x + a) - 450*(x*e + d)^2*A*a^2*b^3*d*e^3*sgn(b*x + a) + 150*(x*e + d)*B*a^3*b^2*d^2*e^3*sgn(b*x + a) + 150*(x*e + d)*A*a^2*b^3*d^2*e^3*sgn(b*x + a) - 30*B*a^3*b^2*d^3*e^3*sgn(b*x + a) - 30*A*a^2*b^3*d^3*e^3*sgn(b*x + a) + 75*(x*e + d)^2*B*a^4*b*e^4*sgn(b*x + a) + 150*(x*e + d)^2*A*a^3*b^2*e^4*sgn(b*x + a) - 50*(x*e + d)*B*a^4*b*d*e^4*sgn(b*x + a) - 100*(x*e + d)*A*a^3*b^2*d*e^4*sgn(b*x + a) + 15*B*a^4*b*d^2*e^4*sgn(b*x + a) + 30*A*a^3*b^2*d^2*e^4*sgn(b*x + a) + 5*(x*e + d)*B*a^5*e^5*sgn(b*x + a) + 25*(x*e + d)*A*a^4*b*e^5*sgn(b*x + a) - 3*B*a^5*d*e^5*sgn(b*x + a) - 15*A*a^4*b*d*e^5*sgn(b*x + a) + 3*A*a^5*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(5/2)","B",0
1859,1,497,0,0.234120," ","integrate((B*x+A)*(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - A b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, B a^{2} b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, A a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{3} b d e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - B a^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + A a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{4}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} e^{7} \mathrm{sgn}\left(b x + a\right) - 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d e^{7} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d e^{7} \mathrm{sgn}\left(b x + a\right) - 105 \, \sqrt{x e + d} B a b^{5} d^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} A b^{6} d^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} e^{8} \mathrm{sgn}\left(b x + a\right) - 35 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} e^{8} \mathrm{sgn}\left(b x + a\right) + 210 \, \sqrt{x e + d} B a^{2} b^{4} d e^{8} \mathrm{sgn}\left(b x + a\right) - 210 \, \sqrt{x e + d} A a b^{5} d e^{8} \mathrm{sgn}\left(b x + a\right) - 105 \, \sqrt{x e + d} B a^{3} b^{3} e^{9} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} A a^{2} b^{4} e^{9} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{105 \, b^{7}}"," ",0,"-2*(B*a*b^3*d^3*sgn(b*x + a) - A*b^4*d^3*sgn(b*x + a) - 3*B*a^2*b^2*d^2*e*sgn(b*x + a) + 3*A*a*b^3*d^2*e*sgn(b*x + a) + 3*B*a^3*b*d*e^2*sgn(b*x + a) - 3*A*a^2*b^2*d*e^2*sgn(b*x + a) - B*a^4*e^3*sgn(b*x + a) + A*a^3*b*e^3*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) + 2/105*(15*(x*e + d)^(7/2)*B*b^6*e^6*sgn(b*x + a) - 21*(x*e + d)^(5/2)*B*a*b^5*e^7*sgn(b*x + a) + 21*(x*e + d)^(5/2)*A*b^6*e^7*sgn(b*x + a) - 35*(x*e + d)^(3/2)*B*a*b^5*d*e^7*sgn(b*x + a) + 35*(x*e + d)^(3/2)*A*b^6*d*e^7*sgn(b*x + a) - 105*sqrt(x*e + d)*B*a*b^5*d^2*e^7*sgn(b*x + a) + 105*sqrt(x*e + d)*A*b^6*d^2*e^7*sgn(b*x + a) + 35*(x*e + d)^(3/2)*B*a^2*b^4*e^8*sgn(b*x + a) - 35*(x*e + d)^(3/2)*A*a*b^5*e^8*sgn(b*x + a) + 210*sqrt(x*e + d)*B*a^2*b^4*d*e^8*sgn(b*x + a) - 210*sqrt(x*e + d)*A*a*b^5*d*e^8*sgn(b*x + a) - 105*sqrt(x*e + d)*B*a^3*b^3*e^9*sgn(b*x + a) + 105*sqrt(x*e + d)*A*a^2*b^4*e^9*sgn(b*x + a))*e^(-7)/b^7","B",0
1860,1,306,0,0.215529," ","integrate((B*x+A)*(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, B a^{2} b d e \mathrm{sgn}\left(b x + a\right) + 2 \, A a b^{2} d e \mathrm{sgn}\left(b x + a\right) + B a^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - A a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{3}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 15 \, \sqrt{x e + d} B a b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} A b^{4} d e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} B a^{2} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 15 \, \sqrt{x e + d} A a b^{3} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{15 \, b^{5}}"," ",0,"-2*(B*a*b^2*d^2*sgn(b*x + a) - A*b^3*d^2*sgn(b*x + a) - 2*B*a^2*b*d*e*sgn(b*x + a) + 2*A*a*b^2*d*e*sgn(b*x + a) + B*a^3*e^2*sgn(b*x + a) - A*a^2*b*e^2*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^3) + 2/15*(3*(x*e + d)^(5/2)*B*b^4*e^4*sgn(b*x + a) - 5*(x*e + d)^(3/2)*B*a*b^3*e^5*sgn(b*x + a) + 5*(x*e + d)^(3/2)*A*b^4*e^5*sgn(b*x + a) - 15*sqrt(x*e + d)*B*a*b^3*d*e^5*sgn(b*x + a) + 15*sqrt(x*e + d)*A*b^4*d*e^5*sgn(b*x + a) + 15*sqrt(x*e + d)*B*a^2*b^2*e^6*sgn(b*x + a) - 15*sqrt(x*e + d)*A*a*b^3*e^6*sgn(b*x + a))*e^(-5)/b^5","A",0
1861,1,168,0,0.242218," ","integrate((B*x+A)*(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a b d \mathrm{sgn}\left(b x + a\right) - A b^{2} d \mathrm{sgn}\left(b x + a\right) - B a^{2} e \mathrm{sgn}\left(b x + a\right) + A a b e \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{2}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, \sqrt{x e + d} B a b e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, \sqrt{x e + d} A b^{2} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{3 \, b^{3}}"," ",0,"-2*(B*a*b*d*sgn(b*x + a) - A*b^2*d*sgn(b*x + a) - B*a^2*e*sgn(b*x + a) + A*a*b*e*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^2) + 2/3*((x*e + d)^(3/2)*B*b^2*e^2*sgn(b*x + a) - 3*sqrt(x*e + d)*B*a*b*e^3*sgn(b*x + a) + 3*sqrt(x*e + d)*A*b^2*e^3*sgn(b*x + a))*e^(-3)/b^3","A",0
1862,1,87,0,0.170013," ","integrate((B*x+A)/(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{b} - \frac{2 \, {\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b}"," ",0,"2*sqrt(x*e + d)*B*e^(-1)*sgn(b*x + a)/b - 2*(B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b)","A",0
1863,1,117,0,0.291589," ","integrate((B*x+A)/(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a \mathrm{sgn}\left(b x + a\right) - A b \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} {\left(b d - a e\right)}} - \frac{2 \, {\left(B d \mathrm{sgn}\left(b x + a\right) - A e \mathrm{sgn}\left(b x + a\right)\right)}}{{\left(b d e - a e^{2}\right)} \sqrt{x e + d}}"," ",0,"-2*(B*a*sgn(b*x + a) - A*b*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*(b*d - a*e)) - 2*(B*d*sgn(b*x + a) - A*e*sgn(b*x + a))/((b*d*e - a*e^2)*sqrt(x*e + d))","A",0
1864,1,209,0,0.206743," ","integrate((B*x+A)/(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a b \mathrm{sgn}\left(b x + a\right) - A b^{2} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(B b d^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)} B a e \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)} A b e \mathrm{sgn}\left(b x + a\right) - B a d e \mathrm{sgn}\left(b x + a\right) - A b d e \mathrm{sgn}\left(b x + a\right) + A a e^{2} \mathrm{sgn}\left(b x + a\right)\right)}}{3 \, {\left(b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-2*(B*a*b*sgn(b*x + a) - A*b^2*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-b^2*d + a*b*e)) - 2/3*(B*b*d^2*sgn(b*x + a) + 3*(x*e + d)*B*a*e*sgn(b*x + a) - 3*(x*e + d)*A*b*e*sgn(b*x + a) - B*a*d*e*sgn(b*x + a) - A*b*d*e*sgn(b*x + a) + A*a*e^2*sgn(b*x + a))/((b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3)*(x*e + d)^(3/2))","A",0
1865,1,368,0,0.273423," ","integrate((B*x+A)/(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a b^{2} \mathrm{sgn}\left(b x + a\right) - A b^{3} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\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{-b^{2} d + a b e}} - \frac{2 \, {\left(3 \, B b^{2} d^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{2} B a b e \mathrm{sgn}\left(b x + a\right) - 15 \, {\left(x e + d\right)}^{2} A b^{2} e \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)} B a b d e \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)} A b^{2} d e \mathrm{sgn}\left(b x + a\right) - 6 \, B a b d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, A b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)} B a^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)} A a b e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, B a^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, A a b d e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, A a^{2} e^{3} \mathrm{sgn}\left(b x + a\right)\right)}}{15 \, {\left(b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}\right)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2*(B*a*b^2*sgn(b*x + a) - A*b^3*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-b^2*d + a*b*e)) - 2/15*(3*B*b^2*d^3*sgn(b*x + a) + 15*(x*e + d)^2*B*a*b*e*sgn(b*x + a) - 15*(x*e + d)^2*A*b^2*e*sgn(b*x + a) + 5*(x*e + d)*B*a*b*d*e*sgn(b*x + a) - 5*(x*e + d)*A*b^2*d*e*sgn(b*x + a) - 6*B*a*b*d^2*e*sgn(b*x + a) - 3*A*b^2*d^2*e*sgn(b*x + a) - 5*(x*e + d)*B*a^2*e^2*sgn(b*x + a) + 5*(x*e + d)*A*a*b*e^2*sgn(b*x + a) + 3*B*a^2*d*e^2*sgn(b*x + a) + 6*A*a*b*d*e^2*sgn(b*x + a) - 3*A*a^2*e^3*sgn(b*x + a))/((b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4)*(x*e + d)^(5/2))","A",0
1866,1,685,0,0.439472," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{7 \, {\left(4 \, B b^{3} d^{3} e^{2} - 17 \, B a b^{2} d^{2} e^{3} + 5 \, A b^{3} d^{2} e^{3} + 22 \, B a^{2} b d e^{4} - 10 \, A a b^{2} d e^{4} - 9 \, B a^{3} e^{5} + 5 \, A a^{2} b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{\left(-1\right)}}{4 \, \sqrt{-b^{2} d + a b e} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{{\left(4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{2} - 4 \, \sqrt{x e + d} B b^{4} d^{4} e^{2} - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{3} + 13 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{3} + 27 \, \sqrt{x e + d} B a b^{3} d^{3} e^{3} - 11 \, \sqrt{x e + d} A b^{4} d^{3} e^{3} + 38 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{4} - 26 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{4} - 57 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{4} + 33 \, \sqrt{x e + d} A a b^{3} d^{2} e^{4} - 17 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{5} + 13 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{5} + 49 \, \sqrt{x e + d} B a^{3} b d e^{5} - 33 \, \sqrt{x e + d} A a^{2} b^{2} d e^{5} - 15 \, \sqrt{x e + d} B a^{4} e^{6} + 11 \, \sqrt{x e + d} A a^{3} b e^{6}\right)} e^{\left(-1\right)}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{12} e^{6} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{12} d e^{6} + 45 \, \sqrt{x e + d} B b^{12} d^{2} e^{6} - 15 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{11} e^{7} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{12} e^{7} - 135 \, \sqrt{x e + d} B a b^{11} d e^{7} + 45 \, \sqrt{x e + d} A b^{12} d e^{7} + 90 \, \sqrt{x e + d} B a^{2} b^{10} e^{8} - 45 \, \sqrt{x e + d} A a b^{11} e^{8}\right)} e^{\left(-5\right)}}{15 \, b^{15} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"7/4*(4*B*b^3*d^3*e^2 - 17*B*a*b^2*d^2*e^3 + 5*A*b^3*d^2*e^3 + 22*B*a^2*b*d*e^4 - 10*A*a*b^2*d*e^4 - 9*B*a^3*e^5 + 5*A*a^2*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^(-1)/(sqrt(-b^2*d + a*b*e)*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/4*(4*(x*e + d)^(3/2)*B*b^4*d^3*e^2 - 4*sqrt(x*e + d)*B*b^4*d^4*e^2 - 25*(x*e + d)^(3/2)*B*a*b^3*d^2*e^3 + 13*(x*e + d)^(3/2)*A*b^4*d^2*e^3 + 27*sqrt(x*e + d)*B*a*b^3*d^3*e^3 - 11*sqrt(x*e + d)*A*b^4*d^3*e^3 + 38*(x*e + d)^(3/2)*B*a^2*b^2*d*e^4 - 26*(x*e + d)^(3/2)*A*a*b^3*d*e^4 - 57*sqrt(x*e + d)*B*a^2*b^2*d^2*e^4 + 33*sqrt(x*e + d)*A*a*b^3*d^2*e^4 - 17*(x*e + d)^(3/2)*B*a^3*b*e^5 + 13*(x*e + d)^(3/2)*A*a^2*b^2*e^5 + 49*sqrt(x*e + d)*B*a^3*b*d*e^5 - 33*sqrt(x*e + d)*A*a^2*b^2*d*e^5 - 15*sqrt(x*e + d)*B*a^4*e^6 + 11*sqrt(x*e + d)*A*a^3*b*e^6)*e^(-1)/(((x*e + d)*b - b*d + a*e)^2*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/15*(3*(x*e + d)^(5/2)*B*b^12*e^6 + 10*(x*e + d)^(3/2)*B*b^12*d*e^6 + 45*sqrt(x*e + d)*B*b^12*d^2*e^6 - 15*(x*e + d)^(3/2)*B*a*b^11*e^7 + 5*(x*e + d)^(3/2)*A*b^12*e^7 - 135*sqrt(x*e + d)*B*a*b^11*d*e^7 + 45*sqrt(x*e + d)*A*b^12*d*e^7 + 90*sqrt(x*e + d)*B*a^2*b^10*e^8 - 45*sqrt(x*e + d)*A*a*b^11*e^8)*e^(-5)/(b^15*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
1867,1,478,0,0.366083," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{5 \, {\left(4 \, B b^{2} d^{2} e^{2} - 11 \, B a b d e^{3} + 3 \, A b^{2} d e^{3} + 7 \, B a^{2} e^{4} - 3 \, A a b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{\left(-1\right)}}{4 \, \sqrt{-b^{2} d + a b e} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{{\left(4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d^{2} e^{2} - 4 \, \sqrt{x e + d} B b^{3} d^{3} e^{2} - 17 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} d e^{3} + 9 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} d e^{3} + 19 \, \sqrt{x e + d} B a b^{2} d^{2} e^{3} - 7 \, \sqrt{x e + d} A b^{3} d^{2} e^{3} + 13 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b e^{4} - 9 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{2} e^{4} - 26 \, \sqrt{x e + d} B a^{2} b d e^{4} + 14 \, \sqrt{x e + d} A a b^{2} d e^{4} + 11 \, \sqrt{x e + d} B a^{3} e^{5} - 7 \, \sqrt{x e + d} A a^{2} b e^{5}\right)} e^{\left(-1\right)}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{6} e^{4} + 6 \, \sqrt{x e + d} B b^{6} d e^{4} - 9 \, \sqrt{x e + d} B a b^{5} e^{5} + 3 \, \sqrt{x e + d} A b^{6} e^{5}\right)} e^{\left(-3\right)}}{3 \, b^{9} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"5/4*(4*B*b^2*d^2*e^2 - 11*B*a*b*d*e^3 + 3*A*b^2*d*e^3 + 7*B*a^2*e^4 - 3*A*a*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^(-1)/(sqrt(-b^2*d + a*b*e)*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/4*(4*(x*e + d)^(3/2)*B*b^3*d^2*e^2 - 4*sqrt(x*e + d)*B*b^3*d^3*e^2 - 17*(x*e + d)^(3/2)*B*a*b^2*d*e^3 + 9*(x*e + d)^(3/2)*A*b^3*d*e^3 + 19*sqrt(x*e + d)*B*a*b^2*d^2*e^3 - 7*sqrt(x*e + d)*A*b^3*d^2*e^3 + 13*(x*e + d)^(3/2)*B*a^2*b*e^4 - 9*(x*e + d)^(3/2)*A*a*b^2*e^4 - 26*sqrt(x*e + d)*B*a^2*b*d*e^4 + 14*sqrt(x*e + d)*A*a*b^2*d*e^4 + 11*sqrt(x*e + d)*B*a^3*e^5 - 7*sqrt(x*e + d)*A*a^2*b*e^5)*e^(-1)/(((x*e + d)*b - b*d + a*e)^2*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/3*((x*e + d)^(3/2)*B*b^6*e^4 + 6*sqrt(x*e + d)*B*b^6*d*e^4 - 9*sqrt(x*e + d)*B*a*b^5*e^5 + 3*sqrt(x*e + d)*A*b^6*e^5)*e^(-3)/(b^9*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
1868,1,312,0,0.299980," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e}{b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{3 \, {\left(4 \, B b d e^{2} - 5 \, B a e^{3} + A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{\left(-1\right)}}{4 \, \sqrt{-b^{2} d + a b e} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{{\left(4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} d e^{2} - 4 \, \sqrt{x e + d} B b^{2} d^{2} e^{2} - 9 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b e^{3} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} e^{3} + 11 \, \sqrt{x e + d} B a b d e^{3} - 3 \, \sqrt{x e + d} A b^{2} d e^{3} - 7 \, \sqrt{x e + d} B a^{2} e^{4} + 3 \, \sqrt{x e + d} A a b e^{4}\right)} e^{\left(-1\right)}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"2*sqrt(x*e + d)*B*e/(b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 3/4*(4*B*b*d*e^2 - 5*B*a*e^3 + A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^(-1)/(sqrt(-b^2*d + a*b*e)*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/4*(4*(x*e + d)^(3/2)*B*b^2*d*e^2 - 4*sqrt(x*e + d)*B*b^2*d^2*e^2 - 9*(x*e + d)^(3/2)*B*a*b*e^3 + 5*(x*e + d)^(3/2)*A*b^2*e^3 + 11*sqrt(x*e + d)*B*a*b*d*e^3 - 3*sqrt(x*e + d)*A*b^2*d*e^3 - 7*sqrt(x*e + d)*B*a^2*e^4 + 3*sqrt(x*e + d)*A*a*b*e^4)*e^(-1)/(((x*e + d)*b - b*d + a*e)^2*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
1869,1,337,0,0.358865," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(4 \, B b d e^{2} - 3 \, B a e^{3} - A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, {\left(b^{3} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} d e^{2} - 4 \, \sqrt{x e + d} B b^{2} d^{2} e^{2} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b e^{3} + {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} e^{3} + 7 \, \sqrt{x e + d} B a b d e^{3} + \sqrt{x e + d} A b^{2} d e^{3} - 3 \, \sqrt{x e + d} B a^{2} e^{4} - \sqrt{x e + d} A a b e^{4}}{4 \, {\left(b^{3} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"1/4*(4*B*b*d*e^2 - 3*B*a*e^3 - A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^3*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/4*(4*(x*e + d)^(3/2)*B*b^2*d*e^2 - 4*sqrt(x*e + d)*B*b^2*d^2*e^2 - 5*(x*e + d)^(3/2)*B*a*b*e^3 + (x*e + d)^(3/2)*A*b^2*e^3 + 7*sqrt(x*e + d)*B*a*b*d*e^3 + sqrt(x*e + d)*A*b^2*d*e^3 - 3*sqrt(x*e + d)*B*a^2*e^4 - sqrt(x*e + d)*A*a*b*e^4)/((b^3*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","B",0
1870,1,402,0,0.300193," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, B b d e^{2} - B a e^{3} - 3 \, A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, {\left(b^{3} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{2} d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} d e^{2} - 4 \, \sqrt{x e + d} B b^{2} d^{2} e^{2} - {\left(x e + d\right)}^{\frac{3}{2}} B a b e^{3} - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} e^{3} + 3 \, \sqrt{x e + d} B a b d e^{3} + 5 \, \sqrt{x e + d} A b^{2} d e^{3} + \sqrt{x e + d} B a^{2} e^{4} - 5 \, \sqrt{x e + d} A a b e^{4}}{4 \, {\left(b^{3} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{2} d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"-1/4*(4*B*b*d*e^2 - B*a*e^3 - 3*A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^3*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^2*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/4*(4*(x*e + d)^(3/2)*B*b^2*d*e^2 - 4*sqrt(x*e + d)*B*b^2*d^2*e^2 - (x*e + d)^(3/2)*B*a*b*e^3 - 3*(x*e + d)^(3/2)*A*b^2*e^3 + 3*sqrt(x*e + d)*B*a*b*d*e^3 + 5*sqrt(x*e + d)*A*b^2*d*e^3 + sqrt(x*e + d)*B*a^2*e^4 - 5*sqrt(x*e + d)*A*a*b*e^4)/((b^3*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^2*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","B",0
1871,1,616,0,0.400109," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, B b d e^{2} + B a e^{3} - 5 \, A b e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, {\left(b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(B d e^{2} - A e^{3}\right)}}{{\left(b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{x e + d}} - \frac{4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{2} d e^{2} - 4 \, \sqrt{x e + d} B b^{2} d^{2} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b e^{3} - 7 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{2} e^{3} - \sqrt{x e + d} B a b d e^{3} + 9 \, \sqrt{x e + d} A b^{2} d e^{3} + 5 \, \sqrt{x e + d} B a^{2} e^{4} - 9 \, \sqrt{x e + d} A a b e^{4}}{4 \, {\left(b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"-3/4*(4*B*b*d*e^2 + B*a*e^3 - 5*A*b*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 2*(B*d*e^2 - A*e^3)/((b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(x*e + d)) - 1/4*(4*(x*e + d)^(3/2)*B*b^2*d*e^2 - 4*sqrt(x*e + d)*B*b^2*d^2*e^2 + 3*(x*e + d)^(3/2)*B*a*b*e^3 - 7*(x*e + d)^(3/2)*A*b^2*e^3 - sqrt(x*e + d)*B*a*b*d*e^3 + 9*sqrt(x*e + d)*A*b^2*d*e^3 + 5*sqrt(x*e + d)*B*a^2*e^4 - 9*sqrt(x*e + d)*A*a*b*e^4)/((b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","B",0
1872,1,785,0,0.493222," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{5 \, {\left(4 \, B b^{2} d e^{2} + 3 \, B a b e^{3} - 7 \, A b^{2} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, {\left(b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(6 \, {\left(x e + d\right)} B b d e^{2} + B b d^{2} e^{2} + 3 \, {\left(x e + d\right)} B a e^{3} - 9 \, {\left(x e + d\right)} A b e^{3} - B a d e^{3} - A b d e^{3} + A a e^{4}\right)}}{3 \, {\left(b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{3}{2}}} - \frac{4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{3} d e^{2} - 4 \, \sqrt{x e + d} B b^{3} d^{2} e^{2} + 7 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{2} e^{3} - 11 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{3} e^{3} - 5 \, \sqrt{x e + d} B a b^{2} d e^{3} + 13 \, \sqrt{x e + d} A b^{3} d e^{3} + 9 \, \sqrt{x e + d} B a^{2} b e^{4} - 13 \, \sqrt{x e + d} A a b^{2} e^{4}}{4 \, {\left(b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"-5/4*(4*B*b^2*d*e^2 + 3*B*a*b*e^3 - 7*A*b^2*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 2/3*(6*(x*e + d)*B*b*d*e^2 + B*b*d^2*e^2 + 3*(x*e + d)*B*a*e^3 - 9*(x*e + d)*A*b*e^3 - B*a*d*e^3 - A*b*d*e^3 + A*a*e^4)/((b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(3/2)) - 1/4*(4*(x*e + d)^(3/2)*B*b^3*d*e^2 - 4*sqrt(x*e + d)*B*b^3*d^2*e^2 + 7*(x*e + d)^(3/2)*B*a*b^2*e^3 - 11*(x*e + d)^(3/2)*A*b^3*e^3 - 5*sqrt(x*e + d)*B*a*b^2*d*e^3 + 13*sqrt(x*e + d)*A*b^3*d*e^3 + 9*sqrt(x*e + d)*B*a^2*b*e^4 - 13*sqrt(x*e + d)*A*a*b^2*e^4)/((b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","B",0
1873,1,1011,0,0.573547," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{7 \, {\left(4 \, B b^{3} d e^{2} + 5 \, B a b^{2} e^{3} - 9 \, A b^{3} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, {\left(b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{4 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d e^{2} - 4 \, \sqrt{x e + d} B b^{4} d^{2} e^{2} + 11 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} e^{3} - 15 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} e^{3} - 9 \, \sqrt{x e + d} B a b^{3} d e^{3} + 17 \, \sqrt{x e + d} A b^{4} d e^{3} + 13 \, \sqrt{x e + d} B a^{2} b^{2} e^{4} - 17 \, \sqrt{x e + d} A a b^{3} e^{4}}{4 \, {\left(b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}} - \frac{2 \, {\left(45 \, {\left(x e + d\right)}^{2} B b^{2} d e^{2} + 10 \, {\left(x e + d\right)} B b^{2} d^{2} e^{2} + 3 \, B b^{2} d^{3} e^{2} + 45 \, {\left(x e + d\right)}^{2} B a b e^{3} - 90 \, {\left(x e + d\right)}^{2} A b^{2} e^{3} - 5 \, {\left(x e + d\right)} B a b d e^{3} - 15 \, {\left(x e + d\right)} A b^{2} d e^{3} - 6 \, B a b d^{2} e^{3} - 3 \, A b^{2} d^{2} e^{3} - 5 \, {\left(x e + d\right)} B a^{2} e^{4} + 15 \, {\left(x e + d\right)} A a b e^{4} + 3 \, B a^{2} d e^{4} + 6 \, A a b d e^{4} - 3 \, A a^{2} e^{5}\right)}}{15 \, {\left(b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-7/4*(4*B*b^3*d*e^2 + 5*B*a*b^2*e^3 - 9*A*b^3*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/4*(4*(x*e + d)^(3/2)*B*b^4*d*e^2 - 4*sqrt(x*e + d)*B*b^4*d^2*e^2 + 11*(x*e + d)^(3/2)*B*a*b^3*e^3 - 15*(x*e + d)^(3/2)*A*b^4*e^3 - 9*sqrt(x*e + d)*B*a*b^3*d*e^3 + 17*sqrt(x*e + d)*A*b^4*d*e^3 + 13*sqrt(x*e + d)*B*a^2*b^2*e^4 - 17*sqrt(x*e + d)*A*a*b^3*e^4)/((b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2) - 2/15*(45*(x*e + d)^2*B*b^2*d*e^2 + 10*(x*e + d)*B*b^2*d^2*e^2 + 3*B*b^2*d^3*e^2 + 45*(x*e + d)^2*B*a*b*e^3 - 90*(x*e + d)^2*A*b^2*e^3 - 5*(x*e + d)*B*a*b*d*e^3 - 15*(x*e + d)*A*b^2*d*e^3 - 6*B*a*b*d^2*e^3 - 3*A*b^2*d^2*e^3 - 5*(x*e + d)*B*a^2*e^4 + 15*(x*e + d)*A*a*b*e^4 + 3*B*a^2*d*e^4 + 6*A*a*b*d*e^4 - 3*A*a^2*e^5)/((b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(5/2))","B",0
1874,1,1167,0,0.611557," ","integrate((B*x+A)*(e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{231 \, {\left(8 \, B b^{3} d^{3} e^{3} - 29 \, B a b^{2} d^{2} e^{4} + 5 \, A b^{3} d^{2} e^{4} + 34 \, B a^{2} b d e^{5} - 10 \, A a b^{2} d e^{5} - 13 \, B a^{3} e^{6} + 5 \, A a^{2} b e^{6}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{2136 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} d^{3} e^{3} - 5912 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} d^{4} e^{3} + 5480 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d^{5} e^{3} - 1704 \, \sqrt{x e + d} B b^{6} d^{6} e^{3} - 8703 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{5} d^{2} e^{4} + 2295 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{6} d^{2} e^{4} + 29503 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} d^{3} e^{4} - 5855 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} d^{3} e^{4} - 32553 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d^{4} e^{4} + 5153 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d^{4} e^{4} + 11769 \, \sqrt{x e + d} B a b^{5} d^{5} e^{4} - 1545 \, \sqrt{x e + d} A b^{6} d^{5} e^{4} + 10998 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{4} d e^{5} - 4590 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{5} d e^{5} - 53037 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{4} d^{2} e^{5} + 17565 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{5} d^{2} e^{5} + 75412 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} d^{3} e^{5} - 20612 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} d^{3} e^{5} - 33285 \, \sqrt{x e + d} B a^{2} b^{4} d^{4} e^{5} + 7725 \, \sqrt{x e + d} A a b^{5} d^{4} e^{5} - 4431 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{3} b^{3} e^{6} + 2295 \, {\left(x e + d\right)}^{\frac{7}{2}} A a^{2} b^{4} e^{6} + 41213 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{3} d e^{6} - 17565 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{4} d e^{6} - 85718 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{3} d^{2} e^{6} + 30918 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{4} d^{2} e^{6} + 49530 \, \sqrt{x e + d} B a^{3} b^{3} d^{3} e^{6} - 15450 \, \sqrt{x e + d} A a^{2} b^{4} d^{3} e^{6} - 11767 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{4} b^{2} e^{7} + 5855 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{3} b^{3} e^{7} + 48012 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b^{2} d e^{7} - 20612 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{3} d e^{7} - 41010 \, \sqrt{x e + d} B a^{4} b^{2} d^{2} e^{7} + 15450 \, \sqrt{x e + d} A a^{3} b^{3} d^{2} e^{7} - 10633 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{5} b e^{8} + 5153 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{4} b^{2} e^{8} + 17949 \, \sqrt{x e + d} B a^{5} b d e^{8} - 7725 \, \sqrt{x e + d} A a^{4} b^{2} d e^{8} - 3249 \, \sqrt{x e + d} B a^{6} e^{9} + 1545 \, \sqrt{x e + d} A a^{5} b e^{9}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{20} e^{3} + 20 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{20} d e^{3} + 150 \, \sqrt{x e + d} B b^{20} d^{2} e^{3} - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{19} e^{4} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{20} e^{4} - 375 \, \sqrt{x e + d} B a b^{19} d e^{4} + 75 \, \sqrt{x e + d} A b^{20} d e^{4} + 225 \, \sqrt{x e + d} B a^{2} b^{18} e^{5} - 75 \, \sqrt{x e + d} A a b^{19} e^{5}\right)}}{15 \, b^{25} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"231/64*(8*B*b^3*d^3*e^3 - 29*B*a*b^2*d^2*e^4 + 5*A*b^3*d^2*e^4 + 34*B*a^2*b*d*e^5 - 10*A*a*b^2*d*e^5 - 13*B*a^3*e^6 + 5*A*a^2*b*e^6)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^7*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/192*(2136*(x*e + d)^(7/2)*B*b^6*d^3*e^3 - 5912*(x*e + d)^(5/2)*B*b^6*d^4*e^3 + 5480*(x*e + d)^(3/2)*B*b^6*d^5*e^3 - 1704*sqrt(x*e + d)*B*b^6*d^6*e^3 - 8703*(x*e + d)^(7/2)*B*a*b^5*d^2*e^4 + 2295*(x*e + d)^(7/2)*A*b^6*d^2*e^4 + 29503*(x*e + d)^(5/2)*B*a*b^5*d^3*e^4 - 5855*(x*e + d)^(5/2)*A*b^6*d^3*e^4 - 32553*(x*e + d)^(3/2)*B*a*b^5*d^4*e^4 + 5153*(x*e + d)^(3/2)*A*b^6*d^4*e^4 + 11769*sqrt(x*e + d)*B*a*b^5*d^5*e^4 - 1545*sqrt(x*e + d)*A*b^6*d^5*e^4 + 10998*(x*e + d)^(7/2)*B*a^2*b^4*d*e^5 - 4590*(x*e + d)^(7/2)*A*a*b^5*d*e^5 - 53037*(x*e + d)^(5/2)*B*a^2*b^4*d^2*e^5 + 17565*(x*e + d)^(5/2)*A*a*b^5*d^2*e^5 + 75412*(x*e + d)^(3/2)*B*a^2*b^4*d^3*e^5 - 20612*(x*e + d)^(3/2)*A*a*b^5*d^3*e^5 - 33285*sqrt(x*e + d)*B*a^2*b^4*d^4*e^5 + 7725*sqrt(x*e + d)*A*a*b^5*d^4*e^5 - 4431*(x*e + d)^(7/2)*B*a^3*b^3*e^6 + 2295*(x*e + d)^(7/2)*A*a^2*b^4*e^6 + 41213*(x*e + d)^(5/2)*B*a^3*b^3*d*e^6 - 17565*(x*e + d)^(5/2)*A*a^2*b^4*d*e^6 - 85718*(x*e + d)^(3/2)*B*a^3*b^3*d^2*e^6 + 30918*(x*e + d)^(3/2)*A*a^2*b^4*d^2*e^6 + 49530*sqrt(x*e + d)*B*a^3*b^3*d^3*e^6 - 15450*sqrt(x*e + d)*A*a^2*b^4*d^3*e^6 - 11767*(x*e + d)^(5/2)*B*a^4*b^2*e^7 + 5855*(x*e + d)^(5/2)*A*a^3*b^3*e^7 + 48012*(x*e + d)^(3/2)*B*a^4*b^2*d*e^7 - 20612*(x*e + d)^(3/2)*A*a^3*b^3*d*e^7 - 41010*sqrt(x*e + d)*B*a^4*b^2*d^2*e^7 + 15450*sqrt(x*e + d)*A*a^3*b^3*d^2*e^7 - 10633*(x*e + d)^(3/2)*B*a^5*b*e^8 + 5153*(x*e + d)^(3/2)*A*a^4*b^2*e^8 + 17949*sqrt(x*e + d)*B*a^5*b*d*e^8 - 7725*sqrt(x*e + d)*A*a^4*b^2*d*e^8 - 3249*sqrt(x*e + d)*B*a^6*e^9 + 1545*sqrt(x*e + d)*A*a^5*b*e^9)/(((x*e + d)*b - b*d + a*e)^4*b^7*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/15*(3*(x*e + d)^(5/2)*B*b^20*e^3 + 20*(x*e + d)^(3/2)*B*b^20*d*e^3 + 150*sqrt(x*e + d)*B*b^20*d^2*e^3 - 25*(x*e + d)^(3/2)*B*a*b^19*e^4 + 5*(x*e + d)^(3/2)*A*b^20*e^4 - 375*sqrt(x*e + d)*B*a*b^19*d*e^4 + 75*sqrt(x*e + d)*A*b^20*d*e^4 + 225*sqrt(x*e + d)*B*a^2*b^18*e^5 - 75*sqrt(x*e + d)*A*a*b^19*e^5)/(b^25*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
1875,1,872,0,0.523006," ","integrate((B*x+A)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{105 \, {\left(8 \, B b^{2} d^{2} e^{3} - 19 \, B a b d e^{4} + 3 \, A b^{2} d e^{4} + 11 \, B a^{2} e^{5} - 3 \, A a b e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{1320 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d^{2} e^{3} - 3560 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{3} e^{3} + 3224 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{4} e^{3} - 984 \, \sqrt{x e + d} B b^{5} d^{5} e^{3} - 3615 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} d e^{4} + 975 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} d e^{4} + 12975 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d^{2} e^{4} - 2295 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d^{2} e^{4} - 14825 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{3} e^{4} + 1929 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{3} e^{4} + 5481 \, \sqrt{x e + d} B a b^{4} d^{4} e^{4} - 561 \, \sqrt{x e + d} A b^{5} d^{4} e^{4} + 2295 \, {\left(x e + d\right)}^{\frac{7}{2}} B a^{2} b^{3} e^{5} - 975 \, {\left(x e + d\right)}^{\frac{7}{2}} A a b^{4} e^{5} - 15270 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} d e^{5} + 4590 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} d e^{5} + 25131 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{2} e^{5} - 5787 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d^{2} e^{5} - 12084 \, \sqrt{x e + d} B a^{2} b^{3} d^{3} e^{5} + 2244 \, \sqrt{x e + d} A a b^{4} d^{3} e^{5} + 5855 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{3} b^{2} e^{6} - 2295 \, {\left(x e + d\right)}^{\frac{5}{2}} A a^{2} b^{3} e^{6} - 18683 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} d e^{6} + 5787 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} d e^{6} + 13206 \, \sqrt{x e + d} B a^{3} b^{2} d^{2} e^{6} - 3366 \, \sqrt{x e + d} A a^{2} b^{3} d^{2} e^{6} + 5153 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{4} b e^{7} - 1929 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{3} b^{2} e^{7} - 7164 \, \sqrt{x e + d} B a^{4} b d e^{7} + 2244 \, \sqrt{x e + d} A a^{3} b^{2} d e^{7} + 1545 \, \sqrt{x e + d} B a^{5} e^{8} - 561 \, \sqrt{x e + d} A a^{4} b e^{8}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} B b^{10} e^{3} + 12 \, \sqrt{x e + d} B b^{10} d e^{3} - 15 \, \sqrt{x e + d} B a b^{9} e^{4} + 3 \, \sqrt{x e + d} A b^{10} e^{4}\right)}}{3 \, b^{15} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"105/64*(8*B*b^2*d^2*e^3 - 19*B*a*b*d*e^4 + 3*A*b^2*d*e^4 + 11*B*a^2*e^5 - 3*A*a*b*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^6*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/192*(1320*(x*e + d)^(7/2)*B*b^5*d^2*e^3 - 3560*(x*e + d)^(5/2)*B*b^5*d^3*e^3 + 3224*(x*e + d)^(3/2)*B*b^5*d^4*e^3 - 984*sqrt(x*e + d)*B*b^5*d^5*e^3 - 3615*(x*e + d)^(7/2)*B*a*b^4*d*e^4 + 975*(x*e + d)^(7/2)*A*b^5*d*e^4 + 12975*(x*e + d)^(5/2)*B*a*b^4*d^2*e^4 - 2295*(x*e + d)^(5/2)*A*b^5*d^2*e^4 - 14825*(x*e + d)^(3/2)*B*a*b^4*d^3*e^4 + 1929*(x*e + d)^(3/2)*A*b^5*d^3*e^4 + 5481*sqrt(x*e + d)*B*a*b^4*d^4*e^4 - 561*sqrt(x*e + d)*A*b^5*d^4*e^4 + 2295*(x*e + d)^(7/2)*B*a^2*b^3*e^5 - 975*(x*e + d)^(7/2)*A*a*b^4*e^5 - 15270*(x*e + d)^(5/2)*B*a^2*b^3*d*e^5 + 4590*(x*e + d)^(5/2)*A*a*b^4*d*e^5 + 25131*(x*e + d)^(3/2)*B*a^2*b^3*d^2*e^5 - 5787*(x*e + d)^(3/2)*A*a*b^4*d^2*e^5 - 12084*sqrt(x*e + d)*B*a^2*b^3*d^3*e^5 + 2244*sqrt(x*e + d)*A*a*b^4*d^3*e^5 + 5855*(x*e + d)^(5/2)*B*a^3*b^2*e^6 - 2295*(x*e + d)^(5/2)*A*a^2*b^3*e^6 - 18683*(x*e + d)^(3/2)*B*a^3*b^2*d*e^6 + 5787*(x*e + d)^(3/2)*A*a^2*b^3*d*e^6 + 13206*sqrt(x*e + d)*B*a^3*b^2*d^2*e^6 - 3366*sqrt(x*e + d)*A*a^2*b^3*d^2*e^6 + 5153*(x*e + d)^(3/2)*B*a^4*b*e^7 - 1929*(x*e + d)^(3/2)*A*a^3*b^2*e^7 - 7164*sqrt(x*e + d)*B*a^4*b*d*e^7 + 2244*sqrt(x*e + d)*A*a^3*b^2*d*e^7 + 1545*sqrt(x*e + d)*B*a^5*e^8 - 561*sqrt(x*e + d)*A*a^4*b*e^8)/(((x*e + d)*b - b*d + a*e)^4*b^6*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/3*((x*e + d)^(3/2)*B*b^10*e^3 + 12*sqrt(x*e + d)*B*b^10*d*e^3 - 15*sqrt(x*e + d)*B*a*b^9*e^4 + 3*sqrt(x*e + d)*A*b^10*e^4)/(b^15*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
1876,1,620,0,0.487665," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} B e^{3}}{b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{35 \, {\left(8 \, B b d e^{3} - 9 \, B a e^{4} + A b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{696 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} d e^{3} - 1784 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{3} + 1544 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{3} - 456 \, \sqrt{x e + d} B b^{4} d^{4} e^{3} - 975 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{3} e^{4} + 279 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} e^{4} + 4079 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{4} - 511 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{4} - 5017 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{4} + 385 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{4} + 1929 \, \sqrt{x e + d} B a b^{3} d^{3} e^{4} - 105 \, \sqrt{x e + d} A b^{4} d^{3} e^{4} - 2295 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{5} + 511 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{5} + 5402 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{5} - 770 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{5} - 3051 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{5} + 315 \, \sqrt{x e + d} A a b^{3} d^{2} e^{5} - 1929 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{6} + 385 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{6} + 2139 \, \sqrt{x e + d} B a^{3} b d e^{6} - 315 \, \sqrt{x e + d} A a^{2} b^{2} d e^{6} - 561 \, \sqrt{x e + d} B a^{4} e^{7} + 105 \, \sqrt{x e + d} A a^{3} b e^{7}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"2*sqrt(x*e + d)*B*e^3/(b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 35/64*(8*B*b*d*e^3 - 9*B*a*e^4 + A*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/192*(696*(x*e + d)^(7/2)*B*b^4*d*e^3 - 1784*(x*e + d)^(5/2)*B*b^4*d^2*e^3 + 1544*(x*e + d)^(3/2)*B*b^4*d^3*e^3 - 456*sqrt(x*e + d)*B*b^4*d^4*e^3 - 975*(x*e + d)^(7/2)*B*a*b^3*e^4 + 279*(x*e + d)^(7/2)*A*b^4*e^4 + 4079*(x*e + d)^(5/2)*B*a*b^3*d*e^4 - 511*(x*e + d)^(5/2)*A*b^4*d*e^4 - 5017*(x*e + d)^(3/2)*B*a*b^3*d^2*e^4 + 385*(x*e + d)^(3/2)*A*b^4*d^2*e^4 + 1929*sqrt(x*e + d)*B*a*b^3*d^3*e^4 - 105*sqrt(x*e + d)*A*b^4*d^3*e^4 - 2295*(x*e + d)^(5/2)*B*a^2*b^2*e^5 + 511*(x*e + d)^(5/2)*A*a*b^3*e^5 + 5402*(x*e + d)^(3/2)*B*a^2*b^2*d*e^5 - 770*(x*e + d)^(3/2)*A*a*b^3*d*e^5 - 3051*sqrt(x*e + d)*B*a^2*b^2*d^2*e^5 + 315*sqrt(x*e + d)*A*a*b^3*d^2*e^5 - 1929*(x*e + d)^(3/2)*B*a^3*b*e^6 + 385*(x*e + d)^(3/2)*A*a^2*b^2*e^6 + 2139*sqrt(x*e + d)*B*a^3*b*d*e^6 - 315*sqrt(x*e + d)*A*a^2*b^2*d*e^6 - 561*sqrt(x*e + d)*B*a^4*e^7 + 105*sqrt(x*e + d)*A*a^3*b*e^7)/(((x*e + d)*b - b*d + a*e)^4*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
1877,1,647,0,0.479584," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{5 \, {\left(8 \, B b d e^{3} - 7 \, B a e^{4} - A b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, {\left(b^{5} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{264 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} d e^{3} - 584 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{3} + 440 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{3} - 120 \, \sqrt{x e + d} B b^{4} d^{4} e^{3} - 279 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{3} e^{4} + 15 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} e^{4} + 1095 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{4} + 73 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{4} - 1265 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{4} - 55 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{4} + 465 \, \sqrt{x e + d} B a b^{3} d^{3} e^{4} + 15 \, \sqrt{x e + d} A b^{4} d^{3} e^{4} - 511 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{5} - 73 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{5} + 1210 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{5} + 110 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{5} - 675 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{5} - 45 \, \sqrt{x e + d} A a b^{3} d^{2} e^{5} - 385 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{6} - 55 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{6} + 435 \, \sqrt{x e + d} B a^{3} b d e^{6} + 45 \, \sqrt{x e + d} A a^{2} b^{2} d e^{6} - 105 \, \sqrt{x e + d} B a^{4} e^{7} - 15 \, \sqrt{x e + d} A a^{3} b e^{7}}{192 \, {\left(b^{5} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"5/64*(8*B*b*d*e^3 - 7*B*a*e^4 - A*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^5*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/192*(264*(x*e + d)^(7/2)*B*b^4*d*e^3 - 584*(x*e + d)^(5/2)*B*b^4*d^2*e^3 + 440*(x*e + d)^(3/2)*B*b^4*d^3*e^3 - 120*sqrt(x*e + d)*B*b^4*d^4*e^3 - 279*(x*e + d)^(7/2)*B*a*b^3*e^4 + 15*(x*e + d)^(7/2)*A*b^4*e^4 + 1095*(x*e + d)^(5/2)*B*a*b^3*d*e^4 + 73*(x*e + d)^(5/2)*A*b^4*d*e^4 - 1265*(x*e + d)^(3/2)*B*a*b^3*d^2*e^4 - 55*(x*e + d)^(3/2)*A*b^4*d^2*e^4 + 465*sqrt(x*e + d)*B*a*b^3*d^3*e^4 + 15*sqrt(x*e + d)*A*b^4*d^3*e^4 - 511*(x*e + d)^(5/2)*B*a^2*b^2*e^5 - 73*(x*e + d)^(5/2)*A*a*b^3*e^5 + 1210*(x*e + d)^(3/2)*B*a^2*b^2*d*e^5 + 110*(x*e + d)^(3/2)*A*a*b^3*d*e^5 - 675*sqrt(x*e + d)*B*a^2*b^2*d^2*e^5 - 45*sqrt(x*e + d)*A*a*b^3*d^2*e^5 - 385*(x*e + d)^(3/2)*B*a^3*b*e^6 - 55*(x*e + d)^(3/2)*A*a^2*b^2*e^6 + 435*sqrt(x*e + d)*B*a^3*b*d*e^6 + 45*sqrt(x*e + d)*A*a^2*b^2*d*e^6 - 105*sqrt(x*e + d)*B*a^4*e^7 - 15*sqrt(x*e + d)*A*a^3*b*e^7)/((b^5*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1878,1,715,0,0.448166," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{{\left(8 \, B b d e^{3} - 5 \, B a e^{4} - 3 \, A b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, {\left(b^{5} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{4} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} d e^{3} + 40 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{3} - 88 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{3} + 24 \, \sqrt{x e + d} B b^{4} d^{4} e^{3} - 15 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{3} e^{4} - 9 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} e^{4} - 113 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{4} + 33 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{4} + 231 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{4} + 33 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{4} - 87 \, \sqrt{x e + d} B a b^{3} d^{3} e^{4} - 9 \, \sqrt{x e + d} A b^{4} d^{3} e^{4} + 73 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{5} - 33 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{5} - 198 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{5} - 66 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{5} + 117 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{5} + 27 \, \sqrt{x e + d} A a b^{3} d^{2} e^{5} + 55 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{6} + 33 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{6} - 69 \, \sqrt{x e + d} B a^{3} b d e^{6} - 27 \, \sqrt{x e + d} A a^{2} b^{2} d e^{6} + 15 \, \sqrt{x e + d} B a^{4} e^{7} + 9 \, \sqrt{x e + d} A a^{3} b e^{7}}{192 \, {\left(b^{5} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{4} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-1/64*(8*B*b*d*e^3 - 5*B*a*e^4 - 3*A*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^5*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^4*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/192*(24*(x*e + d)^(7/2)*B*b^4*d*e^3 + 40*(x*e + d)^(5/2)*B*b^4*d^2*e^3 - 88*(x*e + d)^(3/2)*B*b^4*d^3*e^3 + 24*sqrt(x*e + d)*B*b^4*d^4*e^3 - 15*(x*e + d)^(7/2)*B*a*b^3*e^4 - 9*(x*e + d)^(7/2)*A*b^4*e^4 - 113*(x*e + d)^(5/2)*B*a*b^3*d*e^4 + 33*(x*e + d)^(5/2)*A*b^4*d*e^4 + 231*(x*e + d)^(3/2)*B*a*b^3*d^2*e^4 + 33*(x*e + d)^(3/2)*A*b^4*d^2*e^4 - 87*sqrt(x*e + d)*B*a*b^3*d^3*e^4 - 9*sqrt(x*e + d)*A*b^4*d^3*e^4 + 73*(x*e + d)^(5/2)*B*a^2*b^2*e^5 - 33*(x*e + d)^(5/2)*A*a*b^3*e^5 - 198*(x*e + d)^(3/2)*B*a^2*b^2*d*e^5 - 66*(x*e + d)^(3/2)*A*a*b^3*d*e^5 + 117*sqrt(x*e + d)*B*a^2*b^2*d^2*e^5 + 27*sqrt(x*e + d)*A*a*b^3*d^2*e^5 + 55*(x*e + d)^(3/2)*B*a^3*b*e^6 + 33*(x*e + d)^(3/2)*A*a^2*b^2*e^6 - 69*sqrt(x*e + d)*B*a^3*b*d*e^6 - 27*sqrt(x*e + d)*A*a^2*b^2*d*e^6 + 15*sqrt(x*e + d)*B*a^4*e^7 + 9*sqrt(x*e + d)*A*a^3*b*e^7)/((b^5*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^4*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1879,1,787,0,0.443405," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(8 \, B b d e^{3} - 3 \, B a e^{4} - 5 \, A b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, {\left(b^{5} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{4} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b^{3} d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} b^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} d e^{3} - 88 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{3} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{3} + 24 \, \sqrt{x e + d} B b^{4} d^{4} e^{3} - 9 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{3} e^{4} - 15 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} e^{4} + 121 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{4} + 55 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{4} - 47 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{4} - 73 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{4} - 81 \, \sqrt{x e + d} B a b^{3} d^{3} e^{4} - 15 \, \sqrt{x e + d} A b^{4} d^{3} e^{4} - 33 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{5} - 55 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{5} - 26 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{5} + 146 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{5} + 99 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{5} + 45 \, \sqrt{x e + d} A a b^{3} d^{2} e^{5} + 33 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{6} - 73 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{6} - 51 \, \sqrt{x e + d} B a^{3} b d e^{6} - 45 \, \sqrt{x e + d} A a^{2} b^{2} d e^{6} + 9 \, \sqrt{x e + d} B a^{4} e^{7} + 15 \, \sqrt{x e + d} A a^{3} b e^{7}}{192 \, {\left(b^{5} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{4} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b^{3} d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} b^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"1/64*(8*B*b*d*e^3 - 3*B*a*e^4 - 5*A*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^5*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^4*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b^3*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*b^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 1/192*(24*(x*e + d)^(7/2)*B*b^4*d*e^3 - 88*(x*e + d)^(5/2)*B*b^4*d^2*e^3 + 40*(x*e + d)^(3/2)*B*b^4*d^3*e^3 + 24*sqrt(x*e + d)*B*b^4*d^4*e^3 - 9*(x*e + d)^(7/2)*B*a*b^3*e^4 - 15*(x*e + d)^(7/2)*A*b^4*e^4 + 121*(x*e + d)^(5/2)*B*a*b^3*d*e^4 + 55*(x*e + d)^(5/2)*A*b^4*d*e^4 - 47*(x*e + d)^(3/2)*B*a*b^3*d^2*e^4 - 73*(x*e + d)^(3/2)*A*b^4*d^2*e^4 - 81*sqrt(x*e + d)*B*a*b^3*d^3*e^4 - 15*sqrt(x*e + d)*A*b^4*d^3*e^4 - 33*(x*e + d)^(5/2)*B*a^2*b^2*e^5 - 55*(x*e + d)^(5/2)*A*a*b^3*e^5 - 26*(x*e + d)^(3/2)*B*a^2*b^2*d*e^5 + 146*(x*e + d)^(3/2)*A*a*b^3*d*e^5 + 99*sqrt(x*e + d)*B*a^2*b^2*d^2*e^5 + 45*sqrt(x*e + d)*A*a*b^3*d^2*e^5 + 33*(x*e + d)^(3/2)*B*a^3*b*e^6 - 73*(x*e + d)^(3/2)*A*a^2*b^2*e^6 - 51*sqrt(x*e + d)*B*a^3*b*d*e^6 - 45*sqrt(x*e + d)*A*a^2*b^2*d*e^6 + 9*sqrt(x*e + d)*B*a^4*e^7 + 15*sqrt(x*e + d)*A*a^3*b*e^7)/((b^5*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^4*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b^3*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*b^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1880,1,851,0,0.410779," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{5 \, {\left(8 \, B b d e^{3} - B a e^{4} - 7 \, A b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, {\left(b^{5} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{4} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b^{2} d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} b e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{120 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} d e^{3} - 440 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{3} + 584 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{3} - 264 \, \sqrt{x e + d} B b^{4} d^{4} e^{3} - 15 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{3} e^{4} - 105 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} e^{4} + 495 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{4} + 385 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{4} - 1241 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{4} - 511 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{4} + 777 \, \sqrt{x e + d} B a b^{3} d^{3} e^{4} + 279 \, \sqrt{x e + d} A b^{4} d^{3} e^{4} - 55 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{5} - 385 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{5} + 730 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{5} + 1022 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{5} - 747 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{5} - 837 \, \sqrt{x e + d} A a b^{3} d^{2} e^{5} - 73 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{6} - 511 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{6} + 219 \, \sqrt{x e + d} B a^{3} b d e^{6} + 837 \, \sqrt{x e + d} A a^{2} b^{2} d e^{6} + 15 \, \sqrt{x e + d} B a^{4} e^{7} - 279 \, \sqrt{x e + d} A a^{3} b e^{7}}{192 \, {\left(b^{5} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{4} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b^{2} d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} b e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-5/64*(8*B*b*d*e^3 - B*a*e^4 - 7*A*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^5*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^4*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^3*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b^2*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*b*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/192*(120*(x*e + d)^(7/2)*B*b^4*d*e^3 - 440*(x*e + d)^(5/2)*B*b^4*d^2*e^3 + 584*(x*e + d)^(3/2)*B*b^4*d^3*e^3 - 264*sqrt(x*e + d)*B*b^4*d^4*e^3 - 15*(x*e + d)^(7/2)*B*a*b^3*e^4 - 105*(x*e + d)^(7/2)*A*b^4*e^4 + 495*(x*e + d)^(5/2)*B*a*b^3*d*e^4 + 385*(x*e + d)^(5/2)*A*b^4*d*e^4 - 1241*(x*e + d)^(3/2)*B*a*b^3*d^2*e^4 - 511*(x*e + d)^(3/2)*A*b^4*d^2*e^4 + 777*sqrt(x*e + d)*B*a*b^3*d^3*e^4 + 279*sqrt(x*e + d)*A*b^4*d^3*e^4 - 55*(x*e + d)^(5/2)*B*a^2*b^2*e^5 - 385*(x*e + d)^(5/2)*A*a*b^3*e^5 + 730*(x*e + d)^(3/2)*B*a^2*b^2*d*e^5 + 1022*(x*e + d)^(3/2)*A*a*b^3*d*e^5 - 747*sqrt(x*e + d)*B*a^2*b^2*d^2*e^5 - 837*sqrt(x*e + d)*A*a*b^3*d^2*e^5 - 73*(x*e + d)^(3/2)*B*a^3*b*e^6 - 511*(x*e + d)^(3/2)*A*a^2*b^2*e^6 + 219*sqrt(x*e + d)*B*a^3*b*d*e^6 + 837*sqrt(x*e + d)*A*a^2*b^2*d*e^6 + 15*sqrt(x*e + d)*B*a^4*e^7 - 279*sqrt(x*e + d)*A*a^3*b*e^7)/((b^5*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^4*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^3*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b^2*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*b*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1881,1,1132,0,0.625496," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{35 \, {\left(8 \, B b d e^{3} + B a e^{4} - 9 \, A b e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(B d e^{3} - A e^{4}\right)}}{{\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{x e + d}} - \frac{456 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{4} d e^{3} - 1544 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{4} d^{2} e^{3} + 1784 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{4} d^{3} e^{3} - 696 \, \sqrt{x e + d} B b^{4} d^{4} e^{3} + 105 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{3} e^{4} - 561 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{4} e^{4} + 1159 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{3} d e^{4} + 1929 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{4} d e^{4} - 3057 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{3} d^{2} e^{4} - 2295 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{4} d^{2} e^{4} + 1809 \, \sqrt{x e + d} B a b^{3} d^{3} e^{4} + 975 \, \sqrt{x e + d} A b^{4} d^{3} e^{4} + 385 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{2} e^{5} - 1929 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{3} e^{5} + 762 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{2} d e^{5} + 4590 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{3} d e^{5} - 1251 \, \sqrt{x e + d} B a^{2} b^{2} d^{2} e^{5} - 2925 \, \sqrt{x e + d} A a b^{3} d^{2} e^{5} + 511 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b e^{6} - 2295 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{2} e^{6} - 141 \, \sqrt{x e + d} B a^{3} b d e^{6} + 2925 \, \sqrt{x e + d} A a^{2} b^{2} d e^{6} + 279 \, \sqrt{x e + d} B a^{4} e^{7} - 975 \, \sqrt{x e + d} A a^{3} b e^{7}}{192 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-35/64*(8*B*b*d*e^3 + B*a*e^4 - 9*A*b*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 2*(B*d*e^3 - A*e^4)/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(x*e + d)) - 1/192*(456*(x*e + d)^(7/2)*B*b^4*d*e^3 - 1544*(x*e + d)^(5/2)*B*b^4*d^2*e^3 + 1784*(x*e + d)^(3/2)*B*b^4*d^3*e^3 - 696*sqrt(x*e + d)*B*b^4*d^4*e^3 + 105*(x*e + d)^(7/2)*B*a*b^3*e^4 - 561*(x*e + d)^(7/2)*A*b^4*e^4 + 1159*(x*e + d)^(5/2)*B*a*b^3*d*e^4 + 1929*(x*e + d)^(5/2)*A*b^4*d*e^4 - 3057*(x*e + d)^(3/2)*B*a*b^3*d^2*e^4 - 2295*(x*e + d)^(3/2)*A*b^4*d^2*e^4 + 1809*sqrt(x*e + d)*B*a*b^3*d^3*e^4 + 975*sqrt(x*e + d)*A*b^4*d^3*e^4 + 385*(x*e + d)^(5/2)*B*a^2*b^2*e^5 - 1929*(x*e + d)^(5/2)*A*a*b^3*e^5 + 762*(x*e + d)^(3/2)*B*a^2*b^2*d*e^5 + 4590*(x*e + d)^(3/2)*A*a*b^3*d*e^5 - 1251*sqrt(x*e + d)*B*a^2*b^2*d^2*e^5 - 2925*sqrt(x*e + d)*A*a*b^3*d^2*e^5 + 511*(x*e + d)^(3/2)*B*a^3*b*e^6 - 2295*(x*e + d)^(3/2)*A*a^2*b^2*e^6 - 141*sqrt(x*e + d)*B*a^3*b*d*e^6 + 2925*sqrt(x*e + d)*A*a^2*b^2*d*e^6 + 279*sqrt(x*e + d)*B*a^4*e^7 - 975*sqrt(x*e + d)*A*a^3*b*e^7)/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1882,1,1301,0,0.710909," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{105 \, {\left(8 \, B b^{2} d e^{3} + 3 \, B a b e^{4} - 11 \, A b^{2} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(12 \, {\left(x e + d\right)} B b d e^{3} + B b d^{2} e^{3} + 3 \, {\left(x e + d\right)} B a e^{4} - 15 \, {\left(x e + d\right)} A b e^{4} - B a d e^{4} - A b d e^{4} + A a e^{5}\right)}}{3 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{3}{2}}} - \frac{984 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{5} d e^{3} - 3224 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{5} d^{2} e^{3} + 3560 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{5} d^{3} e^{3} - 1320 \, \sqrt{x e + d} B b^{5} d^{4} e^{3} + 561 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{4} e^{4} - 1545 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{5} e^{4} + 1295 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{4} d e^{4} + 5153 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{5} d e^{4} - 4825 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{4} d^{2} e^{4} - 5855 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{5} d^{2} e^{4} + 2985 \, \sqrt{x e + d} B a b^{4} d^{3} e^{4} + 2295 \, \sqrt{x e + d} A b^{5} d^{3} e^{4} + 1929 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{3} e^{5} - 5153 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{4} e^{5} - 1030 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{3} d e^{5} + 11710 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{4} d e^{5} - 1035 \, \sqrt{x e + d} B a^{2} b^{3} d^{2} e^{5} - 6885 \, \sqrt{x e + d} A a b^{4} d^{2} e^{5} + 2295 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{2} e^{6} - 5855 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{3} e^{6} - 1605 \, \sqrt{x e + d} B a^{3} b^{2} d e^{6} + 6885 \, \sqrt{x e + d} A a^{2} b^{3} d e^{6} + 975 \, \sqrt{x e + d} B a^{4} b e^{7} - 2295 \, \sqrt{x e + d} A a^{3} b^{2} e^{7}}{192 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-105/64*(8*B*b^2*d*e^3 + 3*B*a*b*e^4 - 11*A*b^2*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 2/3*(12*(x*e + d)*B*b*d*e^3 + B*b*d^2*e^3 + 3*(x*e + d)*B*a*e^4 - 15*(x*e + d)*A*b*e^4 - B*a*d*e^4 - A*b*d*e^4 + A*a*e^5)/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(3/2)) - 1/192*(984*(x*e + d)^(7/2)*B*b^5*d*e^3 - 3224*(x*e + d)^(5/2)*B*b^5*d^2*e^3 + 3560*(x*e + d)^(3/2)*B*b^5*d^3*e^3 - 1320*sqrt(x*e + d)*B*b^5*d^4*e^3 + 561*(x*e + d)^(7/2)*B*a*b^4*e^4 - 1545*(x*e + d)^(7/2)*A*b^5*e^4 + 1295*(x*e + d)^(5/2)*B*a*b^4*d*e^4 + 5153*(x*e + d)^(5/2)*A*b^5*d*e^4 - 4825*(x*e + d)^(3/2)*B*a*b^4*d^2*e^4 - 5855*(x*e + d)^(3/2)*A*b^5*d^2*e^4 + 2985*sqrt(x*e + d)*B*a*b^4*d^3*e^4 + 2295*sqrt(x*e + d)*A*b^5*d^3*e^4 + 1929*(x*e + d)^(5/2)*B*a^2*b^3*e^5 - 5153*(x*e + d)^(5/2)*A*a*b^4*e^5 - 1030*(x*e + d)^(3/2)*B*a^2*b^3*d*e^5 + 11710*(x*e + d)^(3/2)*A*a*b^4*d*e^5 - 1035*sqrt(x*e + d)*B*a^2*b^3*d^2*e^5 - 6885*sqrt(x*e + d)*A*a*b^4*d^2*e^5 + 2295*(x*e + d)^(3/2)*B*a^3*b^2*e^6 - 5855*(x*e + d)^(3/2)*A*a^2*b^3*e^6 - 1605*sqrt(x*e + d)*B*a^3*b^2*d*e^6 + 6885*sqrt(x*e + d)*A*a^2*b^3*d*e^6 + 975*sqrt(x*e + d)*B*a^4*b*e^7 - 2295*sqrt(x*e + d)*A*a^3*b^2*e^7)/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1883,1,1527,0,0.850655," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{231 \, {\left(8 \, B b^{3} d e^{3} + 5 \, B a b^{2} e^{4} - 13 \, A b^{3} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, {\left(b^{7} d^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 7 \, a b^{6} d^{6} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 21 \, a^{2} b^{5} d^{5} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 35 \, a^{3} b^{4} d^{4} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 35 \, a^{4} b^{3} d^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 21 \, a^{5} b^{2} d^{2} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 7 \, a^{6} b d e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{7} e^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} B b^{2} d e^{3} + 20 \, {\left(x e + d\right)} B b^{2} d^{2} e^{3} + 3 \, B b^{2} d^{3} e^{3} + 75 \, {\left(x e + d\right)}^{2} B a b e^{4} - 225 \, {\left(x e + d\right)}^{2} A b^{2} e^{4} - 15 \, {\left(x e + d\right)} B a b d e^{4} - 25 \, {\left(x e + d\right)} A b^{2} d e^{4} - 6 \, B a b d^{2} e^{4} - 3 \, A b^{2} d^{2} e^{4} - 5 \, {\left(x e + d\right)} B a^{2} e^{5} + 25 \, {\left(x e + d\right)} A a b e^{5} + 3 \, B a^{2} d e^{5} + 6 \, A a b d e^{5} - 3 \, A a^{2} e^{6}\right)}}{15 \, {\left(b^{7} d^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 7 \, a b^{6} d^{6} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 21 \, a^{2} b^{5} d^{5} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 35 \, a^{3} b^{4} d^{4} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 35 \, a^{4} b^{3} d^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 21 \, a^{5} b^{2} d^{2} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 7 \, a^{6} b d e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{7} e^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{5}{2}}} - \frac{1704 \, {\left(x e + d\right)}^{\frac{7}{2}} B b^{6} d e^{3} - 5480 \, {\left(x e + d\right)}^{\frac{5}{2}} B b^{6} d^{2} e^{3} + 5912 \, {\left(x e + d\right)}^{\frac{3}{2}} B b^{6} d^{3} e^{3} - 2136 \, \sqrt{x e + d} B b^{6} d^{4} e^{3} + 1545 \, {\left(x e + d\right)}^{\frac{7}{2}} B a b^{5} e^{4} - 3249 \, {\left(x e + d\right)}^{\frac{7}{2}} A b^{6} e^{4} + 327 \, {\left(x e + d\right)}^{\frac{5}{2}} B a b^{5} d e^{4} + 10633 \, {\left(x e + d\right)}^{\frac{5}{2}} A b^{6} d e^{4} - 5969 \, {\left(x e + d\right)}^{\frac{3}{2}} B a b^{5} d^{2} e^{4} - 11767 \, {\left(x e + d\right)}^{\frac{3}{2}} A b^{6} d^{2} e^{4} + 4113 \, \sqrt{x e + d} B a b^{5} d^{3} e^{4} + 4431 \, \sqrt{x e + d} A b^{6} d^{3} e^{4} + 5153 \, {\left(x e + d\right)}^{\frac{5}{2}} B a^{2} b^{4} e^{5} - 10633 \, {\left(x e + d\right)}^{\frac{5}{2}} A a b^{5} e^{5} - 5798 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{2} b^{4} d e^{5} + 23534 \, {\left(x e + d\right)}^{\frac{3}{2}} A a b^{5} d e^{5} + 477 \, \sqrt{x e + d} B a^{2} b^{4} d^{2} e^{5} - 13293 \, \sqrt{x e + d} A a b^{5} d^{2} e^{5} + 5855 \, {\left(x e + d\right)}^{\frac{3}{2}} B a^{3} b^{3} e^{6} - 11767 \, {\left(x e + d\right)}^{\frac{3}{2}} A a^{2} b^{4} e^{6} - 4749 \, \sqrt{x e + d} B a^{3} b^{3} d e^{6} + 13293 \, \sqrt{x e + d} A a^{2} b^{4} d e^{6} + 2295 \, \sqrt{x e + d} B a^{4} b^{2} e^{7} - 4431 \, \sqrt{x e + d} A a^{3} b^{3} e^{7}}{192 \, {\left(b^{7} d^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 7 \, a b^{6} d^{6} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 21 \, a^{2} b^{5} d^{5} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 35 \, a^{3} b^{4} d^{4} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 35 \, a^{4} b^{3} d^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 21 \, a^{5} b^{2} d^{2} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 7 \, a^{6} b d e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{7} e^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-231/64*(8*B*b^3*d*e^3 + 5*B*a*b^2*e^4 - 13*A*b^3*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^7*d^7*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 7*a*b^6*d^6*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 21*a^2*b^5*d^5*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 35*a^3*b^4*d^4*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 35*a^4*b^3*d^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 21*a^5*b^2*d^2*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 7*a^6*b*d*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^7*e^7*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 2/15*(150*(x*e + d)^2*B*b^2*d*e^3 + 20*(x*e + d)*B*b^2*d^2*e^3 + 3*B*b^2*d^3*e^3 + 75*(x*e + d)^2*B*a*b*e^4 - 225*(x*e + d)^2*A*b^2*e^4 - 15*(x*e + d)*B*a*b*d*e^4 - 25*(x*e + d)*A*b^2*d*e^4 - 6*B*a*b*d^2*e^4 - 3*A*b^2*d^2*e^4 - 5*(x*e + d)*B*a^2*e^5 + 25*(x*e + d)*A*a*b*e^5 + 3*B*a^2*d*e^5 + 6*A*a*b*d*e^5 - 3*A*a^2*e^6)/((b^7*d^7*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 7*a*b^6*d^6*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 21*a^2*b^5*d^5*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 35*a^3*b^4*d^4*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 35*a^4*b^3*d^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 21*a^5*b^2*d^2*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 7*a^6*b*d*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^7*e^7*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(5/2)) - 1/192*(1704*(x*e + d)^(7/2)*B*b^6*d*e^3 - 5480*(x*e + d)^(5/2)*B*b^6*d^2*e^3 + 5912*(x*e + d)^(3/2)*B*b^6*d^3*e^3 - 2136*sqrt(x*e + d)*B*b^6*d^4*e^3 + 1545*(x*e + d)^(7/2)*B*a*b^5*e^4 - 3249*(x*e + d)^(7/2)*A*b^6*e^4 + 327*(x*e + d)^(5/2)*B*a*b^5*d*e^4 + 10633*(x*e + d)^(5/2)*A*b^6*d*e^4 - 5969*(x*e + d)^(3/2)*B*a*b^5*d^2*e^4 - 11767*(x*e + d)^(3/2)*A*b^6*d^2*e^4 + 4113*sqrt(x*e + d)*B*a*b^5*d^3*e^4 + 4431*sqrt(x*e + d)*A*b^6*d^3*e^4 + 5153*(x*e + d)^(5/2)*B*a^2*b^4*e^5 - 10633*(x*e + d)^(5/2)*A*a*b^5*e^5 - 5798*(x*e + d)^(3/2)*B*a^2*b^4*d*e^5 + 23534*(x*e + d)^(3/2)*A*a*b^5*d*e^5 + 477*sqrt(x*e + d)*B*a^2*b^4*d^2*e^5 - 13293*sqrt(x*e + d)*A*a*b^5*d^2*e^5 + 5855*(x*e + d)^(3/2)*B*a^3*b^3*e^6 - 11767*(x*e + d)^(3/2)*A*a^2*b^4*e^6 - 4749*sqrt(x*e + d)*B*a^3*b^3*d*e^6 + 13293*sqrt(x*e + d)*A*a^2*b^4*d*e^6 + 2295*sqrt(x*e + d)*B*a^4*b^2*e^7 - 4431*sqrt(x*e + d)*A*a^3*b^3*e^7)/((b^7*d^7*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 7*a*b^6*d^6*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 21*a^2*b^5*d^5*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 35*a^3*b^4*d^4*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 35*a^4*b^3*d^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 21*a^5*b^2*d^2*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 7*a^6*b*d*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^7*e^7*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1884,1,4381,0,0.318933," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B b^{4} m^{5} x^{6} e^{6} + {\left(x e + d\right)}^{m} B b^{4} d m^{5} x^{5} e^{5} + 4 \, {\left(x e + d\right)}^{m} B a b^{3} m^{5} x^{5} e^{6} + {\left(x e + d\right)}^{m} A b^{4} m^{5} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} B b^{4} m^{4} x^{6} e^{6} + 4 \, {\left(x e + d\right)}^{m} B a b^{3} d m^{5} x^{4} e^{5} + {\left(x e + d\right)}^{m} A b^{4} d m^{5} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} B b^{4} d m^{4} x^{5} e^{5} - 5 \, {\left(x e + d\right)}^{m} B b^{4} d^{2} m^{4} x^{4} e^{4} + 6 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} m^{5} x^{4} e^{6} + 4 \, {\left(x e + d\right)}^{m} A a b^{3} m^{5} x^{4} e^{6} + 64 \, {\left(x e + d\right)}^{m} B a b^{3} m^{4} x^{5} e^{6} + 16 \, {\left(x e + d\right)}^{m} A b^{4} m^{4} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} B b^{4} m^{3} x^{6} e^{6} + 6 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d m^{5} x^{3} e^{5} + 4 \, {\left(x e + d\right)}^{m} A a b^{3} d m^{5} x^{3} e^{5} + 48 \, {\left(x e + d\right)}^{m} B a b^{3} d m^{4} x^{4} e^{5} + 12 \, {\left(x e + d\right)}^{m} A b^{4} d m^{4} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} B b^{4} d m^{3} x^{5} e^{5} - 16 \, {\left(x e + d\right)}^{m} B a b^{3} d^{2} m^{4} x^{3} e^{4} - 4 \, {\left(x e + d\right)}^{m} A b^{4} d^{2} m^{4} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B b^{4} d^{2} m^{3} x^{4} e^{4} + 20 \, {\left(x e + d\right)}^{m} B b^{4} d^{3} m^{3} x^{3} e^{3} + 4 \, {\left(x e + d\right)}^{m} B a^{3} b m^{5} x^{3} e^{6} + 6 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} m^{5} x^{3} e^{6} + 102 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} m^{4} x^{4} e^{6} + 68 \, {\left(x e + d\right)}^{m} A a b^{3} m^{4} x^{4} e^{6} + 380 \, {\left(x e + d\right)}^{m} B a b^{3} m^{3} x^{5} e^{6} + 95 \, {\left(x e + d\right)}^{m} A b^{4} m^{3} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} B b^{4} m^{2} x^{6} e^{6} + 4 \, {\left(x e + d\right)}^{m} B a^{3} b d m^{5} x^{2} e^{5} + 6 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d m^{5} x^{2} e^{5} + 84 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d m^{4} x^{3} e^{5} + 56 \, {\left(x e + d\right)}^{m} A a b^{3} d m^{4} x^{3} e^{5} + 188 \, {\left(x e + d\right)}^{m} B a b^{3} d m^{3} x^{4} e^{5} + 47 \, {\left(x e + d\right)}^{m} A b^{4} d m^{3} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} B b^{4} d m^{2} x^{5} e^{5} - 18 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{2} m^{4} x^{2} e^{4} - 12 \, {\left(x e + d\right)}^{m} A a b^{3} d^{2} m^{4} x^{2} e^{4} - 144 \, {\left(x e + d\right)}^{m} B a b^{3} d^{2} m^{3} x^{3} e^{4} - 36 \, {\left(x e + d\right)}^{m} A b^{4} d^{2} m^{3} x^{3} e^{4} - 55 \, {\left(x e + d\right)}^{m} B b^{4} d^{2} m^{2} x^{4} e^{4} + 48 \, {\left(x e + d\right)}^{m} B a b^{3} d^{3} m^{3} x^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} A b^{4} d^{3} m^{3} x^{2} e^{3} + 60 \, {\left(x e + d\right)}^{m} B b^{4} d^{3} m^{2} x^{3} e^{3} - 60 \, {\left(x e + d\right)}^{m} B b^{4} d^{4} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a^{4} m^{5} x^{2} e^{6} + 4 \, {\left(x e + d\right)}^{m} A a^{3} b m^{5} x^{2} e^{6} + 72 \, {\left(x e + d\right)}^{m} B a^{3} b m^{4} x^{3} e^{6} + 108 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} m^{4} x^{3} e^{6} + 642 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} m^{3} x^{4} e^{6} + 428 \, {\left(x e + d\right)}^{m} A a b^{3} m^{3} x^{4} e^{6} + 1040 \, {\left(x e + d\right)}^{m} B a b^{3} m^{2} x^{5} e^{6} + 260 \, {\left(x e + d\right)}^{m} A b^{4} m^{2} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} B b^{4} m x^{6} e^{6} + {\left(x e + d\right)}^{m} B a^{4} d m^{5} x e^{5} + 4 \, {\left(x e + d\right)}^{m} A a^{3} b d m^{5} x e^{5} + 64 \, {\left(x e + d\right)}^{m} B a^{3} b d m^{4} x^{2} e^{5} + 96 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d m^{4} x^{2} e^{5} + 390 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d m^{3} x^{3} e^{5} + 260 \, {\left(x e + d\right)}^{m} A a b^{3} d m^{3} x^{3} e^{5} + 288 \, {\left(x e + d\right)}^{m} B a b^{3} d m^{2} x^{4} e^{5} + 72 \, {\left(x e + d\right)}^{m} A b^{4} d m^{2} x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} B b^{4} d m x^{5} e^{5} - 8 \, {\left(x e + d\right)}^{m} B a^{3} b d^{2} m^{4} x e^{4} - 12 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{2} m^{4} x e^{4} - 216 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{2} m^{3} x^{2} e^{4} - 144 \, {\left(x e + d\right)}^{m} A a b^{3} d^{2} m^{3} x^{2} e^{4} - 320 \, {\left(x e + d\right)}^{m} B a b^{3} d^{2} m^{2} x^{3} e^{4} - 80 \, {\left(x e + d\right)}^{m} A b^{4} d^{2} m^{2} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B b^{4} d^{2} m x^{4} e^{4} + 36 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{3} m^{3} x e^{3} + 24 \, {\left(x e + d\right)}^{m} A a b^{3} d^{3} m^{3} x e^{3} + 336 \, {\left(x e + d\right)}^{m} B a b^{3} d^{3} m^{2} x^{2} e^{3} + 84 \, {\left(x e + d\right)}^{m} A b^{4} d^{3} m^{2} x^{2} e^{3} + 40 \, {\left(x e + d\right)}^{m} B b^{4} d^{3} m x^{3} e^{3} - 96 \, {\left(x e + d\right)}^{m} B a b^{3} d^{4} m^{2} x e^{2} - 24 \, {\left(x e + d\right)}^{m} A b^{4} d^{4} m^{2} x e^{2} - 60 \, {\left(x e + d\right)}^{m} B b^{4} d^{4} m x^{2} e^{2} + 120 \, {\left(x e + d\right)}^{m} B b^{4} d^{5} m x e + {\left(x e + d\right)}^{m} A a^{4} m^{5} x e^{6} + 19 \, {\left(x e + d\right)}^{m} B a^{4} m^{4} x^{2} e^{6} + 76 \, {\left(x e + d\right)}^{m} A a^{3} b m^{4} x^{2} e^{6} + 484 \, {\left(x e + d\right)}^{m} B a^{3} b m^{3} x^{3} e^{6} + 726 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} m^{3} x^{3} e^{6} + 1842 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} m^{2} x^{4} e^{6} + 1228 \, {\left(x e + d\right)}^{m} A a b^{3} m^{2} x^{4} e^{6} + 1296 \, {\left(x e + d\right)}^{m} B a b^{3} m x^{5} e^{6} + 324 \, {\left(x e + d\right)}^{m} A b^{4} m x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} B b^{4} x^{6} e^{6} + {\left(x e + d\right)}^{m} A a^{4} d m^{5} e^{5} + 18 \, {\left(x e + d\right)}^{m} B a^{4} d m^{4} x e^{5} + 72 \, {\left(x e + d\right)}^{m} A a^{3} b d m^{4} x e^{5} + 356 \, {\left(x e + d\right)}^{m} B a^{3} b d m^{3} x^{2} e^{5} + 534 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d m^{3} x^{2} e^{5} + 672 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d m^{2} x^{3} e^{5} + 448 \, {\left(x e + d\right)}^{m} A a b^{3} d m^{2} x^{3} e^{5} + 144 \, {\left(x e + d\right)}^{m} B a b^{3} d m x^{4} e^{5} + 36 \, {\left(x e + d\right)}^{m} A b^{4} d m x^{4} e^{5} - {\left(x e + d\right)}^{m} B a^{4} d^{2} m^{4} e^{4} - 4 \, {\left(x e + d\right)}^{m} A a^{3} b d^{2} m^{4} e^{4} - 120 \, {\left(x e + d\right)}^{m} B a^{3} b d^{2} m^{3} x e^{4} - 180 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{2} m^{3} x e^{4} - 738 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{2} m^{2} x^{2} e^{4} - 492 \, {\left(x e + d\right)}^{m} A a b^{3} d^{2} m^{2} x^{2} e^{4} - 192 \, {\left(x e + d\right)}^{m} B a b^{3} d^{2} m x^{3} e^{4} - 48 \, {\left(x e + d\right)}^{m} A b^{4} d^{2} m x^{3} e^{4} + 8 \, {\left(x e + d\right)}^{m} B a^{3} b d^{3} m^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{3} m^{3} e^{3} + 396 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{3} m^{2} x e^{3} + 264 \, {\left(x e + d\right)}^{m} A a b^{3} d^{3} m^{2} x e^{3} + 288 \, {\left(x e + d\right)}^{m} B a b^{3} d^{3} m x^{2} e^{3} + 72 \, {\left(x e + d\right)}^{m} A b^{4} d^{3} m x^{2} e^{3} - 36 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{4} m^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} A a b^{3} d^{4} m^{2} e^{2} - 576 \, {\left(x e + d\right)}^{m} B a b^{3} d^{4} m x e^{2} - 144 \, {\left(x e + d\right)}^{m} A b^{4} d^{4} m x e^{2} + 96 \, {\left(x e + d\right)}^{m} B a b^{3} d^{5} m e + 24 \, {\left(x e + d\right)}^{m} A b^{4} d^{5} m e - 120 \, {\left(x e + d\right)}^{m} B b^{4} d^{6} + 20 \, {\left(x e + d\right)}^{m} A a^{4} m^{4} x e^{6} + 137 \, {\left(x e + d\right)}^{m} B a^{4} m^{3} x^{2} e^{6} + 548 \, {\left(x e + d\right)}^{m} A a^{3} b m^{3} x^{2} e^{6} + 1488 \, {\left(x e + d\right)}^{m} B a^{3} b m^{2} x^{3} e^{6} + 2232 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} m^{2} x^{3} e^{6} + 2376 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} m x^{4} e^{6} + 1584 \, {\left(x e + d\right)}^{m} A a b^{3} m x^{4} e^{6} + 576 \, {\left(x e + d\right)}^{m} B a b^{3} x^{5} e^{6} + 144 \, {\left(x e + d\right)}^{m} A b^{4} x^{5} e^{6} + 20 \, {\left(x e + d\right)}^{m} A a^{4} d m^{4} e^{5} + 119 \, {\left(x e + d\right)}^{m} B a^{4} d m^{3} x e^{5} + 476 \, {\left(x e + d\right)}^{m} A a^{3} b d m^{3} x e^{5} + 776 \, {\left(x e + d\right)}^{m} B a^{3} b d m^{2} x^{2} e^{5} + 1164 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d m^{2} x^{2} e^{5} + 360 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d m x^{3} e^{5} + 240 \, {\left(x e + d\right)}^{m} A a b^{3} d m x^{3} e^{5} - 18 \, {\left(x e + d\right)}^{m} B a^{4} d^{2} m^{3} e^{4} - 72 \, {\left(x e + d\right)}^{m} A a^{3} b d^{2} m^{3} e^{4} - 592 \, {\left(x e + d\right)}^{m} B a^{3} b d^{2} m^{2} x e^{4} - 888 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{2} m^{2} x e^{4} - 540 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{2} m x^{2} e^{4} - 360 \, {\left(x e + d\right)}^{m} A a b^{3} d^{2} m x^{2} e^{4} + 120 \, {\left(x e + d\right)}^{m} B a^{3} b d^{3} m^{2} e^{3} + 180 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{3} m^{2} e^{3} + 1080 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{3} m x e^{3} + 720 \, {\left(x e + d\right)}^{m} A a b^{3} d^{3} m x e^{3} - 396 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{4} m e^{2} - 264 \, {\left(x e + d\right)}^{m} A a b^{3} d^{4} m e^{2} + 576 \, {\left(x e + d\right)}^{m} B a b^{3} d^{5} e + 144 \, {\left(x e + d\right)}^{m} A b^{4} d^{5} e + 155 \, {\left(x e + d\right)}^{m} A a^{4} m^{3} x e^{6} + 461 \, {\left(x e + d\right)}^{m} B a^{4} m^{2} x^{2} e^{6} + 1844 \, {\left(x e + d\right)}^{m} A a^{3} b m^{2} x^{2} e^{6} + 2032 \, {\left(x e + d\right)}^{m} B a^{3} b m x^{3} e^{6} + 3048 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} m x^{3} e^{6} + 1080 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} x^{4} e^{6} + 720 \, {\left(x e + d\right)}^{m} A a b^{3} x^{4} e^{6} + 155 \, {\left(x e + d\right)}^{m} A a^{4} d m^{3} e^{5} + 342 \, {\left(x e + d\right)}^{m} B a^{4} d m^{2} x e^{5} + 1368 \, {\left(x e + d\right)}^{m} A a^{3} b d m^{2} x e^{5} + 480 \, {\left(x e + d\right)}^{m} B a^{3} b d m x^{2} e^{5} + 720 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d m x^{2} e^{5} - 119 \, {\left(x e + d\right)}^{m} B a^{4} d^{2} m^{2} e^{4} - 476 \, {\left(x e + d\right)}^{m} A a^{3} b d^{2} m^{2} e^{4} - 960 \, {\left(x e + d\right)}^{m} B a^{3} b d^{2} m x e^{4} - 1440 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{2} m x e^{4} + 592 \, {\left(x e + d\right)}^{m} B a^{3} b d^{3} m e^{3} + 888 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{3} m e^{3} - 1080 \, {\left(x e + d\right)}^{m} B a^{2} b^{2} d^{4} e^{2} - 720 \, {\left(x e + d\right)}^{m} A a b^{3} d^{4} e^{2} + 580 \, {\left(x e + d\right)}^{m} A a^{4} m^{2} x e^{6} + 702 \, {\left(x e + d\right)}^{m} B a^{4} m x^{2} e^{6} + 2808 \, {\left(x e + d\right)}^{m} A a^{3} b m x^{2} e^{6} + 960 \, {\left(x e + d\right)}^{m} B a^{3} b x^{3} e^{6} + 1440 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} x^{3} e^{6} + 580 \, {\left(x e + d\right)}^{m} A a^{4} d m^{2} e^{5} + 360 \, {\left(x e + d\right)}^{m} B a^{4} d m x e^{5} + 1440 \, {\left(x e + d\right)}^{m} A a^{3} b d m x e^{5} - 342 \, {\left(x e + d\right)}^{m} B a^{4} d^{2} m e^{4} - 1368 \, {\left(x e + d\right)}^{m} A a^{3} b d^{2} m e^{4} + 960 \, {\left(x e + d\right)}^{m} B a^{3} b d^{3} e^{3} + 1440 \, {\left(x e + d\right)}^{m} A a^{2} b^{2} d^{3} e^{3} + 1044 \, {\left(x e + d\right)}^{m} A a^{4} m x e^{6} + 360 \, {\left(x e + d\right)}^{m} B a^{4} x^{2} e^{6} + 1440 \, {\left(x e + d\right)}^{m} A a^{3} b x^{2} e^{6} + 1044 \, {\left(x e + d\right)}^{m} A a^{4} d m e^{5} - 360 \, {\left(x e + d\right)}^{m} B a^{4} d^{2} e^{4} - 1440 \, {\left(x e + d\right)}^{m} A a^{3} b d^{2} e^{4} + 720 \, {\left(x e + d\right)}^{m} A a^{4} x e^{6} + 720 \, {\left(x e + d\right)}^{m} A a^{4} d e^{5}}{m^{6} e^{6} + 21 \, m^{5} e^{6} + 175 \, m^{4} e^{6} + 735 \, m^{3} e^{6} + 1624 \, m^{2} e^{6} + 1764 \, m e^{6} + 720 \, e^{6}}"," ",0,"((x*e + d)^m*B*b^4*m^5*x^6*e^6 + (x*e + d)^m*B*b^4*d*m^5*x^5*e^5 + 4*(x*e + d)^m*B*a*b^3*m^5*x^5*e^6 + (x*e + d)^m*A*b^4*m^5*x^5*e^6 + 15*(x*e + d)^m*B*b^4*m^4*x^6*e^6 + 4*(x*e + d)^m*B*a*b^3*d*m^5*x^4*e^5 + (x*e + d)^m*A*b^4*d*m^5*x^4*e^5 + 10*(x*e + d)^m*B*b^4*d*m^4*x^5*e^5 - 5*(x*e + d)^m*B*b^4*d^2*m^4*x^4*e^4 + 6*(x*e + d)^m*B*a^2*b^2*m^5*x^4*e^6 + 4*(x*e + d)^m*A*a*b^3*m^5*x^4*e^6 + 64*(x*e + d)^m*B*a*b^3*m^4*x^5*e^6 + 16*(x*e + d)^m*A*b^4*m^4*x^5*e^6 + 85*(x*e + d)^m*B*b^4*m^3*x^6*e^6 + 6*(x*e + d)^m*B*a^2*b^2*d*m^5*x^3*e^5 + 4*(x*e + d)^m*A*a*b^3*d*m^5*x^3*e^5 + 48*(x*e + d)^m*B*a*b^3*d*m^4*x^4*e^5 + 12*(x*e + d)^m*A*b^4*d*m^4*x^4*e^5 + 35*(x*e + d)^m*B*b^4*d*m^3*x^5*e^5 - 16*(x*e + d)^m*B*a*b^3*d^2*m^4*x^3*e^4 - 4*(x*e + d)^m*A*b^4*d^2*m^4*x^3*e^4 - 30*(x*e + d)^m*B*b^4*d^2*m^3*x^4*e^4 + 20*(x*e + d)^m*B*b^4*d^3*m^3*x^3*e^3 + 4*(x*e + d)^m*B*a^3*b*m^5*x^3*e^6 + 6*(x*e + d)^m*A*a^2*b^2*m^5*x^3*e^6 + 102*(x*e + d)^m*B*a^2*b^2*m^4*x^4*e^6 + 68*(x*e + d)^m*A*a*b^3*m^4*x^4*e^6 + 380*(x*e + d)^m*B*a*b^3*m^3*x^5*e^6 + 95*(x*e + d)^m*A*b^4*m^3*x^5*e^6 + 225*(x*e + d)^m*B*b^4*m^2*x^6*e^6 + 4*(x*e + d)^m*B*a^3*b*d*m^5*x^2*e^5 + 6*(x*e + d)^m*A*a^2*b^2*d*m^5*x^2*e^5 + 84*(x*e + d)^m*B*a^2*b^2*d*m^4*x^3*e^5 + 56*(x*e + d)^m*A*a*b^3*d*m^4*x^3*e^5 + 188*(x*e + d)^m*B*a*b^3*d*m^3*x^4*e^5 + 47*(x*e + d)^m*A*b^4*d*m^3*x^4*e^5 + 50*(x*e + d)^m*B*b^4*d*m^2*x^5*e^5 - 18*(x*e + d)^m*B*a^2*b^2*d^2*m^4*x^2*e^4 - 12*(x*e + d)^m*A*a*b^3*d^2*m^4*x^2*e^4 - 144*(x*e + d)^m*B*a*b^3*d^2*m^3*x^3*e^4 - 36*(x*e + d)^m*A*b^4*d^2*m^3*x^3*e^4 - 55*(x*e + d)^m*B*b^4*d^2*m^2*x^4*e^4 + 48*(x*e + d)^m*B*a*b^3*d^3*m^3*x^2*e^3 + 12*(x*e + d)^m*A*b^4*d^3*m^3*x^2*e^3 + 60*(x*e + d)^m*B*b^4*d^3*m^2*x^3*e^3 - 60*(x*e + d)^m*B*b^4*d^4*m^2*x^2*e^2 + (x*e + d)^m*B*a^4*m^5*x^2*e^6 + 4*(x*e + d)^m*A*a^3*b*m^5*x^2*e^6 + 72*(x*e + d)^m*B*a^3*b*m^4*x^3*e^6 + 108*(x*e + d)^m*A*a^2*b^2*m^4*x^3*e^6 + 642*(x*e + d)^m*B*a^2*b^2*m^3*x^4*e^6 + 428*(x*e + d)^m*A*a*b^3*m^3*x^4*e^6 + 1040*(x*e + d)^m*B*a*b^3*m^2*x^5*e^6 + 260*(x*e + d)^m*A*b^4*m^2*x^5*e^6 + 274*(x*e + d)^m*B*b^4*m*x^6*e^6 + (x*e + d)^m*B*a^4*d*m^5*x*e^5 + 4*(x*e + d)^m*A*a^3*b*d*m^5*x*e^5 + 64*(x*e + d)^m*B*a^3*b*d*m^4*x^2*e^5 + 96*(x*e + d)^m*A*a^2*b^2*d*m^4*x^2*e^5 + 390*(x*e + d)^m*B*a^2*b^2*d*m^3*x^3*e^5 + 260*(x*e + d)^m*A*a*b^3*d*m^3*x^3*e^5 + 288*(x*e + d)^m*B*a*b^3*d*m^2*x^4*e^5 + 72*(x*e + d)^m*A*b^4*d*m^2*x^4*e^5 + 24*(x*e + d)^m*B*b^4*d*m*x^5*e^5 - 8*(x*e + d)^m*B*a^3*b*d^2*m^4*x*e^4 - 12*(x*e + d)^m*A*a^2*b^2*d^2*m^4*x*e^4 - 216*(x*e + d)^m*B*a^2*b^2*d^2*m^3*x^2*e^4 - 144*(x*e + d)^m*A*a*b^3*d^2*m^3*x^2*e^4 - 320*(x*e + d)^m*B*a*b^3*d^2*m^2*x^3*e^4 - 80*(x*e + d)^m*A*b^4*d^2*m^2*x^3*e^4 - 30*(x*e + d)^m*B*b^4*d^2*m*x^4*e^4 + 36*(x*e + d)^m*B*a^2*b^2*d^3*m^3*x*e^3 + 24*(x*e + d)^m*A*a*b^3*d^3*m^3*x*e^3 + 336*(x*e + d)^m*B*a*b^3*d^3*m^2*x^2*e^3 + 84*(x*e + d)^m*A*b^4*d^3*m^2*x^2*e^3 + 40*(x*e + d)^m*B*b^4*d^3*m*x^3*e^3 - 96*(x*e + d)^m*B*a*b^3*d^4*m^2*x*e^2 - 24*(x*e + d)^m*A*b^4*d^4*m^2*x*e^2 - 60*(x*e + d)^m*B*b^4*d^4*m*x^2*e^2 + 120*(x*e + d)^m*B*b^4*d^5*m*x*e + (x*e + d)^m*A*a^4*m^5*x*e^6 + 19*(x*e + d)^m*B*a^4*m^4*x^2*e^6 + 76*(x*e + d)^m*A*a^3*b*m^4*x^2*e^6 + 484*(x*e + d)^m*B*a^3*b*m^3*x^3*e^6 + 726*(x*e + d)^m*A*a^2*b^2*m^3*x^3*e^6 + 1842*(x*e + d)^m*B*a^2*b^2*m^2*x^4*e^6 + 1228*(x*e + d)^m*A*a*b^3*m^2*x^4*e^6 + 1296*(x*e + d)^m*B*a*b^3*m*x^5*e^6 + 324*(x*e + d)^m*A*b^4*m*x^5*e^6 + 120*(x*e + d)^m*B*b^4*x^6*e^6 + (x*e + d)^m*A*a^4*d*m^5*e^5 + 18*(x*e + d)^m*B*a^4*d*m^4*x*e^5 + 72*(x*e + d)^m*A*a^3*b*d*m^4*x*e^5 + 356*(x*e + d)^m*B*a^3*b*d*m^3*x^2*e^5 + 534*(x*e + d)^m*A*a^2*b^2*d*m^3*x^2*e^5 + 672*(x*e + d)^m*B*a^2*b^2*d*m^2*x^3*e^5 + 448*(x*e + d)^m*A*a*b^3*d*m^2*x^3*e^5 + 144*(x*e + d)^m*B*a*b^3*d*m*x^4*e^5 + 36*(x*e + d)^m*A*b^4*d*m*x^4*e^5 - (x*e + d)^m*B*a^4*d^2*m^4*e^4 - 4*(x*e + d)^m*A*a^3*b*d^2*m^4*e^4 - 120*(x*e + d)^m*B*a^3*b*d^2*m^3*x*e^4 - 180*(x*e + d)^m*A*a^2*b^2*d^2*m^3*x*e^4 - 738*(x*e + d)^m*B*a^2*b^2*d^2*m^2*x^2*e^4 - 492*(x*e + d)^m*A*a*b^3*d^2*m^2*x^2*e^4 - 192*(x*e + d)^m*B*a*b^3*d^2*m*x^3*e^4 - 48*(x*e + d)^m*A*b^4*d^2*m*x^3*e^4 + 8*(x*e + d)^m*B*a^3*b*d^3*m^3*e^3 + 12*(x*e + d)^m*A*a^2*b^2*d^3*m^3*e^3 + 396*(x*e + d)^m*B*a^2*b^2*d^3*m^2*x*e^3 + 264*(x*e + d)^m*A*a*b^3*d^3*m^2*x*e^3 + 288*(x*e + d)^m*B*a*b^3*d^3*m*x^2*e^3 + 72*(x*e + d)^m*A*b^4*d^3*m*x^2*e^3 - 36*(x*e + d)^m*B*a^2*b^2*d^4*m^2*e^2 - 24*(x*e + d)^m*A*a*b^3*d^4*m^2*e^2 - 576*(x*e + d)^m*B*a*b^3*d^4*m*x*e^2 - 144*(x*e + d)^m*A*b^4*d^4*m*x*e^2 + 96*(x*e + d)^m*B*a*b^3*d^5*m*e + 24*(x*e + d)^m*A*b^4*d^5*m*e - 120*(x*e + d)^m*B*b^4*d^6 + 20*(x*e + d)^m*A*a^4*m^4*x*e^6 + 137*(x*e + d)^m*B*a^4*m^3*x^2*e^6 + 548*(x*e + d)^m*A*a^3*b*m^3*x^2*e^6 + 1488*(x*e + d)^m*B*a^3*b*m^2*x^3*e^6 + 2232*(x*e + d)^m*A*a^2*b^2*m^2*x^3*e^6 + 2376*(x*e + d)^m*B*a^2*b^2*m*x^4*e^6 + 1584*(x*e + d)^m*A*a*b^3*m*x^4*e^6 + 576*(x*e + d)^m*B*a*b^3*x^5*e^6 + 144*(x*e + d)^m*A*b^4*x^5*e^6 + 20*(x*e + d)^m*A*a^4*d*m^4*e^5 + 119*(x*e + d)^m*B*a^4*d*m^3*x*e^5 + 476*(x*e + d)^m*A*a^3*b*d*m^3*x*e^5 + 776*(x*e + d)^m*B*a^3*b*d*m^2*x^2*e^5 + 1164*(x*e + d)^m*A*a^2*b^2*d*m^2*x^2*e^5 + 360*(x*e + d)^m*B*a^2*b^2*d*m*x^3*e^5 + 240*(x*e + d)^m*A*a*b^3*d*m*x^3*e^5 - 18*(x*e + d)^m*B*a^4*d^2*m^3*e^4 - 72*(x*e + d)^m*A*a^3*b*d^2*m^3*e^4 - 592*(x*e + d)^m*B*a^3*b*d^2*m^2*x*e^4 - 888*(x*e + d)^m*A*a^2*b^2*d^2*m^2*x*e^4 - 540*(x*e + d)^m*B*a^2*b^2*d^2*m*x^2*e^4 - 360*(x*e + d)^m*A*a*b^3*d^2*m*x^2*e^4 + 120*(x*e + d)^m*B*a^3*b*d^3*m^2*e^3 + 180*(x*e + d)^m*A*a^2*b^2*d^3*m^2*e^3 + 1080*(x*e + d)^m*B*a^2*b^2*d^3*m*x*e^3 + 720*(x*e + d)^m*A*a*b^3*d^3*m*x*e^3 - 396*(x*e + d)^m*B*a^2*b^2*d^4*m*e^2 - 264*(x*e + d)^m*A*a*b^3*d^4*m*e^2 + 576*(x*e + d)^m*B*a*b^3*d^5*e + 144*(x*e + d)^m*A*b^4*d^5*e + 155*(x*e + d)^m*A*a^4*m^3*x*e^6 + 461*(x*e + d)^m*B*a^4*m^2*x^2*e^6 + 1844*(x*e + d)^m*A*a^3*b*m^2*x^2*e^6 + 2032*(x*e + d)^m*B*a^3*b*m*x^3*e^6 + 3048*(x*e + d)^m*A*a^2*b^2*m*x^3*e^6 + 1080*(x*e + d)^m*B*a^2*b^2*x^4*e^6 + 720*(x*e + d)^m*A*a*b^3*x^4*e^6 + 155*(x*e + d)^m*A*a^4*d*m^3*e^5 + 342*(x*e + d)^m*B*a^4*d*m^2*x*e^5 + 1368*(x*e + d)^m*A*a^3*b*d*m^2*x*e^5 + 480*(x*e + d)^m*B*a^3*b*d*m*x^2*e^5 + 720*(x*e + d)^m*A*a^2*b^2*d*m*x^2*e^5 - 119*(x*e + d)^m*B*a^4*d^2*m^2*e^4 - 476*(x*e + d)^m*A*a^3*b*d^2*m^2*e^4 - 960*(x*e + d)^m*B*a^3*b*d^2*m*x*e^4 - 1440*(x*e + d)^m*A*a^2*b^2*d^2*m*x*e^4 + 592*(x*e + d)^m*B*a^3*b*d^3*m*e^3 + 888*(x*e + d)^m*A*a^2*b^2*d^3*m*e^3 - 1080*(x*e + d)^m*B*a^2*b^2*d^4*e^2 - 720*(x*e + d)^m*A*a*b^3*d^4*e^2 + 580*(x*e + d)^m*A*a^4*m^2*x*e^6 + 702*(x*e + d)^m*B*a^4*m*x^2*e^6 + 2808*(x*e + d)^m*A*a^3*b*m*x^2*e^6 + 960*(x*e + d)^m*B*a^3*b*x^3*e^6 + 1440*(x*e + d)^m*A*a^2*b^2*x^3*e^6 + 580*(x*e + d)^m*A*a^4*d*m^2*e^5 + 360*(x*e + d)^m*B*a^4*d*m*x*e^5 + 1440*(x*e + d)^m*A*a^3*b*d*m*x*e^5 - 342*(x*e + d)^m*B*a^4*d^2*m*e^4 - 1368*(x*e + d)^m*A*a^3*b*d^2*m*e^4 + 960*(x*e + d)^m*B*a^3*b*d^3*e^3 + 1440*(x*e + d)^m*A*a^2*b^2*d^3*e^3 + 1044*(x*e + d)^m*A*a^4*m*x*e^6 + 360*(x*e + d)^m*B*a^4*x^2*e^6 + 1440*(x*e + d)^m*A*a^3*b*x^2*e^6 + 1044*(x*e + d)^m*A*a^4*d*m*e^5 - 360*(x*e + d)^m*B*a^4*d^2*e^4 - 1440*(x*e + d)^m*A*a^3*b*d^2*e^4 + 720*(x*e + d)^m*A*a^4*x*e^6 + 720*(x*e + d)^m*A*a^4*d*e^5)/(m^6*e^6 + 21*m^5*e^6 + 175*m^4*e^6 + 735*m^3*e^6 + 1624*m^2*e^6 + 1764*m*e^6 + 720*e^6)","B",0
1885,1,1267,0,0.263938," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B b^{2} m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} B b^{2} d m^{3} x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} B a b m^{3} x^{3} e^{4} + {\left(x e + d\right)}^{m} A b^{2} m^{3} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B b^{2} m^{2} x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} B a b d m^{3} x^{2} e^{3} + {\left(x e + d\right)}^{m} A b^{2} d m^{3} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} B b^{2} d m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a^{2} m^{3} x^{2} e^{4} + 2 \, {\left(x e + d\right)}^{m} A a b m^{3} x^{2} e^{4} + 14 \, {\left(x e + d\right)}^{m} B a b m^{2} x^{3} e^{4} + 7 \, {\left(x e + d\right)}^{m} A b^{2} m^{2} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} B b^{2} m x^{4} e^{4} + {\left(x e + d\right)}^{m} B a^{2} d m^{3} x e^{3} + 2 \, {\left(x e + d\right)}^{m} A a b d m^{3} x e^{3} + 10 \, {\left(x e + d\right)}^{m} B a b d m^{2} x^{2} e^{3} + 5 \, {\left(x e + d\right)}^{m} A b^{2} d m^{2} x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} B b^{2} d m x^{3} e^{3} - 4 \, {\left(x e + d\right)}^{m} B a b d^{2} m^{2} x e^{2} - 2 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m^{2} x e^{2} - 3 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} B b^{2} d^{3} m x e + {\left(x e + d\right)}^{m} A a^{2} m^{3} x e^{4} + 8 \, {\left(x e + d\right)}^{m} B a^{2} m^{2} x^{2} e^{4} + 16 \, {\left(x e + d\right)}^{m} A a b m^{2} x^{2} e^{4} + 28 \, {\left(x e + d\right)}^{m} B a b m x^{3} e^{4} + 14 \, {\left(x e + d\right)}^{m} A b^{2} m x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B b^{2} x^{4} e^{4} + {\left(x e + d\right)}^{m} A a^{2} d m^{3} e^{3} + 7 \, {\left(x e + d\right)}^{m} B a^{2} d m^{2} x e^{3} + 14 \, {\left(x e + d\right)}^{m} A a b d m^{2} x e^{3} + 8 \, {\left(x e + d\right)}^{m} B a b d m x^{2} e^{3} + 4 \, {\left(x e + d\right)}^{m} A b^{2} d m x^{2} e^{3} - {\left(x e + d\right)}^{m} B a^{2} d^{2} m^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} A a b d^{2} m^{2} e^{2} - 16 \, {\left(x e + d\right)}^{m} B a b d^{2} m x e^{2} - 8 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m x e^{2} + 4 \, {\left(x e + d\right)}^{m} B a b d^{3} m e + 2 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} m e - 6 \, {\left(x e + d\right)}^{m} B b^{2} d^{4} + 9 \, {\left(x e + d\right)}^{m} A a^{2} m^{2} x e^{4} + 19 \, {\left(x e + d\right)}^{m} B a^{2} m x^{2} e^{4} + 38 \, {\left(x e + d\right)}^{m} A a b m x^{2} e^{4} + 16 \, {\left(x e + d\right)}^{m} B a b x^{3} e^{4} + 8 \, {\left(x e + d\right)}^{m} A b^{2} x^{3} e^{4} + 9 \, {\left(x e + d\right)}^{m} A a^{2} d m^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} B a^{2} d m x e^{3} + 24 \, {\left(x e + d\right)}^{m} A a b d m x e^{3} - 7 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} m e^{2} - 14 \, {\left(x e + d\right)}^{m} A a b d^{2} m e^{2} + 16 \, {\left(x e + d\right)}^{m} B a b d^{3} e + 8 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} e + 26 \, {\left(x e + d\right)}^{m} A a^{2} m x e^{4} + 12 \, {\left(x e + d\right)}^{m} B a^{2} x^{2} e^{4} + 24 \, {\left(x e + d\right)}^{m} A a b x^{2} e^{4} + 26 \, {\left(x e + d\right)}^{m} A a^{2} d m e^{3} - 12 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} A a b d^{2} e^{2} + 24 \, {\left(x e + d\right)}^{m} A a^{2} x e^{4} + 24 \, {\left(x e + d\right)}^{m} A a^{2} d e^{3}}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"((x*e + d)^m*B*b^2*m^3*x^4*e^4 + (x*e + d)^m*B*b^2*d*m^3*x^3*e^3 + 2*(x*e + d)^m*B*a*b*m^3*x^3*e^4 + (x*e + d)^m*A*b^2*m^3*x^3*e^4 + 6*(x*e + d)^m*B*b^2*m^2*x^4*e^4 + 2*(x*e + d)^m*B*a*b*d*m^3*x^2*e^3 + (x*e + d)^m*A*b^2*d*m^3*x^2*e^3 + 3*(x*e + d)^m*B*b^2*d*m^2*x^3*e^3 - 3*(x*e + d)^m*B*b^2*d^2*m^2*x^2*e^2 + (x*e + d)^m*B*a^2*m^3*x^2*e^4 + 2*(x*e + d)^m*A*a*b*m^3*x^2*e^4 + 14*(x*e + d)^m*B*a*b*m^2*x^3*e^4 + 7*(x*e + d)^m*A*b^2*m^2*x^3*e^4 + 11*(x*e + d)^m*B*b^2*m*x^4*e^4 + (x*e + d)^m*B*a^2*d*m^3*x*e^3 + 2*(x*e + d)^m*A*a*b*d*m^3*x*e^3 + 10*(x*e + d)^m*B*a*b*d*m^2*x^2*e^3 + 5*(x*e + d)^m*A*b^2*d*m^2*x^2*e^3 + 2*(x*e + d)^m*B*b^2*d*m*x^3*e^3 - 4*(x*e + d)^m*B*a*b*d^2*m^2*x*e^2 - 2*(x*e + d)^m*A*b^2*d^2*m^2*x*e^2 - 3*(x*e + d)^m*B*b^2*d^2*m*x^2*e^2 + 6*(x*e + d)^m*B*b^2*d^3*m*x*e + (x*e + d)^m*A*a^2*m^3*x*e^4 + 8*(x*e + d)^m*B*a^2*m^2*x^2*e^4 + 16*(x*e + d)^m*A*a*b*m^2*x^2*e^4 + 28*(x*e + d)^m*B*a*b*m*x^3*e^4 + 14*(x*e + d)^m*A*b^2*m*x^3*e^4 + 6*(x*e + d)^m*B*b^2*x^4*e^4 + (x*e + d)^m*A*a^2*d*m^3*e^3 + 7*(x*e + d)^m*B*a^2*d*m^2*x*e^3 + 14*(x*e + d)^m*A*a*b*d*m^2*x*e^3 + 8*(x*e + d)^m*B*a*b*d*m*x^2*e^3 + 4*(x*e + d)^m*A*b^2*d*m*x^2*e^3 - (x*e + d)^m*B*a^2*d^2*m^2*e^2 - 2*(x*e + d)^m*A*a*b*d^2*m^2*e^2 - 16*(x*e + d)^m*B*a*b*d^2*m*x*e^2 - 8*(x*e + d)^m*A*b^2*d^2*m*x*e^2 + 4*(x*e + d)^m*B*a*b*d^3*m*e + 2*(x*e + d)^m*A*b^2*d^3*m*e - 6*(x*e + d)^m*B*b^2*d^4 + 9*(x*e + d)^m*A*a^2*m^2*x*e^4 + 19*(x*e + d)^m*B*a^2*m*x^2*e^4 + 38*(x*e + d)^m*A*a*b*m*x^2*e^4 + 16*(x*e + d)^m*B*a*b*x^3*e^4 + 8*(x*e + d)^m*A*b^2*x^3*e^4 + 9*(x*e + d)^m*A*a^2*d*m^2*e^3 + 12*(x*e + d)^m*B*a^2*d*m*x*e^3 + 24*(x*e + d)^m*A*a*b*d*m*x*e^3 - 7*(x*e + d)^m*B*a^2*d^2*m*e^2 - 14*(x*e + d)^m*A*a*b*d^2*m*e^2 + 16*(x*e + d)^m*B*a*b*d^3*e + 8*(x*e + d)^m*A*b^2*d^3*e + 26*(x*e + d)^m*A*a^2*m*x*e^4 + 12*(x*e + d)^m*B*a^2*x^2*e^4 + 24*(x*e + d)^m*A*a*b*x^2*e^4 + 26*(x*e + d)^m*A*a^2*d*m*e^3 - 12*(x*e + d)^m*B*a^2*d^2*e^2 - 24*(x*e + d)^m*A*a*b*d^2*e^2 + 24*(x*e + d)^m*A*a^2*x*e^4 + 24*(x*e + d)^m*A*a^2*d*e^3)/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
1886,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1887,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^2, x)","F",0
1888,1,8708,0,0.844560," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B b^{5} m^{6} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B b^{5} d m^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} B a b^{4} m^{6} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A b^{5} m^{6} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{m} B b^{5} m^{5} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} B a b^{4} d m^{6} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A b^{5} d m^{6} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} B b^{5} d m^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} B b^{5} d^{2} m^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} m^{6} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} A a b^{4} m^{6} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 110 \, {\left(x e + d\right)}^{m} B a b^{4} m^{5} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 22 \, {\left(x e + d\right)}^{m} A b^{5} m^{5} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 175 \, {\left(x e + d\right)}^{m} B b^{5} m^{4} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d m^{6} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} A a b^{4} d m^{6} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 85 \, {\left(x e + d\right)}^{m} B a b^{4} d m^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 17 \, {\left(x e + d\right)}^{m} A b^{5} d m^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 85 \, {\left(x e + d\right)}^{m} B b^{5} d m^{4} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 25 \, {\left(x e + d\right)}^{m} B a b^{4} d^{2} m^{5} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)}^{m} A b^{5} d^{2} m^{5} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} B b^{5} d^{2} m^{4} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} B b^{5} d^{3} m^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} m^{6} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} m^{6} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 230 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} m^{5} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 115 \, {\left(x e + d\right)}^{m} A a b^{4} m^{5} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 950 \, {\left(x e + d\right)}^{m} B a b^{4} m^{4} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 190 \, {\left(x e + d\right)}^{m} A b^{5} m^{4} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 735 \, {\left(x e + d\right)}^{m} B b^{5} m^{3} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d m^{6} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d m^{6} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 190 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d m^{5} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 95 \, {\left(x e + d\right)}^{m} A a b^{4} d m^{5} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 525 \, {\left(x e + d\right)}^{m} B a b^{4} d m^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 105 \, {\left(x e + d\right)}^{m} A b^{5} d m^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 225 \, {\left(x e + d\right)}^{m} B b^{5} d m^{3} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 40 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{2} m^{5} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)}^{m} A a b^{4} d^{2} m^{5} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 325 \, {\left(x e + d\right)}^{m} B a b^{4} d^{2} m^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 65 \, {\left(x e + d\right)}^{m} A b^{5} d^{2} m^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)}^{m} B b^{5} d^{2} m^{3} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 100 \, {\left(x e + d\right)}^{m} B a b^{4} d^{3} m^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} A b^{5} d^{3} m^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} B b^{5} d^{3} m^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} B b^{5} d^{4} m^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} B a^{4} b m^{6} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} m^{6} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 240 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} m^{5} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 240 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} m^{5} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 2070 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} m^{4} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 1035 \, {\left(x e + d\right)}^{m} A a b^{4} m^{4} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 4100 \, {\left(x e + d\right)}^{m} B a b^{4} m^{3} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 820 \, {\left(x e + d\right)}^{m} A b^{5} m^{3} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 1624 \, {\left(x e + d\right)}^{m} B b^{5} m^{2} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} B a^{4} b d m^{6} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d m^{6} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d m^{5} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d m^{5} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1310 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d m^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 655 \, {\left(x e + d\right)}^{m} A a b^{4} d m^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1475 \, {\left(x e + d\right)}^{m} B a b^{4} d m^{3} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 295 \, {\left(x e + d\right)}^{m} A b^{5} d m^{3} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 274 \, {\left(x e + d\right)}^{m} B b^{5} d m^{2} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{2} m^{5} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{2} m^{5} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 640 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{2} m^{4} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 320 \, {\left(x e + d\right)}^{m} A a b^{4} d^{2} m^{4} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 1325 \, {\left(x e + d\right)}^{m} B a b^{4} d^{2} m^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 265 \, {\left(x e + d\right)}^{m} A b^{5} d^{2} m^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 300 \, {\left(x e + d\right)}^{m} B b^{5} d^{2} m^{2} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{3} m^{4} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} A a b^{4} d^{3} m^{4} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1000 \, {\left(x e + d\right)}^{m} B a b^{4} d^{3} m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 200 \, {\left(x e + d\right)}^{m} A b^{5} d^{3} m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 330 \, {\left(x e + d\right)}^{m} B b^{5} d^{3} m^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 300 \, {\left(x e + d\right)}^{m} B a b^{4} d^{4} m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} A b^{5} d^{4} m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 360 \, {\left(x e + d\right)}^{m} B b^{5} d^{4} m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 360 \, {\left(x e + d\right)}^{m} B b^{5} d^{5} m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B a^{5} m^{6} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} A a^{4} b m^{6} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 125 \, {\left(x e + d\right)}^{m} B a^{4} b m^{5} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 250 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} m^{5} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 2260 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} m^{4} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 2260 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} m^{4} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 9250 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} m^{3} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 4625 \, {\left(x e + d\right)}^{m} A a b^{4} m^{3} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 9245 \, {\left(x e + d\right)}^{m} B a b^{4} m^{2} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 1849 \, {\left(x e + d\right)}^{m} A b^{5} m^{2} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 1764 \, {\left(x e + d\right)}^{m} B b^{5} m x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B a^{5} d m^{6} x e^{6} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} A a^{4} b d m^{6} x e^{6} \mathrm{sgn}\left(b x + a\right) + 115 \, {\left(x e + d\right)}^{m} B a^{4} b d m^{5} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 230 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d m^{5} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 1630 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d m^{4} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1630 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d m^{4} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 4010 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d m^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 2005 \, {\left(x e + d\right)}^{m} A a b^{4} d m^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1870 \, {\left(x e + d\right)}^{m} B a b^{4} d m^{2} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 374 \, {\left(x e + d\right)}^{m} A b^{5} d m^{2} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} B b^{5} d m x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 10 \, {\left(x e + d\right)}^{m} B a^{4} b d^{2} m^{5} x e^{5} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{2} m^{5} x e^{5} \mathrm{sgn}\left(b x + a\right) - 570 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{2} m^{4} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 570 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{2} m^{4} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 3320 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{2} m^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 1660 \, {\left(x e + d\right)}^{m} A a b^{4} d^{2} m^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 2075 \, {\left(x e + d\right)}^{m} B a b^{4} d^{2} m^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 415 \, {\left(x e + d\right)}^{m} A b^{5} d^{2} m^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 144 \, {\left(x e + d\right)}^{m} B b^{5} d^{2} m x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{3} m^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{3} m^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 1680 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{3} m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 840 \, {\left(x e + d\right)}^{m} A a b^{4} d^{3} m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 2300 \, {\left(x e + d\right)}^{m} B a b^{4} d^{3} m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 460 \, {\left(x e + d\right)}^{m} A b^{5} d^{3} m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} B b^{5} d^{3} m x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 240 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{4} m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} A a b^{4} d^{4} m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) - 2400 \, {\left(x e + d\right)}^{m} B a b^{4} d^{4} m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 480 \, {\left(x e + d\right)}^{m} A b^{5} d^{4} m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 240 \, {\left(x e + d\right)}^{m} B b^{5} d^{4} m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 600 \, {\left(x e + d\right)}^{m} B a b^{4} d^{5} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} A b^{5} d^{5} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 360 \, {\left(x e + d\right)}^{m} B b^{5} d^{5} m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 720 \, {\left(x e + d\right)}^{m} B b^{5} d^{6} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A a^{5} m^{6} x e^{7} \mathrm{sgn}\left(b x + a\right) + 26 \, {\left(x e + d\right)}^{m} B a^{5} m^{5} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 130 \, {\left(x e + d\right)}^{m} A a^{4} b m^{5} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 1235 \, {\left(x e + d\right)}^{m} B a^{4} b m^{4} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 2470 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} m^{4} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 10560 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} m^{3} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 10560 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} m^{3} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 21440 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} m^{2} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 10720 \, {\left(x e + d\right)}^{m} A a b^{4} m^{2} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 10190 \, {\left(x e + d\right)}^{m} B a b^{4} m x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 2038 \, {\left(x e + d\right)}^{m} A b^{5} m x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} B b^{5} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A a^{5} d m^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 25 \, {\left(x e + d\right)}^{m} B a^{5} d m^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 125 \, {\left(x e + d\right)}^{m} A a^{4} b d m^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 1005 \, {\left(x e + d\right)}^{m} B a^{4} b d m^{4} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 2010 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d m^{4} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 5670 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d m^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 5670 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d m^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 5400 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d m^{2} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 2700 \, {\left(x e + d\right)}^{m} A a b^{4} d m^{2} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 840 \, {\left(x e + d\right)}^{m} B a b^{4} d m x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 168 \, {\left(x e + d\right)}^{m} A b^{5} d m x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) - {\left(x e + d\right)}^{m} B a^{5} d^{2} m^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)}^{m} A a^{4} b d^{2} m^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 220 \, {\left(x e + d\right)}^{m} B a^{4} b d^{2} m^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) - 440 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{2} m^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) - 3750 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{2} m^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 3750 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{2} m^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 6080 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{2} m^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 3040 \, {\left(x e + d\right)}^{m} A a b^{4} d^{2} m^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 1050 \, {\left(x e + d\right)}^{m} B a b^{4} d^{2} m x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)}^{m} A b^{5} d^{2} m x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} B a^{4} b d^{3} m^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{3} m^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 1080 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{3} m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 1080 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{3} m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 6600 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{3} m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3300 \, {\left(x e + d\right)}^{m} A a b^{4} d^{3} m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1400 \, {\left(x e + d\right)}^{m} B a b^{4} d^{3} m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 280 \, {\left(x e + d\right)}^{m} A b^{5} d^{3} m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{4} m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{4} m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 3120 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{4} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) - 1560 \, {\left(x e + d\right)}^{m} A a b^{4} d^{4} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) - 2100 \, {\left(x e + d\right)}^{m} B a b^{4} d^{4} m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)}^{m} A b^{5} d^{4} m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 240 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{5} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} A a b^{4} d^{5} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 4200 \, {\left(x e + d\right)}^{m} B a b^{4} d^{5} m x e^{2} \mathrm{sgn}\left(b x + a\right) + 840 \, {\left(x e + d\right)}^{m} A b^{5} d^{5} m x e^{2} \mathrm{sgn}\left(b x + a\right) - 600 \, {\left(x e + d\right)}^{m} B a b^{4} d^{6} m e \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} A b^{5} d^{6} m e \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} B b^{5} d^{7} \mathrm{sgn}\left(b x + a\right) + 27 \, {\left(x e + d\right)}^{m} A a^{5} m^{5} x e^{7} \mathrm{sgn}\left(b x + a\right) + 270 \, {\left(x e + d\right)}^{m} B a^{5} m^{4} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 1350 \, {\left(x e + d\right)}^{m} A a^{4} b m^{4} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 6095 \, {\left(x e + d\right)}^{m} B a^{4} b m^{3} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 12190 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} m^{3} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 25450 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} m^{2} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 25450 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} m^{2} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 24120 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} m x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 12060 \, {\left(x e + d\right)}^{m} A a b^{4} m x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 4200 \, {\left(x e + d\right)}^{m} B a b^{4} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 840 \, {\left(x e + d\right)}^{m} A b^{5} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 27 \, {\left(x e + d\right)}^{m} A a^{5} d m^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 245 \, {\left(x e + d\right)}^{m} B a^{5} d m^{4} x e^{6} \mathrm{sgn}\left(b x + a\right) + 1225 \, {\left(x e + d\right)}^{m} A a^{4} b d m^{4} x e^{6} \mathrm{sgn}\left(b x + a\right) + 4085 \, {\left(x e + d\right)}^{m} B a^{4} b d m^{3} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 8170 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d m^{3} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 8440 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d m^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 8440 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d m^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 2520 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d m x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1260 \, {\left(x e + d\right)}^{m} A a b^{4} d m x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) - 25 \, {\left(x e + d\right)}^{m} B a^{5} d^{2} m^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 125 \, {\left(x e + d\right)}^{m} A a^{4} b d^{2} m^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 1790 \, {\left(x e + d\right)}^{m} B a^{4} b d^{2} m^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) - 3580 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{2} m^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) - 9510 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{2} m^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 9510 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{2} m^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 3360 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{2} m x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 1680 \, {\left(x e + d\right)}^{m} A a b^{4} d^{2} m x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 220 \, {\left(x e + d\right)}^{m} B a^{4} b d^{3} m^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 440 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{3} m^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6420 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{3} m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 6420 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{3} m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{3} m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 2520 \, {\left(x e + d\right)}^{m} A a b^{4} d^{3} m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 1080 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{4} m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 1080 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{4} m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 10080 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{4} m x e^{3} \mathrm{sgn}\left(b x + a\right) - 5040 \, {\left(x e + d\right)}^{m} A a b^{4} d^{4} m x e^{3} \mathrm{sgn}\left(b x + a\right) + 3120 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{5} m e^{2} \mathrm{sgn}\left(b x + a\right) + 1560 \, {\left(x e + d\right)}^{m} A a b^{4} d^{5} m e^{2} \mathrm{sgn}\left(b x + a\right) - 4200 \, {\left(x e + d\right)}^{m} B a b^{4} d^{6} e \mathrm{sgn}\left(b x + a\right) - 840 \, {\left(x e + d\right)}^{m} A b^{5} d^{6} e \mathrm{sgn}\left(b x + a\right) + 295 \, {\left(x e + d\right)}^{m} A a^{5} m^{4} x e^{7} \mathrm{sgn}\left(b x + a\right) + 1420 \, {\left(x e + d\right)}^{m} B a^{5} m^{3} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 7100 \, {\left(x e + d\right)}^{m} A a^{4} b m^{3} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 15560 \, {\left(x e + d\right)}^{m} B a^{4} b m^{2} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 31120 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} m^{2} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 29520 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} m x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 29520 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} m x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 10080 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} A a b^{4} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 295 \, {\left(x e + d\right)}^{m} A a^{5} d m^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1175 \, {\left(x e + d\right)}^{m} B a^{5} d m^{3} x e^{6} \mathrm{sgn}\left(b x + a\right) + 5875 \, {\left(x e + d\right)}^{m} A a^{4} b d m^{3} x e^{6} \mathrm{sgn}\left(b x + a\right) + 7390 \, {\left(x e + d\right)}^{m} B a^{4} b d m^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 14780 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d m^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 4200 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d m x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 4200 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d m x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) - 245 \, {\left(x e + d\right)}^{m} B a^{5} d^{2} m^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 1225 \, {\left(x e + d\right)}^{m} A a^{4} b d^{2} m^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 6380 \, {\left(x e + d\right)}^{m} B a^{4} b d^{2} m^{2} x e^{5} \mathrm{sgn}\left(b x + a\right) - 12760 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{2} m^{2} x e^{5} \mathrm{sgn}\left(b x + a\right) - 6300 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{2} m x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 6300 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{2} m x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1790 \, {\left(x e + d\right)}^{m} B a^{4} b d^{3} m^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3580 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{3} m^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 12600 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{3} m x e^{4} \mathrm{sgn}\left(b x + a\right) + 12600 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{3} m x e^{4} \mathrm{sgn}\left(b x + a\right) - 6420 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{4} m e^{3} \mathrm{sgn}\left(b x + a\right) - 6420 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{4} m e^{3} \mathrm{sgn}\left(b x + a\right) + 10080 \, {\left(x e + d\right)}^{m} B a^{2} b^{3} d^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} A a b^{4} d^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 1665 \, {\left(x e + d\right)}^{m} A a^{5} m^{3} x e^{7} \mathrm{sgn}\left(b x + a\right) + 3929 \, {\left(x e + d\right)}^{m} B a^{5} m^{2} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 19645 \, {\left(x e + d\right)}^{m} A a^{4} b m^{2} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 18980 \, {\left(x e + d\right)}^{m} B a^{4} b m x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 37960 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} m x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 12600 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 12600 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 1665 \, {\left(x e + d\right)}^{m} A a^{5} d m^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 2754 \, {\left(x e + d\right)}^{m} B a^{5} d m^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 13770 \, {\left(x e + d\right)}^{m} A a^{4} b d m^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 4200 \, {\left(x e + d\right)}^{m} B a^{4} b d m x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 8400 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d m x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 1175 \, {\left(x e + d\right)}^{m} B a^{5} d^{2} m^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 5875 \, {\left(x e + d\right)}^{m} A a^{4} b d^{2} m^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 8400 \, {\left(x e + d\right)}^{m} B a^{4} b d^{2} m x e^{5} \mathrm{sgn}\left(b x + a\right) - 16800 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{2} m x e^{5} \mathrm{sgn}\left(b x + a\right) + 6380 \, {\left(x e + d\right)}^{m} B a^{4} b d^{3} m e^{4} \mathrm{sgn}\left(b x + a\right) + 12760 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{3} m e^{4} \mathrm{sgn}\left(b x + a\right) - 12600 \, {\left(x e + d\right)}^{m} B a^{3} b^{2} d^{4} e^{3} \mathrm{sgn}\left(b x + a\right) - 12600 \, {\left(x e + d\right)}^{m} A a^{2} b^{3} d^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 5104 \, {\left(x e + d\right)}^{m} A a^{5} m^{2} x e^{7} \mathrm{sgn}\left(b x + a\right) + 5274 \, {\left(x e + d\right)}^{m} B a^{5} m x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 26370 \, {\left(x e + d\right)}^{m} A a^{4} b m x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 8400 \, {\left(x e + d\right)}^{m} B a^{4} b x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 16800 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 5104 \, {\left(x e + d\right)}^{m} A a^{5} d m^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 2520 \, {\left(x e + d\right)}^{m} B a^{5} d m x e^{6} \mathrm{sgn}\left(b x + a\right) + 12600 \, {\left(x e + d\right)}^{m} A a^{4} b d m x e^{6} \mathrm{sgn}\left(b x + a\right) - 2754 \, {\left(x e + d\right)}^{m} B a^{5} d^{2} m e^{5} \mathrm{sgn}\left(b x + a\right) - 13770 \, {\left(x e + d\right)}^{m} A a^{4} b d^{2} m e^{5} \mathrm{sgn}\left(b x + a\right) + 8400 \, {\left(x e + d\right)}^{m} B a^{4} b d^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 16800 \, {\left(x e + d\right)}^{m} A a^{3} b^{2} d^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 8028 \, {\left(x e + d\right)}^{m} A a^{5} m x e^{7} \mathrm{sgn}\left(b x + a\right) + 2520 \, {\left(x e + d\right)}^{m} B a^{5} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 12600 \, {\left(x e + d\right)}^{m} A a^{4} b x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 8028 \, {\left(x e + d\right)}^{m} A a^{5} d m e^{6} \mathrm{sgn}\left(b x + a\right) - 2520 \, {\left(x e + d\right)}^{m} B a^{5} d^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 12600 \, {\left(x e + d\right)}^{m} A a^{4} b d^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} A a^{5} x e^{7} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} A a^{5} d e^{6} \mathrm{sgn}\left(b x + a\right)}{m^{7} e^{7} + 28 \, m^{6} e^{7} + 322 \, m^{5} e^{7} + 1960 \, m^{4} e^{7} + 6769 \, m^{3} e^{7} + 13132 \, m^{2} e^{7} + 13068 \, m e^{7} + 5040 \, e^{7}}"," ",0,"((x*e + d)^m*B*b^5*m^6*x^7*e^7*sgn(b*x + a) + (x*e + d)^m*B*b^5*d*m^6*x^6*e^6*sgn(b*x + a) + 5*(x*e + d)^m*B*a*b^4*m^6*x^6*e^7*sgn(b*x + a) + (x*e + d)^m*A*b^5*m^6*x^6*e^7*sgn(b*x + a) + 21*(x*e + d)^m*B*b^5*m^5*x^7*e^7*sgn(b*x + a) + 5*(x*e + d)^m*B*a*b^4*d*m^6*x^5*e^6*sgn(b*x + a) + (x*e + d)^m*A*b^5*d*m^6*x^5*e^6*sgn(b*x + a) + 15*(x*e + d)^m*B*b^5*d*m^5*x^6*e^6*sgn(b*x + a) - 6*(x*e + d)^m*B*b^5*d^2*m^5*x^5*e^5*sgn(b*x + a) + 10*(x*e + d)^m*B*a^2*b^3*m^6*x^5*e^7*sgn(b*x + a) + 5*(x*e + d)^m*A*a*b^4*m^6*x^5*e^7*sgn(b*x + a) + 110*(x*e + d)^m*B*a*b^4*m^5*x^6*e^7*sgn(b*x + a) + 22*(x*e + d)^m*A*b^5*m^5*x^6*e^7*sgn(b*x + a) + 175*(x*e + d)^m*B*b^5*m^4*x^7*e^7*sgn(b*x + a) + 10*(x*e + d)^m*B*a^2*b^3*d*m^6*x^4*e^6*sgn(b*x + a) + 5*(x*e + d)^m*A*a*b^4*d*m^6*x^4*e^6*sgn(b*x + a) + 85*(x*e + d)^m*B*a*b^4*d*m^5*x^5*e^6*sgn(b*x + a) + 17*(x*e + d)^m*A*b^5*d*m^5*x^5*e^6*sgn(b*x + a) + 85*(x*e + d)^m*B*b^5*d*m^4*x^6*e^6*sgn(b*x + a) - 25*(x*e + d)^m*B*a*b^4*d^2*m^5*x^4*e^5*sgn(b*x + a) - 5*(x*e + d)^m*A*b^5*d^2*m^5*x^4*e^5*sgn(b*x + a) - 60*(x*e + d)^m*B*b^5*d^2*m^4*x^5*e^5*sgn(b*x + a) + 30*(x*e + d)^m*B*b^5*d^3*m^4*x^4*e^4*sgn(b*x + a) + 10*(x*e + d)^m*B*a^3*b^2*m^6*x^4*e^7*sgn(b*x + a) + 10*(x*e + d)^m*A*a^2*b^3*m^6*x^4*e^7*sgn(b*x + a) + 230*(x*e + d)^m*B*a^2*b^3*m^5*x^5*e^7*sgn(b*x + a) + 115*(x*e + d)^m*A*a*b^4*m^5*x^5*e^7*sgn(b*x + a) + 950*(x*e + d)^m*B*a*b^4*m^4*x^6*e^7*sgn(b*x + a) + 190*(x*e + d)^m*A*b^5*m^4*x^6*e^7*sgn(b*x + a) + 735*(x*e + d)^m*B*b^5*m^3*x^7*e^7*sgn(b*x + a) + 10*(x*e + d)^m*B*a^3*b^2*d*m^6*x^3*e^6*sgn(b*x + a) + 10*(x*e + d)^m*A*a^2*b^3*d*m^6*x^3*e^6*sgn(b*x + a) + 190*(x*e + d)^m*B*a^2*b^3*d*m^5*x^4*e^6*sgn(b*x + a) + 95*(x*e + d)^m*A*a*b^4*d*m^5*x^4*e^6*sgn(b*x + a) + 525*(x*e + d)^m*B*a*b^4*d*m^4*x^5*e^6*sgn(b*x + a) + 105*(x*e + d)^m*A*b^5*d*m^4*x^5*e^6*sgn(b*x + a) + 225*(x*e + d)^m*B*b^5*d*m^3*x^6*e^6*sgn(b*x + a) - 40*(x*e + d)^m*B*a^2*b^3*d^2*m^5*x^3*e^5*sgn(b*x + a) - 20*(x*e + d)^m*A*a*b^4*d^2*m^5*x^3*e^5*sgn(b*x + a) - 325*(x*e + d)^m*B*a*b^4*d^2*m^4*x^4*e^5*sgn(b*x + a) - 65*(x*e + d)^m*A*b^5*d^2*m^4*x^4*e^5*sgn(b*x + a) - 210*(x*e + d)^m*B*b^5*d^2*m^3*x^5*e^5*sgn(b*x + a) + 100*(x*e + d)^m*B*a*b^4*d^3*m^4*x^3*e^4*sgn(b*x + a) + 20*(x*e + d)^m*A*b^5*d^3*m^4*x^3*e^4*sgn(b*x + a) + 180*(x*e + d)^m*B*b^5*d^3*m^3*x^4*e^4*sgn(b*x + a) - 120*(x*e + d)^m*B*b^5*d^4*m^3*x^3*e^3*sgn(b*x + a) + 5*(x*e + d)^m*B*a^4*b*m^6*x^3*e^7*sgn(b*x + a) + 10*(x*e + d)^m*A*a^3*b^2*m^6*x^3*e^7*sgn(b*x + a) + 240*(x*e + d)^m*B*a^3*b^2*m^5*x^4*e^7*sgn(b*x + a) + 240*(x*e + d)^m*A*a^2*b^3*m^5*x^4*e^7*sgn(b*x + a) + 2070*(x*e + d)^m*B*a^2*b^3*m^4*x^5*e^7*sgn(b*x + a) + 1035*(x*e + d)^m*A*a*b^4*m^4*x^5*e^7*sgn(b*x + a) + 4100*(x*e + d)^m*B*a*b^4*m^3*x^6*e^7*sgn(b*x + a) + 820*(x*e + d)^m*A*b^5*m^3*x^6*e^7*sgn(b*x + a) + 1624*(x*e + d)^m*B*b^5*m^2*x^7*e^7*sgn(b*x + a) + 5*(x*e + d)^m*B*a^4*b*d*m^6*x^2*e^6*sgn(b*x + a) + 10*(x*e + d)^m*A*a^3*b^2*d*m^6*x^2*e^6*sgn(b*x + a) + 210*(x*e + d)^m*B*a^3*b^2*d*m^5*x^3*e^6*sgn(b*x + a) + 210*(x*e + d)^m*A*a^2*b^3*d*m^5*x^3*e^6*sgn(b*x + a) + 1310*(x*e + d)^m*B*a^2*b^3*d*m^4*x^4*e^6*sgn(b*x + a) + 655*(x*e + d)^m*A*a*b^4*d*m^4*x^4*e^6*sgn(b*x + a) + 1475*(x*e + d)^m*B*a*b^4*d*m^3*x^5*e^6*sgn(b*x + a) + 295*(x*e + d)^m*A*b^5*d*m^3*x^5*e^6*sgn(b*x + a) + 274*(x*e + d)^m*B*b^5*d*m^2*x^6*e^6*sgn(b*x + a) - 30*(x*e + d)^m*B*a^3*b^2*d^2*m^5*x^2*e^5*sgn(b*x + a) - 30*(x*e + d)^m*A*a^2*b^3*d^2*m^5*x^2*e^5*sgn(b*x + a) - 640*(x*e + d)^m*B*a^2*b^3*d^2*m^4*x^3*e^5*sgn(b*x + a) - 320*(x*e + d)^m*A*a*b^4*d^2*m^4*x^3*e^5*sgn(b*x + a) - 1325*(x*e + d)^m*B*a*b^4*d^2*m^3*x^4*e^5*sgn(b*x + a) - 265*(x*e + d)^m*A*b^5*d^2*m^3*x^4*e^5*sgn(b*x + a) - 300*(x*e + d)^m*B*b^5*d^2*m^2*x^5*e^5*sgn(b*x + a) + 120*(x*e + d)^m*B*a^2*b^3*d^3*m^4*x^2*e^4*sgn(b*x + a) + 60*(x*e + d)^m*A*a*b^4*d^3*m^4*x^2*e^4*sgn(b*x + a) + 1000*(x*e + d)^m*B*a*b^4*d^3*m^3*x^3*e^4*sgn(b*x + a) + 200*(x*e + d)^m*A*b^5*d^3*m^3*x^3*e^4*sgn(b*x + a) + 330*(x*e + d)^m*B*b^5*d^3*m^2*x^4*e^4*sgn(b*x + a) - 300*(x*e + d)^m*B*a*b^4*d^4*m^3*x^2*e^3*sgn(b*x + a) - 60*(x*e + d)^m*A*b^5*d^4*m^3*x^2*e^3*sgn(b*x + a) - 360*(x*e + d)^m*B*b^5*d^4*m^2*x^3*e^3*sgn(b*x + a) + 360*(x*e + d)^m*B*b^5*d^5*m^2*x^2*e^2*sgn(b*x + a) + (x*e + d)^m*B*a^5*m^6*x^2*e^7*sgn(b*x + a) + 5*(x*e + d)^m*A*a^4*b*m^6*x^2*e^7*sgn(b*x + a) + 125*(x*e + d)^m*B*a^4*b*m^5*x^3*e^7*sgn(b*x + a) + 250*(x*e + d)^m*A*a^3*b^2*m^5*x^3*e^7*sgn(b*x + a) + 2260*(x*e + d)^m*B*a^3*b^2*m^4*x^4*e^7*sgn(b*x + a) + 2260*(x*e + d)^m*A*a^2*b^3*m^4*x^4*e^7*sgn(b*x + a) + 9250*(x*e + d)^m*B*a^2*b^3*m^3*x^5*e^7*sgn(b*x + a) + 4625*(x*e + d)^m*A*a*b^4*m^3*x^5*e^7*sgn(b*x + a) + 9245*(x*e + d)^m*B*a*b^4*m^2*x^6*e^7*sgn(b*x + a) + 1849*(x*e + d)^m*A*b^5*m^2*x^6*e^7*sgn(b*x + a) + 1764*(x*e + d)^m*B*b^5*m*x^7*e^7*sgn(b*x + a) + (x*e + d)^m*B*a^5*d*m^6*x*e^6*sgn(b*x + a) + 5*(x*e + d)^m*A*a^4*b*d*m^6*x*e^6*sgn(b*x + a) + 115*(x*e + d)^m*B*a^4*b*d*m^5*x^2*e^6*sgn(b*x + a) + 230*(x*e + d)^m*A*a^3*b^2*d*m^5*x^2*e^6*sgn(b*x + a) + 1630*(x*e + d)^m*B*a^3*b^2*d*m^4*x^3*e^6*sgn(b*x + a) + 1630*(x*e + d)^m*A*a^2*b^3*d*m^4*x^3*e^6*sgn(b*x + a) + 4010*(x*e + d)^m*B*a^2*b^3*d*m^3*x^4*e^6*sgn(b*x + a) + 2005*(x*e + d)^m*A*a*b^4*d*m^3*x^4*e^6*sgn(b*x + a) + 1870*(x*e + d)^m*B*a*b^4*d*m^2*x^5*e^6*sgn(b*x + a) + 374*(x*e + d)^m*A*b^5*d*m^2*x^5*e^6*sgn(b*x + a) + 120*(x*e + d)^m*B*b^5*d*m*x^6*e^6*sgn(b*x + a) - 10*(x*e + d)^m*B*a^4*b*d^2*m^5*x*e^5*sgn(b*x + a) - 20*(x*e + d)^m*A*a^3*b^2*d^2*m^5*x*e^5*sgn(b*x + a) - 570*(x*e + d)^m*B*a^3*b^2*d^2*m^4*x^2*e^5*sgn(b*x + a) - 570*(x*e + d)^m*A*a^2*b^3*d^2*m^4*x^2*e^5*sgn(b*x + a) - 3320*(x*e + d)^m*B*a^2*b^3*d^2*m^3*x^3*e^5*sgn(b*x + a) - 1660*(x*e + d)^m*A*a*b^4*d^2*m^3*x^3*e^5*sgn(b*x + a) - 2075*(x*e + d)^m*B*a*b^4*d^2*m^2*x^4*e^5*sgn(b*x + a) - 415*(x*e + d)^m*A*b^5*d^2*m^2*x^4*e^5*sgn(b*x + a) - 144*(x*e + d)^m*B*b^5*d^2*m*x^5*e^5*sgn(b*x + a) + 60*(x*e + d)^m*B*a^3*b^2*d^3*m^4*x*e^4*sgn(b*x + a) + 60*(x*e + d)^m*A*a^2*b^3*d^3*m^4*x*e^4*sgn(b*x + a) + 1680*(x*e + d)^m*B*a^2*b^3*d^3*m^3*x^2*e^4*sgn(b*x + a) + 840*(x*e + d)^m*A*a*b^4*d^3*m^3*x^2*e^4*sgn(b*x + a) + 2300*(x*e + d)^m*B*a*b^4*d^3*m^2*x^3*e^4*sgn(b*x + a) + 460*(x*e + d)^m*A*b^5*d^3*m^2*x^3*e^4*sgn(b*x + a) + 180*(x*e + d)^m*B*b^5*d^3*m*x^4*e^4*sgn(b*x + a) - 240*(x*e + d)^m*B*a^2*b^3*d^4*m^3*x*e^3*sgn(b*x + a) - 120*(x*e + d)^m*A*a*b^4*d^4*m^3*x*e^3*sgn(b*x + a) - 2400*(x*e + d)^m*B*a*b^4*d^4*m^2*x^2*e^3*sgn(b*x + a) - 480*(x*e + d)^m*A*b^5*d^4*m^2*x^2*e^3*sgn(b*x + a) - 240*(x*e + d)^m*B*b^5*d^4*m*x^3*e^3*sgn(b*x + a) + 600*(x*e + d)^m*B*a*b^4*d^5*m^2*x*e^2*sgn(b*x + a) + 120*(x*e + d)^m*A*b^5*d^5*m^2*x*e^2*sgn(b*x + a) + 360*(x*e + d)^m*B*b^5*d^5*m*x^2*e^2*sgn(b*x + a) - 720*(x*e + d)^m*B*b^5*d^6*m*x*e*sgn(b*x + a) + (x*e + d)^m*A*a^5*m^6*x*e^7*sgn(b*x + a) + 26*(x*e + d)^m*B*a^5*m^5*x^2*e^7*sgn(b*x + a) + 130*(x*e + d)^m*A*a^4*b*m^5*x^2*e^7*sgn(b*x + a) + 1235*(x*e + d)^m*B*a^4*b*m^4*x^3*e^7*sgn(b*x + a) + 2470*(x*e + d)^m*A*a^3*b^2*m^4*x^3*e^7*sgn(b*x + a) + 10560*(x*e + d)^m*B*a^3*b^2*m^3*x^4*e^7*sgn(b*x + a) + 10560*(x*e + d)^m*A*a^2*b^3*m^3*x^4*e^7*sgn(b*x + a) + 21440*(x*e + d)^m*B*a^2*b^3*m^2*x^5*e^7*sgn(b*x + a) + 10720*(x*e + d)^m*A*a*b^4*m^2*x^5*e^7*sgn(b*x + a) + 10190*(x*e + d)^m*B*a*b^4*m*x^6*e^7*sgn(b*x + a) + 2038*(x*e + d)^m*A*b^5*m*x^6*e^7*sgn(b*x + a) + 720*(x*e + d)^m*B*b^5*x^7*e^7*sgn(b*x + a) + (x*e + d)^m*A*a^5*d*m^6*e^6*sgn(b*x + a) + 25*(x*e + d)^m*B*a^5*d*m^5*x*e^6*sgn(b*x + a) + 125*(x*e + d)^m*A*a^4*b*d*m^5*x*e^6*sgn(b*x + a) + 1005*(x*e + d)^m*B*a^4*b*d*m^4*x^2*e^6*sgn(b*x + a) + 2010*(x*e + d)^m*A*a^3*b^2*d*m^4*x^2*e^6*sgn(b*x + a) + 5670*(x*e + d)^m*B*a^3*b^2*d*m^3*x^3*e^6*sgn(b*x + a) + 5670*(x*e + d)^m*A*a^2*b^3*d*m^3*x^3*e^6*sgn(b*x + a) + 5400*(x*e + d)^m*B*a^2*b^3*d*m^2*x^4*e^6*sgn(b*x + a) + 2700*(x*e + d)^m*A*a*b^4*d*m^2*x^4*e^6*sgn(b*x + a) + 840*(x*e + d)^m*B*a*b^4*d*m*x^5*e^6*sgn(b*x + a) + 168*(x*e + d)^m*A*b^5*d*m*x^5*e^6*sgn(b*x + a) - (x*e + d)^m*B*a^5*d^2*m^5*e^5*sgn(b*x + a) - 5*(x*e + d)^m*A*a^4*b*d^2*m^5*e^5*sgn(b*x + a) - 220*(x*e + d)^m*B*a^4*b*d^2*m^4*x*e^5*sgn(b*x + a) - 440*(x*e + d)^m*A*a^3*b^2*d^2*m^4*x*e^5*sgn(b*x + a) - 3750*(x*e + d)^m*B*a^3*b^2*d^2*m^3*x^2*e^5*sgn(b*x + a) - 3750*(x*e + d)^m*A*a^2*b^3*d^2*m^3*x^2*e^5*sgn(b*x + a) - 6080*(x*e + d)^m*B*a^2*b^3*d^2*m^2*x^3*e^5*sgn(b*x + a) - 3040*(x*e + d)^m*A*a*b^4*d^2*m^2*x^3*e^5*sgn(b*x + a) - 1050*(x*e + d)^m*B*a*b^4*d^2*m*x^4*e^5*sgn(b*x + a) - 210*(x*e + d)^m*A*b^5*d^2*m*x^4*e^5*sgn(b*x + a) + 10*(x*e + d)^m*B*a^4*b*d^3*m^4*e^4*sgn(b*x + a) + 20*(x*e + d)^m*A*a^3*b^2*d^3*m^4*e^4*sgn(b*x + a) + 1080*(x*e + d)^m*B*a^3*b^2*d^3*m^3*x*e^4*sgn(b*x + a) + 1080*(x*e + d)^m*A*a^2*b^3*d^3*m^3*x*e^4*sgn(b*x + a) + 6600*(x*e + d)^m*B*a^2*b^3*d^3*m^2*x^2*e^4*sgn(b*x + a) + 3300*(x*e + d)^m*A*a*b^4*d^3*m^2*x^2*e^4*sgn(b*x + a) + 1400*(x*e + d)^m*B*a*b^4*d^3*m*x^3*e^4*sgn(b*x + a) + 280*(x*e + d)^m*A*b^5*d^3*m*x^3*e^4*sgn(b*x + a) - 60*(x*e + d)^m*B*a^3*b^2*d^4*m^3*e^3*sgn(b*x + a) - 60*(x*e + d)^m*A*a^2*b^3*d^4*m^3*e^3*sgn(b*x + a) - 3120*(x*e + d)^m*B*a^2*b^3*d^4*m^2*x*e^3*sgn(b*x + a) - 1560*(x*e + d)^m*A*a*b^4*d^4*m^2*x*e^3*sgn(b*x + a) - 2100*(x*e + d)^m*B*a*b^4*d^4*m*x^2*e^3*sgn(b*x + a) - 420*(x*e + d)^m*A*b^5*d^4*m*x^2*e^3*sgn(b*x + a) + 240*(x*e + d)^m*B*a^2*b^3*d^5*m^2*e^2*sgn(b*x + a) + 120*(x*e + d)^m*A*a*b^4*d^5*m^2*e^2*sgn(b*x + a) + 4200*(x*e + d)^m*B*a*b^4*d^5*m*x*e^2*sgn(b*x + a) + 840*(x*e + d)^m*A*b^5*d^5*m*x*e^2*sgn(b*x + a) - 600*(x*e + d)^m*B*a*b^4*d^6*m*e*sgn(b*x + a) - 120*(x*e + d)^m*A*b^5*d^6*m*e*sgn(b*x + a) + 720*(x*e + d)^m*B*b^5*d^7*sgn(b*x + a) + 27*(x*e + d)^m*A*a^5*m^5*x*e^7*sgn(b*x + a) + 270*(x*e + d)^m*B*a^5*m^4*x^2*e^7*sgn(b*x + a) + 1350*(x*e + d)^m*A*a^4*b*m^4*x^2*e^7*sgn(b*x + a) + 6095*(x*e + d)^m*B*a^4*b*m^3*x^3*e^7*sgn(b*x + a) + 12190*(x*e + d)^m*A*a^3*b^2*m^3*x^3*e^7*sgn(b*x + a) + 25450*(x*e + d)^m*B*a^3*b^2*m^2*x^4*e^7*sgn(b*x + a) + 25450*(x*e + d)^m*A*a^2*b^3*m^2*x^4*e^7*sgn(b*x + a) + 24120*(x*e + d)^m*B*a^2*b^3*m*x^5*e^7*sgn(b*x + a) + 12060*(x*e + d)^m*A*a*b^4*m*x^5*e^7*sgn(b*x + a) + 4200*(x*e + d)^m*B*a*b^4*x^6*e^7*sgn(b*x + a) + 840*(x*e + d)^m*A*b^5*x^6*e^7*sgn(b*x + a) + 27*(x*e + d)^m*A*a^5*d*m^5*e^6*sgn(b*x + a) + 245*(x*e + d)^m*B*a^5*d*m^4*x*e^6*sgn(b*x + a) + 1225*(x*e + d)^m*A*a^4*b*d*m^4*x*e^6*sgn(b*x + a) + 4085*(x*e + d)^m*B*a^4*b*d*m^3*x^2*e^6*sgn(b*x + a) + 8170*(x*e + d)^m*A*a^3*b^2*d*m^3*x^2*e^6*sgn(b*x + a) + 8440*(x*e + d)^m*B*a^3*b^2*d*m^2*x^3*e^6*sgn(b*x + a) + 8440*(x*e + d)^m*A*a^2*b^3*d*m^2*x^3*e^6*sgn(b*x + a) + 2520*(x*e + d)^m*B*a^2*b^3*d*m*x^4*e^6*sgn(b*x + a) + 1260*(x*e + d)^m*A*a*b^4*d*m*x^4*e^6*sgn(b*x + a) - 25*(x*e + d)^m*B*a^5*d^2*m^4*e^5*sgn(b*x + a) - 125*(x*e + d)^m*A*a^4*b*d^2*m^4*e^5*sgn(b*x + a) - 1790*(x*e + d)^m*B*a^4*b*d^2*m^3*x*e^5*sgn(b*x + a) - 3580*(x*e + d)^m*A*a^3*b^2*d^2*m^3*x*e^5*sgn(b*x + a) - 9510*(x*e + d)^m*B*a^3*b^2*d^2*m^2*x^2*e^5*sgn(b*x + a) - 9510*(x*e + d)^m*A*a^2*b^3*d^2*m^2*x^2*e^5*sgn(b*x + a) - 3360*(x*e + d)^m*B*a^2*b^3*d^2*m*x^3*e^5*sgn(b*x + a) - 1680*(x*e + d)^m*A*a*b^4*d^2*m*x^3*e^5*sgn(b*x + a) + 220*(x*e + d)^m*B*a^4*b*d^3*m^3*e^4*sgn(b*x + a) + 440*(x*e + d)^m*A*a^3*b^2*d^3*m^3*e^4*sgn(b*x + a) + 6420*(x*e + d)^m*B*a^3*b^2*d^3*m^2*x*e^4*sgn(b*x + a) + 6420*(x*e + d)^m*A*a^2*b^3*d^3*m^2*x*e^4*sgn(b*x + a) + 5040*(x*e + d)^m*B*a^2*b^3*d^3*m*x^2*e^4*sgn(b*x + a) + 2520*(x*e + d)^m*A*a*b^4*d^3*m*x^2*e^4*sgn(b*x + a) - 1080*(x*e + d)^m*B*a^3*b^2*d^4*m^2*e^3*sgn(b*x + a) - 1080*(x*e + d)^m*A*a^2*b^3*d^4*m^2*e^3*sgn(b*x + a) - 10080*(x*e + d)^m*B*a^2*b^3*d^4*m*x*e^3*sgn(b*x + a) - 5040*(x*e + d)^m*A*a*b^4*d^4*m*x*e^3*sgn(b*x + a) + 3120*(x*e + d)^m*B*a^2*b^3*d^5*m*e^2*sgn(b*x + a) + 1560*(x*e + d)^m*A*a*b^4*d^5*m*e^2*sgn(b*x + a) - 4200*(x*e + d)^m*B*a*b^4*d^6*e*sgn(b*x + a) - 840*(x*e + d)^m*A*b^5*d^6*e*sgn(b*x + a) + 295*(x*e + d)^m*A*a^5*m^4*x*e^7*sgn(b*x + a) + 1420*(x*e + d)^m*B*a^5*m^3*x^2*e^7*sgn(b*x + a) + 7100*(x*e + d)^m*A*a^4*b*m^3*x^2*e^7*sgn(b*x + a) + 15560*(x*e + d)^m*B*a^4*b*m^2*x^3*e^7*sgn(b*x + a) + 31120*(x*e + d)^m*A*a^3*b^2*m^2*x^3*e^7*sgn(b*x + a) + 29520*(x*e + d)^m*B*a^3*b^2*m*x^4*e^7*sgn(b*x + a) + 29520*(x*e + d)^m*A*a^2*b^3*m*x^4*e^7*sgn(b*x + a) + 10080*(x*e + d)^m*B*a^2*b^3*x^5*e^7*sgn(b*x + a) + 5040*(x*e + d)^m*A*a*b^4*x^5*e^7*sgn(b*x + a) + 295*(x*e + d)^m*A*a^5*d*m^4*e^6*sgn(b*x + a) + 1175*(x*e + d)^m*B*a^5*d*m^3*x*e^6*sgn(b*x + a) + 5875*(x*e + d)^m*A*a^4*b*d*m^3*x*e^6*sgn(b*x + a) + 7390*(x*e + d)^m*B*a^4*b*d*m^2*x^2*e^6*sgn(b*x + a) + 14780*(x*e + d)^m*A*a^3*b^2*d*m^2*x^2*e^6*sgn(b*x + a) + 4200*(x*e + d)^m*B*a^3*b^2*d*m*x^3*e^6*sgn(b*x + a) + 4200*(x*e + d)^m*A*a^2*b^3*d*m*x^3*e^6*sgn(b*x + a) - 245*(x*e + d)^m*B*a^5*d^2*m^3*e^5*sgn(b*x + a) - 1225*(x*e + d)^m*A*a^4*b*d^2*m^3*e^5*sgn(b*x + a) - 6380*(x*e + d)^m*B*a^4*b*d^2*m^2*x*e^5*sgn(b*x + a) - 12760*(x*e + d)^m*A*a^3*b^2*d^2*m^2*x*e^5*sgn(b*x + a) - 6300*(x*e + d)^m*B*a^3*b^2*d^2*m*x^2*e^5*sgn(b*x + a) - 6300*(x*e + d)^m*A*a^2*b^3*d^2*m*x^2*e^5*sgn(b*x + a) + 1790*(x*e + d)^m*B*a^4*b*d^3*m^2*e^4*sgn(b*x + a) + 3580*(x*e + d)^m*A*a^3*b^2*d^3*m^2*e^4*sgn(b*x + a) + 12600*(x*e + d)^m*B*a^3*b^2*d^3*m*x*e^4*sgn(b*x + a) + 12600*(x*e + d)^m*A*a^2*b^3*d^3*m*x*e^4*sgn(b*x + a) - 6420*(x*e + d)^m*B*a^3*b^2*d^4*m*e^3*sgn(b*x + a) - 6420*(x*e + d)^m*A*a^2*b^3*d^4*m*e^3*sgn(b*x + a) + 10080*(x*e + d)^m*B*a^2*b^3*d^5*e^2*sgn(b*x + a) + 5040*(x*e + d)^m*A*a*b^4*d^5*e^2*sgn(b*x + a) + 1665*(x*e + d)^m*A*a^5*m^3*x*e^7*sgn(b*x + a) + 3929*(x*e + d)^m*B*a^5*m^2*x^2*e^7*sgn(b*x + a) + 19645*(x*e + d)^m*A*a^4*b*m^2*x^2*e^7*sgn(b*x + a) + 18980*(x*e + d)^m*B*a^4*b*m*x^3*e^7*sgn(b*x + a) + 37960*(x*e + d)^m*A*a^3*b^2*m*x^3*e^7*sgn(b*x + a) + 12600*(x*e + d)^m*B*a^3*b^2*x^4*e^7*sgn(b*x + a) + 12600*(x*e + d)^m*A*a^2*b^3*x^4*e^7*sgn(b*x + a) + 1665*(x*e + d)^m*A*a^5*d*m^3*e^6*sgn(b*x + a) + 2754*(x*e + d)^m*B*a^5*d*m^2*x*e^6*sgn(b*x + a) + 13770*(x*e + d)^m*A*a^4*b*d*m^2*x*e^6*sgn(b*x + a) + 4200*(x*e + d)^m*B*a^4*b*d*m*x^2*e^6*sgn(b*x + a) + 8400*(x*e + d)^m*A*a^3*b^2*d*m*x^2*e^6*sgn(b*x + a) - 1175*(x*e + d)^m*B*a^5*d^2*m^2*e^5*sgn(b*x + a) - 5875*(x*e + d)^m*A*a^4*b*d^2*m^2*e^5*sgn(b*x + a) - 8400*(x*e + d)^m*B*a^4*b*d^2*m*x*e^5*sgn(b*x + a) - 16800*(x*e + d)^m*A*a^3*b^2*d^2*m*x*e^5*sgn(b*x + a) + 6380*(x*e + d)^m*B*a^4*b*d^3*m*e^4*sgn(b*x + a) + 12760*(x*e + d)^m*A*a^3*b^2*d^3*m*e^4*sgn(b*x + a) - 12600*(x*e + d)^m*B*a^3*b^2*d^4*e^3*sgn(b*x + a) - 12600*(x*e + d)^m*A*a^2*b^3*d^4*e^3*sgn(b*x + a) + 5104*(x*e + d)^m*A*a^5*m^2*x*e^7*sgn(b*x + a) + 5274*(x*e + d)^m*B*a^5*m*x^2*e^7*sgn(b*x + a) + 26370*(x*e + d)^m*A*a^4*b*m*x^2*e^7*sgn(b*x + a) + 8400*(x*e + d)^m*B*a^4*b*x^3*e^7*sgn(b*x + a) + 16800*(x*e + d)^m*A*a^3*b^2*x^3*e^7*sgn(b*x + a) + 5104*(x*e + d)^m*A*a^5*d*m^2*e^6*sgn(b*x + a) + 2520*(x*e + d)^m*B*a^5*d*m*x*e^6*sgn(b*x + a) + 12600*(x*e + d)^m*A*a^4*b*d*m*x*e^6*sgn(b*x + a) - 2754*(x*e + d)^m*B*a^5*d^2*m*e^5*sgn(b*x + a) - 13770*(x*e + d)^m*A*a^4*b*d^2*m*e^5*sgn(b*x + a) + 8400*(x*e + d)^m*B*a^4*b*d^3*e^4*sgn(b*x + a) + 16800*(x*e + d)^m*A*a^3*b^2*d^3*e^4*sgn(b*x + a) + 8028*(x*e + d)^m*A*a^5*m*x*e^7*sgn(b*x + a) + 2520*(x*e + d)^m*B*a^5*x^2*e^7*sgn(b*x + a) + 12600*(x*e + d)^m*A*a^4*b*x^2*e^7*sgn(b*x + a) + 8028*(x*e + d)^m*A*a^5*d*m*e^6*sgn(b*x + a) - 2520*(x*e + d)^m*B*a^5*d^2*e^5*sgn(b*x + a) - 12600*(x*e + d)^m*A*a^4*b*d^2*e^5*sgn(b*x + a) + 5040*(x*e + d)^m*A*a^5*x*e^7*sgn(b*x + a) + 5040*(x*e + d)^m*A*a^5*d*e^6*sgn(b*x + a))/(m^7*e^7 + 28*m^6*e^7 + 322*m^5*e^7 + 1960*m^4*e^7 + 6769*m^3*e^7 + 13132*m^2*e^7 + 13068*m*e^7 + 5040*e^7)","B",0
1889,1,3208,0,0.424619," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B b^{3} m^{4} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B b^{3} d m^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} B a b^{2} m^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A b^{3} m^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} B b^{3} m^{3} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A b^{3} d m^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} B b^{3} d m^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} B a^{2} b m^{4} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} A a b^{2} m^{4} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 33 \, {\left(x e + d\right)}^{m} B a b^{2} m^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(x e + d\right)}^{m} A b^{3} m^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{m} B b^{3} m^{2} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{4} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{4} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 8 \, {\left(x e + d\right)}^{m} A b^{3} d m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(x e + d\right)}^{m} B b^{3} d m^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 9 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 12 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B a^{3} m^{4} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} A a^{2} b m^{4} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(x e + d\right)}^{m} B a^{2} b m^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(x e + d\right)}^{m} A a b^{2} m^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 123 \, {\left(x e + d\right)}^{m} B a b^{2} m^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 41 \, {\left(x e + d\right)}^{m} A b^{3} m^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 50 \, {\left(x e + d\right)}^{m} B b^{3} m x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B a^{3} d m^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 51 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 17 \, {\left(x e + d\right)}^{m} A b^{3} d m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} B b^{3} d m x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) - 54 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 18 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 8 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(x e + d\right)}^{m} B a b^{2} d^{3} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 24 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A a^{3} m^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) + 13 \, {\left(x e + d\right)}^{m} B a^{3} m^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 39 \, {\left(x e + d\right)}^{m} A a^{2} b m^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 147 \, {\left(x e + d\right)}^{m} B a^{2} b m^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 147 \, {\left(x e + d\right)}^{m} A a b^{2} m^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 183 \, {\left(x e + d\right)}^{m} B a b^{2} m x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 61 \, {\left(x e + d\right)}^{m} A b^{3} m x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} B b^{3} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A a^{3} d m^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(x e + d\right)}^{m} B a^{3} d m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 87 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 87 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} B a b^{2} d m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} A b^{3} d m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 54 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) - 54 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) - 45 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 15 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 90 \, {\left(x e + d\right)}^{m} B a b^{2} d^{3} m x e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m x e^{2} \mathrm{sgn}\left(b x + a\right) - 18 \, {\left(x e + d\right)}^{m} B a b^{2} d^{4} m e \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m e \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} \mathrm{sgn}\left(b x + a\right) + 14 \, {\left(x e + d\right)}^{m} A a^{3} m^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) + 59 \, {\left(x e + d\right)}^{m} B a^{3} m^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 177 \, {\left(x e + d\right)}^{m} A a^{2} b m^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 234 \, {\left(x e + d\right)}^{m} B a^{2} b m x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 234 \, {\left(x e + d\right)}^{m} A a b^{2} m x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 90 \, {\left(x e + d\right)}^{m} B a b^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} A b^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 14 \, {\left(x e + d\right)}^{m} A a^{3} d m^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 47 \, {\left(x e + d\right)}^{m} B a^{3} d m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 141 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} B a^{2} b d m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} A a b^{2} d m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 36 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m x e^{3} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m x e^{3} \mathrm{sgn}\left(b x + a\right) + 54 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} m e^{2} \mathrm{sgn}\left(b x + a\right) + 54 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} m e^{2} \mathrm{sgn}\left(b x + a\right) - 90 \, {\left(x e + d\right)}^{m} B a b^{2} d^{4} e \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} e \mathrm{sgn}\left(b x + a\right) + 71 \, {\left(x e + d\right)}^{m} A a^{3} m^{2} x e^{5} \mathrm{sgn}\left(b x + a\right) + 107 \, {\left(x e + d\right)}^{m} B a^{3} m x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 321 \, {\left(x e + d\right)}^{m} A a^{2} b m x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} B a^{2} b x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} A a b^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 71 \, {\left(x e + d\right)}^{m} A a^{3} d m^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} B a^{3} d m x e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} A a^{2} b d m x e^{4} \mathrm{sgn}\left(b x + a\right) - 47 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m e^{3} \mathrm{sgn}\left(b x + a\right) - 141 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m e^{3} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 154 \, {\left(x e + d\right)}^{m} A a^{3} m x e^{5} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} B a^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} A a^{2} b x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 154 \, {\left(x e + d\right)}^{m} A a^{3} d m e^{4} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 180 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} A a^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} A a^{3} d e^{4} \mathrm{sgn}\left(b x + a\right)}{m^{5} e^{5} + 15 \, m^{4} e^{5} + 85 \, m^{3} e^{5} + 225 \, m^{2} e^{5} + 274 \, m e^{5} + 120 \, e^{5}}"," ",0,"((x*e + d)^m*B*b^3*m^4*x^5*e^5*sgn(b*x + a) + (x*e + d)^m*B*b^3*d*m^4*x^4*e^4*sgn(b*x + a) + 3*(x*e + d)^m*B*a*b^2*m^4*x^4*e^5*sgn(b*x + a) + (x*e + d)^m*A*b^3*m^4*x^4*e^5*sgn(b*x + a) + 10*(x*e + d)^m*B*b^3*m^3*x^5*e^5*sgn(b*x + a) + 3*(x*e + d)^m*B*a*b^2*d*m^4*x^3*e^4*sgn(b*x + a) + (x*e + d)^m*A*b^3*d*m^4*x^3*e^4*sgn(b*x + a) + 6*(x*e + d)^m*B*b^3*d*m^3*x^4*e^4*sgn(b*x + a) - 4*(x*e + d)^m*B*b^3*d^2*m^3*x^3*e^3*sgn(b*x + a) + 3*(x*e + d)^m*B*a^2*b*m^4*x^3*e^5*sgn(b*x + a) + 3*(x*e + d)^m*A*a*b^2*m^4*x^3*e^5*sgn(b*x + a) + 33*(x*e + d)^m*B*a*b^2*m^3*x^4*e^5*sgn(b*x + a) + 11*(x*e + d)^m*A*b^3*m^3*x^4*e^5*sgn(b*x + a) + 35*(x*e + d)^m*B*b^3*m^2*x^5*e^5*sgn(b*x + a) + 3*(x*e + d)^m*B*a^2*b*d*m^4*x^2*e^4*sgn(b*x + a) + 3*(x*e + d)^m*A*a*b^2*d*m^4*x^2*e^4*sgn(b*x + a) + 24*(x*e + d)^m*B*a*b^2*d*m^3*x^3*e^4*sgn(b*x + a) + 8*(x*e + d)^m*A*b^3*d*m^3*x^3*e^4*sgn(b*x + a) + 11*(x*e + d)^m*B*b^3*d*m^2*x^4*e^4*sgn(b*x + a) - 9*(x*e + d)^m*B*a*b^2*d^2*m^3*x^2*e^3*sgn(b*x + a) - 3*(x*e + d)^m*A*b^3*d^2*m^3*x^2*e^3*sgn(b*x + a) - 12*(x*e + d)^m*B*b^3*d^2*m^2*x^3*e^3*sgn(b*x + a) + 12*(x*e + d)^m*B*b^3*d^3*m^2*x^2*e^2*sgn(b*x + a) + (x*e + d)^m*B*a^3*m^4*x^2*e^5*sgn(b*x + a) + 3*(x*e + d)^m*A*a^2*b*m^4*x^2*e^5*sgn(b*x + a) + 36*(x*e + d)^m*B*a^2*b*m^3*x^3*e^5*sgn(b*x + a) + 36*(x*e + d)^m*A*a*b^2*m^3*x^3*e^5*sgn(b*x + a) + 123*(x*e + d)^m*B*a*b^2*m^2*x^4*e^5*sgn(b*x + a) + 41*(x*e + d)^m*A*b^3*m^2*x^4*e^5*sgn(b*x + a) + 50*(x*e + d)^m*B*b^3*m*x^5*e^5*sgn(b*x + a) + (x*e + d)^m*B*a^3*d*m^4*x*e^4*sgn(b*x + a) + 3*(x*e + d)^m*A*a^2*b*d*m^4*x*e^4*sgn(b*x + a) + 30*(x*e + d)^m*B*a^2*b*d*m^3*x^2*e^4*sgn(b*x + a) + 30*(x*e + d)^m*A*a*b^2*d*m^3*x^2*e^4*sgn(b*x + a) + 51*(x*e + d)^m*B*a*b^2*d*m^2*x^3*e^4*sgn(b*x + a) + 17*(x*e + d)^m*A*b^3*d*m^2*x^3*e^4*sgn(b*x + a) + 6*(x*e + d)^m*B*b^3*d*m*x^4*e^4*sgn(b*x + a) - 6*(x*e + d)^m*B*a^2*b*d^2*m^3*x*e^3*sgn(b*x + a) - 6*(x*e + d)^m*A*a*b^2*d^2*m^3*x*e^3*sgn(b*x + a) - 54*(x*e + d)^m*B*a*b^2*d^2*m^2*x^2*e^3*sgn(b*x + a) - 18*(x*e + d)^m*A*b^3*d^2*m^2*x^2*e^3*sgn(b*x + a) - 8*(x*e + d)^m*B*b^3*d^2*m*x^3*e^3*sgn(b*x + a) + 18*(x*e + d)^m*B*a*b^2*d^3*m^2*x*e^2*sgn(b*x + a) + 6*(x*e + d)^m*A*b^3*d^3*m^2*x*e^2*sgn(b*x + a) + 12*(x*e + d)^m*B*b^3*d^3*m*x^2*e^2*sgn(b*x + a) - 24*(x*e + d)^m*B*b^3*d^4*m*x*e*sgn(b*x + a) + (x*e + d)^m*A*a^3*m^4*x*e^5*sgn(b*x + a) + 13*(x*e + d)^m*B*a^3*m^3*x^2*e^5*sgn(b*x + a) + 39*(x*e + d)^m*A*a^2*b*m^3*x^2*e^5*sgn(b*x + a) + 147*(x*e + d)^m*B*a^2*b*m^2*x^3*e^5*sgn(b*x + a) + 147*(x*e + d)^m*A*a*b^2*m^2*x^3*e^5*sgn(b*x + a) + 183*(x*e + d)^m*B*a*b^2*m*x^4*e^5*sgn(b*x + a) + 61*(x*e + d)^m*A*b^3*m*x^4*e^5*sgn(b*x + a) + 24*(x*e + d)^m*B*b^3*x^5*e^5*sgn(b*x + a) + (x*e + d)^m*A*a^3*d*m^4*e^4*sgn(b*x + a) + 12*(x*e + d)^m*B*a^3*d*m^3*x*e^4*sgn(b*x + a) + 36*(x*e + d)^m*A*a^2*b*d*m^3*x*e^4*sgn(b*x + a) + 87*(x*e + d)^m*B*a^2*b*d*m^2*x^2*e^4*sgn(b*x + a) + 87*(x*e + d)^m*A*a*b^2*d*m^2*x^2*e^4*sgn(b*x + a) + 30*(x*e + d)^m*B*a*b^2*d*m*x^3*e^4*sgn(b*x + a) + 10*(x*e + d)^m*A*b^3*d*m*x^3*e^4*sgn(b*x + a) - (x*e + d)^m*B*a^3*d^2*m^3*e^3*sgn(b*x + a) - 3*(x*e + d)^m*A*a^2*b*d^2*m^3*e^3*sgn(b*x + a) - 54*(x*e + d)^m*B*a^2*b*d^2*m^2*x*e^3*sgn(b*x + a) - 54*(x*e + d)^m*A*a*b^2*d^2*m^2*x*e^3*sgn(b*x + a) - 45*(x*e + d)^m*B*a*b^2*d^2*m*x^2*e^3*sgn(b*x + a) - 15*(x*e + d)^m*A*b^3*d^2*m*x^2*e^3*sgn(b*x + a) + 6*(x*e + d)^m*B*a^2*b*d^3*m^2*e^2*sgn(b*x + a) + 6*(x*e + d)^m*A*a*b^2*d^3*m^2*e^2*sgn(b*x + a) + 90*(x*e + d)^m*B*a*b^2*d^3*m*x*e^2*sgn(b*x + a) + 30*(x*e + d)^m*A*b^3*d^3*m*x*e^2*sgn(b*x + a) - 18*(x*e + d)^m*B*a*b^2*d^4*m*e*sgn(b*x + a) - 6*(x*e + d)^m*A*b^3*d^4*m*e*sgn(b*x + a) + 24*(x*e + d)^m*B*b^3*d^5*sgn(b*x + a) + 14*(x*e + d)^m*A*a^3*m^3*x*e^5*sgn(b*x + a) + 59*(x*e + d)^m*B*a^3*m^2*x^2*e^5*sgn(b*x + a) + 177*(x*e + d)^m*A*a^2*b*m^2*x^2*e^5*sgn(b*x + a) + 234*(x*e + d)^m*B*a^2*b*m*x^3*e^5*sgn(b*x + a) + 234*(x*e + d)^m*A*a*b^2*m*x^3*e^5*sgn(b*x + a) + 90*(x*e + d)^m*B*a*b^2*x^4*e^5*sgn(b*x + a) + 30*(x*e + d)^m*A*b^3*x^4*e^5*sgn(b*x + a) + 14*(x*e + d)^m*A*a^3*d*m^3*e^4*sgn(b*x + a) + 47*(x*e + d)^m*B*a^3*d*m^2*x*e^4*sgn(b*x + a) + 141*(x*e + d)^m*A*a^2*b*d*m^2*x*e^4*sgn(b*x + a) + 60*(x*e + d)^m*B*a^2*b*d*m*x^2*e^4*sgn(b*x + a) + 60*(x*e + d)^m*A*a*b^2*d*m*x^2*e^4*sgn(b*x + a) - 12*(x*e + d)^m*B*a^3*d^2*m^2*e^3*sgn(b*x + a) - 36*(x*e + d)^m*A*a^2*b*d^2*m^2*e^3*sgn(b*x + a) - 120*(x*e + d)^m*B*a^2*b*d^2*m*x*e^3*sgn(b*x + a) - 120*(x*e + d)^m*A*a*b^2*d^2*m*x*e^3*sgn(b*x + a) + 54*(x*e + d)^m*B*a^2*b*d^3*m*e^2*sgn(b*x + a) + 54*(x*e + d)^m*A*a*b^2*d^3*m*e^2*sgn(b*x + a) - 90*(x*e + d)^m*B*a*b^2*d^4*e*sgn(b*x + a) - 30*(x*e + d)^m*A*b^3*d^4*e*sgn(b*x + a) + 71*(x*e + d)^m*A*a^3*m^2*x*e^5*sgn(b*x + a) + 107*(x*e + d)^m*B*a^3*m*x^2*e^5*sgn(b*x + a) + 321*(x*e + d)^m*A*a^2*b*m*x^2*e^5*sgn(b*x + a) + 120*(x*e + d)^m*B*a^2*b*x^3*e^5*sgn(b*x + a) + 120*(x*e + d)^m*A*a*b^2*x^3*e^5*sgn(b*x + a) + 71*(x*e + d)^m*A*a^3*d*m^2*e^4*sgn(b*x + a) + 60*(x*e + d)^m*B*a^3*d*m*x*e^4*sgn(b*x + a) + 180*(x*e + d)^m*A*a^2*b*d*m*x*e^4*sgn(b*x + a) - 47*(x*e + d)^m*B*a^3*d^2*m*e^3*sgn(b*x + a) - 141*(x*e + d)^m*A*a^2*b*d^2*m*e^3*sgn(b*x + a) + 120*(x*e + d)^m*B*a^2*b*d^3*e^2*sgn(b*x + a) + 120*(x*e + d)^m*A*a*b^2*d^3*e^2*sgn(b*x + a) + 154*(x*e + d)^m*A*a^3*m*x*e^5*sgn(b*x + a) + 60*(x*e + d)^m*B*a^3*x^2*e^5*sgn(b*x + a) + 180*(x*e + d)^m*A*a^2*b*x^2*e^5*sgn(b*x + a) + 154*(x*e + d)^m*A*a^3*d*m*e^4*sgn(b*x + a) - 60*(x*e + d)^m*B*a^3*d^2*e^3*sgn(b*x + a) - 180*(x*e + d)^m*A*a^2*b*d^2*e^3*sgn(b*x + a) + 120*(x*e + d)^m*A*a^3*x*e^5*sgn(b*x + a) + 120*(x*e + d)^m*A*a^3*d*e^4*sgn(b*x + a))/(m^5*e^5 + 15*m^4*e^5 + 85*m^3*e^5 + 225*m^2*e^5 + 274*m*e^5 + 120*e^5)","B",0
1890,1,659,0,0.215850," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B b m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B b d m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B a m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A b m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} B b m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B a d m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A b d m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} B b d m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, {\left(x e + d\right)}^{m} B b d^{2} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A a m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(x e + d\right)}^{m} B a m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(x e + d\right)}^{m} A b m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} B b x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} A a d m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} B a d m x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} A b d m x e^{2} \mathrm{sgn}\left(b x + a\right) - {\left(x e + d\right)}^{m} B a d^{2} m e \mathrm{sgn}\left(b x + a\right) - {\left(x e + d\right)}^{m} A b d^{2} m e \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} B b d^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} A a m x e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} B a x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} A b x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} A a d m e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)}^{m} B a d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)}^{m} A b d^{2} e \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} A a x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} A a d e^{2} \mathrm{sgn}\left(b x + a\right)}{m^{3} e^{3} + 6 \, m^{2} e^{3} + 11 \, m e^{3} + 6 \, e^{3}}"," ",0,"((x*e + d)^m*B*b*m^2*x^3*e^3*sgn(b*x + a) + (x*e + d)^m*B*b*d*m^2*x^2*e^2*sgn(b*x + a) + (x*e + d)^m*B*a*m^2*x^2*e^3*sgn(b*x + a) + (x*e + d)^m*A*b*m^2*x^2*e^3*sgn(b*x + a) + 3*(x*e + d)^m*B*b*m*x^3*e^3*sgn(b*x + a) + (x*e + d)^m*B*a*d*m^2*x*e^2*sgn(b*x + a) + (x*e + d)^m*A*b*d*m^2*x*e^2*sgn(b*x + a) + (x*e + d)^m*B*b*d*m*x^2*e^2*sgn(b*x + a) - 2*(x*e + d)^m*B*b*d^2*m*x*e*sgn(b*x + a) + (x*e + d)^m*A*a*m^2*x*e^3*sgn(b*x + a) + 4*(x*e + d)^m*B*a*m*x^2*e^3*sgn(b*x + a) + 4*(x*e + d)^m*A*b*m*x^2*e^3*sgn(b*x + a) + 2*(x*e + d)^m*B*b*x^3*e^3*sgn(b*x + a) + (x*e + d)^m*A*a*d*m^2*e^2*sgn(b*x + a) + 3*(x*e + d)^m*B*a*d*m*x*e^2*sgn(b*x + a) + 3*(x*e + d)^m*A*b*d*m*x*e^2*sgn(b*x + a) - (x*e + d)^m*B*a*d^2*m*e*sgn(b*x + a) - (x*e + d)^m*A*b*d^2*m*e*sgn(b*x + a) + 2*(x*e + d)^m*B*b*d^3*sgn(b*x + a) + 5*(x*e + d)^m*A*a*m*x*e^3*sgn(b*x + a) + 3*(x*e + d)^m*B*a*x^2*e^3*sgn(b*x + a) + 3*(x*e + d)^m*A*b*x^2*e^3*sgn(b*x + a) + 5*(x*e + d)^m*A*a*d*m*e^2*sgn(b*x + a) - 3*(x*e + d)^m*B*a*d^2*e*sgn(b*x + a) - 3*(x*e + d)^m*A*b*d^2*e*sgn(b*x + a) + 6*(x*e + d)^m*A*a*x*e^3*sgn(b*x + a) + 6*(x*e + d)^m*A*a*d*e^2*sgn(b*x + a))/(m^3*e^3 + 6*m^2*e^3 + 11*m*e^3 + 6*e^3)","B",0
1891,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/sqrt(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1892,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^(3/2), x)","F",0
1893,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((B*x + A)*(b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^m, x)","F",0
1894,1,1352,0,0.341938," ","integrate((e*x+d)^(-3-2*p)*(g*x+f)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d g p x^{3} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d^{2} g p x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b g p x^{3} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d f p x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d g x^{3} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d^{2} f p x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b d^{2} g p x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d^{2} g x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b f p x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} g p x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} f x^{3} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b g x^{3} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} d g p x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d f x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b d g x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b d^{2} f p e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d^{2} f x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} f p x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} g x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} d f p e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b d f x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} - 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} d g x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b d^{2} f e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} - {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} d^{2} g e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} - {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} f x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} - {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} d f e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)}}{2 \, {\left(2 \, b^{2} d^{2} p^{2} - 4 \, a b d p^{2} e + 3 \, b^{2} d^{2} p + 2 \, a^{2} p^{2} e^{2} - 6 \, a b d p e + b^{2} d^{2} + 3 \, a^{2} p e^{2} - 2 \, a b d e + a^{2} e^{2}\right)}}"," ",0,"1/2*(2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d*g*p*x^3*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d^2*g*p*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*g*p*x^3*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d*f*p*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + (b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d*g*x^3*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d^2*f*p*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*d^2*g*p*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) + (b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d^2*g*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*f*p*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*g*p*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) + (b^2*x^2 + 2*a*b*x + a^2)^p*b^2*f*x^3*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*g*x^3*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*d*g*p*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d*f*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*d*g*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*d^2*f*p*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d^2*f*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*f*p*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*g*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*d*f*p*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*d*f*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) - 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*d*g*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*d^2*f*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) - (b^2*x^2 + 2*a*b*x + a^2)^p*a^2*d^2*g*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) - (b^2*x^2 + 2*a*b*x + a^2)^p*a^2*f*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 2) - (b^2*x^2 + 2*a*b*x + a^2)^p*a^2*d*f*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1))/(2*b^2*d^2*p^2 - 4*a*b*d*p^2*e + 3*b^2*d^2*p + 2*a^2*p^2*e^2 - 6*a*b*d*p*e + b^2*d^2 + 3*a^2*p*e^2 - 2*a*b*d*e + a^2*e^2)","B",0
1895,1,291,0,0.153667," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} e^{5} + \frac{5}{8} \, b^{3} d x^{8} e^{4} + \frac{10}{7} \, b^{3} d^{2} x^{7} e^{3} + \frac{5}{3} \, b^{3} d^{3} x^{6} e^{2} + b^{3} d^{4} x^{5} e + \frac{1}{4} \, b^{3} d^{5} x^{4} + \frac{3}{8} \, a b^{2} x^{8} e^{5} + \frac{15}{7} \, a b^{2} d x^{7} e^{4} + 5 \, a b^{2} d^{2} x^{6} e^{3} + 6 \, a b^{2} d^{3} x^{5} e^{2} + \frac{15}{4} \, a b^{2} d^{4} x^{4} e + a b^{2} d^{5} x^{3} + \frac{3}{7} \, a^{2} b x^{7} e^{5} + \frac{5}{2} \, a^{2} b d x^{6} e^{4} + 6 \, a^{2} b d^{2} x^{5} e^{3} + \frac{15}{2} \, a^{2} b d^{3} x^{4} e^{2} + 5 \, a^{2} b d^{4} x^{3} e + \frac{3}{2} \, a^{2} b d^{5} x^{2} + \frac{1}{6} \, a^{3} x^{6} e^{5} + a^{3} d x^{5} e^{4} + \frac{5}{2} \, a^{3} d^{2} x^{4} e^{3} + \frac{10}{3} \, a^{3} d^{3} x^{3} e^{2} + \frac{5}{2} \, a^{3} d^{4} x^{2} e + a^{3} d^{5} x"," ",0,"1/9*b^3*x^9*e^5 + 5/8*b^3*d*x^8*e^4 + 10/7*b^3*d^2*x^7*e^3 + 5/3*b^3*d^3*x^6*e^2 + b^3*d^4*x^5*e + 1/4*b^3*d^5*x^4 + 3/8*a*b^2*x^8*e^5 + 15/7*a*b^2*d*x^7*e^4 + 5*a*b^2*d^2*x^6*e^3 + 6*a*b^2*d^3*x^5*e^2 + 15/4*a*b^2*d^4*x^4*e + a*b^2*d^5*x^3 + 3/7*a^2*b*x^7*e^5 + 5/2*a^2*b*d*x^6*e^4 + 6*a^2*b*d^2*x^5*e^3 + 15/2*a^2*b*d^3*x^4*e^2 + 5*a^2*b*d^4*x^3*e + 3/2*a^2*b*d^5*x^2 + 1/6*a^3*x^6*e^5 + a^3*d*x^5*e^4 + 5/2*a^3*d^2*x^4*e^3 + 10/3*a^3*d^3*x^3*e^2 + 5/2*a^3*d^4*x^2*e + a^3*d^5*x","B",0
1896,1,237,0,0.162348," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{8} \, b^{3} x^{8} e^{4} + \frac{4}{7} \, b^{3} d x^{7} e^{3} + b^{3} d^{2} x^{6} e^{2} + \frac{4}{5} \, b^{3} d^{3} x^{5} e + \frac{1}{4} \, b^{3} d^{4} x^{4} + \frac{3}{7} \, a b^{2} x^{7} e^{4} + 2 \, a b^{2} d x^{6} e^{3} + \frac{18}{5} \, a b^{2} d^{2} x^{5} e^{2} + 3 \, a b^{2} d^{3} x^{4} e + a b^{2} d^{4} x^{3} + \frac{1}{2} \, a^{2} b x^{6} e^{4} + \frac{12}{5} \, a^{2} b d x^{5} e^{3} + \frac{9}{2} \, a^{2} b d^{2} x^{4} e^{2} + 4 \, a^{2} b d^{3} x^{3} e + \frac{3}{2} \, a^{2} b d^{4} x^{2} + \frac{1}{5} \, a^{3} x^{5} e^{4} + a^{3} d x^{4} e^{3} + 2 \, a^{3} d^{2} x^{3} e^{2} + 2 \, a^{3} d^{3} x^{2} e + a^{3} d^{4} x"," ",0,"1/8*b^3*x^8*e^4 + 4/7*b^3*d*x^7*e^3 + b^3*d^2*x^6*e^2 + 4/5*b^3*d^3*x^5*e + 1/4*b^3*d^4*x^4 + 3/7*a*b^2*x^7*e^4 + 2*a*b^2*d*x^6*e^3 + 18/5*a*b^2*d^2*x^5*e^2 + 3*a*b^2*d^3*x^4*e + a*b^2*d^4*x^3 + 1/2*a^2*b*x^6*e^4 + 12/5*a^2*b*d*x^5*e^3 + 9/2*a^2*b*d^2*x^4*e^2 + 4*a^2*b*d^3*x^3*e + 3/2*a^2*b*d^4*x^2 + 1/5*a^3*x^5*e^4 + a^3*d*x^4*e^3 + 2*a^3*d^2*x^3*e^2 + 2*a^3*d^3*x^2*e + a^3*d^4*x","B",0
1897,1,184,0,0.149694," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{7} \, b^{3} x^{7} e^{3} + \frac{1}{2} \, b^{3} d x^{6} e^{2} + \frac{3}{5} \, b^{3} d^{2} x^{5} e + \frac{1}{4} \, b^{3} d^{3} x^{4} + \frac{1}{2} \, a b^{2} x^{6} e^{3} + \frac{9}{5} \, a b^{2} d x^{5} e^{2} + \frac{9}{4} \, a b^{2} d^{2} x^{4} e + a b^{2} d^{3} x^{3} + \frac{3}{5} \, a^{2} b x^{5} e^{3} + \frac{9}{4} \, a^{2} b d x^{4} e^{2} + 3 \, a^{2} b d^{2} x^{3} e + \frac{3}{2} \, a^{2} b d^{3} x^{2} + \frac{1}{4} \, a^{3} x^{4} e^{3} + a^{3} d x^{3} e^{2} + \frac{3}{2} \, a^{3} d^{2} x^{2} e + a^{3} d^{3} x"," ",0,"1/7*b^3*x^7*e^3 + 1/2*b^3*d*x^6*e^2 + 3/5*b^3*d^2*x^5*e + 1/4*b^3*d^3*x^4 + 1/2*a*b^2*x^6*e^3 + 9/5*a*b^2*d*x^5*e^2 + 9/4*a*b^2*d^2*x^4*e + a*b^2*d^3*x^3 + 3/5*a^2*b*x^5*e^3 + 9/4*a^2*b*d*x^4*e^2 + 3*a^2*b*d^2*x^3*e + 3/2*a^2*b*d^3*x^2 + 1/4*a^3*x^4*e^3 + a^3*d*x^3*e^2 + 3/2*a^3*d^2*x^2*e + a^3*d^3*x","B",0
1898,1,130,0,0.152095," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{6} \, b^{3} x^{6} e^{2} + \frac{2}{5} \, b^{3} d x^{5} e + \frac{1}{4} \, b^{3} d^{2} x^{4} + \frac{3}{5} \, a b^{2} x^{5} e^{2} + \frac{3}{2} \, a b^{2} d x^{4} e + a b^{2} d^{2} x^{3} + \frac{3}{4} \, a^{2} b x^{4} e^{2} + 2 \, a^{2} b d x^{3} e + \frac{3}{2} \, a^{2} b d^{2} x^{2} + \frac{1}{3} \, a^{3} x^{3} e^{2} + a^{3} d x^{2} e + a^{3} d^{2} x"," ",0,"1/6*b^3*x^6*e^2 + 2/5*b^3*d*x^5*e + 1/4*b^3*d^2*x^4 + 3/5*a*b^2*x^5*e^2 + 3/2*a*b^2*d*x^4*e + a*b^2*d^2*x^3 + 3/4*a^2*b*x^4*e^2 + 2*a^2*b*d*x^3*e + 3/2*a^2*b*d^2*x^2 + 1/3*a^3*x^3*e^2 + a^3*d*x^2*e + a^3*d^2*x","B",0
1899,1,76,0,0.165529," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{5} \, b^{3} x^{5} e + \frac{1}{4} \, b^{3} d x^{4} + \frac{3}{4} \, a b^{2} x^{4} e + a b^{2} d x^{3} + a^{2} b x^{3} e + \frac{3}{2} \, a^{2} b d x^{2} + \frac{1}{2} \, a^{3} x^{2} e + a^{3} d x"," ",0,"1/5*b^3*x^5*e + 1/4*b^3*d*x^4 + 3/4*a*b^2*x^4*e + a*b^2*d*x^3 + a^2*b*x^3*e + 3/2*a^2*b*d*x^2 + 1/2*a^3*x^2*e + a^3*d*x","B",0
1900,1,31,0,0.153126," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} a^{2} + \frac{1}{4} \, {\left(b x^{2} + 2 \, a x\right)}^{2} b"," ",0,"1/2*(b*x^2 + 2*a*x)*a^2 + 1/4*(b*x^2 + 2*a*x)^2*b","B",0
1901,1,113,0,0.181604," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d),x, algorithm=""giac"")","-{\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, b^{3} x^{3} e^{2} - 3 \, b^{3} d x^{2} e + 6 \, b^{3} d^{2} x + 9 \, a b^{2} x^{2} e^{2} - 18 \, a b^{2} d x e + 18 \, a^{2} b x e^{2}\right)} e^{\left(-3\right)}"," ",0,"-(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*e^(-4)*log(abs(x*e + d)) + 1/6*(2*b^3*x^3*e^2 - 3*b^3*d*x^2*e + 6*b^3*d^2*x + 9*a*b^2*x^2*e^2 - 18*a*b^2*d*x*e + 18*a^2*b*x*e^2)*e^(-3)","A",0
1902,1,164,0,0.158216," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(b^{3} - \frac{6 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)} - 3 \, {\left(b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{b^{3} d^{3} e^{2}}{x e + d} - \frac{3 \, a b^{2} d^{2} e^{3}}{x e + d} + \frac{3 \, a^{2} b d e^{4}}{x e + d} - \frac{a^{3} e^{5}}{x e + d}\right)} e^{\left(-6\right)}"," ",0,"1/2*(b^3 - 6*(b^3*d*e - a*b^2*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4) - 3*(b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (b^3*d^3*e^2/(x*e + d) - 3*a*b^2*d^2*e^3/(x*e + d) + 3*a^2*b*d*e^4/(x*e + d) - a^3*e^5/(x*e + d))*e^(-6)","B",0
1903,1,110,0,0.162377," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^3,x, algorithm=""giac"")","b^{3} x e^{\left(-3\right)} - 3 \, {\left(b^{3} d - a b^{2} e\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, b^{3} d^{3} - 9 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} + a^{3} e^{3} + 6 \, {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"b^3*x*e^(-3) - 3*(b^3*d - a*b^2*e)*e^(-4)*log(abs(x*e + d)) - 1/2*(5*b^3*d^3 - 9*a*b^2*d^2*e + 3*a^2*b*d*e^2 + a^3*e^3 + 6*(b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*e^(-4)/(x*e + d)^2","A",0
1904,1,117,0,0.164949," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^4,x, algorithm=""giac"")","b^{3} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(18 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x^{2} + 9 \, {\left(3 \, b^{3} d^{2} - 2 \, a b^{2} d e - a^{2} b e^{2}\right)} x + {\left(11 \, b^{3} d^{3} - 6 \, a b^{2} d^{2} e - 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3}\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"b^3*e^(-4)*log(abs(x*e + d)) + 1/6*(18*(b^3*d*e - a*b^2*e^2)*x^2 + 9*(3*b^3*d^2 - 2*a*b^2*d*e - a^2*b*e^2)*x + (11*b^3*d^3 - 6*a*b^2*d^2*e - 3*a^2*b*d*e^2 - 2*a^3*e^3)*e^(-1))*e^(-3)/(x*e + d)^3","A",0
1905,1,555,0,0.223487," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{12} \, b^{5} x^{12} e^{6} + \frac{6}{11} \, b^{5} d x^{11} e^{5} + \frac{3}{2} \, b^{5} d^{2} x^{10} e^{4} + \frac{20}{9} \, b^{5} d^{3} x^{9} e^{3} + \frac{15}{8} \, b^{5} d^{4} x^{8} e^{2} + \frac{6}{7} \, b^{5} d^{5} x^{7} e + \frac{1}{6} \, b^{5} d^{6} x^{6} + \frac{5}{11} \, a b^{4} x^{11} e^{6} + 3 \, a b^{4} d x^{10} e^{5} + \frac{25}{3} \, a b^{4} d^{2} x^{9} e^{4} + \frac{25}{2} \, a b^{4} d^{3} x^{8} e^{3} + \frac{75}{7} \, a b^{4} d^{4} x^{7} e^{2} + 5 \, a b^{4} d^{5} x^{6} e + a b^{4} d^{6} x^{5} + a^{2} b^{3} x^{10} e^{6} + \frac{20}{3} \, a^{2} b^{3} d x^{9} e^{5} + \frac{75}{4} \, a^{2} b^{3} d^{2} x^{8} e^{4} + \frac{200}{7} \, a^{2} b^{3} d^{3} x^{7} e^{3} + 25 \, a^{2} b^{3} d^{4} x^{6} e^{2} + 12 \, a^{2} b^{3} d^{5} x^{5} e + \frac{5}{2} \, a^{2} b^{3} d^{6} x^{4} + \frac{10}{9} \, a^{3} b^{2} x^{9} e^{6} + \frac{15}{2} \, a^{3} b^{2} d x^{8} e^{5} + \frac{150}{7} \, a^{3} b^{2} d^{2} x^{7} e^{4} + \frac{100}{3} \, a^{3} b^{2} d^{3} x^{6} e^{3} + 30 \, a^{3} b^{2} d^{4} x^{5} e^{2} + 15 \, a^{3} b^{2} d^{5} x^{4} e + \frac{10}{3} \, a^{3} b^{2} d^{6} x^{3} + \frac{5}{8} \, a^{4} b x^{8} e^{6} + \frac{30}{7} \, a^{4} b d x^{7} e^{5} + \frac{25}{2} \, a^{4} b d^{2} x^{6} e^{4} + 20 \, a^{4} b d^{3} x^{5} e^{3} + \frac{75}{4} \, a^{4} b d^{4} x^{4} e^{2} + 10 \, a^{4} b d^{5} x^{3} e + \frac{5}{2} \, a^{4} b d^{6} x^{2} + \frac{1}{7} \, a^{5} x^{7} e^{6} + a^{5} d x^{6} e^{5} + 3 \, a^{5} d^{2} x^{5} e^{4} + 5 \, a^{5} d^{3} x^{4} e^{3} + 5 \, a^{5} d^{4} x^{3} e^{2} + 3 \, a^{5} d^{5} x^{2} e + a^{5} d^{6} x"," ",0,"1/12*b^5*x^12*e^6 + 6/11*b^5*d*x^11*e^5 + 3/2*b^5*d^2*x^10*e^4 + 20/9*b^5*d^3*x^9*e^3 + 15/8*b^5*d^4*x^8*e^2 + 6/7*b^5*d^5*x^7*e + 1/6*b^5*d^6*x^6 + 5/11*a*b^4*x^11*e^6 + 3*a*b^4*d*x^10*e^5 + 25/3*a*b^4*d^2*x^9*e^4 + 25/2*a*b^4*d^3*x^8*e^3 + 75/7*a*b^4*d^4*x^7*e^2 + 5*a*b^4*d^5*x^6*e + a*b^4*d^6*x^5 + a^2*b^3*x^10*e^6 + 20/3*a^2*b^3*d*x^9*e^5 + 75/4*a^2*b^3*d^2*x^8*e^4 + 200/7*a^2*b^3*d^3*x^7*e^3 + 25*a^2*b^3*d^4*x^6*e^2 + 12*a^2*b^3*d^5*x^5*e + 5/2*a^2*b^3*d^6*x^4 + 10/9*a^3*b^2*x^9*e^6 + 15/2*a^3*b^2*d*x^8*e^5 + 150/7*a^3*b^2*d^2*x^7*e^4 + 100/3*a^3*b^2*d^3*x^6*e^3 + 30*a^3*b^2*d^4*x^5*e^2 + 15*a^3*b^2*d^5*x^4*e + 10/3*a^3*b^2*d^6*x^3 + 5/8*a^4*b*x^8*e^6 + 30/7*a^4*b*d*x^7*e^5 + 25/2*a^4*b*d^2*x^6*e^4 + 20*a^4*b*d^3*x^5*e^3 + 75/4*a^4*b*d^4*x^4*e^2 + 10*a^4*b*d^5*x^3*e + 5/2*a^4*b*d^6*x^2 + 1/7*a^5*x^7*e^6 + a^5*d*x^6*e^5 + 3*a^5*d^2*x^5*e^4 + 5*a^5*d^3*x^4*e^3 + 5*a^5*d^4*x^3*e^2 + 3*a^5*d^5*x^2*e + a^5*d^6*x","B",0
1906,1,470,0,0.179672," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{5} x^{11} e^{5} + \frac{1}{2} \, b^{5} d x^{10} e^{4} + \frac{10}{9} \, b^{5} d^{2} x^{9} e^{3} + \frac{5}{4} \, b^{5} d^{3} x^{8} e^{2} + \frac{5}{7} \, b^{5} d^{4} x^{7} e + \frac{1}{6} \, b^{5} d^{5} x^{6} + \frac{1}{2} \, a b^{4} x^{10} e^{5} + \frac{25}{9} \, a b^{4} d x^{9} e^{4} + \frac{25}{4} \, a b^{4} d^{2} x^{8} e^{3} + \frac{50}{7} \, a b^{4} d^{3} x^{7} e^{2} + \frac{25}{6} \, a b^{4} d^{4} x^{6} e + a b^{4} d^{5} x^{5} + \frac{10}{9} \, a^{2} b^{3} x^{9} e^{5} + \frac{25}{4} \, a^{2} b^{3} d x^{8} e^{4} + \frac{100}{7} \, a^{2} b^{3} d^{2} x^{7} e^{3} + \frac{50}{3} \, a^{2} b^{3} d^{3} x^{6} e^{2} + 10 \, a^{2} b^{3} d^{4} x^{5} e + \frac{5}{2} \, a^{2} b^{3} d^{5} x^{4} + \frac{5}{4} \, a^{3} b^{2} x^{8} e^{5} + \frac{50}{7} \, a^{3} b^{2} d x^{7} e^{4} + \frac{50}{3} \, a^{3} b^{2} d^{2} x^{6} e^{3} + 20 \, a^{3} b^{2} d^{3} x^{5} e^{2} + \frac{25}{2} \, a^{3} b^{2} d^{4} x^{4} e + \frac{10}{3} \, a^{3} b^{2} d^{5} x^{3} + \frac{5}{7} \, a^{4} b x^{7} e^{5} + \frac{25}{6} \, a^{4} b d x^{6} e^{4} + 10 \, a^{4} b d^{2} x^{5} e^{3} + \frac{25}{2} \, a^{4} b d^{3} x^{4} e^{2} + \frac{25}{3} \, a^{4} b d^{4} x^{3} e + \frac{5}{2} \, a^{4} b d^{5} x^{2} + \frac{1}{6} \, a^{5} x^{6} e^{5} + a^{5} d x^{5} e^{4} + \frac{5}{2} \, a^{5} d^{2} x^{4} e^{3} + \frac{10}{3} \, a^{5} d^{3} x^{3} e^{2} + \frac{5}{2} \, a^{5} d^{4} x^{2} e + a^{5} d^{5} x"," ",0,"1/11*b^5*x^11*e^5 + 1/2*b^5*d*x^10*e^4 + 10/9*b^5*d^2*x^9*e^3 + 5/4*b^5*d^3*x^8*e^2 + 5/7*b^5*d^4*x^7*e + 1/6*b^5*d^5*x^6 + 1/2*a*b^4*x^10*e^5 + 25/9*a*b^4*d*x^9*e^4 + 25/4*a*b^4*d^2*x^8*e^3 + 50/7*a*b^4*d^3*x^7*e^2 + 25/6*a*b^4*d^4*x^6*e + a*b^4*d^5*x^5 + 10/9*a^2*b^3*x^9*e^5 + 25/4*a^2*b^3*d*x^8*e^4 + 100/7*a^2*b^3*d^2*x^7*e^3 + 50/3*a^2*b^3*d^3*x^6*e^2 + 10*a^2*b^3*d^4*x^5*e + 5/2*a^2*b^3*d^5*x^4 + 5/4*a^3*b^2*x^8*e^5 + 50/7*a^3*b^2*d*x^7*e^4 + 50/3*a^3*b^2*d^2*x^6*e^3 + 20*a^3*b^2*d^3*x^5*e^2 + 25/2*a^3*b^2*d^4*x^4*e + 10/3*a^3*b^2*d^5*x^3 + 5/7*a^4*b*x^7*e^5 + 25/6*a^4*b*d*x^6*e^4 + 10*a^4*b*d^2*x^5*e^3 + 25/2*a^4*b*d^3*x^4*e^2 + 25/3*a^4*b*d^4*x^3*e + 5/2*a^4*b*d^5*x^2 + 1/6*a^5*x^6*e^5 + a^5*d*x^5*e^4 + 5/2*a^5*d^2*x^4*e^3 + 10/3*a^5*d^3*x^3*e^2 + 5/2*a^5*d^4*x^2*e + a^5*d^5*x","B",0
1907,1,384,0,0.160227," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{5} x^{10} e^{4} + \frac{4}{9} \, b^{5} d x^{9} e^{3} + \frac{3}{4} \, b^{5} d^{2} x^{8} e^{2} + \frac{4}{7} \, b^{5} d^{3} x^{7} e + \frac{1}{6} \, b^{5} d^{4} x^{6} + \frac{5}{9} \, a b^{4} x^{9} e^{4} + \frac{5}{2} \, a b^{4} d x^{8} e^{3} + \frac{30}{7} \, a b^{4} d^{2} x^{7} e^{2} + \frac{10}{3} \, a b^{4} d^{3} x^{6} e + a b^{4} d^{4} x^{5} + \frac{5}{4} \, a^{2} b^{3} x^{8} e^{4} + \frac{40}{7} \, a^{2} b^{3} d x^{7} e^{3} + 10 \, a^{2} b^{3} d^{2} x^{6} e^{2} + 8 \, a^{2} b^{3} d^{3} x^{5} e + \frac{5}{2} \, a^{2} b^{3} d^{4} x^{4} + \frac{10}{7} \, a^{3} b^{2} x^{7} e^{4} + \frac{20}{3} \, a^{3} b^{2} d x^{6} e^{3} + 12 \, a^{3} b^{2} d^{2} x^{5} e^{2} + 10 \, a^{3} b^{2} d^{3} x^{4} e + \frac{10}{3} \, a^{3} b^{2} d^{4} x^{3} + \frac{5}{6} \, a^{4} b x^{6} e^{4} + 4 \, a^{4} b d x^{5} e^{3} + \frac{15}{2} \, a^{4} b d^{2} x^{4} e^{2} + \frac{20}{3} \, a^{4} b d^{3} x^{3} e + \frac{5}{2} \, a^{4} b d^{4} x^{2} + \frac{1}{5} \, a^{5} x^{5} e^{4} + a^{5} d x^{4} e^{3} + 2 \, a^{5} d^{2} x^{3} e^{2} + 2 \, a^{5} d^{3} x^{2} e + a^{5} d^{4} x"," ",0,"1/10*b^5*x^10*e^4 + 4/9*b^5*d*x^9*e^3 + 3/4*b^5*d^2*x^8*e^2 + 4/7*b^5*d^3*x^7*e + 1/6*b^5*d^4*x^6 + 5/9*a*b^4*x^9*e^4 + 5/2*a*b^4*d*x^8*e^3 + 30/7*a*b^4*d^2*x^7*e^2 + 10/3*a*b^4*d^3*x^6*e + a*b^4*d^4*x^5 + 5/4*a^2*b^3*x^8*e^4 + 40/7*a^2*b^3*d*x^7*e^3 + 10*a^2*b^3*d^2*x^6*e^2 + 8*a^2*b^3*d^3*x^5*e + 5/2*a^2*b^3*d^4*x^4 + 10/7*a^3*b^2*x^7*e^4 + 20/3*a^3*b^2*d*x^6*e^3 + 12*a^3*b^2*d^2*x^5*e^2 + 10*a^3*b^2*d^3*x^4*e + 10/3*a^3*b^2*d^4*x^3 + 5/6*a^4*b*x^6*e^4 + 4*a^4*b*d*x^5*e^3 + 15/2*a^4*b*d^2*x^4*e^2 + 20/3*a^4*b*d^3*x^3*e + 5/2*a^4*b*d^4*x^2 + 1/5*a^5*x^5*e^4 + a^5*d*x^4*e^3 + 2*a^5*d^2*x^3*e^2 + 2*a^5*d^3*x^2*e + a^5*d^4*x","B",0
1908,1,297,0,0.173425," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{5} x^{9} e^{3} + \frac{3}{8} \, b^{5} d x^{8} e^{2} + \frac{3}{7} \, b^{5} d^{2} x^{7} e + \frac{1}{6} \, b^{5} d^{3} x^{6} + \frac{5}{8} \, a b^{4} x^{8} e^{3} + \frac{15}{7} \, a b^{4} d x^{7} e^{2} + \frac{5}{2} \, a b^{4} d^{2} x^{6} e + a b^{4} d^{3} x^{5} + \frac{10}{7} \, a^{2} b^{3} x^{7} e^{3} + 5 \, a^{2} b^{3} d x^{6} e^{2} + 6 \, a^{2} b^{3} d^{2} x^{5} e + \frac{5}{2} \, a^{2} b^{3} d^{3} x^{4} + \frac{5}{3} \, a^{3} b^{2} x^{6} e^{3} + 6 \, a^{3} b^{2} d x^{5} e^{2} + \frac{15}{2} \, a^{3} b^{2} d^{2} x^{4} e + \frac{10}{3} \, a^{3} b^{2} d^{3} x^{3} + a^{4} b x^{5} e^{3} + \frac{15}{4} \, a^{4} b d x^{4} e^{2} + 5 \, a^{4} b d^{2} x^{3} e + \frac{5}{2} \, a^{4} b d^{3} x^{2} + \frac{1}{4} \, a^{5} x^{4} e^{3} + a^{5} d x^{3} e^{2} + \frac{3}{2} \, a^{5} d^{2} x^{2} e + a^{5} d^{3} x"," ",0,"1/9*b^5*x^9*e^3 + 3/8*b^5*d*x^8*e^2 + 3/7*b^5*d^2*x^7*e + 1/6*b^5*d^3*x^6 + 5/8*a*b^4*x^8*e^3 + 15/7*a*b^4*d*x^7*e^2 + 5/2*a*b^4*d^2*x^6*e + a*b^4*d^3*x^5 + 10/7*a^2*b^3*x^7*e^3 + 5*a^2*b^3*d*x^6*e^2 + 6*a^2*b^3*d^2*x^5*e + 5/2*a^2*b^3*d^3*x^4 + 5/3*a^3*b^2*x^6*e^3 + 6*a^3*b^2*d*x^5*e^2 + 15/2*a^3*b^2*d^2*x^4*e + 10/3*a^3*b^2*d^3*x^3 + a^4*b*x^5*e^3 + 15/4*a^4*b*d*x^4*e^2 + 5*a^4*b*d^2*x^3*e + 5/2*a^4*b*d^3*x^2 + 1/4*a^5*x^4*e^3 + a^5*d*x^3*e^2 + 3/2*a^5*d^2*x^2*e + a^5*d^3*x","B",0
1909,1,212,0,0.155867," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{8} \, b^{5} x^{8} e^{2} + \frac{2}{7} \, b^{5} d x^{7} e + \frac{1}{6} \, b^{5} d^{2} x^{6} + \frac{5}{7} \, a b^{4} x^{7} e^{2} + \frac{5}{3} \, a b^{4} d x^{6} e + a b^{4} d^{2} x^{5} + \frac{5}{3} \, a^{2} b^{3} x^{6} e^{2} + 4 \, a^{2} b^{3} d x^{5} e + \frac{5}{2} \, a^{2} b^{3} d^{2} x^{4} + 2 \, a^{3} b^{2} x^{5} e^{2} + 5 \, a^{3} b^{2} d x^{4} e + \frac{10}{3} \, a^{3} b^{2} d^{2} x^{3} + \frac{5}{4} \, a^{4} b x^{4} e^{2} + \frac{10}{3} \, a^{4} b d x^{3} e + \frac{5}{2} \, a^{4} b d^{2} x^{2} + \frac{1}{3} \, a^{5} x^{3} e^{2} + a^{5} d x^{2} e + a^{5} d^{2} x"," ",0,"1/8*b^5*x^8*e^2 + 2/7*b^5*d*x^7*e + 1/6*b^5*d^2*x^6 + 5/7*a*b^4*x^7*e^2 + 5/3*a*b^4*d*x^6*e + a*b^4*d^2*x^5 + 5/3*a^2*b^3*x^6*e^2 + 4*a^2*b^3*d*x^5*e + 5/2*a^2*b^3*d^2*x^4 + 2*a^3*b^2*x^5*e^2 + 5*a^3*b^2*d*x^4*e + 10/3*a^3*b^2*d^2*x^3 + 5/4*a^4*b*x^4*e^2 + 10/3*a^4*b*d*x^3*e + 5/2*a^4*b*d^2*x^2 + 1/3*a^5*x^3*e^2 + a^5*d*x^2*e + a^5*d^2*x","B",0
1910,1,127,0,0.150142," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{5} x^{7} e + \frac{1}{6} \, b^{5} d x^{6} + \frac{5}{6} \, a b^{4} x^{6} e + a b^{4} d x^{5} + 2 \, a^{2} b^{3} x^{5} e + \frac{5}{2} \, a^{2} b^{3} d x^{4} + \frac{5}{2} \, a^{3} b^{2} x^{4} e + \frac{10}{3} \, a^{3} b^{2} d x^{3} + \frac{5}{3} \, a^{4} b x^{3} e + \frac{5}{2} \, a^{4} b d x^{2} + \frac{1}{2} \, a^{5} x^{2} e + a^{5} d x"," ",0,"1/7*b^5*x^7*e + 1/6*b^5*d*x^6 + 5/6*a*b^4*x^6*e + a*b^4*d*x^5 + 2*a^2*b^3*x^5*e + 5/2*a^2*b^3*d*x^4 + 5/2*a^3*b^2*x^4*e + 10/3*a^3*b^2*d*x^3 + 5/3*a^4*b*x^3*e + 5/2*a^4*b*d*x^2 + 1/2*a^5*x^2*e + a^5*d*x","B",0
1911,1,51,0,0.151319," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} a^{4} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)}^{2} a^{2} b + \frac{1}{6} \, {\left(b x^{2} + 2 \, a x\right)}^{3} b^{2}"," ",0,"1/2*(b*x^2 + 2*a*x)*a^4 + 1/2*(b*x^2 + 2*a*x)^2*a^2*b + 1/6*(b*x^2 + 2*a*x)^3*b^2","B",0
1912,1,259,0,0.155286," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d),x, algorithm=""giac"")","-{\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)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(12 \, b^{5} x^{5} e^{4} - 15 \, b^{5} d x^{4} e^{3} + 20 \, b^{5} d^{2} x^{3} e^{2} - 30 \, b^{5} d^{3} x^{2} e + 60 \, b^{5} d^{4} x + 75 \, a b^{4} x^{4} e^{4} - 100 \, a b^{4} d x^{3} e^{3} + 150 \, a b^{4} d^{2} x^{2} e^{2} - 300 \, a b^{4} d^{3} x e + 200 \, a^{2} b^{3} x^{3} e^{4} - 300 \, a^{2} b^{3} d x^{2} e^{3} + 600 \, a^{2} b^{3} d^{2} x e^{2} + 300 \, a^{3} b^{2} x^{2} e^{4} - 600 \, a^{3} b^{2} d x e^{3} + 300 \, a^{4} b x e^{4}\right)} e^{\left(-5\right)}"," ",0,"-(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)*e^(-6)*log(abs(x*e + d)) + 1/60*(12*b^5*x^5*e^4 - 15*b^5*d*x^4*e^3 + 20*b^5*d^2*x^3*e^2 - 30*b^5*d^3*x^2*e + 60*b^5*d^4*x + 75*a*b^4*x^4*e^4 - 100*a*b^4*d*x^3*e^3 + 150*a*b^4*d^2*x^2*e^2 - 300*a*b^4*d^3*x*e + 200*a^2*b^3*x^3*e^4 - 300*a^2*b^3*d*x^2*e^3 + 600*a^2*b^3*d^2*x*e^2 + 300*a^3*b^2*x^2*e^4 - 600*a^3*b^2*d*x*e^3 + 300*a^4*b*x*e^4)*e^(-5)","B",0
1913,1,328,0,0.189836," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, b^{5} - \frac{20 \, {\left(b^{5} d e - a b^{4} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{60 \, {\left(b^{5} d^{2} e^{2} - 2 \, a b^{4} d e^{3} + a^{2} b^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{120 \, {\left(b^{5} d^{3} e^{3} - 3 \, a b^{4} d^{2} e^{4} + 3 \, a^{2} b^{3} d e^{5} - a^{3} b^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{4} e^{\left(-6\right)} - 5 \, {\left(b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{b^{5} d^{5} e^{4}}{x e + d} - \frac{5 \, a b^{4} d^{4} e^{5}}{x e + d} + \frac{10 \, a^{2} b^{3} d^{3} e^{6}}{x e + d} - \frac{10 \, a^{3} b^{2} d^{2} e^{7}}{x e + d} + \frac{5 \, a^{4} b d e^{8}}{x e + d} - \frac{a^{5} e^{9}}{x e + d}\right)} e^{\left(-10\right)}"," ",0,"1/12*(3*b^5 - 20*(b^5*d*e - a*b^4*e^2)*e^(-1)/(x*e + d) + 60*(b^5*d^2*e^2 - 2*a*b^4*d*e^3 + a^2*b^3*e^4)*e^(-2)/(x*e + d)^2 - 120*(b^5*d^3*e^3 - 3*a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 - a^3*b^2*e^6)*e^(-3)/(x*e + d)^3)*(x*e + d)^4*e^(-6) - 5*(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (b^5*d^5*e^4/(x*e + d) - 5*a*b^4*d^4*e^5/(x*e + d) + 10*a^2*b^3*d^3*e^6/(x*e + d) - 10*a^3*b^2*d^2*e^7/(x*e + d) + 5*a^4*b*d*e^8/(x*e + d) - a^5*e^9/(x*e + d))*e^(-10)","B",0
1914,1,250,0,0.158760," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^3,x, algorithm=""giac"")","-10 \, {\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)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, b^{5} x^{3} e^{6} - 9 \, b^{5} d x^{2} e^{5} + 36 \, b^{5} d^{2} x e^{4} + 15 \, a b^{4} x^{2} e^{6} - 90 \, a b^{4} d x e^{5} + 60 \, a^{2} b^{3} x e^{6}\right)} e^{\left(-9\right)} - \frac{{\left(9 \, b^{5} d^{5} - 35 \, a b^{4} d^{4} e + 50 \, a^{2} b^{3} d^{3} e^{2} - 30 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} + a^{5} e^{5} + 10 \, {\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)} e^{\left(-6\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-10*(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)*e^(-6)*log(abs(x*e + d)) + 1/6*(2*b^5*x^3*e^6 - 9*b^5*d*x^2*e^5 + 36*b^5*d^2*x*e^4 + 15*a*b^4*x^2*e^6 - 90*a*b^4*d*x*e^5 + 60*a^2*b^3*x*e^6)*e^(-9) - 1/2*(9*b^5*d^5 - 35*a*b^4*d^4*e + 50*a^2*b^3*d^3*e^2 - 30*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 + a^5*e^5 + 10*(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)*e^(-6)/(x*e + d)^2","A",0
1915,1,249,0,0.157971," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^4,x, algorithm=""giac"")","10 \, {\left(b^{5} d^{2} - 2 \, a b^{4} d e + a^{2} b^{3} e^{2}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{5} x^{2} e^{4} - 8 \, b^{5} d x e^{3} + 10 \, a b^{4} x e^{4}\right)} e^{\left(-8\right)} + \frac{{\left(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} + 60 \, {\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} + 15 \, {\left(7 \, b^{5} d^{4} e - 20 \, a b^{4} d^{3} e^{2} + 18 \, a^{2} b^{3} d^{2} e^{3} - 4 \, a^{3} b^{2} d e^{4} - a^{4} b e^{5}\right)} x\right)} e^{\left(-6\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"10*(b^5*d^2 - 2*a*b^4*d*e + a^2*b^3*e^2)*e^(-6)*log(abs(x*e + d)) + 1/2*(b^5*x^2*e^4 - 8*b^5*d*x*e^3 + 10*a*b^4*x*e^4)*e^(-8) + 1/6*(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 + 60*(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 + 15*(7*b^5*d^4*e - 20*a*b^4*d^3*e^2 + 18*a^2*b^3*d^2*e^3 - 4*a^3*b^2*d*e^4 - a^4*b*e^5)*x)*e^(-6)/(x*e + d)^3","B",0
1916,1,766,0,0.270366," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{14} \, b^{7} x^{14} e^{6} + \frac{6}{13} \, b^{7} d x^{13} e^{5} + \frac{5}{4} \, b^{7} d^{2} x^{12} e^{4} + \frac{20}{11} \, b^{7} d^{3} x^{11} e^{3} + \frac{3}{2} \, b^{7} d^{4} x^{10} e^{2} + \frac{2}{3} \, b^{7} d^{5} x^{9} e + \frac{1}{8} \, b^{7} d^{6} x^{8} + \frac{7}{13} \, a b^{6} x^{13} e^{6} + \frac{7}{2} \, a b^{6} d x^{12} e^{5} + \frac{105}{11} \, a b^{6} d^{2} x^{11} e^{4} + 14 \, a b^{6} d^{3} x^{10} e^{3} + \frac{35}{3} \, a b^{6} d^{4} x^{9} e^{2} + \frac{21}{4} \, a b^{6} d^{5} x^{8} e + a b^{6} d^{6} x^{7} + \frac{7}{4} \, a^{2} b^{5} x^{12} e^{6} + \frac{126}{11} \, a^{2} b^{5} d x^{11} e^{5} + \frac{63}{2} \, a^{2} b^{5} d^{2} x^{10} e^{4} + \frac{140}{3} \, a^{2} b^{5} d^{3} x^{9} e^{3} + \frac{315}{8} \, a^{2} b^{5} d^{4} x^{8} e^{2} + 18 \, a^{2} b^{5} d^{5} x^{7} e + \frac{7}{2} \, a^{2} b^{5} d^{6} x^{6} + \frac{35}{11} \, a^{3} b^{4} x^{11} e^{6} + 21 \, a^{3} b^{4} d x^{10} e^{5} + \frac{175}{3} \, a^{3} b^{4} d^{2} x^{9} e^{4} + \frac{175}{2} \, a^{3} b^{4} d^{3} x^{8} e^{3} + 75 \, a^{3} b^{4} d^{4} x^{7} e^{2} + 35 \, a^{3} b^{4} d^{5} x^{6} e + 7 \, a^{3} b^{4} d^{6} x^{5} + \frac{7}{2} \, a^{4} b^{3} x^{10} e^{6} + \frac{70}{3} \, a^{4} b^{3} d x^{9} e^{5} + \frac{525}{8} \, a^{4} b^{3} d^{2} x^{8} e^{4} + 100 \, a^{4} b^{3} d^{3} x^{7} e^{3} + \frac{175}{2} \, a^{4} b^{3} d^{4} x^{6} e^{2} + 42 \, a^{4} b^{3} d^{5} x^{5} e + \frac{35}{4} \, a^{4} b^{3} d^{6} x^{4} + \frac{7}{3} \, a^{5} b^{2} x^{9} e^{6} + \frac{63}{4} \, a^{5} b^{2} d x^{8} e^{5} + 45 \, a^{5} b^{2} d^{2} x^{7} e^{4} + 70 \, a^{5} b^{2} d^{3} x^{6} e^{3} + 63 \, a^{5} b^{2} d^{4} x^{5} e^{2} + \frac{63}{2} \, a^{5} b^{2} d^{5} x^{4} e + 7 \, a^{5} b^{2} d^{6} x^{3} + \frac{7}{8} \, a^{6} b x^{8} e^{6} + 6 \, a^{6} b d x^{7} e^{5} + \frac{35}{2} \, a^{6} b d^{2} x^{6} e^{4} + 28 \, a^{6} b d^{3} x^{5} e^{3} + \frac{105}{4} \, a^{6} b d^{4} x^{4} e^{2} + 14 \, a^{6} b d^{5} x^{3} e + \frac{7}{2} \, a^{6} b d^{6} x^{2} + \frac{1}{7} \, a^{7} x^{7} e^{6} + a^{7} d x^{6} e^{5} + 3 \, a^{7} d^{2} x^{5} e^{4} + 5 \, a^{7} d^{3} x^{4} e^{3} + 5 \, a^{7} d^{4} x^{3} e^{2} + 3 \, a^{7} d^{5} x^{2} e + a^{7} d^{6} x"," ",0,"1/14*b^7*x^14*e^6 + 6/13*b^7*d*x^13*e^5 + 5/4*b^7*d^2*x^12*e^4 + 20/11*b^7*d^3*x^11*e^3 + 3/2*b^7*d^4*x^10*e^2 + 2/3*b^7*d^5*x^9*e + 1/8*b^7*d^6*x^8 + 7/13*a*b^6*x^13*e^6 + 7/2*a*b^6*d*x^12*e^5 + 105/11*a*b^6*d^2*x^11*e^4 + 14*a*b^6*d^3*x^10*e^3 + 35/3*a*b^6*d^4*x^9*e^2 + 21/4*a*b^6*d^5*x^8*e + a*b^6*d^6*x^7 + 7/4*a^2*b^5*x^12*e^6 + 126/11*a^2*b^5*d*x^11*e^5 + 63/2*a^2*b^5*d^2*x^10*e^4 + 140/3*a^2*b^5*d^3*x^9*e^3 + 315/8*a^2*b^5*d^4*x^8*e^2 + 18*a^2*b^5*d^5*x^7*e + 7/2*a^2*b^5*d^6*x^6 + 35/11*a^3*b^4*x^11*e^6 + 21*a^3*b^4*d*x^10*e^5 + 175/3*a^3*b^4*d^2*x^9*e^4 + 175/2*a^3*b^4*d^3*x^8*e^3 + 75*a^3*b^4*d^4*x^7*e^2 + 35*a^3*b^4*d^5*x^6*e + 7*a^3*b^4*d^6*x^5 + 7/2*a^4*b^3*x^10*e^6 + 70/3*a^4*b^3*d*x^9*e^5 + 525/8*a^4*b^3*d^2*x^8*e^4 + 100*a^4*b^3*d^3*x^7*e^3 + 175/2*a^4*b^3*d^4*x^6*e^2 + 42*a^4*b^3*d^5*x^5*e + 35/4*a^4*b^3*d^6*x^4 + 7/3*a^5*b^2*x^9*e^6 + 63/4*a^5*b^2*d*x^8*e^5 + 45*a^5*b^2*d^2*x^7*e^4 + 70*a^5*b^2*d^3*x^6*e^3 + 63*a^5*b^2*d^4*x^5*e^2 + 63/2*a^5*b^2*d^5*x^4*e + 7*a^5*b^2*d^6*x^3 + 7/8*a^6*b*x^8*e^6 + 6*a^6*b*d*x^7*e^5 + 35/2*a^6*b*d^2*x^6*e^4 + 28*a^6*b*d^3*x^5*e^3 + 105/4*a^6*b*d^4*x^4*e^2 + 14*a^6*b*d^5*x^3*e + 7/2*a^6*b*d^6*x^2 + 1/7*a^7*x^7*e^6 + a^7*d*x^6*e^5 + 3*a^7*d^2*x^5*e^4 + 5*a^7*d^3*x^4*e^3 + 5*a^7*d^4*x^3*e^2 + 3*a^7*d^5*x^2*e + a^7*d^6*x","B",0
1917,1,646,0,0.164201," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{7} x^{13} e^{5} + \frac{5}{12} \, b^{7} d x^{12} e^{4} + \frac{10}{11} \, b^{7} d^{2} x^{11} e^{3} + b^{7} d^{3} x^{10} e^{2} + \frac{5}{9} \, b^{7} d^{4} x^{9} e + \frac{1}{8} \, b^{7} d^{5} x^{8} + \frac{7}{12} \, a b^{6} x^{12} e^{5} + \frac{35}{11} \, a b^{6} d x^{11} e^{4} + 7 \, a b^{6} d^{2} x^{10} e^{3} + \frac{70}{9} \, a b^{6} d^{3} x^{9} e^{2} + \frac{35}{8} \, a b^{6} d^{4} x^{8} e + a b^{6} d^{5} x^{7} + \frac{21}{11} \, a^{2} b^{5} x^{11} e^{5} + \frac{21}{2} \, a^{2} b^{5} d x^{10} e^{4} + \frac{70}{3} \, a^{2} b^{5} d^{2} x^{9} e^{3} + \frac{105}{4} \, a^{2} b^{5} d^{3} x^{8} e^{2} + 15 \, a^{2} b^{5} d^{4} x^{7} e + \frac{7}{2} \, a^{2} b^{5} d^{5} x^{6} + \frac{7}{2} \, a^{3} b^{4} x^{10} e^{5} + \frac{175}{9} \, a^{3} b^{4} d x^{9} e^{4} + \frac{175}{4} \, a^{3} b^{4} d^{2} x^{8} e^{3} + 50 \, a^{3} b^{4} d^{3} x^{7} e^{2} + \frac{175}{6} \, a^{3} b^{4} d^{4} x^{6} e + 7 \, a^{3} b^{4} d^{5} x^{5} + \frac{35}{9} \, a^{4} b^{3} x^{9} e^{5} + \frac{175}{8} \, a^{4} b^{3} d x^{8} e^{4} + 50 \, a^{4} b^{3} d^{2} x^{7} e^{3} + \frac{175}{3} \, a^{4} b^{3} d^{3} x^{6} e^{2} + 35 \, a^{4} b^{3} d^{4} x^{5} e + \frac{35}{4} \, a^{4} b^{3} d^{5} x^{4} + \frac{21}{8} \, a^{5} b^{2} x^{8} e^{5} + 15 \, a^{5} b^{2} d x^{7} e^{4} + 35 \, a^{5} b^{2} d^{2} x^{6} e^{3} + 42 \, a^{5} b^{2} d^{3} x^{5} e^{2} + \frac{105}{4} \, a^{5} b^{2} d^{4} x^{4} e + 7 \, a^{5} b^{2} d^{5} x^{3} + a^{6} b x^{7} e^{5} + \frac{35}{6} \, a^{6} b d x^{6} e^{4} + 14 \, a^{6} b d^{2} x^{5} e^{3} + \frac{35}{2} \, a^{6} b d^{3} x^{4} e^{2} + \frac{35}{3} \, a^{6} b d^{4} x^{3} e + \frac{7}{2} \, a^{6} b d^{5} x^{2} + \frac{1}{6} \, a^{7} x^{6} e^{5} + a^{7} d x^{5} e^{4} + \frac{5}{2} \, a^{7} d^{2} x^{4} e^{3} + \frac{10}{3} \, a^{7} d^{3} x^{3} e^{2} + \frac{5}{2} \, a^{7} d^{4} x^{2} e + a^{7} d^{5} x"," ",0,"1/13*b^7*x^13*e^5 + 5/12*b^7*d*x^12*e^4 + 10/11*b^7*d^2*x^11*e^3 + b^7*d^3*x^10*e^2 + 5/9*b^7*d^4*x^9*e + 1/8*b^7*d^5*x^8 + 7/12*a*b^6*x^12*e^5 + 35/11*a*b^6*d*x^11*e^4 + 7*a*b^6*d^2*x^10*e^3 + 70/9*a*b^6*d^3*x^9*e^2 + 35/8*a*b^6*d^4*x^8*e + a*b^6*d^5*x^7 + 21/11*a^2*b^5*x^11*e^5 + 21/2*a^2*b^5*d*x^10*e^4 + 70/3*a^2*b^5*d^2*x^9*e^3 + 105/4*a^2*b^5*d^3*x^8*e^2 + 15*a^2*b^5*d^4*x^7*e + 7/2*a^2*b^5*d^5*x^6 + 7/2*a^3*b^4*x^10*e^5 + 175/9*a^3*b^4*d*x^9*e^4 + 175/4*a^3*b^4*d^2*x^8*e^3 + 50*a^3*b^4*d^3*x^7*e^2 + 175/6*a^3*b^4*d^4*x^6*e + 7*a^3*b^4*d^5*x^5 + 35/9*a^4*b^3*x^9*e^5 + 175/8*a^4*b^3*d*x^8*e^4 + 50*a^4*b^3*d^2*x^7*e^3 + 175/3*a^4*b^3*d^3*x^6*e^2 + 35*a^4*b^3*d^4*x^5*e + 35/4*a^4*b^3*d^5*x^4 + 21/8*a^5*b^2*x^8*e^5 + 15*a^5*b^2*d*x^7*e^4 + 35*a^5*b^2*d^2*x^6*e^3 + 42*a^5*b^2*d^3*x^5*e^2 + 105/4*a^5*b^2*d^4*x^4*e + 7*a^5*b^2*d^5*x^3 + a^6*b*x^7*e^5 + 35/6*a^6*b*d*x^6*e^4 + 14*a^6*b*d^2*x^5*e^3 + 35/2*a^6*b*d^3*x^4*e^2 + 35/3*a^6*b*d^4*x^3*e + 7/2*a^6*b*d^5*x^2 + 1/6*a^7*x^6*e^5 + a^7*d*x^5*e^4 + 5/2*a^7*d^2*x^4*e^3 + 10/3*a^7*d^3*x^3*e^2 + 5/2*a^7*d^4*x^2*e + a^7*d^5*x","B",0
1918,1,530,0,0.187701," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{12} \, b^{7} x^{12} e^{4} + \frac{4}{11} \, b^{7} d x^{11} e^{3} + \frac{3}{5} \, b^{7} d^{2} x^{10} e^{2} + \frac{4}{9} \, b^{7} d^{3} x^{9} e + \frac{1}{8} \, b^{7} d^{4} x^{8} + \frac{7}{11} \, a b^{6} x^{11} e^{4} + \frac{14}{5} \, a b^{6} d x^{10} e^{3} + \frac{14}{3} \, a b^{6} d^{2} x^{9} e^{2} + \frac{7}{2} \, a b^{6} d^{3} x^{8} e + a b^{6} d^{4} x^{7} + \frac{21}{10} \, a^{2} b^{5} x^{10} e^{4} + \frac{28}{3} \, a^{2} b^{5} d x^{9} e^{3} + \frac{63}{4} \, a^{2} b^{5} d^{2} x^{8} e^{2} + 12 \, a^{2} b^{5} d^{3} x^{7} e + \frac{7}{2} \, a^{2} b^{5} d^{4} x^{6} + \frac{35}{9} \, a^{3} b^{4} x^{9} e^{4} + \frac{35}{2} \, a^{3} b^{4} d x^{8} e^{3} + 30 \, a^{3} b^{4} d^{2} x^{7} e^{2} + \frac{70}{3} \, a^{3} b^{4} d^{3} x^{6} e + 7 \, a^{3} b^{4} d^{4} x^{5} + \frac{35}{8} \, a^{4} b^{3} x^{8} e^{4} + 20 \, a^{4} b^{3} d x^{7} e^{3} + 35 \, a^{4} b^{3} d^{2} x^{6} e^{2} + 28 \, a^{4} b^{3} d^{3} x^{5} e + \frac{35}{4} \, a^{4} b^{3} d^{4} x^{4} + 3 \, a^{5} b^{2} x^{7} e^{4} + 14 \, a^{5} b^{2} d x^{6} e^{3} + \frac{126}{5} \, a^{5} b^{2} d^{2} x^{5} e^{2} + 21 \, a^{5} b^{2} d^{3} x^{4} e + 7 \, a^{5} b^{2} d^{4} x^{3} + \frac{7}{6} \, a^{6} b x^{6} e^{4} + \frac{28}{5} \, a^{6} b d x^{5} e^{3} + \frac{21}{2} \, a^{6} b d^{2} x^{4} e^{2} + \frac{28}{3} \, a^{6} b d^{3} x^{3} e + \frac{7}{2} \, a^{6} b d^{4} x^{2} + \frac{1}{5} \, a^{7} x^{5} e^{4} + a^{7} d x^{4} e^{3} + 2 \, a^{7} d^{2} x^{3} e^{2} + 2 \, a^{7} d^{3} x^{2} e + a^{7} d^{4} x"," ",0,"1/12*b^7*x^12*e^4 + 4/11*b^7*d*x^11*e^3 + 3/5*b^7*d^2*x^10*e^2 + 4/9*b^7*d^3*x^9*e + 1/8*b^7*d^4*x^8 + 7/11*a*b^6*x^11*e^4 + 14/5*a*b^6*d*x^10*e^3 + 14/3*a*b^6*d^2*x^9*e^2 + 7/2*a*b^6*d^3*x^8*e + a*b^6*d^4*x^7 + 21/10*a^2*b^5*x^10*e^4 + 28/3*a^2*b^5*d*x^9*e^3 + 63/4*a^2*b^5*d^2*x^8*e^2 + 12*a^2*b^5*d^3*x^7*e + 7/2*a^2*b^5*d^4*x^6 + 35/9*a^3*b^4*x^9*e^4 + 35/2*a^3*b^4*d*x^8*e^3 + 30*a^3*b^4*d^2*x^7*e^2 + 70/3*a^3*b^4*d^3*x^6*e + 7*a^3*b^4*d^4*x^5 + 35/8*a^4*b^3*x^8*e^4 + 20*a^4*b^3*d*x^7*e^3 + 35*a^4*b^3*d^2*x^6*e^2 + 28*a^4*b^3*d^3*x^5*e + 35/4*a^4*b^3*d^4*x^4 + 3*a^5*b^2*x^7*e^4 + 14*a^5*b^2*d*x^6*e^3 + 126/5*a^5*b^2*d^2*x^5*e^2 + 21*a^5*b^2*d^3*x^4*e + 7*a^5*b^2*d^4*x^3 + 7/6*a^6*b*x^6*e^4 + 28/5*a^6*b*d*x^5*e^3 + 21/2*a^6*b*d^2*x^4*e^2 + 28/3*a^6*b*d^3*x^3*e + 7/2*a^6*b*d^4*x^2 + 1/5*a^7*x^5*e^4 + a^7*d*x^4*e^3 + 2*a^7*d^2*x^3*e^2 + 2*a^7*d^3*x^2*e + a^7*d^4*x","B",0
1919,1,412,0,0.174073," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{11} \, b^{7} x^{11} e^{3} + \frac{3}{10} \, b^{7} d x^{10} e^{2} + \frac{1}{3} \, b^{7} d^{2} x^{9} e + \frac{1}{8} \, b^{7} d^{3} x^{8} + \frac{7}{10} \, a b^{6} x^{10} e^{3} + \frac{7}{3} \, a b^{6} d x^{9} e^{2} + \frac{21}{8} \, a b^{6} d^{2} x^{8} e + a b^{6} d^{3} x^{7} + \frac{7}{3} \, a^{2} b^{5} x^{9} e^{3} + \frac{63}{8} \, a^{2} b^{5} d x^{8} e^{2} + 9 \, a^{2} b^{5} d^{2} x^{7} e + \frac{7}{2} \, a^{2} b^{5} d^{3} x^{6} + \frac{35}{8} \, a^{3} b^{4} x^{8} e^{3} + 15 \, a^{3} b^{4} d x^{7} e^{2} + \frac{35}{2} \, a^{3} b^{4} d^{2} x^{6} e + 7 \, a^{3} b^{4} d^{3} x^{5} + 5 \, a^{4} b^{3} x^{7} e^{3} + \frac{35}{2} \, a^{4} b^{3} d x^{6} e^{2} + 21 \, a^{4} b^{3} d^{2} x^{5} e + \frac{35}{4} \, a^{4} b^{3} d^{3} x^{4} + \frac{7}{2} \, a^{5} b^{2} x^{6} e^{3} + \frac{63}{5} \, a^{5} b^{2} d x^{5} e^{2} + \frac{63}{4} \, a^{5} b^{2} d^{2} x^{4} e + 7 \, a^{5} b^{2} d^{3} x^{3} + \frac{7}{5} \, a^{6} b x^{5} e^{3} + \frac{21}{4} \, a^{6} b d x^{4} e^{2} + 7 \, a^{6} b d^{2} x^{3} e + \frac{7}{2} \, a^{6} b d^{3} x^{2} + \frac{1}{4} \, a^{7} x^{4} e^{3} + a^{7} d x^{3} e^{2} + \frac{3}{2} \, a^{7} d^{2} x^{2} e + a^{7} d^{3} x"," ",0,"1/11*b^7*x^11*e^3 + 3/10*b^7*d*x^10*e^2 + 1/3*b^7*d^2*x^9*e + 1/8*b^7*d^3*x^8 + 7/10*a*b^6*x^10*e^3 + 7/3*a*b^6*d*x^9*e^2 + 21/8*a*b^6*d^2*x^8*e + a*b^6*d^3*x^7 + 7/3*a^2*b^5*x^9*e^3 + 63/8*a^2*b^5*d*x^8*e^2 + 9*a^2*b^5*d^2*x^7*e + 7/2*a^2*b^5*d^3*x^6 + 35/8*a^3*b^4*x^8*e^3 + 15*a^3*b^4*d*x^7*e^2 + 35/2*a^3*b^4*d^2*x^6*e + 7*a^3*b^4*d^3*x^5 + 5*a^4*b^3*x^7*e^3 + 35/2*a^4*b^3*d*x^6*e^2 + 21*a^4*b^3*d^2*x^5*e + 35/4*a^4*b^3*d^3*x^4 + 7/2*a^5*b^2*x^6*e^3 + 63/5*a^5*b^2*d*x^5*e^2 + 63/4*a^5*b^2*d^2*x^4*e + 7*a^5*b^2*d^3*x^3 + 7/5*a^6*b*x^5*e^3 + 21/4*a^6*b*d*x^4*e^2 + 7*a^6*b*d^2*x^3*e + 7/2*a^6*b*d^3*x^2 + 1/4*a^7*x^4*e^3 + a^7*d*x^3*e^2 + 3/2*a^7*d^2*x^2*e + a^7*d^3*x","B",0
1920,1,294,0,0.186391," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{7} x^{10} e^{2} + \frac{2}{9} \, b^{7} d x^{9} e + \frac{1}{8} \, b^{7} d^{2} x^{8} + \frac{7}{9} \, a b^{6} x^{9} e^{2} + \frac{7}{4} \, a b^{6} d x^{8} e + a b^{6} d^{2} x^{7} + \frac{21}{8} \, a^{2} b^{5} x^{8} e^{2} + 6 \, a^{2} b^{5} d x^{7} e + \frac{7}{2} \, a^{2} b^{5} d^{2} x^{6} + 5 \, a^{3} b^{4} x^{7} e^{2} + \frac{35}{3} \, a^{3} b^{4} d x^{6} e + 7 \, a^{3} b^{4} d^{2} x^{5} + \frac{35}{6} \, a^{4} b^{3} x^{6} e^{2} + 14 \, a^{4} b^{3} d x^{5} e + \frac{35}{4} \, a^{4} b^{3} d^{2} x^{4} + \frac{21}{5} \, a^{5} b^{2} x^{5} e^{2} + \frac{21}{2} \, a^{5} b^{2} d x^{4} e + 7 \, a^{5} b^{2} d^{2} x^{3} + \frac{7}{4} \, a^{6} b x^{4} e^{2} + \frac{14}{3} \, a^{6} b d x^{3} e + \frac{7}{2} \, a^{6} b d^{2} x^{2} + \frac{1}{3} \, a^{7} x^{3} e^{2} + a^{7} d x^{2} e + a^{7} d^{2} x"," ",0,"1/10*b^7*x^10*e^2 + 2/9*b^7*d*x^9*e + 1/8*b^7*d^2*x^8 + 7/9*a*b^6*x^9*e^2 + 7/4*a*b^6*d*x^8*e + a*b^6*d^2*x^7 + 21/8*a^2*b^5*x^8*e^2 + 6*a^2*b^5*d*x^7*e + 7/2*a^2*b^5*d^2*x^6 + 5*a^3*b^4*x^7*e^2 + 35/3*a^3*b^4*d*x^6*e + 7*a^3*b^4*d^2*x^5 + 35/6*a^4*b^3*x^6*e^2 + 14*a^4*b^3*d*x^5*e + 35/4*a^4*b^3*d^2*x^4 + 21/5*a^5*b^2*x^5*e^2 + 21/2*a^5*b^2*d*x^4*e + 7*a^5*b^2*d^2*x^3 + 7/4*a^6*b*x^4*e^2 + 14/3*a^6*b*d*x^3*e + 7/2*a^6*b*d^2*x^2 + 1/3*a^7*x^3*e^2 + a^7*d*x^2*e + a^7*d^2*x","B",0
1921,1,177,0,0.210257," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{9} \, b^{7} x^{9} e + \frac{1}{8} \, b^{7} d x^{8} + \frac{7}{8} \, a b^{6} x^{8} e + a b^{6} d x^{7} + 3 \, a^{2} b^{5} x^{7} e + \frac{7}{2} \, a^{2} b^{5} d x^{6} + \frac{35}{6} \, a^{3} b^{4} x^{6} e + 7 \, a^{3} b^{4} d x^{5} + 7 \, a^{4} b^{3} x^{5} e + \frac{35}{4} \, a^{4} b^{3} d x^{4} + \frac{21}{4} \, a^{5} b^{2} x^{4} e + 7 \, a^{5} b^{2} d x^{3} + \frac{7}{3} \, a^{6} b x^{3} e + \frac{7}{2} \, a^{6} b d x^{2} + \frac{1}{2} \, a^{7} x^{2} e + a^{7} d x"," ",0,"1/9*b^7*x^9*e + 1/8*b^7*d*x^8 + 7/8*a*b^6*x^8*e + a*b^6*d*x^7 + 3*a^2*b^5*x^7*e + 7/2*a^2*b^5*d*x^6 + 35/6*a^3*b^4*x^6*e + 7*a^3*b^4*d*x^5 + 7*a^4*b^3*x^5*e + 35/4*a^4*b^3*d*x^4 + 21/4*a^5*b^2*x^4*e + 7*a^5*b^2*d*x^3 + 7/3*a^6*b*x^3*e + 7/2*a^6*b*d*x^2 + 1/2*a^7*x^2*e + a^7*d*x","B",0
1922,1,71,0,0.183254," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} a^{6} + \frac{3}{4} \, {\left(b x^{2} + 2 \, a x\right)}^{2} a^{4} b + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)}^{3} a^{2} b^{2} + \frac{1}{8} \, {\left(b x^{2} + 2 \, a x\right)}^{4} b^{3}"," ",0,"1/2*(b*x^2 + 2*a*x)*a^6 + 3/4*(b*x^2 + 2*a*x)^2*a^4*b + 1/2*(b*x^2 + 2*a*x)^3*a^2*b^2 + 1/8*(b*x^2 + 2*a*x)^4*b^3","B",0
1923,1,469,0,0.168519," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d),x, algorithm=""giac"")","-{\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)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{420} \, {\left(60 \, b^{7} x^{7} e^{6} - 70 \, b^{7} d x^{6} e^{5} + 84 \, b^{7} d^{2} x^{5} e^{4} - 105 \, b^{7} d^{3} x^{4} e^{3} + 140 \, b^{7} d^{4} x^{3} e^{2} - 210 \, b^{7} d^{5} x^{2} e + 420 \, b^{7} d^{6} x + 490 \, a b^{6} x^{6} e^{6} - 588 \, a b^{6} d x^{5} e^{5} + 735 \, a b^{6} d^{2} x^{4} e^{4} - 980 \, a b^{6} d^{3} x^{3} e^{3} + 1470 \, a b^{6} d^{4} x^{2} e^{2} - 2940 \, a b^{6} d^{5} x e + 1764 \, a^{2} b^{5} x^{5} e^{6} - 2205 \, a^{2} b^{5} d x^{4} e^{5} + 2940 \, a^{2} b^{5} d^{2} x^{3} e^{4} - 4410 \, a^{2} b^{5} d^{3} x^{2} e^{3} + 8820 \, a^{2} b^{5} d^{4} x e^{2} + 3675 \, a^{3} b^{4} x^{4} e^{6} - 4900 \, a^{3} b^{4} d x^{3} e^{5} + 7350 \, a^{3} b^{4} d^{2} x^{2} e^{4} - 14700 \, a^{3} b^{4} d^{3} x e^{3} + 4900 \, a^{4} b^{3} x^{3} e^{6} - 7350 \, a^{4} b^{3} d x^{2} e^{5} + 14700 \, a^{4} b^{3} d^{2} x e^{4} + 4410 \, a^{5} b^{2} x^{2} e^{6} - 8820 \, a^{5} b^{2} d x e^{5} + 2940 \, a^{6} b x e^{6}\right)} e^{\left(-7\right)}"," ",0,"-(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)*e^(-8)*log(abs(x*e + d)) + 1/420*(60*b^7*x^7*e^6 - 70*b^7*d*x^6*e^5 + 84*b^7*d^2*x^5*e^4 - 105*b^7*d^3*x^4*e^3 + 140*b^7*d^4*x^3*e^2 - 210*b^7*d^5*x^2*e + 420*b^7*d^6*x + 490*a*b^6*x^6*e^6 - 588*a*b^6*d*x^5*e^5 + 735*a*b^6*d^2*x^4*e^4 - 980*a*b^6*d^3*x^3*e^3 + 1470*a*b^6*d^4*x^2*e^2 - 2940*a*b^6*d^5*x*e + 1764*a^2*b^5*x^5*e^6 - 2205*a^2*b^5*d*x^4*e^5 + 2940*a^2*b^5*d^2*x^3*e^4 - 4410*a^2*b^5*d^3*x^2*e^3 + 8820*a^2*b^5*d^4*x*e^2 + 3675*a^3*b^4*x^4*e^6 - 4900*a^3*b^4*d*x^3*e^5 + 7350*a^3*b^4*d^2*x^2*e^4 - 14700*a^3*b^4*d^3*x*e^3 + 4900*a^4*b^3*x^3*e^6 - 7350*a^4*b^3*d*x^2*e^5 + 14700*a^4*b^3*d^2*x*e^4 + 4410*a^5*b^2*x^2*e^6 - 8820*a^5*b^2*d*x*e^5 + 2940*a^6*b*x*e^6)*e^(-7)","B",0
1924,1,542,0,0.214096," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{60} \, {\left(10 \, b^{7} - \frac{84 \, {\left(b^{7} d e - a b^{6} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{315 \, {\left(b^{7} d^{2} e^{2} - 2 \, a b^{6} d e^{3} + a^{2} b^{5} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{700 \, {\left(b^{7} d^{3} e^{3} - 3 \, a b^{6} d^{2} e^{4} + 3 \, a^{2} b^{5} d e^{5} - a^{3} b^{4} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{1050 \, {\left(b^{7} d^{4} e^{4} - 4 \, a b^{6} d^{3} e^{5} + 6 \, a^{2} b^{5} d^{2} e^{6} - 4 \, a^{3} b^{4} d e^{7} + a^{4} b^{3} e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{1260 \, {\left(b^{7} d^{5} e^{5} - 5 \, a b^{6} d^{4} e^{6} + 10 \, a^{2} b^{5} d^{3} e^{7} - 10 \, a^{3} b^{4} d^{2} e^{8} + 5 \, a^{4} b^{3} d e^{9} - a^{5} b^{2} e^{10}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}}\right)} {\left(x e + d\right)}^{6} e^{\left(-8\right)} - 7 \, {\left(b^{7} d^{6} - 6 \, a b^{6} d^{5} e + 15 \, a^{2} b^{5} d^{4} e^{2} - 20 \, a^{3} b^{4} d^{3} e^{3} + 15 \, a^{4} b^{3} d^{2} e^{4} - 6 \, a^{5} b^{2} d e^{5} + a^{6} b e^{6}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{b^{7} d^{7} e^{6}}{x e + d} - \frac{7 \, a b^{6} d^{6} e^{7}}{x e + d} + \frac{21 \, a^{2} b^{5} d^{5} e^{8}}{x e + d} - \frac{35 \, a^{3} b^{4} d^{4} e^{9}}{x e + d} + \frac{35 \, a^{4} b^{3} d^{3} e^{10}}{x e + d} - \frac{21 \, a^{5} b^{2} d^{2} e^{11}}{x e + d} + \frac{7 \, a^{6} b d e^{12}}{x e + d} - \frac{a^{7} e^{13}}{x e + d}\right)} e^{\left(-14\right)}"," ",0,"1/60*(10*b^7 - 84*(b^7*d*e - a*b^6*e^2)*e^(-1)/(x*e + d) + 315*(b^7*d^2*e^2 - 2*a*b^6*d*e^3 + a^2*b^5*e^4)*e^(-2)/(x*e + d)^2 - 700*(b^7*d^3*e^3 - 3*a*b^6*d^2*e^4 + 3*a^2*b^5*d*e^5 - a^3*b^4*e^6)*e^(-3)/(x*e + d)^3 + 1050*(b^7*d^4*e^4 - 4*a*b^6*d^3*e^5 + 6*a^2*b^5*d^2*e^6 - 4*a^3*b^4*d*e^7 + a^4*b^3*e^8)*e^(-4)/(x*e + d)^4 - 1260*(b^7*d^5*e^5 - 5*a*b^6*d^4*e^6 + 10*a^2*b^5*d^3*e^7 - 10*a^3*b^4*d^2*e^8 + 5*a^4*b^3*d*e^9 - a^5*b^2*e^10)*e^(-5)/(x*e + d)^5)*(x*e + d)^6*e^(-8) - 7*(b^7*d^6 - 6*a*b^6*d^5*e + 15*a^2*b^5*d^4*e^2 - 20*a^3*b^4*d^3*e^3 + 15*a^4*b^3*d^2*e^4 - 6*a^5*b^2*d*e^5 + a^6*b*e^6)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (b^7*d^7*e^6/(x*e + d) - 7*a*b^6*d^6*e^7/(x*e + d) + 21*a^2*b^5*d^5*e^8/(x*e + d) - 35*a^3*b^4*d^4*e^9/(x*e + d) + 35*a^4*b^3*d^3*e^10/(x*e + d) - 21*a^5*b^2*d^2*e^11/(x*e + d) + 7*a^6*b*d*e^12/(x*e + d) - a^7*e^13/(x*e + d))*e^(-14)","B",0
1925,1,448,0,0.211585," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^3,x, algorithm=""giac"")","-21 \, {\left(b^{7} d^{5} - 5 \, a b^{6} d^{4} e + 10 \, a^{2} b^{5} d^{3} e^{2} - 10 \, a^{3} b^{4} d^{2} e^{3} + 5 \, a^{4} b^{3} d e^{4} - a^{5} b^{2} e^{5}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{20} \, {\left(4 \, b^{7} x^{5} e^{12} - 15 \, b^{7} d x^{4} e^{11} + 40 \, b^{7} d^{2} x^{3} e^{10} - 100 \, b^{7} d^{3} x^{2} e^{9} + 300 \, b^{7} d^{4} x e^{8} + 35 \, a b^{6} x^{4} e^{12} - 140 \, a b^{6} d x^{3} e^{11} + 420 \, a b^{6} d^{2} x^{2} e^{10} - 1400 \, a b^{6} d^{3} x e^{9} + 140 \, a^{2} b^{5} x^{3} e^{12} - 630 \, a^{2} b^{5} d x^{2} e^{11} + 2520 \, a^{2} b^{5} d^{2} x e^{10} + 350 \, a^{3} b^{4} x^{2} e^{12} - 2100 \, a^{3} b^{4} d x e^{11} + 700 \, a^{4} b^{3} x e^{12}\right)} e^{\left(-15\right)} - \frac{{\left(13 \, b^{7} d^{7} - 77 \, a b^{6} d^{6} e + 189 \, a^{2} b^{5} d^{5} e^{2} - 245 \, a^{3} b^{4} d^{4} e^{3} + 175 \, a^{4} b^{3} d^{3} e^{4} - 63 \, a^{5} b^{2} d^{2} e^{5} + 7 \, a^{6} b d e^{6} + a^{7} e^{7} + 14 \, {\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)} e^{\left(-8\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-21*(b^7*d^5 - 5*a*b^6*d^4*e + 10*a^2*b^5*d^3*e^2 - 10*a^3*b^4*d^2*e^3 + 5*a^4*b^3*d*e^4 - a^5*b^2*e^5)*e^(-8)*log(abs(x*e + d)) + 1/20*(4*b^7*x^5*e^12 - 15*b^7*d*x^4*e^11 + 40*b^7*d^2*x^3*e^10 - 100*b^7*d^3*x^2*e^9 + 300*b^7*d^4*x*e^8 + 35*a*b^6*x^4*e^12 - 140*a*b^6*d*x^3*e^11 + 420*a*b^6*d^2*x^2*e^10 - 1400*a*b^6*d^3*x*e^9 + 140*a^2*b^5*x^3*e^12 - 630*a^2*b^5*d*x^2*e^11 + 2520*a^2*b^5*d^2*x*e^10 + 350*a^3*b^4*x^2*e^12 - 2100*a^3*b^4*d*x*e^11 + 700*a^4*b^3*x*e^12)*e^(-15) - 1/2*(13*b^7*d^7 - 77*a*b^6*d^6*e + 189*a^2*b^5*d^5*e^2 - 245*a^3*b^4*d^4*e^3 + 175*a^4*b^3*d^3*e^4 - 63*a^5*b^2*d^2*e^5 + 7*a^6*b*d*e^6 + a^7*e^7 + 14*(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)*e^(-8)/(x*e + d)^2","B",0
1926,1,442,0,0.177155," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^4,x, algorithm=""giac"")","35 \, {\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)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, b^{7} x^{4} e^{12} - 16 \, b^{7} d x^{3} e^{11} + 60 \, b^{7} d^{2} x^{2} e^{10} - 240 \, b^{7} d^{3} x e^{9} + 28 \, a b^{6} x^{3} e^{12} - 168 \, a b^{6} d x^{2} e^{11} + 840 \, a b^{6} d^{2} x e^{10} + 126 \, a^{2} b^{5} x^{2} e^{12} - 1008 \, a^{2} b^{5} d x e^{11} + 420 \, a^{3} b^{4} x e^{12}\right)} e^{\left(-16\right)} + \frac{{\left(107 \, b^{7} d^{7} - 518 \, a b^{6} d^{6} e + 987 \, a^{2} b^{5} d^{5} e^{2} - 910 \, a^{3} b^{4} d^{4} e^{3} + 385 \, a^{4} b^{3} d^{3} e^{4} - 42 \, a^{5} b^{2} d^{2} e^{5} - 7 \, a^{6} b d e^{6} - 2 \, a^{7} e^{7} + 126 \, {\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} + 21 \, {\left(11 \, b^{7} d^{6} e - 54 \, a b^{6} d^{5} e^{2} + 105 \, a^{2} b^{5} d^{4} e^{3} - 100 \, a^{3} b^{4} d^{3} e^{4} + 45 \, a^{4} b^{3} d^{2} e^{5} - 6 \, a^{5} b^{2} d e^{6} - a^{6} b e^{7}\right)} x\right)} e^{\left(-8\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"35*(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)*e^(-8)*log(abs(x*e + d)) + 1/12*(3*b^7*x^4*e^12 - 16*b^7*d*x^3*e^11 + 60*b^7*d^2*x^2*e^10 - 240*b^7*d^3*x*e^9 + 28*a*b^6*x^3*e^12 - 168*a*b^6*d*x^2*e^11 + 840*a*b^6*d^2*x*e^10 + 126*a^2*b^5*x^2*e^12 - 1008*a^2*b^5*d*x*e^11 + 420*a^3*b^4*x*e^12)*e^(-16) + 1/6*(107*b^7*d^7 - 518*a*b^6*d^6*e + 987*a^2*b^5*d^5*e^2 - 910*a^3*b^4*d^4*e^3 + 385*a^4*b^3*d^3*e^4 - 42*a^5*b^2*d^2*e^5 - 7*a^6*b*d*e^6 - 2*a^7*e^7 + 126*(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 + 21*(11*b^7*d^6*e - 54*a*b^6*d^5*e^2 + 105*a^2*b^5*d^4*e^3 - 100*a^3*b^4*d^3*e^4 + 45*a^4*b^3*d^2*e^5 - 6*a^5*b^2*d*e^6 - a^6*b*e^7)*x)*e^(-8)/(x*e + d)^3","B",0
1927,1,174,0,0.183804," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{3 \, b^{3} x^{4} e^{4} + 16 \, b^{3} d x^{3} e^{3} + 36 \, b^{3} d^{2} x^{2} e^{2} + 48 \, b^{3} d^{3} x e - 4 \, a b^{2} x^{3} e^{4} - 24 \, a b^{2} d x^{2} e^{3} - 72 \, a b^{2} d^{2} x e^{2} + 6 \, a^{2} b x^{2} e^{4} + 48 \, a^{2} b d x e^{3} - 12 \, a^{3} x e^{4}}{12 \, b^{4}} + \frac{{\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({\left| b x + a \right|}\right)}{b^{5}}"," ",0,"1/12*(3*b^3*x^4*e^4 + 16*b^3*d*x^3*e^3 + 36*b^3*d^2*x^2*e^2 + 48*b^3*d^3*x*e - 4*a*b^2*x^3*e^4 - 24*a*b^2*d*x^2*e^3 - 72*a*b^2*d^2*x*e^2 + 6*a^2*b*x^2*e^4 + 48*a^2*b*d*x*e^3 - 12*a^3*x*e^4)/b^4 + (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(abs(b*x + a))/b^5","A",0
1928,1,110,0,0.158278," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, b^{2} x^{3} e^{3} + 9 \, b^{2} d x^{2} e^{2} + 18 \, b^{2} d^{2} x e - 3 \, a b x^{2} e^{3} - 18 \, a b d x e^{2} + 6 \, a^{2} x e^{3}}{6 \, b^{3}} + \frac{{\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({\left| b x + a \right|}\right)}{b^{4}}"," ",0,"1/6*(2*b^2*x^3*e^3 + 9*b^2*d*x^2*e^2 + 18*b^2*d^2*x*e - 3*a*b*x^2*e^3 - 18*a*b*d*x*e^2 + 6*a^2*x*e^3)/b^3 + (b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*log(abs(b*x + a))/b^4","A",0
1929,1,59,0,0.153073," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{b x^{2} e^{2} + 4 \, b d x e - 2 \, a x e^{2}}{2 \, b^{2}} + \frac{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}}"," ",0,"1/2*(b*x^2*e^2 + 4*b*d*x*e - 2*a*x*e^2)/b^2 + (b^2*d^2 - 2*a*b*d*e + a^2*e^2)*log(abs(b*x + a))/b^3","A",0
1930,1,28,0,0.164154," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{x e}{b} + \frac{{\left(b d - a e\right)} \log\left({\left| b x + a \right|}\right)}{b^{2}}"," ",0,"x*e/b + (b*d - a*e)*log(abs(b*x + a))/b^2","A",0
1931,1,22,0,0.153398," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{\log\left(a^{2} + {\left(b x^{2} + 2 \, a x\right)} b\right)}{2 \, b}"," ",0,"1/2*log(a^2 + (b*x^2 + 2*a*x)*b)/b","B",0
1932,1,49,0,0.157476," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{b \log\left({\left| b x + a \right|}\right)}{b^{2} d - a b e} - \frac{e \log\left({\left| x e + d \right|}\right)}{b d e - a e^{2}}"," ",0,"b*log(abs(b*x + a))/(b^2*d - a*b*e) - e*log(abs(x*e + d))/(b*d*e - a*e^2)","A",0
1933,1,82,0,0.170366," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{b e \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}} + \frac{e}{{\left(b d e - a e^{2}\right)} {\left(x e + d\right)}}"," ",0,"b*e*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3) + e/((b*d*e - a*e^2)*(x*e + d))","A",0
1934,1,166,0,0.157606," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| b x + a \right|}\right)}{b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}} - \frac{b^{2} e \log\left({\left| x e + d \right|}\right)}{b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}} + \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 d - a e\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"b^3*log(abs(b*x + a))/(b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3) - b^2*e*log(abs(x*e + d))/(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4) + 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)/((b*d - a*e)^3*(x*e + d)^2)","B",0
1935,1,238,0,0.171664," ","integrate((b*x+a)/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{b^{4} \log\left({\left| b x + a \right|}\right)}{b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}} - \frac{b^{3} e \log\left({\left| x e + d \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} + \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 d - a e\right)}^{4} {\left(x e + d\right)}^{3}}"," ",0,"b^4*log(abs(b*x + a))/(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4) - b^3*e*log(abs(x*e + d))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) + 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)/((b*d - a*e)^4*(x*e + d)^3)","B",0
1936,1,172,0,0.156756," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{6 \, {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}} + \frac{b^{3} x^{2} e^{4} + 8 \, b^{3} d x e^{3} - 6 \, a b^{2} x e^{4}}{2 \, b^{6}} - \frac{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} + 8 \, {\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 x + a\right)}^{2} b^{5}}"," ",0,"6*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*log(abs(b*x + a))/b^5 + 1/2*(b^3*x^2*e^4 + 8*b^3*d*x*e^3 - 6*a*b^2*x*e^4)/b^6 - 1/2*(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 + 8*(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)/((b*x + a)^2*b^5)","A",0
1937,1,107,0,0.156381," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{x e^{3}}{b^{3}} + \frac{3 \, {\left(b d e^{2} - a e^{3}\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}} - \frac{b^{3} d^{3} + 3 \, a b^{2} d^{2} e - 9 \, a^{2} b d e^{2} + 5 \, a^{3} e^{3} + 6 \, {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x}{2 \, {\left(b x + a\right)}^{2} b^{4}}"," ",0,"x*e^3/b^3 + 3*(b*d*e^2 - a*e^3)*log(abs(b*x + a))/b^4 - 1/2*(b^3*d^3 + 3*a*b^2*d^2*e - 9*a^2*b*d*e^2 + 5*a^3*e^3 + 6*(b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)/((b*x + a)^2*b^4)","A",0
1938,1,67,0,0.152736," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{e^{2} \log\left({\left| b x + a \right|}\right)}{b^{3}} - \frac{4 \, {\left(b d e - a e^{2}\right)} x + \frac{b^{2} d^{2} + 2 \, a b d e - 3 \, a^{2} e^{2}}{b}}{2 \, {\left(b x + a\right)}^{2} b^{2}}"," ",0,"e^2*log(abs(b*x + a))/b^3 - 1/2*(4*(b*d*e - a*e^2)*x + (b^2*d^2 + 2*a*b*d*e - 3*a^2*e^2)/b)/((b*x + a)^2*b^2)","A",0
1939,1,26,0,0.155569," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{2 \, b x e + b d + a e}{2 \, {\left(b x + a\right)}^{2} b^{2}}"," ",0,"-1/2*(2*b*x*e + b*d + a*e)/((b*x + a)^2*b^2)","A",0
1940,1,23,0,0.152386," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(a^{2} + {\left(b x^{2} + 2 \, a x\right)} b\right)} b}"," ",0,"-1/2/((a^2 + (b*x^2 + 2*a*x)*b)*b)","A",0
1941,1,162,0,0.162216," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{b e^{2} \log\left({\left| b x + a \right|}\right)}{b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}} - \frac{e^{3} \log\left({\left| x e + d \right|}\right)}{b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}} - \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 d - a e\right)}^{3} {\left(b x + a\right)}^{2}}"," ",0,"b*e^2*log(abs(b*x + a))/(b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3) - e^3*log(abs(x*e + d))/(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4) - 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)/((b*d - a*e)^3*(b*x + a)^2)","B",0
1942,1,212,0,0.186741," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{3 \, b e^{3} \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} + \frac{e^{5}}{{\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)} {\left(x e + d\right)}} + \frac{5 \, b^{3} e^{2} - \frac{6 \, {\left(b^{3} d e^{3} - a b^{2} e^{4}\right)} e^{\left(-1\right)}}{x e + d}}{2 \, {\left(b d - a e\right)}^{4} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{2}}"," ",0,"3*b*e^3*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) + e^5/((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*e + d)) + 1/2*(5*b^3*e^2 - 6*(b^3*d*e^3 - a*b^2*e^4)*e^(-1)/(x*e + d))/((b*d - a*e)^4*(b - b*d/(x*e + d) + a*e/(x*e + d))^2)","A",0
1943,1,332,0,0.201309," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{6 \, b^{3} e^{2} \log\left({\left| b x + a \right|}\right)}{b^{6} d^{5} - 5 \, a b^{5} d^{4} e + 10 \, a^{2} b^{4} d^{3} e^{2} - 10 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - a^{5} b e^{5}} - \frac{6 \, b^{2} e^{3} \log\left({\left| x e + d \right|}\right)}{b^{5} d^{5} e - 5 \, a b^{4} d^{4} e^{2} + 10 \, a^{2} b^{3} d^{3} e^{3} - 10 \, a^{3} b^{2} d^{2} e^{4} + 5 \, a^{4} b d e^{5} - a^{5} e^{6}} + \frac{12 \, b^{3} x^{3} e^{3} + 18 \, b^{3} d x^{2} e^{2} + 4 \, b^{3} d^{2} x e - b^{3} d^{3} + 18 \, a b^{2} x^{2} e^{3} + 28 \, a b^{2} d x e^{2} + 7 \, a b^{2} d^{2} e + 4 \, a^{2} b x e^{3} + 7 \, a^{2} b d e^{2} - a^{3} e^{3}}{2 \, {\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)} {\left(b x^{2} e + b d x + a x e + a d\right)}^{2}}"," ",0,"6*b^3*e^2*log(abs(b*x + a))/(b^6*d^5 - 5*a*b^5*d^4*e + 10*a^2*b^4*d^3*e^2 - 10*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - a^5*b*e^5) - 6*b^2*e^3*log(abs(x*e + d))/(b^5*d^5*e - 5*a*b^4*d^4*e^2 + 10*a^2*b^3*d^3*e^3 - 10*a^3*b^2*d^2*e^4 + 5*a^4*b*d*e^5 - a^5*e^6) + 1/2*(12*b^3*x^3*e^3 + 18*b^3*d*x^2*e^2 + 4*b^3*d^2*x*e - b^3*d^3 + 18*a*b^2*x^2*e^3 + 28*a*b^2*d*x*e^2 + 7*a*b^2*d^2*e + 4*a^2*b*x*e^3 + 7*a^2*b*d*e^2 - a^3*e^3)/((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)*(b*x^2*e + b*d*x + a*x*e + a*d)^2)","B",0
1944,1,435,0,0.165879," ","integrate((b*x+a)/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{10 \, b^{4} e^{2} \log\left({\left| b x + a \right|}\right)}{b^{7} d^{6} - 6 \, a b^{6} d^{5} e + 15 \, a^{2} b^{5} d^{4} e^{2} - 20 \, a^{3} b^{4} d^{3} e^{3} + 15 \, a^{4} b^{3} d^{2} e^{4} - 6 \, a^{5} b^{2} d e^{5} + a^{6} b e^{6}} - \frac{10 \, b^{3} e^{3} \log\left({\left| x e + d \right|}\right)}{b^{6} d^{6} e - 6 \, a b^{5} d^{5} e^{2} + 15 \, a^{2} b^{4} d^{4} e^{3} - 20 \, a^{3} b^{3} d^{3} e^{4} + 15 \, a^{4} b^{2} d^{2} e^{5} - 6 \, a^{5} b d e^{6} + a^{6} e^{7}} - \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}{6 \, {\left(b d - a e\right)}^{6} {\left(b x + a\right)}^{2} {\left(x e + d\right)}^{3}}"," ",0,"10*b^4*e^2*log(abs(b*x + a))/(b^7*d^6 - 6*a*b^6*d^5*e + 15*a^2*b^5*d^4*e^2 - 20*a^3*b^4*d^3*e^3 + 15*a^4*b^3*d^2*e^4 - 6*a^5*b^2*d*e^5 + a^6*b*e^6) - 10*b^3*e^3*log(abs(x*e + d))/(b^6*d^6*e - 6*a*b^5*d^5*e^2 + 15*a^2*b^4*d^4*e^3 - 20*a^3*b^3*d^3*e^4 + 15*a^4*b^2*d^2*e^5 - 6*a^5*b*d*e^6 + a^6*e^7) - 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)/((b*d - a*e)^6*(b*x + a)^2*(x*e + d)^3)","B",0
1945,1,174,0,0.178792," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{e^{4} \log\left({\left| b x + a \right|}\right)}{b^{5}} - \frac{48 \, {\left(b^{3} d e^{3} - a b^{2} e^{4}\right)} x^{3} + 36 \, {\left(b^{3} d^{2} e^{2} + 2 \, a b^{2} d e^{3} - 3 \, a^{2} b e^{4}\right)} x^{2} + 8 \, {\left(2 \, b^{3} d^{3} e + 3 \, a b^{2} d^{2} e^{2} + 6 \, a^{2} b d e^{3} - 11 \, a^{3} e^{4}\right)} x + \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}}{b}}{12 \, {\left(b x + a\right)}^{4} b^{4}}"," ",0,"e^4*log(abs(b*x + a))/b^5 - 1/12*(48*(b^3*d*e^3 - a*b^2*e^4)*x^3 + 36*(b^3*d^2*e^2 + 2*a*b^2*d*e^3 - 3*a^2*b*e^4)*x^2 + 8*(2*b^3*d^3*e + 3*a*b^2*d^2*e^2 + 6*a^2*b*d*e^3 - 11*a^3*e^4)*x + (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)/b)/((b*x + a)^4*b^4)","A",0
1946,1,106,0,0.161644," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{3} e^{3} + 6 \, b^{3} d x^{2} e^{2} + 4 \, b^{3} d^{2} x e + b^{3} d^{3} + 6 \, a b^{2} x^{2} e^{3} + 4 \, a b^{2} d x e^{2} + a b^{2} d^{2} e + 4 \, a^{2} b x e^{3} + a^{2} b d e^{2} + a^{3} e^{3}}{4 \, {\left(b x + a\right)}^{4} b^{4}}"," ",0,"-1/4*(4*b^3*x^3*e^3 + 6*b^3*d*x^2*e^2 + 4*b^3*d^2*x*e + b^3*d^3 + 6*a*b^2*x^2*e^3 + 4*a*b^2*d*x*e^2 + a*b^2*d^2*e + 4*a^2*b*x*e^3 + a^2*b*d*e^2 + a^3*e^3)/((b*x + a)^4*b^4)","B",0
1947,1,60,0,0.154719," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{6 \, b^{2} x^{2} e^{2} + 8 \, b^{2} d x e + 3 \, b^{2} d^{2} + 4 \, a b x e^{2} + 2 \, a b d e + a^{2} e^{2}}{12 \, {\left(b x + a\right)}^{4} b^{3}}"," ",0,"-1/12*(6*b^2*x^2*e^2 + 8*b^2*d*x*e + 3*b^2*d^2 + 4*a*b*x*e^2 + 2*a*b*d*e + a^2*e^2)/((b*x + a)^4*b^3)","A",0
1948,1,27,0,0.156115," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{4 \, b x e + 3 \, b d + a e}{12 \, {\left(b x + a\right)}^{4} b^{2}}"," ",0,"-1/12*(4*b*x*e + 3*b*d + a*e)/((b*x + a)^4*b^2)","A",0
1949,1,23,0,0.152360," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(a^{2} + {\left(b x^{2} + 2 \, a x\right)} b\right)}^{2} b}"," ",0,"-1/4/((a^2 + (b*x^2 + 2*a*x)*b)^2*b)","A",0
1950,1,322,0,0.178652," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{b e^{4} \log\left({\left| b x + a \right|}\right)}{b^{6} d^{5} - 5 \, a b^{5} d^{4} e + 10 \, a^{2} b^{4} d^{3} e^{2} - 10 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - a^{5} b e^{5}} - \frac{e^{5} \log\left({\left| x e + d \right|}\right)}{b^{5} d^{5} e - 5 \, a b^{4} d^{4} e^{2} + 10 \, a^{2} b^{3} d^{3} e^{3} - 10 \, a^{3} b^{2} d^{2} e^{4} + 5 \, a^{4} b d e^{5} - a^{5} e^{6}} - \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 d - a e\right)}^{5} {\left(b x + a\right)}^{4}}"," ",0,"b*e^4*log(abs(b*x + a))/(b^6*d^5 - 5*a*b^5*d^4*e + 10*a^2*b^4*d^3*e^2 - 10*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - a^5*b*e^5) - e^5*log(abs(x*e + d))/(b^5*d^5*e - 5*a*b^4*d^4*e^2 + 10*a^2*b^3*d^3*e^3 - 10*a^3*b^2*d^2*e^4 + 5*a^4*b*d*e^5 - a^5*e^6) - 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)/((b*d - a*e)^5*(b*x + a)^4)","B",0
1951,1,358,0,0.206350," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{5 \, b e^{5} \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{6} d^{6} e - 6 \, a b^{5} d^{5} e^{2} + 15 \, a^{2} b^{4} d^{4} e^{3} - 20 \, a^{3} b^{3} d^{3} e^{4} + 15 \, a^{4} b^{2} d^{2} e^{5} - 6 \, a^{5} b d e^{6} + a^{6} e^{7}} + \frac{e^{9}}{{\left(b^{5} d^{5} e^{5} - 5 \, a b^{4} d^{4} e^{6} + 10 \, a^{2} b^{3} d^{3} e^{7} - 10 \, a^{3} b^{2} d^{2} e^{8} + 5 \, a^{4} b d e^{9} - a^{5} e^{10}\right)} {\left(x e + d\right)}} + \frac{77 \, b^{5} e^{4} - \frac{260 \, {\left(b^{5} d e^{5} - a b^{4} e^{6}\right)} e^{\left(-1\right)}}{x e + d} + \frac{300 \, {\left(b^{5} d^{2} e^{6} - 2 \, a b^{4} d e^{7} + a^{2} b^{3} e^{8}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{120 \, {\left(b^{5} d^{3} e^{7} - 3 \, a b^{4} d^{2} e^{8} + 3 \, a^{2} b^{3} d e^{9} - a^{3} b^{2} e^{10}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{12 \, {\left(b d - a e\right)}^{6} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{4}}"," ",0,"5*b*e^5*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^6*d^6*e - 6*a*b^5*d^5*e^2 + 15*a^2*b^4*d^4*e^3 - 20*a^3*b^3*d^3*e^4 + 15*a^4*b^2*d^2*e^5 - 6*a^5*b*d*e^6 + a^6*e^7) + e^9/((b^5*d^5*e^5 - 5*a*b^4*d^4*e^6 + 10*a^2*b^3*d^3*e^7 - 10*a^3*b^2*d^2*e^8 + 5*a^4*b*d*e^9 - a^5*e^10)*(x*e + d)) + 1/12*(77*b^5*e^4 - 260*(b^5*d*e^5 - a*b^4*e^6)*e^(-1)/(x*e + d) + 300*(b^5*d^2*e^6 - 2*a*b^4*d*e^7 + a^2*b^3*e^8)*e^(-2)/(x*e + d)^2 - 120*(b^5*d^3*e^7 - 3*a*b^4*d^2*e^8 + 3*a^2*b^3*d*e^9 - a^3*b^2*e^10)*e^(-3)/(x*e + d)^3)/((b*d - a*e)^6*(b - b*d/(x*e + d) + a*e/(x*e + d))^4)","B",0
1952,1,547,0,0.173643," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{15 \, b^{3} e^{4} \log\left({\left| b x + a \right|}\right)}{b^{8} d^{7} - 7 \, a b^{7} d^{6} e + 21 \, a^{2} b^{6} d^{5} e^{2} - 35 \, a^{3} b^{5} d^{4} e^{3} + 35 \, a^{4} b^{4} d^{3} e^{4} - 21 \, a^{5} b^{3} d^{2} e^{5} + 7 \, a^{6} b^{2} d e^{6} - a^{7} b e^{7}} - \frac{15 \, b^{2} e^{5} \log\left({\left| x e + d \right|}\right)}{b^{7} d^{7} e - 7 \, a b^{6} d^{6} e^{2} + 21 \, a^{2} b^{5} d^{5} e^{3} - 35 \, a^{3} b^{4} d^{4} e^{4} + 35 \, a^{4} b^{3} d^{3} e^{5} - 21 \, a^{5} b^{2} d^{2} e^{6} + 7 \, a^{6} b d e^{7} - a^{7} e^{8}} - \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}{4 \, {\left(b d - a e\right)}^{7} {\left(b x + a\right)}^{4} {\left(x e + d\right)}^{2}}"," ",0,"15*b^3*e^4*log(abs(b*x + a))/(b^8*d^7 - 7*a*b^7*d^6*e + 21*a^2*b^6*d^5*e^2 - 35*a^3*b^5*d^4*e^3 + 35*a^4*b^4*d^3*e^4 - 21*a^5*b^3*d^2*e^5 + 7*a^6*b^2*d*e^6 - a^7*b*e^7) - 15*b^2*e^5*log(abs(x*e + d))/(b^7*d^7*e - 7*a*b^6*d^6*e^2 + 21*a^2*b^5*d^5*e^3 - 35*a^3*b^4*d^4*e^4 + 35*a^4*b^3*d^3*e^5 - 21*a^5*b^2*d^2*e^6 + 7*a^6*b*d*e^7 - a^7*e^8) - 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)/((b*d - a*e)^7*(b*x + a)^4*(x*e + d)^2)","B",0
1953,1,673,0,0.175663," ","integrate((b*x+a)/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{35 \, b^{4} e^{4} \log\left({\left| b x + a \right|}\right)}{b^{9} d^{8} - 8 \, a b^{8} d^{7} e + 28 \, a^{2} b^{7} d^{6} e^{2} - 56 \, a^{3} b^{6} d^{5} e^{3} + 70 \, a^{4} b^{5} d^{4} e^{4} - 56 \, a^{5} b^{4} d^{3} e^{5} + 28 \, a^{6} b^{3} d^{2} e^{6} - 8 \, a^{7} b^{2} d e^{7} + a^{8} b e^{8}} - \frac{35 \, b^{3} e^{5} \log\left({\left| x e + d \right|}\right)}{b^{8} d^{8} e - 8 \, a b^{7} d^{7} e^{2} + 28 \, a^{2} b^{6} d^{6} e^{3} - 56 \, a^{3} b^{5} d^{5} e^{4} + 70 \, a^{4} b^{4} d^{4} e^{5} - 56 \, a^{5} b^{3} d^{3} e^{6} + 28 \, a^{6} b^{2} d^{2} e^{7} - 8 \, a^{7} b d e^{8} + a^{8} e^{9}} - \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}{12 \, {\left(b d - a e\right)}^{8} {\left(b x + a\right)}^{4} {\left(x e + d\right)}^{3}}"," ",0,"35*b^4*e^4*log(abs(b*x + a))/(b^9*d^8 - 8*a*b^8*d^7*e + 28*a^2*b^7*d^6*e^2 - 56*a^3*b^6*d^5*e^3 + 70*a^4*b^5*d^4*e^4 - 56*a^5*b^4*d^3*e^5 + 28*a^6*b^3*d^2*e^6 - 8*a^7*b^2*d*e^7 + a^8*b*e^8) - 35*b^3*e^5*log(abs(x*e + d))/(b^8*d^8*e - 8*a*b^7*d^7*e^2 + 28*a^2*b^6*d^6*e^3 - 56*a^3*b^5*d^5*e^4 + 70*a^4*b^4*d^4*e^5 - 56*a^5*b^3*d^3*e^6 + 28*a^6*b^2*d^2*e^7 - 8*a^7*b*d*e^8 + a^8*e^9) - 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)/((b*d - a*e)^8*(b*x + a)^4*(x*e + d)^3)","B",0
1954,1,311,0,0.166711," ","integrate((b*x+a)*(e*x+d)^5*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, b^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, b^{2} d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, b^{2} d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, b^{2} d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, b^{2} d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, b^{2} d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, a b x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a b d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, a b d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a b d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a b d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + a b d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, a^{2} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + a^{2} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{2} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{2} d^{5} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/8*b^2*x^8*e^5*sgn(b*x + a) + 5/7*b^2*d*x^7*e^4*sgn(b*x + a) + 5/3*b^2*d^2*x^6*e^3*sgn(b*x + a) + 2*b^2*d^3*x^5*e^2*sgn(b*x + a) + 5/4*b^2*d^4*x^4*e*sgn(b*x + a) + 1/3*b^2*d^5*x^3*sgn(b*x + a) + 2/7*a*b*x^7*e^5*sgn(b*x + a) + 5/3*a*b*d*x^6*e^4*sgn(b*x + a) + 4*a*b*d^2*x^5*e^3*sgn(b*x + a) + 5*a*b*d^3*x^4*e^2*sgn(b*x + a) + 10/3*a*b*d^4*x^3*e*sgn(b*x + a) + a*b*d^5*x^2*sgn(b*x + a) + 1/6*a^2*x^6*e^5*sgn(b*x + a) + a^2*d*x^5*e^4*sgn(b*x + a) + 5/2*a^2*d^2*x^4*e^3*sgn(b*x + a) + 10/3*a^2*d^3*x^3*e^2*sgn(b*x + a) + 5/2*a^2*d^4*x^2*e*sgn(b*x + a) + a^2*d^5*x*sgn(b*x + a)","B",0
1955,1,254,0,0.182821," ","integrate((b*x+a)*(e*x+d)^4*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, b^{2} d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, b^{2} d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + b^{2} d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, b^{2} d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{8}{5} \, a b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{8}{3} \, a b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + a b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a^{2} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + a^{2} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{2} d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/7*b^2*x^7*e^4*sgn(b*x + a) + 2/3*b^2*d*x^6*e^3*sgn(b*x + a) + 6/5*b^2*d^2*x^5*e^2*sgn(b*x + a) + b^2*d^3*x^4*e*sgn(b*x + a) + 1/3*b^2*d^4*x^3*sgn(b*x + a) + 1/3*a*b*x^6*e^4*sgn(b*x + a) + 8/5*a*b*d*x^5*e^3*sgn(b*x + a) + 3*a*b*d^2*x^4*e^2*sgn(b*x + a) + 8/3*a*b*d^3*x^3*e*sgn(b*x + a) + a*b*d^4*x^2*sgn(b*x + a) + 1/5*a^2*x^5*e^4*sgn(b*x + a) + a^2*d*x^4*e^3*sgn(b*x + a) + 2*a^2*d^2*x^3*e^2*sgn(b*x + a) + 2*a^2*d^3*x^2*e*sgn(b*x + a) + a^2*d^4*x*sgn(b*x + a)","B",0
1956,1,199,0,0.159253," ","integrate((b*x+a)*(e*x+d)^3*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, b^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, b^{2} d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, b^{2} d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, b^{2} d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, a b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + a b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + a^{2} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{2} d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*b^2*x^6*e^3*sgn(b*x + a) + 3/5*b^2*d*x^5*e^2*sgn(b*x + a) + 3/4*b^2*d^2*x^4*e*sgn(b*x + a) + 1/3*b^2*d^3*x^3*sgn(b*x + a) + 2/5*a*b*x^5*e^3*sgn(b*x + a) + 3/2*a*b*d*x^4*e^2*sgn(b*x + a) + 2*a*b*d^2*x^3*e*sgn(b*x + a) + a*b*d^3*x^2*sgn(b*x + a) + 1/4*a^2*x^4*e^3*sgn(b*x + a) + a^2*d*x^3*e^2*sgn(b*x + a) + 3/2*a^2*d^2*x^2*e*sgn(b*x + a) + a^2*d^3*x*sgn(b*x + a)","A",0
1957,1,143,0,0.159142," ","integrate((b*x+a)*(e*x+d)^2*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, b^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b^{2} d x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, b^{2} d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, a b d x^{3} e \mathrm{sgn}\left(b x + a\right) + a b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + a^{2} d x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{2} d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/5*b^2*x^5*e^2*sgn(b*x + a) + 1/2*b^2*d*x^4*e*sgn(b*x + a) + 1/3*b^2*d^2*x^3*sgn(b*x + a) + 1/2*a*b*x^4*e^2*sgn(b*x + a) + 4/3*a*b*d*x^3*e*sgn(b*x + a) + a*b*d^2*x^2*sgn(b*x + a) + 1/3*a^2*x^3*e^2*sgn(b*x + a) + a^2*d*x^2*e*sgn(b*x + a) + a^2*d^2*x*sgn(b*x + a)","A",0
1958,1,88,0,0.158769," ","integrate((b*x+a)*(e*x+d)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, b^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, b^{2} d x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, a b x^{3} e \mathrm{sgn}\left(b x + a\right) + a b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{2} d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/4*b^2*x^4*e*sgn(b*x + a) + 1/3*b^2*d*x^3*sgn(b*x + a) + 2/3*a*b*x^3*e*sgn(b*x + a) + a*b*d*x^2*sgn(b*x + a) + 1/2*a^2*x^2*e*sgn(b*x + a) + a^2*d*x*sgn(b*x + a)","A",0
1959,1,18,0,0.148491," ","integrate((b*x+a)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{3} \mathrm{sgn}\left(b x + a\right)}{3 \, b}"," ",0,"1/3*(b*x + a)^3*sgn(b*x + a)/b","A",0
1960,1,97,0,0.156161," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","{\left(b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b d e \mathrm{sgn}\left(b x + a\right) + a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) - 2 \, b^{2} d x \mathrm{sgn}\left(b x + a\right) + 4 \, a b x e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}"," ",0,"(b^2*d^2*sgn(b*x + a) - 2*a*b*d*e*sgn(b*x + a) + a^2*e^2*sgn(b*x + a))*e^(-3)*log(abs(x*e + d)) + 1/2*(b^2*x^2*e*sgn(b*x + a) - 2*b^2*d*x*sgn(b*x + a) + 4*a*b*x*e*sgn(b*x + a))*e^(-2)","A",0
1961,1,101,0,0.153836," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","b^{2} x e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) - 2 \, {\left(b^{2} d \mathrm{sgn}\left(b x + a\right) - a b e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b d e \mathrm{sgn}\left(b x + a\right) + a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{x e + d}"," ",0,"b^2*x*e^(-2)*sgn(b*x + a) - 2*(b^2*d*sgn(b*x + a) - a*b*e*sgn(b*x + a))*e^(-3)*log(abs(x*e + d)) - (b^2*d^2*sgn(b*x + a) - 2*a*b*d*e*sgn(b*x + a) + a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)","A",0
1962,1,105,0,0.155143," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","b^{2} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(4 \, {\left(b^{2} d \mathrm{sgn}\left(b x + a\right) - a b e \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(3 \, b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b d e \mathrm{sgn}\left(b x + a\right) - a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"b^2*e^(-3)*log(abs(x*e + d))*sgn(b*x + a) + 1/2*(4*(b^2*d*sgn(b*x + a) - a*b*e*sgn(b*x + a))*x + (3*b^2*d^2*sgn(b*x + a) - 2*a*b*d*e*sgn(b*x + a) - a^2*e^2*sgn(b*x + a))*e^(-1))*e^(-2)/(x*e + d)^2","A",0
1963,1,94,0,0.156433," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, b^{2} d x e \mathrm{sgn}\left(b x + a\right) + b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b x e^{2} \mathrm{sgn}\left(b x + a\right) + a b d e \mathrm{sgn}\left(b x + a\right) + a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/3*(3*b^2*x^2*e^2*sgn(b*x + a) + 3*b^2*d*x*e*sgn(b*x + a) + b^2*d^2*sgn(b*x + a) + 3*a*b*x*e^2*sgn(b*x + a) + a*b*d*e*sgn(b*x + a) + a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^3","B",0
1964,1,96,0,0.170392," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{{\left(6 \, b^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, b^{2} d x e \mathrm{sgn}\left(b x + a\right) + b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a b x e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a b d e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{12 \, {\left(x e + d\right)}^{4}}"," ",0,"-1/12*(6*b^2*x^2*e^2*sgn(b*x + a) + 4*b^2*d*x*e*sgn(b*x + a) + b^2*d^2*sgn(b*x + a) + 8*a*b*x*e^2*sgn(b*x + a) + 2*a*b*d*e*sgn(b*x + a) + 3*a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^4","A",0
1965,1,96,0,0.205707," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(10 \, b^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, b^{2} d x e \mathrm{sgn}\left(b x + a\right) + b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, a b x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b d e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{30 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/30*(10*b^2*x^2*e^2*sgn(b*x + a) + 5*b^2*d*x*e*sgn(b*x + a) + b^2*d^2*sgn(b*x + a) + 15*a*b*x*e^2*sgn(b*x + a) + 3*a*b*d*e*sgn(b*x + a) + 6*a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^5","A",0
1966,1,96,0,0.160138," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(15 \, b^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, b^{2} d x e \mathrm{sgn}\left(b x + a\right) + b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 24 \, a b x e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a b d e \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(15*b^2*x^2*e^2*sgn(b*x + a) + 6*b^2*d*x*e*sgn(b*x + a) + b^2*d^2*sgn(b*x + a) + 24*a*b*x*e^2*sgn(b*x + a) + 4*a*b*d*e*sgn(b*x + a) + 10*a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^6","A",0
1967,1,96,0,0.204149," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(21 \, b^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, b^{2} d x e \mathrm{sgn}\left(b x + a\right) + b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, a b x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a b d e \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{105 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/105*(21*b^2*x^2*e^2*sgn(b*x + a) + 7*b^2*d*x*e*sgn(b*x + a) + b^2*d^2*sgn(b*x + a) + 35*a*b*x*e^2*sgn(b*x + a) + 5*a*b*d*e*sgn(b*x + a) + 15*a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^7","A",0
1968,1,761,0,0.207986," ","integrate((b*x+a)*(e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{12} \, b^{4} x^{12} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{7}{11} \, b^{4} d x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{21}{10} \, b^{4} d^{2} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{35}{9} \, b^{4} d^{3} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{35}{8} \, b^{4} d^{4} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, b^{4} d^{5} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{7}{6} \, b^{4} d^{6} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, b^{4} d^{7} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{4}{11} \, a b^{3} x^{11} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{14}{5} \, a b^{3} d x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{28}{3} \, a b^{3} d^{2} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{35}{2} \, a b^{3} d^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, a b^{3} d^{4} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 14 \, a b^{3} d^{5} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{28}{5} \, a b^{3} d^{6} x^{5} e \mathrm{sgn}\left(b x + a\right) + a b^{3} d^{7} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, a^{2} b^{2} x^{10} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{14}{3} \, a^{2} b^{2} d x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{63}{4} \, a^{2} b^{2} d^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{2} b^{2} d^{3} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{2} b^{2} d^{4} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{126}{5} \, a^{2} b^{2} d^{5} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{21}{2} \, a^{2} b^{2} d^{6} x^{4} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} d^{7} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{4}{9} \, a^{3} b x^{9} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{7}{2} \, a^{3} b d x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{3} b d^{2} x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{70}{3} \, a^{3} b d^{3} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 28 \, a^{3} b d^{4} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{3} b d^{5} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{28}{3} \, a^{3} b d^{6} x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d^{7} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, a^{4} x^{8} e^{7} \mathrm{sgn}\left(b x + a\right) + a^{4} d x^{7} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{7}{2} \, a^{4} d^{2} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{4} d^{3} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{35}{4} \, a^{4} d^{4} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{4} d^{5} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{7}{2} \, a^{4} d^{6} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{4} d^{7} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/12*b^4*x^12*e^7*sgn(b*x + a) + 7/11*b^4*d*x^11*e^6*sgn(b*x + a) + 21/10*b^4*d^2*x^10*e^5*sgn(b*x + a) + 35/9*b^4*d^3*x^9*e^4*sgn(b*x + a) + 35/8*b^4*d^4*x^8*e^3*sgn(b*x + a) + 3*b^4*d^5*x^7*e^2*sgn(b*x + a) + 7/6*b^4*d^6*x^6*e*sgn(b*x + a) + 1/5*b^4*d^7*x^5*sgn(b*x + a) + 4/11*a*b^3*x^11*e^7*sgn(b*x + a) + 14/5*a*b^3*d*x^10*e^6*sgn(b*x + a) + 28/3*a*b^3*d^2*x^9*e^5*sgn(b*x + a) + 35/2*a*b^3*d^3*x^8*e^4*sgn(b*x + a) + 20*a*b^3*d^4*x^7*e^3*sgn(b*x + a) + 14*a*b^3*d^5*x^6*e^2*sgn(b*x + a) + 28/5*a*b^3*d^6*x^5*e*sgn(b*x + a) + a*b^3*d^7*x^4*sgn(b*x + a) + 3/5*a^2*b^2*x^10*e^7*sgn(b*x + a) + 14/3*a^2*b^2*d*x^9*e^6*sgn(b*x + a) + 63/4*a^2*b^2*d^2*x^8*e^5*sgn(b*x + a) + 30*a^2*b^2*d^3*x^7*e^4*sgn(b*x + a) + 35*a^2*b^2*d^4*x^6*e^3*sgn(b*x + a) + 126/5*a^2*b^2*d^5*x^5*e^2*sgn(b*x + a) + 21/2*a^2*b^2*d^6*x^4*e*sgn(b*x + a) + 2*a^2*b^2*d^7*x^3*sgn(b*x + a) + 4/9*a^3*b*x^9*e^7*sgn(b*x + a) + 7/2*a^3*b*d*x^8*e^6*sgn(b*x + a) + 12*a^3*b*d^2*x^7*e^5*sgn(b*x + a) + 70/3*a^3*b*d^3*x^6*e^4*sgn(b*x + a) + 28*a^3*b*d^4*x^5*e^3*sgn(b*x + a) + 21*a^3*b*d^5*x^4*e^2*sgn(b*x + a) + 28/3*a^3*b*d^6*x^3*e*sgn(b*x + a) + 2*a^3*b*d^7*x^2*sgn(b*x + a) + 1/8*a^4*x^8*e^7*sgn(b*x + a) + a^4*d*x^7*e^6*sgn(b*x + a) + 7/2*a^4*d^2*x^6*e^5*sgn(b*x + a) + 7*a^4*d^3*x^5*e^4*sgn(b*x + a) + 35/4*a^4*d^4*x^4*e^3*sgn(b*x + a) + 7*a^4*d^5*x^3*e^2*sgn(b*x + a) + 7/2*a^4*d^6*x^2*e*sgn(b*x + a) + a^4*d^7*x*sgn(b*x + a)","B",0
1969,1,660,0,0.220098," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{11} \, b^{4} x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, b^{4} d x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, b^{4} d^{2} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, b^{4} d^{3} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, b^{4} d^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + b^{4} d^{5} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, b^{4} d^{6} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, a b^{3} x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{8}{3} \, a b^{3} d x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a b^{3} d^{2} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{80}{7} \, a b^{3} d^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a b^{3} d^{4} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{24}{5} \, a b^{3} d^{5} x^{5} e \mathrm{sgn}\left(b x + a\right) + a b^{3} d^{6} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, a^{2} b^{2} x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, a^{2} b^{2} d x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{90}{7} \, a^{2} b^{2} d^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{2} b^{2} d^{3} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b^{2} d^{4} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, a^{2} b^{2} d^{5} x^{4} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} d^{6} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{3} b x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{24}{7} \, a^{3} b d x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b d^{2} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 16 \, a^{3} b d^{3} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{3} b d^{4} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a^{3} b d^{5} x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d^{6} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, a^{4} x^{7} e^{6} \mathrm{sgn}\left(b x + a\right) + a^{4} d x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{4} d^{2} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} d^{3} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} d^{4} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{4} d^{5} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{4} d^{6} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/11*b^4*x^11*e^6*sgn(b*x + a) + 3/5*b^4*d*x^10*e^5*sgn(b*x + a) + 5/3*b^4*d^2*x^9*e^4*sgn(b*x + a) + 5/2*b^4*d^3*x^8*e^3*sgn(b*x + a) + 15/7*b^4*d^4*x^7*e^2*sgn(b*x + a) + b^4*d^5*x^6*e*sgn(b*x + a) + 1/5*b^4*d^6*x^5*sgn(b*x + a) + 2/5*a*b^3*x^10*e^6*sgn(b*x + a) + 8/3*a*b^3*d*x^9*e^5*sgn(b*x + a) + 15/2*a*b^3*d^2*x^8*e^4*sgn(b*x + a) + 80/7*a*b^3*d^3*x^7*e^3*sgn(b*x + a) + 10*a*b^3*d^4*x^6*e^2*sgn(b*x + a) + 24/5*a*b^3*d^5*x^5*e*sgn(b*x + a) + a*b^3*d^6*x^4*sgn(b*x + a) + 2/3*a^2*b^2*x^9*e^6*sgn(b*x + a) + 9/2*a^2*b^2*d*x^8*e^5*sgn(b*x + a) + 90/7*a^2*b^2*d^2*x^7*e^4*sgn(b*x + a) + 20*a^2*b^2*d^3*x^6*e^3*sgn(b*x + a) + 18*a^2*b^2*d^4*x^5*e^2*sgn(b*x + a) + 9*a^2*b^2*d^5*x^4*e*sgn(b*x + a) + 2*a^2*b^2*d^6*x^3*sgn(b*x + a) + 1/2*a^3*b*x^8*e^6*sgn(b*x + a) + 24/7*a^3*b*d*x^7*e^5*sgn(b*x + a) + 10*a^3*b*d^2*x^6*e^4*sgn(b*x + a) + 16*a^3*b*d^3*x^5*e^3*sgn(b*x + a) + 15*a^3*b*d^4*x^4*e^2*sgn(b*x + a) + 8*a^3*b*d^5*x^3*e*sgn(b*x + a) + 2*a^3*b*d^6*x^2*sgn(b*x + a) + 1/7*a^4*x^7*e^6*sgn(b*x + a) + a^4*d*x^6*e^5*sgn(b*x + a) + 3*a^4*d^2*x^5*e^4*sgn(b*x + a) + 5*a^4*d^3*x^4*e^3*sgn(b*x + a) + 5*a^4*d^4*x^3*e^2*sgn(b*x + a) + 3*a^4*d^5*x^2*e*sgn(b*x + a) + a^4*d^6*x*sgn(b*x + a)","B",0
1970,1,561,0,0.190429," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{10} \, b^{4} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, b^{4} d x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, b^{4} d^{2} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, b^{4} d^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, b^{4} d^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, b^{4} d^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{4}{9} \, a b^{3} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a b^{3} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{40}{7} \, a b^{3} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, a b^{3} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{3} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + a b^{3} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, a^{2} b^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, a^{2} b^{2} d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{2} d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{2} b^{2} d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a^{2} b^{2} d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{4}{7} \, a^{3} b x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} b d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 8 \, a^{3} b d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, a^{3} b d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, a^{4} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + a^{4} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{4} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{4} d^{5} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/10*b^4*x^10*e^5*sgn(b*x + a) + 5/9*b^4*d*x^9*e^4*sgn(b*x + a) + 5/4*b^4*d^2*x^8*e^3*sgn(b*x + a) + 10/7*b^4*d^3*x^7*e^2*sgn(b*x + a) + 5/6*b^4*d^4*x^6*e*sgn(b*x + a) + 1/5*b^4*d^5*x^5*sgn(b*x + a) + 4/9*a*b^3*x^9*e^5*sgn(b*x + a) + 5/2*a*b^3*d*x^8*e^4*sgn(b*x + a) + 40/7*a*b^3*d^2*x^7*e^3*sgn(b*x + a) + 20/3*a*b^3*d^3*x^6*e^2*sgn(b*x + a) + 4*a*b^3*d^4*x^5*e*sgn(b*x + a) + a*b^3*d^5*x^4*sgn(b*x + a) + 3/4*a^2*b^2*x^8*e^5*sgn(b*x + a) + 30/7*a^2*b^2*d*x^7*e^4*sgn(b*x + a) + 10*a^2*b^2*d^2*x^6*e^3*sgn(b*x + a) + 12*a^2*b^2*d^3*x^5*e^2*sgn(b*x + a) + 15/2*a^2*b^2*d^4*x^4*e*sgn(b*x + a) + 2*a^2*b^2*d^5*x^3*sgn(b*x + a) + 4/7*a^3*b*x^7*e^5*sgn(b*x + a) + 10/3*a^3*b*d*x^6*e^4*sgn(b*x + a) + 8*a^3*b*d^2*x^5*e^3*sgn(b*x + a) + 10*a^3*b*d^3*x^4*e^2*sgn(b*x + a) + 20/3*a^3*b*d^4*x^3*e*sgn(b*x + a) + 2*a^3*b*d^5*x^2*sgn(b*x + a) + 1/6*a^4*x^6*e^5*sgn(b*x + a) + a^4*d*x^5*e^4*sgn(b*x + a) + 5/2*a^4*d^2*x^4*e^3*sgn(b*x + a) + 10/3*a^4*d^3*x^3*e^2*sgn(b*x + a) + 5/2*a^4*d^4*x^2*e*sgn(b*x + a) + a^4*d^5*x*sgn(b*x + a)","B",0
1971,1,461,0,0.194536," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, b^{4} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b^{4} d x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, b^{4} d^{2} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, b^{4} d^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, b^{4} d^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a b^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{16}{7} \, a b^{3} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{3} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{16}{5} \, a b^{3} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + a b^{3} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, a^{2} b^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{2} b^{2} d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{36}{5} \, a^{2} b^{2} d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, a^{3} b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{16}{5} \, a^{3} b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{3} b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{16}{3} \, a^{3} b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a^{4} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + a^{4} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{4} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{4} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{4} d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/9*b^4*x^9*e^4*sgn(b*x + a) + 1/2*b^4*d*x^8*e^3*sgn(b*x + a) + 6/7*b^4*d^2*x^7*e^2*sgn(b*x + a) + 2/3*b^4*d^3*x^6*e*sgn(b*x + a) + 1/5*b^4*d^4*x^5*sgn(b*x + a) + 1/2*a*b^3*x^8*e^4*sgn(b*x + a) + 16/7*a*b^3*d*x^7*e^3*sgn(b*x + a) + 4*a*b^3*d^2*x^6*e^2*sgn(b*x + a) + 16/5*a*b^3*d^3*x^5*e*sgn(b*x + a) + a*b^3*d^4*x^4*sgn(b*x + a) + 6/7*a^2*b^2*x^7*e^4*sgn(b*x + a) + 4*a^2*b^2*d*x^6*e^3*sgn(b*x + a) + 36/5*a^2*b^2*d^2*x^5*e^2*sgn(b*x + a) + 6*a^2*b^2*d^3*x^4*e*sgn(b*x + a) + 2*a^2*b^2*d^4*x^3*sgn(b*x + a) + 2/3*a^3*b*x^6*e^4*sgn(b*x + a) + 16/5*a^3*b*d*x^5*e^3*sgn(b*x + a) + 6*a^3*b*d^2*x^4*e^2*sgn(b*x + a) + 16/3*a^3*b*d^3*x^3*e*sgn(b*x + a) + 2*a^3*b*d^4*x^2*sgn(b*x + a) + 1/5*a^4*x^5*e^4*sgn(b*x + a) + a^4*d*x^4*e^3*sgn(b*x + a) + 2*a^4*d^2*x^3*e^2*sgn(b*x + a) + 2*a^4*d^3*x^2*e*sgn(b*x + a) + a^4*d^4*x*sgn(b*x + a)","B",0
1972,1,360,0,0.205059," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, b^{4} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, b^{4} d x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b^{4} d^{2} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, b^{4} d^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{4}{7} \, a b^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a b^{3} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{12}{5} \, a b^{3} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + a b^{3} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + a^{2} b^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{18}{5} \, a^{2} b^{2} d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, a^{2} b^{2} d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, a^{3} b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{3} b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a^{4} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{4} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{4} d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/8*b^4*x^8*e^3*sgn(b*x + a) + 3/7*b^4*d*x^7*e^2*sgn(b*x + a) + 1/2*b^4*d^2*x^6*e*sgn(b*x + a) + 1/5*b^4*d^3*x^5*sgn(b*x + a) + 4/7*a*b^3*x^7*e^3*sgn(b*x + a) + 2*a*b^3*d*x^6*e^2*sgn(b*x + a) + 12/5*a*b^3*d^2*x^5*e*sgn(b*x + a) + a*b^3*d^3*x^4*sgn(b*x + a) + a^2*b^2*x^6*e^3*sgn(b*x + a) + 18/5*a^2*b^2*d*x^5*e^2*sgn(b*x + a) + 9/2*a^2*b^2*d^2*x^4*e*sgn(b*x + a) + 2*a^2*b^2*d^3*x^3*sgn(b*x + a) + 4/5*a^3*b*x^5*e^3*sgn(b*x + a) + 3*a^3*b*d*x^4*e^2*sgn(b*x + a) + 4*a^3*b*d^2*x^3*e*sgn(b*x + a) + 2*a^3*b*d^3*x^2*sgn(b*x + a) + 1/4*a^4*x^4*e^3*sgn(b*x + a) + a^4*d*x^3*e^2*sgn(b*x + a) + 3/2*a^4*d^2*x^2*e*sgn(b*x + a) + a^4*d^3*x*sgn(b*x + a)","B",0
1973,1,260,0,0.175036," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, b^{4} d x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, b^{4} d^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, a b^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{8}{5} \, a b^{3} d x^{5} e \mathrm{sgn}\left(b x + a\right) + a b^{3} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, a^{2} b^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{2} d x^{4} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + a^{3} b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{8}{3} \, a^{3} b d x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a^{4} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + a^{4} d x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{4} d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/7*b^4*x^7*e^2*sgn(b*x + a) + 1/3*b^4*d*x^6*e*sgn(b*x + a) + 1/5*b^4*d^2*x^5*sgn(b*x + a) + 2/3*a*b^3*x^6*e^2*sgn(b*x + a) + 8/5*a*b^3*d*x^5*e*sgn(b*x + a) + a*b^3*d^2*x^4*sgn(b*x + a) + 6/5*a^2*b^2*x^5*e^2*sgn(b*x + a) + 3*a^2*b^2*d*x^4*e*sgn(b*x + a) + 2*a^2*b^2*d^2*x^3*sgn(b*x + a) + a^3*b*x^4*e^2*sgn(b*x + a) + 8/3*a^3*b*d*x^3*e*sgn(b*x + a) + 2*a^3*b*d^2*x^2*sgn(b*x + a) + 1/3*a^4*x^3*e^2*sgn(b*x + a) + a^4*d*x^2*e*sgn(b*x + a) + a^4*d^2*x*sgn(b*x + a)","B",0
1974,1,162,0,0.180914," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, b^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, b^{4} d x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, a b^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + a b^{3} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} b^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} d x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, a^{3} b x^{3} e \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{4} d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*b^4*x^6*e*sgn(b*x + a) + 1/5*b^4*d*x^5*sgn(b*x + a) + 4/5*a*b^3*x^5*e*sgn(b*x + a) + a*b^3*d*x^4*sgn(b*x + a) + 3/2*a^2*b^2*x^4*e*sgn(b*x + a) + 2*a^2*b^2*d*x^3*sgn(b*x + a) + 4/3*a^3*b*x^3*e*sgn(b*x + a) + 2*a^3*b*d*x^2*sgn(b*x + a) + 1/2*a^4*x^2*e*sgn(b*x + a) + a^4*d*x*sgn(b*x + a)","B",0
1975,1,86,0,0.198539," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{5} \, b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + a b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b x^{2} \mathrm{sgn}\left(b x + a\right) + a^{4} x \mathrm{sgn}\left(b x + a\right) + \frac{a^{5} \mathrm{sgn}\left(b x + a\right)}{5 \, b}"," ",0,"1/5*b^4*x^5*sgn(b*x + a) + a*b^3*x^4*sgn(b*x + a) + 2*a^2*b^2*x^3*sgn(b*x + a) + 2*a^3*b*x^2*sgn(b*x + a) + a^4*x*sgn(b*x + a) + 1/5*a^5*sgn(b*x + a)/b","B",0
1976,1,266,0,0.173490," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d),x, algorithm=""giac"")","{\left(b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, b^{4} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) - 4 \, b^{4} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, b^{4} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) - 12 \, b^{4} d^{3} x \mathrm{sgn}\left(b x + a\right) + 16 \, a b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 24 \, a b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 48 \, a b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + 36 \, a^{2} b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 72 \, a^{2} b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 48 \, a^{3} b x e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}"," ",0,"(b^4*d^4*sgn(b*x + a) - 4*a*b^3*d^3*e*sgn(b*x + a) + 6*a^2*b^2*d^2*e^2*sgn(b*x + a) - 4*a^3*b*d*e^3*sgn(b*x + a) + a^4*e^4*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) + 1/12*(3*b^4*x^4*e^3*sgn(b*x + a) - 4*b^4*d*x^3*e^2*sgn(b*x + a) + 6*b^4*d^2*x^2*e*sgn(b*x + a) - 12*b^4*d^3*x*sgn(b*x + a) + 16*a*b^3*x^3*e^3*sgn(b*x + a) - 24*a*b^3*d*x^2*e^2*sgn(b*x + a) + 48*a*b^3*d^2*x*e*sgn(b*x + a) + 36*a^2*b^2*x^2*e^3*sgn(b*x + a) - 72*a^2*b^2*d*x*e^2*sgn(b*x + a) + 48*a^3*b*x*e^3*sgn(b*x + a))*e^(-4)","A",0
1977,1,268,0,0.208277," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","-4 \, {\left(b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{3} \, {\left(b^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, b^{4} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 9 \, b^{4} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 24 \, a b^{3} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b^{2} x e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} - \frac{{\left(b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{x e + d}"," ",0,"-4*(b^4*d^3*sgn(b*x + a) - 3*a*b^3*d^2*e*sgn(b*x + a) + 3*a^2*b^2*d*e^2*sgn(b*x + a) - a^3*b*e^3*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) + 1/3*(b^4*x^3*e^4*sgn(b*x + a) - 3*b^4*d*x^2*e^3*sgn(b*x + a) + 9*b^4*d^2*x*e^2*sgn(b*x + a) + 6*a*b^3*x^2*e^4*sgn(b*x + a) - 24*a*b^3*d*x*e^3*sgn(b*x + a) + 18*a^2*b^2*x*e^4*sgn(b*x + a))*e^(-6) - (b^4*d^4*sgn(b*x + a) - 4*a*b^3*d^3*e*sgn(b*x + a) + 6*a^2*b^2*d^2*e^2*sgn(b*x + a) - 4*a^3*b*d*e^3*sgn(b*x + a) + a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)","A",0
1978,1,265,0,0.175410," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","6 \, {\left(b^{4} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{3} d e \mathrm{sgn}\left(b x + a\right) + a^{2} b^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{4} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, b^{4} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a b^{3} x e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} + \frac{{\left(7 \, b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 20 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) - a^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 8 \, {\left(b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - a^{3} b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"6*(b^4*d^2*sgn(b*x + a) - 2*a*b^3*d*e*sgn(b*x + a) + a^2*b^2*e^2*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) + 1/2*(b^4*x^2*e^3*sgn(b*x + a) - 6*b^4*d*x*e^2*sgn(b*x + a) + 8*a*b^3*x*e^3*sgn(b*x + a))*e^(-6) + 1/2*(7*b^4*d^4*sgn(b*x + a) - 20*a*b^3*d^3*e*sgn(b*x + a) + 18*a^2*b^2*d^2*e^2*sgn(b*x + a) - 4*a^3*b*d*e^3*sgn(b*x + a) - a^4*e^4*sgn(b*x + a) + 8*(b^4*d^3*e*sgn(b*x + a) - 3*a*b^3*d^2*e^2*sgn(b*x + a) + 3*a^2*b^2*d*e^3*sgn(b*x + a) - a^3*b*e^4*sgn(b*x + a))*x)*e^(-5)/(x*e + d)^2","A",0
1979,1,260,0,0.197500," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","b^{4} x e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) - 4 \, {\left(b^{4} d \mathrm{sgn}\left(b x + a\right) - a b^{3} e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(13 \, b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 22 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{2} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 6 \, {\left(5 \, b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) - 9 \, a b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{3} b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"b^4*x*e^(-4)*sgn(b*x + a) - 4*(b^4*d*sgn(b*x + a) - a*b^3*e*sgn(b*x + a))*e^(-5)*log(abs(x*e + d)) - 1/3*(13*b^4*d^4*sgn(b*x + a) - 22*a*b^3*d^3*e*sgn(b*x + a) + 6*a^2*b^2*d^2*e^2*sgn(b*x + a) + 2*a^3*b*d*e^3*sgn(b*x + a) + a^4*e^4*sgn(b*x + a) + 18*(b^4*d^2*e^2*sgn(b*x + a) - 2*a*b^3*d*e^3*sgn(b*x + a) + a^2*b^2*e^4*sgn(b*x + a))*x^2 + 6*(5*b^4*d^3*e*sgn(b*x + a) - 9*a*b^3*d^2*e^2*sgn(b*x + a) + 3*a^2*b^2*d*e^3*sgn(b*x + a) + a^3*b*e^4*sgn(b*x + a))*x)*e^(-5)/(x*e + d)^3","A",0
1980,1,268,0,0.174057," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","b^{4} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(48 \, {\left(b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) - a b^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 36 \, {\left(3 \, b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{2} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 8 \, {\left(11 \, b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(25 \, b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) - 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-4\right)}}{12 \, {\left(x e + d\right)}^{4}}"," ",0,"b^4*e^(-5)*log(abs(x*e + d))*sgn(b*x + a) + 1/12*(48*(b^4*d*e^2*sgn(b*x + a) - a*b^3*e^3*sgn(b*x + a))*x^3 + 36*(3*b^4*d^2*e*sgn(b*x + a) - 2*a*b^3*d*e^2*sgn(b*x + a) - a^2*b^2*e^3*sgn(b*x + a))*x^2 + 8*(11*b^4*d^3*sgn(b*x + a) - 6*a*b^3*d^2*e*sgn(b*x + a) - 3*a^2*b^2*d*e^2*sgn(b*x + a) - 2*a^3*b*e^3*sgn(b*x + a))*x + (25*b^4*d^4*sgn(b*x + a) - 12*a*b^3*d^3*e*sgn(b*x + a) - 6*a^2*b^2*d^2*e^2*sgn(b*x + a) - 4*a^3*b*d*e^3*sgn(b*x + a) - 3*a^4*e^4*sgn(b*x + a))*e^(-1))*e^(-4)/(x*e + d)^4","A",0
1981,1,260,0,0.205368," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(5 \, b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{2} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b x e^{4} \mathrm{sgn}\left(b x + a\right) + a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{5 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/5*(5*b^4*x^4*e^4*sgn(b*x + a) + 10*b^4*d*x^3*e^3*sgn(b*x + a) + 10*b^4*d^2*x^2*e^2*sgn(b*x + a) + 5*b^4*d^3*x*e*sgn(b*x + a) + b^4*d^4*sgn(b*x + a) + 10*a*b^3*x^3*e^4*sgn(b*x + a) + 10*a*b^3*d*x^2*e^3*sgn(b*x + a) + 5*a*b^3*d^2*x*e^2*sgn(b*x + a) + a*b^3*d^3*e*sgn(b*x + a) + 10*a^2*b^2*x^2*e^4*sgn(b*x + a) + 5*a^2*b^2*d*x*e^3*sgn(b*x + a) + a^2*b^2*d^2*e^2*sgn(b*x + a) + 5*a^3*b*x*e^4*sgn(b*x + a) + a^3*b*d*e^3*sgn(b*x + a) + a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^5","B",0
1982,1,264,0,0.207679," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(15 \, b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 40 \, a b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 30 \, a b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, a b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 45 \, a^{2} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 24 \, a^{3} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{30 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/30*(15*b^4*x^4*e^4*sgn(b*x + a) + 20*b^4*d*x^3*e^3*sgn(b*x + a) + 15*b^4*d^2*x^2*e^2*sgn(b*x + a) + 6*b^4*d^3*x*e*sgn(b*x + a) + b^4*d^4*sgn(b*x + a) + 40*a*b^3*x^3*e^4*sgn(b*x + a) + 30*a*b^3*d*x^2*e^3*sgn(b*x + a) + 12*a*b^3*d^2*x*e^2*sgn(b*x + a) + 2*a*b^3*d^3*e*sgn(b*x + a) + 45*a^2*b^2*x^2*e^4*sgn(b*x + a) + 18*a^2*b^2*d*x*e^3*sgn(b*x + a) + 3*a^2*b^2*d^2*e^2*sgn(b*x + a) + 24*a^3*b*x*e^4*sgn(b*x + a) + 4*a^3*b*d*e^3*sgn(b*x + a) + 5*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^6","B",0
1983,1,264,0,0.172818," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(35 \, b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, a b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 63 \, a b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, a b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 126 \, a^{2} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 42 \, a^{2} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{3} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{105 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/105*(35*b^4*x^4*e^4*sgn(b*x + a) + 35*b^4*d*x^3*e^3*sgn(b*x + a) + 21*b^4*d^2*x^2*e^2*sgn(b*x + a) + 7*b^4*d^3*x*e*sgn(b*x + a) + b^4*d^4*sgn(b*x + a) + 105*a*b^3*x^3*e^4*sgn(b*x + a) + 63*a*b^3*d*x^2*e^3*sgn(b*x + a) + 21*a*b^3*d^2*x*e^2*sgn(b*x + a) + 3*a*b^3*d^3*e*sgn(b*x + a) + 126*a^2*b^2*x^2*e^4*sgn(b*x + a) + 42*a^2*b^2*d*x*e^3*sgn(b*x + a) + 6*a^2*b^2*d^2*e^2*sgn(b*x + a) + 70*a^3*b*x*e^4*sgn(b*x + a) + 10*a^3*b*d*e^3*sgn(b*x + a) + 15*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^7","B",0
1984,1,264,0,0.204556," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(70 \, b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 224 \, a b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 112 \, a b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 32 \, a b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 280 \, a^{2} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 80 \, a^{2} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 160 \, a^{3} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(70*b^4*x^4*e^4*sgn(b*x + a) + 56*b^4*d*x^3*e^3*sgn(b*x + a) + 28*b^4*d^2*x^2*e^2*sgn(b*x + a) + 8*b^4*d^3*x*e*sgn(b*x + a) + b^4*d^4*sgn(b*x + a) + 224*a*b^3*x^3*e^4*sgn(b*x + a) + 112*a*b^3*d*x^2*e^3*sgn(b*x + a) + 32*a*b^3*d^2*x*e^2*sgn(b*x + a) + 4*a*b^3*d^3*e*sgn(b*x + a) + 280*a^2*b^2*x^2*e^4*sgn(b*x + a) + 80*a^2*b^2*d*x*e^3*sgn(b*x + a) + 10*a^2*b^2*d^2*e^2*sgn(b*x + a) + 160*a^3*b*x*e^4*sgn(b*x + a) + 20*a^3*b*d*e^3*sgn(b*x + a) + 35*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^8","A",0
1985,1,264,0,0.172185," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(126 \, b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 420 \, a b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, a b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, a b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 540 \, a^{2} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 135 \, a^{2} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 315 \, a^{3} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{630 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/630*(126*b^4*x^4*e^4*sgn(b*x + a) + 84*b^4*d*x^3*e^3*sgn(b*x + a) + 36*b^4*d^2*x^2*e^2*sgn(b*x + a) + 9*b^4*d^3*x*e*sgn(b*x + a) + b^4*d^4*sgn(b*x + a) + 420*a*b^3*x^3*e^4*sgn(b*x + a) + 180*a*b^3*d*x^2*e^3*sgn(b*x + a) + 45*a*b^3*d^2*x*e^2*sgn(b*x + a) + 5*a*b^3*d^3*e*sgn(b*x + a) + 540*a^2*b^2*x^2*e^4*sgn(b*x + a) + 135*a^2*b^2*d*x*e^3*sgn(b*x + a) + 15*a^2*b^2*d^2*e^2*sgn(b*x + a) + 315*a^3*b*x*e^4*sgn(b*x + a) + 35*a^3*b*d*e^3*sgn(b*x + a) + 70*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^9","A",0
1986,1,264,0,0.197755," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(210 \, b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 120 \, b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 720 \, a b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 270 \, a b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, a b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 945 \, a^{2} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 210 \, a^{2} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 560 \, a^{3} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 126 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{1260 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/1260*(210*b^4*x^4*e^4*sgn(b*x + a) + 120*b^4*d*x^3*e^3*sgn(b*x + a) + 45*b^4*d^2*x^2*e^2*sgn(b*x + a) + 10*b^4*d^3*x*e*sgn(b*x + a) + b^4*d^4*sgn(b*x + a) + 720*a*b^3*x^3*e^4*sgn(b*x + a) + 270*a*b^3*d*x^2*e^3*sgn(b*x + a) + 60*a*b^3*d^2*x*e^2*sgn(b*x + a) + 6*a*b^3*d^3*e*sgn(b*x + a) + 945*a^2*b^2*x^2*e^4*sgn(b*x + a) + 210*a^2*b^2*d*x*e^3*sgn(b*x + a) + 21*a^2*b^2*d^2*e^2*sgn(b*x + a) + 560*a^3*b*x*e^4*sgn(b*x + a) + 56*a^3*b*d*e^3*sgn(b*x + a) + 126*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^10","A",0
1987,1,264,0,0.171608," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(330 \, b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 165 \, b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 55 \, b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 11 \, b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 1155 \, a b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 385 \, a b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 77 \, a b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 1540 \, a^{2} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 308 \, a^{2} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 924 \, a^{3} b x e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 210 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{2310 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/2310*(330*b^4*x^4*e^4*sgn(b*x + a) + 165*b^4*d*x^3*e^3*sgn(b*x + a) + 55*b^4*d^2*x^2*e^2*sgn(b*x + a) + 11*b^4*d^3*x*e*sgn(b*x + a) + b^4*d^4*sgn(b*x + a) + 1155*a*b^3*x^3*e^4*sgn(b*x + a) + 385*a*b^3*d*x^2*e^3*sgn(b*x + a) + 77*a*b^3*d^2*x*e^2*sgn(b*x + a) + 7*a*b^3*d^3*e*sgn(b*x + a) + 1540*a^2*b^2*x^2*e^4*sgn(b*x + a) + 308*a^2*b^2*d*x*e^3*sgn(b*x + a) + 28*a^2*b^2*d^2*e^2*sgn(b*x + a) + 924*a^3*b*x*e^4*sgn(b*x + a) + 84*a^3*b*d*e^3*sgn(b*x + a) + 210*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^11","A",0
1988,1,1387,0,0.288050," ","integrate((b*x+a)*(e*x+d)^9*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{16} \, b^{6} x^{16} e^{9} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, b^{6} d x^{15} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{18}{7} \, b^{6} d^{2} x^{14} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{84}{13} \, b^{6} d^{3} x^{13} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{21}{2} \, b^{6} d^{4} x^{12} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{126}{11} \, b^{6} d^{5} x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{42}{5} \, b^{6} d^{6} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, b^{6} d^{7} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{8} \, b^{6} d^{8} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{9} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, a b^{5} x^{15} e^{9} \mathrm{sgn}\left(b x + a\right) + \frac{27}{7} \, a b^{5} d x^{14} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{216}{13} \, a b^{5} d^{2} x^{13} e^{7} \mathrm{sgn}\left(b x + a\right) + 42 \, a b^{5} d^{3} x^{12} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{756}{11} \, a b^{5} d^{4} x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{378}{5} \, a b^{5} d^{5} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, a b^{5} d^{6} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + 27 \, a b^{5} d^{7} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{54}{7} \, a b^{5} d^{8} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{9} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{15}{14} \, a^{2} b^{4} x^{14} e^{9} \mathrm{sgn}\left(b x + a\right) + \frac{135}{13} \, a^{2} b^{4} d x^{13} e^{8} \mathrm{sgn}\left(b x + a\right) + 45 \, a^{2} b^{4} d^{2} x^{12} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1260}{11} \, a^{2} b^{4} d^{3} x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + 189 \, a^{2} b^{4} d^{4} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, a^{2} b^{4} d^{5} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{315}{2} \, a^{2} b^{4} d^{6} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{540}{7} \, a^{2} b^{4} d^{7} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{45}{2} \, a^{2} b^{4} d^{8} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{9} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{20}{13} \, a^{3} b^{3} x^{13} e^{9} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{3} b^{3} d x^{12} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{720}{11} \, a^{3} b^{3} d^{2} x^{11} e^{7} \mathrm{sgn}\left(b x + a\right) + 168 \, a^{3} b^{3} d^{3} x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + 280 \, a^{3} b^{3} d^{4} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + 315 \, a^{3} b^{3} d^{5} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + 240 \, a^{3} b^{3} d^{6} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 120 \, a^{3} b^{3} d^{7} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 36 \, a^{3} b^{3} d^{8} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{9} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{4} b^{2} x^{12} e^{9} \mathrm{sgn}\left(b x + a\right) + \frac{135}{11} \, a^{4} b^{2} d x^{11} e^{8} \mathrm{sgn}\left(b x + a\right) + 54 \, a^{4} b^{2} d^{2} x^{10} e^{7} \mathrm{sgn}\left(b x + a\right) + 140 \, a^{4} b^{2} d^{3} x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{945}{4} \, a^{4} b^{2} d^{4} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + 270 \, a^{4} b^{2} d^{5} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 210 \, a^{4} b^{2} d^{6} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 108 \, a^{4} b^{2} d^{7} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{135}{4} \, a^{4} b^{2} d^{8} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{9} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{6}{11} \, a^{5} b x^{11} e^{9} \mathrm{sgn}\left(b x + a\right) + \frac{27}{5} \, a^{5} b d x^{10} e^{8} \mathrm{sgn}\left(b x + a\right) + 24 \, a^{5} b d^{2} x^{9} e^{7} \mathrm{sgn}\left(b x + a\right) + 63 \, a^{5} b d^{3} x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + 108 \, a^{5} b d^{4} x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, a^{5} b d^{5} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{504}{5} \, a^{5} b d^{6} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 54 \, a^{5} b d^{7} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{5} b d^{8} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{9} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{10} \, a^{6} x^{10} e^{9} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{9} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, a^{6} d^{2} x^{8} e^{7} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{6} d^{3} x^{7} e^{6} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{6} d^{4} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{126}{5} \, a^{6} d^{5} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{6} d^{6} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{6} d^{7} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, a^{6} d^{8} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{9} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/16*b^6*x^16*e^9*sgn(b*x + a) + 3/5*b^6*d*x^15*e^8*sgn(b*x + a) + 18/7*b^6*d^2*x^14*e^7*sgn(b*x + a) + 84/13*b^6*d^3*x^13*e^6*sgn(b*x + a) + 21/2*b^6*d^4*x^12*e^5*sgn(b*x + a) + 126/11*b^6*d^5*x^11*e^4*sgn(b*x + a) + 42/5*b^6*d^6*x^10*e^3*sgn(b*x + a) + 4*b^6*d^7*x^9*e^2*sgn(b*x + a) + 9/8*b^6*d^8*x^8*e*sgn(b*x + a) + 1/7*b^6*d^9*x^7*sgn(b*x + a) + 2/5*a*b^5*x^15*e^9*sgn(b*x + a) + 27/7*a*b^5*d*x^14*e^8*sgn(b*x + a) + 216/13*a*b^5*d^2*x^13*e^7*sgn(b*x + a) + 42*a*b^5*d^3*x^12*e^6*sgn(b*x + a) + 756/11*a*b^5*d^4*x^11*e^5*sgn(b*x + a) + 378/5*a*b^5*d^5*x^10*e^4*sgn(b*x + a) + 56*a*b^5*d^6*x^9*e^3*sgn(b*x + a) + 27*a*b^5*d^7*x^8*e^2*sgn(b*x + a) + 54/7*a*b^5*d^8*x^7*e*sgn(b*x + a) + a*b^5*d^9*x^6*sgn(b*x + a) + 15/14*a^2*b^4*x^14*e^9*sgn(b*x + a) + 135/13*a^2*b^4*d*x^13*e^8*sgn(b*x + a) + 45*a^2*b^4*d^2*x^12*e^7*sgn(b*x + a) + 1260/11*a^2*b^4*d^3*x^11*e^6*sgn(b*x + a) + 189*a^2*b^4*d^4*x^10*e^5*sgn(b*x + a) + 210*a^2*b^4*d^5*x^9*e^4*sgn(b*x + a) + 315/2*a^2*b^4*d^6*x^8*e^3*sgn(b*x + a) + 540/7*a^2*b^4*d^7*x^7*e^2*sgn(b*x + a) + 45/2*a^2*b^4*d^8*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^9*x^5*sgn(b*x + a) + 20/13*a^3*b^3*x^13*e^9*sgn(b*x + a) + 15*a^3*b^3*d*x^12*e^8*sgn(b*x + a) + 720/11*a^3*b^3*d^2*x^11*e^7*sgn(b*x + a) + 168*a^3*b^3*d^3*x^10*e^6*sgn(b*x + a) + 280*a^3*b^3*d^4*x^9*e^5*sgn(b*x + a) + 315*a^3*b^3*d^5*x^8*e^4*sgn(b*x + a) + 240*a^3*b^3*d^6*x^7*e^3*sgn(b*x + a) + 120*a^3*b^3*d^7*x^6*e^2*sgn(b*x + a) + 36*a^3*b^3*d^8*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^9*x^4*sgn(b*x + a) + 5/4*a^4*b^2*x^12*e^9*sgn(b*x + a) + 135/11*a^4*b^2*d*x^11*e^8*sgn(b*x + a) + 54*a^4*b^2*d^2*x^10*e^7*sgn(b*x + a) + 140*a^4*b^2*d^3*x^9*e^6*sgn(b*x + a) + 945/4*a^4*b^2*d^4*x^8*e^5*sgn(b*x + a) + 270*a^4*b^2*d^5*x^7*e^4*sgn(b*x + a) + 210*a^4*b^2*d^6*x^6*e^3*sgn(b*x + a) + 108*a^4*b^2*d^7*x^5*e^2*sgn(b*x + a) + 135/4*a^4*b^2*d^8*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^9*x^3*sgn(b*x + a) + 6/11*a^5*b*x^11*e^9*sgn(b*x + a) + 27/5*a^5*b*d*x^10*e^8*sgn(b*x + a) + 24*a^5*b*d^2*x^9*e^7*sgn(b*x + a) + 63*a^5*b*d^3*x^8*e^6*sgn(b*x + a) + 108*a^5*b*d^4*x^7*e^5*sgn(b*x + a) + 126*a^5*b*d^5*x^6*e^4*sgn(b*x + a) + 504/5*a^5*b*d^6*x^5*e^3*sgn(b*x + a) + 54*a^5*b*d^7*x^4*e^2*sgn(b*x + a) + 18*a^5*b*d^8*x^3*e*sgn(b*x + a) + 3*a^5*b*d^9*x^2*sgn(b*x + a) + 1/10*a^6*x^10*e^9*sgn(b*x + a) + a^6*d*x^9*e^8*sgn(b*x + a) + 9/2*a^6*d^2*x^8*e^7*sgn(b*x + a) + 12*a^6*d^3*x^7*e^6*sgn(b*x + a) + 21*a^6*d^4*x^6*e^5*sgn(b*x + a) + 126/5*a^6*d^5*x^5*e^4*sgn(b*x + a) + 21*a^6*d^6*x^4*e^3*sgn(b*x + a) + 12*a^6*d^7*x^3*e^2*sgn(b*x + a) + 9/2*a^6*d^8*x^2*e*sgn(b*x + a) + a^6*d^9*x*sgn(b*x + a)","B",0
1989,1,1242,0,0.236468," ","integrate((b*x+a)*(e*x+d)^8*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{15} \, b^{6} x^{15} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{4}{7} \, b^{6} d x^{14} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{28}{13} \, b^{6} d^{2} x^{13} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{14}{3} \, b^{6} d^{3} x^{12} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{70}{11} \, b^{6} d^{4} x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{28}{5} \, b^{6} d^{5} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{28}{9} \, b^{6} d^{6} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + b^{6} d^{7} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{8} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, a b^{5} x^{14} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{48}{13} \, a b^{5} d x^{13} e^{7} \mathrm{sgn}\left(b x + a\right) + 14 \, a b^{5} d^{2} x^{12} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{336}{11} \, a b^{5} d^{3} x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + 42 \, a b^{5} d^{4} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{112}{3} \, a b^{5} d^{5} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, a b^{5} d^{6} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{48}{7} \, a b^{5} d^{7} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{8} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{15}{13} \, a^{2} b^{4} x^{13} e^{8} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{4} d x^{12} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{420}{11} \, a^{2} b^{4} d^{2} x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{2} b^{4} d^{3} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{350}{3} \, a^{2} b^{4} d^{4} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, a^{2} b^{4} d^{5} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, a^{2} b^{4} d^{6} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{2} b^{4} d^{7} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{8} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{3} b^{3} x^{12} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{160}{11} \, a^{3} b^{3} d x^{11} e^{7} \mathrm{sgn}\left(b x + a\right) + 56 \, a^{3} b^{3} d^{2} x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1120}{9} \, a^{3} b^{3} d^{3} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + 175 \, a^{3} b^{3} d^{4} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + 160 \, a^{3} b^{3} d^{5} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{280}{3} \, a^{3} b^{3} d^{6} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 32 \, a^{3} b^{3} d^{7} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{8} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{15}{11} \, a^{4} b^{2} x^{11} e^{8} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{4} b^{2} d x^{10} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{140}{3} \, a^{4} b^{2} d^{2} x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + 105 \, a^{4} b^{2} d^{3} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + 150 \, a^{4} b^{2} d^{4} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 140 \, a^{4} b^{2} d^{5} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{4} b^{2} d^{6} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{4} b^{2} d^{7} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{8} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, a^{5} b x^{10} e^{8} \mathrm{sgn}\left(b x + a\right) + \frac{16}{3} \, a^{5} b d x^{9} e^{7} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{5} b d^{2} x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + 48 \, a^{5} b d^{3} x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{5} b d^{4} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{336}{5} \, a^{5} b d^{5} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 42 \, a^{5} b d^{6} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 16 \, a^{5} b d^{7} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{8} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{9} \, a^{6} x^{9} e^{8} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{8} e^{7} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{6} d^{2} x^{7} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{28}{3} \, a^{6} d^{3} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + 14 \, a^{6} d^{4} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + 14 \, a^{6} d^{5} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{28}{3} \, a^{6} d^{6} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{6} d^{7} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{8} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/15*b^6*x^15*e^8*sgn(b*x + a) + 4/7*b^6*d*x^14*e^7*sgn(b*x + a) + 28/13*b^6*d^2*x^13*e^6*sgn(b*x + a) + 14/3*b^6*d^3*x^12*e^5*sgn(b*x + a) + 70/11*b^6*d^4*x^11*e^4*sgn(b*x + a) + 28/5*b^6*d^5*x^10*e^3*sgn(b*x + a) + 28/9*b^6*d^6*x^9*e^2*sgn(b*x + a) + b^6*d^7*x^8*e*sgn(b*x + a) + 1/7*b^6*d^8*x^7*sgn(b*x + a) + 3/7*a*b^5*x^14*e^8*sgn(b*x + a) + 48/13*a*b^5*d*x^13*e^7*sgn(b*x + a) + 14*a*b^5*d^2*x^12*e^6*sgn(b*x + a) + 336/11*a*b^5*d^3*x^11*e^5*sgn(b*x + a) + 42*a*b^5*d^4*x^10*e^4*sgn(b*x + a) + 112/3*a*b^5*d^5*x^9*e^3*sgn(b*x + a) + 21*a*b^5*d^6*x^8*e^2*sgn(b*x + a) + 48/7*a*b^5*d^7*x^7*e*sgn(b*x + a) + a*b^5*d^8*x^6*sgn(b*x + a) + 15/13*a^2*b^4*x^13*e^8*sgn(b*x + a) + 10*a^2*b^4*d*x^12*e^7*sgn(b*x + a) + 420/11*a^2*b^4*d^2*x^11*e^6*sgn(b*x + a) + 84*a^2*b^4*d^3*x^10*e^5*sgn(b*x + a) + 350/3*a^2*b^4*d^4*x^9*e^4*sgn(b*x + a) + 105*a^2*b^4*d^5*x^8*e^3*sgn(b*x + a) + 60*a^2*b^4*d^6*x^7*e^2*sgn(b*x + a) + 20*a^2*b^4*d^7*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^8*x^5*sgn(b*x + a) + 5/3*a^3*b^3*x^12*e^8*sgn(b*x + a) + 160/11*a^3*b^3*d*x^11*e^7*sgn(b*x + a) + 56*a^3*b^3*d^2*x^10*e^6*sgn(b*x + a) + 1120/9*a^3*b^3*d^3*x^9*e^5*sgn(b*x + a) + 175*a^3*b^3*d^4*x^8*e^4*sgn(b*x + a) + 160*a^3*b^3*d^5*x^7*e^3*sgn(b*x + a) + 280/3*a^3*b^3*d^6*x^6*e^2*sgn(b*x + a) + 32*a^3*b^3*d^7*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^8*x^4*sgn(b*x + a) + 15/11*a^4*b^2*x^11*e^8*sgn(b*x + a) + 12*a^4*b^2*d*x^10*e^7*sgn(b*x + a) + 140/3*a^4*b^2*d^2*x^9*e^6*sgn(b*x + a) + 105*a^4*b^2*d^3*x^8*e^5*sgn(b*x + a) + 150*a^4*b^2*d^4*x^7*e^4*sgn(b*x + a) + 140*a^4*b^2*d^5*x^6*e^3*sgn(b*x + a) + 84*a^4*b^2*d^6*x^5*e^2*sgn(b*x + a) + 30*a^4*b^2*d^7*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^8*x^3*sgn(b*x + a) + 3/5*a^5*b*x^10*e^8*sgn(b*x + a) + 16/3*a^5*b*d*x^9*e^7*sgn(b*x + a) + 21*a^5*b*d^2*x^8*e^6*sgn(b*x + a) + 48*a^5*b*d^3*x^7*e^5*sgn(b*x + a) + 70*a^5*b*d^4*x^6*e^4*sgn(b*x + a) + 336/5*a^5*b*d^5*x^5*e^3*sgn(b*x + a) + 42*a^5*b*d^6*x^4*e^2*sgn(b*x + a) + 16*a^5*b*d^7*x^3*e*sgn(b*x + a) + 3*a^5*b*d^8*x^2*sgn(b*x + a) + 1/9*a^6*x^9*e^8*sgn(b*x + a) + a^6*d*x^8*e^7*sgn(b*x + a) + 4*a^6*d^2*x^7*e^6*sgn(b*x + a) + 28/3*a^6*d^3*x^6*e^5*sgn(b*x + a) + 14*a^6*d^4*x^5*e^4*sgn(b*x + a) + 14*a^6*d^5*x^4*e^3*sgn(b*x + a) + 28/3*a^6*d^6*x^3*e^2*sgn(b*x + a) + 4*a^6*d^7*x^2*e*sgn(b*x + a) + a^6*d^8*x*sgn(b*x + a)","B",0
1990,1,1099,0,0.281508," ","integrate((b*x+a)*(e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{14} \, b^{6} x^{14} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{7}{13} \, b^{6} d x^{13} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{7}{4} \, b^{6} d^{2} x^{12} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{35}{11} \, b^{6} d^{3} x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{7}{2} \, b^{6} d^{4} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{7}{3} \, b^{6} d^{5} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{7}{8} \, b^{6} d^{6} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{7} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{6}{13} \, a b^{5} x^{13} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{7}{2} \, a b^{5} d x^{12} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{126}{11} \, a b^{5} d^{2} x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + 21 \, a b^{5} d^{3} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{70}{3} \, a b^{5} d^{4} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{63}{4} \, a b^{5} d^{5} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{5} d^{6} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{7} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{2} b^{4} x^{12} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{105}{11} \, a^{2} b^{4} d x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{63}{2} \, a^{2} b^{4} d^{2} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{175}{3} \, a^{2} b^{4} d^{3} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{525}{8} \, a^{2} b^{4} d^{4} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, a^{2} b^{4} d^{5} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{35}{2} \, a^{2} b^{4} d^{6} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{7} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{20}{11} \, a^{3} b^{3} x^{11} e^{7} \mathrm{sgn}\left(b x + a\right) + 14 \, a^{3} b^{3} d x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{140}{3} \, a^{3} b^{3} d^{2} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{175}{2} \, a^{3} b^{3} d^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + 100 \, a^{3} b^{3} d^{4} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{3} b^{3} d^{5} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 28 \, a^{3} b^{3} d^{6} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{7} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{4} b^{2} x^{10} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{35}{3} \, a^{4} b^{2} d x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{315}{8} \, a^{4} b^{2} d^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + 75 \, a^{4} b^{2} d^{3} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{175}{2} \, a^{4} b^{2} d^{4} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 63 \, a^{4} b^{2} d^{5} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{105}{4} \, a^{4} b^{2} d^{6} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{7} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, a^{5} b x^{9} e^{7} \mathrm{sgn}\left(b x + a\right) + \frac{21}{4} \, a^{5} b d x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{5} b d^{2} x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{5} b d^{3} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 42 \, a^{5} b d^{4} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{63}{2} \, a^{5} b d^{5} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 14 \, a^{5} b d^{6} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{7} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{8} \, a^{6} x^{8} e^{7} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{7} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{7}{2} \, a^{6} d^{2} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{6} d^{3} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{35}{4} \, a^{6} d^{4} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{6} d^{5} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{7}{2} \, a^{6} d^{6} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{7} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/14*b^6*x^14*e^7*sgn(b*x + a) + 7/13*b^6*d*x^13*e^6*sgn(b*x + a) + 7/4*b^6*d^2*x^12*e^5*sgn(b*x + a) + 35/11*b^6*d^3*x^11*e^4*sgn(b*x + a) + 7/2*b^6*d^4*x^10*e^3*sgn(b*x + a) + 7/3*b^6*d^5*x^9*e^2*sgn(b*x + a) + 7/8*b^6*d^6*x^8*e*sgn(b*x + a) + 1/7*b^6*d^7*x^7*sgn(b*x + a) + 6/13*a*b^5*x^13*e^7*sgn(b*x + a) + 7/2*a*b^5*d*x^12*e^6*sgn(b*x + a) + 126/11*a*b^5*d^2*x^11*e^5*sgn(b*x + a) + 21*a*b^5*d^3*x^10*e^4*sgn(b*x + a) + 70/3*a*b^5*d^4*x^9*e^3*sgn(b*x + a) + 63/4*a*b^5*d^5*x^8*e^2*sgn(b*x + a) + 6*a*b^5*d^6*x^7*e*sgn(b*x + a) + a*b^5*d^7*x^6*sgn(b*x + a) + 5/4*a^2*b^4*x^12*e^7*sgn(b*x + a) + 105/11*a^2*b^4*d*x^11*e^6*sgn(b*x + a) + 63/2*a^2*b^4*d^2*x^10*e^5*sgn(b*x + a) + 175/3*a^2*b^4*d^3*x^9*e^4*sgn(b*x + a) + 525/8*a^2*b^4*d^4*x^8*e^3*sgn(b*x + a) + 45*a^2*b^4*d^5*x^7*e^2*sgn(b*x + a) + 35/2*a^2*b^4*d^6*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^7*x^5*sgn(b*x + a) + 20/11*a^3*b^3*x^11*e^7*sgn(b*x + a) + 14*a^3*b^3*d*x^10*e^6*sgn(b*x + a) + 140/3*a^3*b^3*d^2*x^9*e^5*sgn(b*x + a) + 175/2*a^3*b^3*d^3*x^8*e^4*sgn(b*x + a) + 100*a^3*b^3*d^4*x^7*e^3*sgn(b*x + a) + 70*a^3*b^3*d^5*x^6*e^2*sgn(b*x + a) + 28*a^3*b^3*d^6*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^7*x^4*sgn(b*x + a) + 3/2*a^4*b^2*x^10*e^7*sgn(b*x + a) + 35/3*a^4*b^2*d*x^9*e^6*sgn(b*x + a) + 315/8*a^4*b^2*d^2*x^8*e^5*sgn(b*x + a) + 75*a^4*b^2*d^3*x^7*e^4*sgn(b*x + a) + 175/2*a^4*b^2*d^4*x^6*e^3*sgn(b*x + a) + 63*a^4*b^2*d^5*x^5*e^2*sgn(b*x + a) + 105/4*a^4*b^2*d^6*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^7*x^3*sgn(b*x + a) + 2/3*a^5*b*x^9*e^7*sgn(b*x + a) + 21/4*a^5*b*d*x^8*e^6*sgn(b*x + a) + 18*a^5*b*d^2*x^7*e^5*sgn(b*x + a) + 35*a^5*b*d^3*x^6*e^4*sgn(b*x + a) + 42*a^5*b*d^4*x^5*e^3*sgn(b*x + a) + 63/2*a^5*b*d^5*x^4*e^2*sgn(b*x + a) + 14*a^5*b*d^6*x^3*e*sgn(b*x + a) + 3*a^5*b*d^7*x^2*sgn(b*x + a) + 1/8*a^6*x^8*e^7*sgn(b*x + a) + a^6*d*x^7*e^6*sgn(b*x + a) + 7/2*a^6*d^2*x^6*e^5*sgn(b*x + a) + 7*a^6*d^3*x^5*e^4*sgn(b*x + a) + 35/4*a^6*d^4*x^4*e^3*sgn(b*x + a) + 7*a^6*d^5*x^3*e^2*sgn(b*x + a) + 7/2*a^6*d^6*x^2*e*sgn(b*x + a) + a^6*d^7*x*sgn(b*x + a)","B",0
1991,1,955,0,0.214534," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{13} \, b^{6} x^{13} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b^{6} d x^{12} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{11} \, b^{6} d^{2} x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, b^{6} d^{3} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, b^{6} d^{4} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, b^{6} d^{5} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{6} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a b^{5} x^{12} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{36}{11} \, a b^{5} d x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + 9 \, a b^{5} d^{2} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{40}{3} \, a b^{5} d^{3} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{45}{4} \, a b^{5} d^{4} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{36}{7} \, a b^{5} d^{5} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{6} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{15}{11} \, a^{2} b^{4} x^{11} e^{6} \mathrm{sgn}\left(b x + a\right) + 9 \, a^{2} b^{4} d x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + 25 \, a^{2} b^{4} d^{2} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{75}{2} \, a^{2} b^{4} d^{3} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{225}{7} \, a^{2} b^{4} d^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{4} d^{5} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{6} x^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b^{3} x^{10} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{40}{3} \, a^{3} b^{3} d x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{75}{2} \, a^{3} b^{3} d^{2} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{400}{7} \, a^{3} b^{3} d^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 50 \, a^{3} b^{3} d^{4} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 24 \, a^{3} b^{3} d^{5} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{6} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{4} b^{2} x^{9} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{45}{4} \, a^{4} b^{2} d x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{225}{7} \, a^{4} b^{2} d^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 50 \, a^{4} b^{2} d^{3} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, a^{4} b^{2} d^{4} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{45}{2} \, a^{4} b^{2} d^{5} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{6} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, a^{5} b x^{8} e^{6} \mathrm{sgn}\left(b x + a\right) + \frac{36}{7} \, a^{5} b d x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{5} b d^{2} x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 24 \, a^{5} b d^{3} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{45}{2} \, a^{5} b d^{4} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{5} b d^{5} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{6} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, a^{6} x^{7} e^{6} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{6} d^{2} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{6} d^{3} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{6} d^{4} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{6} d^{5} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{6} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/13*b^6*x^13*e^6*sgn(b*x + a) + 1/2*b^6*d*x^12*e^5*sgn(b*x + a) + 15/11*b^6*d^2*x^11*e^4*sgn(b*x + a) + 2*b^6*d^3*x^10*e^3*sgn(b*x + a) + 5/3*b^6*d^4*x^9*e^2*sgn(b*x + a) + 3/4*b^6*d^5*x^8*e*sgn(b*x + a) + 1/7*b^6*d^6*x^7*sgn(b*x + a) + 1/2*a*b^5*x^12*e^6*sgn(b*x + a) + 36/11*a*b^5*d*x^11*e^5*sgn(b*x + a) + 9*a*b^5*d^2*x^10*e^4*sgn(b*x + a) + 40/3*a*b^5*d^3*x^9*e^3*sgn(b*x + a) + 45/4*a*b^5*d^4*x^8*e^2*sgn(b*x + a) + 36/7*a*b^5*d^5*x^7*e*sgn(b*x + a) + a*b^5*d^6*x^6*sgn(b*x + a) + 15/11*a^2*b^4*x^11*e^6*sgn(b*x + a) + 9*a^2*b^4*d*x^10*e^5*sgn(b*x + a) + 25*a^2*b^4*d^2*x^9*e^4*sgn(b*x + a) + 75/2*a^2*b^4*d^3*x^8*e^3*sgn(b*x + a) + 225/7*a^2*b^4*d^4*x^7*e^2*sgn(b*x + a) + 15*a^2*b^4*d^5*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^6*x^5*sgn(b*x + a) + 2*a^3*b^3*x^10*e^6*sgn(b*x + a) + 40/3*a^3*b^3*d*x^9*e^5*sgn(b*x + a) + 75/2*a^3*b^3*d^2*x^8*e^4*sgn(b*x + a) + 400/7*a^3*b^3*d^3*x^7*e^3*sgn(b*x + a) + 50*a^3*b^3*d^4*x^6*e^2*sgn(b*x + a) + 24*a^3*b^3*d^5*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^6*x^4*sgn(b*x + a) + 5/3*a^4*b^2*x^9*e^6*sgn(b*x + a) + 45/4*a^4*b^2*d*x^8*e^5*sgn(b*x + a) + 225/7*a^4*b^2*d^2*x^7*e^4*sgn(b*x + a) + 50*a^4*b^2*d^3*x^6*e^3*sgn(b*x + a) + 45*a^4*b^2*d^4*x^5*e^2*sgn(b*x + a) + 45/2*a^4*b^2*d^5*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^6*x^3*sgn(b*x + a) + 3/4*a^5*b*x^8*e^6*sgn(b*x + a) + 36/7*a^5*b*d*x^7*e^5*sgn(b*x + a) + 15*a^5*b*d^2*x^6*e^4*sgn(b*x + a) + 24*a^5*b*d^3*x^5*e^3*sgn(b*x + a) + 45/2*a^5*b*d^4*x^4*e^2*sgn(b*x + a) + 12*a^5*b*d^5*x^3*e*sgn(b*x + a) + 3*a^5*b*d^6*x^2*sgn(b*x + a) + 1/7*a^6*x^7*e^6*sgn(b*x + a) + a^6*d*x^6*e^5*sgn(b*x + a) + 3*a^6*d^2*x^5*e^4*sgn(b*x + a) + 5*a^6*d^3*x^4*e^3*sgn(b*x + a) + 5*a^6*d^4*x^3*e^2*sgn(b*x + a) + 3*a^6*d^5*x^2*e*sgn(b*x + a) + a^6*d^6*x*sgn(b*x + a)","B",0
1992,1,810,0,0.211015," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{12} \, b^{6} x^{12} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{11} \, b^{6} d x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + b^{6} d^{2} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, b^{6} d^{3} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, b^{6} d^{4} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{5} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{6}{11} \, a b^{5} x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{5} d x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, a b^{5} d^{2} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a b^{5} d^{3} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, a b^{5} d^{4} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} b^{4} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{25}{3} \, a^{2} b^{4} d x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{75}{4} \, a^{2} b^{4} d^{2} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{150}{7} \, a^{2} b^{4} d^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, a^{2} b^{4} d^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{20}{9} \, a^{3} b^{3} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, a^{3} b^{3} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{200}{7} \, a^{3} b^{3} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{100}{3} \, a^{3} b^{3} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b^{3} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{15}{8} \, a^{4} b^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{75}{7} \, a^{4} b^{2} d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 25 \, a^{4} b^{2} d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{4} b^{2} d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{75}{4} \, a^{4} b^{2} d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, a^{5} b x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{5} b d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{5} b d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{5} b d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{5} b d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, a^{6} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{6} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{6} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{6} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{5} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/12*b^6*x^12*e^5*sgn(b*x + a) + 5/11*b^6*d*x^11*e^4*sgn(b*x + a) + b^6*d^2*x^10*e^3*sgn(b*x + a) + 10/9*b^6*d^3*x^9*e^2*sgn(b*x + a) + 5/8*b^6*d^4*x^8*e*sgn(b*x + a) + 1/7*b^6*d^5*x^7*sgn(b*x + a) + 6/11*a*b^5*x^11*e^5*sgn(b*x + a) + 3*a*b^5*d*x^10*e^4*sgn(b*x + a) + 20/3*a*b^5*d^2*x^9*e^3*sgn(b*x + a) + 15/2*a*b^5*d^3*x^8*e^2*sgn(b*x + a) + 30/7*a*b^5*d^4*x^7*e*sgn(b*x + a) + a*b^5*d^5*x^6*sgn(b*x + a) + 3/2*a^2*b^4*x^10*e^5*sgn(b*x + a) + 25/3*a^2*b^4*d*x^9*e^4*sgn(b*x + a) + 75/4*a^2*b^4*d^2*x^8*e^3*sgn(b*x + a) + 150/7*a^2*b^4*d^3*x^7*e^2*sgn(b*x + a) + 25/2*a^2*b^4*d^4*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^5*x^5*sgn(b*x + a) + 20/9*a^3*b^3*x^9*e^5*sgn(b*x + a) + 25/2*a^3*b^3*d*x^8*e^4*sgn(b*x + a) + 200/7*a^3*b^3*d^2*x^7*e^3*sgn(b*x + a) + 100/3*a^3*b^3*d^3*x^6*e^2*sgn(b*x + a) + 20*a^3*b^3*d^4*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^5*x^4*sgn(b*x + a) + 15/8*a^4*b^2*x^8*e^5*sgn(b*x + a) + 75/7*a^4*b^2*d*x^7*e^4*sgn(b*x + a) + 25*a^4*b^2*d^2*x^6*e^3*sgn(b*x + a) + 30*a^4*b^2*d^3*x^5*e^2*sgn(b*x + a) + 75/4*a^4*b^2*d^4*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^5*x^3*sgn(b*x + a) + 6/7*a^5*b*x^7*e^5*sgn(b*x + a) + 5*a^5*b*d*x^6*e^4*sgn(b*x + a) + 12*a^5*b*d^2*x^5*e^3*sgn(b*x + a) + 15*a^5*b*d^3*x^4*e^2*sgn(b*x + a) + 10*a^5*b*d^4*x^3*e*sgn(b*x + a) + 3*a^5*b*d^5*x^2*sgn(b*x + a) + 1/6*a^6*x^6*e^5*sgn(b*x + a) + a^6*d*x^5*e^4*sgn(b*x + a) + 5/2*a^6*d^2*x^4*e^3*sgn(b*x + a) + 10/3*a^6*d^3*x^3*e^2*sgn(b*x + a) + 5/2*a^6*d^4*x^2*e*sgn(b*x + a) + a^6*d^5*x*sgn(b*x + a)","B",0
1993,1,666,0,0.193894," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{11} \, b^{6} x^{11} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, b^{6} d x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, b^{6} d^{2} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b^{6} d^{3} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{4} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, a b^{5} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{8}{3} \, a b^{5} d x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, a b^{5} d^{2} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{24}{7} \, a b^{5} d^{3} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{2} b^{4} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a^{2} b^{4} d x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{90}{7} \, a^{2} b^{4} d^{2} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{4} d^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{3} b^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{80}{7} \, a^{3} b^{3} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b^{3} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 16 \, a^{3} b^{3} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, a^{4} b^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{4} b^{2} d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{4} b^{2} d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b^{2} d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + a^{5} b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{24}{5} \, a^{5} b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + 9 \, a^{5} b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a^{5} b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a^{6} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{6} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{6} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/11*b^6*x^11*e^4*sgn(b*x + a) + 2/5*b^6*d*x^10*e^3*sgn(b*x + a) + 2/3*b^6*d^2*x^9*e^2*sgn(b*x + a) + 1/2*b^6*d^3*x^8*e*sgn(b*x + a) + 1/7*b^6*d^4*x^7*sgn(b*x + a) + 3/5*a*b^5*x^10*e^4*sgn(b*x + a) + 8/3*a*b^5*d*x^9*e^3*sgn(b*x + a) + 9/2*a*b^5*d^2*x^8*e^2*sgn(b*x + a) + 24/7*a*b^5*d^3*x^7*e*sgn(b*x + a) + a*b^5*d^4*x^6*sgn(b*x + a) + 5/3*a^2*b^4*x^9*e^4*sgn(b*x + a) + 15/2*a^2*b^4*d*x^8*e^3*sgn(b*x + a) + 90/7*a^2*b^4*d^2*x^7*e^2*sgn(b*x + a) + 10*a^2*b^4*d^3*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^4*x^5*sgn(b*x + a) + 5/2*a^3*b^3*x^8*e^4*sgn(b*x + a) + 80/7*a^3*b^3*d*x^7*e^3*sgn(b*x + a) + 20*a^3*b^3*d^2*x^6*e^2*sgn(b*x + a) + 16*a^3*b^3*d^3*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^4*x^4*sgn(b*x + a) + 15/7*a^4*b^2*x^7*e^4*sgn(b*x + a) + 10*a^4*b^2*d*x^6*e^3*sgn(b*x + a) + 18*a^4*b^2*d^2*x^5*e^2*sgn(b*x + a) + 15*a^4*b^2*d^3*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^4*x^3*sgn(b*x + a) + a^5*b*x^6*e^4*sgn(b*x + a) + 24/5*a^5*b*d*x^5*e^3*sgn(b*x + a) + 9*a^5*b*d^2*x^4*e^2*sgn(b*x + a) + 8*a^5*b*d^3*x^3*e*sgn(b*x + a) + 3*a^5*b*d^4*x^2*sgn(b*x + a) + 1/5*a^6*x^5*e^4*sgn(b*x + a) + a^6*d*x^4*e^3*sgn(b*x + a) + 2*a^6*d^2*x^3*e^2*sgn(b*x + a) + 2*a^6*d^3*x^2*e*sgn(b*x + a) + a^6*d^4*x*sgn(b*x + a)","B",0
1994,1,523,0,0.223885," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{10} \, b^{6} x^{10} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, b^{6} d x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, b^{6} d^{2} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, a b^{5} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{9}{4} \, a b^{5} d x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{18}{7} \, a b^{5} d^{2} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{15}{8} \, a^{2} b^{4} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{45}{7} \, a^{2} b^{4} d x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a^{2} b^{4} d^{2} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{20}{7} \, a^{3} b^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{3} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{3} b^{3} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} b^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 9 \, a^{4} b^{2} d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{45}{4} \, a^{4} b^{2} d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{6}{5} \, a^{5} b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, a^{5} b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{5} b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a^{6} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{6} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/10*b^6*x^10*e^3*sgn(b*x + a) + 1/3*b^6*d*x^9*e^2*sgn(b*x + a) + 3/8*b^6*d^2*x^8*e*sgn(b*x + a) + 1/7*b^6*d^3*x^7*sgn(b*x + a) + 2/3*a*b^5*x^9*e^3*sgn(b*x + a) + 9/4*a*b^5*d*x^8*e^2*sgn(b*x + a) + 18/7*a*b^5*d^2*x^7*e*sgn(b*x + a) + a*b^5*d^3*x^6*sgn(b*x + a) + 15/8*a^2*b^4*x^8*e^3*sgn(b*x + a) + 45/7*a^2*b^4*d*x^7*e^2*sgn(b*x + a) + 15/2*a^2*b^4*d^2*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^3*x^5*sgn(b*x + a) + 20/7*a^3*b^3*x^7*e^3*sgn(b*x + a) + 10*a^3*b^3*d*x^6*e^2*sgn(b*x + a) + 12*a^3*b^3*d^2*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^3*x^4*sgn(b*x + a) + 5/2*a^4*b^2*x^6*e^3*sgn(b*x + a) + 9*a^4*b^2*d*x^5*e^2*sgn(b*x + a) + 45/4*a^4*b^2*d^2*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^3*x^3*sgn(b*x + a) + 6/5*a^5*b*x^5*e^3*sgn(b*x + a) + 9/2*a^5*b*d*x^4*e^2*sgn(b*x + a) + 6*a^5*b*d^2*x^3*e*sgn(b*x + a) + 3*a^5*b*d^3*x^2*sgn(b*x + a) + 1/4*a^6*x^4*e^3*sgn(b*x + a) + a^6*d*x^3*e^2*sgn(b*x + a) + 3/2*a^6*d^2*x^2*e*sgn(b*x + a) + a^6*d^3*x*sgn(b*x + a)","B",0
1995,1,379,0,0.175416," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{9} \, b^{6} x^{9} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, b^{6} d x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, a b^{5} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{12}{7} \, a b^{5} d x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, a^{2} b^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{2} b^{4} d x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} b^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a^{3} b^{3} d x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{4} b^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a^{4} b^{2} d x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{5} b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{5} b d x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a^{6} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + a^{6} d x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/9*b^6*x^9*e^2*sgn(b*x + a) + 1/4*b^6*d*x^8*e*sgn(b*x + a) + 1/7*b^6*d^2*x^7*sgn(b*x + a) + 3/4*a*b^5*x^8*e^2*sgn(b*x + a) + 12/7*a*b^5*d*x^7*e*sgn(b*x + a) + a*b^5*d^2*x^6*sgn(b*x + a) + 15/7*a^2*b^4*x^7*e^2*sgn(b*x + a) + 5*a^2*b^4*d*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d^2*x^5*sgn(b*x + a) + 10/3*a^3*b^3*x^6*e^2*sgn(b*x + a) + 8*a^3*b^3*d*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d^2*x^4*sgn(b*x + a) + 3*a^4*b^2*x^5*e^2*sgn(b*x + a) + 15/2*a^4*b^2*d*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d^2*x^3*sgn(b*x + a) + 3/2*a^5*b*x^4*e^2*sgn(b*x + a) + 4*a^5*b*d*x^3*e*sgn(b*x + a) + 3*a^5*b*d^2*x^2*sgn(b*x + a) + 1/3*a^6*x^3*e^2*sgn(b*x + a) + a^6*d*x^2*e*sgn(b*x + a) + a^6*d^2*x*sgn(b*x + a)","B",0
1996,1,236,0,0.168285," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, b^{6} x^{8} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{7} \, b^{6} d x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{6}{7} \, a b^{5} x^{7} e \mathrm{sgn}\left(b x + a\right) + a b^{5} d x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} b^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d x^{5} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} b^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, a^{4} b^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d x^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{5} b x^{3} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{6} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{6} d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/8*b^6*x^8*e*sgn(b*x + a) + 1/7*b^6*d*x^7*sgn(b*x + a) + 6/7*a*b^5*x^7*e*sgn(b*x + a) + a*b^5*d*x^6*sgn(b*x + a) + 5/2*a^2*b^4*x^6*e*sgn(b*x + a) + 3*a^2*b^4*d*x^5*sgn(b*x + a) + 4*a^3*b^3*x^5*e*sgn(b*x + a) + 5*a^3*b^3*d*x^4*sgn(b*x + a) + 15/4*a^4*b^2*x^4*e*sgn(b*x + a) + 5*a^4*b^2*d*x^3*sgn(b*x + a) + 2*a^5*b*x^3*e*sgn(b*x + a) + 3*a^5*b*d*x^2*sgn(b*x + a) + 1/2*a^6*x^2*e*sgn(b*x + a) + a^6*d*x*sgn(b*x + a)","B",0
1997,1,120,0,0.186534," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{6} x^{7} \mathrm{sgn}\left(b x + a\right) + a b^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b x^{2} \mathrm{sgn}\left(b x + a\right) + a^{6} x \mathrm{sgn}\left(b x + a\right) + \frac{a^{7} \mathrm{sgn}\left(b x + a\right)}{7 \, b}"," ",0,"1/7*b^6*x^7*sgn(b*x + a) + a*b^5*x^6*sgn(b*x + a) + 3*a^2*b^4*x^5*sgn(b*x + a) + 5*a^3*b^3*x^4*sgn(b*x + a) + 5*a^4*b^2*x^3*sgn(b*x + a) + 3*a^5*b*x^2*sgn(b*x + a) + a^6*x*sgn(b*x + a) + 1/7*a^7*sgn(b*x + a)/b","B",0
1998,1,522,0,0.218735," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d),x, algorithm=""giac"")","{\left(b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, b^{6} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) - 12 \, b^{6} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, b^{6} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) - 20 \, b^{6} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, b^{6} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) - 60 \, b^{6} d^{5} x \mathrm{sgn}\left(b x + a\right) + 72 \, a b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 90 \, a b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 120 \, a b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 180 \, a b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 360 \, a b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + 225 \, a^{2} b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 300 \, a^{2} b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 450 \, a^{2} b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 900 \, a^{2} b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + 400 \, a^{3} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 600 \, a^{3} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1200 \, a^{3} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 450 \, a^{4} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 900 \, a^{4} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 360 \, a^{5} b x e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}"," ",0,"(b^6*d^6*sgn(b*x + a) - 6*a*b^5*d^5*e*sgn(b*x + a) + 15*a^2*b^4*d^4*e^2*sgn(b*x + a) - 20*a^3*b^3*d^3*e^3*sgn(b*x + a) + 15*a^4*b^2*d^2*e^4*sgn(b*x + a) - 6*a^5*b*d*e^5*sgn(b*x + a) + a^6*e^6*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/60*(10*b^6*x^6*e^5*sgn(b*x + a) - 12*b^6*d*x^5*e^4*sgn(b*x + a) + 15*b^6*d^2*x^4*e^3*sgn(b*x + a) - 20*b^6*d^3*x^3*e^2*sgn(b*x + a) + 30*b^6*d^4*x^2*e*sgn(b*x + a) - 60*b^6*d^5*x*sgn(b*x + a) + 72*a*b^5*x^5*e^5*sgn(b*x + a) - 90*a*b^5*d*x^4*e^4*sgn(b*x + a) + 120*a*b^5*d^2*x^3*e^3*sgn(b*x + a) - 180*a*b^5*d^3*x^2*e^2*sgn(b*x + a) + 360*a*b^5*d^4*x*e*sgn(b*x + a) + 225*a^2*b^4*x^4*e^5*sgn(b*x + a) - 300*a^2*b^4*d*x^3*e^4*sgn(b*x + a) + 450*a^2*b^4*d^2*x^2*e^3*sgn(b*x + a) - 900*a^2*b^4*d^3*x*e^2*sgn(b*x + a) + 400*a^3*b^3*x^3*e^5*sgn(b*x + a) - 600*a^3*b^3*d*x^2*e^4*sgn(b*x + a) + 1200*a^3*b^3*d^2*x*e^3*sgn(b*x + a) + 450*a^4*b^2*x^2*e^5*sgn(b*x + a) - 900*a^4*b^2*d*x*e^4*sgn(b*x + a) + 360*a^5*b*x*e^5*sgn(b*x + a))*e^(-6)","B",0
1999,1,519,0,0.195956," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","-6 \, {\left(b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{10} \, {\left(2 \, b^{6} x^{5} e^{8} \mathrm{sgn}\left(b x + a\right) - 5 \, b^{6} d x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 10 \, b^{6} d^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) - 20 \, b^{6} d^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 50 \, b^{6} d^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, a b^{5} x^{4} e^{8} \mathrm{sgn}\left(b x + a\right) - 40 \, a b^{5} d x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 90 \, a b^{5} d^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 240 \, a b^{5} d^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) + 50 \, a^{2} b^{4} x^{3} e^{8} \mathrm{sgn}\left(b x + a\right) - 150 \, a^{2} b^{4} d x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 450 \, a^{2} b^{4} d^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 100 \, a^{3} b^{3} x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) - 400 \, a^{3} b^{3} d x e^{7} \mathrm{sgn}\left(b x + a\right) + 150 \, a^{4} b^{2} x e^{8} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-10\right)} - \frac{{\left(b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{x e + d}"," ",0,"-6*(b^6*d^5*sgn(b*x + a) - 5*a*b^5*d^4*e*sgn(b*x + a) + 10*a^2*b^4*d^3*e^2*sgn(b*x + a) - 10*a^3*b^3*d^2*e^3*sgn(b*x + a) + 5*a^4*b^2*d*e^4*sgn(b*x + a) - a^5*b*e^5*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/10*(2*b^6*x^5*e^8*sgn(b*x + a) - 5*b^6*d*x^4*e^7*sgn(b*x + a) + 10*b^6*d^2*x^3*e^6*sgn(b*x + a) - 20*b^6*d^3*x^2*e^5*sgn(b*x + a) + 50*b^6*d^4*x*e^4*sgn(b*x + a) + 15*a*b^5*x^4*e^8*sgn(b*x + a) - 40*a*b^5*d*x^3*e^7*sgn(b*x + a) + 90*a*b^5*d^2*x^2*e^6*sgn(b*x + a) - 240*a*b^5*d^3*x*e^5*sgn(b*x + a) + 50*a^2*b^4*x^3*e^8*sgn(b*x + a) - 150*a^2*b^4*d*x^2*e^7*sgn(b*x + a) + 450*a^2*b^4*d^2*x*e^6*sgn(b*x + a) + 100*a^3*b^3*x^2*e^8*sgn(b*x + a) - 400*a^3*b^3*d*x*e^7*sgn(b*x + a) + 150*a^4*b^2*x*e^8*sgn(b*x + a))*e^(-10) - (b^6*d^6*sgn(b*x + a) - 6*a*b^5*d^5*e*sgn(b*x + a) + 15*a^2*b^4*d^4*e^2*sgn(b*x + a) - 20*a^3*b^3*d^3*e^3*sgn(b*x + a) + 15*a^4*b^2*d^2*e^4*sgn(b*x + a) - 6*a^5*b*d*e^5*sgn(b*x + a) + a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)","A",0
2000,1,509,0,0.187668," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","15 \, {\left(b^{6} d^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{4} \, {\left(b^{6} x^{4} e^{9} \mathrm{sgn}\left(b x + a\right) - 4 \, b^{6} d x^{3} e^{8} \mathrm{sgn}\left(b x + a\right) + 12 \, b^{6} d^{2} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) - 40 \, b^{6} d^{3} x e^{6} \mathrm{sgn}\left(b x + a\right) + 8 \, a b^{5} x^{3} e^{9} \mathrm{sgn}\left(b x + a\right) - 36 \, a b^{5} d x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) + 144 \, a b^{5} d^{2} x e^{7} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{2} b^{4} x^{2} e^{9} \mathrm{sgn}\left(b x + a\right) - 180 \, a^{2} b^{4} d x e^{8} \mathrm{sgn}\left(b x + a\right) + 80 \, a^{3} b^{3} x e^{9} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-12\right)} + \frac{{\left(11 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 54 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 105 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 100 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) - a^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(b^{6} d^{5} e \mathrm{sgn}\left(b x + a\right) - 5 \, a b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 10 \, a^{3} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) - a^{5} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"15*(b^6*d^4*sgn(b*x + a) - 4*a*b^5*d^3*e*sgn(b*x + a) + 6*a^2*b^4*d^2*e^2*sgn(b*x + a) - 4*a^3*b^3*d*e^3*sgn(b*x + a) + a^4*b^2*e^4*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/4*(b^6*x^4*e^9*sgn(b*x + a) - 4*b^6*d*x^3*e^8*sgn(b*x + a) + 12*b^6*d^2*x^2*e^7*sgn(b*x + a) - 40*b^6*d^3*x*e^6*sgn(b*x + a) + 8*a*b^5*x^3*e^9*sgn(b*x + a) - 36*a*b^5*d*x^2*e^8*sgn(b*x + a) + 144*a*b^5*d^2*x*e^7*sgn(b*x + a) + 30*a^2*b^4*x^2*e^9*sgn(b*x + a) - 180*a^2*b^4*d*x*e^8*sgn(b*x + a) + 80*a^3*b^3*x*e^9*sgn(b*x + a))*e^(-12) + 1/2*(11*b^6*d^6*sgn(b*x + a) - 54*a*b^5*d^5*e*sgn(b*x + a) + 105*a^2*b^4*d^4*e^2*sgn(b*x + a) - 100*a^3*b^3*d^3*e^3*sgn(b*x + a) + 45*a^4*b^2*d^2*e^4*sgn(b*x + a) - 6*a^5*b*d*e^5*sgn(b*x + a) - a^6*e^6*sgn(b*x + a) + 12*(b^6*d^5*e*sgn(b*x + a) - 5*a*b^5*d^4*e^2*sgn(b*x + a) + 10*a^2*b^4*d^3*e^3*sgn(b*x + a) - 10*a^3*b^3*d^2*e^4*sgn(b*x + a) + 5*a^4*b^2*d*e^5*sgn(b*x + a) - a^5*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^2","A",0
2001,1,503,0,0.189086," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","-20 \, {\left(b^{6} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{3} \, {\left(b^{6} x^{3} e^{8} \mathrm{sgn}\left(b x + a\right) - 6 \, b^{6} d x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 30 \, b^{6} d^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 9 \, a b^{5} x^{2} e^{8} \mathrm{sgn}\left(b x + a\right) - 72 \, a b^{5} d x e^{7} \mathrm{sgn}\left(b x + a\right) + 45 \, a^{2} b^{4} x e^{8} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-12\right)} - \frac{{\left(37 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 141 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 195 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 110 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(b^{6} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{4} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 9 \, {\left(9 \, b^{6} d^{5} e \mathrm{sgn}\left(b x + a\right) - 35 \, a b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 50 \, a^{2} b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, a^{3} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{5} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-20*(b^6*d^3*sgn(b*x + a) - 3*a*b^5*d^2*e*sgn(b*x + a) + 3*a^2*b^4*d*e^2*sgn(b*x + a) - a^3*b^3*e^3*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/3*(b^6*x^3*e^8*sgn(b*x + a) - 6*b^6*d*x^2*e^7*sgn(b*x + a) + 30*b^6*d^2*x*e^6*sgn(b*x + a) + 9*a*b^5*x^2*e^8*sgn(b*x + a) - 72*a*b^5*d*x*e^7*sgn(b*x + a) + 45*a^2*b^4*x*e^8*sgn(b*x + a))*e^(-12) - 1/3*(37*b^6*d^6*sgn(b*x + a) - 141*a*b^5*d^5*e*sgn(b*x + a) + 195*a^2*b^4*d^4*e^2*sgn(b*x + a) - 110*a^3*b^3*d^3*e^3*sgn(b*x + a) + 15*a^4*b^2*d^2*e^4*sgn(b*x + a) + 3*a^5*b*d*e^5*sgn(b*x + a) + a^6*e^6*sgn(b*x + a) + 45*(b^6*d^4*e^2*sgn(b*x + a) - 4*a*b^5*d^3*e^3*sgn(b*x + a) + 6*a^2*b^4*d^2*e^4*sgn(b*x + a) - 4*a^3*b^3*d*e^5*sgn(b*x + a) + a^4*b^2*e^6*sgn(b*x + a))*x^2 + 9*(9*b^6*d^5*e*sgn(b*x + a) - 35*a*b^5*d^4*e^2*sgn(b*x + a) + 50*a^2*b^4*d^3*e^3*sgn(b*x + a) - 30*a^3*b^3*d^2*e^4*sgn(b*x + a) + 5*a^4*b^2*d*e^5*sgn(b*x + a) + a^5*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^3","A",0
2002,1,504,0,0.230375," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","15 \, {\left(b^{6} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{5} d e \mathrm{sgn}\left(b x + a\right) + a^{2} b^{4} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{6} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 10 \, b^{6} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 12 \, a b^{5} x e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-10\right)} + \frac{{\left(57 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 154 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 125 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) - a^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 80 \, {\left(b^{6} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{5} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d e^{5} \mathrm{sgn}\left(b x + a\right) - a^{3} b^{3} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 30 \, {\left(7 \, b^{6} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) - a^{4} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 4 \, {\left(47 \, b^{6} d^{5} e \mathrm{sgn}\left(b x + a\right) - 130 \, a b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 110 \, a^{2} b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 5 \, a^{4} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) - 2 \, a^{5} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{4 \, {\left(x e + d\right)}^{4}}"," ",0,"15*(b^6*d^2*sgn(b*x + a) - 2*a*b^5*d*e*sgn(b*x + a) + a^2*b^4*e^2*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) + 1/2*(b^6*x^2*e^5*sgn(b*x + a) - 10*b^6*d*x*e^4*sgn(b*x + a) + 12*a*b^5*x*e^5*sgn(b*x + a))*e^(-10) + 1/4*(57*b^6*d^6*sgn(b*x + a) - 154*a*b^5*d^5*e*sgn(b*x + a) + 125*a^2*b^4*d^4*e^2*sgn(b*x + a) - 20*a^3*b^3*d^3*e^3*sgn(b*x + a) - 5*a^4*b^2*d^2*e^4*sgn(b*x + a) - 2*a^5*b*d*e^5*sgn(b*x + a) - a^6*e^6*sgn(b*x + a) + 80*(b^6*d^3*e^3*sgn(b*x + a) - 3*a*b^5*d^2*e^4*sgn(b*x + a) + 3*a^2*b^4*d*e^5*sgn(b*x + a) - a^3*b^3*e^6*sgn(b*x + a))*x^3 + 30*(7*b^6*d^4*e^2*sgn(b*x + a) - 20*a*b^5*d^3*e^3*sgn(b*x + a) + 18*a^2*b^4*d^2*e^4*sgn(b*x + a) - 4*a^3*b^3*d*e^5*sgn(b*x + a) - a^4*b^2*e^6*sgn(b*x + a))*x^2 + 4*(47*b^6*d^5*e*sgn(b*x + a) - 130*a*b^5*d^4*e^2*sgn(b*x + a) + 110*a^2*b^4*d^3*e^3*sgn(b*x + a) - 20*a^3*b^3*d^2*e^4*sgn(b*x + a) - 5*a^4*b^2*d*e^5*sgn(b*x + a) - 2*a^5*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^4","A",0
2003,1,499,0,0.198813," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^6,x, algorithm=""giac"")","b^{6} x e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(b^{6} d \mathrm{sgn}\left(b x + a\right) - a b^{5} e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(87 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 137 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 30 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 150 \, {\left(b^{6} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{5} d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{2} b^{4} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{4} + 100 \, {\left(5 \, b^{6} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 9 \, a b^{5} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{3} b^{3} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 50 \, {\left(13 \, b^{6} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 22 \, a b^{5} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{4} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b^{3} d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{4} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 5 \, {\left(77 \, b^{6} d^{5} e \mathrm{sgn}\left(b x + a\right) - 125 \, a b^{5} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{2} b^{4} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{3} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d e^{5} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} b e^{6} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-7\right)}}{10 \, {\left(x e + d\right)}^{5}}"," ",0,"b^6*x*e^(-6)*sgn(b*x + a) - 6*(b^6*d*sgn(b*x + a) - a*b^5*e*sgn(b*x + a))*e^(-7)*log(abs(x*e + d)) - 1/10*(87*b^6*d^6*sgn(b*x + a) - 137*a*b^5*d^5*e*sgn(b*x + a) + 30*a^2*b^4*d^4*e^2*sgn(b*x + a) + 10*a^3*b^3*d^3*e^3*sgn(b*x + a) + 5*a^4*b^2*d^2*e^4*sgn(b*x + a) + 3*a^5*b*d*e^5*sgn(b*x + a) + 2*a^6*e^6*sgn(b*x + a) + 150*(b^6*d^2*e^4*sgn(b*x + a) - 2*a*b^5*d*e^5*sgn(b*x + a) + a^2*b^4*e^6*sgn(b*x + a))*x^4 + 100*(5*b^6*d^3*e^3*sgn(b*x + a) - 9*a*b^5*d^2*e^4*sgn(b*x + a) + 3*a^2*b^4*d*e^5*sgn(b*x + a) + a^3*b^3*e^6*sgn(b*x + a))*x^3 + 50*(13*b^6*d^4*e^2*sgn(b*x + a) - 22*a*b^5*d^3*e^3*sgn(b*x + a) + 6*a^2*b^4*d^2*e^4*sgn(b*x + a) + 2*a^3*b^3*d*e^5*sgn(b*x + a) + a^4*b^2*e^6*sgn(b*x + a))*x^2 + 5*(77*b^6*d^5*e*sgn(b*x + a) - 125*a*b^5*d^4*e^2*sgn(b*x + a) + 30*a^2*b^4*d^3*e^3*sgn(b*x + a) + 10*a^3*b^3*d^2*e^4*sgn(b*x + a) + 5*a^4*b^2*d*e^5*sgn(b*x + a) + 3*a^5*b*e^6*sgn(b*x + a))*x)*e^(-7)/(x*e + d)^5","A",0
2004,1,507,0,0.190092," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^7,x, algorithm=""giac"")","b^{6} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(360 \, {\left(b^{6} d e^{4} \mathrm{sgn}\left(b x + a\right) - a b^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{5} + 450 \, {\left(3 \, b^{6} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{5} d e^{4} \mathrm{sgn}\left(b x + a\right) - a^{2} b^{4} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{4} + 200 \, {\left(11 \, b^{6} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{5} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a^{2} b^{4} d e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, a^{3} b^{3} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 75 \, {\left(25 \, b^{6} d^{4} e \mathrm{sgn}\left(b x + a\right) - 12 \, a b^{5} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, a^{2} b^{4} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{3} d e^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, a^{4} b^{2} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 6 \, {\left(137 \, b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) - 60 \, a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 30 \, a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 15 \, a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(147 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 60 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) - 30 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) - 10 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"b^6*e^(-7)*log(abs(x*e + d))*sgn(b*x + a) + 1/60*(360*(b^6*d*e^4*sgn(b*x + a) - a*b^5*e^5*sgn(b*x + a))*x^5 + 450*(3*b^6*d^2*e^3*sgn(b*x + a) - 2*a*b^5*d*e^4*sgn(b*x + a) - a^2*b^4*e^5*sgn(b*x + a))*x^4 + 200*(11*b^6*d^3*e^2*sgn(b*x + a) - 6*a*b^5*d^2*e^3*sgn(b*x + a) - 3*a^2*b^4*d*e^4*sgn(b*x + a) - 2*a^3*b^3*e^5*sgn(b*x + a))*x^3 + 75*(25*b^6*d^4*e*sgn(b*x + a) - 12*a*b^5*d^3*e^2*sgn(b*x + a) - 6*a^2*b^4*d^2*e^3*sgn(b*x + a) - 4*a^3*b^3*d*e^4*sgn(b*x + a) - 3*a^4*b^2*e^5*sgn(b*x + a))*x^2 + 6*(137*b^6*d^5*sgn(b*x + a) - 60*a*b^5*d^4*e*sgn(b*x + a) - 30*a^2*b^4*d^3*e^2*sgn(b*x + a) - 20*a^3*b^3*d^2*e^3*sgn(b*x + a) - 15*a^4*b^2*d*e^4*sgn(b*x + a) - 12*a^5*b*e^5*sgn(b*x + a))*x + (147*b^6*d^6*sgn(b*x + a) - 60*a*b^5*d^5*e*sgn(b*x + a) - 30*a^2*b^4*d^4*e^2*sgn(b*x + a) - 20*a^3*b^3*d^3*e^3*sgn(b*x + a) - 15*a^4*b^2*d^2*e^4*sgn(b*x + a) - 12*a^5*b*d*e^5*sgn(b*x + a) - 10*a^6*e^6*sgn(b*x + a))*e^(-1))*e^(-6)/(x*e + d)^6","A",0
2005,1,514,0,0.193566," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(7 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 21 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 21 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 35 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 21 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 7 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 35 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{7 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/7*(7*b^6*x^6*e^6*sgn(b*x + a) + 21*b^6*d*x^5*e^5*sgn(b*x + a) + 35*b^6*d^2*x^4*e^4*sgn(b*x + a) + 35*b^6*d^3*x^3*e^3*sgn(b*x + a) + 21*b^6*d^4*x^2*e^2*sgn(b*x + a) + 7*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 21*a*b^5*x^5*e^6*sgn(b*x + a) + 35*a*b^5*d*x^4*e^5*sgn(b*x + a) + 35*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 21*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 7*a*b^5*d^4*x*e^2*sgn(b*x + a) + a*b^5*d^5*e*sgn(b*x + a) + 35*a^2*b^4*x^4*e^6*sgn(b*x + a) + 35*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 21*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 7*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + a^2*b^4*d^4*e^2*sgn(b*x + a) + 35*a^3*b^3*x^3*e^6*sgn(b*x + a) + 21*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 7*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + a^3*b^3*d^3*e^3*sgn(b*x + a) + 21*a^4*b^2*x^2*e^6*sgn(b*x + a) + 7*a^4*b^2*d*x*e^5*sgn(b*x + a) + a^4*b^2*d^2*e^4*sgn(b*x + a) + 7*a^5*b*x*e^6*sgn(b*x + a) + a^5*b*d*e^5*sgn(b*x + a) + a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^7","B",0
2006,1,520,0,0.239601," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(28 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 56 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 112 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 140 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 112 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 16 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 210 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 168 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 24 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 224 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 112 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 32 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 140 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 40 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 48 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{56 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/56*(28*b^6*x^6*e^6*sgn(b*x + a) + 56*b^6*d*x^5*e^5*sgn(b*x + a) + 70*b^6*d^2*x^4*e^4*sgn(b*x + a) + 56*b^6*d^3*x^3*e^3*sgn(b*x + a) + 28*b^6*d^4*x^2*e^2*sgn(b*x + a) + 8*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 112*a*b^5*x^5*e^6*sgn(b*x + a) + 140*a*b^5*d*x^4*e^5*sgn(b*x + a) + 112*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 56*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 16*a*b^5*d^4*x*e^2*sgn(b*x + a) + 2*a*b^5*d^5*e*sgn(b*x + a) + 210*a^2*b^4*x^4*e^6*sgn(b*x + a) + 168*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 84*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 24*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 3*a^2*b^4*d^4*e^2*sgn(b*x + a) + 224*a^3*b^3*x^3*e^6*sgn(b*x + a) + 112*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 32*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 4*a^3*b^3*d^3*e^3*sgn(b*x + a) + 140*a^4*b^2*x^2*e^6*sgn(b*x + a) + 40*a^4*b^2*d*x*e^5*sgn(b*x + a) + 5*a^4*b^2*d^2*e^4*sgn(b*x + a) + 48*a^5*b*x*e^6*sgn(b*x + a) + 6*a^5*b*d*e^5*sgn(b*x + a) + 7*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^8","B",0
2007,1,520,0,0.193596," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(84 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 126 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 378 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 378 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 252 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 108 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 27 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 756 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 504 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 216 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 54 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 840 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 360 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 90 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 540 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 135 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 189 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 28 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{252 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/252*(84*b^6*x^6*e^6*sgn(b*x + a) + 126*b^6*d*x^5*e^5*sgn(b*x + a) + 126*b^6*d^2*x^4*e^4*sgn(b*x + a) + 84*b^6*d^3*x^3*e^3*sgn(b*x + a) + 36*b^6*d^4*x^2*e^2*sgn(b*x + a) + 9*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 378*a*b^5*x^5*e^6*sgn(b*x + a) + 378*a*b^5*d*x^4*e^5*sgn(b*x + a) + 252*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 108*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 27*a*b^5*d^4*x*e^2*sgn(b*x + a) + 3*a*b^5*d^5*e*sgn(b*x + a) + 756*a^2*b^4*x^4*e^6*sgn(b*x + a) + 504*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 216*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 54*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 6*a^2*b^4*d^4*e^2*sgn(b*x + a) + 840*a^3*b^3*x^3*e^6*sgn(b*x + a) + 360*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 90*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 10*a^3*b^3*d^3*e^3*sgn(b*x + a) + 540*a^4*b^2*x^2*e^6*sgn(b*x + a) + 135*a^4*b^2*d*x*e^5*sgn(b*x + a) + 15*a^4*b^2*d^2*e^4*sgn(b*x + a) + 189*a^5*b*x*e^6*sgn(b*x + a) + 21*a^5*b*d*e^5*sgn(b*x + a) + 28*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^9","B",0
2008,1,520,0,0.203090," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(210 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 252 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 120 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 1008 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 840 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 480 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 40 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 2100 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1200 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 450 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 100 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 2400 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 900 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 200 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 1575 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 350 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 560 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 56 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{840 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/840*(210*b^6*x^6*e^6*sgn(b*x + a) + 252*b^6*d*x^5*e^5*sgn(b*x + a) + 210*b^6*d^2*x^4*e^4*sgn(b*x + a) + 120*b^6*d^3*x^3*e^3*sgn(b*x + a) + 45*b^6*d^4*x^2*e^2*sgn(b*x + a) + 10*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 1008*a*b^5*x^5*e^6*sgn(b*x + a) + 840*a*b^5*d*x^4*e^5*sgn(b*x + a) + 480*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 180*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 40*a*b^5*d^4*x*e^2*sgn(b*x + a) + 4*a*b^5*d^5*e*sgn(b*x + a) + 2100*a^2*b^4*x^4*e^6*sgn(b*x + a) + 1200*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 450*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 100*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 10*a^2*b^4*d^4*e^2*sgn(b*x + a) + 2400*a^3*b^3*x^3*e^6*sgn(b*x + a) + 900*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 200*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 20*a^3*b^3*d^3*e^3*sgn(b*x + a) + 1575*a^4*b^2*x^2*e^6*sgn(b*x + a) + 350*a^4*b^2*d*x*e^5*sgn(b*x + a) + 35*a^4*b^2*d^2*e^4*sgn(b*x + a) + 560*a^5*b*x*e^6*sgn(b*x + a) + 56*a^5*b*d*e^5*sgn(b*x + a) + 84*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^10","B",0
2009,1,520,0,0.199111," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(462 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 462 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 330 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 165 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 55 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 11 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 2310 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 1650 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 825 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 275 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 55 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 4950 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 2475 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 825 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 165 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 5775 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1925 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 385 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 3850 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 770 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1386 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 126 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{2310 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/2310*(462*b^6*x^6*e^6*sgn(b*x + a) + 462*b^6*d*x^5*e^5*sgn(b*x + a) + 330*b^6*d^2*x^4*e^4*sgn(b*x + a) + 165*b^6*d^3*x^3*e^3*sgn(b*x + a) + 55*b^6*d^4*x^2*e^2*sgn(b*x + a) + 11*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 2310*a*b^5*x^5*e^6*sgn(b*x + a) + 1650*a*b^5*d*x^4*e^5*sgn(b*x + a) + 825*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 275*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 55*a*b^5*d^4*x*e^2*sgn(b*x + a) + 5*a*b^5*d^5*e*sgn(b*x + a) + 4950*a^2*b^4*x^4*e^6*sgn(b*x + a) + 2475*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 825*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 165*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 15*a^2*b^4*d^4*e^2*sgn(b*x + a) + 5775*a^3*b^3*x^3*e^6*sgn(b*x + a) + 1925*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 385*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 35*a^3*b^3*d^3*e^3*sgn(b*x + a) + 3850*a^4*b^2*x^2*e^6*sgn(b*x + a) + 770*a^4*b^2*d*x*e^5*sgn(b*x + a) + 70*a^4*b^2*d^2*e^4*sgn(b*x + a) + 1386*a^5*b*x*e^6*sgn(b*x + a) + 126*a^5*b*d*e^5*sgn(b*x + a) + 210*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^11","A",0
2010,1,520,0,0.241801," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^13,x, algorithm=""giac"")","-\frac{{\left(924 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 792 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 495 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 220 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 66 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 4752 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 2970 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 1320 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 396 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 72 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 10395 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 4620 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 1386 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 252 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 12320 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 3696 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 672 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 8316 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 1512 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 3024 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 252 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 462 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{5544 \, {\left(x e + d\right)}^{12}}"," ",0,"-1/5544*(924*b^6*x^6*e^6*sgn(b*x + a) + 792*b^6*d*x^5*e^5*sgn(b*x + a) + 495*b^6*d^2*x^4*e^4*sgn(b*x + a) + 220*b^6*d^3*x^3*e^3*sgn(b*x + a) + 66*b^6*d^4*x^2*e^2*sgn(b*x + a) + 12*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 4752*a*b^5*x^5*e^6*sgn(b*x + a) + 2970*a*b^5*d*x^4*e^5*sgn(b*x + a) + 1320*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 396*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 72*a*b^5*d^4*x*e^2*sgn(b*x + a) + 6*a*b^5*d^5*e*sgn(b*x + a) + 10395*a^2*b^4*x^4*e^6*sgn(b*x + a) + 4620*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 1386*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 252*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 21*a^2*b^4*d^4*e^2*sgn(b*x + a) + 12320*a^3*b^3*x^3*e^6*sgn(b*x + a) + 3696*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 672*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 56*a^3*b^3*d^3*e^3*sgn(b*x + a) + 8316*a^4*b^2*x^2*e^6*sgn(b*x + a) + 1512*a^4*b^2*d*x*e^5*sgn(b*x + a) + 126*a^4*b^2*d^2*e^4*sgn(b*x + a) + 3024*a^5*b*x*e^6*sgn(b*x + a) + 252*a^5*b*d*e^5*sgn(b*x + a) + 462*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^12","A",0
2011,1,520,0,0.204515," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^14,x, algorithm=""giac"")","-\frac{{\left(1716 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 1287 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 715 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 286 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 78 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 13 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 9009 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 5005 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 2002 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 546 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 91 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 20020 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 8008 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 2184 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 364 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 24024 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 6552 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1092 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 16380 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 2730 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 6006 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 462 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 924 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{12012 \, {\left(x e + d\right)}^{13}}"," ",0,"-1/12012*(1716*b^6*x^6*e^6*sgn(b*x + a) + 1287*b^6*d*x^5*e^5*sgn(b*x + a) + 715*b^6*d^2*x^4*e^4*sgn(b*x + a) + 286*b^6*d^3*x^3*e^3*sgn(b*x + a) + 78*b^6*d^4*x^2*e^2*sgn(b*x + a) + 13*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 9009*a*b^5*x^5*e^6*sgn(b*x + a) + 5005*a*b^5*d*x^4*e^5*sgn(b*x + a) + 2002*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 546*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 91*a*b^5*d^4*x*e^2*sgn(b*x + a) + 7*a*b^5*d^5*e*sgn(b*x + a) + 20020*a^2*b^4*x^4*e^6*sgn(b*x + a) + 8008*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 2184*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 364*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 28*a^2*b^4*d^4*e^2*sgn(b*x + a) + 24024*a^3*b^3*x^3*e^6*sgn(b*x + a) + 6552*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 1092*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 84*a^3*b^3*d^3*e^3*sgn(b*x + a) + 16380*a^4*b^2*x^2*e^6*sgn(b*x + a) + 2730*a^4*b^2*d*x*e^5*sgn(b*x + a) + 210*a^4*b^2*d^2*e^4*sgn(b*x + a) + 6006*a^5*b*x*e^6*sgn(b*x + a) + 462*a^5*b*d*e^5*sgn(b*x + a) + 924*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^13","A",0
2012,1,520,0,0.202827," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^15,x, algorithm=""giac"")","-\frac{{\left(3003 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 2002 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 1001 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 364 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 91 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 14 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 16016 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 8008 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 2912 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 728 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 112 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 36036 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 13104 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 3276 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 504 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 43680 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 10920 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1680 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 120 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 30030 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 4620 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 330 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 11088 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 792 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 1716 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{24024 \, {\left(x e + d\right)}^{14}}"," ",0,"-1/24024*(3003*b^6*x^6*e^6*sgn(b*x + a) + 2002*b^6*d*x^5*e^5*sgn(b*x + a) + 1001*b^6*d^2*x^4*e^4*sgn(b*x + a) + 364*b^6*d^3*x^3*e^3*sgn(b*x + a) + 91*b^6*d^4*x^2*e^2*sgn(b*x + a) + 14*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 16016*a*b^5*x^5*e^6*sgn(b*x + a) + 8008*a*b^5*d*x^4*e^5*sgn(b*x + a) + 2912*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 728*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 112*a*b^5*d^4*x*e^2*sgn(b*x + a) + 8*a*b^5*d^5*e*sgn(b*x + a) + 36036*a^2*b^4*x^4*e^6*sgn(b*x + a) + 13104*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 3276*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 504*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 36*a^2*b^4*d^4*e^2*sgn(b*x + a) + 43680*a^3*b^3*x^3*e^6*sgn(b*x + a) + 10920*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 1680*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 120*a^3*b^3*d^3*e^3*sgn(b*x + a) + 30030*a^4*b^2*x^2*e^6*sgn(b*x + a) + 4620*a^4*b^2*d*x*e^5*sgn(b*x + a) + 330*a^4*b^2*d^2*e^4*sgn(b*x + a) + 11088*a^5*b*x*e^6*sgn(b*x + a) + 792*a^5*b*d*e^5*sgn(b*x + a) + 1716*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^14","A",0
2013,1,520,0,0.192516," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^16,x, algorithm=""giac"")","-\frac{{\left(5005 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 3003 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 1365 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 455 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 105 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 27027 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 12285 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 4095 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 945 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 135 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 61425 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 20475 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 4725 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 675 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 75075 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 17325 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 2475 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 165 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 51975 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 7425 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 495 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 19305 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 1287 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 3003 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{45045 \, {\left(x e + d\right)}^{15}}"," ",0,"-1/45045*(5005*b^6*x^6*e^6*sgn(b*x + a) + 3003*b^6*d*x^5*e^5*sgn(b*x + a) + 1365*b^6*d^2*x^4*e^4*sgn(b*x + a) + 455*b^6*d^3*x^3*e^3*sgn(b*x + a) + 105*b^6*d^4*x^2*e^2*sgn(b*x + a) + 15*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 27027*a*b^5*x^5*e^6*sgn(b*x + a) + 12285*a*b^5*d*x^4*e^5*sgn(b*x + a) + 4095*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 945*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 135*a*b^5*d^4*x*e^2*sgn(b*x + a) + 9*a*b^5*d^5*e*sgn(b*x + a) + 61425*a^2*b^4*x^4*e^6*sgn(b*x + a) + 20475*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 4725*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 675*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 45*a^2*b^4*d^4*e^2*sgn(b*x + a) + 75075*a^3*b^3*x^3*e^6*sgn(b*x + a) + 17325*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 2475*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 165*a^3*b^3*d^3*e^3*sgn(b*x + a) + 51975*a^4*b^2*x^2*e^6*sgn(b*x + a) + 7425*a^4*b^2*d*x*e^5*sgn(b*x + a) + 495*a^4*b^2*d^2*e^4*sgn(b*x + a) + 19305*a^5*b*x*e^6*sgn(b*x + a) + 1287*a^5*b*d*e^5*sgn(b*x + a) + 3003*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^15","A",0
2014,1,520,0,0.224748," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^17,x, algorithm=""giac"")","-\frac{{\left(8008 \, b^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 4368 \, b^{6} d x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 1820 \, b^{6} d^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 560 \, b^{6} d^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 120 \, b^{6} d^{4} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 16 \, b^{6} d^{5} x e \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 43680 \, a b^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 18200 \, a b^{5} d x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 5600 \, a b^{5} d^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 1200 \, a b^{5} d^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 160 \, a b^{5} d^{4} x e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 100100 \, a^{2} b^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 30800 \, a^{2} b^{4} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 6600 \, a^{2} b^{4} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 880 \, a^{2} b^{4} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 55 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 123200 \, a^{3} b^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 26400 \, a^{3} b^{3} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 3520 \, a^{3} b^{3} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 220 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 85800 \, a^{4} b^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 11440 \, a^{4} b^{2} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 715 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 32032 \, a^{5} b x e^{6} \mathrm{sgn}\left(b x + a\right) + 2002 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 5005 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{80080 \, {\left(x e + d\right)}^{16}}"," ",0,"-1/80080*(8008*b^6*x^6*e^6*sgn(b*x + a) + 4368*b^6*d*x^5*e^5*sgn(b*x + a) + 1820*b^6*d^2*x^4*e^4*sgn(b*x + a) + 560*b^6*d^3*x^3*e^3*sgn(b*x + a) + 120*b^6*d^4*x^2*e^2*sgn(b*x + a) + 16*b^6*d^5*x*e*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) + 43680*a*b^5*x^5*e^6*sgn(b*x + a) + 18200*a*b^5*d*x^4*e^5*sgn(b*x + a) + 5600*a*b^5*d^2*x^3*e^4*sgn(b*x + a) + 1200*a*b^5*d^3*x^2*e^3*sgn(b*x + a) + 160*a*b^5*d^4*x*e^2*sgn(b*x + a) + 10*a*b^5*d^5*e*sgn(b*x + a) + 100100*a^2*b^4*x^4*e^6*sgn(b*x + a) + 30800*a^2*b^4*d*x^3*e^5*sgn(b*x + a) + 6600*a^2*b^4*d^2*x^2*e^4*sgn(b*x + a) + 880*a^2*b^4*d^3*x*e^3*sgn(b*x + a) + 55*a^2*b^4*d^4*e^2*sgn(b*x + a) + 123200*a^3*b^3*x^3*e^6*sgn(b*x + a) + 26400*a^3*b^3*d*x^2*e^5*sgn(b*x + a) + 3520*a^3*b^3*d^2*x*e^4*sgn(b*x + a) + 220*a^3*b^3*d^3*e^3*sgn(b*x + a) + 85800*a^4*b^2*x^2*e^6*sgn(b*x + a) + 11440*a^4*b^2*d*x*e^5*sgn(b*x + a) + 715*a^4*b^2*d^2*e^4*sgn(b*x + a) + 32032*a^5*b*x*e^6*sgn(b*x + a) + 2002*a^5*b*d*e^5*sgn(b*x + a) + 5005*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^16","A",0
2015,1,18,0,0.152221," ","integrate((b*x+a)*(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(x e + d\right)}^{5} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/5*(x*e + d)^5*e^(-1)*sgn(b*x + a)","A",0
2016,1,18,0,0.169063," ","integrate((b*x+a)*(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(x e + d\right)}^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/4*(x*e + d)^4*e^(-1)*sgn(b*x + a)","A",0
2017,1,18,0,0.184288," ","integrate((b*x+a)*(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(x e + d\right)}^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/3*(x*e + d)^3*e^(-1)*sgn(b*x + a)","A",0
2018,1,19,0,0.148057," ","integrate((b*x+a)*(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/2*(x^2*e + 2*d*x)*sgn(b*x + a)","A",0
2019,1,20,0,0.149962," ","integrate((b*x+a)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","x \mathrm{sgn}\left(b x + a\right) + \frac{a \mathrm{sgn}\left(b x + a\right)}{b}"," ",0,"x*sgn(b*x + a) + a*sgn(b*x + a)/b","A",0
2020,1,17,0,0.164089," ","integrate((b*x+a)/(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right)"," ",0,"e^(-1)*log(abs(x*e + d))*sgn(b*x + a)","A",0
2021,1,18,0,0.170452," ","integrate((b*x+a)/(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{x e + d}"," ",0,"-e^(-1)*sgn(b*x + a)/(x*e + d)","A",0
2022,1,18,0,0.150904," ","integrate((b*x+a)/(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-1/2*e^(-1)*sgn(b*x + a)/(x*e + d)^2","A",0
2023,1,18,0,0.159719," ","integrate((b*x+a)/(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/3*e^(-1)*sgn(b*x + a)/(x*e + d)^3","A",0
2024,1,18,0,0.152720," ","integrate((b*x+a)/(e*x+d)^5/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{4 \, {\left(x e + d\right)}^{4}}"," ",0,"-1/4*e^(-1)*sgn(b*x + a)/(x*e + d)^4","A",0
2025,1,237,0,0.333463," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} {\left(x {\left(\frac{x e^{4}}{b^{3}} + \frac{2 \, {\left(3 \, b^{13} d e^{3} - 2 \, a b^{12} e^{4}\right)}}{b^{16}}\right)} + \frac{18 \, b^{13} d^{2} e^{2} - 30 \, a b^{12} d e^{3} + 13 \, a^{2} b^{11} e^{4}}{b^{16}}\right)} - \frac{4 \, {\left(b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}\right)} \log\left({\left| -3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{2} a b - a^{3} b - {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{3} {\left| b \right|} - 3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)} a^{2} {\left| b \right|} \right|}\right)}{3 \, b^{4} {\left| b \right|}}"," ",0,"1/3*sqrt(b^2*x^2 + 2*a*b*x + a^2)*(x*(x*e^4/b^3 + 2*(3*b^13*d*e^3 - 2*a*b^12*e^4)/b^16) + (18*b^13*d^2*e^2 - 30*a*b^12*d*e^3 + 13*a^2*b^11*e^4)/b^16) - 4/3*(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4)*log(abs(-3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^2*a*b - a^3*b - (x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^3*abs(b) - 3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))*a^2*abs(b)))/(b^4*abs(b))","A",0
2026,1,185,0,0.338588," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} {\left(\frac{x e^{3}}{b^{3}} + \frac{6 \, b^{7} d e^{2} - 5 \, a b^{6} e^{3}}{b^{10}}\right)} - \frac{{\left(b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}\right)} \log\left({\left| -3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{2} a b - a^{3} b - {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{3} {\left| b \right|} - 3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)} a^{2} {\left| b \right|} \right|}\right)}{b^{3} {\left| b \right|}}"," ",0,"1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2)*(x*e^3/b^3 + (6*b^7*d*e^2 - 5*a*b^6*e^3)/b^10) - (b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3)*log(abs(-3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^2*a*b - a^3*b - (x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^3*abs(b) - 3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))*a^2*abs(b)))/(b^3*abs(b))","A",0
2027,1,148,0,0.357491," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(b d e - a e^{2}\right)} \log\left({\left| -3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{2} a b - a^{3} b - {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{3} {\left| b \right|} - 3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)} a^{2} {\left| b \right|} \right|}\right)}{3 \, b^{2} {\left| b \right|}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} e^{2}}{b^{3}}"," ",0,"-2/3*(b*d*e - a*e^2)*log(abs(-3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^2*a*b - a^3*b - (x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^3*abs(b) - 3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))*a^2*abs(b)))/(b^2*abs(b)) + sqrt(b^2*x^2 + 2*a*b*x + a^2)*e^2/b^3","B",0
2028,1,114,0,0.332133," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{e \log\left({\left| -3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{2} a b - a^{3} b - {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}^{3} {\left| b \right|} - 3 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)} a^{2} {\left| b \right|} \right|}\right)}{3 \, b {\left| b \right|}}"," ",0,"-1/3*e*log(abs(-3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^2*a*b - a^3*b - (x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))^3*abs(b) - 3*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2))*a^2*abs(b)))/(b*abs(b))","B",0
2029,0,0,0,0.000000," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
2030,1,203,0,0.244955," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{a e \log\left({\left| b + \frac{a}{x} \right|}\right)}{a b^{2} d^{2} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) - 2 \, a^{2} b d e \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) + a^{3} e^{2} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right)} + \frac{d e \log\left({\left| \frac{d}{x} + e \right|}\right)}{b^{2} d^{3} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) - 2 \, a b d^{2} e \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) + a^{2} d e^{2} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right)} + \frac{b^{2} d - a b e}{{\left(b d - a e\right)}^{2} a {\left(b + \frac{a}{x}\right)} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right)}"," ",0,"-a*e*log(abs(b + a/x))/(a*b^2*d^2*sgn(b/x + a/x^2) - 2*a^2*b*d*e*sgn(b/x + a/x^2) + a^3*e^2*sgn(b/x + a/x^2)) + d*e*log(abs(d/x + e))/(b^2*d^3*sgn(b/x + a/x^2) - 2*a*b*d^2*e*sgn(b/x + a/x^2) + a^2*d*e^2*sgn(b/x + a/x^2)) + (b^2*d - a*b*e)/((b*d - a*e)^2*a*(b + a/x)*sgn(b/x + a/x^2))","B",0
2031,1,486,0,0.463535," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, b e^{2} \log\left({\left| -b + \frac{b d}{x e + d} - \frac{a e}{x e + d} \right|}\right)}{b^{3} d^{3} e \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 3 \, a b^{2} d^{2} e^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 3 \, a^{2} b d e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - a^{3} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} + \frac{e^{3}}{{\left(b^{2} d^{2} e^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 2 \, a b d e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + a^{2} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)\right)} {\left(x e + d\right)}} + \frac{b^{2} e}{{\left(b d - a e\right)}^{3} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}"," ",0,"2*b*e^2*log(abs(-b + b*d/(x*e + d) - a*e/(x*e + d)))/(b^3*d^3*e*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 3*a*b^2*d^2*e^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 3*a^2*b*d*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - a^3*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) + e^3/((b^2*d^2*e^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 2*a*b*d*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + a^2*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))*(x*e + d)) + b^2*e/((b*d - a*e)^3*(b - b*d/(x*e + d) + a*e/(x*e + d))*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))","B",0
2032,1,461,0,2.845580," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{3 \, a b^{2} e \log\left({\left| b + \frac{a}{x} \right|}\right)}{a b^{4} d^{4} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) - 4 \, a^{2} b^{3} d^{3} e \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) + 6 \, a^{3} b^{2} d^{2} e^{2} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) - 4 \, a^{4} b d e^{3} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) + a^{5} e^{4} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right)} + \frac{3 \, b^{2} d e \log\left({\left| \frac{d}{x} + e \right|}\right)}{b^{4} d^{5} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) - 4 \, a b^{3} d^{4} e \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) + 6 \, a^{2} b^{2} d^{3} e^{2} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) - 4 \, a^{3} b d^{2} e^{3} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right) + a^{4} d e^{4} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right)} + \frac{2 \, b^{4} d^{3} e^{2} + 3 \, a b^{3} d^{2} e^{3} - 6 \, a^{2} b^{2} d e^{4} + a^{3} b e^{5} + \frac{4 \, b^{4} d^{4} e + 2 \, a b^{3} d^{3} e^{2} - 3 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}}{x} + \frac{2 \, {\left(b^{4} d^{5} - a b^{3} d^{4} e + 3 \, a^{2} b^{2} d^{3} e^{2} - 4 \, a^{3} b d^{2} e^{3} + a^{4} d e^{4}\right)}}{x^{2}}}{2 \, {\left(b d - a e\right)}^{4} a {\left(b + \frac{a}{x}\right)} d^{2} {\left(\frac{d}{x} + e\right)}^{2} \mathrm{sgn}\left(\frac{b}{x} + \frac{a}{x^{2}}\right)}"," ",0,"-3*a*b^2*e*log(abs(b + a/x))/(a*b^4*d^4*sgn(b/x + a/x^2) - 4*a^2*b^3*d^3*e*sgn(b/x + a/x^2) + 6*a^3*b^2*d^2*e^2*sgn(b/x + a/x^2) - 4*a^4*b*d*e^3*sgn(b/x + a/x^2) + a^5*e^4*sgn(b/x + a/x^2)) + 3*b^2*d*e*log(abs(d/x + e))/(b^4*d^5*sgn(b/x + a/x^2) - 4*a*b^3*d^4*e*sgn(b/x + a/x^2) + 6*a^2*b^2*d^3*e^2*sgn(b/x + a/x^2) - 4*a^3*b*d^2*e^3*sgn(b/x + a/x^2) + a^4*d*e^4*sgn(b/x + a/x^2)) + 1/2*(2*b^4*d^3*e^2 + 3*a*b^3*d^2*e^3 - 6*a^2*b^2*d*e^4 + a^3*b*e^5 + (4*b^4*d^4*e + 2*a*b^3*d^3*e^2 - 3*a^2*b^2*d^2*e^3 - 4*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 - 4*a^3*b*d^2*e^3 + a^4*d*e^4)/x^2)/((b*d - a*e)^4*a*(b + a/x)*d^2*(d/x + e)^2*sgn(b/x + a/x^2))","B",0
2033,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{5}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^5/(b^2*x^2 + 2*a*b*x + a^2)^(5/2), x)","F",0
2034,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{4}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^4/(b^2*x^2 + 2*a*b*x + a^2)^(5/2), x)","F",0
2035,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{3}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^3/(b^2*x^2 + 2*a*b*x + a^2)^(5/2), x)","F",0
2036,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{2}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^2/(b^2*x^2 + 2*a*b*x + a^2)^(5/2), x)","F",0
2037,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)/(b^2*x^2 + 2*a*b*x + a^2)^(5/2), x)","F",0
2038,1,23,0,0.199954," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{1}{3 \, {\left(a^{2} + {\left(b x^{2} + 2 \, a x\right)} b\right)}^{\frac{3}{2}} b}"," ",0,"-1/3/((a^2 + (b*x^2 + 2*a*x)*b)^(3/2)*b)","A",0
2039,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{b x + a}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate((b*x + a)/((b^2*x^2 + 2*a*b*x + a^2)^(5/2)*(e*x + d)), x)","F",0
2040,1,774,0,0.505872," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{4 \, b e^{4} \log\left({\left| -b + \frac{b d}{x e + d} - \frac{a e}{x e + d} \right|}\right)}{b^{5} d^{5} e \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 5 \, a b^{4} d^{4} e^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 10 \, a^{2} b^{3} d^{3} e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 10 \, a^{3} b^{2} d^{2} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 5 \, a^{4} b d e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - a^{5} e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} + \frac{e^{7}}{{\left(b^{4} d^{4} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 4 \, a b^{3} d^{3} e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 6 \, a^{2} b^{2} d^{2} e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 4 \, a^{3} b d e^{7} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + a^{4} e^{8} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)\right)} {\left(x e + d\right)}} + \frac{13 \, b^{4} e^{3} - \frac{30 \, {\left(b^{4} d e^{4} - a b^{3} e^{5}\right)} e^{\left(-1\right)}}{x e + d} + \frac{18 \, {\left(b^{4} d^{2} e^{5} - 2 \, a b^{3} d e^{6} + a^{2} b^{2} e^{7}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}}{3 \, {\left(b d - a e\right)}^{5} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}"," ",0,"4*b*e^4*log(abs(-b + b*d/(x*e + d) - a*e/(x*e + d)))/(b^5*d^5*e*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 5*a*b^4*d^4*e^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 10*a^2*b^3*d^3*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 10*a^3*b^2*d^2*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 5*a^4*b*d*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - a^5*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) + e^7/((b^4*d^4*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 4*a*b^3*d^3*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 6*a^2*b^2*d^2*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 4*a^3*b*d*e^7*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + a^4*e^8*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))*(x*e + d)) + 1/3*(13*b^4*e^3 - 30*(b^4*d*e^4 - a*b^3*e^5)*e^(-1)/(x*e + d) + 18*(b^4*d^2*e^5 - 2*a*b^3*d*e^6 + a^2*b^2*e^7)*e^(-2)/(x*e + d)^2)/((b*d - a*e)^5*(b - b*d/(x*e + d) + a*e/(x*e + d))^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))","B",0
2041,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{b x + a}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}} {\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*x + a)/((b^2*x^2 + 2*a*b*x + a^2)^(5/2)*(e*x + d)^3), x)","F",0
2042,1,1270,0,0.257797," ","integrate((b*x+a)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{4} e^{\left(-1\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{4} e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{4} e^{\left(-3\right)} + 36036 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d^{3} e^{\left(-1\right)} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d^{3} e^{\left(-2\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d^{3} e^{\left(-3\right)} + 45045 \, \sqrt{x e + d} a^{3} d^{4} + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d^{3} + 23166 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b d^{2} e^{\left(-1\right)} + 2574 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} d^{2} e^{\left(-2\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} d^{2} e^{\left(-3\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} d^{2} + 1716 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b d e^{\left(-1\right)} + 780 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{2} d e^{\left(-2\right)} + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} d e^{\left(-3\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} d + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b e^{\left(-1\right)} + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{2} e^{\left(-2\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{3} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^4*e^(-1) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^4*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^4*e^(-3) + 36036*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d^3*e^(-1) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d^3*e^(-2) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d^3*e^(-3) + 45045*sqrt(x*e + d)*a^3*d^4 + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d^3 + 23166*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*d^2*e^(-1) + 2574*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*d^2*e^(-2) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*d^2*e^(-3) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*d^2 + 1716*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b*d*e^(-1) + 780*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^2*d*e^(-2) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*d*e^(-3) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*d + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b*e^(-1) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^2*e^(-2) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^3*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3)*e^(-1)","B",0
2043,1,908,0,0.219391," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{3} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{3} e^{\left(-2\right)} + 429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{3} e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d^{2} e^{\left(-1\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d^{2} e^{\left(-2\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d^{2} e^{\left(-3\right)} + 15015 \, \sqrt{x e + d} a^{3} d^{3} + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d^{2} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b d e^{\left(-1\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} d e^{\left(-2\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} d e^{\left(-3\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} d + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b e^{\left(-1\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{2} e^{\left(-2\right)} + 5 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} e^{\left(-3\right)} + 429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/15015*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^3*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^3*e^(-2) + 429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^3*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d^2*e^(-1) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d^2*e^(-2) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d^2*e^(-3) + 15015*sqrt(x*e + d)*a^3*d^3 + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d^2 + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*d*e^(-1) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*d*e^(-2) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*d*e^(-3) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*d + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b*e^(-1) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^2*e^(-2) + 5*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*e^(-3) + 429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3)*e^(-1)","B",0
2044,1,598,0,0.183645," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{2} e^{\left(-1\right)} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{2} e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{2} e^{\left(-3\right)} + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d e^{\left(-1\right)} + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d e^{\left(-2\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d e^{\left(-3\right)} + 3465 \, \sqrt{x e + d} a^{3} d^{2} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b e^{\left(-1\right)} + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} e^{\left(-2\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} e^{\left(-3\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^2*e^(-1) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^2*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^2*e^(-3) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d*e^(-1) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d*e^(-2) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d*e^(-3) + 3465*sqrt(x*e + d)*a^3*d^2 + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*e^(-1) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*e^(-2) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*e^(-3) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3)*e^(-1)","B",0
2045,1,339,0,0.244192," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(315 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d e^{\left(-1\right)} + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d e^{\left(-2\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d e^{\left(-3\right)} + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b e^{\left(-1\right)} + 27 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} e^{\left(-2\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} e^{\left(-3\right)} + 315 \, \sqrt{x e + d} a^{3} d + 105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/315*(315*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d*e^(-1) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d*e^(-2) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d*e^(-3) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*e^(-1) + 27*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*e^(-2) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*e^(-3) + 315*sqrt(x*e + d)*a^3*d + 105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3)*e^(-1)","B",0
2046,1,143,0,0.192222," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b e^{\left(-1\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} e^{\left(-2\right)} + {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} e^{\left(-3\right)} + 35 \, \sqrt{x e + d} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/35*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*e^(-1) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*e^(-2) + (5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*e^(-3) + 35*sqrt(x*e + d)*a^3)*e^(-1)","A",0
2047,1,150,0,0.187944," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left({\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{16} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{16} + 15 \, \sqrt{x e + d} b^{3} d^{2} e^{16} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} e^{17} - 30 \, \sqrt{x e + d} a b^{2} d e^{17} + 15 \, \sqrt{x e + d} a^{2} b e^{18}\right)} e^{\left(-20\right)} + \frac{2 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} e^{\left(-4\right)}}{\sqrt{x e + d}}"," ",0,"2/5*((x*e + d)^(5/2)*b^3*e^16 - 5*(x*e + d)^(3/2)*b^3*d*e^16 + 15*sqrt(x*e + d)*b^3*d^2*e^16 + 5*(x*e + d)^(3/2)*a*b^2*e^17 - 30*sqrt(x*e + d)*a*b^2*d*e^17 + 15*sqrt(x*e + d)*a^2*b*e^18)*e^(-20) + 2*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*e^(-4)/sqrt(x*e + d)","A",0
2048,1,142,0,0.175185," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{8} - 9 \, \sqrt{x e + d} b^{3} d e^{8} + 9 \, \sqrt{x e + d} a b^{2} e^{9}\right)} e^{\left(-12\right)} - \frac{2 \, {\left(9 \, {\left(x e + d\right)} b^{3} d^{2} - b^{3} d^{3} - 18 \, {\left(x e + d\right)} a b^{2} d e + 3 \, a b^{2} d^{2} e + 9 \, {\left(x e + d\right)} a^{2} b e^{2} - 3 \, a^{2} b d e^{2} + a^{3} e^{3}\right)} e^{\left(-4\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*b^3*e^8 - 9*sqrt(x*e + d)*b^3*d*e^8 + 9*sqrt(x*e + d)*a*b^2*e^9)*e^(-12) - 2/3*(9*(x*e + d)*b^3*d^2 - b^3*d^3 - 18*(x*e + d)*a*b^2*d*e + 3*a*b^2*d^2*e + 9*(x*e + d)*a^2*b*e^2 - 3*a^2*b*d*e^2 + a^3*e^3)*e^(-4)/(x*e + d)^(3/2)","A",0
2049,1,136,0,0.185059," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(7/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b^{3} e^{\left(-4\right)} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} b^{3} d - 5 \, {\left(x e + d\right)} b^{3} d^{2} + b^{3} d^{3} - 15 \, {\left(x e + d\right)}^{2} a b^{2} e + 10 \, {\left(x e + d\right)} a b^{2} d e - 3 \, a b^{2} d^{2} e - 5 \, {\left(x e + d\right)} a^{2} b e^{2} + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} e^{\left(-4\right)}}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2*sqrt(x*e + d)*b^3*e^(-4) + 2/5*(15*(x*e + d)^2*b^3*d - 5*(x*e + d)*b^3*d^2 + b^3*d^3 - 15*(x*e + d)^2*a*b^2*e + 10*(x*e + d)*a*b^2*d*e - 3*a*b^2*d^2*e - 5*(x*e + d)*a^2*b*e^2 + 3*a^2*b*d*e^2 - a^3*e^3)*e^(-4)/(x*e + d)^(5/2)","A",0
2050,1,2325,0,0.310726," ","integrate((b*x+a)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(24249225 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b d^{4} e^{\left(-1\right)} + 9699690 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} d^{4} e^{\left(-2\right)} + 4157010 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} d^{4} e^{\left(-3\right)} + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} d^{4} e^{\left(-4\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} d^{4} e^{\left(-5\right)} + 19399380 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b d^{3} e^{\left(-1\right)} + 16628040 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{2} d^{3} e^{\left(-2\right)} + 1847560 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{3} d^{3} e^{\left(-3\right)} + 419900 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{4} d^{3} e^{\left(-4\right)} + 19380 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{5} d^{3} e^{\left(-5\right)} + 14549535 \, \sqrt{x e + d} a^{5} d^{4} + 19399380 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} d^{3} + 12471030 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b d^{2} e^{\left(-1\right)} + 2771340 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{2} d^{2} e^{\left(-2\right)} + 1259700 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{3} d^{2} e^{\left(-3\right)} + 145350 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{4} d^{2} e^{\left(-4\right)} + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{5} d^{2} e^{\left(-5\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} d^{2} + 923780 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b d e^{\left(-1\right)} + 839800 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{2} d e^{\left(-2\right)} + 193800 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{3} d e^{\left(-3\right)} + 45220 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{4} d e^{\left(-4\right)} + 532 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{5} d e^{\left(-5\right)} + 1662804 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} d + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{4} b e^{\left(-1\right)} + 48450 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{3} b^{2} e^{\left(-2\right)} + 22610 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{2} b^{3} e^{\left(-3\right)} + 665 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a b^{4} e^{\left(-4\right)} + 63 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b^{5} e^{\left(-5\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{5}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(24249225*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*d^4*e^(-1) + 9699690*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*d^4*e^(-2) + 4157010*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*d^4*e^(-3) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*d^4*e^(-4) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*d^4*e^(-5) + 19399380*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b*d^3*e^(-1) + 16628040*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^2*d^3*e^(-2) + 1847560*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^3*d^3*e^(-3) + 419900*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^4*d^3*e^(-4) + 19380*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^5*d^3*e^(-5) + 14549535*sqrt(x*e + d)*a^5*d^4 + 19399380*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*d^3 + 12471030*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b*d^2*e^(-1) + 2771340*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^2*d^2*e^(-2) + 1259700*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^3*d^2*e^(-3) + 145350*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^4*d^2*e^(-4) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^5*d^2*e^(-5) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*d^2 + 923780*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b*d*e^(-1) + 839800*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^2*d*e^(-2) + 193800*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^3*d*e^(-3) + 45220*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^4*d*e^(-4) + 532*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^5*d*e^(-5) + 1662804*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*d + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^4*b*e^(-1) + 48450*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^3*b^2*e^(-2) + 22610*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^2*b^3*e^(-3) + 665*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*b^4*e^(-4) + 63*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b^5*e^(-5) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^5)*e^(-1)","B",0
2051,1,1698,0,0.274093," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(1276275 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b d^{3} e^{\left(-1\right)} + 510510 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} d^{3} e^{\left(-2\right)} + 218790 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} d^{3} e^{\left(-3\right)} + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} d^{3} e^{\left(-4\right)} + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} d^{3} e^{\left(-5\right)} + 765765 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b d^{2} e^{\left(-1\right)} + 656370 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{2} d^{2} e^{\left(-2\right)} + 72930 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{3} d^{2} e^{\left(-3\right)} + 16575 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{4} d^{2} e^{\left(-4\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{5} d^{2} e^{\left(-5\right)} + 765765 \, \sqrt{x e + d} a^{5} d^{3} + 765765 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} d^{2} + 328185 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b d e^{\left(-1\right)} + 72930 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{2} d e^{\left(-2\right)} + 33150 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{3} d e^{\left(-3\right)} + 3825 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{4} d e^{\left(-4\right)} + 357 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{5} d e^{\left(-5\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} d + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b e^{\left(-1\right)} + 11050 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{2} e^{\left(-2\right)} + 2550 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{3} e^{\left(-3\right)} + 595 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{4} e^{\left(-4\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{5} e^{\left(-5\right)} + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(1276275*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*d^3*e^(-1) + 510510*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*d^3*e^(-2) + 218790*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*d^3*e^(-3) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*d^3*e^(-4) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*d^3*e^(-5) + 765765*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b*d^2*e^(-1) + 656370*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^2*d^2*e^(-2) + 72930*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^3*d^2*e^(-3) + 16575*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^4*d^2*e^(-4) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^5*d^2*e^(-5) + 765765*sqrt(x*e + d)*a^5*d^3 + 765765*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*d^2 + 328185*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b*d*e^(-1) + 72930*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^2*d*e^(-2) + 33150*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^3*d*e^(-3) + 3825*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^4*d*e^(-4) + 357*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^5*d*e^(-5) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*d + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b*e^(-1) + 11050*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^2*e^(-2) + 2550*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^3*e^(-3) + 595*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^4*e^(-4) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^5*e^(-5) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5)*e^(-1)","B",0
2052,1,1149,0,0.225034," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(75075 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b d^{2} e^{\left(-1\right)} + 30030 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} d^{2} e^{\left(-2\right)} + 12870 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} d^{2} e^{\left(-3\right)} + 715 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} d^{2} e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} d^{2} e^{\left(-5\right)} + 30030 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b d e^{\left(-1\right)} + 25740 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{2} d e^{\left(-2\right)} + 2860 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{3} d e^{\left(-3\right)} + 650 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{4} d e^{\left(-4\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{5} d e^{\left(-5\right)} + 45045 \, \sqrt{x e + d} a^{5} d^{2} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} d + 6435 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b e^{\left(-1\right)} + 1430 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{2} e^{\left(-2\right)} + 650 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{3} e^{\left(-3\right)} + 75 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{4} e^{\left(-4\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{5} e^{\left(-5\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(75075*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*d^2*e^(-1) + 30030*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*d^2*e^(-2) + 12870*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*d^2*e^(-3) + 715*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*d^2*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*d^2*e^(-5) + 30030*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b*d*e^(-1) + 25740*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^2*d*e^(-2) + 2860*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^3*d*e^(-3) + 650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^4*d*e^(-4) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^5*d*e^(-5) + 45045*sqrt(x*e + d)*a^5*d^2 + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*d + 6435*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b*e^(-1) + 1430*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^2*e^(-2) + 650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^3*e^(-3) + 75*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^4*e^(-4) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^5*e^(-5) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5)*e^(-1)","B",0
2053,1,678,0,0.186697," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{9009} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b d e^{\left(-1\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} d e^{\left(-2\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} d e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} d e^{\left(-4\right)} + 13 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} d e^{\left(-5\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b e^{\left(-1\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{2} e^{\left(-2\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{3} e^{\left(-3\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{4} e^{\left(-4\right)} + 3 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{5} e^{\left(-5\right)} + 9009 \, \sqrt{x e + d} a^{5} d + 3003 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5}\right)} e^{\left(-1\right)}"," ",0,"2/9009*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*d*e^(-1) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*d*e^(-2) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*d*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*d*e^(-4) + 13*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*d*e^(-5) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b*e^(-1) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^2*e^(-2) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^3*e^(-3) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^4*e^(-4) + 3*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^5*e^(-5) + 9009*sqrt(x*e + d)*a^5*d + 3003*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5)*e^(-1)","B",0
2054,1,298,0,0.174545," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{693} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b e^{\left(-1\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} e^{\left(-3\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} e^{\left(-4\right)} + {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} e^{\left(-5\right)} + 693 \, \sqrt{x e + d} a^{5}\right)} e^{\left(-1\right)}"," ",0,"2/693*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*e^(-1) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*e^(-3) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*e^(-4) + (63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*e^(-5) + 693*sqrt(x*e + d)*a^5)*e^(-1)","B",0
2055,1,346,0,0.195829," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{63} \, {\left(7 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{5} e^{48} - 45 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} d e^{48} + 126 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d^{2} e^{48} - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{3} e^{48} + 315 \, \sqrt{x e + d} b^{5} d^{4} e^{48} + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{4} e^{49} - 252 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} d e^{49} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d^{2} e^{49} - 1260 \, \sqrt{x e + d} a b^{4} d^{3} e^{49} + 126 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{3} e^{50} - 630 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} d e^{50} + 1890 \, \sqrt{x e + d} a^{2} b^{3} d^{2} e^{50} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{2} e^{51} - 1260 \, \sqrt{x e + d} a^{3} b^{2} d e^{51} + 315 \, \sqrt{x e + d} a^{4} b e^{52}\right)} e^{\left(-54\right)} + \frac{2 \, {\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)} e^{\left(-6\right)}}{\sqrt{x e + d}}"," ",0,"2/63*(7*(x*e + d)^(9/2)*b^5*e^48 - 45*(x*e + d)^(7/2)*b^5*d*e^48 + 126*(x*e + d)^(5/2)*b^5*d^2*e^48 - 210*(x*e + d)^(3/2)*b^5*d^3*e^48 + 315*sqrt(x*e + d)*b^5*d^4*e^48 + 45*(x*e + d)^(7/2)*a*b^4*e^49 - 252*(x*e + d)^(5/2)*a*b^4*d*e^49 + 630*(x*e + d)^(3/2)*a*b^4*d^2*e^49 - 1260*sqrt(x*e + d)*a*b^4*d^3*e^49 + 126*(x*e + d)^(5/2)*a^2*b^3*e^50 - 630*(x*e + d)^(3/2)*a^2*b^3*d*e^50 + 1890*sqrt(x*e + d)*a^2*b^3*d^2*e^50 + 210*(x*e + d)^(3/2)*a^3*b^2*e^51 - 1260*sqrt(x*e + d)*a^3*b^2*d*e^51 + 315*sqrt(x*e + d)*a^4*b*e^52)*e^(-54) + 2*(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)*e^(-6)/sqrt(x*e + d)","B",0
2056,1,334,0,0.206053," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{21} \, {\left(3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} e^{36} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d e^{36} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{2} e^{36} - 210 \, \sqrt{x e + d} b^{5} d^{3} e^{36} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} e^{37} - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d e^{37} + 630 \, \sqrt{x e + d} a b^{4} d^{2} e^{37} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} e^{38} - 630 \, \sqrt{x e + d} a^{2} b^{3} d e^{38} + 210 \, \sqrt{x e + d} a^{3} b^{2} e^{39}\right)} e^{\left(-42\right)} - \frac{2 \, {\left(15 \, {\left(x e + d\right)} b^{5} d^{4} - b^{5} d^{5} - 60 \, {\left(x e + d\right)} a b^{4} d^{3} e + 5 \, a b^{4} d^{4} e + 90 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} - 10 \, a^{2} b^{3} d^{3} e^{2} - 60 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} + 10 \, a^{3} b^{2} d^{2} e^{3} + 15 \, {\left(x e + d\right)} a^{4} b e^{4} - 5 \, a^{4} b d e^{4} + a^{5} e^{5}\right)} e^{\left(-6\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/21*(3*(x*e + d)^(7/2)*b^5*e^36 - 21*(x*e + d)^(5/2)*b^5*d*e^36 + 70*(x*e + d)^(3/2)*b^5*d^2*e^36 - 210*sqrt(x*e + d)*b^5*d^3*e^36 + 21*(x*e + d)^(5/2)*a*b^4*e^37 - 140*(x*e + d)^(3/2)*a*b^4*d*e^37 + 630*sqrt(x*e + d)*a*b^4*d^2*e^37 + 70*(x*e + d)^(3/2)*a^2*b^3*e^38 - 630*sqrt(x*e + d)*a^2*b^3*d*e^38 + 210*sqrt(x*e + d)*a^3*b^2*e^39)*e^(-42) - 2/3*(15*(x*e + d)*b^5*d^4 - b^5*d^5 - 60*(x*e + d)*a*b^4*d^3*e + 5*a*b^4*d^4*e + 90*(x*e + d)*a^2*b^3*d^2*e^2 - 10*a^2*b^3*d^3*e^2 - 60*(x*e + d)*a^3*b^2*d*e^3 + 10*a^3*b^2*d^2*e^3 + 15*(x*e + d)*a^4*b*e^4 - 5*a^4*b*d*e^4 + a^5*e^5)*e^(-6)/(x*e + d)^(3/2)","B",0
2057,1,333,0,0.202312," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} e^{24} - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d e^{24} + 150 \, \sqrt{x e + d} b^{5} d^{2} e^{24} + 25 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} e^{25} - 300 \, \sqrt{x e + d} a b^{4} d e^{25} + 150 \, \sqrt{x e + d} a^{2} b^{3} e^{26}\right)} e^{\left(-30\right)} + \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} b^{5} d^{3} - 25 \, {\left(x e + d\right)} b^{5} d^{4} + 3 \, b^{5} d^{5} - 450 \, {\left(x e + d\right)}^{2} a b^{4} d^{2} e + 100 \, {\left(x e + d\right)} a b^{4} d^{3} e - 15 \, a b^{4} d^{4} e + 450 \, {\left(x e + d\right)}^{2} a^{2} b^{3} d e^{2} - 150 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} + 30 \, a^{2} b^{3} d^{3} e^{2} - 150 \, {\left(x e + d\right)}^{2} a^{3} b^{2} e^{3} + 100 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} - 30 \, a^{3} b^{2} d^{2} e^{3} - 25 \, {\left(x e + d\right)} a^{4} b e^{4} + 15 \, a^{4} b d e^{4} - 3 \, a^{5} e^{5}\right)} e^{\left(-6\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*b^5*e^24 - 25*(x*e + d)^(3/2)*b^5*d*e^24 + 150*sqrt(x*e + d)*b^5*d^2*e^24 + 25*(x*e + d)^(3/2)*a*b^4*e^25 - 300*sqrt(x*e + d)*a*b^4*d*e^25 + 150*sqrt(x*e + d)*a^2*b^3*e^26)*e^(-30) + 2/15*(150*(x*e + d)^2*b^5*d^3 - 25*(x*e + d)*b^5*d^4 + 3*b^5*d^5 - 450*(x*e + d)^2*a*b^4*d^2*e + 100*(x*e + d)*a*b^4*d^3*e - 15*a*b^4*d^4*e + 450*(x*e + d)^2*a^2*b^3*d*e^2 - 150*(x*e + d)*a^2*b^3*d^2*e^2 + 30*a^2*b^3*d^3*e^2 - 150*(x*e + d)^2*a^3*b^2*e^3 + 100*(x*e + d)*a^3*b^2*d*e^3 - 30*a^3*b^2*d^2*e^3 - 25*(x*e + d)*a^4*b*e^4 + 15*a^4*b*d*e^4 - 3*a^5*e^5)*e^(-6)/(x*e + d)^(5/2)","B",0
2058,1,3640,0,0.409309," ","integrate((b*x+a)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{334639305} \, {\left(780825045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} b d^{4} e^{\left(-1\right)} + 468495027 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b^{2} d^{4} e^{\left(-2\right)} + 334639305 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{3} d^{4} e^{\left(-3\right)} + 37182145 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{4} d^{4} e^{\left(-4\right)} + 10140585 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{5} d^{4} e^{\left(-5\right)} + 780045 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{6} d^{4} e^{\left(-6\right)} + 52003 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{7} d^{4} e^{\left(-7\right)} + 624660036 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} b d^{3} e^{\left(-1\right)} + 803134332 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b^{2} d^{3} e^{\left(-2\right)} + 148728580 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{3} d^{3} e^{\left(-3\right)} + 67603900 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{4} d^{3} e^{\left(-4\right)} + 9360540 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{5} d^{3} e^{\left(-5\right)} + 1456084 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{6} d^{3} e^{\left(-6\right)} + 12236 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{7} d^{3} e^{\left(-7\right)} + 334639305 \, \sqrt{x e + d} a^{7} d^{4} + 446185740 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{7} d^{3} + 401567166 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{6} b d^{2} e^{\left(-1\right)} + 133855722 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{5} b^{2} d^{2} e^{\left(-2\right)} + 101405850 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{4} b^{3} d^{2} e^{\left(-3\right)} + 23401350 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{3} b^{4} d^{2} e^{\left(-4\right)} + 6552378 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{2} b^{5} d^{2} e^{\left(-5\right)} + 128478 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a b^{6} d^{2} e^{\left(-6\right)} + 8694 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b^{7} d^{2} e^{\left(-7\right)} + 133855722 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{7} d^{2} + 29745716 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{6} b d e^{\left(-1\right)} + 40562340 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{5} b^{2} d e^{\left(-2\right)} + 15600900 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{4} b^{3} d e^{\left(-3\right)} + 7280420 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{3} b^{4} d e^{\left(-4\right)} + 256956 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a^{2} b^{5} d e^{\left(-5\right)} + 40572 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} a b^{6} d e^{\left(-6\right)} + 1380 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} b^{7} d e^{\left(-7\right)} + 38244492 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{7} d + 3380195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{6} b e^{\left(-1\right)} + 2340135 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{5} b^{2} e^{\left(-2\right)} + 1820105 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{4} b^{3} e^{\left(-3\right)} + 107065 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a^{3} b^{4} e^{\left(-4\right)} + 30429 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} a^{2} b^{5} e^{\left(-5\right)} + 2415 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} a b^{6} e^{\left(-6\right)} + 165 \, {\left(88179 \, {\left(x e + d\right)}^{\frac{23}{2}} - 1062347 \, {\left(x e + d\right)}^{\frac{21}{2}} d + 5870865 \, {\left(x e + d\right)}^{\frac{19}{2}} d^{2} - 19684665 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{3} + 44618574 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{4} - 72076158 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{5} + 85180914 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{6} - 74364290 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{7} + 47805615 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{8} - 22309287 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{9} + 7436429 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{10} - 2028117 \, \sqrt{x e + d} d^{11}\right)} b^{7} e^{\left(-7\right)} + 1062347 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{7}\right)} e^{\left(-1\right)}"," ",0,"2/334639305*(780825045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*b*d^4*e^(-1) + 468495027*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b^2*d^4*e^(-2) + 334639305*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^3*d^4*e^(-3) + 37182145*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^4*d^4*e^(-4) + 10140585*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^5*d^4*e^(-5) + 780045*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^6*d^4*e^(-6) + 52003*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^7*d^4*e^(-7) + 624660036*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*b*d^3*e^(-1) + 803134332*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b^2*d^3*e^(-2) + 148728580*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^3*d^3*e^(-3) + 67603900*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^4*d^3*e^(-4) + 9360540*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^5*d^3*e^(-5) + 1456084*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^6*d^3*e^(-6) + 12236*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^7*d^3*e^(-7) + 334639305*sqrt(x*e + d)*a^7*d^4 + 446185740*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^7*d^3 + 401567166*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^6*b*d^2*e^(-1) + 133855722*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^5*b^2*d^2*e^(-2) + 101405850*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^4*b^3*d^2*e^(-3) + 23401350*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^3*b^4*d^2*e^(-4) + 6552378*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^2*b^5*d^2*e^(-5) + 128478*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*b^6*d^2*e^(-6) + 8694*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b^7*d^2*e^(-7) + 133855722*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^7*d^2 + 29745716*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^6*b*d*e^(-1) + 40562340*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^5*b^2*d*e^(-2) + 15600900*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^4*b^3*d*e^(-3) + 7280420*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^3*b^4*d*e^(-4) + 256956*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a^2*b^5*d*e^(-5) + 40572*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*a*b^6*d*e^(-6) + 1380*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*b^7*d*e^(-7) + 38244492*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^7*d + 3380195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^6*b*e^(-1) + 2340135*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^5*b^2*e^(-2) + 1820105*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^4*b^3*e^(-3) + 107065*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a^3*b^4*e^(-4) + 30429*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*a^2*b^5*e^(-5) + 2415*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*a*b^6*e^(-6) + 165*(88179*(x*e + d)^(23/2) - 1062347*(x*e + d)^(21/2)*d + 5870865*(x*e + d)^(19/2)*d^2 - 19684665*(x*e + d)^(17/2)*d^3 + 44618574*(x*e + d)^(15/2)*d^4 - 72076158*(x*e + d)^(13/2)*d^5 + 85180914*(x*e + d)^(11/2)*d^6 - 74364290*(x*e + d)^(9/2)*d^7 + 47805615*(x*e + d)^(7/2)*d^8 - 22309287*(x*e + d)^(5/2)*d^9 + 7436429*(x*e + d)^(3/2)*d^10 - 2028117*sqrt(x*e + d)*d^11)*b^7*e^(-7) + 1062347*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^7)*e^(-1)","B",0
2059,1,2696,0,0.429304," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(33948915 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} b d^{3} e^{\left(-1\right)} + 20369349 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b^{2} d^{3} e^{\left(-2\right)} + 14549535 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{3} d^{3} e^{\left(-3\right)} + 1616615 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{4} d^{3} e^{\left(-4\right)} + 440895 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{5} d^{3} e^{\left(-5\right)} + 33915 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{6} d^{3} e^{\left(-6\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{7} d^{3} e^{\left(-7\right)} + 20369349 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} b d^{2} e^{\left(-1\right)} + 26189163 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b^{2} d^{2} e^{\left(-2\right)} + 4849845 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{3} d^{2} e^{\left(-3\right)} + 2204475 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{4} d^{2} e^{\left(-4\right)} + 305235 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{5} d^{2} e^{\left(-5\right)} + 47481 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{6} d^{2} e^{\left(-6\right)} + 399 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{7} d^{2} e^{\left(-7\right)} + 14549535 \, \sqrt{x e + d} a^{7} d^{3} + 14549535 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{7} d^{2} + 8729721 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{6} b d e^{\left(-1\right)} + 2909907 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{5} b^{2} d e^{\left(-2\right)} + 2204475 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{4} b^{3} d e^{\left(-3\right)} + 508725 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{3} b^{4} d e^{\left(-4\right)} + 142443 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{2} b^{5} d e^{\left(-5\right)} + 2793 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a b^{6} d e^{\left(-6\right)} + 189 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b^{7} d e^{\left(-7\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{7} d + 323323 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{6} b e^{\left(-1\right)} + 440895 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{5} b^{2} e^{\left(-2\right)} + 169575 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{4} b^{3} e^{\left(-3\right)} + 79135 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{3} b^{4} e^{\left(-4\right)} + 2793 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a^{2} b^{5} e^{\left(-5\right)} + 441 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} a b^{6} e^{\left(-6\right)} + 15 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} b^{7} e^{\left(-7\right)} + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{7}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(33948915*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*b*d^3*e^(-1) + 20369349*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b^2*d^3*e^(-2) + 14549535*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^3*d^3*e^(-3) + 1616615*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^4*d^3*e^(-4) + 440895*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^5*d^3*e^(-5) + 33915*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^6*d^3*e^(-6) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^7*d^3*e^(-7) + 20369349*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*b*d^2*e^(-1) + 26189163*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b^2*d^2*e^(-2) + 4849845*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^3*d^2*e^(-3) + 2204475*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^4*d^2*e^(-4) + 305235*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^5*d^2*e^(-5) + 47481*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^6*d^2*e^(-6) + 399*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^7*d^2*e^(-7) + 14549535*sqrt(x*e + d)*a^7*d^3 + 14549535*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^7*d^2 + 8729721*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^6*b*d*e^(-1) + 2909907*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^5*b^2*d*e^(-2) + 2204475*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^4*b^3*d*e^(-3) + 508725*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^3*b^4*d*e^(-4) + 142443*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^2*b^5*d*e^(-5) + 2793*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*b^6*d*e^(-6) + 189*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b^7*d*e^(-7) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^7*d + 323323*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^6*b*e^(-1) + 440895*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^5*b^2*e^(-2) + 169575*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^4*b^3*e^(-3) + 79135*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^3*b^4*e^(-4) + 2793*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a^2*b^5*e^(-5) + 441*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*a*b^6*e^(-6) + 15*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*b^7*e^(-7) + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^7)*e^(-1)","B",0
2060,1,1856,0,0.274105," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{2078505} \, {\left(4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} b d^{2} e^{\left(-1\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b^{2} d^{2} e^{\left(-2\right)} + 2078505 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{3} d^{2} e^{\left(-3\right)} + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{4} d^{2} e^{\left(-4\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{5} d^{2} e^{\left(-5\right)} + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{6} d^{2} e^{\left(-6\right)} + 323 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{7} d^{2} e^{\left(-7\right)} + 1939938 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} b d e^{\left(-1\right)} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b^{2} d e^{\left(-2\right)} + 461890 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{3} d e^{\left(-3\right)} + 209950 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{4} d e^{\left(-4\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{5} d e^{\left(-5\right)} + 4522 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{6} d e^{\left(-6\right)} + 38 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{7} d e^{\left(-7\right)} + 2078505 \, \sqrt{x e + d} a^{7} d^{2} + 1385670 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{7} d + 415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{6} b e^{\left(-1\right)} + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{5} b^{2} e^{\left(-2\right)} + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{4} b^{3} e^{\left(-3\right)} + 24225 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{3} b^{4} e^{\left(-4\right)} + 6783 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{2} b^{5} e^{\left(-5\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a b^{6} e^{\left(-6\right)} + 9 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b^{7} e^{\left(-7\right)} + 138567 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{7}\right)} e^{\left(-1\right)}"," ",0,"2/2078505*(4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*b*d^2*e^(-1) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b^2*d^2*e^(-2) + 2078505*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^3*d^2*e^(-3) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^4*d^2*e^(-4) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^5*d^2*e^(-5) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^6*d^2*e^(-6) + 323*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^7*d^2*e^(-7) + 1939938*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*b*d*e^(-1) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b^2*d*e^(-2) + 461890*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^3*d*e^(-3) + 209950*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^4*d*e^(-4) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^5*d*e^(-5) + 4522*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^6*d*e^(-6) + 38*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^7*d*e^(-7) + 2078505*sqrt(x*e + d)*a^7*d^2 + 1385670*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^7*d + 415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^6*b*e^(-1) + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^5*b^2*e^(-2) + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^4*b^3*e^(-3) + 24225*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^3*b^4*e^(-4) + 6783*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^2*b^5*e^(-5) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*b^6*e^(-6) + 9*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b^7*e^(-7) + 138567*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^7)*e^(-1)","B",0
2061,1,1119,0,0.222229," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{109395} \, {\left(255255 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} b d e^{\left(-1\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b^{2} d e^{\left(-2\right)} + 109395 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{3} d e^{\left(-3\right)} + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{4} d e^{\left(-4\right)} + 3315 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{5} d e^{\left(-5\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{6} d e^{\left(-6\right)} + 17 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{7} d e^{\left(-7\right)} + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} b e^{\left(-1\right)} + 65637 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b^{2} e^{\left(-2\right)} + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{3} e^{\left(-3\right)} + 5525 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{4} e^{\left(-4\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{5} e^{\left(-5\right)} + 119 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{6} e^{\left(-6\right)} + {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{7} e^{\left(-7\right)} + 109395 \, \sqrt{x e + d} a^{7} d + 36465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{7}\right)} e^{\left(-1\right)}"," ",0,"2/109395*(255255*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*b*d*e^(-1) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b^2*d*e^(-2) + 109395*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^3*d*e^(-3) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^4*d*e^(-4) + 3315*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^5*d*e^(-5) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^6*d*e^(-6) + 17*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^7*d*e^(-7) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*b*e^(-1) + 65637*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b^2*e^(-2) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^3*e^(-3) + 5525*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^4*e^(-4) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^5*e^(-5) + 119*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^6*e^(-6) + (6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^7*e^(-7) + 109395*sqrt(x*e + d)*a^7*d + 36465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^7)*e^(-1)","B",0
2062,1,505,0,0.192914," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{6435} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} b e^{\left(-1\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b^{2} e^{\left(-2\right)} + 6435 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{3} e^{\left(-3\right)} + 715 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{4} e^{\left(-4\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{5} e^{\left(-5\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{6} e^{\left(-6\right)} + {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{7} e^{\left(-7\right)} + 6435 \, \sqrt{x e + d} a^{7}\right)} e^{\left(-1\right)}"," ",0,"2/6435*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*b*e^(-1) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b^2*e^(-2) + 6435*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^3*e^(-3) + 715*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^4*e^(-4) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^5*e^(-5) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^6*e^(-6) + (429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^7*e^(-7) + 6435*sqrt(x*e + d)*a^7)*e^(-1)","B",0
2063,1,625,0,0.226410," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{429} \, {\left(33 \, {\left(x e + d\right)}^{\frac{13}{2}} b^{7} e^{96} - 273 \, {\left(x e + d\right)}^{\frac{11}{2}} b^{7} d e^{96} + 1001 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{7} d^{2} e^{96} - 2145 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{7} d^{3} e^{96} + 3003 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{7} d^{4} e^{96} - 3003 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{7} d^{5} e^{96} + 3003 \, \sqrt{x e + d} b^{7} d^{6} e^{96} + 273 \, {\left(x e + d\right)}^{\frac{11}{2}} a b^{6} e^{97} - 2002 \, {\left(x e + d\right)}^{\frac{9}{2}} a b^{6} d e^{97} + 6435 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{6} d^{2} e^{97} - 12012 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{6} d^{3} e^{97} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{6} d^{4} e^{97} - 18018 \, \sqrt{x e + d} a b^{6} d^{5} e^{97} + 1001 \, {\left(x e + d\right)}^{\frac{9}{2}} a^{2} b^{5} e^{98} - 6435 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{5} d e^{98} + 18018 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{5} d^{2} e^{98} - 30030 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{5} d^{3} e^{98} + 45045 \, \sqrt{x e + d} a^{2} b^{5} d^{4} e^{98} + 2145 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{3} b^{4} e^{99} - 12012 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{4} d e^{99} + 30030 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{4} d^{2} e^{99} - 60060 \, \sqrt{x e + d} a^{3} b^{4} d^{3} e^{99} + 3003 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{4} b^{3} e^{100} - 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b^{3} d e^{100} + 45045 \, \sqrt{x e + d} a^{4} b^{3} d^{2} e^{100} + 3003 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{5} b^{2} e^{101} - 18018 \, \sqrt{x e + d} a^{5} b^{2} d e^{101} + 3003 \, \sqrt{x e + d} a^{6} b e^{102}\right)} e^{\left(-104\right)} + \frac{2 \, {\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)} e^{\left(-8\right)}}{\sqrt{x e + d}}"," ",0,"2/429*(33*(x*e + d)^(13/2)*b^7*e^96 - 273*(x*e + d)^(11/2)*b^7*d*e^96 + 1001*(x*e + d)^(9/2)*b^7*d^2*e^96 - 2145*(x*e + d)^(7/2)*b^7*d^3*e^96 + 3003*(x*e + d)^(5/2)*b^7*d^4*e^96 - 3003*(x*e + d)^(3/2)*b^7*d^5*e^96 + 3003*sqrt(x*e + d)*b^7*d^6*e^96 + 273*(x*e + d)^(11/2)*a*b^6*e^97 - 2002*(x*e + d)^(9/2)*a*b^6*d*e^97 + 6435*(x*e + d)^(7/2)*a*b^6*d^2*e^97 - 12012*(x*e + d)^(5/2)*a*b^6*d^3*e^97 + 15015*(x*e + d)^(3/2)*a*b^6*d^4*e^97 - 18018*sqrt(x*e + d)*a*b^6*d^5*e^97 + 1001*(x*e + d)^(9/2)*a^2*b^5*e^98 - 6435*(x*e + d)^(7/2)*a^2*b^5*d*e^98 + 18018*(x*e + d)^(5/2)*a^2*b^5*d^2*e^98 - 30030*(x*e + d)^(3/2)*a^2*b^5*d^3*e^98 + 45045*sqrt(x*e + d)*a^2*b^5*d^4*e^98 + 2145*(x*e + d)^(7/2)*a^3*b^4*e^99 - 12012*(x*e + d)^(5/2)*a^3*b^4*d*e^99 + 30030*(x*e + d)^(3/2)*a^3*b^4*d^2*e^99 - 60060*sqrt(x*e + d)*a^3*b^4*d^3*e^99 + 3003*(x*e + d)^(5/2)*a^4*b^3*e^100 - 15015*(x*e + d)^(3/2)*a^4*b^3*d*e^100 + 45045*sqrt(x*e + d)*a^4*b^3*d^2*e^100 + 3003*(x*e + d)^(3/2)*a^5*b^2*e^101 - 18018*sqrt(x*e + d)*a^5*b^2*d*e^101 + 3003*sqrt(x*e + d)*a^6*b*e^102)*e^(-104) + 2*(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)*e^(-8)/sqrt(x*e + d)","B",0
2064,1,609,0,0.339103," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{99} \, {\left(9 \, {\left(x e + d\right)}^{\frac{11}{2}} b^{7} e^{80} - 77 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{7} d e^{80} + 297 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{7} d^{2} e^{80} - 693 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{7} d^{3} e^{80} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{7} d^{4} e^{80} - 2079 \, \sqrt{x e + d} b^{7} d^{5} e^{80} + 77 \, {\left(x e + d\right)}^{\frac{9}{2}} a b^{6} e^{81} - 594 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{6} d e^{81} + 2079 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{6} d^{2} e^{81} - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{6} d^{3} e^{81} + 10395 \, \sqrt{x e + d} a b^{6} d^{4} e^{81} + 297 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{5} e^{82} - 2079 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{5} d e^{82} + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{5} d^{2} e^{82} - 20790 \, \sqrt{x e + d} a^{2} b^{5} d^{3} e^{82} + 693 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{4} e^{83} - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{4} d e^{83} + 20790 \, \sqrt{x e + d} a^{3} b^{4} d^{2} e^{83} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b^{3} e^{84} - 10395 \, \sqrt{x e + d} a^{4} b^{3} d e^{84} + 2079 \, \sqrt{x e + d} a^{5} b^{2} e^{85}\right)} e^{\left(-88\right)} - \frac{2 \, {\left(21 \, {\left(x e + d\right)} b^{7} d^{6} - b^{7} d^{7} - 126 \, {\left(x e + d\right)} a b^{6} d^{5} e + 7 \, a b^{6} d^{6} e + 315 \, {\left(x e + d\right)} a^{2} b^{5} d^{4} e^{2} - 21 \, a^{2} b^{5} d^{5} e^{2} - 420 \, {\left(x e + d\right)} a^{3} b^{4} d^{3} e^{3} + 35 \, a^{3} b^{4} d^{4} e^{3} + 315 \, {\left(x e + d\right)} a^{4} b^{3} d^{2} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{4} - 126 \, {\left(x e + d\right)} a^{5} b^{2} d e^{5} + 21 \, a^{5} b^{2} d^{2} e^{5} + 21 \, {\left(x e + d\right)} a^{6} b e^{6} - 7 \, a^{6} b d e^{6} + a^{7} e^{7}\right)} e^{\left(-8\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/99*(9*(x*e + d)^(11/2)*b^7*e^80 - 77*(x*e + d)^(9/2)*b^7*d*e^80 + 297*(x*e + d)^(7/2)*b^7*d^2*e^80 - 693*(x*e + d)^(5/2)*b^7*d^3*e^80 + 1155*(x*e + d)^(3/2)*b^7*d^4*e^80 - 2079*sqrt(x*e + d)*b^7*d^5*e^80 + 77*(x*e + d)^(9/2)*a*b^6*e^81 - 594*(x*e + d)^(7/2)*a*b^6*d*e^81 + 2079*(x*e + d)^(5/2)*a*b^6*d^2*e^81 - 4620*(x*e + d)^(3/2)*a*b^6*d^3*e^81 + 10395*sqrt(x*e + d)*a*b^6*d^4*e^81 + 297*(x*e + d)^(7/2)*a^2*b^5*e^82 - 2079*(x*e + d)^(5/2)*a^2*b^5*d*e^82 + 6930*(x*e + d)^(3/2)*a^2*b^5*d^2*e^82 - 20790*sqrt(x*e + d)*a^2*b^5*d^3*e^82 + 693*(x*e + d)^(5/2)*a^3*b^4*e^83 - 4620*(x*e + d)^(3/2)*a^3*b^4*d*e^83 + 20790*sqrt(x*e + d)*a^3*b^4*d^2*e^83 + 1155*(x*e + d)^(3/2)*a^4*b^3*e^84 - 10395*sqrt(x*e + d)*a^4*b^3*d*e^84 + 2079*sqrt(x*e + d)*a^5*b^2*e^85)*e^(-88) - 2/3*(21*(x*e + d)*b^7*d^6 - b^7*d^7 - 126*(x*e + d)*a*b^6*d^5*e + 7*a*b^6*d^6*e + 315*(x*e + d)*a^2*b^5*d^4*e^2 - 21*a^2*b^5*d^5*e^2 - 420*(x*e + d)*a^3*b^4*d^3*e^3 + 35*a^3*b^4*d^4*e^3 + 315*(x*e + d)*a^4*b^3*d^2*e^4 - 35*a^4*b^3*d^3*e^4 - 126*(x*e + d)*a^5*b^2*d*e^5 + 21*a^5*b^2*d^2*e^5 + 21*(x*e + d)*a^6*b*e^6 - 7*a^6*b*d*e^6 + a^7*e^7)*e^(-8)/(x*e + d)^(3/2)","B",0
2065,1,608,0,0.231348," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{45} \, {\left(5 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{7} e^{64} - 45 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{7} d e^{64} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{7} d^{2} e^{64} - 525 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{7} d^{3} e^{64} + 1575 \, \sqrt{x e + d} b^{7} d^{4} e^{64} + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{6} e^{65} - 378 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{6} d e^{65} + 1575 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{6} d^{2} e^{65} - 6300 \, \sqrt{x e + d} a b^{6} d^{3} e^{65} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{5} e^{66} - 1575 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{5} d e^{66} + 9450 \, \sqrt{x e + d} a^{2} b^{5} d^{2} e^{66} + 525 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{4} e^{67} - 6300 \, \sqrt{x e + d} a^{3} b^{4} d e^{67} + 1575 \, \sqrt{x e + d} a^{4} b^{3} e^{68}\right)} e^{\left(-72\right)} + \frac{2 \, {\left(315 \, {\left(x e + d\right)}^{2} b^{7} d^{5} - 35 \, {\left(x e + d\right)} b^{7} d^{6} + 3 \, b^{7} d^{7} - 1575 \, {\left(x e + d\right)}^{2} a b^{6} d^{4} e + 210 \, {\left(x e + d\right)} a b^{6} d^{5} e - 21 \, a b^{6} d^{6} e + 3150 \, {\left(x e + d\right)}^{2} a^{2} b^{5} d^{3} e^{2} - 525 \, {\left(x e + d\right)} a^{2} b^{5} d^{4} e^{2} + 63 \, a^{2} b^{5} d^{5} e^{2} - 3150 \, {\left(x e + d\right)}^{2} a^{3} b^{4} d^{2} e^{3} + 700 \, {\left(x e + d\right)} a^{3} b^{4} d^{3} e^{3} - 105 \, a^{3} b^{4} d^{4} e^{3} + 1575 \, {\left(x e + d\right)}^{2} a^{4} b^{3} d e^{4} - 525 \, {\left(x e + d\right)} a^{4} b^{3} d^{2} e^{4} + 105 \, a^{4} b^{3} d^{3} e^{4} - 315 \, {\left(x e + d\right)}^{2} a^{5} b^{2} e^{5} + 210 \, {\left(x e + d\right)} a^{5} b^{2} d e^{5} - 63 \, a^{5} b^{2} d^{2} e^{5} - 35 \, {\left(x e + d\right)} a^{6} b e^{6} + 21 \, a^{6} b d e^{6} - 3 \, a^{7} e^{7}\right)} e^{\left(-8\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/45*(5*(x*e + d)^(9/2)*b^7*e^64 - 45*(x*e + d)^(7/2)*b^7*d*e^64 + 189*(x*e + d)^(5/2)*b^7*d^2*e^64 - 525*(x*e + d)^(3/2)*b^7*d^3*e^64 + 1575*sqrt(x*e + d)*b^7*d^4*e^64 + 45*(x*e + d)^(7/2)*a*b^6*e^65 - 378*(x*e + d)^(5/2)*a*b^6*d*e^65 + 1575*(x*e + d)^(3/2)*a*b^6*d^2*e^65 - 6300*sqrt(x*e + d)*a*b^6*d^3*e^65 + 189*(x*e + d)^(5/2)*a^2*b^5*e^66 - 1575*(x*e + d)^(3/2)*a^2*b^5*d*e^66 + 9450*sqrt(x*e + d)*a^2*b^5*d^2*e^66 + 525*(x*e + d)^(3/2)*a^3*b^4*e^67 - 6300*sqrt(x*e + d)*a^3*b^4*d*e^67 + 1575*sqrt(x*e + d)*a^4*b^3*e^68)*e^(-72) + 2/15*(315*(x*e + d)^2*b^7*d^5 - 35*(x*e + d)*b^7*d^6 + 3*b^7*d^7 - 1575*(x*e + d)^2*a*b^6*d^4*e + 210*(x*e + d)*a*b^6*d^5*e - 21*a*b^6*d^6*e + 3150*(x*e + d)^2*a^2*b^5*d^3*e^2 - 525*(x*e + d)*a^2*b^5*d^4*e^2 + 63*a^2*b^5*d^5*e^2 - 3150*(x*e + d)^2*a^3*b^4*d^2*e^3 + 700*(x*e + d)*a^3*b^4*d^3*e^3 - 105*a^3*b^4*d^4*e^3 + 1575*(x*e + d)^2*a^4*b^3*d*e^4 - 525*(x*e + d)*a^4*b^3*d^2*e^4 + 105*a^4*b^3*d^3*e^4 - 315*(x*e + d)^2*a^5*b^2*e^5 + 210*(x*e + d)*a^5*b^2*d*e^5 - 63*a^5*b^2*d^2*e^5 - 35*(x*e + d)*a^6*b*e^6 + 21*a^6*b*d*e^6 - 3*a^7*e^7)*e^(-8)/(x*e + d)^(5/2)","B",0
2066,1,264,0,0.185228," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, {\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)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{4}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{2} + 105 \, \sqrt{x e + d} b^{6} d^{3} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} e - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d e - 315 \, \sqrt{x e + d} a b^{5} d^{2} e + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} e^{2} + 315 \, \sqrt{x e + d} a^{2} b^{4} d e^{2} - 105 \, \sqrt{x e + d} a^{3} b^{3} e^{3}\right)}}{105 \, b^{7}}"," ",0,"2*(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)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) + 2/105*(15*(x*e + d)^(7/2)*b^6 + 21*(x*e + d)^(5/2)*b^6*d + 35*(x*e + d)^(3/2)*b^6*d^2 + 105*sqrt(x*e + d)*b^6*d^3 - 21*(x*e + d)^(5/2)*a*b^5*e - 70*(x*e + d)^(3/2)*a*b^5*d*e - 315*sqrt(x*e + d)*a*b^5*d^2*e + 35*(x*e + d)^(3/2)*a^2*b^4*e^2 + 315*sqrt(x*e + d)*a^2*b^4*d*e^2 - 105*sqrt(x*e + d)*a^3*b^3*e^3)/b^7","B",0
2067,1,180,0,0.170514," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{3}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d + 15 \, \sqrt{x e + d} b^{4} d^{2} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} e - 30 \, \sqrt{x e + d} a b^{3} d e + 15 \, \sqrt{x e + d} a^{2} b^{2} e^{2}\right)}}{15 \, b^{5}}"," ",0,"2*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^3) + 2/15*(3*(x*e + d)^(5/2)*b^4 + 5*(x*e + d)^(3/2)*b^4*d + 15*sqrt(x*e + d)*b^4*d^2 - 5*(x*e + d)^(3/2)*a*b^3*e - 30*sqrt(x*e + d)*a*b^3*d*e + 15*sqrt(x*e + d)*a^2*b^2*e^2)/b^5","A",0
2068,1,112,0,0.188241," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{2}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{2} + 3 \, \sqrt{x e + d} b^{2} d - 3 \, \sqrt{x e + d} a b e\right)}}{3 \, b^{3}}"," ",0,"2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^2) + 2/3*((x*e + d)^(3/2)*b^2 + 3*sqrt(x*e + d)*b^2*d - 3*sqrt(x*e + d)*a*b*e)/b^3","A",0
2069,1,67,0,0.162338," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, {\left(b d - a e\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b} + \frac{2 \, \sqrt{x e + d}}{b}"," ",0,"2*(b*d - a*e)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b) + 2*sqrt(x*e + d)/b","A",0
2070,1,41,0,0.228851," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e}}"," ",0,"2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/sqrt(-b^2*d + a*b*e)","A",0
2071,1,75,0,0.175480," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} {\left(b d - a e\right)}} + \frac{2}{{\left(b d - a e\right)} \sqrt{x e + d}}"," ",0,"2*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*(b*d - a*e)) + 2/((b*d - a*e)*sqrt(x*e + d))","A",0
2072,1,119,0,0.175278," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)} b + b d - a e\right)}}{3 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-b^2*d + a*b*e)) + 2/3*(3*(x*e + d)*b + b*d - a*e)/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*(x*e + d)^(3/2))","A",0
2073,1,189,0,0.212825," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\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{-b^{2} d + a b e}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} b^{2} + 5 \, {\left(x e + d\right)} b^{2} d + 3 \, b^{2} d^{2} - 5 \, {\left(x e + d\right)} a b e - 6 \, a b d e + 3 \, a^{2} e^{2}\right)}}{15 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-b^2*d + a*b*e)) + 2/15*(15*(x*e + d)^2*b^2 + 5*(x*e + d)*b^2*d + 3*b^2*d^2 - 5*(x*e + d)*a*b*e - 6*a*b*d*e + 3*a^2*e^2)/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*(x*e + d)^(5/2))","A",0
2074,1,374,0,0.221309," ","integrate((b*x+a)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{63 \, {\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)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, \sqrt{-b^{2} d + a b e} b^{5}} - \frac{17 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{2} - 15 \, \sqrt{x e + d} b^{4} d^{4} e^{2} - 51 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{3} + 60 \, \sqrt{x e + d} a b^{3} d^{3} e^{3} + 51 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{4} - 90 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{4} - 17 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{5} + 60 \, \sqrt{x e + d} a^{3} b d e^{5} - 15 \, \sqrt{x e + d} a^{4} e^{6}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{5}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{5}{2}} b^{12} e^{2} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{12} d e^{2} + 30 \, \sqrt{x e + d} b^{12} d^{2} e^{2} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{11} e^{3} - 60 \, \sqrt{x e + d} a b^{11} d e^{3} + 30 \, \sqrt{x e + d} a^{2} b^{10} e^{4}\right)}}{5 \, b^{15}}"," ",0,"63/4*(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)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5) - 1/4*(17*(x*e + d)^(3/2)*b^4*d^3*e^2 - 15*sqrt(x*e + d)*b^4*d^4*e^2 - 51*(x*e + d)^(3/2)*a*b^3*d^2*e^3 + 60*sqrt(x*e + d)*a*b^3*d^3*e^3 + 51*(x*e + d)^(3/2)*a^2*b^2*d*e^4 - 90*sqrt(x*e + d)*a^2*b^2*d^2*e^4 - 17*(x*e + d)^(3/2)*a^3*b*e^5 + 60*sqrt(x*e + d)*a^3*b*d*e^5 - 15*sqrt(x*e + d)*a^4*e^6)/(((x*e + d)*b - b*d + a*e)^2*b^5) + 2/5*((x*e + d)^(5/2)*b^12*e^2 + 5*(x*e + d)^(3/2)*b^12*d*e^2 + 30*sqrt(x*e + d)*b^12*d^2*e^2 - 5*(x*e + d)^(3/2)*a*b^11*e^3 - 60*sqrt(x*e + d)*a*b^11*d*e^3 + 30*sqrt(x*e + d)*a^2*b^10*e^4)/b^15","B",0
2075,1,265,0,0.195953," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{35 \, {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, \sqrt{-b^{2} d + a b e} b^{4}} - \frac{13 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{2} - 11 \, \sqrt{x e + d} b^{3} d^{3} e^{2} - 26 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{3} + 33 \, \sqrt{x e + d} a b^{2} d^{2} e^{3} + 13 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{4} - 33 \, \sqrt{x e + d} a^{2} b d e^{4} + 11 \, \sqrt{x e + d} a^{3} e^{5}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{4}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{6} e^{2} + 9 \, \sqrt{x e + d} b^{6} d e^{2} - 9 \, \sqrt{x e + d} a b^{5} e^{3}\right)}}{3 \, b^{9}}"," ",0,"35/4*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) - 1/4*(13*(x*e + d)^(3/2)*b^3*d^2*e^2 - 11*sqrt(x*e + d)*b^3*d^3*e^2 - 26*(x*e + d)^(3/2)*a*b^2*d*e^3 + 33*sqrt(x*e + d)*a*b^2*d^2*e^3 + 13*(x*e + d)^(3/2)*a^2*b*e^4 - 33*sqrt(x*e + d)*a^2*b*d*e^4 + 11*sqrt(x*e + d)*a^3*e^5)/(((x*e + d)*b - b*d + a*e)^2*b^4) + 2/3*((x*e + d)^(3/2)*b^6*e^2 + 9*sqrt(x*e + d)*b^6*d*e^2 - 9*sqrt(x*e + d)*a*b^5*e^3)/b^9","B",0
2076,1,174,0,0.232382," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{15 \, {\left(b d e^{2} - a e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, \sqrt{-b^{2} d + a b e} b^{3}} + \frac{2 \, \sqrt{x e + d} e^{2}}{b^{3}} - \frac{9 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{2} - 7 \, \sqrt{x e + d} b^{2} d^{2} e^{2} - 9 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{3} + 14 \, \sqrt{x e + d} a b d e^{3} - 7 \, \sqrt{x e + d} a^{2} e^{4}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{3}}"," ",0,"15/4*(b*d*e^2 - a*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^3) + 2*sqrt(x*e + d)*e^2/b^3 - 1/4*(9*(x*e + d)^(3/2)*b^2*d*e^2 - 7*sqrt(x*e + d)*b^2*d^2*e^2 - 9*(x*e + d)^(3/2)*a*b*e^3 + 14*sqrt(x*e + d)*a*b*d*e^3 - 7*sqrt(x*e + d)*a^2*e^4)/(((x*e + d)*b - b*d + a*e)^2*b^3)","A",0
2077,1,112,0,0.177173," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, \sqrt{-b^{2} d + a b e} b^{2}} - \frac{5 \, {\left(x e + d\right)}^{\frac{3}{2}} b e^{2} - 3 \, \sqrt{x e + d} b d e^{2} + 3 \, \sqrt{x e + d} a e^{3}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{2}}"," ",0,"3/4*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/(sqrt(-b^2*d + a*b*e)*b^2) - 1/4*(5*(x*e + d)^(3/2)*b*e^2 - 3*sqrt(x*e + d)*b*d*e^2 + 3*sqrt(x*e + d)*a*e^3)/(((x*e + d)*b - b*d + a*e)^2*b^2)","A",0
2078,1,132,0,0.176666," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\left(b^{2} d - a b e\right)} \sqrt{-b^{2} d + a b e}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} b e^{2} + \sqrt{x e + d} b d e^{2} - \sqrt{x e + d} a e^{3}}{4 \, {\left(b^{2} d - a b e\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"-1/4*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^2*d - a*b*e)*sqrt(-b^2*d + a*b*e)) - 1/4*((x*e + d)^(3/2)*b*e^2 + sqrt(x*e + d)*b*d*e^2 - sqrt(x*e + d)*a*e^3)/((b^2*d - a*b*e)*((x*e + d)*b - b*d + a*e)^2)","A",0
2079,1,152,0,0.170285," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} + \frac{3 \, {\left(x e + d\right)}^{\frac{3}{2}} b e^{2} - 5 \, \sqrt{x e + d} b d e^{2} + 5 \, \sqrt{x e + d} a e^{3}}{4 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"3/4*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-b^2*d + a*b*e)) + 1/4*(3*(x*e + d)^(3/2)*b*e^2 - 5*sqrt(x*e + d)*b*d*e^2 + 5*sqrt(x*e + d)*a*e^3)/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*((x*e + d)*b - b*d + a*e)^2)","A",0
2080,1,235,0,0.181726," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{15 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\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{-b^{2} d + a b e}} + \frac{2 \, e^{2}}{{\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{x e + d}} + \frac{7 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{2} - 9 \, \sqrt{x e + d} b^{2} d e^{2} + 9 \, \sqrt{x e + d} a b e^{3}}{4 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"15/4*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-b^2*d + a*b*e)) + 2*e^2/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(x*e + d)) + 1/4*(7*(x*e + d)^(3/2)*b^2*e^2 - 9*sqrt(x*e + d)*b^2*d*e^2 + 9*sqrt(x*e + d)*a*b*e^3)/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*((x*e + d)*b - b*d + a*e)^2)","B",0
2081,1,295,0,0.209304," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{35 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(9 \, {\left(x e + d\right)} b e^{2} + b d e^{2} - a e^{3}\right)}}{3 \, {\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)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{11 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{2} - 13 \, \sqrt{x e + d} b^{3} d e^{2} + 13 \, \sqrt{x e + d} a b^{2} e^{3}}{4 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"35/4*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((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)*sqrt(-b^2*d + a*b*e)) + 2/3*(9*(x*e + d)*b*e^2 + b*d*e^2 - a*e^3)/((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)*(x*e + d)^(3/2)) + 1/4*(11*(x*e + d)^(3/2)*b^3*e^2 - 13*sqrt(x*e + d)*b^3*d*e^2 + 13*sqrt(x*e + d)*a*b^2*e^3)/((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)*((x*e + d)*b - b*d + a*e)^2)","B",0
2082,1,379,0,0.233438," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{63 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{15 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{2} - 17 \, \sqrt{x e + d} b^{4} d e^{2} + 17 \, \sqrt{x e + d} a b^{3} e^{3}}{4 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}} + \frac{2 \, {\left(30 \, {\left(x e + d\right)}^{2} b^{2} e^{2} + 5 \, {\left(x e + d\right)} b^{2} d e^{2} + b^{2} d^{2} e^{2} - 5 \, {\left(x e + d\right)} a b e^{3} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}}{5 \, {\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)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"63/4*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((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)*sqrt(-b^2*d + a*b*e)) + 1/4*(15*(x*e + d)^(3/2)*b^4*e^2 - 17*sqrt(x*e + d)*b^4*d*e^2 + 17*sqrt(x*e + d)*a*b^3*e^3)/((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)*((x*e + d)*b - b*d + a*e)^2) + 2/5*(30*(x*e + d)^2*b^2*e^2 + 5*(x*e + d)*b^2*d*e^2 + b^2*d^2*e^2 - 5*(x*e + d)*a*b*e^3 - 2*a*b*d*e^3 + a^2*e^4)/((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)*(x*e + d)^(5/2))","B",0
2083,1,476,0,0.243391," ","integrate((b*x+a)*(e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1155 \, {\left(b^{2} d^{2} e^{4} - 2 \, a b d e^{5} + a^{2} e^{6}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{6}} - \frac{2295 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} d^{2} e^{4} - 5855 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d^{3} e^{4} + 5153 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{4} e^{4} - 1545 \, \sqrt{x e + d} b^{5} d^{5} e^{4} - 4590 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{4} d e^{5} + 17565 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} d^{2} e^{5} - 20612 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d^{3} e^{5} + 7725 \, \sqrt{x e + d} a b^{4} d^{4} e^{5} + 2295 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{3} e^{6} - 17565 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{3} d e^{6} + 30918 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} d^{2} e^{6} - 15450 \, \sqrt{x e + d} a^{2} b^{3} d^{3} e^{6} + 5855 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{2} e^{7} - 20612 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{2} d e^{7} + 15450 \, \sqrt{x e + d} a^{3} b^{2} d^{2} e^{7} + 5153 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b e^{8} - 7725 \, \sqrt{x e + d} a^{4} b d e^{8} + 1545 \, \sqrt{x e + d} a^{5} e^{9}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{6}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{10} e^{4} + 15 \, \sqrt{x e + d} b^{10} d e^{4} - 15 \, \sqrt{x e + d} a b^{9} e^{5}\right)}}{3 \, b^{15}}"," ",0,"1155/64*(b^2*d^2*e^4 - 2*a*b*d*e^5 + a^2*e^6)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^6) - 1/192*(2295*(x*e + d)^(7/2)*b^5*d^2*e^4 - 5855*(x*e + d)^(5/2)*b^5*d^3*e^4 + 5153*(x*e + d)^(3/2)*b^5*d^4*e^4 - 1545*sqrt(x*e + d)*b^5*d^5*e^4 - 4590*(x*e + d)^(7/2)*a*b^4*d*e^5 + 17565*(x*e + d)^(5/2)*a*b^4*d^2*e^5 - 20612*(x*e + d)^(3/2)*a*b^4*d^3*e^5 + 7725*sqrt(x*e + d)*a*b^4*d^4*e^5 + 2295*(x*e + d)^(7/2)*a^2*b^3*e^6 - 17565*(x*e + d)^(5/2)*a^2*b^3*d*e^6 + 30918*(x*e + d)^(3/2)*a^2*b^3*d^2*e^6 - 15450*sqrt(x*e + d)*a^2*b^3*d^3*e^6 + 5855*(x*e + d)^(5/2)*a^3*b^2*e^7 - 20612*(x*e + d)^(3/2)*a^3*b^2*d*e^7 + 15450*sqrt(x*e + d)*a^3*b^2*d^2*e^7 + 5153*(x*e + d)^(3/2)*a^4*b*e^8 - 7725*sqrt(x*e + d)*a^4*b*d*e^8 + 1545*sqrt(x*e + d)*a^5*e^9)/(((x*e + d)*b - b*d + a*e)^4*b^6) + 2/3*((x*e + d)^(3/2)*b^10*e^4 + 15*sqrt(x*e + d)*b^10*d*e^4 - 15*sqrt(x*e + d)*a*b^9*e^5)/b^15","B",0
2084,1,343,0,0.232363," ","integrate((b*x+a)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{315 \, {\left(b d e^{4} - a e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{5}} + \frac{2 \, \sqrt{x e + d} e^{4}}{b^{5}} - \frac{325 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{4} - 765 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{4} + 643 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{4} - 187 \, \sqrt{x e + d} b^{4} d^{4} e^{4} - 325 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{5} + 1530 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{5} - 1929 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{5} + 748 \, \sqrt{x e + d} a b^{3} d^{3} e^{5} - 765 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{6} + 1929 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{6} - 1122 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{6} - 643 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{7} + 748 \, \sqrt{x e + d} a^{3} b d e^{7} - 187 \, \sqrt{x e + d} a^{4} e^{8}}{64 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{5}}"," ",0,"315/64*(b*d*e^4 - a*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5) + 2*sqrt(x*e + d)*e^4/b^5 - 1/64*(325*(x*e + d)^(7/2)*b^4*d*e^4 - 765*(x*e + d)^(5/2)*b^4*d^2*e^4 + 643*(x*e + d)^(3/2)*b^4*d^3*e^4 - 187*sqrt(x*e + d)*b^4*d^4*e^4 - 325*(x*e + d)^(7/2)*a*b^3*e^5 + 1530*(x*e + d)^(5/2)*a*b^3*d*e^5 - 1929*(x*e + d)^(3/2)*a*b^3*d^2*e^5 + 748*sqrt(x*e + d)*a*b^3*d^3*e^5 - 765*(x*e + d)^(5/2)*a^2*b^2*e^6 + 1929*(x*e + d)^(3/2)*a^2*b^2*d*e^6 - 1122*sqrt(x*e + d)*a^2*b^2*d^2*e^6 - 643*(x*e + d)^(3/2)*a^3*b*e^7 + 748*sqrt(x*e + d)*a^3*b*d*e^7 - 187*sqrt(x*e + d)*a^4*e^8)/(((x*e + d)*b - b*d + a*e)^4*b^5)","B",0
2085,1,239,0,0.221863," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{35 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, \sqrt{-b^{2} d + a b e} b^{4}} - \frac{279 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 511 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} + 385 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} - 105 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 511 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} - 770 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} + 315 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} + 385 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} - 315 \, \sqrt{x e + d} a^{2} b d e^{6} + 105 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{4}}"," ",0,"35/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/(sqrt(-b^2*d + a*b*e)*b^4) - 1/192*(279*(x*e + d)^(7/2)*b^3*e^4 - 511*(x*e + d)^(5/2)*b^3*d*e^4 + 385*(x*e + d)^(3/2)*b^3*d^2*e^4 - 105*sqrt(x*e + d)*b^3*d^3*e^4 + 511*(x*e + d)^(5/2)*a*b^2*e^5 - 770*(x*e + d)^(3/2)*a*b^2*d*e^5 + 315*sqrt(x*e + d)*a*b^2*d^2*e^5 + 385*(x*e + d)^(3/2)*a^2*b*e^6 - 315*sqrt(x*e + d)*a^2*b*d*e^6 + 105*sqrt(x*e + d)*a^3*e^7)/(((x*e + d)*b - b*d + a*e)^4*b^4)","A",0
2086,1,265,0,0.208706," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{4} d - a b^{3} e\right)} \sqrt{-b^{2} d + a b e}} - \frac{15 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} + 73 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} - 55 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} + 15 \, \sqrt{x e + d} b^{3} d^{3} e^{4} - 73 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} + 110 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} - 45 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} - 55 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} + 45 \, \sqrt{x e + d} a^{2} b d e^{6} - 15 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\left(b^{4} d - a b^{3} e\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-5/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^4*d - a*b^3*e)*sqrt(-b^2*d + a*b*e)) - 1/192*(15*(x*e + d)^(7/2)*b^3*e^4 + 73*(x*e + d)^(5/2)*b^3*d*e^4 - 55*(x*e + d)^(3/2)*b^3*d^2*e^4 + 15*sqrt(x*e + d)*b^3*d^3*e^4 - 73*(x*e + d)^(5/2)*a*b^2*e^5 + 110*(x*e + d)^(3/2)*a*b^2*d*e^5 - 45*sqrt(x*e + d)*a*b^2*d^2*e^5 - 55*(x*e + d)^(3/2)*a^2*b*e^6 + 45*sqrt(x*e + d)*a^2*b*d*e^6 - 15*sqrt(x*e + d)*a^3*e^7)/((b^4*d - a*b^3*e)*((x*e + d)*b - b*d + a*e)^4)","A",0
2087,1,289,0,0.198182," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} + \frac{3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 11 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} - 11 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} + 3 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 11 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} + 22 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} - 9 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} - 11 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} + 9 \, \sqrt{x e + d} a^{2} b d e^{6} - 3 \, \sqrt{x e + d} a^{3} e^{7}}{64 \, {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"3/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*sqrt(-b^2*d + a*b*e)) + 1/64*(3*(x*e + d)^(7/2)*b^3*e^4 - 11*(x*e + d)^(5/2)*b^3*d*e^4 - 11*(x*e + d)^(3/2)*b^3*d^2*e^4 + 3*sqrt(x*e + d)*b^3*d^3*e^4 + 11*(x*e + d)^(5/2)*a*b^2*e^5 + 22*(x*e + d)^(3/2)*a*b^2*d*e^5 - 9*sqrt(x*e + d)*a*b^2*d^2*e^5 - 11*(x*e + d)^(3/2)*a^2*b*e^6 + 9*sqrt(x*e + d)*a^2*b*d*e^6 - 3*sqrt(x*e + d)*a^3*e^7)/((b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*((x*e + d)*b - b*d + a*e)^4)","B",0
2088,1,313,0,0.192748," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}\right)} \sqrt{-b^{2} d + a b e}} - \frac{15 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 55 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} + 73 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} + 15 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 55 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} - 146 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} - 45 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} + 73 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} + 45 \, \sqrt{x e + d} a^{2} b d e^{6} - 15 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\left(b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-5/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3)*sqrt(-b^2*d + a*b*e)) - 1/192*(15*(x*e + d)^(7/2)*b^3*e^4 - 55*(x*e + d)^(5/2)*b^3*d*e^4 + 73*(x*e + d)^(3/2)*b^3*d^2*e^4 + 15*sqrt(x*e + d)*b^3*d^3*e^4 + 55*(x*e + d)^(5/2)*a*b^2*e^5 - 146*(x*e + d)^(3/2)*a*b^2*d*e^5 - 45*sqrt(x*e + d)*a*b^2*d^2*e^5 + 73*(x*e + d)^(3/2)*a^2*b*e^6 + 45*sqrt(x*e + d)*a^2*b*d*e^6 - 15*sqrt(x*e + d)*a^3*e^7)/((b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3)*((x*e + d)*b - b*d + a*e)^4)","B",0
2089,1,331,0,0.181952," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{35 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{105 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 385 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} + 511 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} - 279 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 385 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} - 1022 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} + 837 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} + 511 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} - 837 \, \sqrt{x e + d} a^{2} b d e^{6} + 279 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"35/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((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)*sqrt(-b^2*d + a*b*e)) + 1/192*(105*(x*e + d)^(7/2)*b^3*e^4 - 385*(x*e + d)^(5/2)*b^3*d*e^4 + 511*(x*e + d)^(3/2)*b^3*d^2*e^4 - 279*sqrt(x*e + d)*b^3*d^3*e^4 + 385*(x*e + d)^(5/2)*a*b^2*e^5 - 1022*(x*e + d)^(3/2)*a*b^2*d*e^5 + 837*sqrt(x*e + d)*a*b^2*d^2*e^5 + 511*(x*e + d)^(3/2)*a^2*b*e^6 - 837*sqrt(x*e + d)*a^2*b*d*e^6 + 279*sqrt(x*e + d)*a^3*e^7)/((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)*((x*e + d)*b - b*d + a*e)^4)","B",0
2090,1,440,0,0.252714," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{315 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, e^{4}}{{\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)} \sqrt{x e + d}} + \frac{187 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} e^{4} - 643 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d e^{4} + 765 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{2} e^{4} - 325 \, \sqrt{x e + d} b^{4} d^{3} e^{4} + 643 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} e^{5} - 1530 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d e^{5} + 975 \, \sqrt{x e + d} a b^{3} d^{2} e^{5} + 765 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} e^{6} - 975 \, \sqrt{x e + d} a^{2} b^{2} d e^{6} + 325 \, \sqrt{x e + d} a^{3} b e^{7}}{64 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"315/64*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((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)*sqrt(-b^2*d + a*b*e)) + 2*e^4/((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)*sqrt(x*e + d)) + 1/64*(187*(x*e + d)^(7/2)*b^4*e^4 - 643*(x*e + d)^(5/2)*b^4*d*e^4 + 765*(x*e + d)^(3/2)*b^4*d^2*e^4 - 325*sqrt(x*e + d)*b^4*d^3*e^4 + 643*(x*e + d)^(5/2)*a*b^3*e^5 - 1530*(x*e + d)^(3/2)*a*b^3*d*e^5 + 975*sqrt(x*e + d)*a*b^3*d^2*e^5 + 765*(x*e + d)^(3/2)*a^2*b^2*e^6 - 975*sqrt(x*e + d)*a^2*b^2*d*e^6 + 325*sqrt(x*e + d)*a^3*b*e^7)/((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)*((x*e + d)*b - b*d + a*e)^4)","B",0
2091,1,500,0,0.269871," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1155 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\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)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)} b e^{4} + b d e^{4} - a e^{5}\right)}}{3 \, {\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)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{1545 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} e^{4} - 5153 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d e^{4} + 5855 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{2} e^{4} - 2295 \, \sqrt{x e + d} b^{5} d^{3} e^{4} + 5153 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} e^{5} - 11710 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d e^{5} + 6885 \, \sqrt{x e + d} a b^{4} d^{2} e^{5} + 5855 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} e^{6} - 6885 \, \sqrt{x e + d} a^{2} b^{3} d e^{6} + 2295 \, \sqrt{x e + d} a^{3} b^{2} e^{7}}{192 \, {\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)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"1155/64*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((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)*sqrt(-b^2*d + a*b*e)) + 2/3*(15*(x*e + d)*b*e^4 + b*d*e^4 - a*e^5)/((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)*(x*e + d)^(3/2)) + 1/192*(1545*(x*e + d)^(7/2)*b^5*e^4 - 5153*(x*e + d)^(5/2)*b^5*d*e^4 + 5855*(x*e + d)^(3/2)*b^5*d^2*e^4 - 2295*sqrt(x*e + d)*b^5*d^3*e^4 + 5153*(x*e + d)^(5/2)*a*b^4*e^5 - 11710*(x*e + d)^(3/2)*a*b^4*d*e^5 + 6885*sqrt(x*e + d)*a*b^4*d^2*e^5 + 5855*(x*e + d)^(3/2)*a^2*b^3*e^6 - 6885*sqrt(x*e + d)*a^2*b^3*d*e^6 + 2295*sqrt(x*e + d)*a^3*b^2*e^7)/((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)*((x*e + d)*b - b*d + a*e)^4)","B",0
2092,1,930,0,0.270627," ","integrate((b*x+a)*(e*x+d)^(7/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{4} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{4} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 24024 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} a^{2} d^{4} \mathrm{sgn}\left(b x + a\right) + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d^{3} \mathrm{sgn}\left(b x + a\right) + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} d \mathrm{sgn}\left(b x + a\right) + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^4*e^(-1)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^4*e^(-2)*sgn(b*x + a) + 24024*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d^3*e^(-1)*sgn(b*x + a) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d^3*e^(-2)*sgn(b*x + a) + 45045*sqrt(x*e + d)*a^2*d^4*sgn(b*x + a) + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d^3*sgn(b*x + a) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*d^2*e^(-1)*sgn(b*x + a) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*d^2*e^(-2)*sgn(b*x + a) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*d^2*sgn(b*x + a) + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*d*e^(-1)*sgn(b*x + a) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*d*e^(-2)*sgn(b*x + a) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*d*sgn(b*x + a) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*e^(-1)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*e^(-2)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*sgn(b*x + a))*e^(-1)","B",0
2093,1,663,0,0.241138," ","integrate((b*x+a)*(e*x+d)^(5/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 3465 \, \sqrt{x e + d} a^{2} d^{3} \mathrm{sgn}\left(b x + a\right) + 3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} d \mathrm{sgn}\left(b x + a\right) + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3465*(2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^3*e^(-1)*sgn(b*x + a) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^3*e^(-2)*sgn(b*x + a) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d^2*e^(-1)*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d^2*e^(-2)*sgn(b*x + a) + 3465*sqrt(x*e + d)*a^2*d^3*sgn(b*x + a) + 3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d^2*sgn(b*x + a) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*d*e^(-1)*sgn(b*x + a) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*d*e^(-2)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*d*sgn(b*x + a) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*e^(-1)*sgn(b*x + a) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*e^(-2)*sgn(b*x + a) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*sgn(b*x + a))*e^(-1)","B",0
2094,1,434,0,0.212740," ","integrate((b*x+a)*(e*x+d)^(3/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 84 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} a^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d \mathrm{sgn}\left(b x + a\right) + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/315*(210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^2*e^(-1)*sgn(b*x + a) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^2*e^(-2)*sgn(b*x + a) + 84*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d*e^(-1)*sgn(b*x + a) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d*e^(-2)*sgn(b*x + a) + 315*sqrt(x*e + d)*a^2*d^2*sgn(b*x + a) + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d*sgn(b*x + a) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*e^(-1)*sgn(b*x + a) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*e^(-2)*sgn(b*x + a) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*sgn(b*x + a))*e^(-1)","B",0
2095,1,246,0,0.174440," ","integrate((b*x+a)*(e*x+d)^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(70 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 14 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} a^{2} d \mathrm{sgn}\left(b x + a\right) + 35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/105*(70*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d*e^(-1)*sgn(b*x + a) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d*e^(-2)*sgn(b*x + a) + 14*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*e^(-1)*sgn(b*x + a) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*e^(-2)*sgn(b*x + a) + 105*sqrt(x*e + d)*a^2*d*sgn(b*x + a) + 35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*sgn(b*x + a))*e^(-1)","B",0
2096,1,103,0,0.191051," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(10 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} a^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/15*(10*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*e^(-1)*sgn(b*x + a) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*e^(-2)*sgn(b*x + a) + 15*sqrt(x*e + d)*a^2*sgn(b*x + a))*e^(-1)","A",0
2097,1,119,0,0.175422," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, \sqrt{x e + d} b^{2} d e^{6} \mathrm{sgn}\left(b x + a\right) + 6 \, \sqrt{x e + d} a b e^{7} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-9\right)} - \frac{2 \, {\left(b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b d e \mathrm{sgn}\left(b x + a\right) + a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{\sqrt{x e + d}}"," ",0,"2/3*((x*e + d)^(3/2)*b^2*e^6*sgn(b*x + a) - 6*sqrt(x*e + d)*b^2*d*e^6*sgn(b*x + a) + 6*sqrt(x*e + d)*a*b*e^7*sgn(b*x + a))*e^(-9) - 2*(b^2*d^2*sgn(b*x + a) - 2*a*b*d*e*sgn(b*x + a) + a^2*e^2*sgn(b*x + a))*e^(-3)/sqrt(x*e + d)","A",0
2098,1,111,0,0.204655," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + \frac{2 \, {\left(6 \, {\left(x e + d\right)} b^{2} d \mathrm{sgn}\left(b x + a\right) - b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)} a b e \mathrm{sgn}\left(b x + a\right) + 2 \, a b d e \mathrm{sgn}\left(b x + a\right) - a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*sqrt(x*e + d)*b^2*e^(-3)*sgn(b*x + a) + 2/3*(6*(x*e + d)*b^2*d*sgn(b*x + a) - b^2*d^2*sgn(b*x + a) - 6*(x*e + d)*a*b*e*sgn(b*x + a) + 2*a*b*d*e*sgn(b*x + a) - a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^(3/2)","A",0
2099,1,108,0,0.196912," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} b^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, {\left(x e + d\right)} b^{2} d \mathrm{sgn}\left(b x + a\right) + 3 \, b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)} a b e \mathrm{sgn}\left(b x + a\right) - 6 \, a b d e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(15*(x*e + d)^2*b^2*sgn(b*x + a) - 10*(x*e + d)*b^2*d*sgn(b*x + a) + 3*b^2*d^2*sgn(b*x + a) + 10*(x*e + d)*a*b*e*sgn(b*x + a) - 6*a*b*d*e*sgn(b*x + a) + 3*a^2*e^2*sgn(b*x + a))*e^(-3)/(x*e + d)^(5/2)","A",0
2100,1,1397,0,0.316471," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 36036 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 23166 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1716 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} a^{4} d^{3} \mathrm{sgn}\left(b x + a\right) + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} d^{2} \mathrm{sgn}\left(b x + a\right) + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 2574 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 780 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} d \mathrm{sgn}\left(b x + a\right) + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d^3*e^(-1)*sgn(b*x + a) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d^3*e^(-2)*sgn(b*x + a) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d^3*e^(-3)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d^3*e^(-4)*sgn(b*x + a) + 36036*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*d^2*e^(-1)*sgn(b*x + a) + 23166*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*d^2*e^(-2)*sgn(b*x + a) + 1716*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*d^2*e^(-3)*sgn(b*x + a) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*d^2*e^(-4)*sgn(b*x + a) + 45045*sqrt(x*e + d)*a^4*d^3*sgn(b*x + a) + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*d^2*sgn(b*x + a) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b*d*e^(-1)*sgn(b*x + a) + 2574*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^2*d*e^(-2)*sgn(b*x + a) + 780*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^3*d*e^(-3)*sgn(b*x + a) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^4*d*e^(-4)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*d*sgn(b*x + a) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b*e^(-1)*sgn(b*x + a) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^2*e^(-2)*sgn(b*x + a) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^3*e^(-3)*sgn(b*x + a) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^4*e^(-4)*sgn(b*x + a) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*sgn(b*x + a))*e^(-1)","B",0
2101,1,944,0,0.270505," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 24024 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} a^{4} d^{2} \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} d \mathrm{sgn}\left(b x + a\right) + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d^2*e^(-1)*sgn(b*x + a) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d^2*e^(-2)*sgn(b*x + a) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d^2*e^(-3)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d^2*e^(-4)*sgn(b*x + a) + 24024*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*d*e^(-1)*sgn(b*x + a) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*d*e^(-2)*sgn(b*x + a) + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*d*e^(-3)*sgn(b*x + a) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*d*e^(-4)*sgn(b*x + a) + 45045*sqrt(x*e + d)*a^4*d^2*sgn(b*x + a) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*d*sgn(b*x + a) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b*e^(-1)*sgn(b*x + a) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^2*e^(-2)*sgn(b*x + a) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^3*e^(-3)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^4*e^(-4)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*sgn(b*x + a))*e^(-1)","B",0
2102,1,556,0,0.209242," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(4620 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 396 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 924 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 44 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 3465 \, \sqrt{x e + d} a^{4} d \mathrm{sgn}\left(b x + a\right) + 1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3465*(4620*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d*e^(-1)*sgn(b*x + a) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d*e^(-2)*sgn(b*x + a) + 396*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d*e^(-3)*sgn(b*x + a) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d*e^(-4)*sgn(b*x + a) + 924*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*e^(-1)*sgn(b*x + a) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*e^(-2)*sgn(b*x + a) + 44*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*e^(-3)*sgn(b*x + a) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*e^(-4)*sgn(b*x + a) + 3465*sqrt(x*e + d)*a^4*d*sgn(b*x + a) + 1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*sgn(b*x + a))*e^(-1)","B",0
2103,1,244,0,0.185883," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(420 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 126 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} a^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/315*(420*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*e^(-1)*sgn(b*x + a) + 126*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*e^(-2)*sgn(b*x + a) + 36*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*e^(-3)*sgn(b*x + a) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*e^(-4)*sgn(b*x + a) + 315*sqrt(x*e + d)*a^4*sgn(b*x + a))*e^(-1)","A",0
2104,1,327,0,0.215505," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} e^{30} \mathrm{sgn}\left(b x + a\right) - 28 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d e^{30} \mathrm{sgn}\left(b x + a\right) + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{2} e^{30} \mathrm{sgn}\left(b x + a\right) - 140 \, \sqrt{x e + d} b^{4} d^{3} e^{30} \mathrm{sgn}\left(b x + a\right) + 28 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} e^{31} \mathrm{sgn}\left(b x + a\right) - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d e^{31} \mathrm{sgn}\left(b x + a\right) + 420 \, \sqrt{x e + d} a b^{3} d^{2} e^{31} \mathrm{sgn}\left(b x + a\right) + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} e^{32} \mathrm{sgn}\left(b x + a\right) - 420 \, \sqrt{x e + d} a^{2} b^{2} d e^{32} \mathrm{sgn}\left(b x + a\right) + 140 \, \sqrt{x e + d} a^{3} b e^{33} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-35\right)} - \frac{2 \, {\left(b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{\sqrt{x e + d}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*b^4*e^30*sgn(b*x + a) - 28*(x*e + d)^(5/2)*b^4*d*e^30*sgn(b*x + a) + 70*(x*e + d)^(3/2)*b^4*d^2*e^30*sgn(b*x + a) - 140*sqrt(x*e + d)*b^4*d^3*e^30*sgn(b*x + a) + 28*(x*e + d)^(5/2)*a*b^3*e^31*sgn(b*x + a) - 140*(x*e + d)^(3/2)*a*b^3*d*e^31*sgn(b*x + a) + 420*sqrt(x*e + d)*a*b^3*d^2*e^31*sgn(b*x + a) + 70*(x*e + d)^(3/2)*a^2*b^2*e^32*sgn(b*x + a) - 420*sqrt(x*e + d)*a^2*b^2*d*e^32*sgn(b*x + a) + 140*sqrt(x*e + d)*a^3*b*e^33*sgn(b*x + a))*e^(-35) - 2*(b^4*d^4*sgn(b*x + a) - 4*a*b^3*d^3*e*sgn(b*x + a) + 6*a^2*b^2*d^2*e^2*sgn(b*x + a) - 4*a^3*b*d*e^3*sgn(b*x + a) + a^4*e^4*sgn(b*x + a))*e^(-5)/sqrt(x*e + d)","A",0
2105,1,319,0,0.255899," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} e^{20} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d e^{20} \mathrm{sgn}\left(b x + a\right) + 90 \, \sqrt{x e + d} b^{4} d^{2} e^{20} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} e^{21} \mathrm{sgn}\left(b x + a\right) - 180 \, \sqrt{x e + d} a b^{3} d e^{21} \mathrm{sgn}\left(b x + a\right) + 90 \, \sqrt{x e + d} a^{2} b^{2} e^{22} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-25\right)} + \frac{2 \, {\left(12 \, {\left(x e + d\right)} b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) - b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 36 \, {\left(x e + d\right)} a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(x e + d\right)} a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 12 \, {\left(x e + d\right)} a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) - a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*b^4*e^20*sgn(b*x + a) - 20*(x*e + d)^(3/2)*b^4*d*e^20*sgn(b*x + a) + 90*sqrt(x*e + d)*b^4*d^2*e^20*sgn(b*x + a) + 20*(x*e + d)^(3/2)*a*b^3*e^21*sgn(b*x + a) - 180*sqrt(x*e + d)*a*b^3*d*e^21*sgn(b*x + a) + 90*sqrt(x*e + d)*a^2*b^2*e^22*sgn(b*x + a))*e^(-25) + 2/3*(12*(x*e + d)*b^4*d^3*sgn(b*x + a) - b^4*d^4*sgn(b*x + a) - 36*(x*e + d)*a*b^3*d^2*e*sgn(b*x + a) + 4*a*b^3*d^3*e*sgn(b*x + a) + 36*(x*e + d)*a^2*b^2*d*e^2*sgn(b*x + a) - 6*a^2*b^2*d^2*e^2*sgn(b*x + a) - 12*(x*e + d)*a^3*b*e^3*sgn(b*x + a) + 4*a^3*b*d*e^3*sgn(b*x + a) - a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^(3/2)","A",0
2106,1,316,0,0.220704," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{10} \mathrm{sgn}\left(b x + a\right) - 12 \, \sqrt{x e + d} b^{4} d e^{10} \mathrm{sgn}\left(b x + a\right) + 12 \, \sqrt{x e + d} a b^{3} e^{11} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-15\right)} - \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} b^{4} d^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)} b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 180 \, {\left(x e + d\right)}^{2} a b^{3} d e \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)} a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 12 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 90 \, {\left(x e + d\right)}^{2} a^{2} b^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)} a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)} a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right) - 12 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*b^4*e^10*sgn(b*x + a) - 12*sqrt(x*e + d)*b^4*d*e^10*sgn(b*x + a) + 12*sqrt(x*e + d)*a*b^3*e^11*sgn(b*x + a))*e^(-15) - 2/15*(90*(x*e + d)^2*b^4*d^2*sgn(b*x + a) - 20*(x*e + d)*b^4*d^3*sgn(b*x + a) + 3*b^4*d^4*sgn(b*x + a) - 180*(x*e + d)^2*a*b^3*d*e*sgn(b*x + a) + 60*(x*e + d)*a*b^3*d^2*e*sgn(b*x + a) - 12*a*b^3*d^3*e*sgn(b*x + a) + 90*(x*e + d)^2*a^2*b^2*e^2*sgn(b*x + a) - 60*(x*e + d)*a^2*b^2*d*e^2*sgn(b*x + a) + 18*a^2*b^2*d^2*e^2*sgn(b*x + a) + 20*(x*e + d)*a^3*b*e^3*sgn(b*x + a) - 12*a^3*b*d*e^3*sgn(b*x + a) + 3*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^(5/2)","A",0
2107,1,310,0,0.233844," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b^{4} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + \frac{2 \, {\left(140 \, {\left(x e + d\right)}^{3} b^{4} d \mathrm{sgn}\left(b x + a\right) - 70 \, {\left(x e + d\right)}^{2} b^{4} d^{2} \mathrm{sgn}\left(b x + a\right) + 28 \, {\left(x e + d\right)} b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 140 \, {\left(x e + d\right)}^{3} a b^{3} e \mathrm{sgn}\left(b x + a\right) + 140 \, {\left(x e + d\right)}^{2} a b^{3} d e \mathrm{sgn}\left(b x + a\right) - 84 \, {\left(x e + d\right)} a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) + 20 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) - 70 \, {\left(x e + d\right)}^{2} a^{2} b^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 84 \, {\left(x e + d\right)} a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 28 \, {\left(x e + d\right)} a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{35 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"2*sqrt(x*e + d)*b^4*e^(-5)*sgn(b*x + a) + 2/35*(140*(x*e + d)^3*b^4*d*sgn(b*x + a) - 70*(x*e + d)^2*b^4*d^2*sgn(b*x + a) + 28*(x*e + d)*b^4*d^3*sgn(b*x + a) - 5*b^4*d^4*sgn(b*x + a) - 140*(x*e + d)^3*a*b^3*e*sgn(b*x + a) + 140*(x*e + d)^2*a*b^3*d*e*sgn(b*x + a) - 84*(x*e + d)*a*b^3*d^2*e*sgn(b*x + a) + 20*a*b^3*d^3*e*sgn(b*x + a) - 70*(x*e + d)^2*a^2*b^2*e^2*sgn(b*x + a) + 84*(x*e + d)*a^2*b^2*d*e^2*sgn(b*x + a) - 30*a^2*b^2*d^2*e^2*sgn(b*x + a) - 28*(x*e + d)*a^3*b*e^3*sgn(b*x + a) + 20*a^3*b*d*e^3*sgn(b*x + a) - 5*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^(7/2)","A",0
2108,1,307,0,0.226773," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","-\frac{2 \, {\left(315 \, {\left(x e + d\right)}^{4} b^{4} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)}^{3} b^{4} d \mathrm{sgn}\left(b x + a\right) + 378 \, {\left(x e + d\right)}^{2} b^{4} d^{2} \mathrm{sgn}\left(b x + a\right) - 180 \, {\left(x e + d\right)} b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 420 \, {\left(x e + d\right)}^{3} a b^{3} e \mathrm{sgn}\left(b x + a\right) - 756 \, {\left(x e + d\right)}^{2} a b^{3} d e \mathrm{sgn}\left(b x + a\right) + 540 \, {\left(x e + d\right)} a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 140 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 378 \, {\left(x e + d\right)}^{2} a^{2} b^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 540 \, {\left(x e + d\right)} a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) + 210 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)} a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right) - 140 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{315 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"-2/315*(315*(x*e + d)^4*b^4*sgn(b*x + a) - 420*(x*e + d)^3*b^4*d*sgn(b*x + a) + 378*(x*e + d)^2*b^4*d^2*sgn(b*x + a) - 180*(x*e + d)*b^4*d^3*sgn(b*x + a) + 35*b^4*d^4*sgn(b*x + a) + 420*(x*e + d)^3*a*b^3*e*sgn(b*x + a) - 756*(x*e + d)^2*a*b^3*d*e*sgn(b*x + a) + 540*(x*e + d)*a*b^3*d^2*e*sgn(b*x + a) - 140*a*b^3*d^3*e*sgn(b*x + a) + 378*(x*e + d)^2*a^2*b^2*e^2*sgn(b*x + a) - 540*(x*e + d)*a^2*b^2*d*e^2*sgn(b*x + a) + 210*a^2*b^2*d^2*e^2*sgn(b*x + a) + 180*(x*e + d)*a^3*b*e^3*sgn(b*x + a) - 140*a^3*b*d*e^3*sgn(b*x + a) + 35*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^(9/2)","A",0
2109,1,307,0,0.236677," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(13/2),x, algorithm=""giac"")","-\frac{2 \, {\left(1155 \, {\left(x e + d\right)}^{4} b^{4} \mathrm{sgn}\left(b x + a\right) - 2772 \, {\left(x e + d\right)}^{3} b^{4} d \mathrm{sgn}\left(b x + a\right) + 2970 \, {\left(x e + d\right)}^{2} b^{4} d^{2} \mathrm{sgn}\left(b x + a\right) - 1540 \, {\left(x e + d\right)} b^{4} d^{3} \mathrm{sgn}\left(b x + a\right) + 315 \, b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) + 2772 \, {\left(x e + d\right)}^{3} a b^{3} e \mathrm{sgn}\left(b x + a\right) - 5940 \, {\left(x e + d\right)}^{2} a b^{3} d e \mathrm{sgn}\left(b x + a\right) + 4620 \, {\left(x e + d\right)} a b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 1260 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 2970 \, {\left(x e + d\right)}^{2} a^{2} b^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4620 \, {\left(x e + d\right)} a^{2} b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) + 1890 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 1540 \, {\left(x e + d\right)} a^{3} b e^{3} \mathrm{sgn}\left(b x + a\right) - 1260 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + 315 \, a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}}{3465 \, {\left(x e + d\right)}^{\frac{11}{2}}}"," ",0,"-2/3465*(1155*(x*e + d)^4*b^4*sgn(b*x + a) - 2772*(x*e + d)^3*b^4*d*sgn(b*x + a) + 2970*(x*e + d)^2*b^4*d^2*sgn(b*x + a) - 1540*(x*e + d)*b^4*d^3*sgn(b*x + a) + 315*b^4*d^4*sgn(b*x + a) + 2772*(x*e + d)^3*a*b^3*e*sgn(b*x + a) - 5940*(x*e + d)^2*a*b^3*d*e*sgn(b*x + a) + 4620*(x*e + d)*a*b^3*d^2*e*sgn(b*x + a) - 1260*a*b^3*d^3*e*sgn(b*x + a) + 2970*(x*e + d)^2*a^2*b^2*e^2*sgn(b*x + a) - 4620*(x*e + d)*a^2*b^2*d*e^2*sgn(b*x + a) + 1890*a^2*b^2*d^2*e^2*sgn(b*x + a) + 1540*(x*e + d)*a^3*b*e^3*sgn(b*x + a) - 1260*a^3*b*d*e^3*sgn(b*x + a) + 315*a^4*e^4*sgn(b*x + a))*e^(-5)/(x*e + d)^(11/2)","A",0
2110,1,2339,0,0.457556," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{4849845} \, {\left(9699690 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 4849845 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 2771340 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 41990 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} d^{3} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 1615 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} d^{3} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 6235515 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 923780 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{5} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{6} d^{2} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 4849845 \, \sqrt{x e + d} a^{6} d^{3} \mathrm{sgn}\left(b x + a\right) + 4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} d^{2} \mathrm{sgn}\left(b x + a\right) + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 419900 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{6} d e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} d \mathrm{sgn}\left(b x + a\right) + 92378 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{5} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{4} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 32300 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{3} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 11305 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{2} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 266 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b^{6} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 138567 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/4849845*(9699690*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*d^3*e^(-1)*sgn(b*x + a) + 4849845*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*d^3*e^(-2)*sgn(b*x + a) + 2771340*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*d^3*e^(-3)*sgn(b*x + a) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*d^3*e^(-4)*sgn(b*x + a) + 41990*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*d^3*e^(-5)*sgn(b*x + a) + 1615*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*d^3*e^(-6)*sgn(b*x + a) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b*d^2*e^(-1)*sgn(b*x + a) + 6235515*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^2*d^2*e^(-2)*sgn(b*x + a) + 923780*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^3*d^2*e^(-3)*sgn(b*x + a) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^4*d^2*e^(-4)*sgn(b*x + a) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^5*d^2*e^(-5)*sgn(b*x + a) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^6*d^2*e^(-6)*sgn(b*x + a) + 4849845*sqrt(x*e + d)*a^6*d^3*sgn(b*x + a) + 4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*d^2*sgn(b*x + a) + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b*d*e^(-1)*sgn(b*x + a) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^2*d*e^(-2)*sgn(b*x + a) + 419900*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^3*d*e^(-3)*sgn(b*x + a) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^4*d*e^(-4)*sgn(b*x + a) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^5*d*e^(-5)*sgn(b*x + a) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^6*d*e^(-6)*sgn(b*x + a) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*d*sgn(b*x + a) + 92378*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^5*b*e^(-1)*sgn(b*x + a) + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^4*b^2*e^(-2)*sgn(b*x + a) + 32300*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^3*b^3*e^(-3)*sgn(b*x + a) + 11305*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^2*b^4*e^(-4)*sgn(b*x + a) + 266*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*b^5*e^(-5)*sgn(b*x + a) + 21*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b^6*e^(-6)*sgn(b*x + a) + 138567*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^6*sgn(b*x + a))*e^(-1)","B",0
2111,1,1609,0,0.384845," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{765765} \, {\left(1531530 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 765765 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 437580 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 36465 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} d^{2} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 612612 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 656370 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 97240 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 33150 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 3060 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{6} d e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 765765 \, \sqrt{x e + d} a^{6} d^{2} \mathrm{sgn}\left(b x + a\right) + 510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} d \mathrm{sgn}\left(b x + a\right) + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 36465 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 22100 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 3825 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 714 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{6} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/765765*(1531530*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*d^2*e^(-1)*sgn(b*x + a) + 765765*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*d^2*e^(-2)*sgn(b*x + a) + 437580*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*d^2*e^(-3)*sgn(b*x + a) + 36465*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*d^2*e^(-4)*sgn(b*x + a) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*d^2*e^(-5)*sgn(b*x + a) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*d^2*e^(-6)*sgn(b*x + a) + 612612*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b*d*e^(-1)*sgn(b*x + a) + 656370*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^2*d*e^(-2)*sgn(b*x + a) + 97240*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^3*d*e^(-3)*sgn(b*x + a) + 33150*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^4*d*e^(-4)*sgn(b*x + a) + 3060*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^5*d*e^(-5)*sgn(b*x + a) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^6*d*e^(-6)*sgn(b*x + a) + 765765*sqrt(x*e + d)*a^6*d^2*sgn(b*x + a) + 510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*d*sgn(b*x + a) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b*e^(-1)*sgn(b*x + a) + 36465*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^2*e^(-2)*sgn(b*x + a) + 22100*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^3*e^(-3)*sgn(b*x + a) + 3825*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^4*e^(-4)*sgn(b*x + a) + 714*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^5*e^(-5)*sgn(b*x + a) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^6*e^(-6)*sgn(b*x + a) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*sgn(b*x + a))*e^(-1)","B",0
2112,1,970,0,0.268025," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(90090 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 25740 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 2145 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} d e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 19305 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 2860 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 90 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{6} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} a^{6} d \mathrm{sgn}\left(b x + a\right) + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(90090*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*d*e^(-1)*sgn(b*x + a) + 45045*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*d*e^(-2)*sgn(b*x + a) + 25740*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*d*e^(-3)*sgn(b*x + a) + 2145*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*d*e^(-4)*sgn(b*x + a) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*d*e^(-5)*sgn(b*x + a) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*d*e^(-6)*sgn(b*x + a) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b*e^(-1)*sgn(b*x + a) + 19305*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^2*e^(-2)*sgn(b*x + a) + 2860*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^3*e^(-3)*sgn(b*x + a) + 975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^4*e^(-4)*sgn(b*x + a) + 90*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^5*e^(-5)*sgn(b*x + a) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^6*e^(-6)*sgn(b*x + a) + 45045*sqrt(x*e + d)*a^6*d*sgn(b*x + a) + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*sgn(b*x + a))*e^(-1)","B",0
2113,1,437,0,0.228694," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3003} \, {\left(6006 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 1716 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 26 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, \sqrt{x e + d} a^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3003*(6006*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*e^(-1)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*e^(-2)*sgn(b*x + a) + 1716*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*e^(-3)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*e^(-4)*sgn(b*x + a) + 26*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*e^(-5)*sgn(b*x + a) + (231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*e^(-6)*sgn(b*x + a) + 3003*sqrt(x*e + d)*a^6*sgn(b*x + a))*e^(-1)","A",0
2114,1,642,0,0.276306," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{231} \, {\left(21 \, {\left(x e + d\right)}^{\frac{11}{2}} b^{6} e^{70} \mathrm{sgn}\left(b x + a\right) - 154 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{6} d e^{70} \mathrm{sgn}\left(b x + a\right) + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} d^{2} e^{70} \mathrm{sgn}\left(b x + a\right) - 924 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d^{3} e^{70} \mathrm{sgn}\left(b x + a\right) + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{4} e^{70} \mathrm{sgn}\left(b x + a\right) - 1386 \, \sqrt{x e + d} b^{6} d^{5} e^{70} \mathrm{sgn}\left(b x + a\right) + 154 \, {\left(x e + d\right)}^{\frac{9}{2}} a b^{5} e^{71} \mathrm{sgn}\left(b x + a\right) - 990 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{5} d e^{71} \mathrm{sgn}\left(b x + a\right) + 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} d^{2} e^{71} \mathrm{sgn}\left(b x + a\right) - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d^{3} e^{71} \mathrm{sgn}\left(b x + a\right) + 6930 \, \sqrt{x e + d} a b^{5} d^{4} e^{71} \mathrm{sgn}\left(b x + a\right) + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{4} e^{72} \mathrm{sgn}\left(b x + a\right) - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{4} d e^{72} \mathrm{sgn}\left(b x + a\right) + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} d^{2} e^{72} \mathrm{sgn}\left(b x + a\right) - 13860 \, \sqrt{x e + d} a^{2} b^{4} d^{3} e^{72} \mathrm{sgn}\left(b x + a\right) + 924 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{3} e^{73} \mathrm{sgn}\left(b x + a\right) - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{3} d e^{73} \mathrm{sgn}\left(b x + a\right) + 13860 \, \sqrt{x e + d} a^{3} b^{3} d^{2} e^{73} \mathrm{sgn}\left(b x + a\right) + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b^{2} e^{74} \mathrm{sgn}\left(b x + a\right) - 6930 \, \sqrt{x e + d} a^{4} b^{2} d e^{74} \mathrm{sgn}\left(b x + a\right) + 1386 \, \sqrt{x e + d} a^{5} b e^{75} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-77\right)} - \frac{2 \, {\left(b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{\sqrt{x e + d}}"," ",0,"2/231*(21*(x*e + d)^(11/2)*b^6*e^70*sgn(b*x + a) - 154*(x*e + d)^(9/2)*b^6*d*e^70*sgn(b*x + a) + 495*(x*e + d)^(7/2)*b^6*d^2*e^70*sgn(b*x + a) - 924*(x*e + d)^(5/2)*b^6*d^3*e^70*sgn(b*x + a) + 1155*(x*e + d)^(3/2)*b^6*d^4*e^70*sgn(b*x + a) - 1386*sqrt(x*e + d)*b^6*d^5*e^70*sgn(b*x + a) + 154*(x*e + d)^(9/2)*a*b^5*e^71*sgn(b*x + a) - 990*(x*e + d)^(7/2)*a*b^5*d*e^71*sgn(b*x + a) + 2772*(x*e + d)^(5/2)*a*b^5*d^2*e^71*sgn(b*x + a) - 4620*(x*e + d)^(3/2)*a*b^5*d^3*e^71*sgn(b*x + a) + 6930*sqrt(x*e + d)*a*b^5*d^4*e^71*sgn(b*x + a) + 495*(x*e + d)^(7/2)*a^2*b^4*e^72*sgn(b*x + a) - 2772*(x*e + d)^(5/2)*a^2*b^4*d*e^72*sgn(b*x + a) + 6930*(x*e + d)^(3/2)*a^2*b^4*d^2*e^72*sgn(b*x + a) - 13860*sqrt(x*e + d)*a^2*b^4*d^3*e^72*sgn(b*x + a) + 924*(x*e + d)^(5/2)*a^3*b^3*e^73*sgn(b*x + a) - 4620*(x*e + d)^(3/2)*a^3*b^3*d*e^73*sgn(b*x + a) + 13860*sqrt(x*e + d)*a^3*b^3*d^2*e^73*sgn(b*x + a) + 1155*(x*e + d)^(3/2)*a^4*b^2*e^74*sgn(b*x + a) - 6930*sqrt(x*e + d)*a^4*b^2*d*e^74*sgn(b*x + a) + 1386*sqrt(x*e + d)*a^5*b*e^75*sgn(b*x + a))*e^(-77) - 2*(b^6*d^6*sgn(b*x + a) - 6*a*b^5*d^5*e*sgn(b*x + a) + 15*a^2*b^4*d^4*e^2*sgn(b*x + a) - 20*a^3*b^3*d^3*e^3*sgn(b*x + a) + 15*a^4*b^2*d^2*e^4*sgn(b*x + a) - 6*a^5*b*d*e^5*sgn(b*x + a) + a^6*e^6*sgn(b*x + a))*e^(-7)/sqrt(x*e + d)","B",0
2115,1,630,0,0.275904," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{63} \, {\left(7 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{6} e^{56} \mathrm{sgn}\left(b x + a\right) - 54 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} d e^{56} \mathrm{sgn}\left(b x + a\right) + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d^{2} e^{56} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{3} e^{56} \mathrm{sgn}\left(b x + a\right) + 945 \, \sqrt{x e + d} b^{6} d^{4} e^{56} \mathrm{sgn}\left(b x + a\right) + 54 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{5} e^{57} \mathrm{sgn}\left(b x + a\right) - 378 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} d e^{57} \mathrm{sgn}\left(b x + a\right) + 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d^{2} e^{57} \mathrm{sgn}\left(b x + a\right) - 3780 \, \sqrt{x e + d} a b^{5} d^{3} e^{57} \mathrm{sgn}\left(b x + a\right) + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{4} e^{58} \mathrm{sgn}\left(b x + a\right) - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} d e^{58} \mathrm{sgn}\left(b x + a\right) + 5670 \, \sqrt{x e + d} a^{2} b^{4} d^{2} e^{58} \mathrm{sgn}\left(b x + a\right) + 420 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{3} e^{59} \mathrm{sgn}\left(b x + a\right) - 3780 \, \sqrt{x e + d} a^{3} b^{3} d e^{59} \mathrm{sgn}\left(b x + a\right) + 945 \, \sqrt{x e + d} a^{4} b^{2} e^{60} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-63\right)} + \frac{2 \, {\left(18 \, {\left(x e + d\right)} b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) - b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 90 \, {\left(x e + d\right)} a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 180 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 90 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 18 \, {\left(x e + d\right)} a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) - a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/63*(7*(x*e + d)^(9/2)*b^6*e^56*sgn(b*x + a) - 54*(x*e + d)^(7/2)*b^6*d*e^56*sgn(b*x + a) + 189*(x*e + d)^(5/2)*b^6*d^2*e^56*sgn(b*x + a) - 420*(x*e + d)^(3/2)*b^6*d^3*e^56*sgn(b*x + a) + 945*sqrt(x*e + d)*b^6*d^4*e^56*sgn(b*x + a) + 54*(x*e + d)^(7/2)*a*b^5*e^57*sgn(b*x + a) - 378*(x*e + d)^(5/2)*a*b^5*d*e^57*sgn(b*x + a) + 1260*(x*e + d)^(3/2)*a*b^5*d^2*e^57*sgn(b*x + a) - 3780*sqrt(x*e + d)*a*b^5*d^3*e^57*sgn(b*x + a) + 189*(x*e + d)^(5/2)*a^2*b^4*e^58*sgn(b*x + a) - 1260*(x*e + d)^(3/2)*a^2*b^4*d*e^58*sgn(b*x + a) + 5670*sqrt(x*e + d)*a^2*b^4*d^2*e^58*sgn(b*x + a) + 420*(x*e + d)^(3/2)*a^3*b^3*e^59*sgn(b*x + a) - 3780*sqrt(x*e + d)*a^3*b^3*d*e^59*sgn(b*x + a) + 945*sqrt(x*e + d)*a^4*b^2*e^60*sgn(b*x + a))*e^(-63) + 2/3*(18*(x*e + d)*b^6*d^5*sgn(b*x + a) - b^6*d^6*sgn(b*x + a) - 90*(x*e + d)*a*b^5*d^4*e*sgn(b*x + a) + 6*a*b^5*d^5*e*sgn(b*x + a) + 180*(x*e + d)*a^2*b^4*d^3*e^2*sgn(b*x + a) - 15*a^2*b^4*d^4*e^2*sgn(b*x + a) - 180*(x*e + d)*a^3*b^3*d^2*e^3*sgn(b*x + a) + 20*a^3*b^3*d^3*e^3*sgn(b*x + a) + 90*(x*e + d)*a^4*b^2*d*e^4*sgn(b*x + a) - 15*a^4*b^2*d^2*e^4*sgn(b*x + a) - 18*(x*e + d)*a^5*b*e^5*sgn(b*x + a) + 6*a^5*b*d*e^5*sgn(b*x + a) - a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(3/2)","B",0
2116,1,626,0,0.298861," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} e^{42} \mathrm{sgn}\left(b x + a\right) - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d e^{42} \mathrm{sgn}\left(b x + a\right) + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{2} e^{42} \mathrm{sgn}\left(b x + a\right) - 700 \, \sqrt{x e + d} b^{6} d^{3} e^{42} \mathrm{sgn}\left(b x + a\right) + 42 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} e^{43} \mathrm{sgn}\left(b x + a\right) - 350 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d e^{43} \mathrm{sgn}\left(b x + a\right) + 2100 \, \sqrt{x e + d} a b^{5} d^{2} e^{43} \mathrm{sgn}\left(b x + a\right) + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} e^{44} \mathrm{sgn}\left(b x + a\right) - 2100 \, \sqrt{x e + d} a^{2} b^{4} d e^{44} \mathrm{sgn}\left(b x + a\right) + 700 \, \sqrt{x e + d} a^{3} b^{3} e^{45} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-49\right)} - \frac{2 \, {\left(75 \, {\left(x e + d\right)}^{2} b^{6} d^{4} \mathrm{sgn}\left(b x + a\right) - 10 \, {\left(x e + d\right)} b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) + b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 300 \, {\left(x e + d\right)}^{2} a b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) + 50 \, {\left(x e + d\right)} a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 450 \, {\left(x e + d\right)}^{2} a^{2} b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 100 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 300 \, {\left(x e + d\right)}^{2} a^{3} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 100 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 75 \, {\left(x e + d\right)}^{2} a^{4} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 50 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)} a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*b^6*e^42*sgn(b*x + a) - 42*(x*e + d)^(5/2)*b^6*d*e^42*sgn(b*x + a) + 175*(x*e + d)^(3/2)*b^6*d^2*e^42*sgn(b*x + a) - 700*sqrt(x*e + d)*b^6*d^3*e^42*sgn(b*x + a) + 42*(x*e + d)^(5/2)*a*b^5*e^43*sgn(b*x + a) - 350*(x*e + d)^(3/2)*a*b^5*d*e^43*sgn(b*x + a) + 2100*sqrt(x*e + d)*a*b^5*d^2*e^43*sgn(b*x + a) + 175*(x*e + d)^(3/2)*a^2*b^4*e^44*sgn(b*x + a) - 2100*sqrt(x*e + d)*a^2*b^4*d*e^44*sgn(b*x + a) + 700*sqrt(x*e + d)*a^3*b^3*e^45*sgn(b*x + a))*e^(-49) - 2/5*(75*(x*e + d)^2*b^6*d^4*sgn(b*x + a) - 10*(x*e + d)*b^6*d^5*sgn(b*x + a) + b^6*d^6*sgn(b*x + a) - 300*(x*e + d)^2*a*b^5*d^3*e*sgn(b*x + a) + 50*(x*e + d)*a*b^5*d^4*e*sgn(b*x + a) - 6*a*b^5*d^5*e*sgn(b*x + a) + 450*(x*e + d)^2*a^2*b^4*d^2*e^2*sgn(b*x + a) - 100*(x*e + d)*a^2*b^4*d^3*e^2*sgn(b*x + a) + 15*a^2*b^4*d^4*e^2*sgn(b*x + a) - 300*(x*e + d)^2*a^3*b^3*d*e^3*sgn(b*x + a) + 100*(x*e + d)*a^3*b^3*d^2*e^3*sgn(b*x + a) - 20*a^3*b^3*d^3*e^3*sgn(b*x + a) + 75*(x*e + d)^2*a^4*b^2*e^4*sgn(b*x + a) - 50*(x*e + d)*a^4*b^2*d*e^4*sgn(b*x + a) + 15*a^4*b^2*d^2*e^4*sgn(b*x + a) + 10*(x*e + d)*a^5*b*e^5*sgn(b*x + a) - 6*a^5*b*d*e^5*sgn(b*x + a) + a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(5/2)","B",0
2117,1,625,0,0.275907," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left({\left(x e + d\right)}^{\frac{5}{2}} b^{6} e^{28} \mathrm{sgn}\left(b x + a\right) - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d e^{28} \mathrm{sgn}\left(b x + a\right) + 75 \, \sqrt{x e + d} b^{6} d^{2} e^{28} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} e^{29} \mathrm{sgn}\left(b x + a\right) - 150 \, \sqrt{x e + d} a b^{5} d e^{29} \mathrm{sgn}\left(b x + a\right) + 75 \, \sqrt{x e + d} a^{2} b^{4} e^{30} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-35\right)} + \frac{2 \, {\left(700 \, {\left(x e + d\right)}^{3} b^{6} d^{3} \mathrm{sgn}\left(b x + a\right) - 175 \, {\left(x e + d\right)}^{2} b^{6} d^{4} \mathrm{sgn}\left(b x + a\right) + 42 \, {\left(x e + d\right)} b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 2100 \, {\left(x e + d\right)}^{3} a b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) + 700 \, {\left(x e + d\right)}^{2} a b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)} a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) + 30 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 2100 \, {\left(x e + d\right)}^{3} a^{2} b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) - 1050 \, {\left(x e + d\right)}^{2} a^{2} b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 420 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 75 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 700 \, {\left(x e + d\right)}^{3} a^{3} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 700 \, {\left(x e + d\right)}^{2} a^{3} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 100 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 175 \, {\left(x e + d\right)}^{2} a^{4} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - 75 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 42 \, {\left(x e + d\right)} a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{35 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"2/5*((x*e + d)^(5/2)*b^6*e^28*sgn(b*x + a) - 10*(x*e + d)^(3/2)*b^6*d*e^28*sgn(b*x + a) + 75*sqrt(x*e + d)*b^6*d^2*e^28*sgn(b*x + a) + 10*(x*e + d)^(3/2)*a*b^5*e^29*sgn(b*x + a) - 150*sqrt(x*e + d)*a*b^5*d*e^29*sgn(b*x + a) + 75*sqrt(x*e + d)*a^2*b^4*e^30*sgn(b*x + a))*e^(-35) + 2/35*(700*(x*e + d)^3*b^6*d^3*sgn(b*x + a) - 175*(x*e + d)^2*b^6*d^4*sgn(b*x + a) + 42*(x*e + d)*b^6*d^5*sgn(b*x + a) - 5*b^6*d^6*sgn(b*x + a) - 2100*(x*e + d)^3*a*b^5*d^2*e*sgn(b*x + a) + 700*(x*e + d)^2*a*b^5*d^3*e*sgn(b*x + a) - 210*(x*e + d)*a*b^5*d^4*e*sgn(b*x + a) + 30*a*b^5*d^5*e*sgn(b*x + a) + 2100*(x*e + d)^3*a^2*b^4*d*e^2*sgn(b*x + a) - 1050*(x*e + d)^2*a^2*b^4*d^2*e^2*sgn(b*x + a) + 420*(x*e + d)*a^2*b^4*d^3*e^2*sgn(b*x + a) - 75*a^2*b^4*d^4*e^2*sgn(b*x + a) - 700*(x*e + d)^3*a^3*b^3*e^3*sgn(b*x + a) + 700*(x*e + d)^2*a^3*b^3*d*e^3*sgn(b*x + a) - 420*(x*e + d)*a^3*b^3*d^2*e^3*sgn(b*x + a) + 100*a^3*b^3*d^3*e^3*sgn(b*x + a) - 175*(x*e + d)^2*a^4*b^2*e^4*sgn(b*x + a) + 210*(x*e + d)*a^4*b^2*d*e^4*sgn(b*x + a) - 75*a^4*b^2*d^2*e^4*sgn(b*x + a) - 42*(x*e + d)*a^5*b*e^5*sgn(b*x + a) + 30*a^5*b*d*e^5*sgn(b*x + a) - 5*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(7/2)","B",0
2118,1,623,0,0.268838," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{6} e^{14} \mathrm{sgn}\left(b x + a\right) - 18 \, \sqrt{x e + d} b^{6} d e^{14} \mathrm{sgn}\left(b x + a\right) + 18 \, \sqrt{x e + d} a b^{5} e^{15} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-21\right)} - \frac{2 \, {\left(945 \, {\left(x e + d\right)}^{4} b^{6} d^{2} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)}^{3} b^{6} d^{3} \mathrm{sgn}\left(b x + a\right) + 189 \, {\left(x e + d\right)}^{2} b^{6} d^{4} \mathrm{sgn}\left(b x + a\right) - 54 \, {\left(x e + d\right)} b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) + 7 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 1890 \, {\left(x e + d\right)}^{4} a b^{5} d e \mathrm{sgn}\left(b x + a\right) + 1260 \, {\left(x e + d\right)}^{3} a b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) - 756 \, {\left(x e + d\right)}^{2} a b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) + 270 \, {\left(x e + d\right)} a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 42 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 945 \, {\left(x e + d\right)}^{4} a^{2} b^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 1260 \, {\left(x e + d\right)}^{3} a^{2} b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) + 1134 \, {\left(x e + d\right)}^{2} a^{2} b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 540 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 105 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 420 \, {\left(x e + d\right)}^{3} a^{3} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 756 \, {\left(x e + d\right)}^{2} a^{3} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 540 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 140 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 189 \, {\left(x e + d\right)}^{2} a^{4} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 270 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 54 \, {\left(x e + d\right)} a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right) - 42 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 7 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{63 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*b^6*e^14*sgn(b*x + a) - 18*sqrt(x*e + d)*b^6*d*e^14*sgn(b*x + a) + 18*sqrt(x*e + d)*a*b^5*e^15*sgn(b*x + a))*e^(-21) - 2/63*(945*(x*e + d)^4*b^6*d^2*sgn(b*x + a) - 420*(x*e + d)^3*b^6*d^3*sgn(b*x + a) + 189*(x*e + d)^2*b^6*d^4*sgn(b*x + a) - 54*(x*e + d)*b^6*d^5*sgn(b*x + a) + 7*b^6*d^6*sgn(b*x + a) - 1890*(x*e + d)^4*a*b^5*d*e*sgn(b*x + a) + 1260*(x*e + d)^3*a*b^5*d^2*e*sgn(b*x + a) - 756*(x*e + d)^2*a*b^5*d^3*e*sgn(b*x + a) + 270*(x*e + d)*a*b^5*d^4*e*sgn(b*x + a) - 42*a*b^5*d^5*e*sgn(b*x + a) + 945*(x*e + d)^4*a^2*b^4*e^2*sgn(b*x + a) - 1260*(x*e + d)^3*a^2*b^4*d*e^2*sgn(b*x + a) + 1134*(x*e + d)^2*a^2*b^4*d^2*e^2*sgn(b*x + a) - 540*(x*e + d)*a^2*b^4*d^3*e^2*sgn(b*x + a) + 105*a^2*b^4*d^4*e^2*sgn(b*x + a) + 420*(x*e + d)^3*a^3*b^3*e^3*sgn(b*x + a) - 756*(x*e + d)^2*a^3*b^3*d*e^3*sgn(b*x + a) + 540*(x*e + d)*a^3*b^3*d^2*e^3*sgn(b*x + a) - 140*a^3*b^3*d^3*e^3*sgn(b*x + a) + 189*(x*e + d)^2*a^4*b^2*e^4*sgn(b*x + a) - 270*(x*e + d)*a^4*b^2*d*e^4*sgn(b*x + a) + 105*a^4*b^2*d^2*e^4*sgn(b*x + a) + 54*(x*e + d)*a^5*b*e^5*sgn(b*x + a) - 42*a^5*b*d*e^5*sgn(b*x + a) + 7*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(9/2)","B",0
2119,1,617,0,0.279165," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(13/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b^{6} e^{\left(-7\right)} \mathrm{sgn}\left(b x + a\right) + \frac{2 \, {\left(1386 \, {\left(x e + d\right)}^{5} b^{6} d \mathrm{sgn}\left(b x + a\right) - 1155 \, {\left(x e + d\right)}^{4} b^{6} d^{2} \mathrm{sgn}\left(b x + a\right) + 924 \, {\left(x e + d\right)}^{3} b^{6} d^{3} \mathrm{sgn}\left(b x + a\right) - 495 \, {\left(x e + d\right)}^{2} b^{6} d^{4} \mathrm{sgn}\left(b x + a\right) + 154 \, {\left(x e + d\right)} b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) - 21 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) - 1386 \, {\left(x e + d\right)}^{5} a b^{5} e \mathrm{sgn}\left(b x + a\right) + 2310 \, {\left(x e + d\right)}^{4} a b^{5} d e \mathrm{sgn}\left(b x + a\right) - 2772 \, {\left(x e + d\right)}^{3} a b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) + 1980 \, {\left(x e + d\right)}^{2} a b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) - 770 \, {\left(x e + d\right)} a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) + 126 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) - 1155 \, {\left(x e + d\right)}^{4} a^{2} b^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 2772 \, {\left(x e + d\right)}^{3} a^{2} b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) - 2970 \, {\left(x e + d\right)}^{2} a^{2} b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 1540 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 315 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 924 \, {\left(x e + d\right)}^{3} a^{3} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 1980 \, {\left(x e + d\right)}^{2} a^{3} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 1540 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 420 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 495 \, {\left(x e + d\right)}^{2} a^{4} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 770 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - 315 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 154 \, {\left(x e + d\right)} a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) - 21 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{231 \, {\left(x e + d\right)}^{\frac{11}{2}}}"," ",0,"2*sqrt(x*e + d)*b^6*e^(-7)*sgn(b*x + a) + 2/231*(1386*(x*e + d)^5*b^6*d*sgn(b*x + a) - 1155*(x*e + d)^4*b^6*d^2*sgn(b*x + a) + 924*(x*e + d)^3*b^6*d^3*sgn(b*x + a) - 495*(x*e + d)^2*b^6*d^4*sgn(b*x + a) + 154*(x*e + d)*b^6*d^5*sgn(b*x + a) - 21*b^6*d^6*sgn(b*x + a) - 1386*(x*e + d)^5*a*b^5*e*sgn(b*x + a) + 2310*(x*e + d)^4*a*b^5*d*e*sgn(b*x + a) - 2772*(x*e + d)^3*a*b^5*d^2*e*sgn(b*x + a) + 1980*(x*e + d)^2*a*b^5*d^3*e*sgn(b*x + a) - 770*(x*e + d)*a*b^5*d^4*e*sgn(b*x + a) + 126*a*b^5*d^5*e*sgn(b*x + a) - 1155*(x*e + d)^4*a^2*b^4*e^2*sgn(b*x + a) + 2772*(x*e + d)^3*a^2*b^4*d*e^2*sgn(b*x + a) - 2970*(x*e + d)^2*a^2*b^4*d^2*e^2*sgn(b*x + a) + 1540*(x*e + d)*a^2*b^4*d^3*e^2*sgn(b*x + a) - 315*a^2*b^4*d^4*e^2*sgn(b*x + a) - 924*(x*e + d)^3*a^3*b^3*e^3*sgn(b*x + a) + 1980*(x*e + d)^2*a^3*b^3*d*e^3*sgn(b*x + a) - 1540*(x*e + d)*a^3*b^3*d^2*e^3*sgn(b*x + a) + 420*a^3*b^3*d^3*e^3*sgn(b*x + a) - 495*(x*e + d)^2*a^4*b^2*e^4*sgn(b*x + a) + 770*(x*e + d)*a^4*b^2*d*e^4*sgn(b*x + a) - 315*a^4*b^2*d^2*e^4*sgn(b*x + a) - 154*(x*e + d)*a^5*b*e^5*sgn(b*x + a) + 126*a^5*b*d*e^5*sgn(b*x + a) - 21*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(11/2)","B",0
2120,1,614,0,0.293162," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(15/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3003 \, {\left(x e + d\right)}^{6} b^{6} \mathrm{sgn}\left(b x + a\right) - 6006 \, {\left(x e + d\right)}^{5} b^{6} d \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(x e + d\right)}^{4} b^{6} d^{2} \mathrm{sgn}\left(b x + a\right) - 8580 \, {\left(x e + d\right)}^{3} b^{6} d^{3} \mathrm{sgn}\left(b x + a\right) + 5005 \, {\left(x e + d\right)}^{2} b^{6} d^{4} \mathrm{sgn}\left(b x + a\right) - 1638 \, {\left(x e + d\right)} b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) + 231 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 6006 \, {\left(x e + d\right)}^{5} a b^{5} e \mathrm{sgn}\left(b x + a\right) - 18018 \, {\left(x e + d\right)}^{4} a b^{5} d e \mathrm{sgn}\left(b x + a\right) + 25740 \, {\left(x e + d\right)}^{3} a b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) - 20020 \, {\left(x e + d\right)}^{2} a b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) + 8190 \, {\left(x e + d\right)} a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 1386 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(x e + d\right)}^{4} a^{2} b^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 25740 \, {\left(x e + d\right)}^{3} a^{2} b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left(x e + d\right)}^{2} a^{2} b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 16380 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 3465 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 8580 \, {\left(x e + d\right)}^{3} a^{3} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 20020 \, {\left(x e + d\right)}^{2} a^{3} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 16380 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 4620 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 5005 \, {\left(x e + d\right)}^{2} a^{4} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 8190 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) + 3465 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1638 \, {\left(x e + d\right)} a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right) - 1386 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 231 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{3003 \, {\left(x e + d\right)}^{\frac{13}{2}}}"," ",0,"-2/3003*(3003*(x*e + d)^6*b^6*sgn(b*x + a) - 6006*(x*e + d)^5*b^6*d*sgn(b*x + a) + 9009*(x*e + d)^4*b^6*d^2*sgn(b*x + a) - 8580*(x*e + d)^3*b^6*d^3*sgn(b*x + a) + 5005*(x*e + d)^2*b^6*d^4*sgn(b*x + a) - 1638*(x*e + d)*b^6*d^5*sgn(b*x + a) + 231*b^6*d^6*sgn(b*x + a) + 6006*(x*e + d)^5*a*b^5*e*sgn(b*x + a) - 18018*(x*e + d)^4*a*b^5*d*e*sgn(b*x + a) + 25740*(x*e + d)^3*a*b^5*d^2*e*sgn(b*x + a) - 20020*(x*e + d)^2*a*b^5*d^3*e*sgn(b*x + a) + 8190*(x*e + d)*a*b^5*d^4*e*sgn(b*x + a) - 1386*a*b^5*d^5*e*sgn(b*x + a) + 9009*(x*e + d)^4*a^2*b^4*e^2*sgn(b*x + a) - 25740*(x*e + d)^3*a^2*b^4*d*e^2*sgn(b*x + a) + 30030*(x*e + d)^2*a^2*b^4*d^2*e^2*sgn(b*x + a) - 16380*(x*e + d)*a^2*b^4*d^3*e^2*sgn(b*x + a) + 3465*a^2*b^4*d^4*e^2*sgn(b*x + a) + 8580*(x*e + d)^3*a^3*b^3*e^3*sgn(b*x + a) - 20020*(x*e + d)^2*a^3*b^3*d*e^3*sgn(b*x + a) + 16380*(x*e + d)*a^3*b^3*d^2*e^3*sgn(b*x + a) - 4620*a^3*b^3*d^3*e^3*sgn(b*x + a) + 5005*(x*e + d)^2*a^4*b^2*e^4*sgn(b*x + a) - 8190*(x*e + d)*a^4*b^2*d*e^4*sgn(b*x + a) + 3465*a^4*b^2*d^2*e^4*sgn(b*x + a) + 1638*(x*e + d)*a^5*b*e^5*sgn(b*x + a) - 1386*a^5*b*d*e^5*sgn(b*x + a) + 231*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(13/2)","B",0
2121,1,614,0,0.288249," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(17/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15015 \, {\left(x e + d\right)}^{6} b^{6} \mathrm{sgn}\left(b x + a\right) - 54054 \, {\left(x e + d\right)}^{5} b^{6} d \mathrm{sgn}\left(b x + a\right) + 96525 \, {\left(x e + d\right)}^{4} b^{6} d^{2} \mathrm{sgn}\left(b x + a\right) - 100100 \, {\left(x e + d\right)}^{3} b^{6} d^{3} \mathrm{sgn}\left(b x + a\right) + 61425 \, {\left(x e + d\right)}^{2} b^{6} d^{4} \mathrm{sgn}\left(b x + a\right) - 20790 \, {\left(x e + d\right)} b^{6} d^{5} \mathrm{sgn}\left(b x + a\right) + 3003 \, b^{6} d^{6} \mathrm{sgn}\left(b x + a\right) + 54054 \, {\left(x e + d\right)}^{5} a b^{5} e \mathrm{sgn}\left(b x + a\right) - 193050 \, {\left(x e + d\right)}^{4} a b^{5} d e \mathrm{sgn}\left(b x + a\right) + 300300 \, {\left(x e + d\right)}^{3} a b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) - 245700 \, {\left(x e + d\right)}^{2} a b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) + 103950 \, {\left(x e + d\right)} a b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 18018 \, a b^{5} d^{5} e \mathrm{sgn}\left(b x + a\right) + 96525 \, {\left(x e + d\right)}^{4} a^{2} b^{4} e^{2} \mathrm{sgn}\left(b x + a\right) - 300300 \, {\left(x e + d\right)}^{3} a^{2} b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) + 368550 \, {\left(x e + d\right)}^{2} a^{2} b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 207900 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 45045 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 100100 \, {\left(x e + d\right)}^{3} a^{3} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 245700 \, {\left(x e + d\right)}^{2} a^{3} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) + 207900 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 60060 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 61425 \, {\left(x e + d\right)}^{2} a^{4} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 103950 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) + 45045 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 20790 \, {\left(x e + d\right)} a^{5} b e^{5} \mathrm{sgn}\left(b x + a\right) - 18018 \, a^{5} b d e^{5} \mathrm{sgn}\left(b x + a\right) + 3003 \, a^{6} e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-7\right)}}{45045 \, {\left(x e + d\right)}^{\frac{15}{2}}}"," ",0,"-2/45045*(15015*(x*e + d)^6*b^6*sgn(b*x + a) - 54054*(x*e + d)^5*b^6*d*sgn(b*x + a) + 96525*(x*e + d)^4*b^6*d^2*sgn(b*x + a) - 100100*(x*e + d)^3*b^6*d^3*sgn(b*x + a) + 61425*(x*e + d)^2*b^6*d^4*sgn(b*x + a) - 20790*(x*e + d)*b^6*d^5*sgn(b*x + a) + 3003*b^6*d^6*sgn(b*x + a) + 54054*(x*e + d)^5*a*b^5*e*sgn(b*x + a) - 193050*(x*e + d)^4*a*b^5*d*e*sgn(b*x + a) + 300300*(x*e + d)^3*a*b^5*d^2*e*sgn(b*x + a) - 245700*(x*e + d)^2*a*b^5*d^3*e*sgn(b*x + a) + 103950*(x*e + d)*a*b^5*d^4*e*sgn(b*x + a) - 18018*a*b^5*d^5*e*sgn(b*x + a) + 96525*(x*e + d)^4*a^2*b^4*e^2*sgn(b*x + a) - 300300*(x*e + d)^3*a^2*b^4*d*e^2*sgn(b*x + a) + 368550*(x*e + d)^2*a^2*b^4*d^2*e^2*sgn(b*x + a) - 207900*(x*e + d)*a^2*b^4*d^3*e^2*sgn(b*x + a) + 45045*a^2*b^4*d^4*e^2*sgn(b*x + a) + 100100*(x*e + d)^3*a^3*b^3*e^3*sgn(b*x + a) - 245700*(x*e + d)^2*a^3*b^3*d*e^3*sgn(b*x + a) + 207900*(x*e + d)*a^3*b^3*d^2*e^3*sgn(b*x + a) - 60060*a^3*b^3*d^3*e^3*sgn(b*x + a) + 61425*(x*e + d)^2*a^4*b^2*e^4*sgn(b*x + a) - 103950*(x*e + d)*a^4*b^2*d*e^4*sgn(b*x + a) + 45045*a^4*b^2*d^2*e^4*sgn(b*x + a) + 20790*(x*e + d)*a^5*b*e^5*sgn(b*x + a) - 18018*a^5*b*d*e^5*sgn(b*x + a) + 3003*a^6*e^6*sgn(b*x + a))*e^(-7)/(x*e + d)^(15/2)","B",0
2122,1,226,0,0.178153," ","integrate((b*x+a)*(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(315 \, \sqrt{x e + d} d^{4} \mathrm{sgn}\left(b x + a\right) + 420 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} d^{3} \mathrm{sgn}\left(b x + a\right) + 126 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} d^{2} \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} d \mathrm{sgn}\left(b x + a\right) + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/315*(315*sqrt(x*e + d)*d^4*sgn(b*x + a) + 420*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*d^3*sgn(b*x + a) + 126*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*d^2*sgn(b*x + a) + 36*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*d*sgn(b*x + a) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*sgn(b*x + a))*e^(-1)","B",0
2123,1,154,0,0.237936," ","integrate((b*x+a)*(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(35 \, \sqrt{x e + d} d^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} d^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} d \mathrm{sgn}\left(b x + a\right) + {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/35*(35*sqrt(x*e + d)*d^3*sgn(b*x + a) + 35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*d^2*sgn(b*x + a) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*d*sgn(b*x + a) + (5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*sgn(b*x + a))*e^(-1)","B",0
2124,1,95,0,0.162167," ","integrate((b*x+a)*(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(15 \, \sqrt{x e + d} d^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} d \mathrm{sgn}\left(b x + a\right) + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/15*(15*sqrt(x*e + d)*d^2*sgn(b*x + a) + 10*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*d*sgn(b*x + a) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*sgn(b*x + a))*e^(-1)","B",0
2125,1,49,0,0.165121," ","integrate((b*x+a)*(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(3 \, \sqrt{x e + d} d \mathrm{sgn}\left(b x + a\right) + {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3*(3*sqrt(x*e + d)*d*sgn(b*x + a) + ((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*sgn(b*x + a))*e^(-1)","A",0
2126,1,18,0,0.157872," ","integrate((b*x+a)/(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"2*sqrt(x*e + d)*e^(-1)*sgn(b*x + a)","A",0
2127,1,18,0,0.160122," ","integrate((b*x+a)/(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{\sqrt{x e + d}}"," ",0,"-2*e^(-1)*sgn(b*x + a)/sqrt(x*e + d)","A",0
2128,1,18,0,0.161125," ","integrate((b*x+a)/(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-2/3*e^(-1)*sgn(b*x + a)/(x*e + d)^(3/2)","A",0
2129,1,18,0,0.166905," ","integrate((b*x+a)/(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right)}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/5*e^(-1)*sgn(b*x + a)/(x*e + d)^(5/2)","A",0
2130,1,359,0,0.303542," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{7 \, {\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)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{\left(-1\right)}}{\sqrt{-b^{2} d + a b e} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{{\left(\sqrt{x e + d} b^{3} d^{3} e^{2} - 3 \, \sqrt{x e + d} a b^{2} d^{2} e^{3} + 3 \, \sqrt{x e + d} a^{2} b d e^{4} - \sqrt{x e + d} a^{3} e^{5}\right)} e^{\left(-1\right)}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{8} e^{6} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{8} d e^{6} + 45 \, \sqrt{x e + d} b^{8} d^{2} e^{6} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{7} e^{7} - 90 \, \sqrt{x e + d} a b^{7} d e^{7} + 45 \, \sqrt{x e + d} a^{2} b^{6} e^{8}\right)} e^{\left(-5\right)}}{15 \, b^{10} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"7*(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)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^(-1)/(sqrt(-b^2*d + a*b*e)*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - (sqrt(x*e + d)*b^3*d^3*e^2 - 3*sqrt(x*e + d)*a*b^2*d^2*e^3 + 3*sqrt(x*e + d)*a^2*b*d*e^4 - sqrt(x*e + d)*a^3*e^5)*e^(-1)/(((x*e + d)*b - b*d + a*e)*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/15*(3*(x*e + d)^(5/2)*b^8*e^6 + 10*(x*e + d)^(3/2)*b^8*d*e^6 + 45*sqrt(x*e + d)*b^8*d^2*e^6 - 10*(x*e + d)^(3/2)*a*b^7*e^7 - 90*sqrt(x*e + d)*a*b^7*d*e^7 + 45*sqrt(x*e + d)*a^2*b^6*e^8)*e^(-5)/(b^10*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
2131,1,269,0,0.275361," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{5 \, {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{\left(-1\right)}}{\sqrt{-b^{2} d + a b e} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{{\left(\sqrt{x e + d} b^{2} d^{2} e^{2} - 2 \, \sqrt{x e + d} a b d e^{3} + \sqrt{x e + d} a^{2} e^{4}\right)} e^{\left(-1\right)}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{4} + 6 \, \sqrt{x e + d} b^{4} d e^{4} - 6 \, \sqrt{x e + d} a b^{3} e^{5}\right)} e^{\left(-3\right)}}{3 \, b^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"5*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^(-1)/(sqrt(-b^2*d + a*b*e)*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - (sqrt(x*e + d)*b^2*d^2*e^2 - 2*sqrt(x*e + d)*a*b*d*e^3 + sqrt(x*e + d)*a^2*e^4)*e^(-1)/(((x*e + d)*b - b*d + a*e)*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/3*((x*e + d)^(3/2)*b^4*e^4 + 6*sqrt(x*e + d)*b^4*d*e^4 - 6*sqrt(x*e + d)*a*b^3*e^5)*e^(-3)/(b^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
2132,1,198,0,0.328371," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, {\left(b d e^{2} - a e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{\left(-1\right)}}{\sqrt{-b^{2} d + a b e} b^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, \sqrt{x e + d} e}{b^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{{\left(\sqrt{x e + d} b d e^{2} - \sqrt{x e + d} a e^{3}\right)} e^{\left(-1\right)}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"3*(b*d*e^2 - a*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^(-1)/(sqrt(-b^2*d + a*b*e)*b^2*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2*sqrt(x*e + d)*e/(b^2*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - (sqrt(x*e + d)*b*d*e^2 - sqrt(x*e + d)*a*e^3)*e^(-1)/(((x*e + d)*b - b*d + a*e)*b^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
2133,1,128,0,0.224248," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e}{\sqrt{-b^{2} d + a b e} b \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{\sqrt{x e + d} e}{{\left({\left(x e + d\right)} b - b d + a e\right)} b \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e/(sqrt(-b^2*d + a*b*e)*b*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - sqrt(x*e + d)*e/(((x*e + d)*b - b*d + a*e)*b*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
2134,1,189,0,0.238298," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{{\left(b d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{\sqrt{x e + d} e^{2}}{{\left(b d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}}"," ",0,"-arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - sqrt(x*e + d)*e^2/((b*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e))","B",0
2135,1,289,0,0.273551," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{3 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{{\left(b^{2} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{3 \, {\left(x e + d\right)} b e^{2} - 2 \, b d e^{2} + 2 \, a e^{3}}{{\left(b^{2} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}}"," ",0,"-3*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^2*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - (3*(x*e + d)*b*e^2 - 2*b*d*e^2 + 2*a*e^3)/((b^2*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e))","B",0
2136,1,494,0,0.362908," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{5 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{{\left(b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{\sqrt{x e + d} b^{2} e^{2}}{{\left(b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}} - \frac{2 \, {\left(6 \, {\left(x e + d\right)} b e^{2} + b d e^{2} - a e^{3}\right)}}{3 \, {\left(b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-5*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - sqrt(x*e + d)*b^2*e^2/((b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)) - 2/3*(6*(x*e + d)*b*e^2 + b*d*e^2 - a*e^3)/((b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(3/2))","B",0
2137,1,640,0,0.395469," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{7 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{{\left(b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{\sqrt{x e + d} b^{3} e^{2}}{{\left(b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}} - \frac{2 \, {\left(45 \, {\left(x e + d\right)}^{2} b^{2} e^{2} + 10 \, {\left(x e + d\right)} b^{2} d e^{2} + 3 \, b^{2} d^{2} e^{2} - 10 \, {\left(x e + d\right)} a b e^{3} - 6 \, a b d e^{3} + 3 \, a^{2} e^{4}\right)}}{15 \, {\left(b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-7*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - sqrt(x*e + d)*b^3*e^2/((b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)) - 2/15*(45*(x*e + d)^2*b^2*e^2 + 10*(x*e + d)*b^2*d*e^2 + 3*b^2*d^2*e^2 - 10*(x*e + d)*a*b*e^3 - 6*a*b*d*e^3 + 3*a^2*e^4)/((b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(5/2))","B",0
2138,1,320,0,0.349964," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{35 \, {\left(b d e^{3} - a e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, \sqrt{-b^{2} d + a b e} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, \sqrt{x e + d} e^{3}}{b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{87 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{3} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{3} + 57 \, \sqrt{x e + d} b^{3} d^{3} e^{3} - 87 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{4} + 272 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{4} - 171 \, \sqrt{x e + d} a b^{2} d^{2} e^{4} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{5} + 171 \, \sqrt{x e + d} a^{2} b d e^{5} - 57 \, \sqrt{x e + d} a^{3} e^{6}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"35/8*(b*d*e^3 - a*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2*sqrt(x*e + d)*e^3/(b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/24*(87*(x*e + d)^(5/2)*b^3*d*e^3 - 136*(x*e + d)^(3/2)*b^3*d^2*e^3 + 57*sqrt(x*e + d)*b^3*d^3*e^3 - 87*(x*e + d)^(5/2)*a*b^2*e^4 + 272*(x*e + d)^(3/2)*a*b^2*d*e^4 - 171*sqrt(x*e + d)*a*b^2*d^2*e^4 - 136*(x*e + d)^(3/2)*a^2*b*e^5 + 171*sqrt(x*e + d)*a^2*b*d*e^5 - 57*sqrt(x*e + d)*a^3*e^6)/(((x*e + d)*b - b*d + a*e)^3*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
2139,1,213,0,0.288053," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, \sqrt{-b^{2} d + a b e} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{33 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} - 40 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} + 15 \, \sqrt{x e + d} b^{2} d^{2} e^{3} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} - 30 \, \sqrt{x e + d} a b d e^{4} + 15 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"5/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/(sqrt(-b^2*d + a*b*e)*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/24*(33*(x*e + d)^(5/2)*b^2*e^3 - 40*(x*e + d)^(3/2)*b^2*d*e^3 + 15*sqrt(x*e + d)*b^2*d^2*e^3 + 40*(x*e + d)^(3/2)*a*b*e^4 - 30*sqrt(x*e + d)*a*b*d*e^4 + 15*sqrt(x*e + d)*a^2*e^5)/(((x*e + d)*b - b*d + a*e)^3*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
2140,1,279,0,0.283597," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{3} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} - 3 \, \sqrt{x e + d} b^{2} d^{2} e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} + 6 \, \sqrt{x e + d} a b d e^{4} - 3 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left(b^{3} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-1/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^3*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/24*(3*(x*e + d)^(5/2)*b^2*e^3 + 8*(x*e + d)^(3/2)*b^2*d*e^3 - 3*sqrt(x*e + d)*b^2*d^2*e^3 - 8*(x*e + d)^(3/2)*a*b*e^4 + 6*sqrt(x*e + d)*a*b*d*e^4 - 3*sqrt(x*e + d)*a^2*e^5)/((b^3*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^3)","A",0
2141,1,343,0,0.288173," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{3} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{2} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} - 3 \, \sqrt{x e + d} b^{2} d^{2} e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} + 6 \, \sqrt{x e + d} a b d e^{4} - 3 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left(b^{3} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{2} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"1/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^3*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^2*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 1/24*(3*(x*e + d)^(5/2)*b^2*e^3 - 8*(x*e + d)^(3/2)*b^2*d*e^3 - 3*sqrt(x*e + d)*b^2*d^2*e^3 + 8*(x*e + d)^(3/2)*a*b*e^4 + 6*sqrt(x*e + d)*a*b*d*e^4 - 3*sqrt(x*e + d)*a^2*e^5)/((b^3*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^2*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^3)","B",0
2142,1,409,0,0.296181," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{3} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{15 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} - 40 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} + 33 \, \sqrt{x e + d} b^{2} d^{2} e^{3} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} - 66 \, \sqrt{x e + d} a b d e^{4} + 33 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left(b^{3} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-5/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^3*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/24*(15*(x*e + d)^(5/2)*b^2*e^3 - 40*(x*e + d)^(3/2)*b^2*d*e^3 + 33*sqrt(x*e + d)*b^2*d^2*e^3 + 40*(x*e + d)^(3/2)*a*b*e^4 - 66*sqrt(x*e + d)*a*b*d*e^4 + 33*sqrt(x*e + d)*a^2*e^5)/((b^3*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^3)","B",0
2143,1,654,0,0.411174," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{35 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, e^{3}}{{\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{x e + d}} - \frac{57 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{3} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{3} + 87 \, \sqrt{x e + d} b^{3} d^{2} e^{3} + 136 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} e^{4} - 174 \, \sqrt{x e + d} a b^{2} d e^{4} + 87 \, \sqrt{x e + d} a^{2} b e^{5}}{24 \, {\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-35/8*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 2*e^3/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(x*e + d)) - 1/24*(57*(x*e + d)^(5/2)*b^3*e^3 - 136*(x*e + d)^(3/2)*b^3*d*e^3 + 87*sqrt(x*e + d)*b^3*d^2*e^3 + 136*(x*e + d)^(3/2)*a*b^2*e^4 - 174*sqrt(x*e + d)*a*b^2*d*e^4 + 87*sqrt(x*e + d)*a^2*b*e^5)/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^3)","B",0
2144,1,691,0,0.473960," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{105 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{315 \, {\left(x e + d\right)}^{4} b^{4} e^{3} - 840 \, {\left(x e + d\right)}^{3} b^{4} d e^{3} + 693 \, {\left(x e + d\right)}^{2} b^{4} d^{2} e^{3} - 144 \, {\left(x e + d\right)} b^{4} d^{3} e^{3} - 16 \, b^{4} d^{4} e^{3} + 840 \, {\left(x e + d\right)}^{3} a b^{3} e^{4} - 1386 \, {\left(x e + d\right)}^{2} a b^{3} d e^{4} + 432 \, {\left(x e + d\right)} a b^{3} d^{2} e^{4} + 64 \, a b^{3} d^{3} e^{4} + 693 \, {\left(x e + d\right)}^{2} a^{2} b^{2} e^{5} - 432 \, {\left(x e + d\right)} a^{2} b^{2} d e^{5} - 96 \, a^{2} b^{2} d^{2} e^{5} + 144 \, {\left(x e + d\right)} a^{3} b e^{6} + 64 \, a^{3} b d e^{6} - 16 \, a^{4} e^{7}}{24 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}^{3}}"," ",0,"-105/8*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/24*(315*(x*e + d)^4*b^4*e^3 - 840*(x*e + d)^3*b^4*d*e^3 + 693*(x*e + d)^2*b^4*d^2*e^3 - 144*(x*e + d)*b^4*d^3*e^3 - 16*b^4*d^4*e^3 + 840*(x*e + d)^3*a*b^3*e^4 - 1386*(x*e + d)^2*a*b^3*d*e^4 + 432*(x*e + d)*a*b^3*d^2*e^4 + 64*a*b^3*d^3*e^4 + 693*(x*e + d)^2*a^2*b^2*e^5 - 432*(x*e + d)*a^2*b^2*d*e^5 - 96*a^2*b^2*d^2*e^5 + 144*(x*e + d)*a^3*b*e^6 + 64*a^3*b*d*e^6 - 16*a^4*e^7)/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e)^3)","B",0
2145,1,932,0,0.554637," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{231 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} b^{2} e^{3} + 20 \, {\left(x e + d\right)} b^{2} d e^{3} + 3 \, b^{2} d^{2} e^{3} - 20 \, {\left(x e + d\right)} a b e^{4} - 6 \, a b d e^{4} + 3 \, a^{2} e^{5}\right)}}{15 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{5}{2}}} - \frac{213 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} e^{3} - 472 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d e^{3} + 267 \, \sqrt{x e + d} b^{5} d^{2} e^{3} + 472 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} e^{4} - 534 \, \sqrt{x e + d} a b^{4} d e^{4} + 267 \, \sqrt{x e + d} a^{2} b^{3} e^{5}}{24 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-231/8*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 2/15*(150*(x*e + d)^2*b^2*e^3 + 20*(x*e + d)*b^2*d*e^3 + 3*b^2*d^2*e^3 - 20*(x*e + d)*a*b*e^4 - 6*a*b*d*e^4 + 3*a^2*e^5)/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(5/2)) - 1/24*(213*(x*e + d)^(5/2)*b^5*e^3 - 472*(x*e + d)^(3/2)*b^5*d*e^3 + 267*sqrt(x*e + d)*b^5*d^2*e^3 + 472*(x*e + d)^(3/2)*a*b^4*e^4 - 534*sqrt(x*e + d)*a*b^4*d*e^4 + 267*sqrt(x*e + d)*a^2*b^3*e^5)/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^3)","B",0
2146,1,5639,0,0.367355," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{7} m^{7} x^{8} e^{8} + {\left(x e + d\right)}^{m} b^{7} d m^{7} x^{7} e^{7} + 7 \, {\left(x e + d\right)}^{m} a b^{6} m^{7} x^{7} e^{8} + 28 \, {\left(x e + d\right)}^{m} b^{7} m^{6} x^{8} e^{8} + 7 \, {\left(x e + d\right)}^{m} a b^{6} d m^{7} x^{6} e^{7} + 21 \, {\left(x e + d\right)}^{m} b^{7} d m^{6} x^{7} e^{7} - 7 \, {\left(x e + d\right)}^{m} b^{7} d^{2} m^{6} x^{6} e^{6} + 21 \, {\left(x e + d\right)}^{m} a^{2} b^{5} m^{7} x^{6} e^{8} + 203 \, {\left(x e + d\right)}^{m} a b^{6} m^{6} x^{7} e^{8} + 322 \, {\left(x e + d\right)}^{m} b^{7} m^{5} x^{8} e^{8} + 21 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d m^{7} x^{5} e^{7} + 161 \, {\left(x e + d\right)}^{m} a b^{6} d m^{6} x^{6} e^{7} + 175 \, {\left(x e + d\right)}^{m} b^{7} d m^{5} x^{7} e^{7} - 42 \, {\left(x e + d\right)}^{m} a b^{6} d^{2} m^{6} x^{5} e^{6} - 105 \, {\left(x e + d\right)}^{m} b^{7} d^{2} m^{5} x^{6} e^{6} + 42 \, {\left(x e + d\right)}^{m} b^{7} d^{3} m^{5} x^{5} e^{5} + 35 \, {\left(x e + d\right)}^{m} a^{3} b^{4} m^{7} x^{5} e^{8} + 630 \, {\left(x e + d\right)}^{m} a^{2} b^{5} m^{6} x^{6} e^{8} + 2401 \, {\left(x e + d\right)}^{m} a b^{6} m^{5} x^{7} e^{8} + 1960 \, {\left(x e + d\right)}^{m} b^{7} m^{4} x^{8} e^{8} + 35 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d m^{7} x^{4} e^{7} + 525 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d m^{6} x^{5} e^{7} + 1435 \, {\left(x e + d\right)}^{m} a b^{6} d m^{5} x^{6} e^{7} + 735 \, {\left(x e + d\right)}^{m} b^{7} d m^{4} x^{7} e^{7} - 105 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{2} m^{6} x^{4} e^{6} - 756 \, {\left(x e + d\right)}^{m} a b^{6} d^{2} m^{5} x^{5} e^{6} - 595 \, {\left(x e + d\right)}^{m} b^{7} d^{2} m^{4} x^{6} e^{6} + 210 \, {\left(x e + d\right)}^{m} a b^{6} d^{3} m^{5} x^{4} e^{5} + 420 \, {\left(x e + d\right)}^{m} b^{7} d^{3} m^{4} x^{5} e^{5} - 210 \, {\left(x e + d\right)}^{m} b^{7} d^{4} m^{4} x^{4} e^{4} + 35 \, {\left(x e + d\right)}^{m} a^{4} b^{3} m^{7} x^{4} e^{8} + 1085 \, {\left(x e + d\right)}^{m} a^{3} b^{4} m^{6} x^{5} e^{8} + 7686 \, {\left(x e + d\right)}^{m} a^{2} b^{5} m^{5} x^{6} e^{8} + 14945 \, {\left(x e + d\right)}^{m} a b^{6} m^{4} x^{7} e^{8} + 6769 \, {\left(x e + d\right)}^{m} b^{7} m^{3} x^{8} e^{8} + 35 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d m^{7} x^{3} e^{7} + 945 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d m^{6} x^{4} e^{7} + 5061 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d m^{5} x^{5} e^{7} + 6335 \, {\left(x e + d\right)}^{m} a b^{6} d m^{4} x^{6} e^{7} + 1624 \, {\left(x e + d\right)}^{m} b^{7} d m^{3} x^{7} e^{7} - 140 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{2} m^{6} x^{3} e^{6} - 2205 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{2} m^{5} x^{4} e^{6} - 4830 \, {\left(x e + d\right)}^{m} a b^{6} d^{2} m^{4} x^{5} e^{6} - 1575 \, {\left(x e + d\right)}^{m} b^{7} d^{2} m^{3} x^{6} e^{6} + 420 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{3} m^{5} x^{3} e^{5} + 2940 \, {\left(x e + d\right)}^{m} a b^{6} d^{3} m^{4} x^{4} e^{5} + 1470 \, {\left(x e + d\right)}^{m} b^{7} d^{3} m^{3} x^{5} e^{5} - 840 \, {\left(x e + d\right)}^{m} a b^{6} d^{4} m^{4} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} b^{7} d^{4} m^{3} x^{4} e^{4} + 840 \, {\left(x e + d\right)}^{m} b^{7} d^{5} m^{3} x^{3} e^{3} + 21 \, {\left(x e + d\right)}^{m} a^{5} b^{2} m^{7} x^{3} e^{8} + 1120 \, {\left(x e + d\right)}^{m} a^{4} b^{3} m^{6} x^{4} e^{8} + 13685 \, {\left(x e + d\right)}^{m} a^{3} b^{4} m^{5} x^{5} e^{8} + 49140 \, {\left(x e + d\right)}^{m} a^{2} b^{5} m^{4} x^{6} e^{8} + 52528 \, {\left(x e + d\right)}^{m} a b^{6} m^{3} x^{7} e^{8} + 13132 \, {\left(x e + d\right)}^{m} b^{7} m^{2} x^{8} e^{8} + 21 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d m^{7} x^{2} e^{7} + 1015 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d m^{6} x^{3} e^{7} + 9905 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d m^{5} x^{4} e^{7} + 23835 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d m^{4} x^{5} e^{7} + 14518 \, {\left(x e + d\right)}^{m} a b^{6} d m^{3} x^{6} e^{7} + 1764 \, {\left(x e + d\right)}^{m} b^{7} d m^{2} x^{7} e^{7} - 105 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{2} m^{6} x^{2} e^{6} - 3360 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{2} m^{5} x^{3} e^{6} - 16485 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{2} m^{4} x^{4} e^{6} - 13860 \, {\left(x e + d\right)}^{m} a b^{6} d^{2} m^{3} x^{5} e^{6} - 1918 \, {\left(x e + d\right)}^{m} b^{7} d^{2} m^{2} x^{6} e^{6} + 420 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{3} m^{5} x^{2} e^{5} + 7560 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{3} m^{4} x^{3} e^{5} + 12390 \, {\left(x e + d\right)}^{m} a b^{6} d^{3} m^{3} x^{4} e^{5} + 2100 \, {\left(x e + d\right)}^{m} b^{7} d^{3} m^{2} x^{5} e^{5} - 1260 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{4} m^{4} x^{2} e^{4} - 9240 \, {\left(x e + d\right)}^{m} a b^{6} d^{4} m^{3} x^{3} e^{4} - 2310 \, {\left(x e + d\right)}^{m} b^{7} d^{4} m^{2} x^{4} e^{4} + 2520 \, {\left(x e + d\right)}^{m} a b^{6} d^{5} m^{3} x^{2} e^{3} + 2520 \, {\left(x e + d\right)}^{m} b^{7} d^{5} m^{2} x^{3} e^{3} - 2520 \, {\left(x e + d\right)}^{m} b^{7} d^{6} m^{2} x^{2} e^{2} + 7 \, {\left(x e + d\right)}^{m} a^{6} b m^{7} x^{2} e^{8} + 693 \, {\left(x e + d\right)}^{m} a^{5} b^{2} m^{6} x^{3} e^{8} + 14630 \, {\left(x e + d\right)}^{m} a^{4} b^{3} m^{5} x^{4} e^{8} + 90335 \, {\left(x e + d\right)}^{m} a^{3} b^{4} m^{4} x^{5} e^{8} + 176589 \, {\left(x e + d\right)}^{m} a^{2} b^{5} m^{3} x^{6} e^{8} + 103292 \, {\left(x e + d\right)}^{m} a b^{6} m^{2} x^{7} e^{8} + 13068 \, {\left(x e + d\right)}^{m} b^{7} m x^{8} e^{8} + 7 \, {\left(x e + d\right)}^{m} a^{6} b d m^{7} x e^{7} + 651 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d m^{6} x^{2} e^{7} + 11585 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d m^{5} x^{3} e^{7} + 50715 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d m^{4} x^{4} e^{7} + 57414 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d m^{3} x^{5} e^{7} + 16184 \, {\left(x e + d\right)}^{m} a b^{6} d m^{2} x^{6} e^{7} + 720 \, {\left(x e + d\right)}^{m} b^{7} d m x^{7} e^{7} - 42 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{2} m^{6} x e^{6} - 2835 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{2} m^{5} x^{2} e^{6} - 29540 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{2} m^{4} x^{3} e^{6} - 53235 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{2} m^{3} x^{4} e^{6} - 17808 \, {\left(x e + d\right)}^{m} a b^{6} d^{2} m^{2} x^{5} e^{6} - 840 \, {\left(x e + d\right)}^{m} b^{7} d^{2} m x^{6} e^{6} + 210 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{3} m^{5} x e^{5} + 9240 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{3} m^{4} x^{2} e^{5} + 43260 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{3} m^{3} x^{3} e^{5} + 19740 \, {\left(x e + d\right)}^{m} a b^{6} d^{3} m^{2} x^{4} e^{5} + 1008 \, {\left(x e + d\right)}^{m} b^{7} d^{3} m x^{5} e^{5} - 840 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{4} m^{4} x e^{4} - 20160 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{4} m^{3} x^{2} e^{4} - 21840 \, {\left(x e + d\right)}^{m} a b^{6} d^{4} m^{2} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} b^{7} d^{4} m x^{4} e^{4} + 2520 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{5} m^{3} x e^{3} + 22680 \, {\left(x e + d\right)}^{m} a b^{6} d^{5} m^{2} x^{2} e^{3} + 1680 \, {\left(x e + d\right)}^{m} b^{7} d^{5} m x^{3} e^{3} - 5040 \, {\left(x e + d\right)}^{m} a b^{6} d^{6} m^{2} x e^{2} - 2520 \, {\left(x e + d\right)}^{m} b^{7} d^{6} m x^{2} e^{2} + 5040 \, {\left(x e + d\right)}^{m} b^{7} d^{7} m x e + {\left(x e + d\right)}^{m} a^{7} m^{7} x e^{8} + 238 \, {\left(x e + d\right)}^{m} a^{6} b m^{6} x^{2} e^{8} + 9387 \, {\left(x e + d\right)}^{m} a^{5} b^{2} m^{5} x^{3} e^{8} + 100240 \, {\left(x e + d\right)}^{m} a^{4} b^{3} m^{4} x^{4} e^{8} + 334040 \, {\left(x e + d\right)}^{m} a^{3} b^{4} m^{3} x^{5} e^{8} + 353430 \, {\left(x e + d\right)}^{m} a^{2} b^{5} m^{2} x^{6} e^{8} + 103824 \, {\left(x e + d\right)}^{m} a b^{6} m x^{7} e^{8} + 5040 \, {\left(x e + d\right)}^{m} b^{7} x^{8} e^{8} + {\left(x e + d\right)}^{m} a^{7} d m^{7} e^{7} + 231 \, {\left(x e + d\right)}^{m} a^{6} b d m^{6} x e^{7} + 8085 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d m^{5} x^{2} e^{7} + 65485 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d m^{4} x^{3} e^{7} + 131180 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d m^{3} x^{4} e^{7} + 66360 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d m^{2} x^{5} e^{7} + 6720 \, {\left(x e + d\right)}^{m} a b^{6} d m x^{6} e^{7} - 7 \, {\left(x e + d\right)}^{m} a^{6} b d^{2} m^{6} e^{6} - 1260 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{2} m^{5} x e^{6} - 29085 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{2} m^{4} x^{2} e^{6} - 114240 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{2} m^{3} x^{3} e^{6} - 74130 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{2} m^{2} x^{4} e^{6} - 8064 \, {\left(x e + d\right)}^{m} a b^{6} d^{2} m x^{5} e^{6} + 42 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{3} m^{5} e^{5} + 5460 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{3} m^{4} x e^{5} + 70140 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{3} m^{3} x^{2} e^{5} + 83160 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{3} m^{2} x^{3} e^{5} + 10080 \, {\left(x e + d\right)}^{m} a b^{6} d^{3} m x^{4} e^{5} - 210 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{4} m^{4} e^{4} - 17640 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{4} m^{3} x e^{4} - 89460 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{4} m^{2} x^{2} e^{4} - 13440 \, {\left(x e + d\right)}^{m} a b^{6} d^{4} m x^{3} e^{4} + 840 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{5} m^{3} e^{3} + 37800 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{5} m^{2} x e^{3} + 20160 \, {\left(x e + d\right)}^{m} a b^{6} d^{5} m x^{2} e^{3} - 2520 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{6} m^{2} e^{2} - 40320 \, {\left(x e + d\right)}^{m} a b^{6} d^{6} m x e^{2} + 5040 \, {\left(x e + d\right)}^{m} a b^{6} d^{7} m e - 5040 \, {\left(x e + d\right)}^{m} b^{7} d^{8} + 35 \, {\left(x e + d\right)}^{m} a^{7} m^{6} x e^{8} + 3346 \, {\left(x e + d\right)}^{m} a^{6} b m^{5} x^{2} e^{8} + 67095 \, {\left(x e + d\right)}^{m} a^{5} b^{2} m^{4} x^{3} e^{8} + 384755 \, {\left(x e + d\right)}^{m} a^{4} b^{3} m^{3} x^{4} e^{8} + 684740 \, {\left(x e + d\right)}^{m} a^{3} b^{4} m^{2} x^{5} e^{8} + 360024 \, {\left(x e + d\right)}^{m} a^{2} b^{5} m x^{6} e^{8} + 40320 \, {\left(x e + d\right)}^{m} a b^{6} x^{7} e^{8} + 35 \, {\left(x e + d\right)}^{m} a^{7} d m^{6} e^{7} + 3115 \, {\left(x e + d\right)}^{m} a^{6} b d m^{5} x e^{7} + 50925 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d m^{4} x^{2} e^{7} + 188300 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d m^{3} x^{3} e^{7} + 160020 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d m^{2} x^{4} e^{7} + 28224 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d m x^{5} e^{7} - 231 \, {\left(x e + d\right)}^{m} a^{6} b d^{2} m^{5} e^{6} - 14910 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{2} m^{4} x e^{6} - 138285 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{2} m^{3} x^{2} e^{6} - 182000 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{2} m^{2} x^{3} e^{6} - 35280 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{2} m x^{4} e^{6} + 1260 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{3} m^{4} e^{5} + 52710 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{3} m^{3} x e^{5} + 202440 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{3} m^{2} x^{2} e^{5} + 47040 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{3} m x^{3} e^{5} - 5460 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{4} m^{3} e^{4} - 122640 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{4} m^{2} x e^{4} - 70560 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{4} m x^{2} e^{4} + 17640 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{5} m^{2} e^{3} + 141120 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{5} m x e^{3} - 37800 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{6} m e^{2} + 40320 \, {\left(x e + d\right)}^{m} a b^{6} d^{7} e + 511 \, {\left(x e + d\right)}^{m} a^{7} m^{5} x e^{8} + 25060 \, {\left(x e + d\right)}^{m} a^{6} b m^{4} x^{2} e^{8} + 270144 \, {\left(x e + d\right)}^{m} a^{5} b^{2} m^{3} x^{3} e^{8} + 815920 \, {\left(x e + d\right)}^{m} a^{4} b^{3} m^{2} x^{4} e^{8} + 710640 \, {\left(x e + d\right)}^{m} a^{3} b^{4} m x^{5} e^{8} + 141120 \, {\left(x e + d\right)}^{m} a^{2} b^{5} x^{6} e^{8} + 511 \, {\left(x e + d\right)}^{m} a^{7} d m^{5} e^{7} + 21945 \, {\left(x e + d\right)}^{m} a^{6} b d m^{4} x e^{7} + 168294 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d m^{3} x^{2} e^{7} + 251020 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d m^{2} x^{3} e^{7} + 70560 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d m x^{4} e^{7} - 3115 \, {\left(x e + d\right)}^{m} a^{6} b d^{2} m^{4} e^{6} - 86940 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{2} m^{3} x e^{6} - 288330 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{2} m^{2} x^{2} e^{6} - 94080 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{2} m x^{3} e^{6} + 14910 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{3} m^{3} e^{5} + 223860 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{3} m^{2} x e^{5} + 141120 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{3} m x^{2} e^{5} - 52710 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{4} m^{2} e^{4} - 282240 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{4} m x e^{4} + 122640 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{5} m e^{3} - 141120 \, {\left(x e + d\right)}^{m} a^{2} b^{5} d^{6} e^{2} + 4025 \, {\left(x e + d\right)}^{m} a^{7} m^{4} x e^{8} + 107023 \, {\left(x e + d\right)}^{m} a^{6} b m^{3} x^{2} e^{8} + 602532 \, {\left(x e + d\right)}^{m} a^{5} b^{2} m^{2} x^{3} e^{8} + 870660 \, {\left(x e + d\right)}^{m} a^{4} b^{3} m x^{4} e^{8} + 282240 \, {\left(x e + d\right)}^{m} a^{3} b^{4} x^{5} e^{8} + 4025 \, {\left(x e + d\right)}^{m} a^{7} d m^{4} e^{7} + 85078 \, {\left(x e + d\right)}^{m} a^{6} b d m^{3} x e^{7} + 265944 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d m^{2} x^{2} e^{7} + 117600 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d m x^{3} e^{7} - 21945 \, {\left(x e + d\right)}^{m} a^{6} b d^{2} m^{3} e^{6} - 249648 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{2} m^{2} x e^{6} - 176400 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{2} m x^{2} e^{6} + 86940 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{3} m^{2} e^{5} + 352800 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{3} m x e^{5} - 223860 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{4} m e^{4} + 282240 \, {\left(x e + d\right)}^{m} a^{3} b^{4} d^{5} e^{3} + 18424 \, {\left(x e + d\right)}^{m} a^{7} m^{3} x e^{8} + 256942 \, {\left(x e + d\right)}^{m} a^{6} b m^{2} x^{2} e^{8} + 673008 \, {\left(x e + d\right)}^{m} a^{5} b^{2} m x^{3} e^{8} + 352800 \, {\left(x e + d\right)}^{m} a^{4} b^{3} x^{4} e^{8} + 18424 \, {\left(x e + d\right)}^{m} a^{7} d m^{3} e^{7} + 171864 \, {\left(x e + d\right)}^{m} a^{6} b d m^{2} x e^{7} + 141120 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d m x^{2} e^{7} - 85078 \, {\left(x e + d\right)}^{m} a^{6} b d^{2} m^{2} e^{6} - 282240 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{2} m x e^{6} + 249648 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{3} m e^{5} - 352800 \, {\left(x e + d\right)}^{m} a^{4} b^{3} d^{4} e^{4} + 48860 \, {\left(x e + d\right)}^{m} a^{7} m^{2} x e^{8} + 312984 \, {\left(x e + d\right)}^{m} a^{6} b m x^{2} e^{8} + 282240 \, {\left(x e + d\right)}^{m} a^{5} b^{2} x^{3} e^{8} + 48860 \, {\left(x e + d\right)}^{m} a^{7} d m^{2} e^{7} + 141120 \, {\left(x e + d\right)}^{m} a^{6} b d m x e^{7} - 171864 \, {\left(x e + d\right)}^{m} a^{6} b d^{2} m e^{6} + 282240 \, {\left(x e + d\right)}^{m} a^{5} b^{2} d^{3} e^{5} + 69264 \, {\left(x e + d\right)}^{m} a^{7} m x e^{8} + 141120 \, {\left(x e + d\right)}^{m} a^{6} b x^{2} e^{8} + 69264 \, {\left(x e + d\right)}^{m} a^{7} d m e^{7} - 141120 \, {\left(x e + d\right)}^{m} a^{6} b d^{2} e^{6} + 40320 \, {\left(x e + d\right)}^{m} a^{7} x e^{8} + 40320 \, {\left(x e + d\right)}^{m} a^{7} d e^{7}}{m^{8} e^{8} + 36 \, m^{7} e^{8} + 546 \, m^{6} e^{8} + 4536 \, m^{5} e^{8} + 22449 \, m^{4} e^{8} + 67284 \, m^{3} e^{8} + 118124 \, m^{2} e^{8} + 109584 \, m e^{8} + 40320 \, e^{8}}"," ",0,"((x*e + d)^m*b^7*m^7*x^8*e^8 + (x*e + d)^m*b^7*d*m^7*x^7*e^7 + 7*(x*e + d)^m*a*b^6*m^7*x^7*e^8 + 28*(x*e + d)^m*b^7*m^6*x^8*e^8 + 7*(x*e + d)^m*a*b^6*d*m^7*x^6*e^7 + 21*(x*e + d)^m*b^7*d*m^6*x^7*e^7 - 7*(x*e + d)^m*b^7*d^2*m^6*x^6*e^6 + 21*(x*e + d)^m*a^2*b^5*m^7*x^6*e^8 + 203*(x*e + d)^m*a*b^6*m^6*x^7*e^8 + 322*(x*e + d)^m*b^7*m^5*x^8*e^8 + 21*(x*e + d)^m*a^2*b^5*d*m^7*x^5*e^7 + 161*(x*e + d)^m*a*b^6*d*m^6*x^6*e^7 + 175*(x*e + d)^m*b^7*d*m^5*x^7*e^7 - 42*(x*e + d)^m*a*b^6*d^2*m^6*x^5*e^6 - 105*(x*e + d)^m*b^7*d^2*m^5*x^6*e^6 + 42*(x*e + d)^m*b^7*d^3*m^5*x^5*e^5 + 35*(x*e + d)^m*a^3*b^4*m^7*x^5*e^8 + 630*(x*e + d)^m*a^2*b^5*m^6*x^6*e^8 + 2401*(x*e + d)^m*a*b^6*m^5*x^7*e^8 + 1960*(x*e + d)^m*b^7*m^4*x^8*e^8 + 35*(x*e + d)^m*a^3*b^4*d*m^7*x^4*e^7 + 525*(x*e + d)^m*a^2*b^5*d*m^6*x^5*e^7 + 1435*(x*e + d)^m*a*b^6*d*m^5*x^6*e^7 + 735*(x*e + d)^m*b^7*d*m^4*x^7*e^7 - 105*(x*e + d)^m*a^2*b^5*d^2*m^6*x^4*e^6 - 756*(x*e + d)^m*a*b^6*d^2*m^5*x^5*e^6 - 595*(x*e + d)^m*b^7*d^2*m^4*x^6*e^6 + 210*(x*e + d)^m*a*b^6*d^3*m^5*x^4*e^5 + 420*(x*e + d)^m*b^7*d^3*m^4*x^5*e^5 - 210*(x*e + d)^m*b^7*d^4*m^4*x^4*e^4 + 35*(x*e + d)^m*a^4*b^3*m^7*x^4*e^8 + 1085*(x*e + d)^m*a^3*b^4*m^6*x^5*e^8 + 7686*(x*e + d)^m*a^2*b^5*m^5*x^6*e^8 + 14945*(x*e + d)^m*a*b^6*m^4*x^7*e^8 + 6769*(x*e + d)^m*b^7*m^3*x^8*e^8 + 35*(x*e + d)^m*a^4*b^3*d*m^7*x^3*e^7 + 945*(x*e + d)^m*a^3*b^4*d*m^6*x^4*e^7 + 5061*(x*e + d)^m*a^2*b^5*d*m^5*x^5*e^7 + 6335*(x*e + d)^m*a*b^6*d*m^4*x^6*e^7 + 1624*(x*e + d)^m*b^7*d*m^3*x^7*e^7 - 140*(x*e + d)^m*a^3*b^4*d^2*m^6*x^3*e^6 - 2205*(x*e + d)^m*a^2*b^5*d^2*m^5*x^4*e^6 - 4830*(x*e + d)^m*a*b^6*d^2*m^4*x^5*e^6 - 1575*(x*e + d)^m*b^7*d^2*m^3*x^6*e^6 + 420*(x*e + d)^m*a^2*b^5*d^3*m^5*x^3*e^5 + 2940*(x*e + d)^m*a*b^6*d^3*m^4*x^4*e^5 + 1470*(x*e + d)^m*b^7*d^3*m^3*x^5*e^5 - 840*(x*e + d)^m*a*b^6*d^4*m^4*x^3*e^4 - 1260*(x*e + d)^m*b^7*d^4*m^3*x^4*e^4 + 840*(x*e + d)^m*b^7*d^5*m^3*x^3*e^3 + 21*(x*e + d)^m*a^5*b^2*m^7*x^3*e^8 + 1120*(x*e + d)^m*a^4*b^3*m^6*x^4*e^8 + 13685*(x*e + d)^m*a^3*b^4*m^5*x^5*e^8 + 49140*(x*e + d)^m*a^2*b^5*m^4*x^6*e^8 + 52528*(x*e + d)^m*a*b^6*m^3*x^7*e^8 + 13132*(x*e + d)^m*b^7*m^2*x^8*e^8 + 21*(x*e + d)^m*a^5*b^2*d*m^7*x^2*e^7 + 1015*(x*e + d)^m*a^4*b^3*d*m^6*x^3*e^7 + 9905*(x*e + d)^m*a^3*b^4*d*m^5*x^4*e^7 + 23835*(x*e + d)^m*a^2*b^5*d*m^4*x^5*e^7 + 14518*(x*e + d)^m*a*b^6*d*m^3*x^6*e^7 + 1764*(x*e + d)^m*b^7*d*m^2*x^7*e^7 - 105*(x*e + d)^m*a^4*b^3*d^2*m^6*x^2*e^6 - 3360*(x*e + d)^m*a^3*b^4*d^2*m^5*x^3*e^6 - 16485*(x*e + d)^m*a^2*b^5*d^2*m^4*x^4*e^6 - 13860*(x*e + d)^m*a*b^6*d^2*m^3*x^5*e^6 - 1918*(x*e + d)^m*b^7*d^2*m^2*x^6*e^6 + 420*(x*e + d)^m*a^3*b^4*d^3*m^5*x^2*e^5 + 7560*(x*e + d)^m*a^2*b^5*d^3*m^4*x^3*e^5 + 12390*(x*e + d)^m*a*b^6*d^3*m^3*x^4*e^5 + 2100*(x*e + d)^m*b^7*d^3*m^2*x^5*e^5 - 1260*(x*e + d)^m*a^2*b^5*d^4*m^4*x^2*e^4 - 9240*(x*e + d)^m*a*b^6*d^4*m^3*x^3*e^4 - 2310*(x*e + d)^m*b^7*d^4*m^2*x^4*e^4 + 2520*(x*e + d)^m*a*b^6*d^5*m^3*x^2*e^3 + 2520*(x*e + d)^m*b^7*d^5*m^2*x^3*e^3 - 2520*(x*e + d)^m*b^7*d^6*m^2*x^2*e^2 + 7*(x*e + d)^m*a^6*b*m^7*x^2*e^8 + 693*(x*e + d)^m*a^5*b^2*m^6*x^3*e^8 + 14630*(x*e + d)^m*a^4*b^3*m^5*x^4*e^8 + 90335*(x*e + d)^m*a^3*b^4*m^4*x^5*e^8 + 176589*(x*e + d)^m*a^2*b^5*m^3*x^6*e^8 + 103292*(x*e + d)^m*a*b^6*m^2*x^7*e^8 + 13068*(x*e + d)^m*b^7*m*x^8*e^8 + 7*(x*e + d)^m*a^6*b*d*m^7*x*e^7 + 651*(x*e + d)^m*a^5*b^2*d*m^6*x^2*e^7 + 11585*(x*e + d)^m*a^4*b^3*d*m^5*x^3*e^7 + 50715*(x*e + d)^m*a^3*b^4*d*m^4*x^4*e^7 + 57414*(x*e + d)^m*a^2*b^5*d*m^3*x^5*e^7 + 16184*(x*e + d)^m*a*b^6*d*m^2*x^6*e^7 + 720*(x*e + d)^m*b^7*d*m*x^7*e^7 - 42*(x*e + d)^m*a^5*b^2*d^2*m^6*x*e^6 - 2835*(x*e + d)^m*a^4*b^3*d^2*m^5*x^2*e^6 - 29540*(x*e + d)^m*a^3*b^4*d^2*m^4*x^3*e^6 - 53235*(x*e + d)^m*a^2*b^5*d^2*m^3*x^4*e^6 - 17808*(x*e + d)^m*a*b^6*d^2*m^2*x^5*e^6 - 840*(x*e + d)^m*b^7*d^2*m*x^6*e^6 + 210*(x*e + d)^m*a^4*b^3*d^3*m^5*x*e^5 + 9240*(x*e + d)^m*a^3*b^4*d^3*m^4*x^2*e^5 + 43260*(x*e + d)^m*a^2*b^5*d^3*m^3*x^3*e^5 + 19740*(x*e + d)^m*a*b^6*d^3*m^2*x^4*e^5 + 1008*(x*e + d)^m*b^7*d^3*m*x^5*e^5 - 840*(x*e + d)^m*a^3*b^4*d^4*m^4*x*e^4 - 20160*(x*e + d)^m*a^2*b^5*d^4*m^3*x^2*e^4 - 21840*(x*e + d)^m*a*b^6*d^4*m^2*x^3*e^4 - 1260*(x*e + d)^m*b^7*d^4*m*x^4*e^4 + 2520*(x*e + d)^m*a^2*b^5*d^5*m^3*x*e^3 + 22680*(x*e + d)^m*a*b^6*d^5*m^2*x^2*e^3 + 1680*(x*e + d)^m*b^7*d^5*m*x^3*e^3 - 5040*(x*e + d)^m*a*b^6*d^6*m^2*x*e^2 - 2520*(x*e + d)^m*b^7*d^6*m*x^2*e^2 + 5040*(x*e + d)^m*b^7*d^7*m*x*e + (x*e + d)^m*a^7*m^7*x*e^8 + 238*(x*e + d)^m*a^6*b*m^6*x^2*e^8 + 9387*(x*e + d)^m*a^5*b^2*m^5*x^3*e^8 + 100240*(x*e + d)^m*a^4*b^3*m^4*x^4*e^8 + 334040*(x*e + d)^m*a^3*b^4*m^3*x^5*e^8 + 353430*(x*e + d)^m*a^2*b^5*m^2*x^6*e^8 + 103824*(x*e + d)^m*a*b^6*m*x^7*e^8 + 5040*(x*e + d)^m*b^7*x^8*e^8 + (x*e + d)^m*a^7*d*m^7*e^7 + 231*(x*e + d)^m*a^6*b*d*m^6*x*e^7 + 8085*(x*e + d)^m*a^5*b^2*d*m^5*x^2*e^7 + 65485*(x*e + d)^m*a^4*b^3*d*m^4*x^3*e^7 + 131180*(x*e + d)^m*a^3*b^4*d*m^3*x^4*e^7 + 66360*(x*e + d)^m*a^2*b^5*d*m^2*x^5*e^7 + 6720*(x*e + d)^m*a*b^6*d*m*x^6*e^7 - 7*(x*e + d)^m*a^6*b*d^2*m^6*e^6 - 1260*(x*e + d)^m*a^5*b^2*d^2*m^5*x*e^6 - 29085*(x*e + d)^m*a^4*b^3*d^2*m^4*x^2*e^6 - 114240*(x*e + d)^m*a^3*b^4*d^2*m^3*x^3*e^6 - 74130*(x*e + d)^m*a^2*b^5*d^2*m^2*x^4*e^6 - 8064*(x*e + d)^m*a*b^6*d^2*m*x^5*e^6 + 42*(x*e + d)^m*a^5*b^2*d^3*m^5*e^5 + 5460*(x*e + d)^m*a^4*b^3*d^3*m^4*x*e^5 + 70140*(x*e + d)^m*a^3*b^4*d^3*m^3*x^2*e^5 + 83160*(x*e + d)^m*a^2*b^5*d^3*m^2*x^3*e^5 + 10080*(x*e + d)^m*a*b^6*d^3*m*x^4*e^5 - 210*(x*e + d)^m*a^4*b^3*d^4*m^4*e^4 - 17640*(x*e + d)^m*a^3*b^4*d^4*m^3*x*e^4 - 89460*(x*e + d)^m*a^2*b^5*d^4*m^2*x^2*e^4 - 13440*(x*e + d)^m*a*b^6*d^4*m*x^3*e^4 + 840*(x*e + d)^m*a^3*b^4*d^5*m^3*e^3 + 37800*(x*e + d)^m*a^2*b^5*d^5*m^2*x*e^3 + 20160*(x*e + d)^m*a*b^6*d^5*m*x^2*e^3 - 2520*(x*e + d)^m*a^2*b^5*d^6*m^2*e^2 - 40320*(x*e + d)^m*a*b^6*d^6*m*x*e^2 + 5040*(x*e + d)^m*a*b^6*d^7*m*e - 5040*(x*e + d)^m*b^7*d^8 + 35*(x*e + d)^m*a^7*m^6*x*e^8 + 3346*(x*e + d)^m*a^6*b*m^5*x^2*e^8 + 67095*(x*e + d)^m*a^5*b^2*m^4*x^3*e^8 + 384755*(x*e + d)^m*a^4*b^3*m^3*x^4*e^8 + 684740*(x*e + d)^m*a^3*b^4*m^2*x^5*e^8 + 360024*(x*e + d)^m*a^2*b^5*m*x^6*e^8 + 40320*(x*e + d)^m*a*b^6*x^7*e^8 + 35*(x*e + d)^m*a^7*d*m^6*e^7 + 3115*(x*e + d)^m*a^6*b*d*m^5*x*e^7 + 50925*(x*e + d)^m*a^5*b^2*d*m^4*x^2*e^7 + 188300*(x*e + d)^m*a^4*b^3*d*m^3*x^3*e^7 + 160020*(x*e + d)^m*a^3*b^4*d*m^2*x^4*e^7 + 28224*(x*e + d)^m*a^2*b^5*d*m*x^5*e^7 - 231*(x*e + d)^m*a^6*b*d^2*m^5*e^6 - 14910*(x*e + d)^m*a^5*b^2*d^2*m^4*x*e^6 - 138285*(x*e + d)^m*a^4*b^3*d^2*m^3*x^2*e^6 - 182000*(x*e + d)^m*a^3*b^4*d^2*m^2*x^3*e^6 - 35280*(x*e + d)^m*a^2*b^5*d^2*m*x^4*e^6 + 1260*(x*e + d)^m*a^5*b^2*d^3*m^4*e^5 + 52710*(x*e + d)^m*a^4*b^3*d^3*m^3*x*e^5 + 202440*(x*e + d)^m*a^3*b^4*d^3*m^2*x^2*e^5 + 47040*(x*e + d)^m*a^2*b^5*d^3*m*x^3*e^5 - 5460*(x*e + d)^m*a^4*b^3*d^4*m^3*e^4 - 122640*(x*e + d)^m*a^3*b^4*d^4*m^2*x*e^4 - 70560*(x*e + d)^m*a^2*b^5*d^4*m*x^2*e^4 + 17640*(x*e + d)^m*a^3*b^4*d^5*m^2*e^3 + 141120*(x*e + d)^m*a^2*b^5*d^5*m*x*e^3 - 37800*(x*e + d)^m*a^2*b^5*d^6*m*e^2 + 40320*(x*e + d)^m*a*b^6*d^7*e + 511*(x*e + d)^m*a^7*m^5*x*e^8 + 25060*(x*e + d)^m*a^6*b*m^4*x^2*e^8 + 270144*(x*e + d)^m*a^5*b^2*m^3*x^3*e^8 + 815920*(x*e + d)^m*a^4*b^3*m^2*x^4*e^8 + 710640*(x*e + d)^m*a^3*b^4*m*x^5*e^8 + 141120*(x*e + d)^m*a^2*b^5*x^6*e^8 + 511*(x*e + d)^m*a^7*d*m^5*e^7 + 21945*(x*e + d)^m*a^6*b*d*m^4*x*e^7 + 168294*(x*e + d)^m*a^5*b^2*d*m^3*x^2*e^7 + 251020*(x*e + d)^m*a^4*b^3*d*m^2*x^3*e^7 + 70560*(x*e + d)^m*a^3*b^4*d*m*x^4*e^7 - 3115*(x*e + d)^m*a^6*b*d^2*m^4*e^6 - 86940*(x*e + d)^m*a^5*b^2*d^2*m^3*x*e^6 - 288330*(x*e + d)^m*a^4*b^3*d^2*m^2*x^2*e^6 - 94080*(x*e + d)^m*a^3*b^4*d^2*m*x^3*e^6 + 14910*(x*e + d)^m*a^5*b^2*d^3*m^3*e^5 + 223860*(x*e + d)^m*a^4*b^3*d^3*m^2*x*e^5 + 141120*(x*e + d)^m*a^3*b^4*d^3*m*x^2*e^5 - 52710*(x*e + d)^m*a^4*b^3*d^4*m^2*e^4 - 282240*(x*e + d)^m*a^3*b^4*d^4*m*x*e^4 + 122640*(x*e + d)^m*a^3*b^4*d^5*m*e^3 - 141120*(x*e + d)^m*a^2*b^5*d^6*e^2 + 4025*(x*e + d)^m*a^7*m^4*x*e^8 + 107023*(x*e + d)^m*a^6*b*m^3*x^2*e^8 + 602532*(x*e + d)^m*a^5*b^2*m^2*x^3*e^8 + 870660*(x*e + d)^m*a^4*b^3*m*x^4*e^8 + 282240*(x*e + d)^m*a^3*b^4*x^5*e^8 + 4025*(x*e + d)^m*a^7*d*m^4*e^7 + 85078*(x*e + d)^m*a^6*b*d*m^3*x*e^7 + 265944*(x*e + d)^m*a^5*b^2*d*m^2*x^2*e^7 + 117600*(x*e + d)^m*a^4*b^3*d*m*x^3*e^7 - 21945*(x*e + d)^m*a^6*b*d^2*m^3*e^6 - 249648*(x*e + d)^m*a^5*b^2*d^2*m^2*x*e^6 - 176400*(x*e + d)^m*a^4*b^3*d^2*m*x^2*e^6 + 86940*(x*e + d)^m*a^5*b^2*d^3*m^2*e^5 + 352800*(x*e + d)^m*a^4*b^3*d^3*m*x*e^5 - 223860*(x*e + d)^m*a^4*b^3*d^4*m*e^4 + 282240*(x*e + d)^m*a^3*b^4*d^5*e^3 + 18424*(x*e + d)^m*a^7*m^3*x*e^8 + 256942*(x*e + d)^m*a^6*b*m^2*x^2*e^8 + 673008*(x*e + d)^m*a^5*b^2*m*x^3*e^8 + 352800*(x*e + d)^m*a^4*b^3*x^4*e^8 + 18424*(x*e + d)^m*a^7*d*m^3*e^7 + 171864*(x*e + d)^m*a^6*b*d*m^2*x*e^7 + 141120*(x*e + d)^m*a^5*b^2*d*m*x^2*e^7 - 85078*(x*e + d)^m*a^6*b*d^2*m^2*e^6 - 282240*(x*e + d)^m*a^5*b^2*d^2*m*x*e^6 + 249648*(x*e + d)^m*a^5*b^2*d^3*m*e^5 - 352800*(x*e + d)^m*a^4*b^3*d^4*e^4 + 48860*(x*e + d)^m*a^7*m^2*x*e^8 + 312984*(x*e + d)^m*a^6*b*m*x^2*e^8 + 282240*(x*e + d)^m*a^5*b^2*x^3*e^8 + 48860*(x*e + d)^m*a^7*d*m^2*e^7 + 141120*(x*e + d)^m*a^6*b*d*m*x*e^7 - 171864*(x*e + d)^m*a^6*b*d^2*m*e^6 + 282240*(x*e + d)^m*a^5*b^2*d^3*e^5 + 69264*(x*e + d)^m*a^7*m*x*e^8 + 141120*(x*e + d)^m*a^6*b*x^2*e^8 + 69264*(x*e + d)^m*a^7*d*m*e^7 - 141120*(x*e + d)^m*a^6*b*d^2*e^6 + 40320*(x*e + d)^m*a^7*x*e^8 + 40320*(x*e + d)^m*a^7*d*e^7)/(m^8*e^8 + 36*m^7*e^8 + 546*m^6*e^8 + 4536*m^5*e^8 + 22449*m^4*e^8 + 67284*m^3*e^8 + 118124*m^2*e^8 + 109584*m*e^8 + 40320*e^8)","B",0
2147,1,2525,0,0.249478," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{5} m^{5} x^{6} e^{6} + {\left(x e + d\right)}^{m} b^{5} d m^{5} x^{5} e^{5} + 5 \, {\left(x e + d\right)}^{m} a b^{4} m^{5} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} b^{5} m^{4} x^{6} e^{6} + 5 \, {\left(x e + d\right)}^{m} a b^{4} d m^{5} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} b^{5} d m^{4} x^{5} e^{5} - 5 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m^{4} x^{4} e^{4} + 10 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{5} x^{4} e^{6} + 80 \, {\left(x e + d\right)}^{m} a b^{4} m^{4} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} b^{5} m^{3} x^{6} e^{6} + 10 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{5} x^{3} e^{5} + 60 \, {\left(x e + d\right)}^{m} a b^{4} d m^{4} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} b^{5} d m^{3} x^{5} e^{5} - 20 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m^{4} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m^{3} x^{4} e^{4} + 20 \, {\left(x e + d\right)}^{m} b^{5} d^{3} m^{3} x^{3} e^{3} + 10 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{5} x^{3} e^{6} + 170 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{4} x^{4} e^{6} + 475 \, {\left(x e + d\right)}^{m} a b^{4} m^{3} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} b^{5} m^{2} x^{6} e^{6} + 10 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{5} x^{2} e^{5} + 140 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{4} x^{3} e^{5} + 235 \, {\left(x e + d\right)}^{m} a b^{4} d m^{3} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} b^{5} d m^{2} x^{5} e^{5} - 30 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m^{4} x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m^{3} x^{3} e^{4} - 55 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m^{2} x^{4} e^{4} + 60 \, {\left(x e + d\right)}^{m} a b^{4} d^{3} m^{3} x^{2} e^{3} + 60 \, {\left(x e + d\right)}^{m} b^{5} d^{3} m^{2} x^{3} e^{3} - 60 \, {\left(x e + d\right)}^{m} b^{5} d^{4} m^{2} x^{2} e^{2} + 5 \, {\left(x e + d\right)}^{m} a^{4} b m^{5} x^{2} e^{6} + 180 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{4} x^{3} e^{6} + 1070 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{3} x^{4} e^{6} + 1300 \, {\left(x e + d\right)}^{m} a b^{4} m^{2} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} b^{5} m x^{6} e^{6} + 5 \, {\left(x e + d\right)}^{m} a^{4} b d m^{5} x e^{5} + 160 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{4} x^{2} e^{5} + 650 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{3} x^{3} e^{5} + 360 \, {\left(x e + d\right)}^{m} a b^{4} d m^{2} x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} b^{5} d m x^{5} e^{5} - 20 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m^{4} x e^{4} - 360 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m^{3} x^{2} e^{4} - 400 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m^{2} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m x^{4} e^{4} + 60 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{3} m^{3} x e^{3} + 420 \, {\left(x e + d\right)}^{m} a b^{4} d^{3} m^{2} x^{2} e^{3} + 40 \, {\left(x e + d\right)}^{m} b^{5} d^{3} m x^{3} e^{3} - 120 \, {\left(x e + d\right)}^{m} a b^{4} d^{4} m^{2} x e^{2} - 60 \, {\left(x e + d\right)}^{m} b^{5} d^{4} m x^{2} e^{2} + 120 \, {\left(x e + d\right)}^{m} b^{5} d^{5} m x e + {\left(x e + d\right)}^{m} a^{5} m^{5} x e^{6} + 95 \, {\left(x e + d\right)}^{m} a^{4} b m^{4} x^{2} e^{6} + 1210 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{3} x^{3} e^{6} + 3070 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{2} x^{4} e^{6} + 1620 \, {\left(x e + d\right)}^{m} a b^{4} m x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} b^{5} x^{6} e^{6} + {\left(x e + d\right)}^{m} a^{5} d m^{5} e^{5} + 90 \, {\left(x e + d\right)}^{m} a^{4} b d m^{4} x e^{5} + 890 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{3} x^{2} e^{5} + 1120 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{2} x^{3} e^{5} + 180 \, {\left(x e + d\right)}^{m} a b^{4} d m x^{4} e^{5} - 5 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m^{4} e^{4} - 300 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m^{3} x e^{4} - 1230 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m^{2} x^{2} e^{4} - 240 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m x^{3} e^{4} + 20 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} m^{3} e^{3} + 660 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{3} m^{2} x e^{3} + 360 \, {\left(x e + d\right)}^{m} a b^{4} d^{3} m x^{2} e^{3} - 60 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{4} m^{2} e^{2} - 720 \, {\left(x e + d\right)}^{m} a b^{4} d^{4} m x e^{2} + 120 \, {\left(x e + d\right)}^{m} a b^{4} d^{5} m e - 120 \, {\left(x e + d\right)}^{m} b^{5} d^{6} + 20 \, {\left(x e + d\right)}^{m} a^{5} m^{4} x e^{6} + 685 \, {\left(x e + d\right)}^{m} a^{4} b m^{3} x^{2} e^{6} + 3720 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{2} x^{3} e^{6} + 3960 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m x^{4} e^{6} + 720 \, {\left(x e + d\right)}^{m} a b^{4} x^{5} e^{6} + 20 \, {\left(x e + d\right)}^{m} a^{5} d m^{4} e^{5} + 595 \, {\left(x e + d\right)}^{m} a^{4} b d m^{3} x e^{5} + 1940 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{2} x^{2} e^{5} + 600 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m x^{3} e^{5} - 90 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m^{3} e^{4} - 1480 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m^{2} x e^{4} - 900 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m x^{2} e^{4} + 300 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} m^{2} e^{3} + 1800 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{3} m x e^{3} - 660 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{4} m e^{2} + 720 \, {\left(x e + d\right)}^{m} a b^{4} d^{5} e + 155 \, {\left(x e + d\right)}^{m} a^{5} m^{3} x e^{6} + 2305 \, {\left(x e + d\right)}^{m} a^{4} b m^{2} x^{2} e^{6} + 5080 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m x^{3} e^{6} + 1800 \, {\left(x e + d\right)}^{m} a^{2} b^{3} x^{4} e^{6} + 155 \, {\left(x e + d\right)}^{m} a^{5} d m^{3} e^{5} + 1710 \, {\left(x e + d\right)}^{m} a^{4} b d m^{2} x e^{5} + 1200 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m x^{2} e^{5} - 595 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m^{2} e^{4} - 2400 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m x e^{4} + 1480 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} m e^{3} - 1800 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{4} e^{2} + 580 \, {\left(x e + d\right)}^{m} a^{5} m^{2} x e^{6} + 3510 \, {\left(x e + d\right)}^{m} a^{4} b m x^{2} e^{6} + 2400 \, {\left(x e + d\right)}^{m} a^{3} b^{2} x^{3} e^{6} + 580 \, {\left(x e + d\right)}^{m} a^{5} d m^{2} e^{5} + 1800 \, {\left(x e + d\right)}^{m} a^{4} b d m x e^{5} - 1710 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m e^{4} + 2400 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} e^{3} + 1044 \, {\left(x e + d\right)}^{m} a^{5} m x e^{6} + 1800 \, {\left(x e + d\right)}^{m} a^{4} b x^{2} e^{6} + 1044 \, {\left(x e + d\right)}^{m} a^{5} d m e^{5} - 1800 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} e^{4} + 720 \, {\left(x e + d\right)}^{m} a^{5} x e^{6} + 720 \, {\left(x e + d\right)}^{m} a^{5} d e^{5}}{m^{6} e^{6} + 21 \, m^{5} e^{6} + 175 \, m^{4} e^{6} + 735 \, m^{3} e^{6} + 1624 \, m^{2} e^{6} + 1764 \, m e^{6} + 720 \, e^{6}}"," ",0,"((x*e + d)^m*b^5*m^5*x^6*e^6 + (x*e + d)^m*b^5*d*m^5*x^5*e^5 + 5*(x*e + d)^m*a*b^4*m^5*x^5*e^6 + 15*(x*e + d)^m*b^5*m^4*x^6*e^6 + 5*(x*e + d)^m*a*b^4*d*m^5*x^4*e^5 + 10*(x*e + d)^m*b^5*d*m^4*x^5*e^5 - 5*(x*e + d)^m*b^5*d^2*m^4*x^4*e^4 + 10*(x*e + d)^m*a^2*b^3*m^5*x^4*e^6 + 80*(x*e + d)^m*a*b^4*m^4*x^5*e^6 + 85*(x*e + d)^m*b^5*m^3*x^6*e^6 + 10*(x*e + d)^m*a^2*b^3*d*m^5*x^3*e^5 + 60*(x*e + d)^m*a*b^4*d*m^4*x^4*e^5 + 35*(x*e + d)^m*b^5*d*m^3*x^5*e^5 - 20*(x*e + d)^m*a*b^4*d^2*m^4*x^3*e^4 - 30*(x*e + d)^m*b^5*d^2*m^3*x^4*e^4 + 20*(x*e + d)^m*b^5*d^3*m^3*x^3*e^3 + 10*(x*e + d)^m*a^3*b^2*m^5*x^3*e^6 + 170*(x*e + d)^m*a^2*b^3*m^4*x^4*e^6 + 475*(x*e + d)^m*a*b^4*m^3*x^5*e^6 + 225*(x*e + d)^m*b^5*m^2*x^6*e^6 + 10*(x*e + d)^m*a^3*b^2*d*m^5*x^2*e^5 + 140*(x*e + d)^m*a^2*b^3*d*m^4*x^3*e^5 + 235*(x*e + d)^m*a*b^4*d*m^3*x^4*e^5 + 50*(x*e + d)^m*b^5*d*m^2*x^5*e^5 - 30*(x*e + d)^m*a^2*b^3*d^2*m^4*x^2*e^4 - 180*(x*e + d)^m*a*b^4*d^2*m^3*x^3*e^4 - 55*(x*e + d)^m*b^5*d^2*m^2*x^4*e^4 + 60*(x*e + d)^m*a*b^4*d^3*m^3*x^2*e^3 + 60*(x*e + d)^m*b^5*d^3*m^2*x^3*e^3 - 60*(x*e + d)^m*b^5*d^4*m^2*x^2*e^2 + 5*(x*e + d)^m*a^4*b*m^5*x^2*e^6 + 180*(x*e + d)^m*a^3*b^2*m^4*x^3*e^6 + 1070*(x*e + d)^m*a^2*b^3*m^3*x^4*e^6 + 1300*(x*e + d)^m*a*b^4*m^2*x^5*e^6 + 274*(x*e + d)^m*b^5*m*x^6*e^6 + 5*(x*e + d)^m*a^4*b*d*m^5*x*e^5 + 160*(x*e + d)^m*a^3*b^2*d*m^4*x^2*e^5 + 650*(x*e + d)^m*a^2*b^3*d*m^3*x^3*e^5 + 360*(x*e + d)^m*a*b^4*d*m^2*x^4*e^5 + 24*(x*e + d)^m*b^5*d*m*x^5*e^5 - 20*(x*e + d)^m*a^3*b^2*d^2*m^4*x*e^4 - 360*(x*e + d)^m*a^2*b^3*d^2*m^3*x^2*e^4 - 400*(x*e + d)^m*a*b^4*d^2*m^2*x^3*e^4 - 30*(x*e + d)^m*b^5*d^2*m*x^4*e^4 + 60*(x*e + d)^m*a^2*b^3*d^3*m^3*x*e^3 + 420*(x*e + d)^m*a*b^4*d^3*m^2*x^2*e^3 + 40*(x*e + d)^m*b^5*d^3*m*x^3*e^3 - 120*(x*e + d)^m*a*b^4*d^4*m^2*x*e^2 - 60*(x*e + d)^m*b^5*d^4*m*x^2*e^2 + 120*(x*e + d)^m*b^5*d^5*m*x*e + (x*e + d)^m*a^5*m^5*x*e^6 + 95*(x*e + d)^m*a^4*b*m^4*x^2*e^6 + 1210*(x*e + d)^m*a^3*b^2*m^3*x^3*e^6 + 3070*(x*e + d)^m*a^2*b^3*m^2*x^4*e^6 + 1620*(x*e + d)^m*a*b^4*m*x^5*e^6 + 120*(x*e + d)^m*b^5*x^6*e^6 + (x*e + d)^m*a^5*d*m^5*e^5 + 90*(x*e + d)^m*a^4*b*d*m^4*x*e^5 + 890*(x*e + d)^m*a^3*b^2*d*m^3*x^2*e^5 + 1120*(x*e + d)^m*a^2*b^3*d*m^2*x^3*e^5 + 180*(x*e + d)^m*a*b^4*d*m*x^4*e^5 - 5*(x*e + d)^m*a^4*b*d^2*m^4*e^4 - 300*(x*e + d)^m*a^3*b^2*d^2*m^3*x*e^4 - 1230*(x*e + d)^m*a^2*b^3*d^2*m^2*x^2*e^4 - 240*(x*e + d)^m*a*b^4*d^2*m*x^3*e^4 + 20*(x*e + d)^m*a^3*b^2*d^3*m^3*e^3 + 660*(x*e + d)^m*a^2*b^3*d^3*m^2*x*e^3 + 360*(x*e + d)^m*a*b^4*d^3*m*x^2*e^3 - 60*(x*e + d)^m*a^2*b^3*d^4*m^2*e^2 - 720*(x*e + d)^m*a*b^4*d^4*m*x*e^2 + 120*(x*e + d)^m*a*b^4*d^5*m*e - 120*(x*e + d)^m*b^5*d^6 + 20*(x*e + d)^m*a^5*m^4*x*e^6 + 685*(x*e + d)^m*a^4*b*m^3*x^2*e^6 + 3720*(x*e + d)^m*a^3*b^2*m^2*x^3*e^6 + 3960*(x*e + d)^m*a^2*b^3*m*x^4*e^6 + 720*(x*e + d)^m*a*b^4*x^5*e^6 + 20*(x*e + d)^m*a^5*d*m^4*e^5 + 595*(x*e + d)^m*a^4*b*d*m^3*x*e^5 + 1940*(x*e + d)^m*a^3*b^2*d*m^2*x^2*e^5 + 600*(x*e + d)^m*a^2*b^3*d*m*x^3*e^5 - 90*(x*e + d)^m*a^4*b*d^2*m^3*e^4 - 1480*(x*e + d)^m*a^3*b^2*d^2*m^2*x*e^4 - 900*(x*e + d)^m*a^2*b^3*d^2*m*x^2*e^4 + 300*(x*e + d)^m*a^3*b^2*d^3*m^2*e^3 + 1800*(x*e + d)^m*a^2*b^3*d^3*m*x*e^3 - 660*(x*e + d)^m*a^2*b^3*d^4*m*e^2 + 720*(x*e + d)^m*a*b^4*d^5*e + 155*(x*e + d)^m*a^5*m^3*x*e^6 + 2305*(x*e + d)^m*a^4*b*m^2*x^2*e^6 + 5080*(x*e + d)^m*a^3*b^2*m*x^3*e^6 + 1800*(x*e + d)^m*a^2*b^3*x^4*e^6 + 155*(x*e + d)^m*a^5*d*m^3*e^5 + 1710*(x*e + d)^m*a^4*b*d*m^2*x*e^5 + 1200*(x*e + d)^m*a^3*b^2*d*m*x^2*e^5 - 595*(x*e + d)^m*a^4*b*d^2*m^2*e^4 - 2400*(x*e + d)^m*a^3*b^2*d^2*m*x*e^4 + 1480*(x*e + d)^m*a^3*b^2*d^3*m*e^3 - 1800*(x*e + d)^m*a^2*b^3*d^4*e^2 + 580*(x*e + d)^m*a^5*m^2*x*e^6 + 3510*(x*e + d)^m*a^4*b*m*x^2*e^6 + 2400*(x*e + d)^m*a^3*b^2*x^3*e^6 + 580*(x*e + d)^m*a^5*d*m^2*e^5 + 1800*(x*e + d)^m*a^4*b*d*m*x*e^5 - 1710*(x*e + d)^m*a^4*b*d^2*m*e^4 + 2400*(x*e + d)^m*a^3*b^2*d^3*e^3 + 1044*(x*e + d)^m*a^5*m*x*e^6 + 1800*(x*e + d)^m*a^4*b*x^2*e^6 + 1044*(x*e + d)^m*a^5*d*m*e^5 - 1800*(x*e + d)^m*a^4*b*d^2*e^4 + 720*(x*e + d)^m*a^5*x*e^6 + 720*(x*e + d)^m*a^5*d*e^5)/(m^6*e^6 + 21*m^5*e^6 + 175*m^4*e^6 + 735*m^3*e^6 + 1624*m^2*e^6 + 1764*m*e^6 + 720*e^6)","B",0
2148,1,835,0,0.181987," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{3} m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} b^{3} d m^{3} x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} a b^{2} m^{3} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} b^{3} m^{2} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} a b^{2} d m^{3} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} b^{3} d m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{2} x^{2} e^{2} + 3 \, {\left(x e + d\right)}^{m} a^{2} b m^{3} x^{2} e^{4} + 21 \, {\left(x e + d\right)}^{m} a b^{2} m^{2} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} b^{3} m x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} a^{2} b d m^{3} x e^{3} + 15 \, {\left(x e + d\right)}^{m} a b^{2} d m^{2} x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} b^{3} d m x^{3} e^{3} - 6 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{2} x e^{2} - 3 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m x e + {\left(x e + d\right)}^{m} a^{3} m^{3} x e^{4} + 24 \, {\left(x e + d\right)}^{m} a^{2} b m^{2} x^{2} e^{4} + 42 \, {\left(x e + d\right)}^{m} a b^{2} m x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} b^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} a^{3} d m^{3} e^{3} + 21 \, {\left(x e + d\right)}^{m} a^{2} b d m^{2} x e^{3} + 12 \, {\left(x e + d\right)}^{m} a b^{2} d m x^{2} e^{3} - 3 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m x e^{2} + 6 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} m e - 6 \, {\left(x e + d\right)}^{m} b^{3} d^{4} + 9 \, {\left(x e + d\right)}^{m} a^{3} m^{2} x e^{4} + 57 \, {\left(x e + d\right)}^{m} a^{2} b m x^{2} e^{4} + 24 \, {\left(x e + d\right)}^{m} a b^{2} x^{3} e^{4} + 9 \, {\left(x e + d\right)}^{m} a^{3} d m^{2} e^{3} + 36 \, {\left(x e + d\right)}^{m} a^{2} b d m x e^{3} - 21 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m e^{2} + 24 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} e + 26 \, {\left(x e + d\right)}^{m} a^{3} m x e^{4} + 36 \, {\left(x e + d\right)}^{m} a^{2} b x^{2} e^{4} + 26 \, {\left(x e + d\right)}^{m} a^{3} d m e^{3} - 36 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} e^{2} + 24 \, {\left(x e + d\right)}^{m} a^{3} x e^{4} + 24 \, {\left(x e + d\right)}^{m} a^{3} d e^{3}}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"((x*e + d)^m*b^3*m^3*x^4*e^4 + (x*e + d)^m*b^3*d*m^3*x^3*e^3 + 3*(x*e + d)^m*a*b^2*m^3*x^3*e^4 + 6*(x*e + d)^m*b^3*m^2*x^4*e^4 + 3*(x*e + d)^m*a*b^2*d*m^3*x^2*e^3 + 3*(x*e + d)^m*b^3*d*m^2*x^3*e^3 - 3*(x*e + d)^m*b^3*d^2*m^2*x^2*e^2 + 3*(x*e + d)^m*a^2*b*m^3*x^2*e^4 + 21*(x*e + d)^m*a*b^2*m^2*x^3*e^4 + 11*(x*e + d)^m*b^3*m*x^4*e^4 + 3*(x*e + d)^m*a^2*b*d*m^3*x*e^3 + 15*(x*e + d)^m*a*b^2*d*m^2*x^2*e^3 + 2*(x*e + d)^m*b^3*d*m*x^3*e^3 - 6*(x*e + d)^m*a*b^2*d^2*m^2*x*e^2 - 3*(x*e + d)^m*b^3*d^2*m*x^2*e^2 + 6*(x*e + d)^m*b^3*d^3*m*x*e + (x*e + d)^m*a^3*m^3*x*e^4 + 24*(x*e + d)^m*a^2*b*m^2*x^2*e^4 + 42*(x*e + d)^m*a*b^2*m*x^3*e^4 + 6*(x*e + d)^m*b^3*x^4*e^4 + (x*e + d)^m*a^3*d*m^3*e^3 + 21*(x*e + d)^m*a^2*b*d*m^2*x*e^3 + 12*(x*e + d)^m*a*b^2*d*m*x^2*e^3 - 3*(x*e + d)^m*a^2*b*d^2*m^2*e^2 - 24*(x*e + d)^m*a*b^2*d^2*m*x*e^2 + 6*(x*e + d)^m*a*b^2*d^3*m*e - 6*(x*e + d)^m*b^3*d^4 + 9*(x*e + d)^m*a^3*m^2*x*e^4 + 57*(x*e + d)^m*a^2*b*m*x^2*e^4 + 24*(x*e + d)^m*a*b^2*x^3*e^4 + 9*(x*e + d)^m*a^3*d*m^2*e^3 + 36*(x*e + d)^m*a^2*b*d*m*x*e^3 - 21*(x*e + d)^m*a^2*b*d^2*m*e^2 + 24*(x*e + d)^m*a*b^2*d^3*e + 26*(x*e + d)^m*a^3*m*x*e^4 + 36*(x*e + d)^m*a^2*b*x^2*e^4 + 26*(x*e + d)^m*a^3*d*m*e^3 - 36*(x*e + d)^m*a^2*b*d^2*e^2 + 24*(x*e + d)^m*a^3*x*e^4 + 24*(x*e + d)^m*a^3*d*e^3)/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
2149,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
2150,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^2, x)","F",0
2151,1,4885,0,0.662961," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{6} m^{6} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b^{6} d m^{6} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a b^{5} m^{6} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{m} b^{6} m^{5} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a b^{5} d m^{6} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} b^{6} d m^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{6} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 132 \, {\left(x e + d\right)}^{m} a b^{5} m^{5} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 175 \, {\left(x e + d\right)}^{m} b^{6} m^{4} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{6} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 102 \, {\left(x e + d\right)}^{m} a b^{5} d m^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 85 \, {\left(x e + d\right)}^{m} b^{6} d m^{4} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{5} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{4} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{6} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 345 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{5} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 1140 \, {\left(x e + d\right)}^{m} a b^{5} m^{4} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 735 \, {\left(x e + d\right)}^{m} b^{6} m^{3} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{6} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 285 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{5} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 630 \, {\left(x e + d\right)}^{m} a b^{5} d m^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 225 \, {\left(x e + d\right)}^{m} b^{6} d m^{3} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{5} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 390 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{3} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} b^{6} d^{4} m^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{6} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 480 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{5} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 3105 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{4} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 4920 \, {\left(x e + d\right)}^{m} a b^{5} m^{3} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 1624 \, {\left(x e + d\right)}^{m} b^{6} m^{2} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{6} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 420 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{5} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1965 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1770 \, {\left(x e + d\right)}^{m} a b^{5} d m^{3} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 274 \, {\left(x e + d\right)}^{m} b^{6} d m^{2} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{5} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 960 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{4} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 1590 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 300 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{2} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m^{4} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1200 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 330 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 360 \, {\left(x e + d\right)}^{m} a b^{5} d^{4} m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 360 \, {\left(x e + d\right)}^{m} b^{6} d^{4} m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 360 \, {\left(x e + d\right)}^{m} b^{6} d^{5} m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a^{5} b m^{6} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 375 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{5} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 4520 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{4} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 13875 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{3} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 11094 \, {\left(x e + d\right)}^{m} a b^{5} m^{2} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 1764 \, {\left(x e + d\right)}^{m} b^{6} m x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a^{5} b d m^{6} x e^{6} \mathrm{sgn}\left(b x + a\right) + 345 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{5} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 3260 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{4} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 6015 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 2244 \, {\left(x e + d\right)}^{m} a b^{5} d m^{2} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} b^{6} d m x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{5} x e^{5} \mathrm{sgn}\left(b x + a\right) - 1140 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{4} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 4980 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 2490 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 144 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 2520 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 2760 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 360 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{4} m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) - 2880 \, {\left(x e + d\right)}^{m} a b^{5} d^{4} m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 240 \, {\left(x e + d\right)}^{m} b^{6} d^{4} m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} a b^{5} d^{5} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 360 \, {\left(x e + d\right)}^{m} b^{6} d^{5} m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 720 \, {\left(x e + d\right)}^{m} b^{6} d^{6} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{6} m^{6} x e^{7} \mathrm{sgn}\left(b x + a\right) + 156 \, {\left(x e + d\right)}^{m} a^{5} b m^{5} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 3705 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{4} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 21120 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{3} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 32160 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{2} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 12228 \, {\left(x e + d\right)}^{m} a b^{5} m x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} b^{6} x^{7} e^{7} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{6} d m^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 150 \, {\left(x e + d\right)}^{m} a^{5} b d m^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 3015 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{4} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 11340 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 8100 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{2} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1008 \, {\left(x e + d\right)}^{m} a b^{5} d m x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 660 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) - 7500 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 9120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 1260 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 2160 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 9900 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 1680 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 4680 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{4} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) - 2520 \, {\left(x e + d\right)}^{m} a b^{5} d^{4} m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 360 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{5} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} a b^{5} d^{5} m x e^{2} \mathrm{sgn}\left(b x + a\right) - 720 \, {\left(x e + d\right)}^{m} a b^{5} d^{6} m e \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} b^{6} d^{7} \mathrm{sgn}\left(b x + a\right) + 27 \, {\left(x e + d\right)}^{m} a^{6} m^{5} x e^{7} \mathrm{sgn}\left(b x + a\right) + 1620 \, {\left(x e + d\right)}^{m} a^{5} b m^{4} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 18285 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{3} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 50900 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{2} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 36180 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} a b^{5} x^{6} e^{7} \mathrm{sgn}\left(b x + a\right) + 27 \, {\left(x e + d\right)}^{m} a^{6} d m^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 1470 \, {\left(x e + d\right)}^{m} a^{5} b d m^{4} x e^{6} \mathrm{sgn}\left(b x + a\right) + 12255 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{3} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 16880 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 3780 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) - 150 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 5370 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) - 19020 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 5040 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 660 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 12840 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 7560 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 2160 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 15120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{4} m x e^{3} \mathrm{sgn}\left(b x + a\right) + 4680 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{5} m e^{2} \mathrm{sgn}\left(b x + a\right) - 5040 \, {\left(x e + d\right)}^{m} a b^{5} d^{6} e \mathrm{sgn}\left(b x + a\right) + 295 \, {\left(x e + d\right)}^{m} a^{6} m^{4} x e^{7} \mathrm{sgn}\left(b x + a\right) + 8520 \, {\left(x e + d\right)}^{m} a^{5} b m^{3} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 46680 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{2} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 59040 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 15120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} x^{5} e^{7} \mathrm{sgn}\left(b x + a\right) + 295 \, {\left(x e + d\right)}^{m} a^{6} d m^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 7050 \, {\left(x e + d\right)}^{m} a^{5} b d m^{3} x e^{6} \mathrm{sgn}\left(b x + a\right) + 22170 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 8400 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) - 1470 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 19140 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{2} x e^{5} \mathrm{sgn}\left(b x + a\right) - 12600 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 5370 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 25200 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m x e^{4} \mathrm{sgn}\left(b x + a\right) - 12840 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} m e^{3} \mathrm{sgn}\left(b x + a\right) + 15120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 1665 \, {\left(x e + d\right)}^{m} a^{6} m^{3} x e^{7} \mathrm{sgn}\left(b x + a\right) + 23574 \, {\left(x e + d\right)}^{m} a^{5} b m^{2} x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 56940 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 25200 \, {\left(x e + d\right)}^{m} a^{3} b^{3} x^{4} e^{7} \mathrm{sgn}\left(b x + a\right) + 1665 \, {\left(x e + d\right)}^{m} a^{6} d m^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 16524 \, {\left(x e + d\right)}^{m} a^{5} b d m^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 12600 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 7050 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 25200 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m x e^{5} \mathrm{sgn}\left(b x + a\right) + 19140 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m e^{4} \mathrm{sgn}\left(b x + a\right) - 25200 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 5104 \, {\left(x e + d\right)}^{m} a^{6} m^{2} x e^{7} \mathrm{sgn}\left(b x + a\right) + 31644 \, {\left(x e + d\right)}^{m} a^{5} b m x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 25200 \, {\left(x e + d\right)}^{m} a^{4} b^{2} x^{3} e^{7} \mathrm{sgn}\left(b x + a\right) + 5104 \, {\left(x e + d\right)}^{m} a^{6} d m^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 15120 \, {\left(x e + d\right)}^{m} a^{5} b d m x e^{6} \mathrm{sgn}\left(b x + a\right) - 16524 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m e^{5} \mathrm{sgn}\left(b x + a\right) + 25200 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 8028 \, {\left(x e + d\right)}^{m} a^{6} m x e^{7} \mathrm{sgn}\left(b x + a\right) + 15120 \, {\left(x e + d\right)}^{m} a^{5} b x^{2} e^{7} \mathrm{sgn}\left(b x + a\right) + 8028 \, {\left(x e + d\right)}^{m} a^{6} d m e^{6} \mathrm{sgn}\left(b x + a\right) - 15120 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} a^{6} x e^{7} \mathrm{sgn}\left(b x + a\right) + 5040 \, {\left(x e + d\right)}^{m} a^{6} d e^{6} \mathrm{sgn}\left(b x + a\right)}{m^{7} e^{7} + 28 \, m^{6} e^{7} + 322 \, m^{5} e^{7} + 1960 \, m^{4} e^{7} + 6769 \, m^{3} e^{7} + 13132 \, m^{2} e^{7} + 13068 \, m e^{7} + 5040 \, e^{7}}"," ",0,"((x*e + d)^m*b^6*m^6*x^7*e^7*sgn(b*x + a) + (x*e + d)^m*b^6*d*m^6*x^6*e^6*sgn(b*x + a) + 6*(x*e + d)^m*a*b^5*m^6*x^6*e^7*sgn(b*x + a) + 21*(x*e + d)^m*b^6*m^5*x^7*e^7*sgn(b*x + a) + 6*(x*e + d)^m*a*b^5*d*m^6*x^5*e^6*sgn(b*x + a) + 15*(x*e + d)^m*b^6*d*m^5*x^6*e^6*sgn(b*x + a) - 6*(x*e + d)^m*b^6*d^2*m^5*x^5*e^5*sgn(b*x + a) + 15*(x*e + d)^m*a^2*b^4*m^6*x^5*e^7*sgn(b*x + a) + 132*(x*e + d)^m*a*b^5*m^5*x^6*e^7*sgn(b*x + a) + 175*(x*e + d)^m*b^6*m^4*x^7*e^7*sgn(b*x + a) + 15*(x*e + d)^m*a^2*b^4*d*m^6*x^4*e^6*sgn(b*x + a) + 102*(x*e + d)^m*a*b^5*d*m^5*x^5*e^6*sgn(b*x + a) + 85*(x*e + d)^m*b^6*d*m^4*x^6*e^6*sgn(b*x + a) - 30*(x*e + d)^m*a*b^5*d^2*m^5*x^4*e^5*sgn(b*x + a) - 60*(x*e + d)^m*b^6*d^2*m^4*x^5*e^5*sgn(b*x + a) + 30*(x*e + d)^m*b^6*d^3*m^4*x^4*e^4*sgn(b*x + a) + 20*(x*e + d)^m*a^3*b^3*m^6*x^4*e^7*sgn(b*x + a) + 345*(x*e + d)^m*a^2*b^4*m^5*x^5*e^7*sgn(b*x + a) + 1140*(x*e + d)^m*a*b^5*m^4*x^6*e^7*sgn(b*x + a) + 735*(x*e + d)^m*b^6*m^3*x^7*e^7*sgn(b*x + a) + 20*(x*e + d)^m*a^3*b^3*d*m^6*x^3*e^6*sgn(b*x + a) + 285*(x*e + d)^m*a^2*b^4*d*m^5*x^4*e^6*sgn(b*x + a) + 630*(x*e + d)^m*a*b^5*d*m^4*x^5*e^6*sgn(b*x + a) + 225*(x*e + d)^m*b^6*d*m^3*x^6*e^6*sgn(b*x + a) - 60*(x*e + d)^m*a^2*b^4*d^2*m^5*x^3*e^5*sgn(b*x + a) - 390*(x*e + d)^m*a*b^5*d^2*m^4*x^4*e^5*sgn(b*x + a) - 210*(x*e + d)^m*b^6*d^2*m^3*x^5*e^5*sgn(b*x + a) + 120*(x*e + d)^m*a*b^5*d^3*m^4*x^3*e^4*sgn(b*x + a) + 180*(x*e + d)^m*b^6*d^3*m^3*x^4*e^4*sgn(b*x + a) - 120*(x*e + d)^m*b^6*d^4*m^3*x^3*e^3*sgn(b*x + a) + 15*(x*e + d)^m*a^4*b^2*m^6*x^3*e^7*sgn(b*x + a) + 480*(x*e + d)^m*a^3*b^3*m^5*x^4*e^7*sgn(b*x + a) + 3105*(x*e + d)^m*a^2*b^4*m^4*x^5*e^7*sgn(b*x + a) + 4920*(x*e + d)^m*a*b^5*m^3*x^6*e^7*sgn(b*x + a) + 1624*(x*e + d)^m*b^6*m^2*x^7*e^7*sgn(b*x + a) + 15*(x*e + d)^m*a^4*b^2*d*m^6*x^2*e^6*sgn(b*x + a) + 420*(x*e + d)^m*a^3*b^3*d*m^5*x^3*e^6*sgn(b*x + a) + 1965*(x*e + d)^m*a^2*b^4*d*m^4*x^4*e^6*sgn(b*x + a) + 1770*(x*e + d)^m*a*b^5*d*m^3*x^5*e^6*sgn(b*x + a) + 274*(x*e + d)^m*b^6*d*m^2*x^6*e^6*sgn(b*x + a) - 60*(x*e + d)^m*a^3*b^3*d^2*m^5*x^2*e^5*sgn(b*x + a) - 960*(x*e + d)^m*a^2*b^4*d^2*m^4*x^3*e^5*sgn(b*x + a) - 1590*(x*e + d)^m*a*b^5*d^2*m^3*x^4*e^5*sgn(b*x + a) - 300*(x*e + d)^m*b^6*d^2*m^2*x^5*e^5*sgn(b*x + a) + 180*(x*e + d)^m*a^2*b^4*d^3*m^4*x^2*e^4*sgn(b*x + a) + 1200*(x*e + d)^m*a*b^5*d^3*m^3*x^3*e^4*sgn(b*x + a) + 330*(x*e + d)^m*b^6*d^3*m^2*x^4*e^4*sgn(b*x + a) - 360*(x*e + d)^m*a*b^5*d^4*m^3*x^2*e^3*sgn(b*x + a) - 360*(x*e + d)^m*b^6*d^4*m^2*x^3*e^3*sgn(b*x + a) + 360*(x*e + d)^m*b^6*d^5*m^2*x^2*e^2*sgn(b*x + a) + 6*(x*e + d)^m*a^5*b*m^6*x^2*e^7*sgn(b*x + a) + 375*(x*e + d)^m*a^4*b^2*m^5*x^3*e^7*sgn(b*x + a) + 4520*(x*e + d)^m*a^3*b^3*m^4*x^4*e^7*sgn(b*x + a) + 13875*(x*e + d)^m*a^2*b^4*m^3*x^5*e^7*sgn(b*x + a) + 11094*(x*e + d)^m*a*b^5*m^2*x^6*e^7*sgn(b*x + a) + 1764*(x*e + d)^m*b^6*m*x^7*e^7*sgn(b*x + a) + 6*(x*e + d)^m*a^5*b*d*m^6*x*e^6*sgn(b*x + a) + 345*(x*e + d)^m*a^4*b^2*d*m^5*x^2*e^6*sgn(b*x + a) + 3260*(x*e + d)^m*a^3*b^3*d*m^4*x^3*e^6*sgn(b*x + a) + 6015*(x*e + d)^m*a^2*b^4*d*m^3*x^4*e^6*sgn(b*x + a) + 2244*(x*e + d)^m*a*b^5*d*m^2*x^5*e^6*sgn(b*x + a) + 120*(x*e + d)^m*b^6*d*m*x^6*e^6*sgn(b*x + a) - 30*(x*e + d)^m*a^4*b^2*d^2*m^5*x*e^5*sgn(b*x + a) - 1140*(x*e + d)^m*a^3*b^3*d^2*m^4*x^2*e^5*sgn(b*x + a) - 4980*(x*e + d)^m*a^2*b^4*d^2*m^3*x^3*e^5*sgn(b*x + a) - 2490*(x*e + d)^m*a*b^5*d^2*m^2*x^4*e^5*sgn(b*x + a) - 144*(x*e + d)^m*b^6*d^2*m*x^5*e^5*sgn(b*x + a) + 120*(x*e + d)^m*a^3*b^3*d^3*m^4*x*e^4*sgn(b*x + a) + 2520*(x*e + d)^m*a^2*b^4*d^3*m^3*x^2*e^4*sgn(b*x + a) + 2760*(x*e + d)^m*a*b^5*d^3*m^2*x^3*e^4*sgn(b*x + a) + 180*(x*e + d)^m*b^6*d^3*m*x^4*e^4*sgn(b*x + a) - 360*(x*e + d)^m*a^2*b^4*d^4*m^3*x*e^3*sgn(b*x + a) - 2880*(x*e + d)^m*a*b^5*d^4*m^2*x^2*e^3*sgn(b*x + a) - 240*(x*e + d)^m*b^6*d^4*m*x^3*e^3*sgn(b*x + a) + 720*(x*e + d)^m*a*b^5*d^5*m^2*x*e^2*sgn(b*x + a) + 360*(x*e + d)^m*b^6*d^5*m*x^2*e^2*sgn(b*x + a) - 720*(x*e + d)^m*b^6*d^6*m*x*e*sgn(b*x + a) + (x*e + d)^m*a^6*m^6*x*e^7*sgn(b*x + a) + 156*(x*e + d)^m*a^5*b*m^5*x^2*e^7*sgn(b*x + a) + 3705*(x*e + d)^m*a^4*b^2*m^4*x^3*e^7*sgn(b*x + a) + 21120*(x*e + d)^m*a^3*b^3*m^3*x^4*e^7*sgn(b*x + a) + 32160*(x*e + d)^m*a^2*b^4*m^2*x^5*e^7*sgn(b*x + a) + 12228*(x*e + d)^m*a*b^5*m*x^6*e^7*sgn(b*x + a) + 720*(x*e + d)^m*b^6*x^7*e^7*sgn(b*x + a) + (x*e + d)^m*a^6*d*m^6*e^6*sgn(b*x + a) + 150*(x*e + d)^m*a^5*b*d*m^5*x*e^6*sgn(b*x + a) + 3015*(x*e + d)^m*a^4*b^2*d*m^4*x^2*e^6*sgn(b*x + a) + 11340*(x*e + d)^m*a^3*b^3*d*m^3*x^3*e^6*sgn(b*x + a) + 8100*(x*e + d)^m*a^2*b^4*d*m^2*x^4*e^6*sgn(b*x + a) + 1008*(x*e + d)^m*a*b^5*d*m*x^5*e^6*sgn(b*x + a) - 6*(x*e + d)^m*a^5*b*d^2*m^5*e^5*sgn(b*x + a) - 660*(x*e + d)^m*a^4*b^2*d^2*m^4*x*e^5*sgn(b*x + a) - 7500*(x*e + d)^m*a^3*b^3*d^2*m^3*x^2*e^5*sgn(b*x + a) - 9120*(x*e + d)^m*a^2*b^4*d^2*m^2*x^3*e^5*sgn(b*x + a) - 1260*(x*e + d)^m*a*b^5*d^2*m*x^4*e^5*sgn(b*x + a) + 30*(x*e + d)^m*a^4*b^2*d^3*m^4*e^4*sgn(b*x + a) + 2160*(x*e + d)^m*a^3*b^3*d^3*m^3*x*e^4*sgn(b*x + a) + 9900*(x*e + d)^m*a^2*b^4*d^3*m^2*x^2*e^4*sgn(b*x + a) + 1680*(x*e + d)^m*a*b^5*d^3*m*x^3*e^4*sgn(b*x + a) - 120*(x*e + d)^m*a^3*b^3*d^4*m^3*e^3*sgn(b*x + a) - 4680*(x*e + d)^m*a^2*b^4*d^4*m^2*x*e^3*sgn(b*x + a) - 2520*(x*e + d)^m*a*b^5*d^4*m*x^2*e^3*sgn(b*x + a) + 360*(x*e + d)^m*a^2*b^4*d^5*m^2*e^2*sgn(b*x + a) + 5040*(x*e + d)^m*a*b^5*d^5*m*x*e^2*sgn(b*x + a) - 720*(x*e + d)^m*a*b^5*d^6*m*e*sgn(b*x + a) + 720*(x*e + d)^m*b^6*d^7*sgn(b*x + a) + 27*(x*e + d)^m*a^6*m^5*x*e^7*sgn(b*x + a) + 1620*(x*e + d)^m*a^5*b*m^4*x^2*e^7*sgn(b*x + a) + 18285*(x*e + d)^m*a^4*b^2*m^3*x^3*e^7*sgn(b*x + a) + 50900*(x*e + d)^m*a^3*b^3*m^2*x^4*e^7*sgn(b*x + a) + 36180*(x*e + d)^m*a^2*b^4*m*x^5*e^7*sgn(b*x + a) + 5040*(x*e + d)^m*a*b^5*x^6*e^7*sgn(b*x + a) + 27*(x*e + d)^m*a^6*d*m^5*e^6*sgn(b*x + a) + 1470*(x*e + d)^m*a^5*b*d*m^4*x*e^6*sgn(b*x + a) + 12255*(x*e + d)^m*a^4*b^2*d*m^3*x^2*e^6*sgn(b*x + a) + 16880*(x*e + d)^m*a^3*b^3*d*m^2*x^3*e^6*sgn(b*x + a) + 3780*(x*e + d)^m*a^2*b^4*d*m*x^4*e^6*sgn(b*x + a) - 150*(x*e + d)^m*a^5*b*d^2*m^4*e^5*sgn(b*x + a) - 5370*(x*e + d)^m*a^4*b^2*d^2*m^3*x*e^5*sgn(b*x + a) - 19020*(x*e + d)^m*a^3*b^3*d^2*m^2*x^2*e^5*sgn(b*x + a) - 5040*(x*e + d)^m*a^2*b^4*d^2*m*x^3*e^5*sgn(b*x + a) + 660*(x*e + d)^m*a^4*b^2*d^3*m^3*e^4*sgn(b*x + a) + 12840*(x*e + d)^m*a^3*b^3*d^3*m^2*x*e^4*sgn(b*x + a) + 7560*(x*e + d)^m*a^2*b^4*d^3*m*x^2*e^4*sgn(b*x + a) - 2160*(x*e + d)^m*a^3*b^3*d^4*m^2*e^3*sgn(b*x + a) - 15120*(x*e + d)^m*a^2*b^4*d^4*m*x*e^3*sgn(b*x + a) + 4680*(x*e + d)^m*a^2*b^4*d^5*m*e^2*sgn(b*x + a) - 5040*(x*e + d)^m*a*b^5*d^6*e*sgn(b*x + a) + 295*(x*e + d)^m*a^6*m^4*x*e^7*sgn(b*x + a) + 8520*(x*e + d)^m*a^5*b*m^3*x^2*e^7*sgn(b*x + a) + 46680*(x*e + d)^m*a^4*b^2*m^2*x^3*e^7*sgn(b*x + a) + 59040*(x*e + d)^m*a^3*b^3*m*x^4*e^7*sgn(b*x + a) + 15120*(x*e + d)^m*a^2*b^4*x^5*e^7*sgn(b*x + a) + 295*(x*e + d)^m*a^6*d*m^4*e^6*sgn(b*x + a) + 7050*(x*e + d)^m*a^5*b*d*m^3*x*e^6*sgn(b*x + a) + 22170*(x*e + d)^m*a^4*b^2*d*m^2*x^2*e^6*sgn(b*x + a) + 8400*(x*e + d)^m*a^3*b^3*d*m*x^3*e^6*sgn(b*x + a) - 1470*(x*e + d)^m*a^5*b*d^2*m^3*e^5*sgn(b*x + a) - 19140*(x*e + d)^m*a^4*b^2*d^2*m^2*x*e^5*sgn(b*x + a) - 12600*(x*e + d)^m*a^3*b^3*d^2*m*x^2*e^5*sgn(b*x + a) + 5370*(x*e + d)^m*a^4*b^2*d^3*m^2*e^4*sgn(b*x + a) + 25200*(x*e + d)^m*a^3*b^3*d^3*m*x*e^4*sgn(b*x + a) - 12840*(x*e + d)^m*a^3*b^3*d^4*m*e^3*sgn(b*x + a) + 15120*(x*e + d)^m*a^2*b^4*d^5*e^2*sgn(b*x + a) + 1665*(x*e + d)^m*a^6*m^3*x*e^7*sgn(b*x + a) + 23574*(x*e + d)^m*a^5*b*m^2*x^2*e^7*sgn(b*x + a) + 56940*(x*e + d)^m*a^4*b^2*m*x^3*e^7*sgn(b*x + a) + 25200*(x*e + d)^m*a^3*b^3*x^4*e^7*sgn(b*x + a) + 1665*(x*e + d)^m*a^6*d*m^3*e^6*sgn(b*x + a) + 16524*(x*e + d)^m*a^5*b*d*m^2*x*e^6*sgn(b*x + a) + 12600*(x*e + d)^m*a^4*b^2*d*m*x^2*e^6*sgn(b*x + a) - 7050*(x*e + d)^m*a^5*b*d^2*m^2*e^5*sgn(b*x + a) - 25200*(x*e + d)^m*a^4*b^2*d^2*m*x*e^5*sgn(b*x + a) + 19140*(x*e + d)^m*a^4*b^2*d^3*m*e^4*sgn(b*x + a) - 25200*(x*e + d)^m*a^3*b^3*d^4*e^3*sgn(b*x + a) + 5104*(x*e + d)^m*a^6*m^2*x*e^7*sgn(b*x + a) + 31644*(x*e + d)^m*a^5*b*m*x^2*e^7*sgn(b*x + a) + 25200*(x*e + d)^m*a^4*b^2*x^3*e^7*sgn(b*x + a) + 5104*(x*e + d)^m*a^6*d*m^2*e^6*sgn(b*x + a) + 15120*(x*e + d)^m*a^5*b*d*m*x*e^6*sgn(b*x + a) - 16524*(x*e + d)^m*a^5*b*d^2*m*e^5*sgn(b*x + a) + 25200*(x*e + d)^m*a^4*b^2*d^3*e^4*sgn(b*x + a) + 8028*(x*e + d)^m*a^6*m*x*e^7*sgn(b*x + a) + 15120*(x*e + d)^m*a^5*b*x^2*e^7*sgn(b*x + a) + 8028*(x*e + d)^m*a^6*d*m*e^6*sgn(b*x + a) - 15120*(x*e + d)^m*a^5*b*d^2*e^5*sgn(b*x + a) + 5040*(x*e + d)^m*a^6*x*e^7*sgn(b*x + a) + 5040*(x*e + d)^m*a^6*d*e^6*sgn(b*x + a))/(m^7*e^7 + 28*m^6*e^7 + 322*m^5*e^7 + 1960*m^4*e^7 + 6769*m^3*e^7 + 13132*m^2*e^7 + 13068*m*e^7 + 5040*e^7)","B",0
2152,1,1949,0,0.325276," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{4} m^{4} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b^{4} d m^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(x e + d\right)}^{m} a b^{3} m^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} b^{4} m^{3} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(x e + d\right)}^{m} a b^{3} d m^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} b^{4} d m^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{4} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 44 \, {\left(x e + d\right)}^{m} a b^{3} m^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{m} b^{4} m^{2} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{4} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 32 \, {\left(x e + d\right)}^{m} a b^{3} d m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(x e + d\right)}^{m} b^{4} d m^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 12 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(x e + d\right)}^{m} a^{3} b m^{4} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 72 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 164 \, {\left(x e + d\right)}^{m} a b^{3} m^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 50 \, {\left(x e + d\right)}^{m} b^{4} m x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(x e + d\right)}^{m} a^{3} b d m^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 68 \, {\left(x e + d\right)}^{m} a b^{3} d m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} b^{4} d m x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) - 72 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 8 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 24 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{4} m^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) + 52 \, {\left(x e + d\right)}^{m} a^{3} b m^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 294 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 244 \, {\left(x e + d\right)}^{m} a b^{3} m x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} b^{4} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{4} d m^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 48 \, {\left(x e + d\right)}^{m} a^{3} b d m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 174 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 40 \, {\left(x e + d\right)}^{m} a b^{3} d m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 108 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m x e^{2} \mathrm{sgn}\left(b x + a\right) - 24 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} m e \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} b^{4} d^{5} \mathrm{sgn}\left(b x + a\right) + 14 \, {\left(x e + d\right)}^{m} a^{4} m^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) + 236 \, {\left(x e + d\right)}^{m} a^{3} b m^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 468 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a b^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 14 \, {\left(x e + d\right)}^{m} a^{4} d m^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 188 \, {\left(x e + d\right)}^{m} a^{3} b d m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 48 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 240 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m x e^{3} \mathrm{sgn}\left(b x + a\right) + 108 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} m e^{2} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} e \mathrm{sgn}\left(b x + a\right) + 71 \, {\left(x e + d\right)}^{m} a^{4} m^{2} x e^{5} \mathrm{sgn}\left(b x + a\right) + 428 \, {\left(x e + d\right)}^{m} a^{3} b m x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 240 \, {\left(x e + d\right)}^{m} a^{2} b^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 71 \, {\left(x e + d\right)}^{m} a^{4} d m^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 240 \, {\left(x e + d\right)}^{m} a^{3} b d m x e^{4} \mathrm{sgn}\left(b x + a\right) - 188 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m e^{3} \mathrm{sgn}\left(b x + a\right) + 240 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 154 \, {\left(x e + d\right)}^{m} a^{4} m x e^{5} \mathrm{sgn}\left(b x + a\right) + 240 \, {\left(x e + d\right)}^{m} a^{3} b x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 154 \, {\left(x e + d\right)}^{m} a^{4} d m e^{4} \mathrm{sgn}\left(b x + a\right) - 240 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a^{4} d e^{4} \mathrm{sgn}\left(b x + a\right)}{m^{5} e^{5} + 15 \, m^{4} e^{5} + 85 \, m^{3} e^{5} + 225 \, m^{2} e^{5} + 274 \, m e^{5} + 120 \, e^{5}}"," ",0,"((x*e + d)^m*b^4*m^4*x^5*e^5*sgn(b*x + a) + (x*e + d)^m*b^4*d*m^4*x^4*e^4*sgn(b*x + a) + 4*(x*e + d)^m*a*b^3*m^4*x^4*e^5*sgn(b*x + a) + 10*(x*e + d)^m*b^4*m^3*x^5*e^5*sgn(b*x + a) + 4*(x*e + d)^m*a*b^3*d*m^4*x^3*e^4*sgn(b*x + a) + 6*(x*e + d)^m*b^4*d*m^3*x^4*e^4*sgn(b*x + a) - 4*(x*e + d)^m*b^4*d^2*m^3*x^3*e^3*sgn(b*x + a) + 6*(x*e + d)^m*a^2*b^2*m^4*x^3*e^5*sgn(b*x + a) + 44*(x*e + d)^m*a*b^3*m^3*x^4*e^5*sgn(b*x + a) + 35*(x*e + d)^m*b^4*m^2*x^5*e^5*sgn(b*x + a) + 6*(x*e + d)^m*a^2*b^2*d*m^4*x^2*e^4*sgn(b*x + a) + 32*(x*e + d)^m*a*b^3*d*m^3*x^3*e^4*sgn(b*x + a) + 11*(x*e + d)^m*b^4*d*m^2*x^4*e^4*sgn(b*x + a) - 12*(x*e + d)^m*a*b^3*d^2*m^3*x^2*e^3*sgn(b*x + a) - 12*(x*e + d)^m*b^4*d^2*m^2*x^3*e^3*sgn(b*x + a) + 12*(x*e + d)^m*b^4*d^3*m^2*x^2*e^2*sgn(b*x + a) + 4*(x*e + d)^m*a^3*b*m^4*x^2*e^5*sgn(b*x + a) + 72*(x*e + d)^m*a^2*b^2*m^3*x^3*e^5*sgn(b*x + a) + 164*(x*e + d)^m*a*b^3*m^2*x^4*e^5*sgn(b*x + a) + 50*(x*e + d)^m*b^4*m*x^5*e^5*sgn(b*x + a) + 4*(x*e + d)^m*a^3*b*d*m^4*x*e^4*sgn(b*x + a) + 60*(x*e + d)^m*a^2*b^2*d*m^3*x^2*e^4*sgn(b*x + a) + 68*(x*e + d)^m*a*b^3*d*m^2*x^3*e^4*sgn(b*x + a) + 6*(x*e + d)^m*b^4*d*m*x^4*e^4*sgn(b*x + a) - 12*(x*e + d)^m*a^2*b^2*d^2*m^3*x*e^3*sgn(b*x + a) - 72*(x*e + d)^m*a*b^3*d^2*m^2*x^2*e^3*sgn(b*x + a) - 8*(x*e + d)^m*b^4*d^2*m*x^3*e^3*sgn(b*x + a) + 24*(x*e + d)^m*a*b^3*d^3*m^2*x*e^2*sgn(b*x + a) + 12*(x*e + d)^m*b^4*d^3*m*x^2*e^2*sgn(b*x + a) - 24*(x*e + d)^m*b^4*d^4*m*x*e*sgn(b*x + a) + (x*e + d)^m*a^4*m^4*x*e^5*sgn(b*x + a) + 52*(x*e + d)^m*a^3*b*m^3*x^2*e^5*sgn(b*x + a) + 294*(x*e + d)^m*a^2*b^2*m^2*x^3*e^5*sgn(b*x + a) + 244*(x*e + d)^m*a*b^3*m*x^4*e^5*sgn(b*x + a) + 24*(x*e + d)^m*b^4*x^5*e^5*sgn(b*x + a) + (x*e + d)^m*a^4*d*m^4*e^4*sgn(b*x + a) + 48*(x*e + d)^m*a^3*b*d*m^3*x*e^4*sgn(b*x + a) + 174*(x*e + d)^m*a^2*b^2*d*m^2*x^2*e^4*sgn(b*x + a) + 40*(x*e + d)^m*a*b^3*d*m*x^3*e^4*sgn(b*x + a) - 4*(x*e + d)^m*a^3*b*d^2*m^3*e^3*sgn(b*x + a) - 108*(x*e + d)^m*a^2*b^2*d^2*m^2*x*e^3*sgn(b*x + a) - 60*(x*e + d)^m*a*b^3*d^2*m*x^2*e^3*sgn(b*x + a) + 12*(x*e + d)^m*a^2*b^2*d^3*m^2*e^2*sgn(b*x + a) + 120*(x*e + d)^m*a*b^3*d^3*m*x*e^2*sgn(b*x + a) - 24*(x*e + d)^m*a*b^3*d^4*m*e*sgn(b*x + a) + 24*(x*e + d)^m*b^4*d^5*sgn(b*x + a) + 14*(x*e + d)^m*a^4*m^3*x*e^5*sgn(b*x + a) + 236*(x*e + d)^m*a^3*b*m^2*x^2*e^5*sgn(b*x + a) + 468*(x*e + d)^m*a^2*b^2*m*x^3*e^5*sgn(b*x + a) + 120*(x*e + d)^m*a*b^3*x^4*e^5*sgn(b*x + a) + 14*(x*e + d)^m*a^4*d*m^3*e^4*sgn(b*x + a) + 188*(x*e + d)^m*a^3*b*d*m^2*x*e^4*sgn(b*x + a) + 120*(x*e + d)^m*a^2*b^2*d*m*x^2*e^4*sgn(b*x + a) - 48*(x*e + d)^m*a^3*b*d^2*m^2*e^3*sgn(b*x + a) - 240*(x*e + d)^m*a^2*b^2*d^2*m*x*e^3*sgn(b*x + a) + 108*(x*e + d)^m*a^2*b^2*d^3*m*e^2*sgn(b*x + a) - 120*(x*e + d)^m*a*b^3*d^4*e*sgn(b*x + a) + 71*(x*e + d)^m*a^4*m^2*x*e^5*sgn(b*x + a) + 428*(x*e + d)^m*a^3*b*m*x^2*e^5*sgn(b*x + a) + 240*(x*e + d)^m*a^2*b^2*x^3*e^5*sgn(b*x + a) + 71*(x*e + d)^m*a^4*d*m^2*e^4*sgn(b*x + a) + 240*(x*e + d)^m*a^3*b*d*m*x*e^4*sgn(b*x + a) - 188*(x*e + d)^m*a^3*b*d^2*m*e^3*sgn(b*x + a) + 240*(x*e + d)^m*a^2*b^2*d^3*e^2*sgn(b*x + a) + 154*(x*e + d)^m*a^4*m*x*e^5*sgn(b*x + a) + 240*(x*e + d)^m*a^3*b*x^2*e^5*sgn(b*x + a) + 154*(x*e + d)^m*a^4*d*m*e^4*sgn(b*x + a) - 240*(x*e + d)^m*a^3*b*d^2*e^3*sgn(b*x + a) + 120*(x*e + d)^m*a^4*x*e^5*sgn(b*x + a) + 120*(x*e + d)^m*a^4*d*e^4*sgn(b*x + a))/(m^5*e^5 + 15*m^4*e^5 + 85*m^3*e^5 + 225*m^2*e^5 + 274*m*e^5 + 120*e^5)","B",0
2153,1,508,0,0.218970," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{2} m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b^{2} d m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} a b m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} b^{2} m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} a b d m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b^{2} d m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{2} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 8 \, {\left(x e + d\right)}^{m} a b m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} b^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{2} d m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a b d m x e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, {\left(x e + d\right)}^{m} a b d^{2} m e \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} b^{2} d^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} a^{2} m x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a b x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} a^{2} d m e^{2} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} a b d^{2} e \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a^{2} d e^{2} \mathrm{sgn}\left(b x + a\right)}{m^{3} e^{3} + 6 \, m^{2} e^{3} + 11 \, m e^{3} + 6 \, e^{3}}"," ",0,"((x*e + d)^m*b^2*m^2*x^3*e^3*sgn(b*x + a) + (x*e + d)^m*b^2*d*m^2*x^2*e^2*sgn(b*x + a) + 2*(x*e + d)^m*a*b*m^2*x^2*e^3*sgn(b*x + a) + 3*(x*e + d)^m*b^2*m*x^3*e^3*sgn(b*x + a) + 2*(x*e + d)^m*a*b*d*m^2*x*e^2*sgn(b*x + a) + (x*e + d)^m*b^2*d*m*x^2*e^2*sgn(b*x + a) - 2*(x*e + d)^m*b^2*d^2*m*x*e*sgn(b*x + a) + (x*e + d)^m*a^2*m^2*x*e^3*sgn(b*x + a) + 8*(x*e + d)^m*a*b*m*x^2*e^3*sgn(b*x + a) + 2*(x*e + d)^m*b^2*x^3*e^3*sgn(b*x + a) + (x*e + d)^m*a^2*d*m^2*e^2*sgn(b*x + a) + 6*(x*e + d)^m*a*b*d*m*x*e^2*sgn(b*x + a) - 2*(x*e + d)^m*a*b*d^2*m*e*sgn(b*x + a) + 2*(x*e + d)^m*b^2*d^3*sgn(b*x + a) + 5*(x*e + d)^m*a^2*m*x*e^3*sgn(b*x + a) + 6*(x*e + d)^m*a*b*x^2*e^3*sgn(b*x + a) + 5*(x*e + d)^m*a^2*d*m*e^2*sgn(b*x + a) - 6*(x*e + d)^m*a*b*d^2*e*sgn(b*x + a) + 6*(x*e + d)^m*a^2*x*e^3*sgn(b*x + a) + 6*(x*e + d)^m*a^2*d*e^2*sgn(b*x + a))/(m^3*e^3 + 6*m^2*e^3 + 11*m*e^3 + 6*e^3)","B",0
2154,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{m}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^m/sqrt(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
2155,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^(3/2), x)","F",0
2156,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x + a)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^(5/2), x)","F",0
2157,1,305,0,0.273928," ","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=""giac"")","\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} c x^{3} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} c d x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b c x^{2} e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b c d x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} c x e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} c d e^{\left(-2 \, p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)}}{2 \, {\left(b d p - a p e + b d - a e\right)}}"," ",0,"1/2*((b^2*x^2 + 2*a*b*x + a^2)^p*b^2*c*x^3*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + (b^2*x^2 + 2*a*b*x + a^2)^p*b^2*c*d*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*c*x^2*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*c*d*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d)) + (b^2*x^2 + 2*a*b*x + a^2)^p*a^2*c*x*e^(-2*p*log(x*e + d) - 3*log(x*e + d) + 1) + (b^2*x^2 + 2*a*b*x + a^2)^p*a^2*c*d*e^(-2*p*log(x*e + d) - 3*log(x*e + d)))/(b*d*p - a*p*e + b*d - a*e)","B",0
2158,1,1805,0,0.291398," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} p^{3} x^{5} e^{3} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d p^{3} x^{4} e^{2} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{2} p^{3} x^{3} e + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{3} p^{3} x^{2} + 8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} p^{3} x^{4} e^{3} + 18 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} p^{2} x^{5} e^{3} + 24 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d p^{3} x^{3} e^{2} + 60 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d p^{2} x^{4} e^{2} + 24 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{2} p^{3} x^{2} e + 66 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{2} p^{2} x^{3} e + 8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{3} p^{3} x + 24 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{3} p^{2} x^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} p^{3} x^{3} e^{3} + 30 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} p^{2} x^{4} e^{3} + 26 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} p x^{5} e^{3} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d p^{3} x^{2} e^{2} + 108 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d p^{2} x^{3} e^{2} + 93 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d p x^{4} e^{2} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d^{2} p^{3} x e + 126 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{2} p^{2} x^{2} e + 114 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{2} p x^{3} e + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d^{3} p^{3} + 48 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{3} p^{2} x + 47 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{3} p x^{2} + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} p^{2} x^{3} e^{3} + 37 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} p x^{4} e^{3} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} x^{5} e^{3} + 36 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d p^{2} x^{2} e^{2} + 144 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d p x^{3} e^{2} + 45 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d x^{4} e^{2} + 54 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d^{2} p^{2} x e + 201 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{2} p x^{2} e + 60 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{2} x^{3} e + 24 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d^{3} p^{2} + 94 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{3} p x + 30 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{5} d^{3} x^{2} - 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b^{2} p^{2} x^{2} e^{3} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} p x^{3} e^{3} + 15 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} x^{4} e^{3} - 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b^{2} d p^{2} x e^{2} + 15 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d p x^{2} e^{2} + 60 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d x^{3} e^{2} - 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b^{2} d^{2} p^{2} e + 60 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d^{2} p x e + 90 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{2} x^{2} e + 47 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d^{3} p + 60 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{4} d^{3} x - 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b^{2} p x^{2} e^{3} - 30 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b^{2} d p x e^{2} - 27 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b^{2} d^{2} p e + 30 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{3} d^{3} + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{4} b p x e^{3} + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{4} b d p e^{2} - 30 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b^{2} d^{2} e + 15 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{4} b d e^{2} - 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{5} e^{3}}{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*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*p^3*x^5*e^3 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d*p^3*x^4*e^2 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^2*p^3*x^3*e + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^3*p^3*x^2 + 8*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*p^3*x^4*e^3 + 18*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*p^2*x^5*e^3 + 24*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d*p^3*x^3*e^2 + 60*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d*p^2*x^4*e^2 + 24*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^2*p^3*x^2*e + 66*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^2*p^2*x^3*e + 8*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^3*p^3*x + 24*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^3*p^2*x^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*p^3*x^3*e^3 + 30*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*p^2*x^4*e^3 + 26*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*p*x^5*e^3 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d*p^3*x^2*e^2 + 108*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d*p^2*x^3*e^2 + 93*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d*p*x^4*e^2 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d^2*p^3*x*e + 126*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^2*p^2*x^2*e + 114*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^2*p*x^3*e + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d^3*p^3 + 48*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^3*p^2*x + 47*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^3*p*x^2 + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*p^2*x^3*e^3 + 37*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*p*x^4*e^3 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*x^5*e^3 + 36*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d*p^2*x^2*e^2 + 144*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d*p*x^3*e^2 + 45*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d*x^4*e^2 + 54*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d^2*p^2*x*e + 201*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^2*p*x^2*e + 60*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^2*x^3*e + 24*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d^3*p^2 + 94*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^3*p*x + 30*(b^2*x^2 + 2*a*b*x + a^2)^p*b^5*d^3*x^2 - 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b^2*p^2*x^2*e^3 + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*p*x^3*e^3 + 15*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*x^4*e^3 - 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b^2*d*p^2*x*e^2 + 15*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d*p*x^2*e^2 + 60*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d*x^3*e^2 - 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b^2*d^2*p^2*e + 60*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d^2*p*x*e + 90*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^2*x^2*e + 47*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d^3*p + 60*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^4*d^3*x - 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b^2*p*x^2*e^3 - 30*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b^2*d*p*x*e^2 - 27*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b^2*d^2*p*e + 30*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^3*d^3 + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^4*b*p*x*e^3 + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^4*b*d*p*e^2 - 30*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b^2*d^2*e + 15*(b^2*x^2 + 2*a*b*x + a^2)^p*a^4*b*d*e^2 - 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a^5*e^3)/(4*b^4*p^4 + 28*b^4*p^3 + 71*b^4*p^2 + 77*b^4*p + 30*b^4)","B",0
2159,1,903,0,0.320017," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} p^{2} x^{4} e^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d p^{2} x^{3} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{2} p^{2} x^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} p^{2} x^{3} e^{2} + 5 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} p x^{4} e^{2} + 8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d p^{2} x^{2} e + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d p x^{3} e + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{2} p^{2} x + 7 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{2} p x^{2} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} p^{2} x^{2} e^{2} + 8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} p x^{3} e^{2} + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} x^{4} e^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d p^{2} x e + 22 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d p x^{2} e + 8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d x^{3} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d^{2} p^{2} + 14 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{2} p x + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{2} x^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} p x^{2} e^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} x^{3} e^{2} + 8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d p x e + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d x^{2} e + 7 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d^{2} p + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{2} x - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b p x e^{2} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b d p e + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d^{2} - 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b d e + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{4} e^{2}}{2 \, {\left(2 \, b^{3} p^{3} + 9 \, b^{3} p^{2} + 13 \, b^{3} p + 6 \, b^{3}\right)}}"," ",0,"1/2*(2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*p^2*x^4*e^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d*p^2*x^3*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^2*p^2*x^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*p^2*x^3*e^2 + 5*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*p*x^4*e^2 + 8*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d*p^2*x^2*e + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d*p*x^3*e + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^2*p^2*x + 7*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^2*p*x^2 + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*p^2*x^2*e^2 + 8*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*p*x^3*e^2 + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*x^4*e^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d*p^2*x*e + 22*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d*p*x^2*e + 8*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d*x^3*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d^2*p^2 + 14*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^2*p*x + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^2*x^2 + (b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*p*x^2*e^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*x^3*e^2 + 8*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d*p*x*e + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d*x^2*e + 7*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d^2*p + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^2*x - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b*p*x*e^2 - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b*d*p*e + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d^2 - 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b*d*e + (b^2*x^2 + 2*a*b*x + a^2)^p*a^4*e^2)/(2*b^3*p^3 + 9*b^3*p^2 + 13*b^3*p + 6*b^3)","B",0
2160,1,353,0,0.221607," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} p x^{3} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d p x^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} p x^{2} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} x^{3} e + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} d p x + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d x^{2} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b p x e + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} x^{2} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b d p + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} d x + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b d - {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} e}{2 \, {\left(2 \, b^{2} p^{2} + 5 \, b^{2} p + 3 \, b^{2}\right)}}"," ",0,"1/2*(2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*p*x^3*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d*p*x^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*p*x^2*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*x^3*e + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*d*p*x + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d*x^2 + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b*p*x*e + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*x^2*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b*d*p + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*d*x + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b*d - (b^2*x^2 + 2*a*b*x + a^2)^p*a^3*e)/(2*b^2*p^2 + 5*b^2*p + 3*b^2)","B",0
2161,1,30,0,0.155068," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p + 1}}{2 \, b {\left(p + 1\right)}}"," ",0,"1/2*(b^2*x^2 + 2*a*b*x + a^2)^(p + 1)/(b*(p + 1))","A",0
2162,0,0,0,0.000000," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((b*x + a)*(b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d), x)","F",0
2163,1,695,0,0.276676," ","integrate((B*x+A)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{{\left(b c x + a c\right)}^{m} B b^{8} m x^{8} + 7 \, {\left(b c x + a c\right)}^{m} B a b^{7} m x^{7} + {\left(b c x + a c\right)}^{m} A b^{8} m x^{7} + 7 \, {\left(b c x + a c\right)}^{m} B b^{8} x^{8} + 21 \, {\left(b c x + a c\right)}^{m} B a^{2} b^{6} m x^{6} + 7 \, {\left(b c x + a c\right)}^{m} A a b^{7} m x^{6} + 48 \, {\left(b c x + a c\right)}^{m} B a b^{7} x^{7} + 8 \, {\left(b c x + a c\right)}^{m} A b^{8} x^{7} + 35 \, {\left(b c x + a c\right)}^{m} B a^{3} b^{5} m x^{5} + 21 \, {\left(b c x + a c\right)}^{m} A a^{2} b^{6} m x^{5} + 140 \, {\left(b c x + a c\right)}^{m} B a^{2} b^{6} x^{6} + 56 \, {\left(b c x + a c\right)}^{m} A a b^{7} x^{6} + 35 \, {\left(b c x + a c\right)}^{m} B a^{4} b^{4} m x^{4} + 35 \, {\left(b c x + a c\right)}^{m} A a^{3} b^{5} m x^{4} + 224 \, {\left(b c x + a c\right)}^{m} B a^{3} b^{5} x^{5} + 168 \, {\left(b c x + a c\right)}^{m} A a^{2} b^{6} x^{5} + 21 \, {\left(b c x + a c\right)}^{m} B a^{5} b^{3} m x^{3} + 35 \, {\left(b c x + a c\right)}^{m} A a^{4} b^{4} m x^{3} + 210 \, {\left(b c x + a c\right)}^{m} B a^{4} b^{4} x^{4} + 280 \, {\left(b c x + a c\right)}^{m} A a^{3} b^{5} x^{4} + 7 \, {\left(b c x + a c\right)}^{m} B a^{6} b^{2} m x^{2} + 21 \, {\left(b c x + a c\right)}^{m} A a^{5} b^{3} m x^{2} + 112 \, {\left(b c x + a c\right)}^{m} B a^{5} b^{3} x^{3} + 280 \, {\left(b c x + a c\right)}^{m} A a^{4} b^{4} x^{3} + {\left(b c x + a c\right)}^{m} B a^{7} b m x + 7 \, {\left(b c x + a c\right)}^{m} A a^{6} b^{2} m x + 28 \, {\left(b c x + a c\right)}^{m} B a^{6} b^{2} x^{2} + 168 \, {\left(b c x + a c\right)}^{m} A a^{5} b^{3} x^{2} + {\left(b c x + a c\right)}^{m} A a^{7} b m + 56 \, {\left(b c x + a c\right)}^{m} A a^{6} b^{2} x - {\left(b c x + a c\right)}^{m} B a^{8} + 8 \, {\left(b c x + a c\right)}^{m} A a^{7} b}{b^{2} m^{2} + 15 \, b^{2} m + 56 \, b^{2}}"," ",0,"((b*c*x + a*c)^m*B*b^8*m*x^8 + 7*(b*c*x + a*c)^m*B*a*b^7*m*x^7 + (b*c*x + a*c)^m*A*b^8*m*x^7 + 7*(b*c*x + a*c)^m*B*b^8*x^8 + 21*(b*c*x + a*c)^m*B*a^2*b^6*m*x^6 + 7*(b*c*x + a*c)^m*A*a*b^7*m*x^6 + 48*(b*c*x + a*c)^m*B*a*b^7*x^7 + 8*(b*c*x + a*c)^m*A*b^8*x^7 + 35*(b*c*x + a*c)^m*B*a^3*b^5*m*x^5 + 21*(b*c*x + a*c)^m*A*a^2*b^6*m*x^5 + 140*(b*c*x + a*c)^m*B*a^2*b^6*x^6 + 56*(b*c*x + a*c)^m*A*a*b^7*x^6 + 35*(b*c*x + a*c)^m*B*a^4*b^4*m*x^4 + 35*(b*c*x + a*c)^m*A*a^3*b^5*m*x^4 + 224*(b*c*x + a*c)^m*B*a^3*b^5*x^5 + 168*(b*c*x + a*c)^m*A*a^2*b^6*x^5 + 21*(b*c*x + a*c)^m*B*a^5*b^3*m*x^3 + 35*(b*c*x + a*c)^m*A*a^4*b^4*m*x^3 + 210*(b*c*x + a*c)^m*B*a^4*b^4*x^4 + 280*(b*c*x + a*c)^m*A*a^3*b^5*x^4 + 7*(b*c*x + a*c)^m*B*a^6*b^2*m*x^2 + 21*(b*c*x + a*c)^m*A*a^5*b^3*m*x^2 + 112*(b*c*x + a*c)^m*B*a^5*b^3*x^3 + 280*(b*c*x + a*c)^m*A*a^4*b^4*x^3 + (b*c*x + a*c)^m*B*a^7*b*m*x + 7*(b*c*x + a*c)^m*A*a^6*b^2*m*x + 28*(b*c*x + a*c)^m*B*a^6*b^2*x^2 + 168*(b*c*x + a*c)^m*A*a^5*b^3*x^2 + (b*c*x + a*c)^m*A*a^7*b*m + 56*(b*c*x + a*c)^m*A*a^6*b^2*x - (b*c*x + a*c)^m*B*a^8 + 8*(b*c*x + a*c)^m*A*a^7*b)/(b^2*m^2 + 15*b^2*m + 56*b^2)","B",0
2164,0,0,0,0.000000," ","integrate((B*x+A)*(b*c*x+a*c)^m/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(b c x + a c\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{3}}\,{d x}"," ",0,"integrate((B*x + A)*(b*c*x + a*c)^m/(b^2*x^2 + 2*a*b*x + a^2)^3, x)","F",0
2165,1,545,0,0.270385," ","integrate((B*x+A)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(b c x + a c\right)}^{m} B b^{5} m x^{5} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(b c x + a c\right)}^{m} B a b^{4} m x^{4} \mathrm{sgn}\left(b x + a\right) + {\left(b c x + a c\right)}^{m} A b^{5} m x^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(b c x + a c\right)}^{m} B b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(b c x + a c\right)}^{m} B a^{2} b^{3} m x^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(b c x + a c\right)}^{m} A a b^{4} m x^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(b c x + a c\right)}^{m} B a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(b c x + a c\right)}^{m} A b^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(b c x + a c\right)}^{m} B a^{3} b^{2} m x^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(b c x + a c\right)}^{m} A a^{2} b^{3} m x^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(b c x + a c\right)}^{m} B a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(b c x + a c\right)}^{m} A a b^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + {\left(b c x + a c\right)}^{m} B a^{4} b m x \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(b c x + a c\right)}^{m} A a^{3} b^{2} m x \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(b c x + a c\right)}^{m} B a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(b c x + a c\right)}^{m} A a^{2} b^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + {\left(b c x + a c\right)}^{m} A a^{4} b m \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(b c x + a c\right)}^{m} A a^{3} b^{2} x \mathrm{sgn}\left(b x + a\right) - {\left(b c x + a c\right)}^{m} B a^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(b c x + a c\right)}^{m} A a^{4} b \mathrm{sgn}\left(b x + a\right)}{b^{2} m^{2} + 9 \, b^{2} m + 20 \, b^{2}}"," ",0,"((b*c*x + a*c)^m*B*b^5*m*x^5*sgn(b*x + a) + 4*(b*c*x + a*c)^m*B*a*b^4*m*x^4*sgn(b*x + a) + (b*c*x + a*c)^m*A*b^5*m*x^4*sgn(b*x + a) + 4*(b*c*x + a*c)^m*B*b^5*x^5*sgn(b*x + a) + 6*(b*c*x + a*c)^m*B*a^2*b^3*m*x^3*sgn(b*x + a) + 4*(b*c*x + a*c)^m*A*a*b^4*m*x^3*sgn(b*x + a) + 15*(b*c*x + a*c)^m*B*a*b^4*x^4*sgn(b*x + a) + 5*(b*c*x + a*c)^m*A*b^5*x^4*sgn(b*x + a) + 4*(b*c*x + a*c)^m*B*a^3*b^2*m*x^2*sgn(b*x + a) + 6*(b*c*x + a*c)^m*A*a^2*b^3*m*x^2*sgn(b*x + a) + 20*(b*c*x + a*c)^m*B*a^2*b^3*x^3*sgn(b*x + a) + 20*(b*c*x + a*c)^m*A*a*b^4*x^3*sgn(b*x + a) + (b*c*x + a*c)^m*B*a^4*b*m*x*sgn(b*x + a) + 4*(b*c*x + a*c)^m*A*a^3*b^2*m*x*sgn(b*x + a) + 10*(b*c*x + a*c)^m*B*a^3*b^2*x^2*sgn(b*x + a) + 30*(b*c*x + a*c)^m*A*a^2*b^3*x^2*sgn(b*x + a) + (b*c*x + a*c)^m*A*a^4*b*m*sgn(b*x + a) + 20*(b*c*x + a*c)^m*A*a^3*b^2*x*sgn(b*x + a) - (b*c*x + a*c)^m*B*a^5*sgn(b*x + a) + 5*(b*c*x + a*c)^m*A*a^4*b*sgn(b*x + a))/(b^2*m^2 + 9*b^2*m + 20*b^2)","B",0
2166,0,0,0,0.000000," ","integrate((B*x+A)*(b*c*x+a*c)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(b c x + a c\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(b*c*x + a*c)^m/(b^2*x^2 + 2*a*b*x + a^2)^(3/2), x)","F",0
2167,1,404,0,0.211291," ","integrate((b*c*x+a*c)^m*(g*x+f)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{2 \, p} b^{2} g m x^{2} e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + 2 \, {\left(b x + a\right)}^{2 \, p} b^{2} g p x^{2} e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} b^{2} f m x e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} a b g m x e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + 2 \, {\left(b x + a\right)}^{2 \, p} b^{2} f p x e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + 2 \, {\left(b x + a\right)}^{2 \, p} a b g p x e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} b^{2} g x^{2} e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} a b f m e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + 2 \, {\left(b x + a\right)}^{2 \, p} a b f p e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + 2 \, {\left(b x + a\right)}^{2 \, p} b^{2} f x e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + 2 \, {\left(b x + a\right)}^{2 \, p} a b f e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} - {\left(b x + a\right)}^{2 \, p} a^{2} g e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)}}{b^{2} m^{2} + 4 \, b^{2} m p + 4 \, b^{2} p^{2} + 3 \, b^{2} m + 6 \, b^{2} p + 2 \, b^{2}}"," ",0,"((b*x + a)^(2*p)*b^2*g*m*x^2*e^(m*log(b*x + a) + m*log(c)) + 2*(b*x + a)^(2*p)*b^2*g*p*x^2*e^(m*log(b*x + a) + m*log(c)) + (b*x + a)^(2*p)*b^2*f*m*x*e^(m*log(b*x + a) + m*log(c)) + (b*x + a)^(2*p)*a*b*g*m*x*e^(m*log(b*x + a) + m*log(c)) + 2*(b*x + a)^(2*p)*b^2*f*p*x*e^(m*log(b*x + a) + m*log(c)) + 2*(b*x + a)^(2*p)*a*b*g*p*x*e^(m*log(b*x + a) + m*log(c)) + (b*x + a)^(2*p)*b^2*g*x^2*e^(m*log(b*x + a) + m*log(c)) + (b*x + a)^(2*p)*a*b*f*m*e^(m*log(b*x + a) + m*log(c)) + 2*(b*x + a)^(2*p)*a*b*f*p*e^(m*log(b*x + a) + m*log(c)) + 2*(b*x + a)^(2*p)*b^2*f*x*e^(m*log(b*x + a) + m*log(c)) + 2*(b*x + a)^(2*p)*a*b*f*e^(m*log(b*x + a) + m*log(c)) - (b*x + a)^(2*p)*a^2*g*e^(m*log(b*x + a) + m*log(c)))/(b^2*m^2 + 4*b^2*m*p + 4*b^2*p^2 + 3*b^2*m + 6*b^2*p + 2*b^2)","B",0
2168,1,221,0,0.258659," ","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=""giac"")","-\frac{2 \, {\left(b x + a\right)}^{2 \, p} b^{2} g x^{2} e^{\left(-2 \, p \log\left(b x + a\right) - 2 \, p \log\left(c\right) - 3 \, \log\left(b x + a\right) - 3 \, \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} b^{2} f x e^{\left(-2 \, p \log\left(b x + a\right) - 2 \, p \log\left(c\right) - 3 \, \log\left(b x + a\right) - 3 \, \log\left(c\right)\right)} + 3 \, {\left(b x + a\right)}^{2 \, p} a b g x e^{\left(-2 \, p \log\left(b x + a\right) - 2 \, p \log\left(c\right) - 3 \, \log\left(b x + a\right) - 3 \, \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} a b f e^{\left(-2 \, p \log\left(b x + a\right) - 2 \, p \log\left(c\right) - 3 \, \log\left(b x + a\right) - 3 \, \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} a^{2} g e^{\left(-2 \, p \log\left(b x + a\right) - 2 \, p \log\left(c\right) - 3 \, \log\left(b x + a\right) - 3 \, \log\left(c\right)\right)}}{2 \, b^{2}}"," ",0,"-1/2*(2*(b*x + a)^(2*p)*b^2*g*x^2*e^(-2*p*log(b*x + a) - 2*p*log(c) - 3*log(b*x + a) - 3*log(c)) + (b*x + a)^(2*p)*b^2*f*x*e^(-2*p*log(b*x + a) - 2*p*log(c) - 3*log(b*x + a) - 3*log(c)) + 3*(b*x + a)^(2*p)*a*b*g*x*e^(-2*p*log(b*x + a) - 2*p*log(c) - 3*log(b*x + a) - 3*log(c)) + (b*x + a)^(2*p)*a*b*f*e^(-2*p*log(b*x + a) - 2*p*log(c) - 3*log(b*x + a) - 3*log(c)) + (b*x + a)^(2*p)*a^2*g*e^(-2*p*log(b*x + a) - 2*p*log(c) - 3*log(b*x + a) - 3*log(c)))/b^2","B",0
2169,1,100,0,0.194111," ","integrate((b*x+a)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{2 \, p} b^{2} x^{2} e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + 2 \, {\left(b x + a\right)}^{2 \, p} a b x e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)} + {\left(b x + a\right)}^{2 \, p} a^{2} e^{\left(m \log\left(b x + a\right) + m \log\left(c\right)\right)}}{b m + 2 \, b p + 2 \, b}"," ",0,"((b*x + a)^(2*p)*b^2*x^2*e^(m*log(b*x + a) + m*log(c)) + 2*(b*x + a)^(2*p)*a*b*x*e^(m*log(b*x + a) + m*log(c)) + (b*x + a)^(2*p)*a^2*e^(m*log(b*x + a) + m*log(c)))/(b*m + 2*b*p + 2*b)","B",0
2170,1,183,0,0.214460," ","integrate((b*x+a)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{{\left(b c x + a c\right)}^{m} b^{8} x^{8} + 8 \, {\left(b c x + a c\right)}^{m} a b^{7} x^{7} + 28 \, {\left(b c x + a c\right)}^{m} a^{2} b^{6} x^{6} + 56 \, {\left(b c x + a c\right)}^{m} a^{3} b^{5} x^{5} + 70 \, {\left(b c x + a c\right)}^{m} a^{4} b^{4} x^{4} + 56 \, {\left(b c x + a c\right)}^{m} a^{5} b^{3} x^{3} + 28 \, {\left(b c x + a c\right)}^{m} a^{6} b^{2} x^{2} + 8 \, {\left(b c x + a c\right)}^{m} a^{7} b x + {\left(b c x + a c\right)}^{m} a^{8}}{b m + 8 \, b}"," ",0,"((b*c*x + a*c)^m*b^8*x^8 + 8*(b*c*x + a*c)^m*a*b^7*x^7 + 28*(b*c*x + a*c)^m*a^2*b^6*x^6 + 56*(b*c*x + a*c)^m*a^3*b^5*x^5 + 70*(b*c*x + a*c)^m*a^4*b^4*x^4 + 56*(b*c*x + a*c)^m*a^5*b^3*x^3 + 28*(b*c*x + a*c)^m*a^6*b^2*x^2 + 8*(b*c*x + a*c)^m*a^7*b*x + (b*c*x + a*c)^m*a^8)/(b*m + 8*b)","B",0
2171,0,0,0,0.000000," ","integrate((b*x+a)*(b*c*x+a*c)^m/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)} {\left(b c x + a c\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{3}}\,{d x}"," ",0,"integrate((b*x + a)*(b*c*x + a*c)^m/(b^2*x^2 + 2*a*b*x + a^2)^3, x)","F",0
2172,1,699,0,0.467032," ","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=""giac"")","\frac{1}{7680} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, g x e^{3} + \frac{{\left(36 \, c^{5} d g e^{10} + 12 \, c^{5} f e^{11} + b c^{4} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x + \frac{{\left(340 \, c^{5} d^{2} g e^{9} + 360 \, c^{5} d f e^{10} + 56 \, b c^{4} d g e^{10} + 12 \, b c^{4} f e^{11} - 9 \, b^{2} c^{3} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x + \frac{{\left(128 \, c^{5} d^{3} g e^{8} + 896 \, c^{5} d^{2} f e^{9} + 380 \, b c^{4} d^{2} g e^{9} + 184 \, b c^{4} d f e^{10} - 152 \, b^{2} c^{3} d g e^{10} - 28 \, b^{2} c^{3} f e^{11} + 21 \, b^{3} c^{2} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x - \frac{{\left(1680 \, c^{5} d^{4} g e^{7} - 480 \, c^{5} d^{3} f e^{8} - 3632 \, b c^{4} d^{3} g e^{8} - 2864 \, b c^{4} d^{2} f e^{9} + 2680 \, b^{2} c^{3} d^{2} g e^{9} + 1064 \, b^{2} c^{3} d f e^{10} - 868 \, b^{3} c^{2} d g e^{10} - 140 \, b^{3} c^{2} f e^{11} + 105 \, b^{4} c g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x - \frac{{\left(5632 \, c^{5} d^{5} g e^{6} + 8704 \, c^{5} d^{4} f e^{7} - 16752 \, b c^{4} d^{4} g e^{7} - 17888 \, b c^{4} d^{3} f e^{8} + 19408 \, b^{2} c^{3} d^{3} g e^{8} + 11984 \, b^{2} c^{3} d^{2} f e^{9} - 10808 \, b^{3} c^{2} d^{2} g e^{9} - 3640 \, b^{3} c^{2} d f e^{10} + 2940 \, b^{4} c d g e^{10} + 420 \, b^{4} c f e^{11} - 315 \, b^{5} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} + \frac{7 \, {\left(64 \, c^{6} d^{6} g + 128 \, c^{6} d^{5} f e - 256 \, b c^{5} d^{5} g e - 320 \, b c^{5} d^{4} f e^{2} + 400 \, b^{2} c^{4} d^{4} g e^{2} + 320 \, b^{2} c^{4} d^{3} f e^{3} - 320 \, b^{3} c^{3} d^{3} g e^{3} - 160 \, b^{3} c^{3} d^{2} f e^{4} + 140 \, b^{4} c^{2} d^{2} g e^{4} + 40 \, b^{4} c^{2} d f e^{5} - 32 \, b^{5} c d g e^{5} - 4 \, b^{5} c f e^{6} + 3 \, b^{6} g e^{6}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{1024 \, c^{6}}"," ",0,"1/7680*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(2*(8*(10*g*x*e^3 + (36*c^5*d*g*e^10 + 12*c^5*f*e^11 + b*c^4*g*e^11)*e^(-8)/c^5)*x + (340*c^5*d^2*g*e^9 + 360*c^5*d*f*e^10 + 56*b*c^4*d*g*e^10 + 12*b*c^4*f*e^11 - 9*b^2*c^3*g*e^11)*e^(-8)/c^5)*x + (128*c^5*d^3*g*e^8 + 896*c^5*d^2*f*e^9 + 380*b*c^4*d^2*g*e^9 + 184*b*c^4*d*f*e^10 - 152*b^2*c^3*d*g*e^10 - 28*b^2*c^3*f*e^11 + 21*b^3*c^2*g*e^11)*e^(-8)/c^5)*x - (1680*c^5*d^4*g*e^7 - 480*c^5*d^3*f*e^8 - 3632*b*c^4*d^3*g*e^8 - 2864*b*c^4*d^2*f*e^9 + 2680*b^2*c^3*d^2*g*e^9 + 1064*b^2*c^3*d*f*e^10 - 868*b^3*c^2*d*g*e^10 - 140*b^3*c^2*f*e^11 + 105*b^4*c*g*e^11)*e^(-8)/c^5)*x - (5632*c^5*d^5*g*e^6 + 8704*c^5*d^4*f*e^7 - 16752*b*c^4*d^4*g*e^7 - 17888*b*c^4*d^3*f*e^8 + 19408*b^2*c^3*d^3*g*e^8 + 11984*b^2*c^3*d^2*f*e^9 - 10808*b^3*c^2*d^2*g*e^9 - 3640*b^3*c^2*d*f*e^10 + 2940*b^4*c*d*g*e^10 + 420*b^4*c*f*e^11 - 315*b^5*g*e^11)*e^(-8)/c^5) + 7/1024*(64*c^6*d^6*g + 128*c^6*d^5*f*e - 256*b*c^5*d^5*g*e - 320*b*c^5*d^4*f*e^2 + 400*b^2*c^4*d^4*g*e^2 + 320*b^2*c^4*d^3*f*e^3 - 320*b^3*c^3*d^3*g*e^3 - 160*b^3*c^3*d^2*f*e^4 + 140*b^4*c^2*d^2*g*e^4 + 40*b^4*c^2*d*f*e^5 - 32*b^5*c*d*g*e^5 - 4*b^5*c*f*e^6 + 3*b^6*g*e^6)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^6","A",0
2173,1,526,0,0.353502," ","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=""giac"")","\frac{1}{1920} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, g x e^{2} + \frac{{\left(20 \, c^{4} d g e^{7} + 10 \, c^{4} f e^{8} + b c^{3} g e^{8}\right)} e^{\left(-6\right)}}{c^{4}}\right)} x + \frac{{\left(64 \, c^{4} d^{2} g e^{6} + 160 \, c^{4} d f e^{7} + 36 \, b c^{3} d g e^{7} + 10 \, b c^{3} f e^{8} - 7 \, b^{2} c^{2} g e^{8}\right)} e^{\left(-6\right)}}{c^{4}}\right)} x - \frac{{\left(240 \, c^{4} d^{3} g e^{5} - 360 \, c^{4} d^{2} f e^{6} - 436 \, b c^{3} d^{2} g e^{6} - 280 \, b c^{3} d f e^{7} + 216 \, b^{2} c^{2} d g e^{7} + 50 \, b^{2} c^{2} f e^{8} - 35 \, b^{3} c g e^{8}\right)} e^{\left(-6\right)}}{c^{4}}\right)} x - \frac{{\left(896 \, c^{4} d^{4} g e^{4} + 1280 \, c^{4} d^{3} f e^{5} - 2192 \, b c^{3} d^{3} g e^{5} - 2280 \, b c^{3} d^{2} f e^{6} + 1996 \, b^{2} c^{2} d^{2} g e^{6} + 1000 \, b^{2} c^{2} d f e^{7} - 760 \, b^{3} c d g e^{7} - 150 \, b^{3} c f e^{8} + 105 \, b^{4} g e^{8}\right)} e^{\left(-6\right)}}{c^{4}}\right)} + \frac{{\left(64 \, c^{5} d^{5} g + 160 \, c^{5} d^{4} f e - 240 \, b c^{4} d^{4} g e - 320 \, b c^{4} d^{3} f e^{2} + 320 \, b^{2} c^{3} d^{3} g e^{2} + 240 \, b^{2} c^{3} d^{2} f e^{3} - 200 \, b^{3} c^{2} d^{2} g e^{3} - 80 \, b^{3} c^{2} d f e^{4} + 60 \, b^{4} c d g e^{4} + 10 \, b^{4} c f e^{5} - 7 \, b^{5} g e^{5}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{256 \, c^{5}}"," ",0,"1/1920*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(6*(8*g*x*e^2 + (20*c^4*d*g*e^7 + 10*c^4*f*e^8 + b*c^3*g*e^8)*e^(-6)/c^4)*x + (64*c^4*d^2*g*e^6 + 160*c^4*d*f*e^7 + 36*b*c^3*d*g*e^7 + 10*b*c^3*f*e^8 - 7*b^2*c^2*g*e^8)*e^(-6)/c^4)*x - (240*c^4*d^3*g*e^5 - 360*c^4*d^2*f*e^6 - 436*b*c^3*d^2*g*e^6 - 280*b*c^3*d*f*e^7 + 216*b^2*c^2*d*g*e^7 + 50*b^2*c^2*f*e^8 - 35*b^3*c*g*e^8)*e^(-6)/c^4)*x - (896*c^4*d^4*g*e^4 + 1280*c^4*d^3*f*e^5 - 2192*b*c^3*d^3*g*e^5 - 2280*b*c^3*d^2*f*e^6 + 1996*b^2*c^2*d^2*g*e^6 + 1000*b^2*c^2*d*f*e^7 - 760*b^3*c*d*g*e^7 - 150*b^3*c*f*e^8 + 105*b^4*g*e^8)*e^(-6)/c^4) + 1/256*(64*c^5*d^5*g + 160*c^5*d^4*f*e - 240*b*c^4*d^4*g*e - 320*b*c^4*d^3*f*e^2 + 320*b^2*c^3*d^3*g*e^2 + 240*b^2*c^3*d^2*f*e^3 - 200*b^3*c^2*d^2*g*e^3 - 80*b^3*c^2*d*f*e^4 + 60*b^4*c*d*g*e^4 + 10*b^4*c*f*e^5 - 7*b^5*g*e^5)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^5","A",0
2174,1,381,0,0.386104," ","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=""giac"")","\frac{1}{192} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(6 \, g x e + \frac{{\left(8 \, c^{3} d g e^{4} + 8 \, c^{3} f e^{5} + b c^{2} g e^{5}\right)} e^{\left(-4\right)}}{c^{3}}\right)} x - \frac{{\left(12 \, c^{3} d^{2} g e^{3} - 48 \, c^{3} d f e^{4} - 20 \, b c^{2} d g e^{4} - 8 \, b c^{2} f e^{5} + 5 \, b^{2} c g e^{5}\right)} e^{\left(-4\right)}}{c^{3}}\right)} x - \frac{{\left(64 \, c^{3} d^{3} g e^{2} + 64 \, c^{3} d^{2} f e^{3} - 116 \, b c^{2} d^{2} g e^{3} - 112 \, b c^{2} d f e^{4} + 76 \, b^{2} c d g e^{4} + 24 \, b^{2} c f e^{5} - 15 \, b^{3} g e^{5}\right)} e^{\left(-4\right)}}{c^{3}}\right)} + \frac{{\left(16 \, c^{4} d^{4} g + 64 \, c^{4} d^{3} f e - 64 \, b c^{3} d^{3} g e - 96 \, b c^{3} d^{2} f e^{2} + 72 \, b^{2} c^{2} d^{2} g e^{2} + 48 \, b^{2} c^{2} d f e^{3} - 32 \, b^{3} c d g e^{3} - 8 \, b^{3} c f e^{4} + 5 \, b^{4} g e^{4}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{128 \, c^{4}}"," ",0,"1/192*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(6*g*x*e + (8*c^3*d*g*e^4 + 8*c^3*f*e^5 + b*c^2*g*e^5)*e^(-4)/c^3)*x - (12*c^3*d^2*g*e^3 - 48*c^3*d*f*e^4 - 20*b*c^2*d*g*e^4 - 8*b*c^2*f*e^5 + 5*b^2*c*g*e^5)*e^(-4)/c^3)*x - (64*c^3*d^3*g*e^2 + 64*c^3*d^2*f*e^3 - 116*b*c^2*d^2*g*e^3 - 112*b*c^2*d*f*e^4 + 76*b^2*c*d*g*e^4 + 24*b^2*c*f*e^5 - 15*b^3*g*e^5)*e^(-4)/c^3) + 1/128*(16*c^4*d^4*g + 64*c^4*d^3*f*e - 64*b*c^3*d^3*g*e - 96*b*c^3*d^2*f*e^2 + 72*b^2*c^2*d^2*g*e^2 + 48*b^2*c^2*d*f*e^3 - 32*b^3*c*d*g*e^3 - 8*b^3*c*f*e^4 + 5*b^4*g*e^4)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^4","A",0
2175,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2176,-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)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2177,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-c*sqrt(-c*exp(2))*g/2/c/exp(2)/exp(1)*ln(abs(2*c*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)-sqrt(-c*exp(2))*b))+(4*exp(2)*g*exp(1)^4*b^2*d-16*c*exp(2)*g*exp(1)^3*b*d^2-3*exp(2)^2*g*exp(1)^2*b^2*d+12*c^2*exp(2)*g*exp(1)^2*d^3+12*c*exp(2)^2*g*exp(1)*b*d^2-8*c^2*exp(2)^2*g*d^3+4*c*exp(2)*exp(1)^4*b*d*f-exp(2)^2*exp(1)^3*b^2*f-4*c^2*exp(2)*exp(1)^3*d^2*f)/2/(-4*exp(1)^6*b*d+4*c*exp(1)^5*d^2+4*exp(2)*exp(1)^4*b*d-4*c*exp(2)*exp(1)^3*d^2)/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))*atan((-d*sqrt(-c*exp(2))+(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1))/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2)))+(4*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)^5*b^2*d-16*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)^4*b*d^2-5*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)^3*b^2*d+12*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)^3*d^3+20*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)^2*b*d^2-16*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)*d^3+4*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*exp(1)^5*b*d*f+exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*exp(1)^4*b^2*f-4*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*exp(1)^4*d^2*f-8*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*exp(1)^3*b*d*f+8*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*exp(1)^2*d^2*f-8*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^6*b^2*d^2+16*c*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^5*b*d^3+12*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^4*b^2*d^2-8*c^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^4*d^4-8*c*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^3*b*d^3-exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^2*b^2*d^2-4*c^2*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^2*d^4-20*c*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)*b*d^3+24*c^2*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*d^4-8*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)^5*b^2*d*f+12*c*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)^4*b*d^2*f+5*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)^3*b^2*d*f-4*c^2*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)^3*d^3*f-8*c^2*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)*d^3*f+4*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^6*b^3*d^2-28*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^5*b^2*d^3-7*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^4*b^3*d^2+44*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^4*b*d^4+55*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^3*b^2*d^3-20*c^3*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^3*d^5+3*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^2*b^3*d^2-80*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^2*b*d^4-24*c*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)*b^2*d^3+32*c^3*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)*d^5+24*c^2*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*b*d^4-4*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^6*b^2*d^2*f-exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^5*b^3*d*f+8*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^5*b*d^3*f-3*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^4*b^2*d^2*f-4*c^3*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^4*d^4*f+exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^3*b^3*d*f+12*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^3*b*d^3*f+4*c*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^2*b^2*d^2*f-8*c^3*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^2*d^4*f-8*c^2*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)*b*d^3*f-8*sqrt(-c*exp(2))*g*exp(1)^7*b^3*d^3+24*c*sqrt(-c*exp(2))*g*exp(1)^6*b^2*d^4+20*exp(2)*sqrt(-c*exp(2))*g*exp(1)^5*b^3*d^3-24*c^2*sqrt(-c*exp(2))*g*exp(1)^5*b*d^5-52*c*exp(2)*sqrt(-c*exp(2))*g*exp(1)^4*b^2*d^4+8*c^3*sqrt(-c*exp(2))*g*exp(1)^4*d^6-17*exp(2)^2*sqrt(-c*exp(2))*g*exp(1)^3*b^3*d^3+44*c^2*exp(2)*sqrt(-c*exp(2))*g*exp(1)^3*b*d^5+33*c*exp(2)^2*sqrt(-c*exp(2))*g*exp(1)^2*b^2*d^4-12*c^3*exp(2)*sqrt(-c*exp(2))*g*exp(1)^2*d^6+5*exp(2)^3*sqrt(-c*exp(2))*g*exp(1)*b^3*d^3-16*c^2*exp(2)^2*sqrt(-c*exp(2))*g*exp(1)*b*d^5-6*c*exp(2)^3*sqrt(-c*exp(2))*g*b^2*d^4+4*c*exp(2)*sqrt(-c*exp(2))*exp(1)^5*b^2*d^3*f+exp(2)^2*sqrt(-c*exp(2))*exp(1)^4*b^3*d^2*f-8*c^2*exp(2)*sqrt(-c*exp(2))*exp(1)^4*b*d^4*f-5*c*exp(2)^2*sqrt(-c*exp(2))*exp(1)^3*b^2*d^3*f+4*c^3*exp(2)*sqrt(-c*exp(2))*exp(1)^3*d^5*f-exp(2)^3*sqrt(-c*exp(2))*exp(1)^2*b^3*d^2*f+4*c^2*exp(2)^2*sqrt(-c*exp(2))*exp(1)^2*b*d^4*f+2*c*exp(2)^3*sqrt(-c*exp(2))*exp(1)*b^2*d^3*f)/(8*exp(1)^6*b*d-8*c*exp(1)^5*d^2-8*exp(2)*exp(1)^4*b*d+8*c*exp(2)*exp(1)^3*d^2)/((sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)-2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*d+exp(1)^2*b*d-c*exp(1)*d^2-exp(2)*b*d)^2)","F(-2)",0
2178,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))*atan((-d*sqrt(-c*exp(2))+(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1))/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))))","F(-2)",0
2179,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{2,[1,0,1,0,3,0]%%%}+%%%{-2,[1,0,1,0,1,1]%%%}+%%%{2,[1,0,1,0,1,0]%%%}+%%%{2,[1,0,0,1,0,1]%%%}+%%%{-2,[0,1,2,0,2,0]%%%}+%%%{2,[0,1,2,0,0,1]%%%}+%%%{-2,[0,1,2,0,0,0]%%%}+%%%{2,[0,1,0,2,0,1]%%%},0,%%%{1,[2,0,2,0,6,0]%%%}+%%%{-2,[2,0,2,0,4,1]%%%}+%%%{-2,[2,0,2,0,4,0]%%%}+%%%{1,[2,0,2,0,2,2]%%%}+%%%{2,[2,0,2,0,2,1]%%%}+%%%{1,[2,0,2,0,2,0]%%%}+%%%{-2,[2,0,1,1,3,1]%%%}+%%%{2,[2,0,1,1,1,2]%%%}+%%%{2,[2,0,1,1,1,1]%%%}+%%%{1,[2,0,0,2,0,2]%%%}+%%%{-2,[1,1,3,0,5,0]%%%}+%%%{4,[1,1,3,0,3,1]%%%}+%%%{4,[1,1,3,0,3,0]%%%}+%%%{-2,[1,1,3,0,1,2]%%%}+%%%{-4,[1,1,3,0,1,1]%%%}+%%%{-2,[1,1,3,0,1,0]%%%}+%%%{2,[1,1,2,1,2,1]%%%}+%%%{-2,[1,1,2,1,0,2]%%%}+%%%{-2,[1,1,2,1,0,1]%%%}+%%%{-2,[1,1,1,2,3,1]%%%}+%%%{2,[1,1,1,2,1,2]%%%}+%%%{2,[1,1,1,2,1,1]%%%}+%%%{2,[1,1,0,3,0,2]%%%}+%%%{1,[0,2,4,0,4,0]%%%}+%%%{-2,[0,2,4,0,2,1]%%%}+%%%{-2,[0,2,4,0,2,0]%%%}+%%%{1,[0,2,4,0,0,2]%%%}+%%%{2,[0,2,4,0,0,1]%%%}+%%%{1,[0,2,4,0,0,0]%%%}+%%%{2,[0,2,2,2,2,1]%%%}+%%%{-2,[0,2,2,2,0,2]%%%}+%%%{-2,[0,2,2,2,0,1]%%%}+%%%{1,[0,2,0,4,0,2]%%%}] at parameters values [-62,52,82,66,20,-30]exp(1)^2*(2*(-(exp(1)*x+d)^-1/exp(1)*(-(exp(1)*x+d)^-1/exp(1)*(-(21*b^3*g*sign((exp(1)*x+d)^-1)*exp(1)^12+3*b^2*c*f*sign((exp(1)*x+d)^-1)*exp(1)^12+12*c^3*d^2*f*sign((exp(1)*x+d)^-1)*exp(1)^10-180*c^3*d^3*g*sign((exp(1)*x+d)^-1)*exp(1)^9-12*b*c^2*d*f*sign((exp(1)*x+d)^-1)*exp(1)^11+264*b*c^2*d^2*g*sign((exp(1)*x+d)^-1)*exp(1)^10-129*b^2*c*d*g*sign((exp(1)*x+d)^-1)*exp(1)^11)/(105*b^3*exp(1)^15-840*c^3*d^3*exp(1)^12+1260*b*c^2*d^2*exp(1)^13-630*b^2*c*d*exp(1)^14)+(exp(1)*x+d)^-1/exp(1)*(-15*b^3*f*sign((exp(1)*x+d)^-1)*exp(1)^14+15*b^3*d*g*sign((exp(1)*x+d)^-1)*exp(1)^13+120*c^3*d^3*f*sign((exp(1)*x+d)^-1)*exp(1)^11-120*c^3*d^4*g*sign((exp(1)*x+d)^-1)*exp(1)^10-180*b*c^2*d^2*f*sign((exp(1)*x+d)^-1)*exp(1)^12+180*b*c^2*d^3*g*sign((exp(1)*x+d)^-1)*exp(1)^11+90*b^2*c*d*f*sign((exp(1)*x+d)^-1)*exp(1)^13-90*b^2*c*d^2*g*sign((exp(1)*x+d)^-1)*exp(1)^12)/(105*b^3*exp(1)^15-840*c^3*d^3*exp(1)^12+1260*b*c^2*d^2*exp(1)^13-630*b^2*c*d*exp(1)^14))-(4*b*c^2*f*sign((exp(1)*x+d)^-1)*exp(1)^10-7*b^2*c*g*sign((exp(1)*x+d)^-1)*exp(1)^10-8*c^3*d*f*sign((exp(1)*x+d)^-1)*exp(1)^9-20*c^3*d^2*g*sign((exp(1)*x+d)^-1)*exp(1)^8+24*b*c^2*d*g*sign((exp(1)*x+d)^-1)*exp(1)^9)/(105*b^3*exp(1)^15-840*c^3*d^3*exp(1)^12+1260*b*c^2*d^2*exp(1)^13-630*b^2*c*d*exp(1)^14))-(8*c^3*f*sign((exp(1)*x+d)^-1)*exp(1)^8-14*b*c^2*g*sign((exp(1)*x+d)^-1)*exp(1)^8+20*c^3*d*g*sign((exp(1)*x+d)^-1)*exp(1)^7)/(105*b^3*exp(1)^15-840*c^3*d^3*exp(1)^12+1260*b*c^2*d^2*exp(1)^13-630*b^2*c*d*exp(1)^14)-C_0*(210*b^2*exp(1)^11+840*c^2*d^2*exp(1)^9-840*b*c*d*exp(1)^10)/(105*b^3*exp(1)^15-840*c^3*d^3*exp(1)^12+1260*b*c^2*d^2*exp(1)^13-630*b^2*c*d*exp(1)^14))*sqrt(-c*exp(2)-b*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^5-b*(exp(1)*x+d)^-1/exp(1)*exp(1)^2*exp(2)+c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^4+b*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^3*exp(2)+2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)-c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^2*exp(2))-2*C_0*ln(abs(-2*((exp(1)*x+d)^-1/exp(1)*sqrt(-b*d*exp(1)^5+c*d^2*exp(1)^4+b*d*exp(1)^3*exp(2)-c*d^2*exp(1)^2*exp(2))+sqrt(-c*exp(2)-b*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^5-b*(exp(1)*x+d)^-1/exp(1)*exp(1)^2*exp(2)+c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^4+b*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^3*exp(2)+2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)-c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^2*exp(2)))*sqrt(-b*d*exp(1)^3+c*d^2*exp(1)^2-c*d^2*exp(2)+b*d*exp(1)*exp(2))+b*exp(1)*exp(2)-2*c*d*exp(2)))/sqrt(-b*d*exp(1)^3+c*d^2*exp(1)^2-c*d^2*exp(2)+b*d*exp(1)*exp(2))/exp(1)-(28*b*c^2*g*sqrt(-c*exp(2))*exp(1)-40*c^3*d*g*sqrt(-c*exp(2))-16*c^3*f*sqrt(-c*exp(2))*exp(1))/(105*b^3*exp(1)^8-630*b^2*c*d*exp(1)^7+1260*b*c^2*d^2*exp(1)^6-840*c^3*d^3*exp(1)^5)*sign((exp(1)*x+d)^-1))","F(-2)",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=""giac"")","\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=""giac"")","\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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2183,1,1138,0,0.641479," ","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=""giac"")","-\frac{1}{573440} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, c g x e^{5} + \frac{{\left(48 \, c^{8} d g e^{16} + 16 \, c^{8} f e^{17} + 17 \, b c^{7} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x + \frac{{\left(140 \, c^{8} d^{2} g e^{15} + 224 \, c^{8} d f e^{16} + 324 \, b c^{7} d g e^{16} + 80 \, b c^{7} f e^{17} + b^{2} c^{6} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x - \frac{{\left(2176 \, c^{8} d^{3} g e^{14} - 1664 \, c^{8} d^{2} f e^{15} - 5932 \, b c^{7} d^{2} g e^{15} - 3936 \, b c^{7} d f e^{16} - 100 \, b^{2} c^{6} d g e^{16} - 16 \, b^{2} c^{6} f e^{17} + 11 \, b^{3} c^{5} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x - \frac{{\left(30800 \, c^{8} d^{4} g e^{13} + 22400 \, c^{8} d^{3} f e^{14} - 37984 \, b c^{7} d^{3} g e^{14} - 60224 \, b c^{7} d^{2} f e^{15} - 3912 \, b^{2} c^{6} d^{2} g e^{15} - 1376 \, b^{2} c^{6} d f e^{16} + 1000 \, b^{3} c^{5} d g e^{16} + 144 \, b^{3} c^{5} f e^{17} - 99 \, b^{4} c^{4} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x - \frac{{\left(22528 \, c^{8} d^{5} g e^{12} + 83968 \, c^{8} d^{4} f e^{13} - 5904 \, b c^{7} d^{4} g e^{13} - 100736 \, b c^{7} d^{3} f e^{14} - 25888 \, b^{2} c^{6} d^{3} g e^{14} - 14784 \, b^{2} c^{6} d^{2} f e^{15} + 11496 \, b^{3} c^{5} d^{2} g e^{15} + 3552 \, b^{3} c^{5} d f e^{16} - 2568 \, b^{4} c^{4} d g e^{16} - 336 \, b^{4} c^{4} f e^{17} + 231 \, b^{5} c^{3} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x + \frac{{\left(60480 \, c^{8} d^{6} g e^{11} - 125440 \, c^{8} d^{5} f e^{12} - 208832 \, b c^{7} d^{5} g e^{12} - 22272 \, b c^{7} d^{4} f e^{13} + 278416 \, b^{2} c^{6} d^{4} g e^{13} + 223744 \, b^{2} c^{6} d^{3} f e^{14} - 188384 \, b^{3} c^{5} d^{3} g e^{14} - 92160 \, b^{3} c^{5} d^{2} f e^{15} + 70668 \, b^{4} c^{4} d^{2} g e^{15} + 19488 \, b^{4} c^{4} d f e^{16} - 14028 \, b^{5} c^{3} d g e^{16} - 1680 \, b^{5} c^{3} f e^{17} + 1155 \, b^{6} c^{2} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x + \frac{{\left(212992 \, c^{8} d^{7} g e^{10} + 376832 \, c^{8} d^{6} f e^{11} - 873408 \, b c^{7} d^{6} g e^{11} - 1255936 \, b c^{7} d^{5} f e^{12} + 1519680 \, b^{2} c^{6} d^{5} g e^{12} + 1558784 \, b^{2} c^{6} d^{4} f e^{13} - 1433392 \, b^{3} c^{5} d^{4} g e^{13} - 964608 \, b^{3} c^{5} d^{3} f e^{14} + 790176 \, b^{4} c^{4} d^{3} g e^{14} + 338688 \, b^{4} c^{4} d^{2} f e^{15} - 256788 \, b^{5} c^{3} d^{2} g e^{15} - 63840 \, b^{5} c^{3} d f e^{16} + 45780 \, b^{6} c^{2} d g e^{16} + 5040 \, b^{6} c^{2} f e^{17} - 3465 \, b^{7} c g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} + \frac{9 \, {\left(768 \, c^{8} d^{8} g + 2048 \, c^{8} d^{7} f e - 4096 \, b c^{7} d^{7} g e - 7168 \, b c^{7} d^{6} f e^{2} + 8960 \, b^{2} c^{6} d^{6} g e^{2} + 10752 \, b^{2} c^{6} d^{5} f e^{3} - 10752 \, b^{3} c^{5} d^{5} g e^{3} - 8960 \, b^{3} c^{5} d^{4} f e^{4} + 7840 \, b^{4} c^{4} d^{4} g e^{4} + 4480 \, b^{4} c^{4} d^{3} f e^{5} - 3584 \, b^{5} c^{3} d^{3} g e^{5} - 1344 \, b^{5} c^{3} d^{2} f e^{6} + 1008 \, b^{6} c^{2} d^{2} g e^{6} + 224 \, b^{6} c^{2} d f e^{7} - 160 \, b^{7} c d g e^{7} - 16 \, b^{7} c f e^{8} + 11 \, b^{8} g e^{8}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{32768 \, c^{7}}"," ",0,"-1/573440*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(2*(8*(10*(4*(14*c*g*x*e^5 + (48*c^8*d*g*e^16 + 16*c^8*f*e^17 + 17*b*c^7*g*e^17)*e^(-12)/c^7)*x + (140*c^8*d^2*g*e^15 + 224*c^8*d*f*e^16 + 324*b*c^7*d*g*e^16 + 80*b*c^7*f*e^17 + b^2*c^6*g*e^17)*e^(-12)/c^7)*x - (2176*c^8*d^3*g*e^14 - 1664*c^8*d^2*f*e^15 - 5932*b*c^7*d^2*g*e^15 - 3936*b*c^7*d*f*e^16 - 100*b^2*c^6*d*g*e^16 - 16*b^2*c^6*f*e^17 + 11*b^3*c^5*g*e^17)*e^(-12)/c^7)*x - (30800*c^8*d^4*g*e^13 + 22400*c^8*d^3*f*e^14 - 37984*b*c^7*d^3*g*e^14 - 60224*b*c^7*d^2*f*e^15 - 3912*b^2*c^6*d^2*g*e^15 - 1376*b^2*c^6*d*f*e^16 + 1000*b^3*c^5*d*g*e^16 + 144*b^3*c^5*f*e^17 - 99*b^4*c^4*g*e^17)*e^(-12)/c^7)*x - (22528*c^8*d^5*g*e^12 + 83968*c^8*d^4*f*e^13 - 5904*b*c^7*d^4*g*e^13 - 100736*b*c^7*d^3*f*e^14 - 25888*b^2*c^6*d^3*g*e^14 - 14784*b^2*c^6*d^2*f*e^15 + 11496*b^3*c^5*d^2*g*e^15 + 3552*b^3*c^5*d*f*e^16 - 2568*b^4*c^4*d*g*e^16 - 336*b^4*c^4*f*e^17 + 231*b^5*c^3*g*e^17)*e^(-12)/c^7)*x + (60480*c^8*d^6*g*e^11 - 125440*c^8*d^5*f*e^12 - 208832*b*c^7*d^5*g*e^12 - 22272*b*c^7*d^4*f*e^13 + 278416*b^2*c^6*d^4*g*e^13 + 223744*b^2*c^6*d^3*f*e^14 - 188384*b^3*c^5*d^3*g*e^14 - 92160*b^3*c^5*d^2*f*e^15 + 70668*b^4*c^4*d^2*g*e^15 + 19488*b^4*c^4*d*f*e^16 - 14028*b^5*c^3*d*g*e^16 - 1680*b^5*c^3*f*e^17 + 1155*b^6*c^2*g*e^17)*e^(-12)/c^7)*x + (212992*c^8*d^7*g*e^10 + 376832*c^8*d^6*f*e^11 - 873408*b*c^7*d^6*g*e^11 - 1255936*b*c^7*d^5*f*e^12 + 1519680*b^2*c^6*d^5*g*e^12 + 1558784*b^2*c^6*d^4*f*e^13 - 1433392*b^3*c^5*d^4*g*e^13 - 964608*b^3*c^5*d^3*f*e^14 + 790176*b^4*c^4*d^3*g*e^14 + 338688*b^4*c^4*d^2*f*e^15 - 256788*b^5*c^3*d^2*g*e^15 - 63840*b^5*c^3*d*f*e^16 + 45780*b^6*c^2*d*g*e^16 + 5040*b^6*c^2*f*e^17 - 3465*b^7*c*g*e^17)*e^(-12)/c^7) + 9/32768*(768*c^8*d^8*g + 2048*c^8*d^7*f*e - 4096*b*c^7*d^7*g*e - 7168*b*c^7*d^6*f*e^2 + 8960*b^2*c^6*d^6*g*e^2 + 10752*b^2*c^6*d^5*f*e^3 - 10752*b^3*c^5*d^5*g*e^3 - 8960*b^3*c^5*d^4*f*e^4 + 7840*b^4*c^4*d^4*g*e^4 + 4480*b^4*c^4*d^3*f*e^5 - 3584*b^5*c^3*d^3*g*e^5 - 1344*b^5*c^3*d^2*f*e^6 + 1008*b^6*c^2*d^2*g*e^6 + 224*b^6*c^2*d*f*e^7 - 160*b^7*c*d*g*e^7 - 16*b^7*c*f*e^8 + 11*b^8*g*e^8)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^7","B",0
2184,1,910,0,0.466809," ","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=""giac"")","-\frac{1}{107520} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, c g x e^{4} + \frac{{\left(28 \, c^{7} d g e^{13} + 14 \, c^{7} f e^{14} + 15 \, b c^{6} g e^{14}\right)} e^{\left(-10\right)}}{c^{6}}\right)} x - \frac{{\left(24 \, c^{7} d^{2} g e^{12} - 336 \, c^{7} d f e^{13} - 556 \, b c^{6} d g e^{13} - 182 \, b c^{6} f e^{14} - 3 \, b^{2} c^{5} g e^{14}\right)} e^{\left(-10\right)}}{c^{6}}\right)} x - \frac{{\left(3920 \, c^{7} d^{3} g e^{11} + 280 \, c^{7} d^{2} f e^{12} - 5636 \, b c^{6} d^{2} g e^{12} - 5656 \, b c^{6} d f e^{13} - 216 \, b^{2} c^{5} d g e^{13} - 42 \, b^{2} c^{5} f e^{14} + 27 \, b^{3} c^{4} g e^{14}\right)} e^{\left(-10\right)}}{c^{6}}\right)} x - \frac{{\left(4992 \, c^{7} d^{4} g e^{10} + 10752 \, c^{7} d^{3} f e^{11} - 3600 \, b c^{6} d^{3} g e^{11} - 15288 \, b c^{6} d^{2} f e^{12} - 1932 \, b^{2} c^{5} d^{2} g e^{12} - 840 \, b^{2} c^{5} d f e^{13} + 568 \, b^{3} c^{4} d g e^{13} + 98 \, b^{3} c^{4} f e^{14} - 63 \, b^{4} c^{3} g e^{14}\right)} e^{\left(-10\right)}}{c^{6}}\right)} x + \frac{{\left(6720 \, c^{7} d^{5} g e^{9} - 30240 \, c^{7} d^{4} f e^{10} - 21648 \, b c^{6} d^{4} g e^{10} + 17472 \, b c^{6} d^{3} f e^{11} + 24480 \, b^{2} c^{5} d^{3} g e^{11} + 17472 \, b^{2} c^{5} d^{2} f e^{12} - 12576 \, b^{3} c^{4} d^{2} g e^{12} - 4704 \, b^{3} c^{4} d f e^{13} + 3164 \, b^{4} c^{3} d g e^{13} + 490 \, b^{4} c^{3} f e^{14} - 315 \, b^{5} c^{2} g e^{14}\right)} e^{\left(-10\right)}}{c^{6}}\right)} x + \frac{{\left(27648 \, c^{7} d^{6} g e^{8} + 43008 \, c^{7} d^{5} f e^{9} - 97728 \, b c^{6} d^{5} g e^{9} - 137760 \, b c^{6} d^{4} f e^{10} + 145776 \, b^{2} c^{5} d^{4} g e^{10} + 146496 \, b^{2} c^{5} d^{3} f e^{11} - 113440 \, b^{3} c^{4} d^{3} g e^{11} - 67424 \, b^{3} c^{4} d^{2} f e^{12} + 47824 \, b^{4} c^{3} d^{2} g e^{12} + 15680 \, b^{4} c^{3} d f e^{13} - 10500 \, b^{5} c^{2} d g e^{13} - 1470 \, b^{5} c^{2} f e^{14} + 945 \, b^{6} c g e^{14}\right)} e^{\left(-10\right)}}{c^{6}}\right)} + \frac{{\left(256 \, c^{7} d^{7} g + 896 \, c^{7} d^{6} f e - 1344 \, b c^{6} d^{6} g e - 2688 \, b c^{6} d^{5} f e^{2} + 2688 \, b^{2} c^{5} d^{5} g e^{2} + 3360 \, b^{2} c^{5} d^{4} f e^{3} - 2800 \, b^{3} c^{4} d^{4} g e^{3} - 2240 \, b^{3} c^{4} d^{3} f e^{4} + 1680 \, b^{4} c^{3} d^{3} g e^{4} + 840 \, b^{4} c^{3} d^{2} f e^{5} - 588 \, b^{5} c^{2} d^{2} g e^{5} - 168 \, b^{5} c^{2} d f e^{6} + 112 \, b^{6} c d g e^{6} + 14 \, b^{6} c f e^{7} - 9 \, b^{7} g e^{7}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{2048 \, c^{6}}"," ",0,"-1/107520*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(2*(8*(10*(12*c*g*x*e^4 + (28*c^7*d*g*e^13 + 14*c^7*f*e^14 + 15*b*c^6*g*e^14)*e^(-10)/c^6)*x - (24*c^7*d^2*g*e^12 - 336*c^7*d*f*e^13 - 556*b*c^6*d*g*e^13 - 182*b*c^6*f*e^14 - 3*b^2*c^5*g*e^14)*e^(-10)/c^6)*x - (3920*c^7*d^3*g*e^11 + 280*c^7*d^2*f*e^12 - 5636*b*c^6*d^2*g*e^12 - 5656*b*c^6*d*f*e^13 - 216*b^2*c^5*d*g*e^13 - 42*b^2*c^5*f*e^14 + 27*b^3*c^4*g*e^14)*e^(-10)/c^6)*x - (4992*c^7*d^4*g*e^10 + 10752*c^7*d^3*f*e^11 - 3600*b*c^6*d^3*g*e^11 - 15288*b*c^6*d^2*f*e^12 - 1932*b^2*c^5*d^2*g*e^12 - 840*b^2*c^5*d*f*e^13 + 568*b^3*c^4*d*g*e^13 + 98*b^3*c^4*f*e^14 - 63*b^4*c^3*g*e^14)*e^(-10)/c^6)*x + (6720*c^7*d^5*g*e^9 - 30240*c^7*d^4*f*e^10 - 21648*b*c^6*d^4*g*e^10 + 17472*b*c^6*d^3*f*e^11 + 24480*b^2*c^5*d^3*g*e^11 + 17472*b^2*c^5*d^2*f*e^12 - 12576*b^3*c^4*d^2*g*e^12 - 4704*b^3*c^4*d*f*e^13 + 3164*b^4*c^3*d*g*e^13 + 490*b^4*c^3*f*e^14 - 315*b^5*c^2*g*e^14)*e^(-10)/c^6)*x + (27648*c^7*d^6*g*e^8 + 43008*c^7*d^5*f*e^9 - 97728*b*c^6*d^5*g*e^9 - 137760*b*c^6*d^4*f*e^10 + 145776*b^2*c^5*d^4*g*e^10 + 146496*b^2*c^5*d^3*f*e^11 - 113440*b^3*c^4*d^3*g*e^11 - 67424*b^3*c^4*d^2*f*e^12 + 47824*b^4*c^3*d^2*g*e^12 + 15680*b^4*c^3*d*f*e^13 - 10500*b^5*c^2*d*g*e^13 - 1470*b^5*c^2*f*e^14 + 945*b^6*c*g*e^14)*e^(-10)/c^6) + 1/2048*(256*c^7*d^7*g + 896*c^7*d^6*f*e - 1344*b*c^6*d^6*g*e - 2688*b*c^6*d^5*f*e^2 + 2688*b^2*c^5*d^5*g*e^2 + 3360*b^2*c^5*d^4*f*e^3 - 2800*b^3*c^4*d^4*g*e^3 - 2240*b^3*c^4*d^3*f*e^4 + 1680*b^4*c^3*d^3*g*e^4 + 840*b^4*c^3*d^2*f*e^5 - 588*b^5*c^2*d^2*g*e^5 - 168*b^5*c^2*d*f*e^6 + 112*b^6*c*d*g*e^6 + 14*b^6*c*f*e^7 - 9*b^7*g*e^7)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^6","B",0
2185,1,708,0,0.453964," ","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=""giac"")","-\frac{1}{7680} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c g x e^{3} + \frac{{\left(12 \, c^{6} d g e^{10} + 12 \, c^{6} f e^{11} + 13 \, b c^{5} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x - \frac{{\left(140 \, c^{6} d^{2} g e^{9} - 120 \, c^{6} d f e^{10} - 272 \, b c^{5} d g e^{10} - 132 \, b c^{5} f e^{11} - 3 \, b^{2} c^{4} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x - \frac{{\left(384 \, c^{6} d^{3} g e^{8} + 384 \, c^{6} d^{2} f e^{9} - 348 \, b c^{5} d^{2} g e^{9} - 744 \, b c^{5} d f e^{10} - 48 \, b^{2} c^{4} d g e^{10} - 12 \, b^{2} c^{4} f e^{11} + 7 \, b^{3} c^{3} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x + \frac{{\left(240 \, c^{6} d^{4} g e^{7} - 2400 \, c^{6} d^{3} f e^{8} - 816 \, b c^{5} d^{3} g e^{8} + 2064 \, b c^{5} d^{2} f e^{9} + 792 \, b^{2} c^{4} d^{2} g e^{9} + 456 \, b^{2} c^{4} d f e^{10} - 276 \, b^{3} c^{3} d g e^{10} - 60 \, b^{3} c^{3} f e^{11} + 35 \, b^{4} c^{2} g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} x + \frac{{\left(1536 \, c^{6} d^{5} g e^{6} + 1536 \, c^{6} d^{4} f e^{7} - 4368 \, b c^{5} d^{4} g e^{7} - 5472 \, b c^{5} d^{3} f e^{8} + 5328 \, b^{2} c^{4} d^{3} g e^{8} + 5136 \, b^{2} c^{4} d^{2} f e^{9} - 3256 \, b^{3} c^{3} d^{2} g e^{9} - 1560 \, b^{3} c^{3} d f e^{10} + 940 \, b^{4} c^{2} d g e^{10} + 180 \, b^{4} c^{2} f e^{11} - 105 \, b^{5} c g e^{11}\right)} e^{\left(-8\right)}}{c^{5}}\right)} + \frac{{\left(64 \, c^{6} d^{6} g + 384 \, c^{6} d^{5} f e - 384 \, b c^{5} d^{5} g e - 960 \, b c^{5} d^{4} f e^{2} + 720 \, b^{2} c^{4} d^{4} g e^{2} + 960 \, b^{2} c^{4} d^{3} f e^{3} - 640 \, b^{3} c^{3} d^{3} g e^{3} - 480 \, b^{3} c^{3} d^{2} f e^{4} + 300 \, b^{4} c^{2} d^{2} g e^{4} + 120 \, b^{4} c^{2} d f e^{5} - 72 \, b^{5} c d g e^{5} - 12 \, b^{5} c f e^{6} + 7 \, b^{6} g e^{6}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{1024 \, c^{5}}"," ",0,"-1/7680*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(2*(8*(10*c*g*x*e^3 + (12*c^6*d*g*e^10 + 12*c^6*f*e^11 + 13*b*c^5*g*e^11)*e^(-8)/c^5)*x - (140*c^6*d^2*g*e^9 - 120*c^6*d*f*e^10 - 272*b*c^5*d*g*e^10 - 132*b*c^5*f*e^11 - 3*b^2*c^4*g*e^11)*e^(-8)/c^5)*x - (384*c^6*d^3*g*e^8 + 384*c^6*d^2*f*e^9 - 348*b*c^5*d^2*g*e^9 - 744*b*c^5*d*f*e^10 - 48*b^2*c^4*d*g*e^10 - 12*b^2*c^4*f*e^11 + 7*b^3*c^3*g*e^11)*e^(-8)/c^5)*x + (240*c^6*d^4*g*e^7 - 2400*c^6*d^3*f*e^8 - 816*b*c^5*d^3*g*e^8 + 2064*b*c^5*d^2*f*e^9 + 792*b^2*c^4*d^2*g*e^9 + 456*b^2*c^4*d*f*e^10 - 276*b^3*c^3*d*g*e^10 - 60*b^3*c^3*f*e^11 + 35*b^4*c^2*g*e^11)*e^(-8)/c^5)*x + (1536*c^6*d^5*g*e^6 + 1536*c^6*d^4*f*e^7 - 4368*b*c^5*d^4*g*e^7 - 5472*b*c^5*d^3*f*e^8 + 5328*b^2*c^4*d^3*g*e^8 + 5136*b^2*c^4*d^2*f*e^9 - 3256*b^3*c^3*d^2*g*e^9 - 1560*b^3*c^3*d*f*e^10 + 940*b^4*c^2*d*g*e^10 + 180*b^4*c^2*f*e^11 - 105*b^5*c*g*e^11)*e^(-8)/c^5) + 1/1024*(64*c^6*d^6*g + 384*c^6*d^5*f*e - 384*b*c^5*d^5*g*e - 960*b*c^5*d^4*f*e^2 + 720*b^2*c^4*d^4*g*e^2 + 960*b^2*c^4*d^3*f*e^3 - 640*b^3*c^3*d^3*g*e^3 - 480*b^3*c^3*d^2*f*e^4 + 300*b^4*c^2*d^2*g*e^4 + 120*b^4*c^2*d*f*e^5 - 72*b^5*c*d*g*e^5 - 12*b^5*c*f*e^6 + 7*b^6*g*e^6)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^5","B",0
2186,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2187,-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)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2188,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-4*exp(1)^3*c^2*g*1/16/exp(1)^4/c*x+(-8*exp(1)^3*c^2*f-10*exp(1)^3*c*g*b+24*exp(1)^2*c^2*g*d)*1/16/exp(1)^4/c)*sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))+2*((3*sqrt(-c*exp(2))*b^2*g*exp(1)^2-24*c*sqrt(-c*exp(2))*b*g*exp(1)*d+12*c*sqrt(-c*exp(2))*b*exp(1)^2*f+36*c^2*sqrt(-c*exp(2))*g*d^2-24*c^2*sqrt(-c*exp(2))*exp(1)*d*f)/16/c/exp(2)/exp(1)*ln(abs(2*c*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)-sqrt(-c*exp(2))*b))+(12*exp(2)*b^2*g*exp(1)^4*d-15*exp(2)^2*b^2*g*exp(1)^2*d+3*exp(2)^2*b^2*exp(1)^3*f-48*c*exp(2)*b*g*exp(1)^3*d^2+60*c*exp(2)^2*b*g*exp(1)*d^2+12*c*exp(2)*b*exp(1)^4*d*f-24*c*exp(2)^2*b*exp(1)^2*d*f+36*c^2*exp(2)*g*exp(1)^2*d^3-48*c^2*exp(2)^2*g*d^3-12*c^2*exp(2)*exp(1)^3*d^2*f+24*c^2*exp(2)^2*exp(1)*d^2*f)/4/exp(1)^5/2/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))*atan((-d*sqrt(-c*exp(2))+(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1))/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2)))-(4*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*b^2*g*exp(1)^5*d-9*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*b^2*g*exp(1)^3*d+5*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*b^2*exp(1)^4*f-16*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*b*g*exp(1)^4*d^2+36*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*b*g*exp(1)^2*d^2+4*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*b*exp(1)^5*d*f-24*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*b*exp(1)^3*d*f+12*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)^3*d^3-32*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*g*exp(1)*d^3-4*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*exp(1)^4*d^2*f+24*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^3*exp(1)^2*d^2*f-8*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b^2*g*exp(1)^6*d^2+20*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b^2*g*exp(1)^4*d^2+3*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b^2*g*exp(1)^2*d^2-16*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b^2*exp(1)^5*d*f+exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b^2*exp(1)^3*d*f+16*c*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b*g*exp(1)^5*d^3-32*c*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b*g*exp(1)^3*d^3-44*c*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b*g*exp(1)*d^3+36*c*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b*exp(1)^4*d^2*f+24*c*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*b*exp(1)^2*d^2*f-8*c^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^4*d^4+12*c^2*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*exp(1)^2*d^4+56*c^2*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*g*d^4-20*c^2*exp(2)*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)^3*d^3*f-40*c^2*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)*d^3*f+4*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^3*g*exp(1)^6*d^2-11*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^3*g*exp(1)^4*d^2+7*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^3*g*exp(1)^2*d^2+3*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^3*exp(1)^5*d*f-3*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^3*exp(1)^3*d*f-28*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^2*g*exp(1)^5*d^3+91*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^2*g*exp(1)^3*d^3-48*c*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^2*g*exp(1)*d^3-4*c*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^2*exp(1)^6*d^2*f-39*c*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^2*exp(1)^4*d^2*f+28*c*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b^2*exp(1)^2*d^2*f+44*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*g*exp(1)^4*d^4-160*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*g*exp(1)^2*d^4+56*c^2*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*g*d^4+8*c^2*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*exp(1)^5*d^3*f+92*c^2*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*exp(1)^3*d^3*f-40*c^2*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*exp(1)*d^3*f-20*c^3*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^3*d^5+80*c^3*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)*d^5-4*c^3*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^4*d^4*f-56*c^3*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^2*d^4*f-8*sqrt(-c*exp(2))*b^3*g*exp(1)^7*d^3+28*exp(2)*sqrt(-c*exp(2))*b^3*g*exp(1)^5*d^3-29*exp(2)^2*sqrt(-c*exp(2))*b^3*g*exp(1)^3*d^3+9*exp(2)^3*sqrt(-c*exp(2))*b^3*g*exp(1)*d^3-8*exp(2)*sqrt(-c*exp(2))*b^3*exp(1)^6*d^2*f+13*exp(2)^2*sqrt(-c*exp(2))*b^3*exp(1)^4*d^2*f-5*exp(2)^3*sqrt(-c*exp(2))*b^3*exp(1)^2*d^2*f+24*c*sqrt(-c*exp(2))*b^2*g*exp(1)^6*d^4-84*c*exp(2)*sqrt(-c*exp(2))*b^2*g*exp(1)^4*d^4+69*c*exp(2)^2*sqrt(-c*exp(2))*b^2*g*exp(1)^2*d^4-14*c*exp(2)^3*sqrt(-c*exp(2))*b^2*g*d^4+36*c*exp(2)*sqrt(-c*exp(2))*b^2*exp(1)^5*d^3*f-41*c*exp(2)^2*sqrt(-c*exp(2))*b^2*exp(1)^3*d^3*f+10*c*exp(2)^3*sqrt(-c*exp(2))*b^2*exp(1)*d^3*f-24*c^2*sqrt(-c*exp(2))*b*g*exp(1)^5*d^5+84*c^2*exp(2)*sqrt(-c*exp(2))*b*g*exp(1)^3*d^5-40*c^2*exp(2)^2*sqrt(-c*exp(2))*b*g*exp(1)*d^5-48*c^2*exp(2)*sqrt(-c*exp(2))*b*exp(1)^4*d^4*f+28*c^2*exp(2)^2*sqrt(-c*exp(2))*b*exp(1)^2*d^4*f+8*c^3*sqrt(-c*exp(2))*g*exp(1)^4*d^6-28*c^3*exp(2)*sqrt(-c*exp(2))*g*exp(1)^2*d^6+20*c^3*exp(2)*sqrt(-c*exp(2))*exp(1)^3*d^5*f)/8/exp(1)^5/((sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)-2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*d+b*exp(1)^2*d-exp(2)*b*d-c*exp(1)*d^2)^2)","F(-2)",0
2189,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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2190,1,849,0,1.748820," ","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=""giac"")","\frac{2}{15} \, {\left(\sqrt{-c e^{2} + \frac{2 \, c d e^{2}}{x e + d} - \frac{b e^{3}}{x e + d}} {\left(\frac{30 \, {\left(4 \, c^{2} d^{2} e^{9} - 4 \, b c d e^{10} + b^{2} e^{11}\right)} C_{0}}{8 \, c^{3} d^{3} e^{12} - 12 \, b c^{2} d^{2} e^{13} + 6 \, b^{2} c d e^{14} - b^{3} e^{15}} - \frac{{\left(\frac{128 \, c^{4} d^{4} g e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, c^{4} d^{3} f e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 232 \, b c^{3} d^{3} g e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 72 \, b c^{3} d^{2} f e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 156 \, b^{2} c^{2} d^{2} g e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 36 \, b^{2} c^{2} d f e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 46 \, b^{3} c d g e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 6 \, b^{3} c f e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, b^{4} g e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{8 \, c^{3} d^{3} e^{12} - 12 \, b c^{2} d^{2} e^{13} + 6 \, b^{2} c d e^{14} - b^{3} e^{15}} - \frac{3 \, {\left(16 \, c^{4} d^{5} g e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, c^{4} d^{4} f e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, b c^{3} d^{4} g e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, b c^{3} d^{3} f e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, b^{2} c^{2} d^{3} g e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, b^{2} c^{2} d^{2} f e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, b^{3} c d^{2} g e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 8 \, b^{3} c d f e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + b^{4} d g e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{4} f e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(8 \, c^{3} d^{3} e^{12} - 12 \, b c^{2} d^{2} e^{13} + 6 \, b^{2} c d e^{14} - b^{3} e^{15}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} + \frac{172 \, c^{4} d^{3} g e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 12 \, c^{4} d^{2} f e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 252 \, b c^{3} d^{2} g e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 12 \, b c^{3} d f e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 123 \, b^{2} c^{2} d g e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{2} c^{2} f e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 20 \, b^{3} c g e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{8 \, c^{3} d^{3} e^{12} - 12 \, b c^{2} d^{2} e^{13} + 6 \, b^{2} c d e^{14} - b^{3} e^{15}}\right)} - \frac{{\left(43 \, \sqrt{-c e^{2}} c^{2} d g - 3 \, \sqrt{-c e^{2}} c^{2} f e - 20 \, \sqrt{-c e^{2}} b c g e\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{2 \, c d e^{5} - b e^{6}}\right)} e^{2}"," ",0,"2/15*(sqrt(-c*e^2 + 2*c*d*e^2/(x*e + d) - b*e^3/(x*e + d))*(30*(4*c^2*d^2*e^9 - 4*b*c*d*e^10 + b^2*e^11)*C_0/(8*c^3*d^3*e^12 - 12*b*c^2*d^2*e^13 + 6*b^2*c*d*e^14 - b^3*e^15) - ((128*c^4*d^4*g*e^8*sgn(1/(x*e + d)) - 48*c^4*d^3*f*e^9*sgn(1/(x*e + d)) - 232*b*c^3*d^3*g*e^9*sgn(1/(x*e + d)) + 72*b*c^3*d^2*f*e^10*sgn(1/(x*e + d)) + 156*b^2*c^2*d^2*g*e^10*sgn(1/(x*e + d)) - 36*b^2*c^2*d*f*e^11*sgn(1/(x*e + d)) - 46*b^3*c*d*g*e^11*sgn(1/(x*e + d)) + 6*b^3*c*f*e^12*sgn(1/(x*e + d)) + 5*b^4*g*e^12*sgn(1/(x*e + d)))/(8*c^3*d^3*e^12 - 12*b*c^2*d^2*e^13 + 6*b^2*c*d*e^14 - b^3*e^15) - 3*(16*c^4*d^5*g*e^9*sgn(1/(x*e + d)) - 16*c^4*d^4*f*e^10*sgn(1/(x*e + d)) - 32*b*c^3*d^4*g*e^10*sgn(1/(x*e + d)) + 32*b*c^3*d^3*f*e^11*sgn(1/(x*e + d)) + 24*b^2*c^2*d^3*g*e^11*sgn(1/(x*e + d)) - 24*b^2*c^2*d^2*f*e^12*sgn(1/(x*e + d)) - 8*b^3*c*d^2*g*e^12*sgn(1/(x*e + d)) + 8*b^3*c*d*f*e^13*sgn(1/(x*e + d)) + b^4*d*g*e^13*sgn(1/(x*e + d)) - b^4*f*e^14*sgn(1/(x*e + d)))*e^(-1)/((8*c^3*d^3*e^12 - 12*b*c^2*d^2*e^13 + 6*b^2*c*d*e^14 - b^3*e^15)*(x*e + d)))*e^(-1)/(x*e + d) + (172*c^4*d^3*g*e^7*sgn(1/(x*e + d)) - 12*c^4*d^2*f*e^8*sgn(1/(x*e + d)) - 252*b*c^3*d^2*g*e^8*sgn(1/(x*e + d)) + 12*b*c^3*d*f*e^9*sgn(1/(x*e + d)) + 123*b^2*c^2*d*g*e^9*sgn(1/(x*e + d)) - 3*b^2*c^2*f*e^10*sgn(1/(x*e + d)) - 20*b^3*c*g*e^10*sgn(1/(x*e + d)))/(8*c^3*d^3*e^12 - 12*b*c^2*d^2*e^13 + 6*b^2*c*d*e^14 - b^3*e^15)) - (43*sqrt(-c*e^2)*c^2*d*g - 3*sqrt(-c*e^2)*c^2*f*e - 20*sqrt(-c*e^2)*b*c*g*e)*sgn(1/(x*e + d))/(2*c*d*e^5 - b*e^6))*e^2","B",0
2191,-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)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""giac"")","\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=""giac"")","\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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2195,1,1686,0,0.944203," ","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=""giac"")","\frac{1}{41287680} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, {\left(18 \, c^{2} g x e^{7} + \frac{{\left(60 \, c^{11} d g e^{22} + 20 \, c^{11} f e^{23} + 41 \, b c^{10} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x + \frac{{\left(324 \, c^{11} d^{2} g e^{21} + 1080 \, c^{11} d f e^{22} + 2976 \, b c^{10} d g e^{22} + 740 \, b c^{10} f e^{23} + 383 \, b^{2} c^{9} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x - \frac{{\left(30720 \, c^{11} d^{3} g e^{20} - 5120 \, c^{11} d^{2} f e^{21} - 59396 \, b c^{10} d^{2} g e^{21} - 47800 \, b c^{10} d f e^{22} - 31264 \, b^{2} c^{9} d g e^{22} - 6180 \, b^{2} c^{9} f e^{23} - 15 \, b^{3} c^{8} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x - \frac{{\left(140112 \, c^{11} d^{4} g e^{19} + 144480 \, c^{11} d^{3} f e^{20} + 16176 \, b c^{10} d^{3} g e^{20} - 278160 \, b c^{10} d^{2} f e^{21} - 298968 \, b^{2} c^{9} d^{2} g e^{21} - 147720 \, b^{2} c^{9} d f e^{22} - 780 \, b^{3} c^{8} d g e^{22} - 100 \, b^{3} c^{8} f e^{23} + 65 \, b^{4} c^{7} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x + \frac{{\left(92160 \, c^{11} d^{5} g e^{18} - 337920 \, c^{11} d^{4} f e^{19} - 762000 \, b c^{10} d^{4} g e^{19} - 46560 \, b c^{10} d^{3} f e^{20} + 733200 \, b^{2} c^{9} d^{3} g e^{20} + 730320 \, b^{2} c^{9} d^{2} f e^{21} + 9960 \, b^{3} c^{8} d^{2} g e^{21} + 2760 \, b^{3} c^{8} d f e^{22} - 1860 \, b^{4} c^{7} d g e^{22} - 220 \, b^{4} c^{7} f e^{23} + 143 \, b^{5} c^{6} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x + \frac{{\left(2358720 \, c^{11} d^{6} g e^{17} + 981120 \, c^{11} d^{5} f e^{18} - 6092160 \, b c^{10} d^{5} g e^{18} - 7859520 \, b c^{10} d^{4} f e^{19} + 3484080 \, b^{2} c^{9} d^{4} g e^{19} + 7487040 \, b^{2} c^{9} d^{3} f e^{20} + 339840 \, b^{3} c^{8} d^{3} g e^{20} + 151520 \, b^{3} c^{8} d^{2} f e^{21} - 106540 \, b^{4} c^{7} d^{2} g e^{21} - 26840 \, b^{4} c^{7} d f e^{22} + 18040 \, b^{5} c^{6} d g e^{22} + 1980 \, b^{5} c^{6} f e^{23} - 1287 \, b^{6} c^{5} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x + \frac{{\left(1966080 \, c^{11} d^{7} g e^{16} + 6553600 \, c^{11} d^{6} f e^{17} - 3081920 \, b c^{10} d^{6} g e^{17} - 16717440 \, b c^{10} d^{5} f e^{18} - 336000 \, b^{2} c^{9} d^{5} g e^{18} + 9107520 \, b^{2} c^{9} d^{4} f e^{19} + 2246160 \, b^{3} c^{8} d^{4} g e^{19} + 1415360 \, b^{3} c^{8} d^{3} f e^{20} - 1045120 \, b^{4} c^{7} d^{3} g e^{20} - 417120 \, b^{4} c^{7} d^{2} f e^{21} + 291324 \, b^{5} c^{6} d^{2} g e^{21} + 67320 \, b^{5} c^{6} d f e^{22} - 45144 \, b^{6} c^{5} d g e^{22} - 4620 \, b^{6} c^{5} f e^{23} + 3003 \, b^{7} c^{4} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x - \frac{{\left(2661120 \, c^{11} d^{8} g e^{15} - 11773440 \, c^{11} d^{7} f e^{16} - 12622080 \, b c^{10} d^{7} g e^{16} + 14992640 \, b c^{10} d^{6} f e^{17} + 24504320 \, b^{2} c^{9} d^{6} g e^{17} + 10945920 \, b^{2} c^{9} d^{5} f e^{18} - 25880640 \, b^{3} c^{8} d^{5} g e^{18} - 21264960 \, b^{3} c^{8} d^{4} f e^{19} + 16587360 \, b^{4} c^{7} d^{4} g e^{19} + 9217120 \, b^{4} c^{7} d^{3} f e^{20} - 6720560 \, b^{5} c^{6} d^{3} g e^{20} - 2431440 \, b^{5} c^{6} d^{2} f e^{21} + 1688544 \, b^{6} c^{5} d^{2} g e^{21} + 360360 \, b^{6} c^{5} d f e^{22} - 241164 \, b^{7} c^{4} d g e^{22} - 23100 \, b^{7} c^{4} f e^{23} + 15015 \, b^{8} c^{3} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} x - \frac{{\left(9830400 \, c^{11} d^{9} g e^{14} + 19005440 \, c^{11} d^{8} f e^{15} - 51078400 \, b c^{10} d^{8} g e^{15} - 87795200 \, b c^{10} d^{7} f e^{16} + 117794560 \, b^{2} c^{9} d^{7} g e^{16} + 161137920 \, b^{2} c^{9} d^{6} f e^{17} - 156115200 \, b^{3} c^{8} d^{6} g e^{17} - 157489280 \, b^{3} c^{8} d^{5} f e^{18} + 130302400 \, b^{4} c^{7} d^{5} g e^{18} + 93114560 \, b^{4} c^{7} d^{4} f e^{19} - 71145184 \, b^{5} c^{6} d^{4} g e^{19} - 35402400 \, b^{5} c^{6} d^{3} f e^{20} + 25545168 \, b^{6} c^{5} d^{3} g e^{20} + 8445360 \, b^{6} c^{5} d^{2} f e^{21} - 5835984 \, b^{7} c^{4} d^{2} g e^{21} - 1155000 \, b^{7} c^{4} d f e^{22} + 771540 \, b^{8} c^{3} d g e^{22} + 69300 \, b^{8} c^{3} f e^{23} - 45045 \, b^{9} c^{2} g e^{23}\right)} e^{\left(-16\right)}}{c^{9}}\right)} + \frac{11 \, {\left(3072 \, c^{10} d^{10} g + 10240 \, c^{10} d^{9} f e - 20480 \, b c^{9} d^{9} g e - 46080 \, b c^{9} d^{8} f e^{2} + 57600 \, b^{2} c^{8} d^{8} g e^{2} + 92160 \, b^{2} c^{8} d^{7} f e^{3} - 92160 \, b^{3} c^{7} d^{7} g e^{3} - 107520 \, b^{3} c^{7} d^{6} f e^{4} + 94080 \, b^{4} c^{6} d^{6} g e^{4} + 80640 \, b^{4} c^{6} d^{5} f e^{5} - 64512 \, b^{5} c^{5} d^{5} g e^{5} - 40320 \, b^{5} c^{5} d^{4} f e^{6} + 30240 \, b^{6} c^{4} d^{4} g e^{6} + 13440 \, b^{6} c^{4} d^{3} f e^{7} - 9600 \, b^{7} c^{3} d^{3} g e^{7} - 2880 \, b^{7} c^{3} d^{2} f e^{8} + 1980 \, b^{8} c^{2} d^{2} g e^{8} + 360 \, b^{8} c^{2} d f e^{9} - 240 \, b^{9} c d g e^{9} - 20 \, b^{9} c f e^{10} + 13 \, b^{10} g e^{10}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{262144 \, c^{8}}"," ",0,"1/41287680*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(2*(8*(2*(4*(14*(16*(18*c^2*g*x*e^7 + (60*c^11*d*g*e^22 + 20*c^11*f*e^23 + 41*b*c^10*g*e^23)*e^(-16)/c^9)*x + (324*c^11*d^2*g*e^21 + 1080*c^11*d*f*e^22 + 2976*b*c^10*d*g*e^22 + 740*b*c^10*f*e^23 + 383*b^2*c^9*g*e^23)*e^(-16)/c^9)*x - (30720*c^11*d^3*g*e^20 - 5120*c^11*d^2*f*e^21 - 59396*b*c^10*d^2*g*e^21 - 47800*b*c^10*d*f*e^22 - 31264*b^2*c^9*d*g*e^22 - 6180*b^2*c^9*f*e^23 - 15*b^3*c^8*g*e^23)*e^(-16)/c^9)*x - (140112*c^11*d^4*g*e^19 + 144480*c^11*d^3*f*e^20 + 16176*b*c^10*d^3*g*e^20 - 278160*b*c^10*d^2*f*e^21 - 298968*b^2*c^9*d^2*g*e^21 - 147720*b^2*c^9*d*f*e^22 - 780*b^3*c^8*d*g*e^22 - 100*b^3*c^8*f*e^23 + 65*b^4*c^7*g*e^23)*e^(-16)/c^9)*x + (92160*c^11*d^5*g*e^18 - 337920*c^11*d^4*f*e^19 - 762000*b*c^10*d^4*g*e^19 - 46560*b*c^10*d^3*f*e^20 + 733200*b^2*c^9*d^3*g*e^20 + 730320*b^2*c^9*d^2*f*e^21 + 9960*b^3*c^8*d^2*g*e^21 + 2760*b^3*c^8*d*f*e^22 - 1860*b^4*c^7*d*g*e^22 - 220*b^4*c^7*f*e^23 + 143*b^5*c^6*g*e^23)*e^(-16)/c^9)*x + (2358720*c^11*d^6*g*e^17 + 981120*c^11*d^5*f*e^18 - 6092160*b*c^10*d^5*g*e^18 - 7859520*b*c^10*d^4*f*e^19 + 3484080*b^2*c^9*d^4*g*e^19 + 7487040*b^2*c^9*d^3*f*e^20 + 339840*b^3*c^8*d^3*g*e^20 + 151520*b^3*c^8*d^2*f*e^21 - 106540*b^4*c^7*d^2*g*e^21 - 26840*b^4*c^7*d*f*e^22 + 18040*b^5*c^6*d*g*e^22 + 1980*b^5*c^6*f*e^23 - 1287*b^6*c^5*g*e^23)*e^(-16)/c^9)*x + (1966080*c^11*d^7*g*e^16 + 6553600*c^11*d^6*f*e^17 - 3081920*b*c^10*d^6*g*e^17 - 16717440*b*c^10*d^5*f*e^18 - 336000*b^2*c^9*d^5*g*e^18 + 9107520*b^2*c^9*d^4*f*e^19 + 2246160*b^3*c^8*d^4*g*e^19 + 1415360*b^3*c^8*d^3*f*e^20 - 1045120*b^4*c^7*d^3*g*e^20 - 417120*b^4*c^7*d^2*f*e^21 + 291324*b^5*c^6*d^2*g*e^21 + 67320*b^5*c^6*d*f*e^22 - 45144*b^6*c^5*d*g*e^22 - 4620*b^6*c^5*f*e^23 + 3003*b^7*c^4*g*e^23)*e^(-16)/c^9)*x - (2661120*c^11*d^8*g*e^15 - 11773440*c^11*d^7*f*e^16 - 12622080*b*c^10*d^7*g*e^16 + 14992640*b*c^10*d^6*f*e^17 + 24504320*b^2*c^9*d^6*g*e^17 + 10945920*b^2*c^9*d^5*f*e^18 - 25880640*b^3*c^8*d^5*g*e^18 - 21264960*b^3*c^8*d^4*f*e^19 + 16587360*b^4*c^7*d^4*g*e^19 + 9217120*b^4*c^7*d^3*f*e^20 - 6720560*b^5*c^6*d^3*g*e^20 - 2431440*b^5*c^6*d^2*f*e^21 + 1688544*b^6*c^5*d^2*g*e^21 + 360360*b^6*c^5*d*f*e^22 - 241164*b^7*c^4*d*g*e^22 - 23100*b^7*c^4*f*e^23 + 15015*b^8*c^3*g*e^23)*e^(-16)/c^9)*x - (9830400*c^11*d^9*g*e^14 + 19005440*c^11*d^8*f*e^15 - 51078400*b*c^10*d^8*g*e^15 - 87795200*b*c^10*d^7*f*e^16 + 117794560*b^2*c^9*d^7*g*e^16 + 161137920*b^2*c^9*d^6*f*e^17 - 156115200*b^3*c^8*d^6*g*e^17 - 157489280*b^3*c^8*d^5*f*e^18 + 130302400*b^4*c^7*d^5*g*e^18 + 93114560*b^4*c^7*d^4*f*e^19 - 71145184*b^5*c^6*d^4*g*e^19 - 35402400*b^5*c^6*d^3*f*e^20 + 25545168*b^6*c^5*d^3*g*e^20 + 8445360*b^6*c^5*d^2*f*e^21 - 5835984*b^7*c^4*d^2*g*e^21 - 1155000*b^7*c^4*d*f*e^22 + 771540*b^8*c^3*d*g*e^22 + 69300*b^8*c^3*f*e^23 - 45045*b^9*c^2*g*e^23)*e^(-16)/c^9) + 11/262144*(3072*c^10*d^10*g + 10240*c^10*d^9*f*e - 20480*b*c^9*d^9*g*e - 46080*b*c^9*d^8*f*e^2 + 57600*b^2*c^8*d^8*g*e^2 + 92160*b^2*c^8*d^7*f*e^3 - 92160*b^3*c^7*d^7*g*e^3 - 107520*b^3*c^7*d^6*f*e^4 + 94080*b^4*c^6*d^6*g*e^4 + 80640*b^4*c^6*d^5*f*e^5 - 64512*b^5*c^5*d^5*g*e^5 - 40320*b^5*c^5*d^4*f*e^6 + 30240*b^6*c^4*d^4*g*e^6 + 13440*b^6*c^4*d^3*f*e^7 - 9600*b^7*c^3*d^3*g*e^7 - 2880*b^7*c^3*d^2*f*e^8 + 1980*b^8*c^2*d^2*g*e^8 + 360*b^8*c^2*d*f*e^9 - 240*b^9*c*d*g*e^9 - 20*b^9*c*f*e^10 + 13*b^10*g*e^10)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^8","B",0
2196,1,1402,0,0.721174," ","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=""giac"")","\frac{1}{2064384} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, c^{2} g x e^{6} + \frac{{\left(36 \, c^{10} d g e^{19} + 18 \, c^{10} f e^{20} + 37 \, b c^{9} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} x - \frac{{\left(320 \, c^{10} d^{2} g e^{18} - 576 \, c^{10} d f e^{19} - 1796 \, b c^{9} d g e^{19} - 594 \, b c^{9} f e^{20} - 309 \, b^{2} c^{8} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} x - \frac{{\left(5712 \, c^{10} d^{3} g e^{17} + 1512 \, c^{10} d^{2} f e^{18} - 5484 \, b c^{9} d^{2} g e^{18} - 8424 \, b c^{9} d f e^{19} - 5928 \, b^{2} c^{8} d g e^{19} - 1458 \, b^{2} c^{8} f e^{20} - 5 \, b^{3} c^{7} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} x - \frac{{\left(3072 \, c^{10} d^{4} g e^{16} + 13824 \, c^{10} d^{3} f e^{17} + 15504 \, b c^{9} d^{3} g e^{17} - 13176 \, b c^{9} d^{2} f e^{18} - 22044 \, b^{2} c^{8} d^{2} g e^{18} - 14472 \, b^{2} c^{8} d f e^{19} - 120 \, b^{3} c^{7} d g e^{19} - 18 \, b^{3} c^{7} f e^{20} + 11 \, b^{4} c^{6} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} x + \frac{{\left(79296 \, c^{10} d^{5} g e^{15} - 30240 \, c^{10} d^{4} f e^{16} - 232272 \, b c^{9} d^{4} g e^{16} - 160704 \, b c^{9} d^{3} f e^{17} + 148416 \, b^{2} c^{8} d^{3} g e^{17} + 225936 \, b^{2} c^{8} d^{2} f e^{18} + 5704 \, b^{3} c^{7} d^{2} g e^{18} + 1872 \, b^{3} c^{7} d f e^{19} - 1180 \, b^{4} c^{6} d g e^{19} - 162 \, b^{4} c^{6} f e^{20} + 99 \, b^{5} c^{5} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} x + \frac{{\left(106496 \, c^{10} d^{6} g e^{14} + 221184 \, c^{10} d^{5} f e^{15} - 192192 \, b c^{9} d^{5} g e^{15} - 643680 \, b c^{9} d^{4} f e^{16} + 52752 \, b^{2} c^{8} d^{4} g e^{16} + 402624 \, b^{2} c^{8} d^{3} f e^{17} + 46144 \, b^{3} c^{7} d^{3} g e^{17} + 24624 \, b^{3} c^{7} d^{2} f e^{18} - 16104 \, b^{4} c^{6} d^{2} g e^{18} - 4752 \, b^{4} c^{6} d f e^{19} + 2988 \, b^{5} c^{5} d g e^{19} + 378 \, b^{5} c^{5} f e^{20} - 231 \, b^{6} c^{4} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} x - \frac{{\left(80640 \, c^{10} d^{7} g e^{13} - 669312 \, c^{10} d^{6} f e^{14} - 373568 \, b c^{9} d^{6} g e^{14} + 1123200 \, b c^{9} d^{5} f e^{15} + 663936 \, b^{2} c^{8} d^{5} g e^{15} - 116640 \, b^{2} c^{8} d^{4} f e^{16} - 604176 \, b^{3} c^{7} d^{4} g e^{16} - 459072 \, b^{3} c^{7} d^{3} f e^{17} + 313328 \, b^{4} c^{6} d^{3} g e^{17} + 147528 \, b^{4} c^{6} d^{2} f e^{18} - 95868 \, b^{5} c^{5} d^{2} g e^{18} - 25704 \, b^{5} c^{5} d f e^{19} + 16128 \, b^{6} c^{4} d g e^{19} + 1890 \, b^{6} c^{4} f e^{20} - 1155 \, b^{7} c^{3} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} x - \frac{{\left(360448 \, c^{10} d^{8} g e^{12} + 589824 \, c^{10} d^{7} f e^{13} - 1656064 \, b c^{9} d^{7} g e^{13} - 2733696 \, b c^{9} d^{6} f e^{14} + 3394752 \, b^{2} c^{8} d^{6} g e^{14} + 4662144 \, b^{2} c^{8} d^{5} f e^{15} - 3950464 \, b^{3} c^{7} d^{5} g e^{15} - 3924000 \, b^{3} c^{7} d^{4} f e^{16} + 2808496 \, b^{4} c^{6} d^{4} g e^{16} + 1847232 \, b^{4} c^{6} d^{3} f e^{17} - 1245456 \, b^{5} c^{5} d^{3} g e^{17} - 524664 \, b^{5} c^{5} d^{2} f e^{18} + 339108 \, b^{6} c^{4} d^{2} g e^{18} + 83160 \, b^{6} c^{4} d f e^{19} - 52080 \, b^{7} c^{3} d g e^{19} - 5670 \, b^{7} c^{3} f e^{20} + 3465 \, b^{8} c^{2} g e^{20}\right)} e^{\left(-14\right)}}{c^{8}}\right)} + \frac{5 \, {\left(1024 \, c^{9} d^{9} g + 4608 \, c^{9} d^{8} f e - 6912 \, b c^{8} d^{8} g e - 18432 \, b c^{8} d^{7} f e^{2} + 18432 \, b^{2} c^{7} d^{7} g e^{2} + 32256 \, b^{2} c^{7} d^{6} f e^{3} - 26880 \, b^{3} c^{6} d^{6} g e^{3} - 32256 \, b^{3} c^{6} d^{5} f e^{4} + 24192 \, b^{4} c^{5} d^{5} g e^{4} + 20160 \, b^{4} c^{5} d^{4} f e^{5} - 14112 \, b^{5} c^{4} d^{4} g e^{5} - 8064 \, b^{5} c^{4} d^{3} f e^{6} + 5376 \, b^{6} c^{3} d^{3} g e^{6} + 2016 \, b^{6} c^{3} d^{2} f e^{7} - 1296 \, b^{7} c^{2} d^{2} g e^{7} - 288 \, b^{7} c^{2} d f e^{8} + 180 \, b^{8} c d g e^{8} + 18 \, b^{8} c f e^{9} - 11 \, b^{9} g e^{9}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{65536 \, c^{7}}"," ",0,"1/2064384*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(2*(8*(2*(4*(14*(16*c^2*g*x*e^6 + (36*c^10*d*g*e^19 + 18*c^10*f*e^20 + 37*b*c^9*g*e^20)*e^(-14)/c^8)*x - (320*c^10*d^2*g*e^18 - 576*c^10*d*f*e^19 - 1796*b*c^9*d*g*e^19 - 594*b*c^9*f*e^20 - 309*b^2*c^8*g*e^20)*e^(-14)/c^8)*x - (5712*c^10*d^3*g*e^17 + 1512*c^10*d^2*f*e^18 - 5484*b*c^9*d^2*g*e^18 - 8424*b*c^9*d*f*e^19 - 5928*b^2*c^8*d*g*e^19 - 1458*b^2*c^8*f*e^20 - 5*b^3*c^7*g*e^20)*e^(-14)/c^8)*x - (3072*c^10*d^4*g*e^16 + 13824*c^10*d^3*f*e^17 + 15504*b*c^9*d^3*g*e^17 - 13176*b*c^9*d^2*f*e^18 - 22044*b^2*c^8*d^2*g*e^18 - 14472*b^2*c^8*d*f*e^19 - 120*b^3*c^7*d*g*e^19 - 18*b^3*c^7*f*e^20 + 11*b^4*c^6*g*e^20)*e^(-14)/c^8)*x + (79296*c^10*d^5*g*e^15 - 30240*c^10*d^4*f*e^16 - 232272*b*c^9*d^4*g*e^16 - 160704*b*c^9*d^3*f*e^17 + 148416*b^2*c^8*d^3*g*e^17 + 225936*b^2*c^8*d^2*f*e^18 + 5704*b^3*c^7*d^2*g*e^18 + 1872*b^3*c^7*d*f*e^19 - 1180*b^4*c^6*d*g*e^19 - 162*b^4*c^6*f*e^20 + 99*b^5*c^5*g*e^20)*e^(-14)/c^8)*x + (106496*c^10*d^6*g*e^14 + 221184*c^10*d^5*f*e^15 - 192192*b*c^9*d^5*g*e^15 - 643680*b*c^9*d^4*f*e^16 + 52752*b^2*c^8*d^4*g*e^16 + 402624*b^2*c^8*d^3*f*e^17 + 46144*b^3*c^7*d^3*g*e^17 + 24624*b^3*c^7*d^2*f*e^18 - 16104*b^4*c^6*d^2*g*e^18 - 4752*b^4*c^6*d*f*e^19 + 2988*b^5*c^5*d*g*e^19 + 378*b^5*c^5*f*e^20 - 231*b^6*c^4*g*e^20)*e^(-14)/c^8)*x - (80640*c^10*d^7*g*e^13 - 669312*c^10*d^6*f*e^14 - 373568*b*c^9*d^6*g*e^14 + 1123200*b*c^9*d^5*f*e^15 + 663936*b^2*c^8*d^5*g*e^15 - 116640*b^2*c^8*d^4*f*e^16 - 604176*b^3*c^7*d^4*g*e^16 - 459072*b^3*c^7*d^3*f*e^17 + 313328*b^4*c^6*d^3*g*e^17 + 147528*b^4*c^6*d^2*f*e^18 - 95868*b^5*c^5*d^2*g*e^18 - 25704*b^5*c^5*d*f*e^19 + 16128*b^6*c^4*d*g*e^19 + 1890*b^6*c^4*f*e^20 - 1155*b^7*c^3*g*e^20)*e^(-14)/c^8)*x - (360448*c^10*d^8*g*e^12 + 589824*c^10*d^7*f*e^13 - 1656064*b*c^9*d^7*g*e^13 - 2733696*b*c^9*d^6*f*e^14 + 3394752*b^2*c^8*d^6*g*e^14 + 4662144*b^2*c^8*d^5*f*e^15 - 3950464*b^3*c^7*d^5*g*e^15 - 3924000*b^3*c^7*d^4*f*e^16 + 2808496*b^4*c^6*d^4*g*e^16 + 1847232*b^4*c^6*d^3*f*e^17 - 1245456*b^5*c^5*d^3*g*e^17 - 524664*b^5*c^5*d^2*f*e^18 + 339108*b^6*c^4*d^2*g*e^18 + 83160*b^6*c^4*d*f*e^19 - 52080*b^7*c^3*d*g*e^19 - 5670*b^7*c^3*f*e^20 + 3465*b^8*c^2*g*e^20)*e^(-14)/c^8) + 5/65536*(1024*c^9*d^9*g + 4608*c^9*d^8*f*e - 6912*b*c^8*d^8*g*e - 18432*b*c^8*d^7*f*e^2 + 18432*b^2*c^7*d^7*g*e^2 + 32256*b^2*c^7*d^6*f*e^3 - 26880*b^3*c^6*d^6*g*e^3 - 32256*b^3*c^6*d^5*f*e^4 + 24192*b^4*c^5*d^5*g*e^4 + 20160*b^4*c^5*d^4*f*e^5 - 14112*b^5*c^4*d^4*g*e^5 - 8064*b^5*c^4*d^3*f*e^6 + 5376*b^6*c^3*d^3*g*e^6 + 2016*b^6*c^3*d^2*f*e^7 - 1296*b^7*c^2*d^2*g*e^7 - 288*b^7*c^2*d*f*e^8 + 180*b^8*c*d*g*e^8 + 18*b^8*c*f*e^9 - 11*b^9*g*e^9)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^7","B",0
2197,1,1144,0,0.655695," ","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=""giac"")","\frac{1}{344064} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, c^{2} g x e^{5} + \frac{{\left(16 \, c^{9} d g e^{16} + 16 \, c^{9} f e^{17} + 33 \, b c^{8} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x - \frac{{\left(476 \, c^{9} d^{2} g e^{15} - 224 \, c^{9} d f e^{16} - 940 \, b c^{8} d g e^{16} - 464 \, b c^{8} f e^{17} - 243 \, b^{2} c^{7} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x - \frac{{\left(1152 \, c^{9} d^{3} g e^{14} + 1152 \, c^{9} d^{2} f e^{15} + 76 \, b c^{8} d^{2} g e^{15} - 2272 \, b c^{8} d f e^{16} - 1820 \, b^{2} c^{7} d g e^{16} - 592 \, b^{2} c^{7} f e^{17} - 3 \, b^{3} c^{6} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x + \frac{{\left(6608 \, c^{9} d^{4} g e^{13} - 11648 \, c^{9} d^{3} f e^{14} - 25824 \, b c^{8} d^{3} g e^{14} - 960 \, b c^{8} d^{2} f e^{15} + 19000 \, b^{2} c^{7} d^{2} g e^{15} + 18656 \, b^{2} c^{7} d f e^{16} + 264 \, b^{3} c^{6} d g e^{16} + 48 \, b^{3} c^{6} f e^{17} - 27 \, b^{4} c^{5} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x + \frac{{\left(18432 \, c^{9} d^{5} g e^{12} + 18432 \, c^{9} d^{4} f e^{13} - 35472 \, b c^{8} d^{4} g e^{13} - 71808 \, b c^{8} d^{3} f e^{14} + 14688 \, b^{2} c^{7} d^{3} g e^{14} + 52416 \, b^{2} c^{7} d^{2} f e^{15} + 2920 \, b^{3} c^{6} d^{2} g e^{15} + 1184 \, b^{3} c^{6} d f e^{16} - 680 \, b^{4} c^{5} d g e^{16} - 112 \, b^{4} c^{5} f e^{17} + 63 \, b^{5} c^{4} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x - \frac{{\left(6720 \, c^{9} d^{6} g e^{11} - 118272 \, c^{9} d^{5} f e^{12} - 34752 \, b c^{8} d^{5} g e^{12} + 221952 \, b c^{8} d^{4} f e^{13} + 58896 \, b^{2} c^{7} d^{4} g e^{13} - 78336 \, b^{2} c^{7} d^{3} f e^{14} - 45792 \, b^{3} c^{6} d^{3} g e^{14} - 30720 \, b^{3} c^{6} d^{2} f e^{15} + 18092 \, b^{4} c^{5} d^{2} g e^{15} + 6496 \, b^{4} c^{5} d f e^{16} - 3724 \, b^{5} c^{4} d g e^{16} - 560 \, b^{5} c^{4} f e^{17} + 315 \, b^{6} c^{3} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} x - \frac{{\left(49152 \, c^{9} d^{7} g e^{10} + 49152 \, c^{9} d^{6} f e^{11} - 189888 \, b c^{8} d^{6} g e^{11} - 265728 \, b c^{8} d^{5} f e^{12} + 333888 \, b^{2} c^{7} d^{5} g e^{12} + 443136 \, b^{2} c^{7} d^{4} f e^{13} - 332464 \, b^{3} c^{6} d^{4} g e^{13} - 321536 \, b^{3} c^{6} d^{3} f e^{14} + 194976 \, b^{4} c^{5} d^{3} g e^{14} + 112896 \, b^{4} c^{5} d^{2} f e^{15} - 66164 \, b^{5} c^{4} d^{2} g e^{15} - 21280 \, b^{5} c^{4} d f e^{16} + 12180 \, b^{6} c^{3} d g e^{16} + 1680 \, b^{6} c^{3} f e^{17} - 945 \, b^{7} c^{2} g e^{17}\right)} e^{\left(-12\right)}}{c^{7}}\right)} + \frac{5 \, {\left(256 \, c^{8} d^{8} g + 2048 \, c^{8} d^{7} f e - 2048 \, b c^{7} d^{7} g e - 7168 \, b c^{7} d^{6} f e^{2} + 5376 \, b^{2} c^{6} d^{6} g e^{2} + 10752 \, b^{2} c^{6} d^{5} f e^{3} - 7168 \, b^{3} c^{5} d^{5} g e^{3} - 8960 \, b^{3} c^{5} d^{4} f e^{4} + 5600 \, b^{4} c^{4} d^{4} g e^{4} + 4480 \, b^{4} c^{4} d^{3} f e^{5} - 2688 \, b^{5} c^{3} d^{3} g e^{5} - 1344 \, b^{5} c^{3} d^{2} f e^{6} + 784 \, b^{6} c^{2} d^{2} g e^{6} + 224 \, b^{6} c^{2} d f e^{7} - 128 \, b^{7} c d g e^{7} - 16 \, b^{7} c f e^{8} + 9 \, b^{8} g e^{8}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{32768 \, c^{6}}"," ",0,"1/344064*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(2*(8*(2*(12*(14*c^2*g*x*e^5 + (16*c^9*d*g*e^16 + 16*c^9*f*e^17 + 33*b*c^8*g*e^17)*e^(-12)/c^7)*x - (476*c^9*d^2*g*e^15 - 224*c^9*d*f*e^16 - 940*b*c^8*d*g*e^16 - 464*b*c^8*f*e^17 - 243*b^2*c^7*g*e^17)*e^(-12)/c^7)*x - (1152*c^9*d^3*g*e^14 + 1152*c^9*d^2*f*e^15 + 76*b*c^8*d^2*g*e^15 - 2272*b*c^8*d*f*e^16 - 1820*b^2*c^7*d*g*e^16 - 592*b^2*c^7*f*e^17 - 3*b^3*c^6*g*e^17)*e^(-12)/c^7)*x + (6608*c^9*d^4*g*e^13 - 11648*c^9*d^3*f*e^14 - 25824*b*c^8*d^3*g*e^14 - 960*b*c^8*d^2*f*e^15 + 19000*b^2*c^7*d^2*g*e^15 + 18656*b^2*c^7*d*f*e^16 + 264*b^3*c^6*d*g*e^16 + 48*b^3*c^6*f*e^17 - 27*b^4*c^5*g*e^17)*e^(-12)/c^7)*x + (18432*c^9*d^5*g*e^12 + 18432*c^9*d^4*f*e^13 - 35472*b*c^8*d^4*g*e^13 - 71808*b*c^8*d^3*f*e^14 + 14688*b^2*c^7*d^3*g*e^14 + 52416*b^2*c^7*d^2*f*e^15 + 2920*b^3*c^6*d^2*g*e^15 + 1184*b^3*c^6*d*f*e^16 - 680*b^4*c^5*d*g*e^16 - 112*b^4*c^5*f*e^17 + 63*b^5*c^4*g*e^17)*e^(-12)/c^7)*x - (6720*c^9*d^6*g*e^11 - 118272*c^9*d^5*f*e^12 - 34752*b*c^8*d^5*g*e^12 + 221952*b*c^8*d^4*f*e^13 + 58896*b^2*c^7*d^4*g*e^13 - 78336*b^2*c^7*d^3*f*e^14 - 45792*b^3*c^6*d^3*g*e^14 - 30720*b^3*c^6*d^2*f*e^15 + 18092*b^4*c^5*d^2*g*e^15 + 6496*b^4*c^5*d*f*e^16 - 3724*b^5*c^4*d*g*e^16 - 560*b^5*c^4*f*e^17 + 315*b^6*c^3*g*e^17)*e^(-12)/c^7)*x - (49152*c^9*d^7*g*e^10 + 49152*c^9*d^6*f*e^11 - 189888*b*c^8*d^6*g*e^11 - 265728*b*c^8*d^5*f*e^12 + 333888*b^2*c^7*d^5*g*e^12 + 443136*b^2*c^7*d^4*f*e^13 - 332464*b^3*c^6*d^4*g*e^13 - 321536*b^3*c^6*d^3*f*e^14 + 194976*b^4*c^5*d^3*g*e^14 + 112896*b^4*c^5*d^2*f*e^15 - 66164*b^5*c^4*d^2*g*e^15 - 21280*b^5*c^4*d*f*e^16 + 12180*b^6*c^3*d*g*e^16 + 1680*b^6*c^3*f*e^17 - 945*b^7*c^2*g*e^17)*e^(-12)/c^7) + 5/32768*(256*c^8*d^8*g + 2048*c^8*d^7*f*e - 2048*b*c^7*d^7*g*e - 7168*b*c^7*d^6*f*e^2 + 5376*b^2*c^6*d^6*g*e^2 + 10752*b^2*c^6*d^5*f*e^3 - 7168*b^3*c^5*d^5*g*e^3 - 8960*b^3*c^5*d^4*f*e^4 + 5600*b^4*c^4*d^4*g*e^4 + 4480*b^4*c^4*d^3*f*e^5 - 2688*b^5*c^3*d^3*g*e^5 - 1344*b^5*c^3*d^2*f*e^6 + 784*b^6*c^2*d^2*g*e^6 + 224*b^6*c^2*d*f*e^7 - 128*b^7*c*d*g*e^7 - 16*b^7*c*f*e^8 + 9*b^8*g*e^8)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^6","B",0
2198,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.42Error: Bad Argument Type","F(-2)",0
2199,-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)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2200,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*g*d^6+12*c^3*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*exp(1)^7*f*d^5+264*c^3*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*exp(1)^5*f*d^5-348*c^3*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*exp(1)^3*f*d^5+72*c^3*exp(2)^4*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*b*exp(1)*f*d^5-20*c^4*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^5*d^7+148*c^4*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)^3*d^7-128*c^4*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*g*exp(1)*d^7-4*c^4*exp(2)*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^6*f*d^6-100*c^4*exp(2)^2*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^4*f*d^6+104*c^4*exp(2)^3*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*exp(1)^2*f*d^6+8*sqrt(-c*exp(2))*b^4*g*exp(1)^10*d^4-44*exp(2)*sqrt(-c*exp(2))*b^4*g*exp(1)^8*d^4+77*exp(2)^2*sqrt(-c*exp(2))*b^4*g*exp(1)^6*d^4-54*exp(2)^3*sqrt(-c*exp(2))*b^4*g*exp(1)^4*d^4+13*exp(2)^4*sqrt(-c*exp(2))*b^4*g*exp(1)^2*d^4+16*exp(2)*sqrt(-c*exp(2))*b^4*exp(1)^9*f*d^3-41*exp(2)^2*sqrt(-c*exp(2))*b^4*exp(1)^7*f*d^3+34*exp(2)^3*sqrt(-c*exp(2))*b^4*exp(1)^5*f*d^3-9*exp(2)^4*sqrt(-c*exp(2))*b^4*exp(1)^3*f*d^3-32*c*sqrt(-c*exp(2))*b^3*g*exp(1)^9*d^5+184*c*exp(2)*sqrt(-c*exp(2))*b^3*g*exp(1)^7*d^5-298*c*exp(2)^2*sqrt(-c*exp(2))*b^3*g*exp(1)^5*d^5+181*c*exp(2)^3*sqrt(-c*exp(2))*b^3*g*exp(1)^3*d^5-35*c*exp(2)^4*sqrt(-c*exp(2))*b^3*g*exp(1)*d^5-84*c*exp(2)*sqrt(-c*exp(2))*b^3*exp(1)^8*f*d^4+186*c*exp(2)^2*sqrt(-c*exp(2))*b^3*exp(1)^6*f*d^4-129*c*exp(2)^3*sqrt(-c*exp(2))*b^3*exp(1)^4*f*d^4+27*c*exp(2)^4*sqrt(-c*exp(2))*b^3*exp(1)^2*f*d^4+48*c^2*sqrt(-c*exp(2))*b^2*g*exp(1)^8*d^6-288*c^2*exp(2)*sqrt(-c*exp(2))*b^2*g*exp(1)^6*d^6+409*c^2*exp(2)^2*sqrt(-c*exp(2))*b^2*g*exp(1)^4*d^6-191*c^2*exp(2)^3*sqrt(-c*exp(2))*b^2*g*exp(1)^2*d^6+22*c^2*exp(2)^4*sqrt(-c*exp(2))*b^2*g*d^6+156*c^2*exp(2)*sqrt(-c*exp(2))*b^2*exp(1)^7*f*d^5-285*c^2*exp(2)^2*sqrt(-c*exp(2))*b^2*exp(1)^5*f*d^5+147*c^2*exp(2)^3*sqrt(-c*exp(2))*b^2*exp(1)^3*f*d^5-18*c^2*exp(2)^4*sqrt(-c*exp(2))*b^2*exp(1)*f*d^5-32*c^3*sqrt(-c*exp(2))*b*g*exp(1)^7*d^7+200*c^3*exp(2)*sqrt(-c*exp(2))*b*g*exp(1)^5*d^7-232*c^3*exp(2)^2*sqrt(-c*exp(2))*b*g*exp(1)^3*d^7+64*c^3*exp(2)^3*sqrt(-c*exp(2))*b*g*exp(1)*d^7-124*c^3*exp(2)*sqrt(-c*exp(2))*b*exp(1)^6*f*d^6+176*c^3*exp(2)^2*sqrt(-c*exp(2))*b*exp(1)^4*f*d^6-52*c^3*exp(2)^3*sqrt(-c*exp(2))*b*exp(1)^2*f*d^6+8*c^4*sqrt(-c*exp(2))*g*exp(1)^6*d^8-52*c^4*exp(2)*sqrt(-c*exp(2))*g*exp(1)^4*d^8+44*c^4*exp(2)^2*sqrt(-c*exp(2))*g*exp(1)^2*d^8+36*c^4*exp(2)*sqrt(-c*exp(2))*exp(1)^5*f*d^7-36*c^4*exp(2)^2*sqrt(-c*exp(2))*exp(1)^3*f*d^7)/8/exp(1)^7/((sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)-2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*d+b*exp(1)^2*d-exp(2)*b*d-c*exp(1)*d^2)^2)","F(-2)",0
2201,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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p(2))*b^4*exp(1)^8*d^4*f+21944598528*c*exp(2)^3*sqrt(-c*exp(2))*b^4*exp(1)^6*d^4*f-14428405760*c*exp(2)^4*sqrt(-c*exp(2))*b^4*exp(1)^4*d^4*f+3154116608*c*exp(2)^5*sqrt(-c*exp(2))*b^4*exp(1)^2*d^4*f+31675383808*c^2*exp(2)*sqrt(-c*exp(2))*b^3*g*exp(1)^8*d^6-102240354304*c^2*exp(2)^2*sqrt(-c*exp(2))*b^3*g*exp(1)^6*d^6+108766691328*c^2*exp(2)^3*sqrt(-c*exp(2))*b^3*g*exp(1)^4*d^6-43721424896*c^2*exp(2)^4*sqrt(-c*exp(2))*b^3*g*exp(1)^2*d^6+4966055936*c^2*exp(2)^5*sqrt(-c*exp(2))*b^3*g*d^6-7516192768*c^2*exp(2)*sqrt(-c*exp(2))*b^3*exp(1)^9*d^5*f+39124467712*c^2*exp(2)^2*sqrt(-c*exp(2))*b^3*exp(1)^7*d^5*f-52294582272*c^2*exp(2)^3*sqrt(-c*exp(2))*b^3*exp(1)^5*d^5*f+24394072064*c^2*exp(2)^4*sqrt(-c*exp(2))*b^3*exp(1)^3*d^5*f-3154116608*c^2*exp(2)^5*sqrt(-c*exp(2))*b^3*exp(1)*d^5*f-39460012032*c^3*exp(2)*sqrt(-c*exp(2))*b^2*g*exp(1)^7*d^7+109018349568*c^3*exp(2)^2*sqrt(-c*exp(2))*b^2*g*exp(1)^5*d^7-85161148416*c^3*exp(2)^3*sqrt(-c*exp(2))*b^2*g*exp(1)^3*d^7+18924699648*c^3*exp(2)^4*sqrt(-c*exp(2))*b^2*g*exp(1)*d^7+11274289152*c^3*exp(2)*sqrt(-c*exp(2))*b^2*exp(1)^8*d^6*f-50130321408*c^3*exp(2)^2*sqrt(-c*exp(2))*b^2*exp(1)^6*d^6*f+47412412416*c^3*exp(2)^3*sqrt(-c*exp(2))*b^2*exp(1)^4*d^6*f-11878268928*c^3*exp(2)^4*sqrt(-c*exp(2))*b^2*exp(1)^2*d^6*f+23622320128*c^4*exp(2)*sqrt(-c*exp(2))*b*g*exp(1)^6*d^8-54022635520*c^4*exp(2)^2*sqrt(-c*exp(2))*b*g*exp(1)^4*d^8+23756537856*c^4*exp(2)^3*sqrt(-c*exp(2))*b*g*exp(1)^2*d^8-7516192768*c^4*exp(2)*sqrt(-c*exp(2))*b*exp(1)^7*d^7*f+29058138112*c^4*exp(2)^2*sqrt(-c*exp(2))*b*exp(1)^5*d^7*f-14898167808*c^4*exp(2)^3*sqrt(-c*exp(2))*b*exp(1)^3*d^7*f-5502926848*c^5*exp(2)*sqrt(-c*exp(2))*g*exp(1)^5*d^9+9932111872*c^5*exp(2)^2*sqrt(-c*exp(2))*g*exp(1)^3*d^9+1879048192*c^5*exp(2)*sqrt(-c*exp(2))*exp(1)^6*d^8*f-6308233216*c^5*exp(2)^2*sqrt(-c*exp(2))*exp(1)^4*d^8*f)/805306368/exp(1)^7/((sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)^2*exp(1)-2*sqrt(-c*exp(2))*(sqrt(-b*d*exp(1)-b*x*exp(2)+c*d^2-c*x^2*exp(2))-sqrt(-c*exp(2))*x)*d+b*exp(1)^2*d-exp(2)*b*d-c*exp(1)*d^2)^3)","F(-2)",0
2202,-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)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2203,-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)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2204,-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)^7,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2209,1,383,0,1.134913," ","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=""giac"")","-\frac{1}{192} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(4 \, {\left(\frac{6 \, g x e}{c} + \frac{{\left(24 \, c^{3} d g e^{4} + 8 \, c^{3} f e^{5} - 7 \, b c^{2} g e^{5}\right)} e^{\left(-4\right)}}{c^{4}}\right)} x + \frac{{\left(180 \, c^{3} d^{2} g e^{3} + 144 \, c^{3} d f e^{4} - 156 \, b c^{2} d g e^{4} - 40 \, b c^{2} f e^{5} + 35 \, b^{2} c g e^{5}\right)} e^{\left(-4\right)}}{c^{4}}\right)} x + \frac{{\left(576 \, c^{3} d^{3} g e^{2} + 704 \, c^{3} d^{2} f e^{3} - 1036 \, b c^{2} d^{2} g e^{3} - 560 \, b c^{2} d f e^{4} + 580 \, b^{2} c d g e^{4} + 120 \, b^{2} c f e^{5} - 105 \, b^{3} g e^{5}\right)} e^{\left(-4\right)}}{c^{4}}\right)} + \frac{5 \, {\left(48 \, c^{4} d^{4} g + 64 \, c^{4} d^{3} f e - 128 \, b c^{3} d^{3} g e - 96 \, b c^{3} d^{2} f e^{2} + 120 \, b^{2} c^{2} d^{2} g e^{2} + 48 \, b^{2} c^{2} d f e^{3} - 48 \, b^{3} c d g e^{3} - 8 \, b^{3} c f e^{4} + 7 \, b^{4} g e^{4}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{128 \, c^{5}}"," ",0,"-1/192*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*(6*g*x*e/c + (24*c^3*d*g*e^4 + 8*c^3*f*e^5 - 7*b*c^2*g*e^5)*e^(-4)/c^4)*x + (180*c^3*d^2*g*e^3 + 144*c^3*d*f*e^4 - 156*b*c^2*d*g*e^4 - 40*b*c^2*f*e^5 + 35*b^2*c*g*e^5)*e^(-4)/c^4)*x + (576*c^3*d^3*g*e^2 + 704*c^3*d^2*f*e^3 - 1036*b*c^2*d^2*g*e^3 - 560*b*c^2*d*f*e^4 + 580*b^2*c*d*g*e^4 + 120*b^2*c*f*e^5 - 105*b^3*g*e^5)*e^(-4)/c^4) + 5/128*(48*c^4*d^4*g + 64*c^4*d^3*f*e - 128*b*c^3*d^3*g*e - 96*b*c^3*d^2*f*e^2 + 120*b^2*c^2*d^2*g*e^2 + 48*b^2*c^2*d*f*e^3 - 48*b^3*c*d*g*e^3 - 8*b^3*c*f*e^4 + 7*b^4*g*e^4)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^5","A",0
2210,1,264,0,0.548330," ","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=""giac"")","-\frac{1}{24} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(2 \, {\left(\frac{4 \, g x}{c} + \frac{{\left(12 \, c^{2} d g e^{2} + 6 \, c^{2} f e^{3} - 5 \, b c g e^{3}\right)} e^{\left(-3\right)}}{c^{3}}\right)} x + \frac{{\left(40 \, c^{2} d^{2} g e + 48 \, c^{2} d f e^{2} - 52 \, b c d g e^{2} - 18 \, b c f e^{3} + 15 \, b^{2} g e^{3}\right)} e^{\left(-3\right)}}{c^{3}}\right)} + \frac{{\left(16 \, c^{3} d^{3} g + 24 \, c^{3} d^{2} f e - 36 \, b c^{2} d^{2} g e - 24 \, b c^{2} d f e^{2} + 24 \, b^{2} c d g e^{2} + 6 \, b^{2} c f e^{3} - 5 \, b^{3} g e^{3}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{16 \, c^{4}}"," ",0,"-1/24*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*(4*g*x/c + (12*c^2*d*g*e^2 + 6*c^2*f*e^3 - 5*b*c*g*e^3)*e^(-3)/c^3)*x + (40*c^2*d^2*g*e + 48*c^2*d*f*e^2 - 52*b*c*d*g*e^2 - 18*b*c*f*e^3 + 15*b^2*g*e^3)*e^(-3)/c^3) + 1/16*(16*c^3*d^3*g + 24*c^3*d^2*f*e - 36*b*c^2*d^2*g*e - 24*b*c^2*d*f*e^2 + 24*b^2*c*d*g*e^2 + 6*b^2*c*f*e^3 - 5*b^3*g*e^3)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^4","A",0
2211,1,179,0,0.539771," ","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=""giac"")","-\frac{1}{4} \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(\frac{2 \, g x e^{\left(-1\right)}}{c} + \frac{{\left(4 \, c d g e + 4 \, c f e^{2} - 3 \, b g e^{2}\right)} e^{\left(-3\right)}}{c^{2}}\right)} + \frac{{\left(4 \, c^{2} d^{2} g + 8 \, c^{2} d f e - 8 \, b c d g e - 4 \, b c f e^{2} + 3 \, b^{2} g e^{2}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{8 \, c^{3}}"," ",0,"-1/4*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(2*g*x*e^(-1)/c + (4*c*d*g*e + 4*c*f*e^2 - 3*b*g*e^2)*e^(-3)/c^2) + 1/8*(4*c^2*d^2*g + 8*c^2*d*f*e - 8*b*c*d*g*e - 4*b*c*f*e^2 + 3*b^2*g*e^2)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^3","A",0
2212,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2213,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^2/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2214,-2,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-1024*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*g*b^2*d*exp(1)^5+256*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*g*b^2*d*exp(1)^3+4096*c*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*g*b*d^2*exp(1)^4-1024*c*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*g*b*d^2*exp(1)^2-3072*c^2*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*g*d^3*exp(1)^3+768*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*b^2*f*exp(1)^4-1024*c*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*b*f*d*exp(1)^5-2048*c*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*b*f*d*exp(1)^3+1024*c^2*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*f*d^2*exp(1)^4+2048*c^2*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^3*f*d^2*exp(1)^2+2048*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*b^2*d^2*exp(1)^6-1024*exp(2)*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*b^2*d^2*exp(1)^4+1280*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*b^2*d^2*exp(1)^2-4096*c*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*b*d^3*exp(1)^5-4096*c*exp(2)*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*b*d^3*exp(1)^3-1024*c*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*b*d^3*exp(1)+2048*c^2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*d^4*exp(1)^4+5120*c^2*exp(2)*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*d^4*exp(1)^2+2048*c^2*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*g*d^4-2304*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*b^2*f*d*exp(1)^3+3072*c*exp(2)*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*b*f*d^2*exp(1)^4+6144*c*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*b*f*d^2*exp(1)^2-3072*c^2*exp(2)*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*f*d^3*exp(1)^3-6144*c^2*exp(2)^2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*f*d^3*exp(1)-1024*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*b^3*d^2*exp(1)^6+768*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*b^3*d^2*exp(1)^4+256*exp(2)^3*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*b^3*d^2*exp(1)^2+7168*c*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*b^2*d^3*exp(1)^5-4864*c*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*b^2*d^3*exp(1)^3-11264*c^2*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*b*d^4*exp(1)^4+2048*c^2*exp(2)^3*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*b*d^4+5120*c^3*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*d^5*exp(1)^3+4096*c^3*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*g*d^5*exp(1)+1280*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b^3*f*d*exp(1)^5-1280*exp(2)^3*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b^3*f*d*exp(1)^3+1024*c*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b^2*f*d^2*exp(1)^6-8448*c*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b^2*f*d^2*exp(1)^4+5120*c*exp(2)^3*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b^2*f*d^2*exp(1)^2-2048*c^2*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b*f*d^3*exp(1)^5+17408*c^2*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b*f*d^3*exp(1)^3-6144*c^2*exp(2)^3*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*b*f*d^3*exp(1)+1024*c^3*exp(2)*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*f*d^4*exp(1)^4-10240*c^3*exp(2)^2*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*f*d^4*exp(1)^2+2048*sqrt(-c*exp(2))*g*b^3*d^3*exp(1)^7-3072*exp(2)*sqrt(-c*exp(2))*g*b^3*d^3*exp(1)^5+1280*exp(2)^2*sqrt(-c*exp(2))*g*b^3*d^3*exp(1)^3-256*exp(2)^3*sqrt(-c*exp(2))*g*b^3*d^3*exp(1)-6144*c*sqrt(-c*exp(2))*g*b^2*d^4*exp(1)^6+5120*c*exp(2)*sqrt(-c*exp(2))*g*b^2*d^4*exp(1)^4+768*c*exp(2)^2*sqrt(-c*exp(2))*g*b^2*d^4*exp(1)^2-512*c*exp(2)^3*sqrt(-c*exp(2))*g*b^2*d^4+6144*c^2*sqrt(-c*exp(2))*g*b*d^5*exp(1)^5-1024*c^2*exp(2)*sqrt(-c*exp(2))*g*b*d^5*exp(1)^3-2048*c^2*exp(2)^2*sqrt(-c*exp(2))*g*b*d^5*exp(1)-2048*c^3*sqrt(-c*exp(2))*g*d^6*exp(1)^4-1024*c^3*exp(2)*sqrt(-c*exp(2))*g*d^6*exp(1)^2-2048*exp(2)*sqrt(-c*exp(2))*b^3*f*d^2*exp(1)^6+2816*exp(2)^2*sqrt(-c*exp(2))*b^3*f*d^2*exp(1)^4-768*exp(2)^3*sqrt(-c*exp(2))*b^3*f*d^2*exp(1)^2+7168*c*exp(2)*sqrt(-c*exp(2))*b^2*f*d^3*exp(1)^5-7936*c*exp(2)^2*sqrt(-c*exp(2))*b^2*f*d^3*exp(1)^3+1536*c*exp(2)^3*sqrt(-c*exp(2))*b^2*f*d^3*exp(1)-8192*c^2*exp(2)*sqrt(-c*exp(2))*b*f*d^4*exp(1)^4+5120*c^2*exp(2)^2*sqrt(-c*exp(2))*b*f*d^4*exp(1)^2+3072*c^3*exp(2)*sqrt(-c*exp(2))*f*d^5*exp(1)^3)/(2048*b^2*d^2*exp(1)^7-4096*exp(2)*b^2*d^2*exp(1)^5+2048*exp(2)^2*b^2*d^2*exp(1)^3-4096*c*b*d^3*exp(1)^6+8192*c*exp(2)*b*d^3*exp(1)^4-4096*c*exp(2)^2*b*d^3*exp(1)^2+2048*c^2*d^4*exp(1)^5-4096*c^2*exp(2)*d^4*exp(1)^3+2048*c^2*exp(2)^2*d^4*exp(1))/((sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)^2*exp(1)-2*sqrt(-c*exp(2))*(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*d+b*d*exp(1)^2-exp(2)*b*d-c*d^2*exp(1))^2+(-8*exp(2)*g*b^2*d*exp(1)^3+2*exp(2)^2*g*b^2*d*exp(1)+32*c*exp(2)*g*b*d^2*exp(1)^2-8*c*exp(2)^2*g*b*d^2-24*c^2*exp(2)*g*d^3*exp(1)+6*exp(2)^2*b^2*f*exp(1)^2-8*c*exp(2)*b*f*d*exp(1)^3-16*c*exp(2)^2*b*f*d*exp(1)+8*c^2*exp(2)*f*d^2*exp(1)^2+16*c^2*exp(2)^2*f*d^2)/16/(b^2*d^2*exp(1)^6-2*exp(2)*b^2*d^2*exp(1)^4+exp(2)^2*b^2*d^2*exp(1)^2-2*c*b*d^3*exp(1)^5+4*c*exp(2)*b*d^3*exp(1)^3-2*c*exp(2)^2*b*d^3*exp(1)+c^2*d^4*exp(1)^4-2*c^2*exp(2)*d^4*exp(1)^2+c^2*exp(2)^2*d^4)/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))*atan((-d*sqrt(-c*exp(2))+(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*exp(1))/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))))","F(-2)",0
2215,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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-3*c^3*exp(2)^2*d^6*exp(1)^2+c^3*exp(2)^3*d^6)/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))*atan((-d*sqrt(-c*exp(2))+(sqrt(-c*exp(2)*x^2-b*exp(2)*x+c*d^2-b*d*exp(1))-sqrt(-c*exp(2))*x)*exp(1))/sqrt(b*d*exp(1)^3-c*d^2*exp(1)^2+c*d^2*exp(2)-b*d*exp(1)*exp(2))))","F(-2)",0
2216,0,0,0,0.000000," ","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=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2217,1,623,0,0.598145," ","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=""giac"")","\frac{\sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left({\left({\left(\frac{2 \, {\left(4 \, c^{4} d^{2} g e^{5} - 4 \, b c^{3} d g e^{6} + b^{2} c^{2} g e^{7}\right)} x}{4 \, c^{5} d^{2} e^{4} - 4 \, b c^{4} d e^{5} + b^{2} c^{3} e^{6}} + \frac{48 \, c^{4} d^{3} g e^{4} + 16 \, c^{4} d^{2} f e^{5} - 68 \, b c^{3} d^{2} g e^{5} - 16 \, b c^{3} d f e^{6} + 32 \, b^{2} c^{2} d g e^{6} + 4 \, b^{2} c^{2} f e^{7} - 5 \, b^{3} c g e^{7}}{4 \, c^{5} d^{2} e^{4} - 4 \, b c^{4} d e^{5} + b^{2} c^{3} e^{6}}\right)} x - \frac{72 \, c^{4} d^{4} g e^{3} + 64 \, c^{4} d^{3} f e^{4} - 224 \, b c^{3} d^{3} g e^{4} - 112 \, b c^{3} d^{2} f e^{5} + 230 \, b^{2} c^{2} d^{2} g e^{5} + 64 \, b^{2} c^{2} d f e^{6} - 98 \, b^{3} c d g e^{6} - 12 \, b^{3} c f e^{7} + 15 \, b^{4} g e^{7}}{4 \, c^{5} d^{2} e^{4} - 4 \, b c^{4} d e^{5} + b^{2} c^{3} e^{6}}\right)} x - \frac{112 \, c^{4} d^{5} g e^{2} + 80 \, c^{4} d^{4} f e^{3} - 284 \, b c^{3} d^{4} g e^{3} - 128 \, b c^{3} d^{3} f e^{4} + 260 \, b^{2} c^{2} d^{3} g e^{4} + 68 \, b^{2} c^{2} d^{2} f e^{5} - 103 \, b^{3} c d^{2} g e^{5} - 12 \, b^{3} c d f e^{6} + 15 \, b^{4} d g e^{6}}{4 \, c^{5} d^{2} e^{4} - 4 \, b c^{4} d e^{5} + b^{2} c^{3} e^{6}}\right)}}{4 \, {\left(c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e\right)}} - \frac{3 \, {\left(12 \, c^{2} d^{2} g + 8 \, c^{2} d f e - 16 \, b c d g e - 4 \, b c f e^{2} + 5 \, b^{2} g e^{2}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{8 \, c^{4}}"," ",0,"1/4*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(((2*(4*c^4*d^2*g*e^5 - 4*b*c^3*d*g*e^6 + b^2*c^2*g*e^7)*x/(4*c^5*d^2*e^4 - 4*b*c^4*d*e^5 + b^2*c^3*e^6) + (48*c^4*d^3*g*e^4 + 16*c^4*d^2*f*e^5 - 68*b*c^3*d^2*g*e^5 - 16*b*c^3*d*f*e^6 + 32*b^2*c^2*d*g*e^6 + 4*b^2*c^2*f*e^7 - 5*b^3*c*g*e^7)/(4*c^5*d^2*e^4 - 4*b*c^4*d*e^5 + b^2*c^3*e^6))*x - (72*c^4*d^4*g*e^3 + 64*c^4*d^3*f*e^4 - 224*b*c^3*d^3*g*e^4 - 112*b*c^3*d^2*f*e^5 + 230*b^2*c^2*d^2*g*e^5 + 64*b^2*c^2*d*f*e^6 - 98*b^3*c*d*g*e^6 - 12*b^3*c*f*e^7 + 15*b^4*g*e^7)/(4*c^5*d^2*e^4 - 4*b*c^4*d*e^5 + b^2*c^3*e^6))*x - (112*c^4*d^5*g*e^2 + 80*c^4*d^4*f*e^3 - 284*b*c^3*d^4*g*e^3 - 128*b*c^3*d^3*f*e^4 + 260*b^2*c^2*d^3*g*e^4 + 68*b^2*c^2*d^2*f*e^5 - 103*b^3*c*d^2*g*e^5 - 12*b^3*c*d*f*e^6 + 15*b^4*d*g*e^6)/(4*c^5*d^2*e^4 - 4*b*c^4*d*e^5 + b^2*c^3*e^6))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e) - 3/8*(12*c^2*d^2*g + 8*c^2*d*f*e - 16*b*c*d*g*e - 4*b*c*f*e^2 + 5*b^2*g*e^2)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^4","B",0
2218,1,427,0,0.615601," ","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=""giac"")","\frac{\sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left({\left(\frac{{\left(4 \, c^{3} d^{2} g e^{3} - 4 \, b c^{2} d g e^{4} + b^{2} c g e^{5}\right)} x}{4 \, c^{4} d^{2} e^{3} - 4 \, b c^{3} d e^{4} + b^{2} c^{2} e^{5}} - \frac{8 \, c^{3} d^{3} g e^{2} + 8 \, c^{3} d^{2} f e^{3} - 20 \, b c^{2} d^{2} g e^{3} - 8 \, b c^{2} d f e^{4} + 14 \, b^{2} c d g e^{4} + 2 \, b^{2} c f e^{5} - 3 \, b^{3} g e^{5}}{4 \, c^{4} d^{2} e^{3} - 4 \, b c^{3} d e^{4} + b^{2} c^{2} e^{5}}\right)} x - \frac{12 \, c^{3} d^{4} g e + 8 \, c^{3} d^{3} f e^{2} - 24 \, b c^{2} d^{3} g e^{2} - 8 \, b c^{2} d^{2} f e^{3} + 15 \, b^{2} c d^{2} g e^{3} + 2 \, b^{2} c d f e^{4} - 3 \, b^{3} d g e^{4}}{4 \, c^{4} d^{2} e^{3} - 4 \, b c^{3} d e^{4} + b^{2} c^{2} e^{5}}\right)}}{c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e} - \frac{{\left(4 \, c d g + 2 \, c f e - 3 \, b g e\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{2 \, c^{3}}"," ",0,"sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(((4*c^3*d^2*g*e^3 - 4*b*c^2*d*g*e^4 + b^2*c*g*e^5)*x/(4*c^4*d^2*e^3 - 4*b*c^3*d*e^4 + b^2*c^2*e^5) - (8*c^3*d^3*g*e^2 + 8*c^3*d^2*f*e^3 - 20*b*c^2*d^2*g*e^3 - 8*b*c^2*d*f*e^4 + 14*b^2*c*d*g*e^4 + 2*b^2*c*f*e^5 - 3*b^3*g*e^5)/(4*c^4*d^2*e^3 - 4*b*c^3*d*e^4 + b^2*c^2*e^5))*x - (12*c^3*d^4*g*e + 8*c^3*d^3*f*e^2 - 24*b*c^2*d^3*g*e^2 - 8*b*c^2*d^2*f*e^3 + 15*b^2*c*d^2*g*e^3 + 2*b^2*c*d*f*e^4 - 3*b^3*d*g*e^4)/(4*c^4*d^2*e^3 - 4*b*c^3*d*e^4 + b^2*c^2*e^5))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e) - 1/2*(4*c*d*g + 2*c*f*e - 3*b*g*e)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^3","B",0
2219,1,282,0,0.564326," ","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=""giac"")","-\frac{\sqrt{-c e^{2}} g e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{c^{2}} - \frac{2 \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left(\frac{{\left(2 \, c^{2} d^{2} g e^{2} + 2 \, c^{2} d f e^{3} - 3 \, b c d g e^{3} - b c f e^{4} + b^{2} g e^{4}\right)} x}{4 \, c^{3} d^{2} e^{3} - 4 \, b c^{2} d e^{4} + b^{2} c e^{5}} + \frac{2 \, c^{2} d^{3} g e + 2 \, c^{2} d^{2} f e^{2} - 3 \, b c d^{2} g e^{2} - b c d f e^{3} + b^{2} d g e^{3}}{4 \, c^{3} d^{2} e^{3} - 4 \, b c^{2} d e^{4} + b^{2} c e^{5}}\right)}}{c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e}"," ",0,"-sqrt(-c*e^2)*g*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^2 - 2*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*((2*c^2*d^2*g*e^2 + 2*c^2*d*f*e^3 - 3*b*c*d*g*e^3 - b*c*f*e^4 + b^2*g*e^4)*x/(4*c^3*d^2*e^3 - 4*b*c^2*d*e^4 + b^2*c*e^5) + (2*c^2*d^3*g*e + 2*c^2*d^2*f*e^2 - 3*b*c*d^2*g*e^2 - b*c*d*f*e^3 + b^2*d*g*e^3)/(4*c^3*d^2*e^3 - 4*b*c^2*d*e^4 + b^2*c*e^5))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e)","B",0
2220,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
2221,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^2/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2222,-2,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
2223,1,1460,0,0.943995," ","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=""giac"")","-\frac{\sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left({\left({\left({\left(3 \, {\left(\frac{2 \, {\left(16 \, c^{7} d^{4} g e^{11} - 32 \, b c^{6} d^{3} g e^{12} + 24 \, b^{2} c^{5} d^{2} g e^{13} - 8 \, b^{3} c^{4} d g e^{14} + b^{4} c^{3} g e^{15}\right)} x}{16 \, c^{8} d^{4} e^{8} - 32 \, b c^{7} d^{3} e^{9} + 24 \, b^{2} c^{6} d^{2} e^{10} - 8 \, b^{3} c^{5} d e^{11} + b^{4} c^{4} e^{12}} + \frac{320 \, c^{7} d^{5} g e^{10} + 64 \, c^{7} d^{4} f e^{11} - 752 \, b c^{6} d^{4} g e^{11} - 128 \, b c^{6} d^{3} f e^{12} + 704 \, b^{2} c^{5} d^{3} g e^{12} + 96 \, b^{2} c^{5} d^{2} f e^{13} - 328 \, b^{3} c^{4} d^{2} g e^{13} - 32 \, b^{3} c^{4} d f e^{14} + 76 \, b^{4} c^{3} d g e^{14} + 4 \, b^{4} c^{3} f e^{15} - 7 \, b^{5} c^{2} g e^{15}}{16 \, c^{8} d^{4} e^{8} - 32 \, b c^{7} d^{3} e^{9} + 24 \, b^{2} c^{6} d^{2} e^{10} - 8 \, b^{3} c^{5} d e^{11} + b^{4} c^{4} e^{12}}\right)} x - \frac{4 \, {\left(880 \, c^{7} d^{6} g e^{9} + 448 \, c^{7} d^{5} f e^{10} - 3344 \, b c^{6} d^{5} g e^{10} - 1216 \, b c^{6} d^{4} f e^{11} + 5048 \, b^{2} c^{5} d^{4} g e^{11} + 1312 \, b^{2} c^{5} d^{3} f e^{12} - 3936 \, b^{3} c^{4} d^{3} g e^{12} - 704 \, b^{3} c^{4} d^{2} f e^{13} + 1687 \, b^{4} c^{3} d^{2} g e^{13} + 188 \, b^{4} c^{3} d f e^{14} - 379 \, b^{5} c^{2} d g e^{14} - 20 \, b^{5} c^{2} f e^{15} + 35 \, b^{6} c g e^{15}\right)}}{16 \, c^{8} d^{4} e^{8} - 32 \, b c^{7} d^{3} e^{9} + 24 \, b^{2} c^{6} d^{2} e^{10} - 8 \, b^{3} c^{5} d e^{11} + b^{4} c^{4} e^{12}}\right)} x - \frac{3 \, {\left(1920 \, c^{7} d^{7} g e^{8} + 896 \, c^{7} d^{6} f e^{9} - 5408 \, b c^{6} d^{6} g e^{9} - 1792 \, b c^{6} d^{5} f e^{10} + 5216 \, b^{2} c^{5} d^{5} g e^{10} + 1024 \, b^{2} c^{5} d^{4} f e^{11} - 1152 \, b^{3} c^{4} d^{4} g e^{11} + 192 \, b^{3} c^{4} d^{3} f e^{12} - 1416 \, b^{4} c^{3} d^{3} g e^{12} - 424 \, b^{4} c^{3} d^{2} f e^{13} + 1142 \, b^{5} c^{2} d^{2} g e^{13} + 160 \, b^{5} c^{2} d f e^{14} - 330 \, b^{6} c d g e^{14} - 20 \, b^{6} c f e^{15} + 35 \, b^{7} g e^{15}\right)}}{16 \, c^{8} d^{4} e^{8} - 32 \, b c^{7} d^{3} e^{9} + 24 \, b^{2} c^{6} d^{2} e^{10} - 8 \, b^{3} c^{5} d e^{11} + b^{4} c^{4} e^{12}}\right)} x + \frac{6 \, {\left(400 \, c^{7} d^{8} g e^{7} + 128 \, c^{7} d^{7} f e^{8} - 2624 \, b c^{6} d^{7} g e^{8} - 896 \, b c^{6} d^{6} f e^{9} + 6168 \, b^{2} c^{5} d^{6} g e^{9} + 1792 \, b^{2} c^{5} d^{5} f e^{10} - 7336 \, b^{3} c^{4} d^{5} g e^{10} - 1664 \, b^{3} c^{4} d^{4} f e^{11} + 4937 \, b^{4} c^{3} d^{4} g e^{11} + 808 \, b^{4} c^{3} d^{3} f e^{12} - 1914 \, b^{5} c^{2} d^{3} g e^{12} - 200 \, b^{5} c^{2} d^{2} f e^{13} + 400 \, b^{6} c d^{2} g e^{13} + 20 \, b^{6} c d f e^{14} - 35 \, b^{7} d g e^{14}\right)}}{16 \, c^{8} d^{4} e^{8} - 32 \, b c^{7} d^{3} e^{9} + 24 \, b^{2} c^{6} d^{2} e^{10} - 8 \, b^{3} c^{5} d e^{11} + b^{4} c^{4} e^{12}}\right)} x + \frac{3776 \, c^{7} d^{9} g e^{6} + 1472 \, c^{7} d^{8} f e^{7} - 16528 \, b c^{6} d^{8} g e^{7} - 5504 \, b c^{6} d^{7} f e^{8} + 30496 \, b^{2} c^{5} d^{7} g e^{8} + 8288 \, b^{2} c^{5} d^{6} f e^{9} - 30792 \, b^{3} c^{4} d^{6} g e^{9} - 6496 \, b^{3} c^{4} d^{5} f e^{10} + 18404 \, b^{4} c^{3} d^{5} g e^{10} + 2812 \, b^{4} c^{3} d^{4} f e^{11} - 6521 \, b^{5} c^{2} d^{4} g e^{11} - 640 \, b^{5} c^{2} d^{3} f e^{12} + 1270 \, b^{6} c d^{3} g e^{12} + 60 \, b^{6} c d^{2} f e^{13} - 105 \, b^{7} d^{2} g e^{13}}{16 \, c^{8} d^{4} e^{8} - 32 \, b c^{7} d^{3} e^{9} + 24 \, b^{2} c^{6} d^{2} e^{10} - 8 \, b^{3} c^{5} d e^{11} + b^{4} c^{4} e^{12}}\right)}}{12 \, {\left(c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e\right)}^{2}} + \frac{5 \, {\left(20 \, c^{2} d^{2} g + 8 \, c^{2} d f e - 24 \, b c d g e - 4 \, b c f e^{2} + 7 \, b^{2} g e^{2}\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{8 \, c^{5}}"," ",0,"-1/12*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*((((3*(2*(16*c^7*d^4*g*e^11 - 32*b*c^6*d^3*g*e^12 + 24*b^2*c^5*d^2*g*e^13 - 8*b^3*c^4*d*g*e^14 + b^4*c^3*g*e^15)*x/(16*c^8*d^4*e^8 - 32*b*c^7*d^3*e^9 + 24*b^2*c^6*d^2*e^10 - 8*b^3*c^5*d*e^11 + b^4*c^4*e^12) + (320*c^7*d^5*g*e^10 + 64*c^7*d^4*f*e^11 - 752*b*c^6*d^4*g*e^11 - 128*b*c^6*d^3*f*e^12 + 704*b^2*c^5*d^3*g*e^12 + 96*b^2*c^5*d^2*f*e^13 - 328*b^3*c^4*d^2*g*e^13 - 32*b^3*c^4*d*f*e^14 + 76*b^4*c^3*d*g*e^14 + 4*b^4*c^3*f*e^15 - 7*b^5*c^2*g*e^15)/(16*c^8*d^4*e^8 - 32*b*c^7*d^3*e^9 + 24*b^2*c^6*d^2*e^10 - 8*b^3*c^5*d*e^11 + b^4*c^4*e^12))*x - 4*(880*c^7*d^6*g*e^9 + 448*c^7*d^5*f*e^10 - 3344*b*c^6*d^5*g*e^10 - 1216*b*c^6*d^4*f*e^11 + 5048*b^2*c^5*d^4*g*e^11 + 1312*b^2*c^5*d^3*f*e^12 - 3936*b^3*c^4*d^3*g*e^12 - 704*b^3*c^4*d^2*f*e^13 + 1687*b^4*c^3*d^2*g*e^13 + 188*b^4*c^3*d*f*e^14 - 379*b^5*c^2*d*g*e^14 - 20*b^5*c^2*f*e^15 + 35*b^6*c*g*e^15)/(16*c^8*d^4*e^8 - 32*b*c^7*d^3*e^9 + 24*b^2*c^6*d^2*e^10 - 8*b^3*c^5*d*e^11 + b^4*c^4*e^12))*x - 3*(1920*c^7*d^7*g*e^8 + 896*c^7*d^6*f*e^9 - 5408*b*c^6*d^6*g*e^9 - 1792*b*c^6*d^5*f*e^10 + 5216*b^2*c^5*d^5*g*e^10 + 1024*b^2*c^5*d^4*f*e^11 - 1152*b^3*c^4*d^4*g*e^11 + 192*b^3*c^4*d^3*f*e^12 - 1416*b^4*c^3*d^3*g*e^12 - 424*b^4*c^3*d^2*f*e^13 + 1142*b^5*c^2*d^2*g*e^13 + 160*b^5*c^2*d*f*e^14 - 330*b^6*c*d*g*e^14 - 20*b^6*c*f*e^15 + 35*b^7*g*e^15)/(16*c^8*d^4*e^8 - 32*b*c^7*d^3*e^9 + 24*b^2*c^6*d^2*e^10 - 8*b^3*c^5*d*e^11 + b^4*c^4*e^12))*x + 6*(400*c^7*d^8*g*e^7 + 128*c^7*d^7*f*e^8 - 2624*b*c^6*d^7*g*e^8 - 896*b*c^6*d^6*f*e^9 + 6168*b^2*c^5*d^6*g*e^9 + 1792*b^2*c^5*d^5*f*e^10 - 7336*b^3*c^4*d^5*g*e^10 - 1664*b^3*c^4*d^4*f*e^11 + 4937*b^4*c^3*d^4*g*e^11 + 808*b^4*c^3*d^3*f*e^12 - 1914*b^5*c^2*d^3*g*e^12 - 200*b^5*c^2*d^2*f*e^13 + 400*b^6*c*d^2*g*e^13 + 20*b^6*c*d*f*e^14 - 35*b^7*d*g*e^14)/(16*c^8*d^4*e^8 - 32*b*c^7*d^3*e^9 + 24*b^2*c^6*d^2*e^10 - 8*b^3*c^5*d*e^11 + b^4*c^4*e^12))*x + (3776*c^7*d^9*g*e^6 + 1472*c^7*d^8*f*e^7 - 16528*b*c^6*d^8*g*e^7 - 5504*b*c^6*d^7*f*e^8 + 30496*b^2*c^5*d^7*g*e^8 + 8288*b^2*c^5*d^6*f*e^9 - 30792*b^3*c^4*d^6*g*e^9 - 6496*b^3*c^4*d^5*f*e^10 + 18404*b^4*c^3*d^5*g*e^10 + 2812*b^4*c^3*d^4*f*e^11 - 6521*b^5*c^2*d^4*g*e^11 - 640*b^5*c^2*d^3*f*e^12 + 1270*b^6*c*d^3*g*e^12 + 60*b^6*c*d^2*f*e^13 - 105*b^7*d^2*g*e^13)/(16*c^8*d^4*e^8 - 32*b*c^7*d^3*e^9 + 24*b^2*c^6*d^2*e^10 - 8*b^3*c^5*d*e^11 + b^4*c^4*e^12))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e)^2 + 5/8*(20*c^2*d^2*g + 8*c^2*d*f*e - 24*b*c*d*g*e - 4*b*c*f*e^2 + 7*b^2*g*e^2)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^5","B",0
2224,1,1116,0,0.866116," ","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=""giac"")","-\frac{\sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left({\left({\left({\left(\frac{3 \, {\left(16 \, c^{6} d^{4} g e^{8} - 32 \, b c^{5} d^{3} g e^{9} + 24 \, b^{2} c^{4} d^{2} g e^{10} - 8 \, b^{3} c^{3} d g e^{11} + b^{4} c^{2} g e^{12}\right)} x}{16 \, c^{7} d^{4} e^{6} - 32 \, b c^{6} d^{3} e^{7} + 24 \, b^{2} c^{5} d^{2} e^{8} - 8 \, b^{3} c^{4} d e^{9} + b^{4} c^{3} e^{10}} - \frac{4 \, {\left(80 \, c^{6} d^{5} g e^{7} + 32 \, c^{6} d^{4} f e^{8} - 240 \, b c^{5} d^{4} g e^{8} - 64 \, b c^{5} d^{3} f e^{9} + 280 \, b^{2} c^{4} d^{3} g e^{9} + 48 \, b^{2} c^{4} d^{2} f e^{10} - 160 \, b^{3} c^{3} d^{2} g e^{10} - 16 \, b^{3} c^{3} d f e^{11} + 45 \, b^{4} c^{2} d g e^{11} + 2 \, b^{4} c^{2} f e^{12} - 5 \, b^{5} c g e^{12}\right)}}{16 \, c^{7} d^{4} e^{6} - 32 \, b c^{6} d^{3} e^{7} + 24 \, b^{2} c^{5} d^{2} e^{8} - 8 \, b^{3} c^{4} d e^{9} + b^{4} c^{3} e^{10}}\right)} x - \frac{3 \, {\left(160 \, c^{6} d^{6} g e^{6} + 64 \, c^{6} d^{5} f e^{7} - 352 \, b c^{5} d^{5} g e^{7} - 96 \, b c^{5} d^{4} f e^{8} + 224 \, b^{2} c^{4} d^{4} g e^{8} + 32 \, b^{2} c^{4} d^{3} f e^{9} + 32 \, b^{3} c^{3} d^{3} g e^{9} + 16 \, b^{3} c^{3} d^{2} f e^{10} - 94 \, b^{4} c^{2} d^{2} g e^{10} - 12 \, b^{4} c^{2} d f e^{11} + 38 \, b^{5} c d g e^{11} + 2 \, b^{5} c f e^{12} - 5 \, b^{6} g e^{12}\right)}}{16 \, c^{7} d^{4} e^{6} - 32 \, b c^{6} d^{3} e^{7} + 24 \, b^{2} c^{5} d^{2} e^{8} - 8 \, b^{3} c^{4} d e^{9} + b^{4} c^{3} e^{10}}\right)} x + \frac{6 \, {\left(32 \, c^{6} d^{7} g e^{5} - 192 \, b c^{5} d^{6} g e^{6} - 32 \, b c^{5} d^{5} f e^{7} + 384 \, b^{2} c^{4} d^{5} g e^{7} + 64 \, b^{2} c^{4} d^{4} f e^{8} - 368 \, b^{3} c^{3} d^{4} g e^{8} - 48 \, b^{3} c^{3} d^{3} f e^{9} + 186 \, b^{4} c^{2} d^{3} g e^{9} + 16 \, b^{4} c^{2} d^{2} f e^{10} - 48 \, b^{5} c d^{2} g e^{10} - 2 \, b^{5} c d f e^{11} + 5 \, b^{6} d g e^{11}\right)}}{16 \, c^{7} d^{4} e^{6} - 32 \, b c^{6} d^{3} e^{7} + 24 \, b^{2} c^{5} d^{2} e^{8} - 8 \, b^{3} c^{4} d e^{9} + b^{4} c^{3} e^{10}}\right)} x + \frac{304 \, c^{6} d^{8} g e^{4} + 64 \, c^{6} d^{7} f e^{5} - 1152 \, b c^{5} d^{7} g e^{5} - 224 \, b c^{5} d^{6} f e^{6} + 1784 \, b^{2} c^{4} d^{6} g e^{6} + 288 \, b^{2} c^{4} d^{5} f e^{7} - 1448 \, b^{3} c^{3} d^{5} g e^{7} - 176 \, b^{3} c^{3} d^{4} f e^{8} + 651 \, b^{4} c^{2} d^{4} g e^{8} + 52 \, b^{4} c^{2} d^{3} f e^{9} - 154 \, b^{5} c d^{3} g e^{9} - 6 \, b^{5} c d^{2} f e^{10} + 15 \, b^{6} d^{2} g e^{10}}{16 \, c^{7} d^{4} e^{6} - 32 \, b c^{6} d^{3} e^{7} + 24 \, b^{2} c^{5} d^{2} e^{8} - 8 \, b^{3} c^{4} d e^{9} + b^{4} c^{3} e^{10}}\right)}}{3 \, {\left(c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e\right)}^{2}} + \frac{{\left(8 \, c d g + 2 \, c f e - 5 \, b g e\right)} \sqrt{-c e^{2}} e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{2 \, c^{4}}"," ",0,"-1/3*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*((((3*(16*c^6*d^4*g*e^8 - 32*b*c^5*d^3*g*e^9 + 24*b^2*c^4*d^2*g*e^10 - 8*b^3*c^3*d*g*e^11 + b^4*c^2*g*e^12)*x/(16*c^7*d^4*e^6 - 32*b*c^6*d^3*e^7 + 24*b^2*c^5*d^2*e^8 - 8*b^3*c^4*d*e^9 + b^4*c^3*e^10) - 4*(80*c^6*d^5*g*e^7 + 32*c^6*d^4*f*e^8 - 240*b*c^5*d^4*g*e^8 - 64*b*c^5*d^3*f*e^9 + 280*b^2*c^4*d^3*g*e^9 + 48*b^2*c^4*d^2*f*e^10 - 160*b^3*c^3*d^2*g*e^10 - 16*b^3*c^3*d*f*e^11 + 45*b^4*c^2*d*g*e^11 + 2*b^4*c^2*f*e^12 - 5*b^5*c*g*e^12)/(16*c^7*d^4*e^6 - 32*b*c^6*d^3*e^7 + 24*b^2*c^5*d^2*e^8 - 8*b^3*c^4*d*e^9 + b^4*c^3*e^10))*x - 3*(160*c^6*d^6*g*e^6 + 64*c^6*d^5*f*e^7 - 352*b*c^5*d^5*g*e^7 - 96*b*c^5*d^4*f*e^8 + 224*b^2*c^4*d^4*g*e^8 + 32*b^2*c^4*d^3*f*e^9 + 32*b^3*c^3*d^3*g*e^9 + 16*b^3*c^3*d^2*f*e^10 - 94*b^4*c^2*d^2*g*e^10 - 12*b^4*c^2*d*f*e^11 + 38*b^5*c*d*g*e^11 + 2*b^5*c*f*e^12 - 5*b^6*g*e^12)/(16*c^7*d^4*e^6 - 32*b*c^6*d^3*e^7 + 24*b^2*c^5*d^2*e^8 - 8*b^3*c^4*d*e^9 + b^4*c^3*e^10))*x + 6*(32*c^6*d^7*g*e^5 - 192*b*c^5*d^6*g*e^6 - 32*b*c^5*d^5*f*e^7 + 384*b^2*c^4*d^5*g*e^7 + 64*b^2*c^4*d^4*f*e^8 - 368*b^3*c^3*d^4*g*e^8 - 48*b^3*c^3*d^3*f*e^9 + 186*b^4*c^2*d^3*g*e^9 + 16*b^4*c^2*d^2*f*e^10 - 48*b^5*c*d^2*g*e^10 - 2*b^5*c*d*f*e^11 + 5*b^6*d*g*e^11)/(16*c^7*d^4*e^6 - 32*b*c^6*d^3*e^7 + 24*b^2*c^5*d^2*e^8 - 8*b^3*c^4*d*e^9 + b^4*c^3*e^10))*x + (304*c^6*d^8*g*e^4 + 64*c^6*d^7*f*e^5 - 1152*b*c^5*d^7*g*e^5 - 224*b*c^5*d^6*f*e^6 + 1784*b^2*c^4*d^6*g*e^6 + 288*b^2*c^4*d^5*f*e^7 - 1448*b^3*c^3*d^5*g*e^7 - 176*b^3*c^3*d^4*f*e^8 + 651*b^4*c^2*d^4*g*e^8 + 52*b^4*c^2*d^3*f*e^9 - 154*b^5*c*d^3*g*e^9 - 6*b^5*c*d^2*f*e^10 + 15*b^6*d^2*g*e^10)/(16*c^7*d^4*e^6 - 32*b*c^6*d^3*e^7 + 24*b^2*c^5*d^2*e^8 - 8*b^3*c^4*d*e^9 + b^4*c^3*e^10))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e)^2 + 1/2*(8*c*d*g + 2*c*f*e - 5*b*g*e)*sqrt(-c*e^2)*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^4","B",0
2225,1,841,0,0.891327," ","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=""giac"")","\frac{\sqrt{-c e^{2}} g e^{\left(-3\right)} \log\left({\left| -2 \, {\left(\sqrt{-c e^{2}} x - \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e}\right)} c - \sqrt{-c e^{2}} b \right|}\right)}{c^{3}} + \frac{2 \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left({\left({\left(\frac{{\left(56 \, c^{5} d^{4} g e^{4} + 8 \, c^{5} d^{3} f e^{5} - 116 \, b c^{4} d^{3} g e^{5} - 12 \, b c^{4} d^{2} f e^{6} + 90 \, b^{2} c^{3} d^{2} g e^{6} + 6 \, b^{2} c^{3} d f e^{7} - 31 \, b^{3} c^{2} d g e^{7} - b^{3} c^{2} f e^{8} + 4 \, b^{4} c g e^{8}\right)} x}{16 \, c^{6} d^{4} e^{3} - 32 \, b c^{5} d^{3} e^{4} + 24 \, b^{2} c^{4} d^{2} e^{5} - 8 \, b^{3} c^{3} d e^{6} + b^{4} c^{2} e^{7}} + \frac{3 \, {\left(24 \, c^{5} d^{5} g e^{3} + 8 \, c^{5} d^{4} f e^{4} - 36 \, b c^{4} d^{4} g e^{4} - 12 \, b c^{4} d^{3} f e^{5} + 10 \, b^{2} c^{3} d^{3} g e^{5} + 6 \, b^{2} c^{3} d^{2} f e^{6} + 9 \, b^{3} c^{2} d^{2} g e^{6} - b^{3} c^{2} d f e^{7} - 6 \, b^{4} c d g e^{7} + b^{5} g e^{8}\right)}}{16 \, c^{6} d^{4} e^{3} - 32 \, b c^{5} d^{3} e^{4} + 24 \, b^{2} c^{4} d^{2} e^{5} - 8 \, b^{3} c^{3} d e^{6} + b^{4} c^{2} e^{7}}\right)} x - \frac{3 \, {\left(8 \, c^{5} d^{6} g e^{2} - 8 \, c^{5} d^{5} f e^{3} - 44 \, b c^{4} d^{5} g e^{3} + 12 \, b c^{4} d^{4} f e^{4} + 70 \, b^{2} c^{3} d^{4} g e^{4} - 6 \, b^{2} c^{3} d^{3} f e^{5} - 49 \, b^{3} c^{2} d^{3} g e^{5} + b^{3} c^{2} d^{2} f e^{6} + 16 \, b^{4} c d^{2} g e^{6} - 2 \, b^{5} d g e^{7}\right)}}{16 \, c^{6} d^{4} e^{3} - 32 \, b c^{5} d^{3} e^{4} + 24 \, b^{2} c^{4} d^{2} e^{5} - 8 \, b^{3} c^{3} d e^{6} + b^{4} c^{2} e^{7}}\right)} x - \frac{40 \, c^{5} d^{7} g e - 8 \, c^{5} d^{6} f e^{2} - 124 \, b c^{4} d^{6} g e^{2} + 12 \, b c^{4} d^{5} f e^{3} + 150 \, b^{2} c^{3} d^{5} g e^{3} - 6 \, b^{2} c^{3} d^{4} f e^{4} - 89 \, b^{3} c^{2} d^{4} g e^{4} + b^{3} c^{2} d^{3} f e^{5} + 26 \, b^{4} c d^{3} g e^{5} - 3 \, b^{5} d^{2} g e^{6}}{16 \, c^{6} d^{4} e^{3} - 32 \, b c^{5} d^{3} e^{4} + 24 \, b^{2} c^{4} d^{2} e^{5} - 8 \, b^{3} c^{3} d e^{6} + b^{4} c^{2} e^{7}}\right)}}{3 \, {\left(c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e\right)}^{2}}"," ",0,"sqrt(-c*e^2)*g*e^(-3)*log(abs(-2*(sqrt(-c*e^2)*x - sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e))*c - sqrt(-c*e^2)*b))/c^3 + 2/3*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*((((56*c^5*d^4*g*e^4 + 8*c^5*d^3*f*e^5 - 116*b*c^4*d^3*g*e^5 - 12*b*c^4*d^2*f*e^6 + 90*b^2*c^3*d^2*g*e^6 + 6*b^2*c^3*d*f*e^7 - 31*b^3*c^2*d*g*e^7 - b^3*c^2*f*e^8 + 4*b^4*c*g*e^8)*x/(16*c^6*d^4*e^3 - 32*b*c^5*d^3*e^4 + 24*b^2*c^4*d^2*e^5 - 8*b^3*c^3*d*e^6 + b^4*c^2*e^7) + 3*(24*c^5*d^5*g*e^3 + 8*c^5*d^4*f*e^4 - 36*b*c^4*d^4*g*e^4 - 12*b*c^4*d^3*f*e^5 + 10*b^2*c^3*d^3*g*e^5 + 6*b^2*c^3*d^2*f*e^6 + 9*b^3*c^2*d^2*g*e^6 - b^3*c^2*d*f*e^7 - 6*b^4*c*d*g*e^7 + b^5*g*e^8)/(16*c^6*d^4*e^3 - 32*b*c^5*d^3*e^4 + 24*b^2*c^4*d^2*e^5 - 8*b^3*c^3*d*e^6 + b^4*c^2*e^7))*x - 3*(8*c^5*d^6*g*e^2 - 8*c^5*d^5*f*e^3 - 44*b*c^4*d^5*g*e^3 + 12*b*c^4*d^4*f*e^4 + 70*b^2*c^3*d^4*g*e^4 - 6*b^2*c^3*d^3*f*e^5 - 49*b^3*c^2*d^3*g*e^5 + b^3*c^2*d^2*f*e^6 + 16*b^4*c*d^2*g*e^6 - 2*b^5*d*g*e^7)/(16*c^6*d^4*e^3 - 32*b*c^5*d^3*e^4 + 24*b^2*c^4*d^2*e^5 - 8*b^3*c^3*d*e^6 + b^4*c^2*e^7))*x - (40*c^5*d^7*g*e - 8*c^5*d^6*f*e^2 - 124*b*c^4*d^6*g*e^2 + 12*b*c^4*d^5*f*e^3 + 150*b^2*c^3*d^5*g*e^3 - 6*b^2*c^3*d^4*f*e^4 - 89*b^3*c^2*d^4*g*e^4 + b^3*c^2*d^3*f*e^5 + 26*b^4*c*d^3*g*e^5 - 3*b^5*d^2*g*e^6)/(16*c^6*d^4*e^3 - 32*b*c^5*d^3*e^4 + 24*b^2*c^4*d^2*e^5 - 8*b^3*c^3*d*e^6 + b^4*c^2*e^7))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e)^2","B",0
2226,1,587,0,0.732950," ","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=""giac"")","\frac{2 \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left({\left({\left(\frac{{\left(16 \, c^{3} d^{3} g e^{3} - 8 \, c^{3} d^{2} f e^{4} - 20 \, b c^{2} d^{2} g e^{4} + 8 \, b c^{2} d f e^{5} + 8 \, b^{2} c d g e^{5} - 2 \, b^{2} c f e^{6} - b^{3} g e^{6}\right)} x}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}} + \frac{3 \, {\left(8 \, c^{3} d^{4} g e^{2} - 8 \, b c^{2} d^{3} g e^{3} - 4 \, b c^{2} d^{2} f e^{4} + 2 \, b^{2} c d^{2} g e^{4} + 4 \, b^{2} c d f e^{5} - b^{3} f e^{6}\right)}}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}}\right)} x + \frac{3 \, {\left(8 \, c^{3} d^{4} f e^{2} + 4 \, b c^{2} d^{4} g e^{2} - 16 \, b c^{2} d^{3} f e^{3} - 4 \, b^{2} c d^{3} g e^{3} + 10 \, b^{2} c d^{2} f e^{4} + b^{3} d^{2} g e^{4} - 2 \, b^{3} d f e^{5}\right)}}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}}\right)} x - \frac{8 \, c^{3} d^{6} g - 16 \, c^{3} d^{5} f e - 16 \, b c^{2} d^{5} g e + 28 \, b c^{2} d^{4} f e^{2} + 10 \, b^{2} c d^{4} g e^{2} - 16 \, b^{2} c d^{3} f e^{3} - 2 \, b^{3} d^{3} g e^{3} + 3 \, b^{3} d^{2} f e^{4}}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}}\right)}}{3 \, {\left(c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e\right)}^{2}}"," ",0,"2/3*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*((((16*c^3*d^3*g*e^3 - 8*c^3*d^2*f*e^4 - 20*b*c^2*d^2*g*e^4 + 8*b*c^2*d*f*e^5 + 8*b^2*c*d*g*e^5 - 2*b^2*c*f*e^6 - b^3*g*e^6)*x/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6) + 3*(8*c^3*d^4*g*e^2 - 8*b*c^2*d^3*g*e^3 - 4*b*c^2*d^2*f*e^4 + 2*b^2*c*d^2*g*e^4 + 4*b^2*c*d*f*e^5 - b^3*f*e^6)/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6))*x + 3*(8*c^3*d^4*f*e^2 + 4*b*c^2*d^4*g*e^2 - 16*b*c^2*d^3*f*e^3 - 4*b^2*c*d^3*g*e^3 + 10*b^2*c*d^2*f*e^4 + b^3*d^2*g*e^4 - 2*b^3*d*f*e^5)/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6))*x - (8*c^3*d^6*g - 16*c^3*d^5*f*e - 16*b*c^2*d^5*g*e + 28*b*c^2*d^4*f*e^2 + 10*b^2*c*d^4*g*e^2 - 16*b^2*c*d^3*f*e^3 - 2*b^3*d^3*g*e^3 + 3*b^3*d^2*f*e^4)/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e)^2","B",0
2227,1,521,0,0.667164," ","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=""giac"")","\frac{2 \, \sqrt{-c x^{2} e^{2} + c d^{2} - b x e^{2} - b d e} {\left({\left({\left(\frac{2 \, {\left(4 \, c^{3} d^{2} g e^{3} - 8 \, c^{3} d f e^{4} + 4 \, b c^{2} f e^{5} - b^{2} c g e^{5}\right)} x}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}} + \frac{3 \, {\left(4 \, b c^{2} d^{2} g e^{3} - 8 \, b c^{2} d f e^{4} + 4 \, b^{2} c f e^{5} - b^{3} g e^{5}\right)}}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}}\right)} x + \frac{3 \, {\left(8 \, c^{3} d^{3} f e^{2} - 4 \, b c^{2} d^{3} g e^{2} - 12 \, b c^{2} d^{2} f e^{3} + 8 \, b^{2} c d^{2} g e^{3} + 2 \, b^{2} c d f e^{4} - 3 \, b^{3} d g e^{4} + b^{3} f e^{5}\right)}}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}}\right)} x + \frac{8 \, c^{3} d^{5} g + 8 \, c^{3} d^{4} f e - 24 \, b c^{2} d^{4} g e - 4 \, b c^{2} d^{3} f e^{2} + 22 \, b^{2} c d^{3} g e^{2} - 6 \, b^{2} c d^{2} f e^{3} - 6 \, b^{3} d^{2} g e^{3} + 3 \, b^{3} d f e^{4}}{16 \, c^{4} d^{4} e^{2} - 32 \, b c^{3} d^{3} e^{3} + 24 \, b^{2} c^{2} d^{2} e^{4} - 8 \, b^{3} c d e^{5} + b^{4} e^{6}}\right)}}{3 \, {\left(c x^{2} e^{2} - c d^{2} + b x e^{2} + b d e\right)}^{2}}"," ",0,"2/3*sqrt(-c*x^2*e^2 + c*d^2 - b*x*e^2 - b*d*e)*(((2*(4*c^3*d^2*g*e^3 - 8*c^3*d*f*e^4 + 4*b*c^2*f*e^5 - b^2*c*g*e^5)*x/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6) + 3*(4*b*c^2*d^2*g*e^3 - 8*b*c^2*d*f*e^4 + 4*b^2*c*f*e^5 - b^3*g*e^5)/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6))*x + 3*(8*c^3*d^3*f*e^2 - 4*b*c^2*d^3*g*e^2 - 12*b*c^2*d^2*f*e^3 + 8*b^2*c*d^2*g*e^3 + 2*b^2*c*d*f*e^4 - 3*b^3*d*g*e^4 + b^3*f*e^5)/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6))*x + (8*c^3*d^5*g + 8*c^3*d^4*f*e - 24*b*c^2*d^4*g*e - 4*b*c^2*d^3*f*e^2 + 22*b^2*c*d^3*g*e^2 - 6*b^2*c*d^2*f*e^3 - 6*b^3*d^2*g*e^3 + 3*b^3*d*f*e^4)/(16*c^4*d^4*e^2 - 32*b*c^3*d^3*e^3 + 24*b^2*c^2*d^2*e^4 - 8*b^3*c*d*e^5 + b^4*e^6))/(c*x^2*e^2 - c*d^2 + b*x*e^2 + b*d*e)^2","B",0
2228,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.55Unable to transpose Error: Bad Argument Value","F(-2)",0
2229,0,0,0,0.000000," ","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=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2230,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.74Unable to transpose Error: Bad Argument Value","F(-2)",0
2231,0,0,0,0.000000," ","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=""giac"")","\int \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(e x + d\right)}^{\frac{5}{2}} {\left(g x + f\right)}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(e*x + d)^(5/2)*(g*x + f), x)","F",0
2232,0,0,0,0.000000," ","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=""giac"")","\int \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(e x + d\right)}^{\frac{3}{2}} {\left(g x + f\right)}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(e*x + d)^(3/2)*(g*x + f), x)","F",0
2233,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2234,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(g x + f\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)/sqrt(e*x + d), x)","F",0
2235,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \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)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)/(e*x + d)^(3/2), x)","F",0
2236,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError >> type","F(-2)",0
2237,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \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)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)/(e*x + d)^(7/2), x)","F",0
2238,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \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)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)/(e*x + d)^(9/2), x)","F",0
2239,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\int \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)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)/(e*x + d)^(11/2), x)","F",0
2240,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2241,0,0,0,0.000000," ","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=""giac"")","\int {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{3}{2}} {\left(g x + f\right)}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(3/2)*(e*x + d)^(3/2)*(g*x + f), x)","F",0
2242,0,0,0,0.000000," ","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=""giac"")","\int {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{3}{2}} \sqrt{e x + d} {\left(g x + f\right)}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(3/2)*sqrt(e*x + d)*(g*x + f), x)","F",0
2243,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{3}{2}} {\left(g x + f\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(3/2)*(g*x + f)/sqrt(e*x + d), x)","F",0
2244,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{3}{2}} {\left(g x + f\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(3/2)*(g*x + f)/(e*x + d)^(3/2), x)","F",0
2245,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument ValueEvaluation time: 2.99Done","F(-2)",0
2246,-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)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2247,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(-d*exp(1)-x*exp(1)^2)]Evaluation time: 121.53Unable to transpose Error: Bad Argument Value","F(-2)",0
2248,-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)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2249,-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)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2250,0,0,0,0.000000," ","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=""giac"")","\int {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{5}{2}} {\left(e x + d\right)}^{\frac{5}{2}} {\left(g x + f\right)}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2)*(e*x + d)^(5/2)*(g*x + f), x)","F",0
2251,0,0,0,0.000000," ","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=""giac"")","\int {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{5}{2}} {\left(e x + d\right)}^{\frac{3}{2}} {\left(g x + f\right)}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2)*(e*x + d)^(3/2)*(g*x + f), x)","F",0
2252,0,0,0,0.000000," ","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=""giac"")","\int {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{5}{2}} \sqrt{e x + d} {\left(g x + f\right)}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2)*sqrt(e*x + d)*(g*x + f), x)","F",0
2253,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{5}{2}} {\left(g x + f\right)}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2)*(g*x + f)/sqrt(e*x + d), x)","F",0
2254,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{5}{2}} {\left(g x + f\right)}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2)*(g*x + f)/(e*x + d)^(3/2), x)","F",0
2255,-2,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument ValueEvaluation time: 6.36Done","F(-2)",0
2256,-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)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2257,-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)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2258,-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)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2259,-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)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2260,-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)^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2261,-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)^(17/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2262,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2263,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2264,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2265,0,0,0,0.000000," ","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=""giac"")","\int \frac{g x + f}{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((g*x + f)/(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)), x)","F",0
2266,0,0,0,0.000000," ","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=""giac"")","\int \frac{g x + f}{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*x + f)/(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(e*x + d)^(3/2)), x)","F",0
2267,0,0,0,0.000000," ","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=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2268,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-80,76,14,-33,-32]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-69,66,23,-29,45]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[66,44,20,6,-14]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[87,21,9,-14,37]Evaluation time: 119.18Unable to transpose Error: Bad Argument Value","F(-2)",0
2269,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-8,-96,87,35,14]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[57,18,-10,85,-42]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-23,67,97,57,86]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[45,19,-66,-61,-5]Evaluation time: 121.97Unable to transpose Error: Bad Argument Value","F(-2)",0
2270,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2271,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2272,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[72,91,-18,-31,46]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-76,-17,63,68,98]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-95,-95,-57,19,-77]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-29,-98,-9,8,96]Evaluation time: 111.17Unable to transpose Error: Bad Argument Value","F(-2)",0
2273,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[72,91,-18,-31,46]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-76,-17,63,68,98]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-95,-95,-57,19,-77]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-29,-98,-9,8,96]Evaluation time: 119.66Unable to transpose Error: Bad Argument Value","F(-2)",0
2274,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.47Unable to transpose Error: Bad Argument Value","F(-2)",0
2275,-2,0,0,0.000000," ","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.24Unable to transpose Error: Bad Argument Value","F(-2)",0
2276,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2277,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2278,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2279,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2280,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2281,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2282,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2283,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2284,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2285,0,0,0,0.000000," ","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=""giac"")","\int {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{5}{2}} {\left(g x + f\right)} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2)*(g*x + f)*(e*x + d)^m, x)","F",0
2286,0,0,0,0.000000," ","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=""giac"")","\int {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{3}{2}} {\left(g x + f\right)} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(3/2)*(g*x + f)*(e*x + d)^m, x)","F",0
2287,0,0,0,0.000000," ","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=""giac"")","\int \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}\,{d x}"," ",0,"integrate(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
2288,0,0,0,0.000000," ","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=""giac"")","\int \frac{{\left(g x + f\right)} {\left(e x + d\right)}^{m}}{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}\,{d x}"," ",0,"integrate((g*x + f)*(e*x + d)^m/sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e), x)","F",0
2289,0,0,0,0.000000," ","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=""giac"")","\int \frac{{\left(g x + f\right)} {\left(e x + d\right)}^{m}}{{\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*x + f)*(e*x + d)^m/(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(3/2), x)","F",0
2290,0,0,0,0.000000," ","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=""giac"")","\int \frac{{\left(g x + f\right)} {\left(e x + d\right)}^{m}}{{\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)*(e*x + d)^m/(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2), x)","F",0
2291,1,173,0,0.460868," ","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=""giac"")","-{\left({\left(x e + d\right)}^{m} c x^{2} e^{\left(p \log\left(-c x e + c d - b e\right) + p \log\left(x e + d\right) + 2\right)} - {\left(x e + d\right)}^{m} c d^{2} e^{\left(p \log\left(-c x e + c d - b e\right) + p \log\left(x e + d\right)\right)} + {\left(x e + d\right)}^{m} b x e^{\left(p \log\left(-c x e + c d - b e\right) + p \log\left(x e + d\right) + 2\right)} + {\left(x e + d\right)}^{m} b d e^{\left(p \log\left(-c x e + c d - b e\right) + p \log\left(x e + d\right) + 1\right)}\right)} e^{\left(-1\right)}"," ",0,"-((x*e + d)^m*c*x^2*e^(p*log(-c*x*e + c*d - b*e) + p*log(x*e + d) + 2) - (x*e + d)^m*c*d^2*e^(p*log(-c*x*e + c*d - b*e) + p*log(x*e + d)) + (x*e + d)^m*b*x*e^(p*log(-c*x*e + c*d - b*e) + p*log(x*e + d) + 2) + (x*e + d)^m*b*d*e^(p*log(-c*x*e + c*d - b*e) + p*log(x*e + d) + 1))*e^(-1)","B",0
2292,1,444,0,0.506558," ","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=""giac"")","-\frac{g p x^{2} e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} + 2 \, d g p x e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + d^{2} g p e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} + 2 \, g x^{2} e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} + 3 \, d g x e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)} + d^{2} g e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right)\right)} + f x e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 2\right)} + d f e^{\left(p \log\left(g p x e + d g p + 2 \, g x e + d g + f e\right) - p \log\left(x e + d\right) - 3 \, \log\left(x e + d\right) + 1\right)}}{p e^{2} + 2 \, e^{2}}"," ",0,"-(g*p*x^2*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d) + 2) + 2*d*g*p*x*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d) + 1) + d^2*g*p*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d)) + 2*g*x^2*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d) + 2) + 3*d*g*x*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d) + 1) + d^2*g*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d)) + f*x*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d) + 2) + d*f*e^(p*log(g*p*x*e + d*g*p + 2*g*x*e + d*g + f*e) - p*log(x*e + d) - 3*log(x*e + d) + 1))/(p*e^2 + 2*e^2)","B",0
2293,1,297,0,0.168338," ","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=""giac"")","-\frac{{\left(c^{2} d^{2} g^{2} - 2 \, c^{2} d f g e - 3 \, c^{2} f^{2} e^{2} + 4 \, b c f g e^{2} - b^{2} g^{2} e^{2}\right)} \log\left({\left| c g x - c f + b g \right|}\right)}{4 \, c^{4} f^{2} g^{3} - 4 \, b c^{3} f g^{4} + b^{2} c^{2} g^{5}} + \frac{{\left(d^{2} g^{2} - 2 \, d f g e + f^{2} e^{2}\right)} \log\left({\left| g x + f \right|}\right)}{4 \, c^{2} f^{2} g^{3} - 4 \, b c f g^{4} + b^{2} g^{5}} - \frac{2 \, c^{3} d^{2} f g^{2} - b c^{2} d^{2} g^{3} + 4 \, c^{3} d f^{2} g e - 6 \, b c^{2} d f g^{2} e + 2 \, b^{2} c d g^{3} e + 2 \, c^{3} f^{3} e^{2} - 5 \, b c^{2} f^{2} g e^{2} + 4 \, b^{2} c f g^{2} e^{2} - b^{3} g^{3} e^{2}}{{\left(c g x - c f + b g\right)} {\left(2 \, c f - b g\right)}^{2} c^{2} g^{3}}"," ",0,"-(c^2*d^2*g^2 - 2*c^2*d*f*g*e - 3*c^2*f^2*e^2 + 4*b*c*f*g*e^2 - b^2*g^2*e^2)*log(abs(c*g*x - c*f + b*g))/(4*c^4*f^2*g^3 - 4*b*c^3*f*g^4 + b^2*c^2*g^5) + (d^2*g^2 - 2*d*f*g*e + f^2*e^2)*log(abs(g*x + f))/(4*c^2*f^2*g^3 - 4*b*c*f*g^4 + b^2*g^5) - (2*c^3*d^2*f*g^2 - b*c^2*d^2*g^3 + 4*c^3*d*f^2*g*e - 6*b*c^2*d*f*g^2*e + 2*b^2*c*d*g^3*e + 2*c^3*f^3*e^2 - 5*b*c^2*f^2*g*e^2 + 4*b^2*c*f*g^2*e^2 - b^3*g^3*e^2)/((c*g*x - c*f + b*g)*(2*c*f - b*g)^2*c^2*g^3)","B",0
2294,1,57,0,0.236202," ","integrate((1+x)^4*(b*x+a)*(x^2-x+1)^4,x, algorithm=""giac"")","\frac{1}{14} \, b x^{14} + \frac{1}{13} \, a x^{13} + \frac{4}{11} \, b x^{11} + \frac{2}{5} \, a x^{10} + \frac{3}{4} \, b x^{8} + \frac{6}{7} \, a x^{7} + \frac{4}{5} \, b x^{5} + a x^{4} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/14*b*x^14 + 1/13*a*x^13 + 4/11*b*x^11 + 2/5*a*x^10 + 3/4*b*x^8 + 6/7*a*x^7 + 4/5*b*x^5 + a*x^4 + 1/2*b*x^2 + a*x","A",0
2295,1,46,0,0.165883," ","integrate((1+x)^3*(b*x+a)*(x^2-x+1)^3,x, algorithm=""giac"")","\frac{1}{11} \, b x^{11} + \frac{1}{10} \, a x^{10} + \frac{3}{8} \, b x^{8} + \frac{3}{7} \, a x^{7} + \frac{3}{5} \, b x^{5} + \frac{3}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/11*b*x^11 + 1/10*a*x^10 + 3/8*b*x^8 + 3/7*a*x^7 + 3/5*b*x^5 + 3/4*a*x^4 + 1/2*b*x^2 + a*x","A",0
2296,1,34,0,0.171931," ","integrate((1+x)^2*(b*x+a)*(x^2-x+1)^2,x, algorithm=""giac"")","\frac{1}{8} \, b x^{8} + \frac{1}{7} \, a x^{7} + \frac{2}{5} \, b x^{5} + \frac{1}{2} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/8*b*x^8 + 1/7*a*x^7 + 2/5*b*x^5 + 1/2*a*x^4 + 1/2*b*x^2 + a*x","A",0
2297,1,22,0,0.167990," ","integrate((1+x)*(b*x+a)*(x^2-x+1),x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} + \frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/5*b*x^5 + 1/4*a*x^4 + 1/2*b*x^2 + a*x","A",0
2298,1,53,0,0.153728," ","integrate((b*x+a)/(1+x)/(x^2-x+1),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\sqrt{3} a + \sqrt{3} 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({\left| x + 1 \right|}\right)"," ",0,"1/3*(sqrt(3)*a + sqrt(3)*b)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*(a - b)*log(x^2 - x + 1) + 1/3*(a - b)*log(abs(x + 1))","A",0
2299,1,101,0,0.191990," ","integrate((b*x+a)/(1+x)^2/(x^2-x+1)^2,x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{3} {\left(2 \, a + b\right)} \arctan\left(-\sqrt{3} {\left(\frac{2}{x + 1} - 1\right)}\right) - \frac{1}{18} \, {\left(2 \, a - b\right)} \log\left(-\frac{3}{x + 1} + \frac{3}{{\left(x + 1\right)}^{2}} + 1\right) - \frac{a}{9 \, {\left(x + 1\right)}} + \frac{b}{9 \, {\left(x + 1\right)}} - \frac{b + \frac{a - b}{x + 1}}{9 \, {\left(\frac{3}{x + 1} - \frac{3}{{\left(x + 1\right)}^{2}} - 1\right)}}"," ",0,"1/9*sqrt(3)*(2*a + b)*arctan(-sqrt(3)*(2/(x + 1) - 1)) - 1/18*(2*a - b)*log(-3/(x + 1) + 3/(x + 1)^2 + 1) - 1/9*a/(x + 1) + 1/9*b/(x + 1) - 1/9*(b + (a - b)/(x + 1))/(3/(x + 1) - 3/(x + 1)^2 - 1)","A",0
2300,1,88,0,0.168192," ","integrate((b*x+a)/(1+x)^3/(x^2-x+1)^3,x, algorithm=""giac"")","\frac{1}{27} \, \sqrt{3} {\left(5 \, a + 2 \, b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{54} \, {\left(5 \, a - 2 \, b\right)} \log\left(x^{2} - x + 1\right) + \frac{1}{27} \, {\left(5 \, a - 2 \, b\right)} \log\left({\left| x + 1 \right|}\right) + \frac{4 \, b x^{5} + 5 \, a x^{4} + 7 \, b x^{2} + 8 \, a x}{18 \, {\left(x^{3} + 1\right)}^{2}}"," ",0,"1/27*sqrt(3)*(5*a + 2*b)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/54*(5*a - 2*b)*log(x^2 - x + 1) + 1/27*(5*a - 2*b)*log(abs(x + 1)) + 1/18*(4*b*x^5 + 5*a*x^4 + 7*b*x^2 + 8*a*x)/(x^3 + 1)^2","A",0
2301,0,0,0,0.000000," ","integrate((1+x)^(3/2)*(b*x+a)*(x^2-x+1)^(3/2),x, algorithm=""giac"")","\int {\left(b x + a\right)} {\left(x^{2} - x + 1\right)}^{\frac{3}{2}} {\left(x + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x + a)*(x^2 - x + 1)^(3/2)*(x + 1)^(3/2), x)","F",0
2302,0,0,0,0.000000," ","integrate((1+x)^(1/2)*(b*x+a)*(x^2-x+1)^(1/2),x, algorithm=""giac"")","\int {\left(b x + a\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}\,{d x}"," ",0,"integrate((b*x + a)*sqrt(x^2 - x + 1)*sqrt(x + 1), x)","F",0
2303,0,0,0,0.000000," ","integrate((b*x+a)/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{b x + a}{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}\,{d x}"," ",0,"integrate((b*x + a)/(sqrt(x^2 - x + 1)*sqrt(x + 1)), x)","F",0
2304,0,0,0,0.000000," ","integrate((b*x+a)/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""giac"")","\int \frac{b x + a}{{\left(x^{2} - x + 1\right)}^{\frac{3}{2}} {\left(x + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x + a)/((x^2 - x + 1)^(3/2)*(x + 1)^(3/2)), x)","F",0
2305,0,0,0,0.000000," ","integrate((b*x+a)/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""giac"")","\int \frac{b x + a}{{\left(x^{2} - x + 1\right)}^{\frac{5}{2}} {\left(x + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x + a)/((x^2 - x + 1)^(5/2)*(x + 1)^(5/2)), x)","F",0
2306,1,312,0,0.177028," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{8} \, B c x^{8} e^{4} + \frac{4}{7} \, B c d x^{7} e^{3} + B c d^{2} x^{6} e^{2} + \frac{4}{5} \, B c d^{3} x^{5} e + \frac{1}{4} \, B c d^{4} x^{4} + \frac{1}{7} \, B b x^{7} e^{4} + \frac{1}{7} \, A c x^{7} e^{4} + \frac{2}{3} \, B b d x^{6} e^{3} + \frac{2}{3} \, A c d x^{6} e^{3} + \frac{6}{5} \, B b d^{2} x^{5} e^{2} + \frac{6}{5} \, A c d^{2} x^{5} e^{2} + B b d^{3} x^{4} e + A c d^{3} x^{4} e + \frac{1}{3} \, B b d^{4} x^{3} + \frac{1}{3} \, A c d^{4} x^{3} + \frac{1}{6} \, B a x^{6} e^{4} + \frac{1}{6} \, A b x^{6} e^{4} + \frac{4}{5} \, B a d x^{5} e^{3} + \frac{4}{5} \, A b d x^{5} e^{3} + \frac{3}{2} \, B a d^{2} x^{4} e^{2} + \frac{3}{2} \, A b d^{2} x^{4} e^{2} + \frac{4}{3} \, B a d^{3} x^{3} e + \frac{4}{3} \, A b d^{3} x^{3} e + \frac{1}{2} \, B a d^{4} x^{2} + \frac{1}{2} \, A b d^{4} x^{2} + \frac{1}{5} \, A a x^{5} e^{4} + A a d x^{4} e^{3} + 2 \, A a d^{2} x^{3} e^{2} + 2 \, A a d^{3} x^{2} e + A a d^{4} x"," ",0,"1/8*B*c*x^8*e^4 + 4/7*B*c*d*x^7*e^3 + B*c*d^2*x^6*e^2 + 4/5*B*c*d^3*x^5*e + 1/4*B*c*d^4*x^4 + 1/7*B*b*x^7*e^4 + 1/7*A*c*x^7*e^4 + 2/3*B*b*d*x^6*e^3 + 2/3*A*c*d*x^6*e^3 + 6/5*B*b*d^2*x^5*e^2 + 6/5*A*c*d^2*x^5*e^2 + B*b*d^3*x^4*e + A*c*d^3*x^4*e + 1/3*B*b*d^4*x^3 + 1/3*A*c*d^4*x^3 + 1/6*B*a*x^6*e^4 + 1/6*A*b*x^6*e^4 + 4/5*B*a*d*x^5*e^3 + 4/5*A*b*d*x^5*e^3 + 3/2*B*a*d^2*x^4*e^2 + 3/2*A*b*d^2*x^4*e^2 + 4/3*B*a*d^3*x^3*e + 4/3*A*b*d^3*x^3*e + 1/2*B*a*d^4*x^2 + 1/2*A*b*d^4*x^2 + 1/5*A*a*x^5*e^4 + A*a*d*x^4*e^3 + 2*A*a*d^2*x^3*e^2 + 2*A*a*d^3*x^2*e + A*a*d^4*x","B",0
2307,1,241,0,0.155444," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{7} \, B c x^{7} e^{3} + \frac{1}{2} \, B c d x^{6} e^{2} + \frac{3}{5} \, B c d^{2} x^{5} e + \frac{1}{4} \, B c d^{3} x^{4} + \frac{1}{6} \, B b x^{6} e^{3} + \frac{1}{6} \, A c x^{6} e^{3} + \frac{3}{5} \, B b d x^{5} e^{2} + \frac{3}{5} \, A c d x^{5} e^{2} + \frac{3}{4} \, B b d^{2} x^{4} e + \frac{3}{4} \, A c d^{2} x^{4} e + \frac{1}{3} \, B b d^{3} x^{3} + \frac{1}{3} \, A c d^{3} x^{3} + \frac{1}{5} \, B a x^{5} e^{3} + \frac{1}{5} \, A b x^{5} e^{3} + \frac{3}{4} \, B a d x^{4} e^{2} + \frac{3}{4} \, A b d x^{4} e^{2} + B a d^{2} x^{3} e + A b d^{2} x^{3} e + \frac{1}{2} \, B a d^{3} x^{2} + \frac{1}{2} \, A b d^{3} x^{2} + \frac{1}{4} \, A a x^{4} e^{3} + A a d x^{3} e^{2} + \frac{3}{2} \, A a d^{2} x^{2} e + A a d^{3} x"," ",0,"1/7*B*c*x^7*e^3 + 1/2*B*c*d*x^6*e^2 + 3/5*B*c*d^2*x^5*e + 1/4*B*c*d^3*x^4 + 1/6*B*b*x^6*e^3 + 1/6*A*c*x^6*e^3 + 3/5*B*b*d*x^5*e^2 + 3/5*A*c*d*x^5*e^2 + 3/4*B*b*d^2*x^4*e + 3/4*A*c*d^2*x^4*e + 1/3*B*b*d^3*x^3 + 1/3*A*c*d^3*x^3 + 1/5*B*a*x^5*e^3 + 1/5*A*b*x^5*e^3 + 3/4*B*a*d*x^4*e^2 + 3/4*A*b*d*x^4*e^2 + B*a*d^2*x^3*e + A*b*d^2*x^3*e + 1/2*B*a*d^3*x^2 + 1/2*A*b*d^3*x^2 + 1/4*A*a*x^4*e^3 + A*a*d*x^3*e^2 + 3/2*A*a*d^2*x^2*e + A*a*d^3*x","A",0
2308,1,171,0,0.169447," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{6} \, B c x^{6} e^{2} + \frac{2}{5} \, B c d x^{5} e + \frac{1}{4} \, B c d^{2} x^{4} + \frac{1}{5} \, B b x^{5} e^{2} + \frac{1}{5} \, A c x^{5} e^{2} + \frac{1}{2} \, B b d x^{4} e + \frac{1}{2} \, A c d x^{4} e + \frac{1}{3} \, B b d^{2} x^{3} + \frac{1}{3} \, A c d^{2} x^{3} + \frac{1}{4} \, B a x^{4} e^{2} + \frac{1}{4} \, A b x^{4} e^{2} + \frac{2}{3} \, B a d x^{3} e + \frac{2}{3} \, A b d x^{3} e + \frac{1}{2} \, B a d^{2} x^{2} + \frac{1}{2} \, A b d^{2} x^{2} + \frac{1}{3} \, A a x^{3} e^{2} + A a d x^{2} e + A a d^{2} x"," ",0,"1/6*B*c*x^6*e^2 + 2/5*B*c*d*x^5*e + 1/4*B*c*d^2*x^4 + 1/5*B*b*x^5*e^2 + 1/5*A*c*x^5*e^2 + 1/2*B*b*d*x^4*e + 1/2*A*c*d*x^4*e + 1/3*B*b*d^2*x^3 + 1/3*A*c*d^2*x^3 + 1/4*B*a*x^4*e^2 + 1/4*A*b*x^4*e^2 + 2/3*B*a*d*x^3*e + 2/3*A*b*d*x^3*e + 1/2*B*a*d^2*x^2 + 1/2*A*b*d^2*x^2 + 1/3*A*a*x^3*e^2 + A*a*d*x^2*e + A*a*d^2*x","A",0
2309,1,100,0,0.153050," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{5} \, B c x^{5} e + \frac{1}{4} \, B c d x^{4} + \frac{1}{4} \, B b x^{4} e + \frac{1}{4} \, A c x^{4} e + \frac{1}{3} \, B b d x^{3} + \frac{1}{3} \, A c d x^{3} + \frac{1}{3} \, B a x^{3} e + \frac{1}{3} \, A b x^{3} e + \frac{1}{2} \, B a d x^{2} + \frac{1}{2} \, A b d x^{2} + \frac{1}{2} \, A a x^{2} e + A a d x"," ",0,"1/5*B*c*x^5*e + 1/4*B*c*d*x^4 + 1/4*B*b*x^4*e + 1/4*A*c*x^4*e + 1/3*B*b*d*x^3 + 1/3*A*c*d*x^3 + 1/3*B*a*x^3*e + 1/3*A*b*x^3*e + 1/2*B*a*d*x^2 + 1/2*A*b*d*x^2 + 1/2*A*a*x^2*e + A*a*d*x","A",0
2310,1,40,0,0.148710," ","integrate((B*x+A)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{4} \, B c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + \frac{1}{2} \, A b x^{2} + A a x"," ",0,"1/4*B*c*x^4 + 1/3*B*b*x^3 + 1/3*A*c*x^3 + 1/2*B*a*x^2 + 1/2*A*b*x^2 + A*a*x","A",0
2311,1,136,0,0.173318," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d),x, algorithm=""giac"")","-{\left(B c d^{3} - B b d^{2} e - A c d^{2} e + B a d e^{2} + A b d e^{2} - A a e^{3}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B c x^{3} e^{2} - 3 \, B c d x^{2} e + 6 \, B c d^{2} x + 3 \, B b x^{2} e^{2} + 3 \, A c x^{2} e^{2} - 6 \, B b d x e - 6 \, A c d x e + 6 \, B a x e^{2} + 6 \, A b x e^{2}\right)} e^{\left(-3\right)}"," ",0,"-(B*c*d^3 - B*b*d^2*e - A*c*d^2*e + B*a*d*e^2 + A*b*d*e^2 - A*a*e^3)*e^(-4)*log(abs(x*e + d)) + 1/6*(2*B*c*x^3*e^2 - 3*B*c*d*x^2*e + 6*B*c*d^2*x + 3*B*b*x^2*e^2 + 3*A*c*x^2*e^2 - 6*B*b*d*x*e - 6*A*c*d*x*e + 6*B*a*x*e^2 + 6*A*b*x*e^2)*e^(-3)","A",0
2312,1,200,0,0.172230," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(B c - \frac{2 \, {\left(3 \, B c d e - B b e^{2} - A c e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)} - {\left(3 \, B c d^{2} - 2 \, B b d e - 2 \, A c d e + B a e^{2} + A b e^{2}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c d^{3} e^{2}}{x e + d} - \frac{B b d^{2} e^{3}}{x e + d} - \frac{A c d^{2} e^{3}}{x e + d} + \frac{B a d e^{4}}{x e + d} + \frac{A b d e^{4}}{x e + d} - \frac{A a e^{5}}{x e + d}\right)} e^{\left(-6\right)}"," ",0,"1/2*(B*c - 2*(3*B*c*d*e - B*b*e^2 - A*c*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4) - (3*B*c*d^2 - 2*B*b*d*e - 2*A*c*d*e + B*a*e^2 + A*b*e^2)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c*d^3*e^2/(x*e + d) - B*b*d^2*e^3/(x*e + d) - A*c*d^2*e^3/(x*e + d) + B*a*d*e^4/(x*e + d) + A*b*d*e^4/(x*e + d) - A*a*e^5/(x*e + d))*e^(-6)","A",0
2313,1,129,0,0.176016," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""giac"")","B c x e^{\left(-3\right)} - {\left(3 \, B c d - B b e - A c e\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, B c d^{3} - 3 \, B b d^{2} e - 3 \, A c d^{2} e + B a d e^{2} + A b d e^{2} + A a e^{3} + 2 \, {\left(3 \, B c d^{2} e - 2 \, B b d e^{2} - 2 \, A c d e^{2} + B a e^{3} + A b e^{3}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"B*c*x*e^(-3) - (3*B*c*d - B*b*e - A*c*e)*e^(-4)*log(abs(x*e + d)) - 1/2*(5*B*c*d^3 - 3*B*b*d^2*e - 3*A*c*d^2*e + B*a*d*e^2 + A*b*d*e^2 + A*a*e^3 + 2*(3*B*c*d^2*e - 2*B*b*d*e^2 - 2*A*c*d*e^2 + B*a*e^3 + A*b*e^3)*x)*e^(-4)/(x*e + d)^2","A",0
2314,1,138,0,0.197340," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""giac"")","B c e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(6 \, {\left(3 \, B c d e - B b e^{2} - A c e^{2}\right)} x^{2} + 3 \, {\left(9 \, B c d^{2} - 2 \, B b d e - 2 \, A c d e - B a e^{2} - A b e^{2}\right)} x + {\left(11 \, B c d^{3} - 2 \, B b d^{2} e - 2 \, A c d^{2} e - B a d e^{2} - A b d e^{2} - 2 \, A a e^{3}\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"B*c*e^(-4)*log(abs(x*e + d)) + 1/6*(6*(3*B*c*d*e - B*b*e^2 - A*c*e^2)*x^2 + 3*(9*B*c*d^2 - 2*B*b*d*e - 2*A*c*d*e - B*a*e^2 - A*b*e^2)*x + (11*B*c*d^3 - 2*B*b*d^2*e - 2*A*c*d^2*e - B*a*d*e^2 - A*b*d*e^2 - 2*A*a*e^3)*e^(-1))*e^(-3)/(x*e + d)^3","A",0
2315,1,220,0,0.181705," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{12 \, B c e^{\left(-1\right)}}{x e + d} - \frac{18 \, B c d e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}} + \frac{12 \, B c d^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c d^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{6 \, B b}{{\left(x e + d\right)}^{2}} + \frac{6 \, A c}{{\left(x e + d\right)}^{2}} - \frac{8 \, B b d}{{\left(x e + d\right)}^{3}} - \frac{8 \, A c d}{{\left(x e + d\right)}^{3}} + \frac{3 \, B b d^{2}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A c d^{2}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a e}{{\left(x e + d\right)}^{3}} + \frac{4 \, A b e}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a d e}{{\left(x e + d\right)}^{4}} - \frac{3 \, A b d e}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a e^{2}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-3\right)}"," ",0,"-1/12*(12*B*c*e^(-1)/(x*e + d) - 18*B*c*d*e^(-1)/(x*e + d)^2 + 12*B*c*d^2*e^(-1)/(x*e + d)^3 - 3*B*c*d^3*e^(-1)/(x*e + d)^4 + 6*B*b/(x*e + d)^2 + 6*A*c/(x*e + d)^2 - 8*B*b*d/(x*e + d)^3 - 8*A*c*d/(x*e + d)^3 + 3*B*b*d^2/(x*e + d)^4 + 3*A*c*d^2/(x*e + d)^4 + 4*B*a*e/(x*e + d)^3 + 4*A*b*e/(x*e + d)^3 - 3*B*a*d*e/(x*e + d)^4 - 3*A*b*d*e/(x*e + d)^4 + 3*A*a*e^2/(x*e + d)^4)*e^(-3)","A",0
2316,1,135,0,0.166553," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(30 \, B c x^{3} e^{3} + 30 \, B c d x^{2} e^{2} + 15 \, B c d^{2} x e + 3 \, B c d^{3} + 20 \, B b x^{2} e^{3} + 20 \, A c x^{2} e^{3} + 10 \, B b d x e^{2} + 10 \, A c d x e^{2} + 2 \, B b d^{2} e + 2 \, A c d^{2} e + 15 \, B a x e^{3} + 15 \, A b x e^{3} + 3 \, B a d e^{2} + 3 \, A b d e^{2} + 12 \, A a e^{3}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/60*(30*B*c*x^3*e^3 + 30*B*c*d*x^2*e^2 + 15*B*c*d^2*x*e + 3*B*c*d^3 + 20*B*b*x^2*e^3 + 20*A*c*x^2*e^3 + 10*B*b*d*x*e^2 + 10*A*c*d*x*e^2 + 2*B*b*d^2*e + 2*A*c*d^2*e + 15*B*a*x*e^3 + 15*A*b*x*e^3 + 3*B*a*d*e^2 + 3*A*b*d*e^2 + 12*A*a*e^3)*e^(-4)/(x*e + d)^5","A",0
2317,1,132,0,0.163568," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(20 \, B c x^{3} e^{3} + 15 \, B c d x^{2} e^{2} + 6 \, B c d^{2} x e + B c d^{3} + 15 \, B b x^{2} e^{3} + 15 \, A c x^{2} e^{3} + 6 \, B b d x e^{2} + 6 \, A c d x e^{2} + B b d^{2} e + A c d^{2} e + 12 \, B a x e^{3} + 12 \, A b x e^{3} + 2 \, B a d e^{2} + 2 \, A b d e^{2} + 10 \, A a e^{3}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(20*B*c*x^3*e^3 + 15*B*c*d*x^2*e^2 + 6*B*c*d^2*x*e + B*c*d^3 + 15*B*b*x^2*e^3 + 15*A*c*x^2*e^3 + 6*B*b*d*x*e^2 + 6*A*c*d*x*e^2 + B*b*d^2*e + A*c*d^2*e + 12*B*a*x*e^3 + 12*A*b*x*e^3 + 2*B*a*d*e^2 + 2*A*b*d*e^2 + 10*A*a*e^3)*e^(-4)/(x*e + d)^6","A",0
2318,1,883,0,0.165210," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, B c^{2} x^{11} e^{5} + \frac{1}{2} \, B c^{2} d x^{10} e^{4} + \frac{10}{9} \, B c^{2} d^{2} x^{9} e^{3} + \frac{5}{4} \, B c^{2} d^{3} x^{8} e^{2} + \frac{5}{7} \, B c^{2} d^{4} x^{7} e + \frac{1}{6} \, B c^{2} d^{5} x^{6} + \frac{1}{5} \, B b c x^{10} e^{5} + \frac{1}{10} \, A c^{2} x^{10} e^{5} + \frac{10}{9} \, B b c d x^{9} e^{4} + \frac{5}{9} \, A c^{2} d x^{9} e^{4} + \frac{5}{2} \, B b c d^{2} x^{8} e^{3} + \frac{5}{4} \, A c^{2} d^{2} x^{8} e^{3} + \frac{20}{7} \, B b c d^{3} x^{7} e^{2} + \frac{10}{7} \, A c^{2} d^{3} x^{7} e^{2} + \frac{5}{3} \, B b c d^{4} x^{6} e + \frac{5}{6} \, A c^{2} d^{4} x^{6} e + \frac{2}{5} \, B b c d^{5} x^{5} + \frac{1}{5} \, A c^{2} d^{5} x^{5} + \frac{1}{9} \, B b^{2} x^{9} e^{5} + \frac{2}{9} \, B a c x^{9} e^{5} + \frac{2}{9} \, A b c x^{9} e^{5} + \frac{5}{8} \, B b^{2} d x^{8} e^{4} + \frac{5}{4} \, B a c d x^{8} e^{4} + \frac{5}{4} \, A b c d x^{8} e^{4} + \frac{10}{7} \, B b^{2} d^{2} x^{7} e^{3} + \frac{20}{7} \, B a c d^{2} x^{7} e^{3} + \frac{20}{7} \, A b c d^{2} x^{7} e^{3} + \frac{5}{3} \, B b^{2} d^{3} x^{6} e^{2} + \frac{10}{3} \, B a c d^{3} x^{6} e^{2} + \frac{10}{3} \, A b c d^{3} x^{6} e^{2} + B b^{2} d^{4} x^{5} e + 2 \, B a c d^{4} x^{5} e + 2 \, A b c d^{4} x^{5} e + \frac{1}{4} \, B b^{2} d^{5} x^{4} + \frac{1}{2} \, B a c d^{5} x^{4} + \frac{1}{2} \, A b c d^{5} x^{4} + \frac{1}{4} \, B a b x^{8} e^{5} + \frac{1}{8} \, A b^{2} x^{8} e^{5} + \frac{1}{4} \, A a c x^{8} e^{5} + \frac{10}{7} \, B a b d x^{7} e^{4} + \frac{5}{7} \, A b^{2} d x^{7} e^{4} + \frac{10}{7} \, A a c d x^{7} e^{4} + \frac{10}{3} \, B a b d^{2} x^{6} e^{3} + \frac{5}{3} \, A b^{2} d^{2} x^{6} e^{3} + \frac{10}{3} \, A a c d^{2} x^{6} e^{3} + 4 \, B a b d^{3} x^{5} e^{2} + 2 \, A b^{2} d^{3} x^{5} e^{2} + 4 \, A a c d^{3} x^{5} e^{2} + \frac{5}{2} \, B a b d^{4} x^{4} e + \frac{5}{4} \, A b^{2} d^{4} x^{4} e + \frac{5}{2} \, A a c d^{4} x^{4} e + \frac{2}{3} \, B a b d^{5} x^{3} + \frac{1}{3} \, A b^{2} d^{5} x^{3} + \frac{2}{3} \, A a c d^{5} x^{3} + \frac{1}{7} \, B a^{2} x^{7} e^{5} + \frac{2}{7} \, A a b x^{7} e^{5} + \frac{5}{6} \, B a^{2} d x^{6} e^{4} + \frac{5}{3} \, A a b d x^{6} e^{4} + 2 \, B a^{2} d^{2} x^{5} e^{3} + 4 \, A a b d^{2} x^{5} e^{3} + \frac{5}{2} \, B a^{2} d^{3} x^{4} e^{2} + 5 \, A a b d^{3} x^{4} e^{2} + \frac{5}{3} \, B a^{2} d^{4} x^{3} e + \frac{10}{3} \, A a b d^{4} x^{3} e + \frac{1}{2} \, B a^{2} d^{5} x^{2} + A a b d^{5} x^{2} + \frac{1}{6} \, A a^{2} x^{6} e^{5} + A a^{2} d x^{5} e^{4} + \frac{5}{2} \, A a^{2} d^{2} x^{4} e^{3} + \frac{10}{3} \, A a^{2} d^{3} x^{3} e^{2} + \frac{5}{2} \, A a^{2} d^{4} x^{2} e + A a^{2} d^{5} x"," ",0,"1/11*B*c^2*x^11*e^5 + 1/2*B*c^2*d*x^10*e^4 + 10/9*B*c^2*d^2*x^9*e^3 + 5/4*B*c^2*d^3*x^8*e^2 + 5/7*B*c^2*d^4*x^7*e + 1/6*B*c^2*d^5*x^6 + 1/5*B*b*c*x^10*e^5 + 1/10*A*c^2*x^10*e^5 + 10/9*B*b*c*d*x^9*e^4 + 5/9*A*c^2*d*x^9*e^4 + 5/2*B*b*c*d^2*x^8*e^3 + 5/4*A*c^2*d^2*x^8*e^3 + 20/7*B*b*c*d^3*x^7*e^2 + 10/7*A*c^2*d^3*x^7*e^2 + 5/3*B*b*c*d^4*x^6*e + 5/6*A*c^2*d^4*x^6*e + 2/5*B*b*c*d^5*x^5 + 1/5*A*c^2*d^5*x^5 + 1/9*B*b^2*x^9*e^5 + 2/9*B*a*c*x^9*e^5 + 2/9*A*b*c*x^9*e^5 + 5/8*B*b^2*d*x^8*e^4 + 5/4*B*a*c*d*x^8*e^4 + 5/4*A*b*c*d*x^8*e^4 + 10/7*B*b^2*d^2*x^7*e^3 + 20/7*B*a*c*d^2*x^7*e^3 + 20/7*A*b*c*d^2*x^7*e^3 + 5/3*B*b^2*d^3*x^6*e^2 + 10/3*B*a*c*d^3*x^6*e^2 + 10/3*A*b*c*d^3*x^6*e^2 + B*b^2*d^4*x^5*e + 2*B*a*c*d^4*x^5*e + 2*A*b*c*d^4*x^5*e + 1/4*B*b^2*d^5*x^4 + 1/2*B*a*c*d^5*x^4 + 1/2*A*b*c*d^5*x^4 + 1/4*B*a*b*x^8*e^5 + 1/8*A*b^2*x^8*e^5 + 1/4*A*a*c*x^8*e^5 + 10/7*B*a*b*d*x^7*e^4 + 5/7*A*b^2*d*x^7*e^4 + 10/7*A*a*c*d*x^7*e^4 + 10/3*B*a*b*d^2*x^6*e^3 + 5/3*A*b^2*d^2*x^6*e^3 + 10/3*A*a*c*d^2*x^6*e^3 + 4*B*a*b*d^3*x^5*e^2 + 2*A*b^2*d^3*x^5*e^2 + 4*A*a*c*d^3*x^5*e^2 + 5/2*B*a*b*d^4*x^4*e + 5/4*A*b^2*d^4*x^4*e + 5/2*A*a*c*d^4*x^4*e + 2/3*B*a*b*d^5*x^3 + 1/3*A*b^2*d^5*x^3 + 2/3*A*a*c*d^5*x^3 + 1/7*B*a^2*x^7*e^5 + 2/7*A*a*b*x^7*e^5 + 5/6*B*a^2*d*x^6*e^4 + 5/3*A*a*b*d*x^6*e^4 + 2*B*a^2*d^2*x^5*e^3 + 4*A*a*b*d^2*x^5*e^3 + 5/2*B*a^2*d^3*x^4*e^2 + 5*A*a*b*d^3*x^4*e^2 + 5/3*B*a^2*d^4*x^3*e + 10/3*A*a*b*d^4*x^3*e + 1/2*B*a^2*d^5*x^2 + A*a*b*d^5*x^2 + 1/6*A*a^2*x^6*e^5 + A*a^2*d*x^5*e^4 + 5/2*A*a^2*d^2*x^4*e^3 + 10/3*A*a^2*d^3*x^3*e^2 + 5/2*A*a^2*d^4*x^2*e + A*a^2*d^5*x","B",0
2319,1,719,0,0.163024," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{10} \, B c^{2} x^{10} e^{4} + \frac{4}{9} \, B c^{2} d x^{9} e^{3} + \frac{3}{4} \, B c^{2} d^{2} x^{8} e^{2} + \frac{4}{7} \, B c^{2} d^{3} x^{7} e + \frac{1}{6} \, B c^{2} d^{4} x^{6} + \frac{2}{9} \, B b c x^{9} e^{4} + \frac{1}{9} \, A c^{2} x^{9} e^{4} + B b c d x^{8} e^{3} + \frac{1}{2} \, A c^{2} d x^{8} e^{3} + \frac{12}{7} \, B b c d^{2} x^{7} e^{2} + \frac{6}{7} \, A c^{2} d^{2} x^{7} e^{2} + \frac{4}{3} \, B b c d^{3} x^{6} e + \frac{2}{3} \, A c^{2} d^{3} x^{6} e + \frac{2}{5} \, B b c d^{4} x^{5} + \frac{1}{5} \, A c^{2} d^{4} x^{5} + \frac{1}{8} \, B b^{2} x^{8} e^{4} + \frac{1}{4} \, B a c x^{8} e^{4} + \frac{1}{4} \, A b c x^{8} e^{4} + \frac{4}{7} \, B b^{2} d x^{7} e^{3} + \frac{8}{7} \, B a c d x^{7} e^{3} + \frac{8}{7} \, A b c d x^{7} e^{3} + B b^{2} d^{2} x^{6} e^{2} + 2 \, B a c d^{2} x^{6} e^{2} + 2 \, A b c d^{2} x^{6} e^{2} + \frac{4}{5} \, B b^{2} d^{3} x^{5} e + \frac{8}{5} \, B a c d^{3} x^{5} e + \frac{8}{5} \, A b c d^{3} x^{5} e + \frac{1}{4} \, B b^{2} d^{4} x^{4} + \frac{1}{2} \, B a c d^{4} x^{4} + \frac{1}{2} \, A b c d^{4} x^{4} + \frac{2}{7} \, B a b x^{7} e^{4} + \frac{1}{7} \, A b^{2} x^{7} e^{4} + \frac{2}{7} \, A a c x^{7} e^{4} + \frac{4}{3} \, B a b d x^{6} e^{3} + \frac{2}{3} \, A b^{2} d x^{6} e^{3} + \frac{4}{3} \, A a c d x^{6} e^{3} + \frac{12}{5} \, B a b d^{2} x^{5} e^{2} + \frac{6}{5} \, A b^{2} d^{2} x^{5} e^{2} + \frac{12}{5} \, A a c d^{2} x^{5} e^{2} + 2 \, B a b d^{3} x^{4} e + A b^{2} d^{3} x^{4} e + 2 \, A a c d^{3} x^{4} e + \frac{2}{3} \, B a b d^{4} x^{3} + \frac{1}{3} \, A b^{2} d^{4} x^{3} + \frac{2}{3} \, A a c d^{4} x^{3} + \frac{1}{6} \, B a^{2} x^{6} e^{4} + \frac{1}{3} \, A a b x^{6} e^{4} + \frac{4}{5} \, B a^{2} d x^{5} e^{3} + \frac{8}{5} \, A a b d x^{5} e^{3} + \frac{3}{2} \, B a^{2} d^{2} x^{4} e^{2} + 3 \, A a b d^{2} x^{4} e^{2} + \frac{4}{3} \, B a^{2} d^{3} x^{3} e + \frac{8}{3} \, A a b d^{3} x^{3} e + \frac{1}{2} \, B a^{2} d^{4} x^{2} + A a b d^{4} x^{2} + \frac{1}{5} \, A a^{2} x^{5} e^{4} + A a^{2} d x^{4} e^{3} + 2 \, A a^{2} d^{2} x^{3} e^{2} + 2 \, A a^{2} d^{3} x^{2} e + A a^{2} d^{4} x"," ",0,"1/10*B*c^2*x^10*e^4 + 4/9*B*c^2*d*x^9*e^3 + 3/4*B*c^2*d^2*x^8*e^2 + 4/7*B*c^2*d^3*x^7*e + 1/6*B*c^2*d^4*x^6 + 2/9*B*b*c*x^9*e^4 + 1/9*A*c^2*x^9*e^4 + B*b*c*d*x^8*e^3 + 1/2*A*c^2*d*x^8*e^3 + 12/7*B*b*c*d^2*x^7*e^2 + 6/7*A*c^2*d^2*x^7*e^2 + 4/3*B*b*c*d^3*x^6*e + 2/3*A*c^2*d^3*x^6*e + 2/5*B*b*c*d^4*x^5 + 1/5*A*c^2*d^4*x^5 + 1/8*B*b^2*x^8*e^4 + 1/4*B*a*c*x^8*e^4 + 1/4*A*b*c*x^8*e^4 + 4/7*B*b^2*d*x^7*e^3 + 8/7*B*a*c*d*x^7*e^3 + 8/7*A*b*c*d*x^7*e^3 + B*b^2*d^2*x^6*e^2 + 2*B*a*c*d^2*x^6*e^2 + 2*A*b*c*d^2*x^6*e^2 + 4/5*B*b^2*d^3*x^5*e + 8/5*B*a*c*d^3*x^5*e + 8/5*A*b*c*d^3*x^5*e + 1/4*B*b^2*d^4*x^4 + 1/2*B*a*c*d^4*x^4 + 1/2*A*b*c*d^4*x^4 + 2/7*B*a*b*x^7*e^4 + 1/7*A*b^2*x^7*e^4 + 2/7*A*a*c*x^7*e^4 + 4/3*B*a*b*d*x^6*e^3 + 2/3*A*b^2*d*x^6*e^3 + 4/3*A*a*c*d*x^6*e^3 + 12/5*B*a*b*d^2*x^5*e^2 + 6/5*A*b^2*d^2*x^5*e^2 + 12/5*A*a*c*d^2*x^5*e^2 + 2*B*a*b*d^3*x^4*e + A*b^2*d^3*x^4*e + 2*A*a*c*d^3*x^4*e + 2/3*B*a*b*d^4*x^3 + 1/3*A*b^2*d^4*x^3 + 2/3*A*a*c*d^4*x^3 + 1/6*B*a^2*x^6*e^4 + 1/3*A*a*b*x^6*e^4 + 4/5*B*a^2*d*x^5*e^3 + 8/5*A*a*b*d*x^5*e^3 + 3/2*B*a^2*d^2*x^4*e^2 + 3*A*a*b*d^2*x^4*e^2 + 4/3*B*a^2*d^3*x^3*e + 8/3*A*a*b*d^3*x^3*e + 1/2*B*a^2*d^4*x^2 + A*a*b*d^4*x^2 + 1/5*A*a^2*x^5*e^4 + A*a^2*d*x^4*e^3 + 2*A*a^2*d^2*x^3*e^2 + 2*A*a^2*d^3*x^2*e + A*a^2*d^4*x","B",0
2320,1,556,0,0.183528," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, B c^{2} x^{9} e^{3} + \frac{3}{8} \, B c^{2} d x^{8} e^{2} + \frac{3}{7} \, B c^{2} d^{2} x^{7} e + \frac{1}{6} \, B c^{2} d^{3} x^{6} + \frac{1}{4} \, B b c x^{8} e^{3} + \frac{1}{8} \, A c^{2} x^{8} e^{3} + \frac{6}{7} \, B b c d x^{7} e^{2} + \frac{3}{7} \, A c^{2} d x^{7} e^{2} + B b c d^{2} x^{6} e + \frac{1}{2} \, A c^{2} d^{2} x^{6} e + \frac{2}{5} \, B b c d^{3} x^{5} + \frac{1}{5} \, A c^{2} d^{3} x^{5} + \frac{1}{7} \, B b^{2} x^{7} e^{3} + \frac{2}{7} \, B a c x^{7} e^{3} + \frac{2}{7} \, A b c x^{7} e^{3} + \frac{1}{2} \, B b^{2} d x^{6} e^{2} + B a c d x^{6} e^{2} + A b c d x^{6} e^{2} + \frac{3}{5} \, B b^{2} d^{2} x^{5} e + \frac{6}{5} \, B a c d^{2} x^{5} e + \frac{6}{5} \, A b c d^{2} x^{5} e + \frac{1}{4} \, B b^{2} d^{3} x^{4} + \frac{1}{2} \, B a c d^{3} x^{4} + \frac{1}{2} \, A b c d^{3} x^{4} + \frac{1}{3} \, B a b x^{6} e^{3} + \frac{1}{6} \, A b^{2} x^{6} e^{3} + \frac{1}{3} \, A a c x^{6} e^{3} + \frac{6}{5} \, B a b d x^{5} e^{2} + \frac{3}{5} \, A b^{2} d x^{5} e^{2} + \frac{6}{5} \, A a c d x^{5} e^{2} + \frac{3}{2} \, B a b d^{2} x^{4} e + \frac{3}{4} \, A b^{2} d^{2} x^{4} e + \frac{3}{2} \, A a c d^{2} x^{4} e + \frac{2}{3} \, B a b d^{3} x^{3} + \frac{1}{3} \, A b^{2} d^{3} x^{3} + \frac{2}{3} \, A a c d^{3} x^{3} + \frac{1}{5} \, B a^{2} x^{5} e^{3} + \frac{2}{5} \, A a b x^{5} e^{3} + \frac{3}{4} \, B a^{2} d x^{4} e^{2} + \frac{3}{2} \, A a b d x^{4} e^{2} + B a^{2} d^{2} x^{3} e + 2 \, A a b d^{2} x^{3} e + \frac{1}{2} \, B a^{2} d^{3} x^{2} + A a b d^{3} x^{2} + \frac{1}{4} \, A a^{2} x^{4} e^{3} + A a^{2} d x^{3} e^{2} + \frac{3}{2} \, A a^{2} d^{2} x^{2} e + A a^{2} d^{3} x"," ",0,"1/9*B*c^2*x^9*e^3 + 3/8*B*c^2*d*x^8*e^2 + 3/7*B*c^2*d^2*x^7*e + 1/6*B*c^2*d^3*x^6 + 1/4*B*b*c*x^8*e^3 + 1/8*A*c^2*x^8*e^3 + 6/7*B*b*c*d*x^7*e^2 + 3/7*A*c^2*d*x^7*e^2 + B*b*c*d^2*x^6*e + 1/2*A*c^2*d^2*x^6*e + 2/5*B*b*c*d^3*x^5 + 1/5*A*c^2*d^3*x^5 + 1/7*B*b^2*x^7*e^3 + 2/7*B*a*c*x^7*e^3 + 2/7*A*b*c*x^7*e^3 + 1/2*B*b^2*d*x^6*e^2 + B*a*c*d*x^6*e^2 + A*b*c*d*x^6*e^2 + 3/5*B*b^2*d^2*x^5*e + 6/5*B*a*c*d^2*x^5*e + 6/5*A*b*c*d^2*x^5*e + 1/4*B*b^2*d^3*x^4 + 1/2*B*a*c*d^3*x^4 + 1/2*A*b*c*d^3*x^4 + 1/3*B*a*b*x^6*e^3 + 1/6*A*b^2*x^6*e^3 + 1/3*A*a*c*x^6*e^3 + 6/5*B*a*b*d*x^5*e^2 + 3/5*A*b^2*d*x^5*e^2 + 6/5*A*a*c*d*x^5*e^2 + 3/2*B*a*b*d^2*x^4*e + 3/4*A*b^2*d^2*x^4*e + 3/2*A*a*c*d^2*x^4*e + 2/3*B*a*b*d^3*x^3 + 1/3*A*b^2*d^3*x^3 + 2/3*A*a*c*d^3*x^3 + 1/5*B*a^2*x^5*e^3 + 2/5*A*a*b*x^5*e^3 + 3/4*B*a^2*d*x^4*e^2 + 3/2*A*a*b*d*x^4*e^2 + B*a^2*d^2*x^3*e + 2*A*a*b*d^2*x^3*e + 1/2*B*a^2*d^3*x^2 + A*a*b*d^3*x^2 + 1/4*A*a^2*x^4*e^3 + A*a^2*d*x^3*e^2 + 3/2*A*a^2*d^2*x^2*e + A*a^2*d^3*x","A",0
2321,1,396,0,0.155528," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, B c^{2} x^{8} e^{2} + \frac{2}{7} \, B c^{2} d x^{7} e + \frac{1}{6} \, B c^{2} d^{2} x^{6} + \frac{2}{7} \, B b c x^{7} e^{2} + \frac{1}{7} \, A c^{2} x^{7} e^{2} + \frac{2}{3} \, B b c d x^{6} e + \frac{1}{3} \, A c^{2} d x^{6} e + \frac{2}{5} \, B b c d^{2} x^{5} + \frac{1}{5} \, A c^{2} d^{2} x^{5} + \frac{1}{6} \, B b^{2} x^{6} e^{2} + \frac{1}{3} \, B a c x^{6} e^{2} + \frac{1}{3} \, A b c x^{6} e^{2} + \frac{2}{5} \, B b^{2} d x^{5} e + \frac{4}{5} \, B a c d x^{5} e + \frac{4}{5} \, A b c d x^{5} e + \frac{1}{4} \, B b^{2} d^{2} x^{4} + \frac{1}{2} \, B a c d^{2} x^{4} + \frac{1}{2} \, A b c d^{2} x^{4} + \frac{2}{5} \, B a b x^{5} e^{2} + \frac{1}{5} \, A b^{2} x^{5} e^{2} + \frac{2}{5} \, A a c x^{5} e^{2} + B a b d x^{4} e + \frac{1}{2} \, A b^{2} d x^{4} e + A a c d x^{4} e + \frac{2}{3} \, B a b d^{2} x^{3} + \frac{1}{3} \, A b^{2} d^{2} x^{3} + \frac{2}{3} \, A a c d^{2} x^{3} + \frac{1}{4} \, B a^{2} x^{4} e^{2} + \frac{1}{2} \, A a b x^{4} e^{2} + \frac{2}{3} \, B a^{2} d x^{3} e + \frac{4}{3} \, A a b d x^{3} e + \frac{1}{2} \, B a^{2} d^{2} x^{2} + A a b d^{2} x^{2} + \frac{1}{3} \, A a^{2} x^{3} e^{2} + A a^{2} d x^{2} e + A a^{2} d^{2} x"," ",0,"1/8*B*c^2*x^8*e^2 + 2/7*B*c^2*d*x^7*e + 1/6*B*c^2*d^2*x^6 + 2/7*B*b*c*x^7*e^2 + 1/7*A*c^2*x^7*e^2 + 2/3*B*b*c*d*x^6*e + 1/3*A*c^2*d*x^6*e + 2/5*B*b*c*d^2*x^5 + 1/5*A*c^2*d^2*x^5 + 1/6*B*b^2*x^6*e^2 + 1/3*B*a*c*x^6*e^2 + 1/3*A*b*c*x^6*e^2 + 2/5*B*b^2*d*x^5*e + 4/5*B*a*c*d*x^5*e + 4/5*A*b*c*d*x^5*e + 1/4*B*b^2*d^2*x^4 + 1/2*B*a*c*d^2*x^4 + 1/2*A*b*c*d^2*x^4 + 2/5*B*a*b*x^5*e^2 + 1/5*A*b^2*x^5*e^2 + 2/5*A*a*c*x^5*e^2 + B*a*b*d*x^4*e + 1/2*A*b^2*d*x^4*e + A*a*c*d*x^4*e + 2/3*B*a*b*d^2*x^3 + 1/3*A*b^2*d^2*x^3 + 2/3*A*a*c*d^2*x^3 + 1/4*B*a^2*x^4*e^2 + 1/2*A*a*b*x^4*e^2 + 2/3*B*a^2*d*x^3*e + 4/3*A*a*b*d*x^3*e + 1/2*B*a^2*d^2*x^2 + A*a*b*d^2*x^2 + 1/3*A*a^2*x^3*e^2 + A*a^2*d*x^2*e + A*a^2*d^2*x","A",0
2322,1,237,0,0.157492," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{7} \, B c^{2} x^{7} e + \frac{1}{6} \, B c^{2} d x^{6} + \frac{1}{3} \, B b c x^{6} e + \frac{1}{6} \, A c^{2} x^{6} e + \frac{2}{5} \, B b c d x^{5} + \frac{1}{5} \, A c^{2} d x^{5} + \frac{1}{5} \, B b^{2} x^{5} e + \frac{2}{5} \, B a c x^{5} e + \frac{2}{5} \, A b c x^{5} e + \frac{1}{4} \, B b^{2} d x^{4} + \frac{1}{2} \, B a c d x^{4} + \frac{1}{2} \, A b c d x^{4} + \frac{1}{2} \, B a b x^{4} e + \frac{1}{4} \, A b^{2} x^{4} e + \frac{1}{2} \, A a c x^{4} e + \frac{2}{3} \, B a b d x^{3} + \frac{1}{3} \, A b^{2} d x^{3} + \frac{2}{3} \, A a c d x^{3} + \frac{1}{3} \, B a^{2} x^{3} e + \frac{2}{3} \, A a b x^{3} e + \frac{1}{2} \, B a^{2} d x^{2} + A a b d x^{2} + \frac{1}{2} \, A a^{2} x^{2} e + A a^{2} d x"," ",0,"1/7*B*c^2*x^7*e + 1/6*B*c^2*d*x^6 + 1/3*B*b*c*x^6*e + 1/6*A*c^2*x^6*e + 2/5*B*b*c*d*x^5 + 1/5*A*c^2*d*x^5 + 1/5*B*b^2*x^5*e + 2/5*B*a*c*x^5*e + 2/5*A*b*c*x^5*e + 1/4*B*b^2*d*x^4 + 1/2*B*a*c*d*x^4 + 1/2*A*b*c*d*x^4 + 1/2*B*a*b*x^4*e + 1/4*A*b^2*x^4*e + 1/2*A*a*c*x^4*e + 2/3*B*a*b*d*x^3 + 1/3*A*b^2*d*x^3 + 2/3*A*a*c*d*x^3 + 1/3*B*a^2*x^3*e + 2/3*A*a*b*x^3*e + 1/2*B*a^2*d*x^2 + A*a*b*d*x^2 + 1/2*A*a^2*x^2*e + A*a^2*d*x","A",0
2323,1,99,0,0.152786," ","integrate((B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, B c^{2} x^{6} + \frac{2}{5} \, B b c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{4} \, B b^{2} x^{4} + \frac{1}{2} \, B a c x^{4} + \frac{1}{2} \, A b c x^{4} + \frac{2}{3} \, B a b x^{3} + \frac{1}{3} \, A b^{2} x^{3} + \frac{2}{3} \, A a c x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a b x^{2} + A a^{2} x"," ",0,"1/6*B*c^2*x^6 + 2/5*B*b*c*x^5 + 1/5*A*c^2*x^5 + 1/4*B*b^2*x^4 + 1/2*B*a*c*x^4 + 1/2*A*b*c*x^4 + 2/3*B*a*b*x^3 + 1/3*A*b^2*x^3 + 2/3*A*a*c*x^3 + 1/2*B*a^2*x^2 + A*a*b*x^2 + A*a^2*x","A",0
2324,1,463,0,0.160576," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""giac"")","-{\left(B c^{2} d^{5} - 2 \, B b c d^{4} e - A c^{2} d^{4} e + B b^{2} d^{3} e^{2} + 2 \, B a c d^{3} e^{2} + 2 \, A b c d^{3} e^{2} - 2 \, B a b d^{2} e^{3} - A b^{2} d^{2} e^{3} - 2 \, A a c d^{2} e^{3} + B a^{2} d e^{4} + 2 \, A a b d e^{4} - A a^{2} e^{5}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(12 \, B c^{2} x^{5} e^{4} - 15 \, B c^{2} d x^{4} e^{3} + 20 \, B c^{2} d^{2} x^{3} e^{2} - 30 \, B c^{2} d^{3} x^{2} e + 60 \, B c^{2} d^{4} x + 30 \, B b c x^{4} e^{4} + 15 \, A c^{2} x^{4} e^{4} - 40 \, B b c d x^{3} e^{3} - 20 \, A c^{2} d x^{3} e^{3} + 60 \, B b c d^{2} x^{2} e^{2} + 30 \, A c^{2} d^{2} x^{2} e^{2} - 120 \, B b c d^{3} x e - 60 \, A c^{2} d^{3} x e + 20 \, B b^{2} x^{3} e^{4} + 40 \, B a c x^{3} e^{4} + 40 \, A b c x^{3} e^{4} - 30 \, B b^{2} d x^{2} e^{3} - 60 \, B a c d x^{2} e^{3} - 60 \, A b c d x^{2} e^{3} + 60 \, B b^{2} d^{2} x e^{2} + 120 \, B a c d^{2} x e^{2} + 120 \, A b c d^{2} x e^{2} + 60 \, B a b x^{2} e^{4} + 30 \, A b^{2} x^{2} e^{4} + 60 \, A a c x^{2} e^{4} - 120 \, B a b d x e^{3} - 60 \, A b^{2} d x e^{3} - 120 \, A a c d x e^{3} + 60 \, B a^{2} x e^{4} + 120 \, A a b x e^{4}\right)} e^{\left(-5\right)}"," ",0,"-(B*c^2*d^5 - 2*B*b*c*d^4*e - A*c^2*d^4*e + B*b^2*d^3*e^2 + 2*B*a*c*d^3*e^2 + 2*A*b*c*d^3*e^2 - 2*B*a*b*d^2*e^3 - A*b^2*d^2*e^3 - 2*A*a*c*d^2*e^3 + B*a^2*d*e^4 + 2*A*a*b*d*e^4 - A*a^2*e^5)*e^(-6)*log(abs(x*e + d)) + 1/60*(12*B*c^2*x^5*e^4 - 15*B*c^2*d*x^4*e^3 + 20*B*c^2*d^2*x^3*e^2 - 30*B*c^2*d^3*x^2*e + 60*B*c^2*d^4*x + 30*B*b*c*x^4*e^4 + 15*A*c^2*x^4*e^4 - 40*B*b*c*d*x^3*e^3 - 20*A*c^2*d*x^3*e^3 + 60*B*b*c*d^2*x^2*e^2 + 30*A*c^2*d^2*x^2*e^2 - 120*B*b*c*d^3*x*e - 60*A*c^2*d^3*x*e + 20*B*b^2*x^3*e^4 + 40*B*a*c*x^3*e^4 + 40*A*b*c*x^3*e^4 - 30*B*b^2*d*x^2*e^3 - 60*B*a*c*d*x^2*e^3 - 60*A*b*c*d*x^2*e^3 + 60*B*b^2*d^2*x*e^2 + 120*B*a*c*d^2*x*e^2 + 120*A*b*c*d^2*x*e^2 + 60*B*a*b*x^2*e^4 + 30*A*b^2*x^2*e^4 + 60*A*a*c*x^2*e^4 - 120*B*a*b*d*x*e^3 - 60*A*b^2*d*x*e^3 - 120*A*a*c*d*x*e^3 + 60*B*a^2*x*e^4 + 120*A*a*b*x*e^4)*e^(-5)","A",0
2325,1,551,0,0.173843," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, B c^{2} - \frac{4 \, {\left(5 \, B c^{2} d e - 2 \, B b c e^{2} - A c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(10 \, B c^{2} d^{2} e^{2} - 8 \, B b c d e^{3} - 4 \, A c^{2} d e^{3} + B b^{2} e^{4} + 2 \, B a c e^{4} + 2 \, A b c e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{12 \, {\left(10 \, B c^{2} d^{3} e^{3} - 12 \, B b c d^{2} e^{4} - 6 \, A c^{2} d^{2} e^{4} + 3 \, B b^{2} d e^{5} + 6 \, B a c d e^{5} + 6 \, A b c d e^{5} - 2 \, B a b e^{6} - A b^{2} e^{6} - 2 \, A a c e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{4} e^{\left(-6\right)} - {\left(5 \, B c^{2} d^{4} - 8 \, B b c d^{3} e - 4 \, A c^{2} d^{3} e + 3 \, B b^{2} d^{2} e^{2} + 6 \, B a c d^{2} e^{2} + 6 \, A b c d^{2} e^{2} - 4 \, B a b d e^{3} - 2 \, A b^{2} d e^{3} - 4 \, A a c d e^{3} + B a^{2} e^{4} + 2 \, A a b e^{4}\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c^{2} d^{5} e^{4}}{x e + d} - \frac{2 \, B b c d^{4} e^{5}}{x e + d} - \frac{A c^{2} d^{4} e^{5}}{x e + d} + \frac{B b^{2} d^{3} e^{6}}{x e + d} + \frac{2 \, B a c d^{3} e^{6}}{x e + d} + \frac{2 \, A b c d^{3} e^{6}}{x e + d} - \frac{2 \, B a b d^{2} e^{7}}{x e + d} - \frac{A b^{2} d^{2} e^{7}}{x e + d} - \frac{2 \, A a c d^{2} e^{7}}{x e + d} + \frac{B a^{2} d e^{8}}{x e + d} + \frac{2 \, A a b d e^{8}}{x e + d} - \frac{A a^{2} e^{9}}{x e + d}\right)} e^{\left(-10\right)}"," ",0,"1/12*(3*B*c^2 - 4*(5*B*c^2*d*e - 2*B*b*c*e^2 - A*c^2*e^2)*e^(-1)/(x*e + d) + 6*(10*B*c^2*d^2*e^2 - 8*B*b*c*d*e^3 - 4*A*c^2*d*e^3 + B*b^2*e^4 + 2*B*a*c*e^4 + 2*A*b*c*e^4)*e^(-2)/(x*e + d)^2 - 12*(10*B*c^2*d^3*e^3 - 12*B*b*c*d^2*e^4 - 6*A*c^2*d^2*e^4 + 3*B*b^2*d*e^5 + 6*B*a*c*d*e^5 + 6*A*b*c*d*e^5 - 2*B*a*b*e^6 - A*b^2*e^6 - 2*A*a*c*e^6)*e^(-3)/(x*e + d)^3)*(x*e + d)^4*e^(-6) - (5*B*c^2*d^4 - 8*B*b*c*d^3*e - 4*A*c^2*d^3*e + 3*B*b^2*d^2*e^2 + 6*B*a*c*d^2*e^2 + 6*A*b*c*d^2*e^2 - 4*B*a*b*d*e^3 - 2*A*b^2*d*e^3 - 4*A*a*c*d*e^3 + B*a^2*e^4 + 2*A*a*b*e^4)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c^2*d^5*e^4/(x*e + d) - 2*B*b*c*d^4*e^5/(x*e + d) - A*c^2*d^4*e^5/(x*e + d) + B*b^2*d^3*e^6/(x*e + d) + 2*B*a*c*d^3*e^6/(x*e + d) + 2*A*b*c*d^3*e^6/(x*e + d) - 2*B*a*b*d^2*e^7/(x*e + d) - A*b^2*d^2*e^7/(x*e + d) - 2*A*a*c*d^2*e^7/(x*e + d) + B*a^2*d*e^8/(x*e + d) + 2*A*a*b*d*e^8/(x*e + d) - A*a^2*e^9/(x*e + d))*e^(-10)","B",0
2326,1,430,0,0.176464," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^3,x, algorithm=""giac"")","-{\left(10 \, B c^{2} d^{3} - 12 \, B b c d^{2} e - 6 \, A c^{2} d^{2} e + 3 \, B b^{2} d e^{2} + 6 \, B a c d e^{2} + 6 \, A b c d e^{2} - 2 \, B a b e^{3} - A b^{2} e^{3} - 2 \, A a c e^{3}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, B c^{2} x^{3} e^{6} - 9 \, B c^{2} d x^{2} e^{5} + 36 \, B c^{2} d^{2} x e^{4} + 6 \, B b c x^{2} e^{6} + 3 \, A c^{2} x^{2} e^{6} - 36 \, B b c d x e^{5} - 18 \, A c^{2} d x e^{5} + 6 \, B b^{2} x e^{6} + 12 \, B a c x e^{6} + 12 \, A b c x e^{6}\right)} e^{\left(-9\right)} - \frac{{\left(9 \, B c^{2} d^{5} - 14 \, B b c d^{4} e - 7 \, A c^{2} d^{4} e + 5 \, B b^{2} d^{3} e^{2} + 10 \, B a c d^{3} e^{2} + 10 \, A b c d^{3} e^{2} - 6 \, B a b d^{2} e^{3} - 3 \, A b^{2} d^{2} e^{3} - 6 \, A a c d^{2} e^{3} + B a^{2} d e^{4} + 2 \, A a b d e^{4} + A a^{2} e^{5} + 2 \, {\left(5 \, B c^{2} d^{4} e - 8 \, B b c d^{3} e^{2} - 4 \, A c^{2} d^{3} e^{2} + 3 \, B b^{2} d^{2} e^{3} + 6 \, B a c d^{2} e^{3} + 6 \, A b c d^{2} e^{3} - 4 \, B a b d e^{4} - 2 \, A b^{2} d e^{4} - 4 \, A a c d e^{4} + B a^{2} e^{5} + 2 \, A a b e^{5}\right)} x\right)} e^{\left(-6\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-(10*B*c^2*d^3 - 12*B*b*c*d^2*e - 6*A*c^2*d^2*e + 3*B*b^2*d*e^2 + 6*B*a*c*d*e^2 + 6*A*b*c*d*e^2 - 2*B*a*b*e^3 - A*b^2*e^3 - 2*A*a*c*e^3)*e^(-6)*log(abs(x*e + d)) + 1/6*(2*B*c^2*x^3*e^6 - 9*B*c^2*d*x^2*e^5 + 36*B*c^2*d^2*x*e^4 + 6*B*b*c*x^2*e^6 + 3*A*c^2*x^2*e^6 - 36*B*b*c*d*x*e^5 - 18*A*c^2*d*x*e^5 + 6*B*b^2*x*e^6 + 12*B*a*c*x*e^6 + 12*A*b*c*x*e^6)*e^(-9) - 1/2*(9*B*c^2*d^5 - 14*B*b*c*d^4*e - 7*A*c^2*d^4*e + 5*B*b^2*d^3*e^2 + 10*B*a*c*d^3*e^2 + 10*A*b*c*d^3*e^2 - 6*B*a*b*d^2*e^3 - 3*A*b^2*d^2*e^3 - 6*A*a*c*d^2*e^3 + B*a^2*d*e^4 + 2*A*a*b*d*e^4 + A*a^2*e^5 + 2*(5*B*c^2*d^4*e - 8*B*b*c*d^3*e^2 - 4*A*c^2*d^3*e^2 + 3*B*b^2*d^2*e^3 + 6*B*a*c*d^2*e^3 + 6*A*b*c*d^2*e^3 - 4*B*a*b*d*e^4 - 2*A*b^2*d*e^4 - 4*A*a*c*d*e^4 + B*a^2*e^5 + 2*A*a*b*e^5)*x)*e^(-6)/(x*e + d)^2","A",0
2327,1,424,0,0.163891," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^4,x, algorithm=""giac"")","{\left(10 \, B c^{2} d^{2} - 8 \, B b c d e - 4 \, A c^{2} d e + B b^{2} e^{2} + 2 \, B a c e^{2} + 2 \, A b c e^{2}\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B c^{2} x^{2} e^{4} - 8 \, B c^{2} d x e^{3} + 4 \, B b c x e^{4} + 2 \, A c^{2} x e^{4}\right)} e^{\left(-8\right)} + \frac{{\left(47 \, B c^{2} d^{5} - 52 \, B b c d^{4} e - 26 \, A c^{2} d^{4} e + 11 \, B b^{2} d^{3} e^{2} + 22 \, B a c d^{3} e^{2} + 22 \, A b c d^{3} e^{2} - 4 \, B a b d^{2} e^{3} - 2 \, A b^{2} d^{2} e^{3} - 4 \, A a c d^{2} e^{3} - B a^{2} d e^{4} - 2 \, A a b d e^{4} - 2 \, A a^{2} e^{5} + 6 \, {\left(10 \, B c^{2} d^{3} e^{2} - 12 \, B b c d^{2} e^{3} - 6 \, A c^{2} d^{2} e^{3} + 3 \, B b^{2} d e^{4} + 6 \, B a c d e^{4} + 6 \, A b c d e^{4} - 2 \, B a b e^{5} - A b^{2} e^{5} - 2 \, A a c e^{5}\right)} x^{2} + 3 \, {\left(35 \, B c^{2} d^{4} e - 40 \, B b c d^{3} e^{2} - 20 \, A c^{2} d^{3} e^{2} + 9 \, B b^{2} d^{2} e^{3} + 18 \, B a c d^{2} e^{3} + 18 \, A b c d^{2} e^{3} - 4 \, B a b d e^{4} - 2 \, A b^{2} d e^{4} - 4 \, A a c d e^{4} - B a^{2} e^{5} - 2 \, A a b e^{5}\right)} x\right)} e^{\left(-6\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"(10*B*c^2*d^2 - 8*B*b*c*d*e - 4*A*c^2*d*e + B*b^2*e^2 + 2*B*a*c*e^2 + 2*A*b*c*e^2)*e^(-6)*log(abs(x*e + d)) + 1/2*(B*c^2*x^2*e^4 - 8*B*c^2*d*x*e^3 + 4*B*b*c*x*e^4 + 2*A*c^2*x*e^4)*e^(-8) + 1/6*(47*B*c^2*d^5 - 52*B*b*c*d^4*e - 26*A*c^2*d^4*e + 11*B*b^2*d^3*e^2 + 22*B*a*c*d^3*e^2 + 22*A*b*c*d^3*e^2 - 4*B*a*b*d^2*e^3 - 2*A*b^2*d^2*e^3 - 4*A*a*c*d^2*e^3 - B*a^2*d*e^4 - 2*A*a*b*d*e^4 - 2*A*a^2*e^5 + 6*(10*B*c^2*d^3*e^2 - 12*B*b*c*d^2*e^3 - 6*A*c^2*d^2*e^3 + 3*B*b^2*d*e^4 + 6*B*a*c*d*e^4 + 6*A*b*c*d*e^4 - 2*B*a*b*e^5 - A*b^2*e^5 - 2*A*a*c*e^5)*x^2 + 3*(35*B*c^2*d^4*e - 40*B*b*c*d^3*e^2 - 20*A*c^2*d^3*e^2 + 9*B*b^2*d^2*e^3 + 18*B*a*c*d^2*e^3 + 18*A*b*c*d^2*e^3 - 4*B*a*b*d*e^4 - 2*A*b^2*d*e^4 - 4*A*a*c*d*e^4 - B*a^2*e^5 - 2*A*a*b*e^5)*x)*e^(-6)/(x*e + d)^3","A",0
2328,1,719,0,0.212146," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^5,x, algorithm=""giac"")","{\left(x e + d\right)} B c^{2} e^{\left(-6\right)} + {\left(5 \, B c^{2} d - 2 \, B b c e - A c^{2} e\right)} e^{\left(-6\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{120 \, B c^{2} d^{2} e^{22}}{x e + d} - \frac{60 \, B c^{2} d^{3} e^{22}}{{\left(x e + d\right)}^{2}} + \frac{20 \, B c^{2} d^{4} e^{22}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c^{2} d^{5} e^{22}}{{\left(x e + d\right)}^{4}} - \frac{96 \, B b c d e^{23}}{x e + d} - \frac{48 \, A c^{2} d e^{23}}{x e + d} + \frac{72 \, B b c d^{2} e^{23}}{{\left(x e + d\right)}^{2}} + \frac{36 \, A c^{2} d^{2} e^{23}}{{\left(x e + d\right)}^{2}} - \frac{32 \, B b c d^{3} e^{23}}{{\left(x e + d\right)}^{3}} - \frac{16 \, A c^{2} d^{3} e^{23}}{{\left(x e + d\right)}^{3}} + \frac{6 \, B b c d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A c^{2} d^{4} e^{23}}{{\left(x e + d\right)}^{4}} + \frac{12 \, B b^{2} e^{24}}{x e + d} + \frac{24 \, B a c e^{24}}{x e + d} + \frac{24 \, A b c e^{24}}{x e + d} - \frac{18 \, B b^{2} d e^{24}}{{\left(x e + d\right)}^{2}} - \frac{36 \, B a c d e^{24}}{{\left(x e + d\right)}^{2}} - \frac{36 \, A b c d e^{24}}{{\left(x e + d\right)}^{2}} + \frac{12 \, B b^{2} d^{2} e^{24}}{{\left(x e + d\right)}^{3}} + \frac{24 \, B a c d^{2} e^{24}}{{\left(x e + d\right)}^{3}} + \frac{24 \, A b c d^{2} e^{24}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B b^{2} d^{3} e^{24}}{{\left(x e + d\right)}^{4}} - \frac{6 \, B a c d^{3} e^{24}}{{\left(x e + d\right)}^{4}} - \frac{6 \, A b c d^{3} e^{24}}{{\left(x e + d\right)}^{4}} + \frac{12 \, B a b e^{25}}{{\left(x e + d\right)}^{2}} + \frac{6 \, A b^{2} e^{25}}{{\left(x e + d\right)}^{2}} + \frac{12 \, A a c e^{25}}{{\left(x e + d\right)}^{2}} - \frac{16 \, B a b d e^{25}}{{\left(x e + d\right)}^{3}} - \frac{8 \, A b^{2} d e^{25}}{{\left(x e + d\right)}^{3}} - \frac{16 \, A a c d e^{25}}{{\left(x e + d\right)}^{3}} + \frac{6 \, B a b d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A b^{2} d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{6 \, A a c d^{2} e^{25}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a^{2} e^{26}}{{\left(x e + d\right)}^{3}} + \frac{8 \, A a b e^{26}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a^{2} d e^{26}}{{\left(x e + d\right)}^{4}} - \frac{6 \, A a b d e^{26}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a^{2} e^{27}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-28\right)}"," ",0,"(x*e + d)*B*c^2*e^(-6) + (5*B*c^2*d - 2*B*b*c*e - A*c^2*e)*e^(-6)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(120*B*c^2*d^2*e^22/(x*e + d) - 60*B*c^2*d^3*e^22/(x*e + d)^2 + 20*B*c^2*d^4*e^22/(x*e + d)^3 - 3*B*c^2*d^5*e^22/(x*e + d)^4 - 96*B*b*c*d*e^23/(x*e + d) - 48*A*c^2*d*e^23/(x*e + d) + 72*B*b*c*d^2*e^23/(x*e + d)^2 + 36*A*c^2*d^2*e^23/(x*e + d)^2 - 32*B*b*c*d^3*e^23/(x*e + d)^3 - 16*A*c^2*d^3*e^23/(x*e + d)^3 + 6*B*b*c*d^4*e^23/(x*e + d)^4 + 3*A*c^2*d^4*e^23/(x*e + d)^4 + 12*B*b^2*e^24/(x*e + d) + 24*B*a*c*e^24/(x*e + d) + 24*A*b*c*e^24/(x*e + d) - 18*B*b^2*d*e^24/(x*e + d)^2 - 36*B*a*c*d*e^24/(x*e + d)^2 - 36*A*b*c*d*e^24/(x*e + d)^2 + 12*B*b^2*d^2*e^24/(x*e + d)^3 + 24*B*a*c*d^2*e^24/(x*e + d)^3 + 24*A*b*c*d^2*e^24/(x*e + d)^3 - 3*B*b^2*d^3*e^24/(x*e + d)^4 - 6*B*a*c*d^3*e^24/(x*e + d)^4 - 6*A*b*c*d^3*e^24/(x*e + d)^4 + 12*B*a*b*e^25/(x*e + d)^2 + 6*A*b^2*e^25/(x*e + d)^2 + 12*A*a*c*e^25/(x*e + d)^2 - 16*B*a*b*d*e^25/(x*e + d)^3 - 8*A*b^2*d*e^25/(x*e + d)^3 - 16*A*a*c*d*e^25/(x*e + d)^3 + 6*B*a*b*d^2*e^25/(x*e + d)^4 + 3*A*b^2*d^2*e^25/(x*e + d)^4 + 6*A*a*c*d^2*e^25/(x*e + d)^4 + 4*B*a^2*e^26/(x*e + d)^3 + 8*A*a*b*e^26/(x*e + d)^3 - 3*B*a^2*d*e^26/(x*e + d)^4 - 6*A*a*b*d*e^26/(x*e + d)^4 + 3*A*a^2*e^27/(x*e + d)^4)*e^(-28)","B",0
2329,1,426,0,0.194497," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^6,x, algorithm=""giac"")","B c^{2} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(60 \, {\left(5 \, B c^{2} d e^{3} - 2 \, B b c e^{4} - A c^{2} e^{4}\right)} x^{4} + 30 \, {\left(30 \, B c^{2} d^{2} e^{2} - 8 \, B b c d e^{3} - 4 \, A c^{2} d e^{3} - B b^{2} e^{4} - 2 \, B a c e^{4} - 2 \, A b c e^{4}\right)} x^{3} + 10 \, {\left(110 \, B c^{2} d^{3} e - 24 \, B b c d^{2} e^{2} - 12 \, A c^{2} d^{2} e^{2} - 3 \, B b^{2} d e^{3} - 6 \, B a c d e^{3} - 6 \, A b c d e^{3} - 4 \, B a b e^{4} - 2 \, A b^{2} e^{4} - 4 \, A a c e^{4}\right)} x^{2} + 5 \, {\left(125 \, B c^{2} d^{4} - 24 \, B b c d^{3} e - 12 \, A c^{2} d^{3} e - 3 \, B b^{2} d^{2} e^{2} - 6 \, B a c d^{2} e^{2} - 6 \, A b c d^{2} e^{2} - 4 \, B a b d e^{3} - 2 \, A b^{2} d e^{3} - 4 \, A a c d e^{3} - 3 \, B a^{2} e^{4} - 6 \, A a b e^{4}\right)} x + {\left(137 \, B c^{2} d^{5} - 24 \, B b c d^{4} e - 12 \, A c^{2} d^{4} e - 3 \, B b^{2} d^{3} e^{2} - 6 \, B a c d^{3} e^{2} - 6 \, A b c d^{3} e^{2} - 4 \, B a b d^{2} e^{3} - 2 \, A b^{2} d^{2} e^{3} - 4 \, A a c d^{2} e^{3} - 3 \, B a^{2} d e^{4} - 6 \, A a b d e^{4} - 12 \, A a^{2} e^{5}\right)} e^{\left(-1\right)}\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"B*c^2*e^(-6)*log(abs(x*e + d)) + 1/60*(60*(5*B*c^2*d*e^3 - 2*B*b*c*e^4 - A*c^2*e^4)*x^4 + 30*(30*B*c^2*d^2*e^2 - 8*B*b*c*d*e^3 - 4*A*c^2*d*e^3 - B*b^2*e^4 - 2*B*a*c*e^4 - 2*A*b*c*e^4)*x^3 + 10*(110*B*c^2*d^3*e - 24*B*b*c*d^2*e^2 - 12*A*c^2*d^2*e^2 - 3*B*b^2*d*e^3 - 6*B*a*c*d*e^3 - 6*A*b*c*d*e^3 - 4*B*a*b*e^4 - 2*A*b^2*e^4 - 4*A*a*c*e^4)*x^2 + 5*(125*B*c^2*d^4 - 24*B*b*c*d^3*e - 12*A*c^2*d^3*e - 3*B*b^2*d^2*e^2 - 6*B*a*c*d^2*e^2 - 6*A*b*c*d^2*e^2 - 4*B*a*b*d*e^3 - 2*A*b^2*d*e^3 - 4*A*a*c*d*e^3 - 3*B*a^2*e^4 - 6*A*a*b*e^4)*x + (137*B*c^2*d^5 - 24*B*b*c*d^4*e - 12*A*c^2*d^4*e - 3*B*b^2*d^3*e^2 - 6*B*a*c*d^3*e^2 - 6*A*b*c*d^3*e^2 - 4*B*a*b*d^2*e^3 - 2*A*b^2*d^2*e^3 - 4*A*a*c*d^2*e^3 - 3*B*a^2*d*e^4 - 6*A*a*b*d*e^4 - 12*A*a^2*e^5)*e^(-1))*e^(-5)/(x*e + d)^5","A",0
2330,1,460,0,0.220336," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(60 \, B c^{2} x^{5} e^{5} + 150 \, B c^{2} d x^{4} e^{4} + 200 \, B c^{2} d^{2} x^{3} e^{3} + 150 \, B c^{2} d^{3} x^{2} e^{2} + 60 \, B c^{2} d^{4} x e + 10 \, B c^{2} d^{5} + 60 \, B b c x^{4} e^{5} + 30 \, A c^{2} x^{4} e^{5} + 80 \, B b c d x^{3} e^{4} + 40 \, A c^{2} d x^{3} e^{4} + 60 \, B b c d^{2} x^{2} e^{3} + 30 \, A c^{2} d^{2} x^{2} e^{3} + 24 \, B b c d^{3} x e^{2} + 12 \, A c^{2} d^{3} x e^{2} + 4 \, B b c d^{4} e + 2 \, A c^{2} d^{4} e + 20 \, B b^{2} x^{3} e^{5} + 40 \, B a c x^{3} e^{5} + 40 \, A b c x^{3} e^{5} + 15 \, B b^{2} d x^{2} e^{4} + 30 \, B a c d x^{2} e^{4} + 30 \, A b c d x^{2} e^{4} + 6 \, B b^{2} d^{2} x e^{3} + 12 \, B a c d^{2} x e^{3} + 12 \, A b c d^{2} x e^{3} + B b^{2} d^{3} e^{2} + 2 \, B a c d^{3} e^{2} + 2 \, A b c d^{3} e^{2} + 30 \, B a b x^{2} e^{5} + 15 \, A b^{2} x^{2} e^{5} + 30 \, A a c x^{2} e^{5} + 12 \, B a b d x e^{4} + 6 \, A b^{2} d x e^{4} + 12 \, A a c d x e^{4} + 2 \, B a b d^{2} e^{3} + A b^{2} d^{2} e^{3} + 2 \, A a c d^{2} e^{3} + 12 \, B a^{2} x e^{5} + 24 \, A a b x e^{5} + 2 \, B a^{2} d e^{4} + 4 \, A a b d e^{4} + 10 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(60*B*c^2*x^5*e^5 + 150*B*c^2*d*x^4*e^4 + 200*B*c^2*d^2*x^3*e^3 + 150*B*c^2*d^3*x^2*e^2 + 60*B*c^2*d^4*x*e + 10*B*c^2*d^5 + 60*B*b*c*x^4*e^5 + 30*A*c^2*x^4*e^5 + 80*B*b*c*d*x^3*e^4 + 40*A*c^2*d*x^3*e^4 + 60*B*b*c*d^2*x^2*e^3 + 30*A*c^2*d^2*x^2*e^3 + 24*B*b*c*d^3*x*e^2 + 12*A*c^2*d^3*x*e^2 + 4*B*b*c*d^4*e + 2*A*c^2*d^4*e + 20*B*b^2*x^3*e^5 + 40*B*a*c*x^3*e^5 + 40*A*b*c*x^3*e^5 + 15*B*b^2*d*x^2*e^4 + 30*B*a*c*d*x^2*e^4 + 30*A*b*c*d*x^2*e^4 + 6*B*b^2*d^2*x*e^3 + 12*B*a*c*d^2*x*e^3 + 12*A*b*c*d^2*x*e^3 + B*b^2*d^3*e^2 + 2*B*a*c*d^3*e^2 + 2*A*b*c*d^3*e^2 + 30*B*a*b*x^2*e^5 + 15*A*b^2*x^2*e^5 + 30*A*a*c*x^2*e^5 + 12*B*a*b*d*x*e^4 + 6*A*b^2*d*x*e^4 + 12*A*a*c*d*x*e^4 + 2*B*a*b*d^2*e^3 + A*b^2*d^2*e^3 + 2*A*a*c*d^2*e^3 + 12*B*a^2*x*e^5 + 24*A*a*b*x*e^5 + 2*B*a^2*d*e^4 + 4*A*a*b*d*e^4 + 10*A*a^2*e^5)*e^(-6)/(x*e + d)^6","A",0
2331,1,462,0,0.165956," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(210 \, B c^{2} x^{5} e^{5} + 350 \, B c^{2} d x^{4} e^{4} + 350 \, B c^{2} d^{2} x^{3} e^{3} + 210 \, B c^{2} d^{3} x^{2} e^{2} + 70 \, B c^{2} d^{4} x e + 10 \, B c^{2} d^{5} + 280 \, B b c x^{4} e^{5} + 140 \, A c^{2} x^{4} e^{5} + 280 \, B b c d x^{3} e^{4} + 140 \, A c^{2} d x^{3} e^{4} + 168 \, B b c d^{2} x^{2} e^{3} + 84 \, A c^{2} d^{2} x^{2} e^{3} + 56 \, B b c d^{3} x e^{2} + 28 \, A c^{2} d^{3} x e^{2} + 8 \, B b c d^{4} e + 4 \, A c^{2} d^{4} e + 105 \, B b^{2} x^{3} e^{5} + 210 \, B a c x^{3} e^{5} + 210 \, A b c x^{3} e^{5} + 63 \, B b^{2} d x^{2} e^{4} + 126 \, B a c d x^{2} e^{4} + 126 \, A b c d x^{2} e^{4} + 21 \, B b^{2} d^{2} x e^{3} + 42 \, B a c d^{2} x e^{3} + 42 \, A b c d^{2} x e^{3} + 3 \, B b^{2} d^{3} e^{2} + 6 \, B a c d^{3} e^{2} + 6 \, A b c d^{3} e^{2} + 168 \, B a b x^{2} e^{5} + 84 \, A b^{2} x^{2} e^{5} + 168 \, A a c x^{2} e^{5} + 56 \, B a b d x e^{4} + 28 \, A b^{2} d x e^{4} + 56 \, A a c d x e^{4} + 8 \, B a b d^{2} e^{3} + 4 \, A b^{2} d^{2} e^{3} + 8 \, A a c d^{2} e^{3} + 70 \, B a^{2} x e^{5} + 140 \, A a b x e^{5} + 10 \, B a^{2} d e^{4} + 20 \, A a b d e^{4} + 60 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{420 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/420*(210*B*c^2*x^5*e^5 + 350*B*c^2*d*x^4*e^4 + 350*B*c^2*d^2*x^3*e^3 + 210*B*c^2*d^3*x^2*e^2 + 70*B*c^2*d^4*x*e + 10*B*c^2*d^5 + 280*B*b*c*x^4*e^5 + 140*A*c^2*x^4*e^5 + 280*B*b*c*d*x^3*e^4 + 140*A*c^2*d*x^3*e^4 + 168*B*b*c*d^2*x^2*e^3 + 84*A*c^2*d^2*x^2*e^3 + 56*B*b*c*d^3*x*e^2 + 28*A*c^2*d^3*x*e^2 + 8*B*b*c*d^4*e + 4*A*c^2*d^4*e + 105*B*b^2*x^3*e^5 + 210*B*a*c*x^3*e^5 + 210*A*b*c*x^3*e^5 + 63*B*b^2*d*x^2*e^4 + 126*B*a*c*d*x^2*e^4 + 126*A*b*c*d*x^2*e^4 + 21*B*b^2*d^2*x*e^3 + 42*B*a*c*d^2*x*e^3 + 42*A*b*c*d^2*x*e^3 + 3*B*b^2*d^3*e^2 + 6*B*a*c*d^3*e^2 + 6*A*b*c*d^3*e^2 + 168*B*a*b*x^2*e^5 + 84*A*b^2*x^2*e^5 + 168*A*a*c*x^2*e^5 + 56*B*a*b*d*x*e^4 + 28*A*b^2*d*x*e^4 + 56*A*a*c*d*x*e^4 + 8*B*a*b*d^2*e^3 + 4*A*b^2*d^2*e^3 + 8*A*a*c*d^2*e^3 + 70*B*a^2*x*e^5 + 140*A*a*b*x*e^5 + 10*B*a^2*d*e^4 + 20*A*a*b*d*e^4 + 60*A*a^2*e^5)*e^(-6)/(x*e + d)^7","A",0
2332,1,462,0,0.161165," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(280 \, B c^{2} x^{5} e^{5} + 350 \, B c^{2} d x^{4} e^{4} + 280 \, B c^{2} d^{2} x^{3} e^{3} + 140 \, B c^{2} d^{3} x^{2} e^{2} + 40 \, B c^{2} d^{4} x e + 5 \, B c^{2} d^{5} + 420 \, B b c x^{4} e^{5} + 210 \, A c^{2} x^{4} e^{5} + 336 \, B b c d x^{3} e^{4} + 168 \, A c^{2} d x^{3} e^{4} + 168 \, B b c d^{2} x^{2} e^{3} + 84 \, A c^{2} d^{2} x^{2} e^{3} + 48 \, B b c d^{3} x e^{2} + 24 \, A c^{2} d^{3} x e^{2} + 6 \, B b c d^{4} e + 3 \, A c^{2} d^{4} e + 168 \, B b^{2} x^{3} e^{5} + 336 \, B a c x^{3} e^{5} + 336 \, A b c x^{3} e^{5} + 84 \, B b^{2} d x^{2} e^{4} + 168 \, B a c d x^{2} e^{4} + 168 \, A b c d x^{2} e^{4} + 24 \, B b^{2} d^{2} x e^{3} + 48 \, B a c d^{2} x e^{3} + 48 \, A b c d^{2} x e^{3} + 3 \, B b^{2} d^{3} e^{2} + 6 \, B a c d^{3} e^{2} + 6 \, A b c d^{3} e^{2} + 280 \, B a b x^{2} e^{5} + 140 \, A b^{2} x^{2} e^{5} + 280 \, A a c x^{2} e^{5} + 80 \, B a b d x e^{4} + 40 \, A b^{2} d x e^{4} + 80 \, A a c d x e^{4} + 10 \, B a b d^{2} e^{3} + 5 \, A b^{2} d^{2} e^{3} + 10 \, A a c d^{2} e^{3} + 120 \, B a^{2} x e^{5} + 240 \, A a b x e^{5} + 15 \, B a^{2} d e^{4} + 30 \, A a b d e^{4} + 105 \, A a^{2} e^{5}\right)} e^{\left(-6\right)}}{840 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/840*(280*B*c^2*x^5*e^5 + 350*B*c^2*d*x^4*e^4 + 280*B*c^2*d^2*x^3*e^3 + 140*B*c^2*d^3*x^2*e^2 + 40*B*c^2*d^4*x*e + 5*B*c^2*d^5 + 420*B*b*c*x^4*e^5 + 210*A*c^2*x^4*e^5 + 336*B*b*c*d*x^3*e^4 + 168*A*c^2*d*x^3*e^4 + 168*B*b*c*d^2*x^2*e^3 + 84*A*c^2*d^2*x^2*e^3 + 48*B*b*c*d^3*x*e^2 + 24*A*c^2*d^3*x*e^2 + 6*B*b*c*d^4*e + 3*A*c^2*d^4*e + 168*B*b^2*x^3*e^5 + 336*B*a*c*x^3*e^5 + 336*A*b*c*x^3*e^5 + 84*B*b^2*d*x^2*e^4 + 168*B*a*c*d*x^2*e^4 + 168*A*b*c*d*x^2*e^4 + 24*B*b^2*d^2*x*e^3 + 48*B*a*c*d^2*x*e^3 + 48*A*b*c*d^2*x*e^3 + 3*B*b^2*d^3*e^2 + 6*B*a*c*d^3*e^2 + 6*A*b*c*d^3*e^2 + 280*B*a*b*x^2*e^5 + 140*A*b^2*x^2*e^5 + 280*A*a*c*x^2*e^5 + 80*B*a*b*d*x*e^4 + 40*A*b^2*d*x*e^4 + 80*A*a*c*d*x*e^4 + 10*B*a*b*d^2*e^3 + 5*A*b^2*d^2*e^3 + 10*A*a*c*d^2*e^3 + 120*B*a^2*x*e^5 + 240*A*a*b*x*e^5 + 15*B*a^2*d*e^4 + 30*A*a*b*d*e^4 + 105*A*a^2*e^5)*e^(-6)/(x*e + d)^8","A",0
2333,1,1603,0,0.180659," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{13} \, B c^{3} x^{13} e^{5} + \frac{5}{12} \, B c^{3} d x^{12} e^{4} + \frac{10}{11} \, B c^{3} d^{2} x^{11} e^{3} + B c^{3} d^{3} x^{10} e^{2} + \frac{5}{9} \, B c^{3} d^{4} x^{9} e + \frac{1}{8} \, B c^{3} d^{5} x^{8} + \frac{1}{4} \, B b c^{2} x^{12} e^{5} + \frac{1}{12} \, A c^{3} x^{12} e^{5} + \frac{15}{11} \, B b c^{2} d x^{11} e^{4} + \frac{5}{11} \, A c^{3} d x^{11} e^{4} + 3 \, B b c^{2} d^{2} x^{10} e^{3} + A c^{3} d^{2} x^{10} e^{3} + \frac{10}{3} \, B b c^{2} d^{3} x^{9} e^{2} + \frac{10}{9} \, A c^{3} d^{3} x^{9} e^{2} + \frac{15}{8} \, B b c^{2} d^{4} x^{8} e + \frac{5}{8} \, A c^{3} d^{4} x^{8} e + \frac{3}{7} \, B b c^{2} d^{5} x^{7} + \frac{1}{7} \, A c^{3} d^{5} x^{7} + \frac{3}{11} \, B b^{2} c x^{11} e^{5} + \frac{3}{11} \, B a c^{2} x^{11} e^{5} + \frac{3}{11} \, A b c^{2} x^{11} e^{5} + \frac{3}{2} \, B b^{2} c d x^{10} e^{4} + \frac{3}{2} \, B a c^{2} d x^{10} e^{4} + \frac{3}{2} \, A b c^{2} d x^{10} e^{4} + \frac{10}{3} \, B b^{2} c d^{2} x^{9} e^{3} + \frac{10}{3} \, B a c^{2} d^{2} x^{9} e^{3} + \frac{10}{3} \, A b c^{2} d^{2} x^{9} e^{3} + \frac{15}{4} \, B b^{2} c d^{3} x^{8} e^{2} + \frac{15}{4} \, B a c^{2} d^{3} x^{8} e^{2} + \frac{15}{4} \, A b c^{2} d^{3} x^{8} e^{2} + \frac{15}{7} \, B b^{2} c d^{4} x^{7} e + \frac{15}{7} \, B a c^{2} d^{4} x^{7} e + \frac{15}{7} \, A b c^{2} d^{4} x^{7} e + \frac{1}{2} \, B b^{2} c d^{5} x^{6} + \frac{1}{2} \, B a c^{2} d^{5} x^{6} + \frac{1}{2} \, A b c^{2} d^{5} x^{6} + \frac{1}{10} \, B b^{3} x^{10} e^{5} + \frac{3}{5} \, B a b c x^{10} e^{5} + \frac{3}{10} \, A b^{2} c x^{10} e^{5} + \frac{3}{10} \, A a c^{2} x^{10} e^{5} + \frac{5}{9} \, B b^{3} d x^{9} e^{4} + \frac{10}{3} \, B a b c d x^{9} e^{4} + \frac{5}{3} \, A b^{2} c d x^{9} e^{4} + \frac{5}{3} \, A a c^{2} d x^{9} e^{4} + \frac{5}{4} \, B b^{3} d^{2} x^{8} e^{3} + \frac{15}{2} \, B a b c d^{2} x^{8} e^{3} + \frac{15}{4} \, A b^{2} c d^{2} x^{8} e^{3} + \frac{15}{4} \, A a c^{2} d^{2} x^{8} e^{3} + \frac{10}{7} \, B b^{3} d^{3} x^{7} e^{2} + \frac{60}{7} \, B a b c d^{3} x^{7} e^{2} + \frac{30}{7} \, A b^{2} c d^{3} x^{7} e^{2} + \frac{30}{7} \, A a c^{2} d^{3} x^{7} e^{2} + \frac{5}{6} \, B b^{3} d^{4} x^{6} e + 5 \, B a b c d^{4} x^{6} e + \frac{5}{2} \, A b^{2} c d^{4} x^{6} e + \frac{5}{2} \, A a c^{2} d^{4} x^{6} e + \frac{1}{5} \, B b^{3} d^{5} x^{5} + \frac{6}{5} \, B a b c d^{5} x^{5} + \frac{3}{5} \, A b^{2} c d^{5} x^{5} + \frac{3}{5} \, A a c^{2} d^{5} x^{5} + \frac{1}{3} \, B a b^{2} x^{9} e^{5} + \frac{1}{9} \, A b^{3} x^{9} e^{5} + \frac{1}{3} \, B a^{2} c x^{9} e^{5} + \frac{2}{3} \, A a b c x^{9} e^{5} + \frac{15}{8} \, B a b^{2} d x^{8} e^{4} + \frac{5}{8} \, A b^{3} d x^{8} e^{4} + \frac{15}{8} \, B a^{2} c d x^{8} e^{4} + \frac{15}{4} \, A a b c d x^{8} e^{4} + \frac{30}{7} \, B a b^{2} d^{2} x^{7} e^{3} + \frac{10}{7} \, A b^{3} d^{2} x^{7} e^{3} + \frac{30}{7} \, B a^{2} c d^{2} x^{7} e^{3} + \frac{60}{7} \, A a b c d^{2} x^{7} e^{3} + 5 \, B a b^{2} d^{3} x^{6} e^{2} + \frac{5}{3} \, A b^{3} d^{3} x^{6} e^{2} + 5 \, B a^{2} c d^{3} x^{6} e^{2} + 10 \, A a b c d^{3} x^{6} e^{2} + 3 \, B a b^{2} d^{4} x^{5} e + A b^{3} d^{4} x^{5} e + 3 \, B a^{2} c d^{4} x^{5} e + 6 \, A a b c d^{4} x^{5} e + \frac{3}{4} \, B a b^{2} d^{5} x^{4} + \frac{1}{4} \, A b^{3} d^{5} x^{4} + \frac{3}{4} \, B a^{2} c d^{5} x^{4} + \frac{3}{2} \, A a b c d^{5} x^{4} + \frac{3}{8} \, B a^{2} b x^{8} e^{5} + \frac{3}{8} \, A a b^{2} x^{8} e^{5} + \frac{3}{8} \, A a^{2} c x^{8} e^{5} + \frac{15}{7} \, B a^{2} b d x^{7} e^{4} + \frac{15}{7} \, A a b^{2} d x^{7} e^{4} + \frac{15}{7} \, A a^{2} c d x^{7} e^{4} + 5 \, B a^{2} b d^{2} x^{6} e^{3} + 5 \, A a b^{2} d^{2} x^{6} e^{3} + 5 \, A a^{2} c d^{2} x^{6} e^{3} + 6 \, B a^{2} b d^{3} x^{5} e^{2} + 6 \, A a b^{2} d^{3} x^{5} e^{2} + 6 \, A a^{2} c d^{3} x^{5} e^{2} + \frac{15}{4} \, B a^{2} b d^{4} x^{4} e + \frac{15}{4} \, A a b^{2} d^{4} x^{4} e + \frac{15}{4} \, A a^{2} c d^{4} x^{4} e + B a^{2} b d^{5} x^{3} + A a b^{2} d^{5} x^{3} + A a^{2} c d^{5} x^{3} + \frac{1}{7} \, B a^{3} x^{7} e^{5} + \frac{3}{7} \, A a^{2} b x^{7} e^{5} + \frac{5}{6} \, B a^{3} d x^{6} e^{4} + \frac{5}{2} \, A a^{2} b d x^{6} e^{4} + 2 \, B a^{3} d^{2} x^{5} e^{3} + 6 \, A a^{2} b d^{2} x^{5} e^{3} + \frac{5}{2} \, B a^{3} d^{3} x^{4} e^{2} + \frac{15}{2} \, A a^{2} b d^{3} x^{4} e^{2} + \frac{5}{3} \, B a^{3} d^{4} x^{3} e + 5 \, A a^{2} b d^{4} x^{3} e + \frac{1}{2} \, B a^{3} d^{5} x^{2} + \frac{3}{2} \, A a^{2} b d^{5} x^{2} + \frac{1}{6} \, A a^{3} x^{6} e^{5} + A a^{3} d x^{5} e^{4} + \frac{5}{2} \, A a^{3} d^{2} x^{4} e^{3} + \frac{10}{3} \, A a^{3} d^{3} x^{3} e^{2} + \frac{5}{2} \, A a^{3} d^{4} x^{2} e + A a^{3} d^{5} x"," ",0,"1/13*B*c^3*x^13*e^5 + 5/12*B*c^3*d*x^12*e^4 + 10/11*B*c^3*d^2*x^11*e^3 + B*c^3*d^3*x^10*e^2 + 5/9*B*c^3*d^4*x^9*e + 1/8*B*c^3*d^5*x^8 + 1/4*B*b*c^2*x^12*e^5 + 1/12*A*c^3*x^12*e^5 + 15/11*B*b*c^2*d*x^11*e^4 + 5/11*A*c^3*d*x^11*e^4 + 3*B*b*c^2*d^2*x^10*e^3 + A*c^3*d^2*x^10*e^3 + 10/3*B*b*c^2*d^3*x^9*e^2 + 10/9*A*c^3*d^3*x^9*e^2 + 15/8*B*b*c^2*d^4*x^8*e + 5/8*A*c^3*d^4*x^8*e + 3/7*B*b*c^2*d^5*x^7 + 1/7*A*c^3*d^5*x^7 + 3/11*B*b^2*c*x^11*e^5 + 3/11*B*a*c^2*x^11*e^5 + 3/11*A*b*c^2*x^11*e^5 + 3/2*B*b^2*c*d*x^10*e^4 + 3/2*B*a*c^2*d*x^10*e^4 + 3/2*A*b*c^2*d*x^10*e^4 + 10/3*B*b^2*c*d^2*x^9*e^3 + 10/3*B*a*c^2*d^2*x^9*e^3 + 10/3*A*b*c^2*d^2*x^9*e^3 + 15/4*B*b^2*c*d^3*x^8*e^2 + 15/4*B*a*c^2*d^3*x^8*e^2 + 15/4*A*b*c^2*d^3*x^8*e^2 + 15/7*B*b^2*c*d^4*x^7*e + 15/7*B*a*c^2*d^4*x^7*e + 15/7*A*b*c^2*d^4*x^7*e + 1/2*B*b^2*c*d^5*x^6 + 1/2*B*a*c^2*d^5*x^6 + 1/2*A*b*c^2*d^5*x^6 + 1/10*B*b^3*x^10*e^5 + 3/5*B*a*b*c*x^10*e^5 + 3/10*A*b^2*c*x^10*e^5 + 3/10*A*a*c^2*x^10*e^5 + 5/9*B*b^3*d*x^9*e^4 + 10/3*B*a*b*c*d*x^9*e^4 + 5/3*A*b^2*c*d*x^9*e^4 + 5/3*A*a*c^2*d*x^9*e^4 + 5/4*B*b^3*d^2*x^8*e^3 + 15/2*B*a*b*c*d^2*x^8*e^3 + 15/4*A*b^2*c*d^2*x^8*e^3 + 15/4*A*a*c^2*d^2*x^8*e^3 + 10/7*B*b^3*d^3*x^7*e^2 + 60/7*B*a*b*c*d^3*x^7*e^2 + 30/7*A*b^2*c*d^3*x^7*e^2 + 30/7*A*a*c^2*d^3*x^7*e^2 + 5/6*B*b^3*d^4*x^6*e + 5*B*a*b*c*d^4*x^6*e + 5/2*A*b^2*c*d^4*x^6*e + 5/2*A*a*c^2*d^4*x^6*e + 1/5*B*b^3*d^5*x^5 + 6/5*B*a*b*c*d^5*x^5 + 3/5*A*b^2*c*d^5*x^5 + 3/5*A*a*c^2*d^5*x^5 + 1/3*B*a*b^2*x^9*e^5 + 1/9*A*b^3*x^9*e^5 + 1/3*B*a^2*c*x^9*e^5 + 2/3*A*a*b*c*x^9*e^5 + 15/8*B*a*b^2*d*x^8*e^4 + 5/8*A*b^3*d*x^8*e^4 + 15/8*B*a^2*c*d*x^8*e^4 + 15/4*A*a*b*c*d*x^8*e^4 + 30/7*B*a*b^2*d^2*x^7*e^3 + 10/7*A*b^3*d^2*x^7*e^3 + 30/7*B*a^2*c*d^2*x^7*e^3 + 60/7*A*a*b*c*d^2*x^7*e^3 + 5*B*a*b^2*d^3*x^6*e^2 + 5/3*A*b^3*d^3*x^6*e^2 + 5*B*a^2*c*d^3*x^6*e^2 + 10*A*a*b*c*d^3*x^6*e^2 + 3*B*a*b^2*d^4*x^5*e + A*b^3*d^4*x^5*e + 3*B*a^2*c*d^4*x^5*e + 6*A*a*b*c*d^4*x^5*e + 3/4*B*a*b^2*d^5*x^4 + 1/4*A*b^3*d^5*x^4 + 3/4*B*a^2*c*d^5*x^4 + 3/2*A*a*b*c*d^5*x^4 + 3/8*B*a^2*b*x^8*e^5 + 3/8*A*a*b^2*x^8*e^5 + 3/8*A*a^2*c*x^8*e^5 + 15/7*B*a^2*b*d*x^7*e^4 + 15/7*A*a*b^2*d*x^7*e^4 + 15/7*A*a^2*c*d*x^7*e^4 + 5*B*a^2*b*d^2*x^6*e^3 + 5*A*a*b^2*d^2*x^6*e^3 + 5*A*a^2*c*d^2*x^6*e^3 + 6*B*a^2*b*d^3*x^5*e^2 + 6*A*a*b^2*d^3*x^5*e^2 + 6*A*a^2*c*d^3*x^5*e^2 + 15/4*B*a^2*b*d^4*x^4*e + 15/4*A*a*b^2*d^4*x^4*e + 15/4*A*a^2*c*d^4*x^4*e + B*a^2*b*d^5*x^3 + A*a*b^2*d^5*x^3 + A*a^2*c*d^5*x^3 + 1/7*B*a^3*x^7*e^5 + 3/7*A*a^2*b*x^7*e^5 + 5/6*B*a^3*d*x^6*e^4 + 5/2*A*a^2*b*d*x^6*e^4 + 2*B*a^3*d^2*x^5*e^3 + 6*A*a^2*b*d^2*x^5*e^3 + 5/2*B*a^3*d^3*x^4*e^2 + 15/2*A*a^2*b*d^3*x^4*e^2 + 5/3*B*a^3*d^4*x^3*e + 5*A*a^2*b*d^4*x^3*e + 1/2*B*a^3*d^5*x^2 + 3/2*A*a^2*b*d^5*x^2 + 1/6*A*a^3*x^6*e^5 + A*a^3*d*x^5*e^4 + 5/2*A*a^3*d^2*x^4*e^3 + 10/3*A*a^3*d^3*x^3*e^2 + 5/2*A*a^3*d^4*x^2*e + A*a^3*d^5*x","B",0
2334,1,1313,0,0.197639," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{12} \, B c^{3} x^{12} e^{4} + \frac{4}{11} \, B c^{3} d x^{11} e^{3} + \frac{3}{5} \, B c^{3} d^{2} x^{10} e^{2} + \frac{4}{9} \, B c^{3} d^{3} x^{9} e + \frac{1}{8} \, B c^{3} d^{4} x^{8} + \frac{3}{11} \, B b c^{2} x^{11} e^{4} + \frac{1}{11} \, A c^{3} x^{11} e^{4} + \frac{6}{5} \, B b c^{2} d x^{10} e^{3} + \frac{2}{5} \, A c^{3} d x^{10} e^{3} + 2 \, B b c^{2} d^{2} x^{9} e^{2} + \frac{2}{3} \, A c^{3} d^{2} x^{9} e^{2} + \frac{3}{2} \, B b c^{2} d^{3} x^{8} e + \frac{1}{2} \, A c^{3} d^{3} x^{8} e + \frac{3}{7} \, B b c^{2} d^{4} x^{7} + \frac{1}{7} \, A c^{3} d^{4} x^{7} + \frac{3}{10} \, B b^{2} c x^{10} e^{4} + \frac{3}{10} \, B a c^{2} x^{10} e^{4} + \frac{3}{10} \, A b c^{2} x^{10} e^{4} + \frac{4}{3} \, B b^{2} c d x^{9} e^{3} + \frac{4}{3} \, B a c^{2} d x^{9} e^{3} + \frac{4}{3} \, A b c^{2} d x^{9} e^{3} + \frac{9}{4} \, B b^{2} c d^{2} x^{8} e^{2} + \frac{9}{4} \, B a c^{2} d^{2} x^{8} e^{2} + \frac{9}{4} \, A b c^{2} d^{2} x^{8} e^{2} + \frac{12}{7} \, B b^{2} c d^{3} x^{7} e + \frac{12}{7} \, B a c^{2} d^{3} x^{7} e + \frac{12}{7} \, A b c^{2} d^{3} x^{7} e + \frac{1}{2} \, B b^{2} c d^{4} x^{6} + \frac{1}{2} \, B a c^{2} d^{4} x^{6} + \frac{1}{2} \, A b c^{2} d^{4} x^{6} + \frac{1}{9} \, B b^{3} x^{9} e^{4} + \frac{2}{3} \, B a b c x^{9} e^{4} + \frac{1}{3} \, A b^{2} c x^{9} e^{4} + \frac{1}{3} \, A a c^{2} x^{9} e^{4} + \frac{1}{2} \, B b^{3} d x^{8} e^{3} + 3 \, B a b c d x^{8} e^{3} + \frac{3}{2} \, A b^{2} c d x^{8} e^{3} + \frac{3}{2} \, A a c^{2} d x^{8} e^{3} + \frac{6}{7} \, B b^{3} d^{2} x^{7} e^{2} + \frac{36}{7} \, B a b c d^{2} x^{7} e^{2} + \frac{18}{7} \, A b^{2} c d^{2} x^{7} e^{2} + \frac{18}{7} \, A a c^{2} d^{2} x^{7} e^{2} + \frac{2}{3} \, B b^{3} d^{3} x^{6} e + 4 \, B a b c d^{3} x^{6} e + 2 \, A b^{2} c d^{3} x^{6} e + 2 \, A a c^{2} d^{3} x^{6} e + \frac{1}{5} \, B b^{3} d^{4} x^{5} + \frac{6}{5} \, B a b c d^{4} x^{5} + \frac{3}{5} \, A b^{2} c d^{4} x^{5} + \frac{3}{5} \, A a c^{2} d^{4} x^{5} + \frac{3}{8} \, B a b^{2} x^{8} e^{4} + \frac{1}{8} \, A b^{3} x^{8} e^{4} + \frac{3}{8} \, B a^{2} c x^{8} e^{4} + \frac{3}{4} \, A a b c x^{8} e^{4} + \frac{12}{7} \, B a b^{2} d x^{7} e^{3} + \frac{4}{7} \, A b^{3} d x^{7} e^{3} + \frac{12}{7} \, B a^{2} c d x^{7} e^{3} + \frac{24}{7} \, A a b c d x^{7} e^{3} + 3 \, B a b^{2} d^{2} x^{6} e^{2} + A b^{3} d^{2} x^{6} e^{2} + 3 \, B a^{2} c d^{2} x^{6} e^{2} + 6 \, A a b c d^{2} x^{6} e^{2} + \frac{12}{5} \, B a b^{2} d^{3} x^{5} e + \frac{4}{5} \, A b^{3} d^{3} x^{5} e + \frac{12}{5} \, B a^{2} c d^{3} x^{5} e + \frac{24}{5} \, A a b c d^{3} x^{5} e + \frac{3}{4} \, B a b^{2} d^{4} x^{4} + \frac{1}{4} \, A b^{3} d^{4} x^{4} + \frac{3}{4} \, B a^{2} c d^{4} x^{4} + \frac{3}{2} \, A a b c d^{4} x^{4} + \frac{3}{7} \, B a^{2} b x^{7} e^{4} + \frac{3}{7} \, A a b^{2} x^{7} e^{4} + \frac{3}{7} \, A a^{2} c x^{7} e^{4} + 2 \, B a^{2} b d x^{6} e^{3} + 2 \, A a b^{2} d x^{6} e^{3} + 2 \, A a^{2} c d x^{6} e^{3} + \frac{18}{5} \, B a^{2} b d^{2} x^{5} e^{2} + \frac{18}{5} \, A a b^{2} d^{2} x^{5} e^{2} + \frac{18}{5} \, A a^{2} c d^{2} x^{5} e^{2} + 3 \, B a^{2} b d^{3} x^{4} e + 3 \, A a b^{2} d^{3} x^{4} e + 3 \, A a^{2} c d^{3} x^{4} e + B a^{2} b d^{4} x^{3} + A a b^{2} d^{4} x^{3} + A a^{2} c d^{4} x^{3} + \frac{1}{6} \, B a^{3} x^{6} e^{4} + \frac{1}{2} \, A a^{2} b x^{6} e^{4} + \frac{4}{5} \, B a^{3} d x^{5} e^{3} + \frac{12}{5} \, A a^{2} b d x^{5} e^{3} + \frac{3}{2} \, B a^{3} d^{2} x^{4} e^{2} + \frac{9}{2} \, A a^{2} b d^{2} x^{4} e^{2} + \frac{4}{3} \, B a^{3} d^{3} x^{3} e + 4 \, A a^{2} b d^{3} x^{3} e + \frac{1}{2} \, B a^{3} d^{4} x^{2} + \frac{3}{2} \, A a^{2} b d^{4} x^{2} + \frac{1}{5} \, A a^{3} x^{5} e^{4} + A a^{3} d x^{4} e^{3} + 2 \, A a^{3} d^{2} x^{3} e^{2} + 2 \, A a^{3} d^{3} x^{2} e + A a^{3} d^{4} x"," ",0,"1/12*B*c^3*x^12*e^4 + 4/11*B*c^3*d*x^11*e^3 + 3/5*B*c^3*d^2*x^10*e^2 + 4/9*B*c^3*d^3*x^9*e + 1/8*B*c^3*d^4*x^8 + 3/11*B*b*c^2*x^11*e^4 + 1/11*A*c^3*x^11*e^4 + 6/5*B*b*c^2*d*x^10*e^3 + 2/5*A*c^3*d*x^10*e^3 + 2*B*b*c^2*d^2*x^9*e^2 + 2/3*A*c^3*d^2*x^9*e^2 + 3/2*B*b*c^2*d^3*x^8*e + 1/2*A*c^3*d^3*x^8*e + 3/7*B*b*c^2*d^4*x^7 + 1/7*A*c^3*d^4*x^7 + 3/10*B*b^2*c*x^10*e^4 + 3/10*B*a*c^2*x^10*e^4 + 3/10*A*b*c^2*x^10*e^4 + 4/3*B*b^2*c*d*x^9*e^3 + 4/3*B*a*c^2*d*x^9*e^3 + 4/3*A*b*c^2*d*x^9*e^3 + 9/4*B*b^2*c*d^2*x^8*e^2 + 9/4*B*a*c^2*d^2*x^8*e^2 + 9/4*A*b*c^2*d^2*x^8*e^2 + 12/7*B*b^2*c*d^3*x^7*e + 12/7*B*a*c^2*d^3*x^7*e + 12/7*A*b*c^2*d^3*x^7*e + 1/2*B*b^2*c*d^4*x^6 + 1/2*B*a*c^2*d^4*x^6 + 1/2*A*b*c^2*d^4*x^6 + 1/9*B*b^3*x^9*e^4 + 2/3*B*a*b*c*x^9*e^4 + 1/3*A*b^2*c*x^9*e^4 + 1/3*A*a*c^2*x^9*e^4 + 1/2*B*b^3*d*x^8*e^3 + 3*B*a*b*c*d*x^8*e^3 + 3/2*A*b^2*c*d*x^8*e^3 + 3/2*A*a*c^2*d*x^8*e^3 + 6/7*B*b^3*d^2*x^7*e^2 + 36/7*B*a*b*c*d^2*x^7*e^2 + 18/7*A*b^2*c*d^2*x^7*e^2 + 18/7*A*a*c^2*d^2*x^7*e^2 + 2/3*B*b^3*d^3*x^6*e + 4*B*a*b*c*d^3*x^6*e + 2*A*b^2*c*d^3*x^6*e + 2*A*a*c^2*d^3*x^6*e + 1/5*B*b^3*d^4*x^5 + 6/5*B*a*b*c*d^4*x^5 + 3/5*A*b^2*c*d^4*x^5 + 3/5*A*a*c^2*d^4*x^5 + 3/8*B*a*b^2*x^8*e^4 + 1/8*A*b^3*x^8*e^4 + 3/8*B*a^2*c*x^8*e^4 + 3/4*A*a*b*c*x^8*e^4 + 12/7*B*a*b^2*d*x^7*e^3 + 4/7*A*b^3*d*x^7*e^3 + 12/7*B*a^2*c*d*x^7*e^3 + 24/7*A*a*b*c*d*x^7*e^3 + 3*B*a*b^2*d^2*x^6*e^2 + A*b^3*d^2*x^6*e^2 + 3*B*a^2*c*d^2*x^6*e^2 + 6*A*a*b*c*d^2*x^6*e^2 + 12/5*B*a*b^2*d^3*x^5*e + 4/5*A*b^3*d^3*x^5*e + 12/5*B*a^2*c*d^3*x^5*e + 24/5*A*a*b*c*d^3*x^5*e + 3/4*B*a*b^2*d^4*x^4 + 1/4*A*b^3*d^4*x^4 + 3/4*B*a^2*c*d^4*x^4 + 3/2*A*a*b*c*d^4*x^4 + 3/7*B*a^2*b*x^7*e^4 + 3/7*A*a*b^2*x^7*e^4 + 3/7*A*a^2*c*x^7*e^4 + 2*B*a^2*b*d*x^6*e^3 + 2*A*a*b^2*d*x^6*e^3 + 2*A*a^2*c*d*x^6*e^3 + 18/5*B*a^2*b*d^2*x^5*e^2 + 18/5*A*a*b^2*d^2*x^5*e^2 + 18/5*A*a^2*c*d^2*x^5*e^2 + 3*B*a^2*b*d^3*x^4*e + 3*A*a*b^2*d^3*x^4*e + 3*A*a^2*c*d^3*x^4*e + B*a^2*b*d^4*x^3 + A*a*b^2*d^4*x^3 + A*a^2*c*d^4*x^3 + 1/6*B*a^3*x^6*e^4 + 1/2*A*a^2*b*x^6*e^4 + 4/5*B*a^3*d*x^5*e^3 + 12/5*A*a^2*b*d*x^5*e^3 + 3/2*B*a^3*d^2*x^4*e^2 + 9/2*A*a^2*b*d^2*x^4*e^2 + 4/3*B*a^3*d^3*x^3*e + 4*A*a^2*b*d^3*x^3*e + 1/2*B*a^3*d^4*x^2 + 3/2*A*a^2*b*d^4*x^2 + 1/5*A*a^3*x^5*e^4 + A*a^3*d*x^4*e^3 + 2*A*a^3*d^2*x^3*e^2 + 2*A*a^3*d^3*x^2*e + A*a^3*d^4*x","B",0
2335,1,1020,0,0.166881," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{11} \, B c^{3} x^{11} e^{3} + \frac{3}{10} \, B c^{3} d x^{10} e^{2} + \frac{1}{3} \, B c^{3} d^{2} x^{9} e + \frac{1}{8} \, B c^{3} d^{3} x^{8} + \frac{3}{10} \, B b c^{2} x^{10} e^{3} + \frac{1}{10} \, A c^{3} x^{10} e^{3} + B b c^{2} d x^{9} e^{2} + \frac{1}{3} \, A c^{3} d x^{9} e^{2} + \frac{9}{8} \, B b c^{2} d^{2} x^{8} e + \frac{3}{8} \, A c^{3} d^{2} x^{8} e + \frac{3}{7} \, B b c^{2} d^{3} x^{7} + \frac{1}{7} \, A c^{3} d^{3} x^{7} + \frac{1}{3} \, B b^{2} c x^{9} e^{3} + \frac{1}{3} \, B a c^{2} x^{9} e^{3} + \frac{1}{3} \, A b c^{2} x^{9} e^{3} + \frac{9}{8} \, B b^{2} c d x^{8} e^{2} + \frac{9}{8} \, B a c^{2} d x^{8} e^{2} + \frac{9}{8} \, A b c^{2} d x^{8} e^{2} + \frac{9}{7} \, B b^{2} c d^{2} x^{7} e + \frac{9}{7} \, B a c^{2} d^{2} x^{7} e + \frac{9}{7} \, A b c^{2} d^{2} x^{7} e + \frac{1}{2} \, B b^{2} c d^{3} x^{6} + \frac{1}{2} \, B a c^{2} d^{3} x^{6} + \frac{1}{2} \, A b c^{2} d^{3} x^{6} + \frac{1}{8} \, B b^{3} x^{8} e^{3} + \frac{3}{4} \, B a b c x^{8} e^{3} + \frac{3}{8} \, A b^{2} c x^{8} e^{3} + \frac{3}{8} \, A a c^{2} x^{8} e^{3} + \frac{3}{7} \, B b^{3} d x^{7} e^{2} + \frac{18}{7} \, B a b c d x^{7} e^{2} + \frac{9}{7} \, A b^{2} c d x^{7} e^{2} + \frac{9}{7} \, A a c^{2} d x^{7} e^{2} + \frac{1}{2} \, B b^{3} d^{2} x^{6} e + 3 \, B a b c d^{2} x^{6} e + \frac{3}{2} \, A b^{2} c d^{2} x^{6} e + \frac{3}{2} \, A a c^{2} d^{2} x^{6} e + \frac{1}{5} \, B b^{3} d^{3} x^{5} + \frac{6}{5} \, B a b c d^{3} x^{5} + \frac{3}{5} \, A b^{2} c d^{3} x^{5} + \frac{3}{5} \, A a c^{2} d^{3} x^{5} + \frac{3}{7} \, B a b^{2} x^{7} e^{3} + \frac{1}{7} \, A b^{3} x^{7} e^{3} + \frac{3}{7} \, B a^{2} c x^{7} e^{3} + \frac{6}{7} \, A a b c x^{7} e^{3} + \frac{3}{2} \, B a b^{2} d x^{6} e^{2} + \frac{1}{2} \, A b^{3} d x^{6} e^{2} + \frac{3}{2} \, B a^{2} c d x^{6} e^{2} + 3 \, A a b c d x^{6} e^{2} + \frac{9}{5} \, B a b^{2} d^{2} x^{5} e + \frac{3}{5} \, A b^{3} d^{2} x^{5} e + \frac{9}{5} \, B a^{2} c d^{2} x^{5} e + \frac{18}{5} \, A a b c d^{2} x^{5} e + \frac{3}{4} \, B a b^{2} d^{3} x^{4} + \frac{1}{4} \, A b^{3} d^{3} x^{4} + \frac{3}{4} \, B a^{2} c d^{3} x^{4} + \frac{3}{2} \, A a b c d^{3} x^{4} + \frac{1}{2} \, B a^{2} b x^{6} e^{3} + \frac{1}{2} \, A a b^{2} x^{6} e^{3} + \frac{1}{2} \, A a^{2} c x^{6} e^{3} + \frac{9}{5} \, B a^{2} b d x^{5} e^{2} + \frac{9}{5} \, A a b^{2} d x^{5} e^{2} + \frac{9}{5} \, A a^{2} c d x^{5} e^{2} + \frac{9}{4} \, B a^{2} b d^{2} x^{4} e + \frac{9}{4} \, A a b^{2} d^{2} x^{4} e + \frac{9}{4} \, A a^{2} c d^{2} x^{4} e + B a^{2} b d^{3} x^{3} + A a b^{2} d^{3} x^{3} + A a^{2} c d^{3} x^{3} + \frac{1}{5} \, B a^{3} x^{5} e^{3} + \frac{3}{5} \, A a^{2} b x^{5} e^{3} + \frac{3}{4} \, B a^{3} d x^{4} e^{2} + \frac{9}{4} \, A a^{2} b d x^{4} e^{2} + B a^{3} d^{2} x^{3} e + 3 \, A a^{2} b d^{2} x^{3} e + \frac{1}{2} \, B a^{3} d^{3} x^{2} + \frac{3}{2} \, A a^{2} b d^{3} x^{2} + \frac{1}{4} \, A a^{3} x^{4} e^{3} + A a^{3} d x^{3} e^{2} + \frac{3}{2} \, A a^{3} d^{2} x^{2} e + A a^{3} d^{3} x"," ",0,"1/11*B*c^3*x^11*e^3 + 3/10*B*c^3*d*x^10*e^2 + 1/3*B*c^3*d^2*x^9*e + 1/8*B*c^3*d^3*x^8 + 3/10*B*b*c^2*x^10*e^3 + 1/10*A*c^3*x^10*e^3 + B*b*c^2*d*x^9*e^2 + 1/3*A*c^3*d*x^9*e^2 + 9/8*B*b*c^2*d^2*x^8*e + 3/8*A*c^3*d^2*x^8*e + 3/7*B*b*c^2*d^3*x^7 + 1/7*A*c^3*d^3*x^7 + 1/3*B*b^2*c*x^9*e^3 + 1/3*B*a*c^2*x^9*e^3 + 1/3*A*b*c^2*x^9*e^3 + 9/8*B*b^2*c*d*x^8*e^2 + 9/8*B*a*c^2*d*x^8*e^2 + 9/8*A*b*c^2*d*x^8*e^2 + 9/7*B*b^2*c*d^2*x^7*e + 9/7*B*a*c^2*d^2*x^7*e + 9/7*A*b*c^2*d^2*x^7*e + 1/2*B*b^2*c*d^3*x^6 + 1/2*B*a*c^2*d^3*x^6 + 1/2*A*b*c^2*d^3*x^6 + 1/8*B*b^3*x^8*e^3 + 3/4*B*a*b*c*x^8*e^3 + 3/8*A*b^2*c*x^8*e^3 + 3/8*A*a*c^2*x^8*e^3 + 3/7*B*b^3*d*x^7*e^2 + 18/7*B*a*b*c*d*x^7*e^2 + 9/7*A*b^2*c*d*x^7*e^2 + 9/7*A*a*c^2*d*x^7*e^2 + 1/2*B*b^3*d^2*x^6*e + 3*B*a*b*c*d^2*x^6*e + 3/2*A*b^2*c*d^2*x^6*e + 3/2*A*a*c^2*d^2*x^6*e + 1/5*B*b^3*d^3*x^5 + 6/5*B*a*b*c*d^3*x^5 + 3/5*A*b^2*c*d^3*x^5 + 3/5*A*a*c^2*d^3*x^5 + 3/7*B*a*b^2*x^7*e^3 + 1/7*A*b^3*x^7*e^3 + 3/7*B*a^2*c*x^7*e^3 + 6/7*A*a*b*c*x^7*e^3 + 3/2*B*a*b^2*d*x^6*e^2 + 1/2*A*b^3*d*x^6*e^2 + 3/2*B*a^2*c*d*x^6*e^2 + 3*A*a*b*c*d*x^6*e^2 + 9/5*B*a*b^2*d^2*x^5*e + 3/5*A*b^3*d^2*x^5*e + 9/5*B*a^2*c*d^2*x^5*e + 18/5*A*a*b*c*d^2*x^5*e + 3/4*B*a*b^2*d^3*x^4 + 1/4*A*b^3*d^3*x^4 + 3/4*B*a^2*c*d^3*x^4 + 3/2*A*a*b*c*d^3*x^4 + 1/2*B*a^2*b*x^6*e^3 + 1/2*A*a*b^2*x^6*e^3 + 1/2*A*a^2*c*x^6*e^3 + 9/5*B*a^2*b*d*x^5*e^2 + 9/5*A*a*b^2*d*x^5*e^2 + 9/5*A*a^2*c*d*x^5*e^2 + 9/4*B*a^2*b*d^2*x^4*e + 9/4*A*a*b^2*d^2*x^4*e + 9/4*A*a^2*c*d^2*x^4*e + B*a^2*b*d^3*x^3 + A*a*b^2*d^3*x^3 + A*a^2*c*d^3*x^3 + 1/5*B*a^3*x^5*e^3 + 3/5*A*a^2*b*x^5*e^3 + 3/4*B*a^3*d*x^4*e^2 + 9/4*A*a^2*b*d*x^4*e^2 + B*a^3*d^2*x^3*e + 3*A*a^2*b*d^2*x^3*e + 1/2*B*a^3*d^3*x^2 + 3/2*A*a^2*b*d^3*x^2 + 1/4*A*a^3*x^4*e^3 + A*a^3*d*x^3*e^2 + 3/2*A*a^3*d^2*x^2*e + A*a^3*d^3*x","A",0
2336,1,727,0,0.164028," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{10} \, B c^{3} x^{10} e^{2} + \frac{2}{9} \, B c^{3} d x^{9} e + \frac{1}{8} \, B c^{3} d^{2} x^{8} + \frac{1}{3} \, B b c^{2} x^{9} e^{2} + \frac{1}{9} \, A c^{3} x^{9} e^{2} + \frac{3}{4} \, B b c^{2} d x^{8} e + \frac{1}{4} \, A c^{3} d x^{8} e + \frac{3}{7} \, B b c^{2} d^{2} x^{7} + \frac{1}{7} \, A c^{3} d^{2} x^{7} + \frac{3}{8} \, B b^{2} c x^{8} e^{2} + \frac{3}{8} \, B a c^{2} x^{8} e^{2} + \frac{3}{8} \, A b c^{2} x^{8} e^{2} + \frac{6}{7} \, B b^{2} c d x^{7} e + \frac{6}{7} \, B a c^{2} d x^{7} e + \frac{6}{7} \, A b c^{2} d x^{7} e + \frac{1}{2} \, B b^{2} c d^{2} x^{6} + \frac{1}{2} \, B a c^{2} d^{2} x^{6} + \frac{1}{2} \, A b c^{2} d^{2} x^{6} + \frac{1}{7} \, B b^{3} x^{7} e^{2} + \frac{6}{7} \, B a b c x^{7} e^{2} + \frac{3}{7} \, A b^{2} c x^{7} e^{2} + \frac{3}{7} \, A a c^{2} x^{7} e^{2} + \frac{1}{3} \, B b^{3} d x^{6} e + 2 \, B a b c d x^{6} e + A b^{2} c d x^{6} e + A a c^{2} d x^{6} e + \frac{1}{5} \, B b^{3} d^{2} x^{5} + \frac{6}{5} \, B a b c d^{2} x^{5} + \frac{3}{5} \, A b^{2} c d^{2} x^{5} + \frac{3}{5} \, A a c^{2} d^{2} x^{5} + \frac{1}{2} \, B a b^{2} x^{6} e^{2} + \frac{1}{6} \, A b^{3} x^{6} e^{2} + \frac{1}{2} \, B a^{2} c x^{6} e^{2} + A a b c x^{6} e^{2} + \frac{6}{5} \, B a b^{2} d x^{5} e + \frac{2}{5} \, A b^{3} d x^{5} e + \frac{6}{5} \, B a^{2} c d x^{5} e + \frac{12}{5} \, A a b c d x^{5} e + \frac{3}{4} \, B a b^{2} d^{2} x^{4} + \frac{1}{4} \, A b^{3} d^{2} x^{4} + \frac{3}{4} \, B a^{2} c d^{2} x^{4} + \frac{3}{2} \, A a b c d^{2} x^{4} + \frac{3}{5} \, B a^{2} b x^{5} e^{2} + \frac{3}{5} \, A a b^{2} x^{5} e^{2} + \frac{3}{5} \, A a^{2} c x^{5} e^{2} + \frac{3}{2} \, B a^{2} b d x^{4} e + \frac{3}{2} \, A a b^{2} d x^{4} e + \frac{3}{2} \, A a^{2} c d x^{4} e + B a^{2} b d^{2} x^{3} + A a b^{2} d^{2} x^{3} + A a^{2} c d^{2} x^{3} + \frac{1}{4} \, B a^{3} x^{4} e^{2} + \frac{3}{4} \, A a^{2} b x^{4} e^{2} + \frac{2}{3} \, B a^{3} d x^{3} e + 2 \, A a^{2} b d x^{3} e + \frac{1}{2} \, B a^{3} d^{2} x^{2} + \frac{3}{2} \, A a^{2} b d^{2} x^{2} + \frac{1}{3} \, A a^{3} x^{3} e^{2} + A a^{3} d x^{2} e + A a^{3} d^{2} x"," ",0,"1/10*B*c^3*x^10*e^2 + 2/9*B*c^3*d*x^9*e + 1/8*B*c^3*d^2*x^8 + 1/3*B*b*c^2*x^9*e^2 + 1/9*A*c^3*x^9*e^2 + 3/4*B*b*c^2*d*x^8*e + 1/4*A*c^3*d*x^8*e + 3/7*B*b*c^2*d^2*x^7 + 1/7*A*c^3*d^2*x^7 + 3/8*B*b^2*c*x^8*e^2 + 3/8*B*a*c^2*x^8*e^2 + 3/8*A*b*c^2*x^8*e^2 + 6/7*B*b^2*c*d*x^7*e + 6/7*B*a*c^2*d*x^7*e + 6/7*A*b*c^2*d*x^7*e + 1/2*B*b^2*c*d^2*x^6 + 1/2*B*a*c^2*d^2*x^6 + 1/2*A*b*c^2*d^2*x^6 + 1/7*B*b^3*x^7*e^2 + 6/7*B*a*b*c*x^7*e^2 + 3/7*A*b^2*c*x^7*e^2 + 3/7*A*a*c^2*x^7*e^2 + 1/3*B*b^3*d*x^6*e + 2*B*a*b*c*d*x^6*e + A*b^2*c*d*x^6*e + A*a*c^2*d*x^6*e + 1/5*B*b^3*d^2*x^5 + 6/5*B*a*b*c*d^2*x^5 + 3/5*A*b^2*c*d^2*x^5 + 3/5*A*a*c^2*d^2*x^5 + 1/2*B*a*b^2*x^6*e^2 + 1/6*A*b^3*x^6*e^2 + 1/2*B*a^2*c*x^6*e^2 + A*a*b*c*x^6*e^2 + 6/5*B*a*b^2*d*x^5*e + 2/5*A*b^3*d*x^5*e + 6/5*B*a^2*c*d*x^5*e + 12/5*A*a*b*c*d*x^5*e + 3/4*B*a*b^2*d^2*x^4 + 1/4*A*b^3*d^2*x^4 + 3/4*B*a^2*c*d^2*x^4 + 3/2*A*a*b*c*d^2*x^4 + 3/5*B*a^2*b*x^5*e^2 + 3/5*A*a*b^2*x^5*e^2 + 3/5*A*a^2*c*x^5*e^2 + 3/2*B*a^2*b*d*x^4*e + 3/2*A*a*b^2*d*x^4*e + 3/2*A*a^2*c*d*x^4*e + B*a^2*b*d^2*x^3 + A*a*b^2*d^2*x^3 + A*a^2*c*d^2*x^3 + 1/4*B*a^3*x^4*e^2 + 3/4*A*a^2*b*x^4*e^2 + 2/3*B*a^3*d*x^3*e + 2*A*a^2*b*d*x^3*e + 1/2*B*a^3*d^2*x^2 + 3/2*A*a^2*b*d^2*x^2 + 1/3*A*a^3*x^3*e^2 + A*a^3*d*x^2*e + A*a^3*d^2*x","A",0
2337,1,437,0,0.163310," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{9} \, B c^{3} x^{9} e + \frac{1}{8} \, B c^{3} d x^{8} + \frac{3}{8} \, B b c^{2} x^{8} e + \frac{1}{8} \, A c^{3} x^{8} e + \frac{3}{7} \, B b c^{2} d x^{7} + \frac{1}{7} \, A c^{3} d x^{7} + \frac{3}{7} \, B b^{2} c x^{7} e + \frac{3}{7} \, B a c^{2} x^{7} e + \frac{3}{7} \, A b c^{2} x^{7} e + \frac{1}{2} \, B b^{2} c d x^{6} + \frac{1}{2} \, B a c^{2} d x^{6} + \frac{1}{2} \, A b c^{2} d x^{6} + \frac{1}{6} \, B b^{3} x^{6} e + B a b c x^{6} e + \frac{1}{2} \, A b^{2} c x^{6} e + \frac{1}{2} \, A a c^{2} x^{6} e + \frac{1}{5} \, B b^{3} d x^{5} + \frac{6}{5} \, B a b c d x^{5} + \frac{3}{5} \, A b^{2} c d x^{5} + \frac{3}{5} \, A a c^{2} d x^{5} + \frac{3}{5} \, B a b^{2} x^{5} e + \frac{1}{5} \, A b^{3} x^{5} e + \frac{3}{5} \, B a^{2} c x^{5} e + \frac{6}{5} \, A a b c x^{5} e + \frac{3}{4} \, B a b^{2} d x^{4} + \frac{1}{4} \, A b^{3} d x^{4} + \frac{3}{4} \, B a^{2} c d x^{4} + \frac{3}{2} \, A a b c d x^{4} + \frac{3}{4} \, B a^{2} b x^{4} e + \frac{3}{4} \, A a b^{2} x^{4} e + \frac{3}{4} \, A a^{2} c x^{4} e + B a^{2} b d x^{3} + A a b^{2} d x^{3} + A a^{2} c d x^{3} + \frac{1}{3} \, B a^{3} x^{3} e + A a^{2} b x^{3} e + \frac{1}{2} \, B a^{3} d x^{2} + \frac{3}{2} \, A a^{2} b d x^{2} + \frac{1}{2} \, A a^{3} x^{2} e + A a^{3} d x"," ",0,"1/9*B*c^3*x^9*e + 1/8*B*c^3*d*x^8 + 3/8*B*b*c^2*x^8*e + 1/8*A*c^3*x^8*e + 3/7*B*b*c^2*d*x^7 + 1/7*A*c^3*d*x^7 + 3/7*B*b^2*c*x^7*e + 3/7*B*a*c^2*x^7*e + 3/7*A*b*c^2*x^7*e + 1/2*B*b^2*c*d*x^6 + 1/2*B*a*c^2*d*x^6 + 1/2*A*b*c^2*d*x^6 + 1/6*B*b^3*x^6*e + B*a*b*c*x^6*e + 1/2*A*b^2*c*x^6*e + 1/2*A*a*c^2*x^6*e + 1/5*B*b^3*d*x^5 + 6/5*B*a*b*c*d*x^5 + 3/5*A*b^2*c*d*x^5 + 3/5*A*a*c^2*d*x^5 + 3/5*B*a*b^2*x^5*e + 1/5*A*b^3*x^5*e + 3/5*B*a^2*c*x^5*e + 6/5*A*a*b*c*x^5*e + 3/4*B*a*b^2*d*x^4 + 1/4*A*b^3*d*x^4 + 3/4*B*a^2*c*d*x^4 + 3/2*A*a*b*c*d*x^4 + 3/4*B*a^2*b*x^4*e + 3/4*A*a*b^2*x^4*e + 3/4*A*a^2*c*x^4*e + B*a^2*b*d*x^3 + A*a*b^2*d*x^3 + A*a^2*c*d*x^3 + 1/3*B*a^3*x^3*e + A*a^2*b*x^3*e + 1/2*B*a^3*d*x^2 + 3/2*A*a^2*b*d*x^2 + 1/2*A*a^3*x^2*e + A*a^3*d*x","A",0
2338,1,187,0,0.151629," ","integrate((B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{8} \, B c^{3} x^{8} + \frac{3}{7} \, B b c^{2} x^{7} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{2} \, B b^{2} c x^{6} + \frac{1}{2} \, B a c^{2} x^{6} + \frac{1}{2} \, A b c^{2} x^{6} + \frac{1}{5} \, B b^{3} x^{5} + \frac{6}{5} \, B a b c x^{5} + \frac{3}{5} \, A b^{2} c x^{5} + \frac{3}{5} \, A a c^{2} x^{5} + \frac{3}{4} \, B a b^{2} x^{4} + \frac{1}{4} \, A b^{3} x^{4} + \frac{3}{4} \, B a^{2} c x^{4} + \frac{3}{2} \, A a b c x^{4} + B a^{2} b x^{3} + A a b^{2} x^{3} + A a^{2} c x^{3} + \frac{1}{2} \, B a^{3} x^{2} + \frac{3}{2} \, A a^{2} b x^{2} + A a^{3} x"," ",0,"1/8*B*c^3*x^8 + 3/7*B*b*c^2*x^7 + 1/7*A*c^3*x^7 + 1/2*B*b^2*c*x^6 + 1/2*B*a*c^2*x^6 + 1/2*A*b*c^2*x^6 + 1/5*B*b^3*x^5 + 6/5*B*a*b*c*x^5 + 3/5*A*b^2*c*x^5 + 3/5*A*a*c^2*x^5 + 3/4*B*a*b^2*x^4 + 1/4*A*b^3*x^4 + 3/4*B*a^2*c*x^4 + 3/2*A*a*b*c*x^4 + B*a^2*b*x^3 + A*a*b^2*x^3 + A*a^2*c*x^3 + 1/2*B*a^3*x^2 + 3/2*A*a^2*b*x^2 + A*a^3*x","A",0
2339,1,1130,0,0.201114," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d),x, algorithm=""giac"")","-{\left(B c^{3} d^{7} - 3 \, B b c^{2} d^{6} e - A c^{3} d^{6} e + 3 \, B b^{2} c d^{5} e^{2} + 3 \, B a c^{2} d^{5} e^{2} + 3 \, A b c^{2} d^{5} e^{2} - B b^{3} d^{4} e^{3} - 6 \, B a b c d^{4} e^{3} - 3 \, A b^{2} c d^{4} e^{3} - 3 \, A a c^{2} d^{4} e^{3} + 3 \, B a b^{2} d^{3} e^{4} + A b^{3} d^{3} e^{4} + 3 \, B a^{2} c d^{3} e^{4} + 6 \, A a b c d^{3} e^{4} - 3 \, B a^{2} b d^{2} e^{5} - 3 \, A a b^{2} d^{2} e^{5} - 3 \, A a^{2} c d^{2} e^{5} + B a^{3} d e^{6} + 3 \, A a^{2} b d e^{6} - A a^{3} e^{7}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{420} \, {\left(60 \, B c^{3} x^{7} e^{6} - 70 \, B c^{3} d x^{6} e^{5} + 84 \, B c^{3} d^{2} x^{5} e^{4} - 105 \, B c^{3} d^{3} x^{4} e^{3} + 140 \, B c^{3} d^{4} x^{3} e^{2} - 210 \, B c^{3} d^{5} x^{2} e + 420 \, B c^{3} d^{6} x + 210 \, B b c^{2} x^{6} e^{6} + 70 \, A c^{3} x^{6} e^{6} - 252 \, B b c^{2} d x^{5} e^{5} - 84 \, A c^{3} d x^{5} e^{5} + 315 \, B b c^{2} d^{2} x^{4} e^{4} + 105 \, A c^{3} d^{2} x^{4} e^{4} - 420 \, B b c^{2} d^{3} x^{3} e^{3} - 140 \, A c^{3} d^{3} x^{3} e^{3} + 630 \, B b c^{2} d^{4} x^{2} e^{2} + 210 \, A c^{3} d^{4} x^{2} e^{2} - 1260 \, B b c^{2} d^{5} x e - 420 \, A c^{3} d^{5} x e + 252 \, B b^{2} c x^{5} e^{6} + 252 \, B a c^{2} x^{5} e^{6} + 252 \, A b c^{2} x^{5} e^{6} - 315 \, B b^{2} c d x^{4} e^{5} - 315 \, B a c^{2} d x^{4} e^{5} - 315 \, A b c^{2} d x^{4} e^{5} + 420 \, B b^{2} c d^{2} x^{3} e^{4} + 420 \, B a c^{2} d^{2} x^{3} e^{4} + 420 \, A b c^{2} d^{2} x^{3} e^{4} - 630 \, B b^{2} c d^{3} x^{2} e^{3} - 630 \, B a c^{2} d^{3} x^{2} e^{3} - 630 \, A b c^{2} d^{3} x^{2} e^{3} + 1260 \, B b^{2} c d^{4} x e^{2} + 1260 \, B a c^{2} d^{4} x e^{2} + 1260 \, A b c^{2} d^{4} x e^{2} + 105 \, B b^{3} x^{4} e^{6} + 630 \, B a b c x^{4} e^{6} + 315 \, A b^{2} c x^{4} e^{6} + 315 \, A a c^{2} x^{4} e^{6} - 140 \, B b^{3} d x^{3} e^{5} - 840 \, B a b c d x^{3} e^{5} - 420 \, A b^{2} c d x^{3} e^{5} - 420 \, A a c^{2} d x^{3} e^{5} + 210 \, B b^{3} d^{2} x^{2} e^{4} + 1260 \, B a b c d^{2} x^{2} e^{4} + 630 \, A b^{2} c d^{2} x^{2} e^{4} + 630 \, A a c^{2} d^{2} x^{2} e^{4} - 420 \, B b^{3} d^{3} x e^{3} - 2520 \, B a b c d^{3} x e^{3} - 1260 \, A b^{2} c d^{3} x e^{3} - 1260 \, A a c^{2} d^{3} x e^{3} + 420 \, B a b^{2} x^{3} e^{6} + 140 \, A b^{3} x^{3} e^{6} + 420 \, B a^{2} c x^{3} e^{6} + 840 \, A a b c x^{3} e^{6} - 630 \, B a b^{2} d x^{2} e^{5} - 210 \, A b^{3} d x^{2} e^{5} - 630 \, B a^{2} c d x^{2} e^{5} - 1260 \, A a b c d x^{2} e^{5} + 1260 \, B a b^{2} d^{2} x e^{4} + 420 \, A b^{3} d^{2} x e^{4} + 1260 \, B a^{2} c d^{2} x e^{4} + 2520 \, A a b c d^{2} x e^{4} + 630 \, B a^{2} b x^{2} e^{6} + 630 \, A a b^{2} x^{2} e^{6} + 630 \, A a^{2} c x^{2} e^{6} - 1260 \, B a^{2} b d x e^{5} - 1260 \, A a b^{2} d x e^{5} - 1260 \, A a^{2} c d x e^{5} + 420 \, B a^{3} x e^{6} + 1260 \, A a^{2} b x e^{6}\right)} e^{\left(-7\right)}"," ",0,"-(B*c^3*d^7 - 3*B*b*c^2*d^6*e - A*c^3*d^6*e + 3*B*b^2*c*d^5*e^2 + 3*B*a*c^2*d^5*e^2 + 3*A*b*c^2*d^5*e^2 - B*b^3*d^4*e^3 - 6*B*a*b*c*d^4*e^3 - 3*A*b^2*c*d^4*e^3 - 3*A*a*c^2*d^4*e^3 + 3*B*a*b^2*d^3*e^4 + A*b^3*d^3*e^4 + 3*B*a^2*c*d^3*e^4 + 6*A*a*b*c*d^3*e^4 - 3*B*a^2*b*d^2*e^5 - 3*A*a*b^2*d^2*e^5 - 3*A*a^2*c*d^2*e^5 + B*a^3*d*e^6 + 3*A*a^2*b*d*e^6 - A*a^3*e^7)*e^(-8)*log(abs(x*e + d)) + 1/420*(60*B*c^3*x^7*e^6 - 70*B*c^3*d*x^6*e^5 + 84*B*c^3*d^2*x^5*e^4 - 105*B*c^3*d^3*x^4*e^3 + 140*B*c^3*d^4*x^3*e^2 - 210*B*c^3*d^5*x^2*e + 420*B*c^3*d^6*x + 210*B*b*c^2*x^6*e^6 + 70*A*c^3*x^6*e^6 - 252*B*b*c^2*d*x^5*e^5 - 84*A*c^3*d*x^5*e^5 + 315*B*b*c^2*d^2*x^4*e^4 + 105*A*c^3*d^2*x^4*e^4 - 420*B*b*c^2*d^3*x^3*e^3 - 140*A*c^3*d^3*x^3*e^3 + 630*B*b*c^2*d^4*x^2*e^2 + 210*A*c^3*d^4*x^2*e^2 - 1260*B*b*c^2*d^5*x*e - 420*A*c^3*d^5*x*e + 252*B*b^2*c*x^5*e^6 + 252*B*a*c^2*x^5*e^6 + 252*A*b*c^2*x^5*e^6 - 315*B*b^2*c*d*x^4*e^5 - 315*B*a*c^2*d*x^4*e^5 - 315*A*b*c^2*d*x^4*e^5 + 420*B*b^2*c*d^2*x^3*e^4 + 420*B*a*c^2*d^2*x^3*e^4 + 420*A*b*c^2*d^2*x^3*e^4 - 630*B*b^2*c*d^3*x^2*e^3 - 630*B*a*c^2*d^3*x^2*e^3 - 630*A*b*c^2*d^3*x^2*e^3 + 1260*B*b^2*c*d^4*x*e^2 + 1260*B*a*c^2*d^4*x*e^2 + 1260*A*b*c^2*d^4*x*e^2 + 105*B*b^3*x^4*e^6 + 630*B*a*b*c*x^4*e^6 + 315*A*b^2*c*x^4*e^6 + 315*A*a*c^2*x^4*e^6 - 140*B*b^3*d*x^3*e^5 - 840*B*a*b*c*d*x^3*e^5 - 420*A*b^2*c*d*x^3*e^5 - 420*A*a*c^2*d*x^3*e^5 + 210*B*b^3*d^2*x^2*e^4 + 1260*B*a*b*c*d^2*x^2*e^4 + 630*A*b^2*c*d^2*x^2*e^4 + 630*A*a*c^2*d^2*x^2*e^4 - 420*B*b^3*d^3*x*e^3 - 2520*B*a*b*c*d^3*x*e^3 - 1260*A*b^2*c*d^3*x*e^3 - 1260*A*a*c^2*d^3*x*e^3 + 420*B*a*b^2*x^3*e^6 + 140*A*b^3*x^3*e^6 + 420*B*a^2*c*x^3*e^6 + 840*A*a*b*c*x^3*e^6 - 630*B*a*b^2*d*x^2*e^5 - 210*A*b^3*d*x^2*e^5 - 630*B*a^2*c*d*x^2*e^5 - 1260*A*a*b*c*d*x^2*e^5 + 1260*B*a*b^2*d^2*x*e^4 + 420*A*b^3*d^2*x*e^4 + 1260*B*a^2*c*d^2*x*e^4 + 2520*A*a*b*c*d^2*x*e^4 + 630*B*a^2*b*x^2*e^6 + 630*A*a*b^2*x^2*e^6 + 630*A*a^2*c*x^2*e^6 - 1260*B*a^2*b*d*x*e^5 - 1260*A*a*b^2*d*x*e^5 - 1260*A*a^2*c*d*x*e^5 + 420*B*a^3*x*e^6 + 1260*A*a^2*b*x*e^6)*e^(-7)","B",0
2340,1,1200,0,0.246184," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{60} \, {\left(10 \, B c^{3} - \frac{12 \, {\left(7 \, B c^{3} d e - 3 \, B b c^{2} e^{2} - A c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{45 \, {\left(7 \, B c^{3} d^{2} e^{2} - 6 \, B b c^{2} d e^{3} - 2 \, A c^{3} d e^{3} + B b^{2} c e^{4} + B a c^{2} e^{4} + A b c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{20 \, {\left(35 \, B c^{3} d^{3} e^{3} - 45 \, B b c^{2} d^{2} e^{4} - 15 \, A c^{3} d^{2} e^{4} + 15 \, B b^{2} c d e^{5} + 15 \, B a c^{2} d e^{5} + 15 \, A b c^{2} d e^{5} - B b^{3} e^{6} - 6 \, B a b c e^{6} - 3 \, A b^{2} c e^{6} - 3 \, A a c^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{30 \, {\left(35 \, B c^{3} d^{4} e^{4} - 60 \, B b c^{2} d^{3} e^{5} - 20 \, A c^{3} d^{3} e^{5} + 30 \, B b^{2} c d^{2} e^{6} + 30 \, B a c^{2} d^{2} e^{6} + 30 \, A b c^{2} d^{2} e^{6} - 4 \, B b^{3} d e^{7} - 24 \, B a b c d e^{7} - 12 \, A b^{2} c d e^{7} - 12 \, A a c^{2} d e^{7} + 3 \, B a b^{2} e^{8} + A b^{3} e^{8} + 3 \, B a^{2} c e^{8} + 6 \, A a b c e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{180 \, {\left(7 \, B c^{3} d^{5} e^{5} - 15 \, B b c^{2} d^{4} e^{6} - 5 \, A c^{3} d^{4} e^{6} + 10 \, B b^{2} c d^{3} e^{7} + 10 \, B a c^{2} d^{3} e^{7} + 10 \, A b c^{2} d^{3} e^{7} - 2 \, B b^{3} d^{2} e^{8} - 12 \, B a b c d^{2} e^{8} - 6 \, A b^{2} c d^{2} e^{8} - 6 \, A a c^{2} d^{2} e^{8} + 3 \, B a b^{2} d e^{9} + A b^{3} d e^{9} + 3 \, B a^{2} c d e^{9} + 6 \, A a b c d e^{9} - B a^{2} b e^{10} - A a b^{2} e^{10} - A a^{2} c e^{10}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}}\right)} {\left(x e + d\right)}^{6} e^{\left(-8\right)} - {\left(7 \, B c^{3} d^{6} - 18 \, B b c^{2} d^{5} e - 6 \, A c^{3} d^{5} e + 15 \, B b^{2} c d^{4} e^{2} + 15 \, B a c^{2} d^{4} e^{2} + 15 \, A b c^{2} d^{4} e^{2} - 4 \, B b^{3} d^{3} e^{3} - 24 \, B a b c d^{3} e^{3} - 12 \, A b^{2} c d^{3} e^{3} - 12 \, A a c^{2} d^{3} e^{3} + 9 \, B a b^{2} d^{2} e^{4} + 3 \, A b^{3} d^{2} e^{4} + 9 \, B a^{2} c d^{2} e^{4} + 18 \, A a b c d^{2} e^{4} - 6 \, B a^{2} b d e^{5} - 6 \, A a b^{2} d e^{5} - 6 \, A a^{2} c d e^{5} + B a^{3} e^{6} + 3 \, A a^{2} b e^{6}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{B c^{3} d^{7} e^{6}}{x e + d} - \frac{3 \, B b c^{2} d^{6} e^{7}}{x e + d} - \frac{A c^{3} d^{6} e^{7}}{x e + d} + \frac{3 \, B b^{2} c d^{5} e^{8}}{x e + d} + \frac{3 \, B a c^{2} d^{5} e^{8}}{x e + d} + \frac{3 \, A b c^{2} d^{5} e^{8}}{x e + d} - \frac{B b^{3} d^{4} e^{9}}{x e + d} - \frac{6 \, B a b c d^{4} e^{9}}{x e + d} - \frac{3 \, A b^{2} c d^{4} e^{9}}{x e + d} - \frac{3 \, A a c^{2} d^{4} e^{9}}{x e + d} + \frac{3 \, B a b^{2} d^{3} e^{10}}{x e + d} + \frac{A b^{3} d^{3} e^{10}}{x e + d} + \frac{3 \, B a^{2} c d^{3} e^{10}}{x e + d} + \frac{6 \, A a b c d^{3} e^{10}}{x e + d} - \frac{3 \, B a^{2} b d^{2} e^{11}}{x e + d} - \frac{3 \, A a b^{2} d^{2} e^{11}}{x e + d} - \frac{3 \, A a^{2} c d^{2} e^{11}}{x e + d} + \frac{B a^{3} d e^{12}}{x e + d} + \frac{3 \, A a^{2} b d e^{12}}{x e + d} - \frac{A a^{3} e^{13}}{x e + d}\right)} e^{\left(-14\right)}"," ",0,"1/60*(10*B*c^3 - 12*(7*B*c^3*d*e - 3*B*b*c^2*e^2 - A*c^3*e^2)*e^(-1)/(x*e + d) + 45*(7*B*c^3*d^2*e^2 - 6*B*b*c^2*d*e^3 - 2*A*c^3*d*e^3 + B*b^2*c*e^4 + B*a*c^2*e^4 + A*b*c^2*e^4)*e^(-2)/(x*e + d)^2 - 20*(35*B*c^3*d^3*e^3 - 45*B*b*c^2*d^2*e^4 - 15*A*c^3*d^2*e^4 + 15*B*b^2*c*d*e^5 + 15*B*a*c^2*d*e^5 + 15*A*b*c^2*d*e^5 - B*b^3*e^6 - 6*B*a*b*c*e^6 - 3*A*b^2*c*e^6 - 3*A*a*c^2*e^6)*e^(-3)/(x*e + d)^3 + 30*(35*B*c^3*d^4*e^4 - 60*B*b*c^2*d^3*e^5 - 20*A*c^3*d^3*e^5 + 30*B*b^2*c*d^2*e^6 + 30*B*a*c^2*d^2*e^6 + 30*A*b*c^2*d^2*e^6 - 4*B*b^3*d*e^7 - 24*B*a*b*c*d*e^7 - 12*A*b^2*c*d*e^7 - 12*A*a*c^2*d*e^7 + 3*B*a*b^2*e^8 + A*b^3*e^8 + 3*B*a^2*c*e^8 + 6*A*a*b*c*e^8)*e^(-4)/(x*e + d)^4 - 180*(7*B*c^3*d^5*e^5 - 15*B*b*c^2*d^4*e^6 - 5*A*c^3*d^4*e^6 + 10*B*b^2*c*d^3*e^7 + 10*B*a*c^2*d^3*e^7 + 10*A*b*c^2*d^3*e^7 - 2*B*b^3*d^2*e^8 - 12*B*a*b*c*d^2*e^8 - 6*A*b^2*c*d^2*e^8 - 6*A*a*c^2*d^2*e^8 + 3*B*a*b^2*d*e^9 + A*b^3*d*e^9 + 3*B*a^2*c*d*e^9 + 6*A*a*b*c*d*e^9 - B*a^2*b*e^10 - A*a*b^2*e^10 - A*a^2*c*e^10)*e^(-5)/(x*e + d)^5)*(x*e + d)^6*e^(-8) - (7*B*c^3*d^6 - 18*B*b*c^2*d^5*e - 6*A*c^3*d^5*e + 15*B*b^2*c*d^4*e^2 + 15*B*a*c^2*d^4*e^2 + 15*A*b*c^2*d^4*e^2 - 4*B*b^3*d^3*e^3 - 24*B*a*b*c*d^3*e^3 - 12*A*b^2*c*d^3*e^3 - 12*A*a*c^2*d^3*e^3 + 9*B*a*b^2*d^2*e^4 + 3*A*b^3*d^2*e^4 + 9*B*a^2*c*d^2*e^4 + 18*A*a*b*c*d^2*e^4 - 6*B*a^2*b*d*e^5 - 6*A*a*b^2*d*e^5 - 6*A*a^2*c*d*e^5 + B*a^3*e^6 + 3*A*a^2*b*e^6)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (B*c^3*d^7*e^6/(x*e + d) - 3*B*b*c^2*d^6*e^7/(x*e + d) - A*c^3*d^6*e^7/(x*e + d) + 3*B*b^2*c*d^5*e^8/(x*e + d) + 3*B*a*c^2*d^5*e^8/(x*e + d) + 3*A*b*c^2*d^5*e^8/(x*e + d) - B*b^3*d^4*e^9/(x*e + d) - 6*B*a*b*c*d^4*e^9/(x*e + d) - 3*A*b^2*c*d^4*e^9/(x*e + d) - 3*A*a*c^2*d^4*e^9/(x*e + d) + 3*B*a*b^2*d^3*e^10/(x*e + d) + A*b^3*d^3*e^10/(x*e + d) + 3*B*a^2*c*d^3*e^10/(x*e + d) + 6*A*a*b*c*d^3*e^10/(x*e + d) - 3*B*a^2*b*d^2*e^11/(x*e + d) - 3*A*a*b^2*d^2*e^11/(x*e + d) - 3*A*a^2*c*d^2*e^11/(x*e + d) + B*a^3*d*e^12/(x*e + d) + 3*A*a^2*b*d*e^12/(x*e + d) - A*a^3*e^13/(x*e + d))*e^(-14)","B",0
2341,1,1048,0,0.197405," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^3,x, algorithm=""giac"")","-3 \, {\left(7 \, B c^{3} d^{5} - 15 \, B b c^{2} d^{4} e - 5 \, A c^{3} d^{4} e + 10 \, B b^{2} c d^{3} e^{2} + 10 \, B a c^{2} d^{3} e^{2} + 10 \, A b c^{2} d^{3} e^{2} - 2 \, B b^{3} d^{2} e^{3} - 12 \, B a b c d^{2} e^{3} - 6 \, A b^{2} c d^{2} e^{3} - 6 \, A a c^{2} d^{2} e^{3} + 3 \, B a b^{2} d e^{4} + A b^{3} d e^{4} + 3 \, B a^{2} c d e^{4} + 6 \, A a b c d e^{4} - B a^{2} b e^{5} - A a b^{2} e^{5} - A a^{2} c e^{5}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{20} \, {\left(4 \, B c^{3} x^{5} e^{12} - 15 \, B c^{3} d x^{4} e^{11} + 40 \, B c^{3} d^{2} x^{3} e^{10} - 100 \, B c^{3} d^{3} x^{2} e^{9} + 300 \, B c^{3} d^{4} x e^{8} + 15 \, B b c^{2} x^{4} e^{12} + 5 \, A c^{3} x^{4} e^{12} - 60 \, B b c^{2} d x^{3} e^{11} - 20 \, A c^{3} d x^{3} e^{11} + 180 \, B b c^{2} d^{2} x^{2} e^{10} + 60 \, A c^{3} d^{2} x^{2} e^{10} - 600 \, B b c^{2} d^{3} x e^{9} - 200 \, A c^{3} d^{3} x e^{9} + 20 \, B b^{2} c x^{3} e^{12} + 20 \, B a c^{2} x^{3} e^{12} + 20 \, A b c^{2} x^{3} e^{12} - 90 \, B b^{2} c d x^{2} e^{11} - 90 \, B a c^{2} d x^{2} e^{11} - 90 \, A b c^{2} d x^{2} e^{11} + 360 \, B b^{2} c d^{2} x e^{10} + 360 \, B a c^{2} d^{2} x e^{10} + 360 \, A b c^{2} d^{2} x e^{10} + 10 \, B b^{3} x^{2} e^{12} + 60 \, B a b c x^{2} e^{12} + 30 \, A b^{2} c x^{2} e^{12} + 30 \, A a c^{2} x^{2} e^{12} - 60 \, B b^{3} d x e^{11} - 360 \, B a b c d x e^{11} - 180 \, A b^{2} c d x e^{11} - 180 \, A a c^{2} d x e^{11} + 60 \, B a b^{2} x e^{12} + 20 \, A b^{3} x e^{12} + 60 \, B a^{2} c x e^{12} + 120 \, A a b c x e^{12}\right)} e^{\left(-15\right)} - \frac{{\left(13 \, B c^{3} d^{7} - 33 \, B b c^{2} d^{6} e - 11 \, A c^{3} d^{6} e + 27 \, B b^{2} c d^{5} e^{2} + 27 \, B a c^{2} d^{5} e^{2} + 27 \, A b c^{2} d^{5} e^{2} - 7 \, B b^{3} d^{4} e^{3} - 42 \, B a b c d^{4} e^{3} - 21 \, A b^{2} c d^{4} e^{3} - 21 \, A a c^{2} d^{4} e^{3} + 15 \, B a b^{2} d^{3} e^{4} + 5 \, A b^{3} d^{3} e^{4} + 15 \, B a^{2} c d^{3} e^{4} + 30 \, A a b c d^{3} e^{4} - 9 \, B a^{2} b d^{2} e^{5} - 9 \, A a b^{2} d^{2} e^{5} - 9 \, A a^{2} c d^{2} e^{5} + B a^{3} d e^{6} + 3 \, A a^{2} b d e^{6} + A a^{3} e^{7} + 2 \, {\left(7 \, B c^{3} d^{6} e - 18 \, B b c^{2} d^{5} e^{2} - 6 \, A c^{3} d^{5} e^{2} + 15 \, B b^{2} c d^{4} e^{3} + 15 \, B a c^{2} d^{4} e^{3} + 15 \, A b c^{2} d^{4} e^{3} - 4 \, B b^{3} d^{3} e^{4} - 24 \, B a b c d^{3} e^{4} - 12 \, A b^{2} c d^{3} e^{4} - 12 \, A a c^{2} d^{3} e^{4} + 9 \, B a b^{2} d^{2} e^{5} + 3 \, A b^{3} d^{2} e^{5} + 9 \, B a^{2} c d^{2} e^{5} + 18 \, A a b c d^{2} e^{5} - 6 \, B a^{2} b d e^{6} - 6 \, A a b^{2} d e^{6} - 6 \, A a^{2} c d e^{6} + B a^{3} e^{7} + 3 \, A a^{2} b e^{7}\right)} x\right)} e^{\left(-8\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-3*(7*B*c^3*d^5 - 15*B*b*c^2*d^4*e - 5*A*c^3*d^4*e + 10*B*b^2*c*d^3*e^2 + 10*B*a*c^2*d^3*e^2 + 10*A*b*c^2*d^3*e^2 - 2*B*b^3*d^2*e^3 - 12*B*a*b*c*d^2*e^3 - 6*A*b^2*c*d^2*e^3 - 6*A*a*c^2*d^2*e^3 + 3*B*a*b^2*d*e^4 + A*b^3*d*e^4 + 3*B*a^2*c*d*e^4 + 6*A*a*b*c*d*e^4 - B*a^2*b*e^5 - A*a*b^2*e^5 - A*a^2*c*e^5)*e^(-8)*log(abs(x*e + d)) + 1/20*(4*B*c^3*x^5*e^12 - 15*B*c^3*d*x^4*e^11 + 40*B*c^3*d^2*x^3*e^10 - 100*B*c^3*d^3*x^2*e^9 + 300*B*c^3*d^4*x*e^8 + 15*B*b*c^2*x^4*e^12 + 5*A*c^3*x^4*e^12 - 60*B*b*c^2*d*x^3*e^11 - 20*A*c^3*d*x^3*e^11 + 180*B*b*c^2*d^2*x^2*e^10 + 60*A*c^3*d^2*x^2*e^10 - 600*B*b*c^2*d^3*x*e^9 - 200*A*c^3*d^3*x*e^9 + 20*B*b^2*c*x^3*e^12 + 20*B*a*c^2*x^3*e^12 + 20*A*b*c^2*x^3*e^12 - 90*B*b^2*c*d*x^2*e^11 - 90*B*a*c^2*d*x^2*e^11 - 90*A*b*c^2*d*x^2*e^11 + 360*B*b^2*c*d^2*x*e^10 + 360*B*a*c^2*d^2*x*e^10 + 360*A*b*c^2*d^2*x*e^10 + 10*B*b^3*x^2*e^12 + 60*B*a*b*c*x^2*e^12 + 30*A*b^2*c*x^2*e^12 + 30*A*a*c^2*x^2*e^12 - 60*B*b^3*d*x*e^11 - 360*B*a*b*c*d*x*e^11 - 180*A*b^2*c*d*x*e^11 - 180*A*a*c^2*d*x*e^11 + 60*B*a*b^2*x*e^12 + 20*A*b^3*x*e^12 + 60*B*a^2*c*x*e^12 + 120*A*a*b*c*x*e^12)*e^(-15) - 1/2*(13*B*c^3*d^7 - 33*B*b*c^2*d^6*e - 11*A*c^3*d^6*e + 27*B*b^2*c*d^5*e^2 + 27*B*a*c^2*d^5*e^2 + 27*A*b*c^2*d^5*e^2 - 7*B*b^3*d^4*e^3 - 42*B*a*b*c*d^4*e^3 - 21*A*b^2*c*d^4*e^3 - 21*A*a*c^2*d^4*e^3 + 15*B*a*b^2*d^3*e^4 + 5*A*b^3*d^3*e^4 + 15*B*a^2*c*d^3*e^4 + 30*A*a*b*c*d^3*e^4 - 9*B*a^2*b*d^2*e^5 - 9*A*a*b^2*d^2*e^5 - 9*A*a^2*c*d^2*e^5 + B*a^3*d*e^6 + 3*A*a^2*b*d*e^6 + A*a^3*e^7 + 2*(7*B*c^3*d^6*e - 18*B*b*c^2*d^5*e^2 - 6*A*c^3*d^5*e^2 + 15*B*b^2*c*d^4*e^3 + 15*B*a*c^2*d^4*e^3 + 15*A*b*c^2*d^4*e^3 - 4*B*b^3*d^3*e^4 - 24*B*a*b*c*d^3*e^4 - 12*A*b^2*c*d^3*e^4 - 12*A*a*c^2*d^3*e^4 + 9*B*a*b^2*d^2*e^5 + 3*A*b^3*d^2*e^5 + 9*B*a^2*c*d^2*e^5 + 18*A*a*b*c*d^2*e^5 - 6*B*a^2*b*d*e^6 - 6*A*a*b^2*d*e^6 - 6*A*a^2*c*d*e^6 + B*a^3*e^7 + 3*A*a^2*b*e^7)*x)*e^(-8)/(x*e + d)^2","A",0
2342,1,1021,0,0.175349," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^4,x, algorithm=""giac"")","{\left(35 \, B c^{3} d^{4} - 60 \, B b c^{2} d^{3} e - 20 \, A c^{3} d^{3} e + 30 \, B b^{2} c d^{2} e^{2} + 30 \, B a c^{2} d^{2} e^{2} + 30 \, A b c^{2} d^{2} e^{2} - 4 \, B b^{3} d e^{3} - 24 \, B a b c d e^{3} - 12 \, A b^{2} c d e^{3} - 12 \, A a c^{2} d e^{3} + 3 \, B a b^{2} e^{4} + A b^{3} e^{4} + 3 \, B a^{2} c e^{4} + 6 \, A a b c e^{4}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, B c^{3} x^{4} e^{12} - 16 \, B c^{3} d x^{3} e^{11} + 60 \, B c^{3} d^{2} x^{2} e^{10} - 240 \, B c^{3} d^{3} x e^{9} + 12 \, B b c^{2} x^{3} e^{12} + 4 \, A c^{3} x^{3} e^{12} - 72 \, B b c^{2} d x^{2} e^{11} - 24 \, A c^{3} d x^{2} e^{11} + 360 \, B b c^{2} d^{2} x e^{10} + 120 \, A c^{3} d^{2} x e^{10} + 18 \, B b^{2} c x^{2} e^{12} + 18 \, B a c^{2} x^{2} e^{12} + 18 \, A b c^{2} x^{2} e^{12} - 144 \, B b^{2} c d x e^{11} - 144 \, B a c^{2} d x e^{11} - 144 \, A b c^{2} d x e^{11} + 12 \, B b^{3} x e^{12} + 72 \, B a b c x e^{12} + 36 \, A b^{2} c x e^{12} + 36 \, A a c^{2} x e^{12}\right)} e^{\left(-16\right)} + \frac{{\left(107 \, B c^{3} d^{7} - 222 \, B b c^{2} d^{6} e - 74 \, A c^{3} d^{6} e + 141 \, B b^{2} c d^{5} e^{2} + 141 \, B a c^{2} d^{5} e^{2} + 141 \, A b c^{2} d^{5} e^{2} - 26 \, B b^{3} d^{4} e^{3} - 156 \, B a b c d^{4} e^{3} - 78 \, A b^{2} c d^{4} e^{3} - 78 \, A a c^{2} d^{4} e^{3} + 33 \, B a b^{2} d^{3} e^{4} + 11 \, A b^{3} d^{3} e^{4} + 33 \, B a^{2} c d^{3} e^{4} + 66 \, A a b c d^{3} e^{4} - 6 \, B a^{2} b d^{2} e^{5} - 6 \, A a b^{2} d^{2} e^{5} - 6 \, A a^{2} c d^{2} e^{5} - B a^{3} d e^{6} - 3 \, A a^{2} b d e^{6} - 2 \, A a^{3} e^{7} + 18 \, {\left(7 \, B c^{3} d^{5} e^{2} - 15 \, B b c^{2} d^{4} e^{3} - 5 \, A c^{3} d^{4} e^{3} + 10 \, B b^{2} c d^{3} e^{4} + 10 \, B a c^{2} d^{3} e^{4} + 10 \, A b c^{2} d^{3} e^{4} - 2 \, B b^{3} d^{2} e^{5} - 12 \, B a b c d^{2} e^{5} - 6 \, A b^{2} c d^{2} e^{5} - 6 \, A a c^{2} d^{2} e^{5} + 3 \, B a b^{2} d e^{6} + A b^{3} d e^{6} + 3 \, B a^{2} c d e^{6} + 6 \, A a b c d e^{6} - B a^{2} b e^{7} - A a b^{2} e^{7} - A a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(77 \, B c^{3} d^{6} e - 162 \, B b c^{2} d^{5} e^{2} - 54 \, A c^{3} d^{5} e^{2} + 105 \, B b^{2} c d^{4} e^{3} + 105 \, B a c^{2} d^{4} e^{3} + 105 \, A b c^{2} d^{4} e^{3} - 20 \, B b^{3} d^{3} e^{4} - 120 \, B a b c d^{3} e^{4} - 60 \, A b^{2} c d^{3} e^{4} - 60 \, A a c^{2} d^{3} e^{4} + 27 \, B a b^{2} d^{2} e^{5} + 9 \, A b^{3} d^{2} e^{5} + 27 \, B a^{2} c d^{2} e^{5} + 54 \, A a b c d^{2} e^{5} - 6 \, B a^{2} b d e^{6} - 6 \, A a b^{2} d e^{6} - 6 \, A a^{2} c d e^{6} - B a^{3} e^{7} - 3 \, A a^{2} b e^{7}\right)} x\right)} e^{\left(-8\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"(35*B*c^3*d^4 - 60*B*b*c^2*d^3*e - 20*A*c^3*d^3*e + 30*B*b^2*c*d^2*e^2 + 30*B*a*c^2*d^2*e^2 + 30*A*b*c^2*d^2*e^2 - 4*B*b^3*d*e^3 - 24*B*a*b*c*d*e^3 - 12*A*b^2*c*d*e^3 - 12*A*a*c^2*d*e^3 + 3*B*a*b^2*e^4 + A*b^3*e^4 + 3*B*a^2*c*e^4 + 6*A*a*b*c*e^4)*e^(-8)*log(abs(x*e + d)) + 1/12*(3*B*c^3*x^4*e^12 - 16*B*c^3*d*x^3*e^11 + 60*B*c^3*d^2*x^2*e^10 - 240*B*c^3*d^3*x*e^9 + 12*B*b*c^2*x^3*e^12 + 4*A*c^3*x^3*e^12 - 72*B*b*c^2*d*x^2*e^11 - 24*A*c^3*d*x^2*e^11 + 360*B*b*c^2*d^2*x*e^10 + 120*A*c^3*d^2*x*e^10 + 18*B*b^2*c*x^2*e^12 + 18*B*a*c^2*x^2*e^12 + 18*A*b*c^2*x^2*e^12 - 144*B*b^2*c*d*x*e^11 - 144*B*a*c^2*d*x*e^11 - 144*A*b*c^2*d*x*e^11 + 12*B*b^3*x*e^12 + 72*B*a*b*c*x*e^12 + 36*A*b^2*c*x*e^12 + 36*A*a*c^2*x*e^12)*e^(-16) + 1/6*(107*B*c^3*d^7 - 222*B*b*c^2*d^6*e - 74*A*c^3*d^6*e + 141*B*b^2*c*d^5*e^2 + 141*B*a*c^2*d^5*e^2 + 141*A*b*c^2*d^5*e^2 - 26*B*b^3*d^4*e^3 - 156*B*a*b*c*d^4*e^3 - 78*A*b^2*c*d^4*e^3 - 78*A*a*c^2*d^4*e^3 + 33*B*a*b^2*d^3*e^4 + 11*A*b^3*d^3*e^4 + 33*B*a^2*c*d^3*e^4 + 66*A*a*b*c*d^3*e^4 - 6*B*a^2*b*d^2*e^5 - 6*A*a*b^2*d^2*e^5 - 6*A*a^2*c*d^2*e^5 - B*a^3*d*e^6 - 3*A*a^2*b*d*e^6 - 2*A*a^3*e^7 + 18*(7*B*c^3*d^5*e^2 - 15*B*b*c^2*d^4*e^3 - 5*A*c^3*d^4*e^3 + 10*B*b^2*c*d^3*e^4 + 10*B*a*c^2*d^3*e^4 + 10*A*b*c^2*d^3*e^4 - 2*B*b^3*d^2*e^5 - 12*B*a*b*c*d^2*e^5 - 6*A*b^2*c*d^2*e^5 - 6*A*a*c^2*d^2*e^5 + 3*B*a*b^2*d*e^6 + A*b^3*d*e^6 + 3*B*a^2*c*d*e^6 + 6*A*a*b*c*d*e^6 - B*a^2*b*e^7 - A*a*b^2*e^7 - A*a^2*c*e^7)*x^2 + 3*(77*B*c^3*d^6*e - 162*B*b*c^2*d^5*e^2 - 54*A*c^3*d^5*e^2 + 105*B*b^2*c*d^4*e^3 + 105*B*a*c^2*d^4*e^3 + 105*A*b*c^2*d^4*e^3 - 20*B*b^3*d^3*e^4 - 120*B*a*b*c*d^3*e^4 - 60*A*b^2*c*d^3*e^4 - 60*A*a*c^2*d^3*e^4 + 27*B*a*b^2*d^2*e^5 + 9*A*b^3*d^2*e^5 + 27*B*a^2*c*d^2*e^5 + 54*A*a*b*c*d^2*e^5 - 6*B*a^2*b*d*e^6 - 6*A*a*b^2*d*e^6 - 6*A*a^2*c*d*e^6 - B*a^3*e^7 - 3*A*a^2*b*e^7)*x)*e^(-8)/(x*e + d)^3","B",0
2343,1,1567,0,0.415401," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{6} \, {\left(2 \, B c^{3} - \frac{3 \, {\left(7 \, B c^{3} d e - 3 \, B b c^{2} e^{2} - A c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{18 \, {\left(7 \, B c^{3} d^{2} e^{2} - 6 \, B b c^{2} d e^{3} - 2 \, A c^{3} d e^{3} + B b^{2} c e^{4} + B a c^{2} e^{4} + A b c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-8\right)} + {\left(35 \, B c^{3} d^{3} - 45 \, B b c^{2} d^{2} e - 15 \, A c^{3} d^{2} e + 15 \, B b^{2} c d e^{2} + 15 \, B a c^{2} d e^{2} + 15 \, A b c^{2} d e^{2} - B b^{3} e^{3} - 6 \, B a b c e^{3} - 3 \, A b^{2} c e^{3} - 3 \, A a c^{2} e^{3}\right)} e^{\left(-8\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{1}{12} \, {\left(\frac{420 \, B c^{3} d^{4} e^{36}}{x e + d} - \frac{126 \, B c^{3} d^{5} e^{36}}{{\left(x e + d\right)}^{2}} + \frac{28 \, B c^{3} d^{6} e^{36}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B c^{3} d^{7} e^{36}}{{\left(x e + d\right)}^{4}} - \frac{720 \, B b c^{2} d^{3} e^{37}}{x e + d} - \frac{240 \, A c^{3} d^{3} e^{37}}{x e + d} + \frac{270 \, B b c^{2} d^{4} e^{37}}{{\left(x e + d\right)}^{2}} + \frac{90 \, A c^{3} d^{4} e^{37}}{{\left(x e + d\right)}^{2}} - \frac{72 \, B b c^{2} d^{5} e^{37}}{{\left(x e + d\right)}^{3}} - \frac{24 \, A c^{3} d^{5} e^{37}}{{\left(x e + d\right)}^{3}} + \frac{9 \, B b c^{2} d^{6} e^{37}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A c^{3} d^{6} e^{37}}{{\left(x e + d\right)}^{4}} + \frac{360 \, B b^{2} c d^{2} e^{38}}{x e + d} + \frac{360 \, B a c^{2} d^{2} e^{38}}{x e + d} + \frac{360 \, A b c^{2} d^{2} e^{38}}{x e + d} - \frac{180 \, B b^{2} c d^{3} e^{38}}{{\left(x e + d\right)}^{2}} - \frac{180 \, B a c^{2} d^{3} e^{38}}{{\left(x e + d\right)}^{2}} - \frac{180 \, A b c^{2} d^{3} e^{38}}{{\left(x e + d\right)}^{2}} + \frac{60 \, B b^{2} c d^{4} e^{38}}{{\left(x e + d\right)}^{3}} + \frac{60 \, B a c^{2} d^{4} e^{38}}{{\left(x e + d\right)}^{3}} + \frac{60 \, A b c^{2} d^{4} e^{38}}{{\left(x e + d\right)}^{3}} - \frac{9 \, B b^{2} c d^{5} e^{38}}{{\left(x e + d\right)}^{4}} - \frac{9 \, B a c^{2} d^{5} e^{38}}{{\left(x e + d\right)}^{4}} - \frac{9 \, A b c^{2} d^{5} e^{38}}{{\left(x e + d\right)}^{4}} - \frac{48 \, B b^{3} d e^{39}}{x e + d} - \frac{288 \, B a b c d e^{39}}{x e + d} - \frac{144 \, A b^{2} c d e^{39}}{x e + d} - \frac{144 \, A a c^{2} d e^{39}}{x e + d} + \frac{36 \, B b^{3} d^{2} e^{39}}{{\left(x e + d\right)}^{2}} + \frac{216 \, B a b c d^{2} e^{39}}{{\left(x e + d\right)}^{2}} + \frac{108 \, A b^{2} c d^{2} e^{39}}{{\left(x e + d\right)}^{2}} + \frac{108 \, A a c^{2} d^{2} e^{39}}{{\left(x e + d\right)}^{2}} - \frac{16 \, B b^{3} d^{3} e^{39}}{{\left(x e + d\right)}^{3}} - \frac{96 \, B a b c d^{3} e^{39}}{{\left(x e + d\right)}^{3}} - \frac{48 \, A b^{2} c d^{3} e^{39}}{{\left(x e + d\right)}^{3}} - \frac{48 \, A a c^{2} d^{3} e^{39}}{{\left(x e + d\right)}^{3}} + \frac{3 \, B b^{3} d^{4} e^{39}}{{\left(x e + d\right)}^{4}} + \frac{18 \, B a b c d^{4} e^{39}}{{\left(x e + d\right)}^{4}} + \frac{9 \, A b^{2} c d^{4} e^{39}}{{\left(x e + d\right)}^{4}} + \frac{9 \, A a c^{2} d^{4} e^{39}}{{\left(x e + d\right)}^{4}} + \frac{36 \, B a b^{2} e^{40}}{x e + d} + \frac{12 \, A b^{3} e^{40}}{x e + d} + \frac{36 \, B a^{2} c e^{40}}{x e + d} + \frac{72 \, A a b c e^{40}}{x e + d} - \frac{54 \, B a b^{2} d e^{40}}{{\left(x e + d\right)}^{2}} - \frac{18 \, A b^{3} d e^{40}}{{\left(x e + d\right)}^{2}} - \frac{54 \, B a^{2} c d e^{40}}{{\left(x e + d\right)}^{2}} - \frac{108 \, A a b c d e^{40}}{{\left(x e + d\right)}^{2}} + \frac{36 \, B a b^{2} d^{2} e^{40}}{{\left(x e + d\right)}^{3}} + \frac{12 \, A b^{3} d^{2} e^{40}}{{\left(x e + d\right)}^{3}} + \frac{36 \, B a^{2} c d^{2} e^{40}}{{\left(x e + d\right)}^{3}} + \frac{72 \, A a b c d^{2} e^{40}}{{\left(x e + d\right)}^{3}} - \frac{9 \, B a b^{2} d^{3} e^{40}}{{\left(x e + d\right)}^{4}} - \frac{3 \, A b^{3} d^{3} e^{40}}{{\left(x e + d\right)}^{4}} - \frac{9 \, B a^{2} c d^{3} e^{40}}{{\left(x e + d\right)}^{4}} - \frac{18 \, A a b c d^{3} e^{40}}{{\left(x e + d\right)}^{4}} + \frac{18 \, B a^{2} b e^{41}}{{\left(x e + d\right)}^{2}} + \frac{18 \, A a b^{2} e^{41}}{{\left(x e + d\right)}^{2}} + \frac{18 \, A a^{2} c e^{41}}{{\left(x e + d\right)}^{2}} - \frac{24 \, B a^{2} b d e^{41}}{{\left(x e + d\right)}^{3}} - \frac{24 \, A a b^{2} d e^{41}}{{\left(x e + d\right)}^{3}} - \frac{24 \, A a^{2} c d e^{41}}{{\left(x e + d\right)}^{3}} + \frac{9 \, B a^{2} b d^{2} e^{41}}{{\left(x e + d\right)}^{4}} + \frac{9 \, A a b^{2} d^{2} e^{41}}{{\left(x e + d\right)}^{4}} + \frac{9 \, A a^{2} c d^{2} e^{41}}{{\left(x e + d\right)}^{4}} + \frac{4 \, B a^{3} e^{42}}{{\left(x e + d\right)}^{3}} + \frac{12 \, A a^{2} b e^{42}}{{\left(x e + d\right)}^{3}} - \frac{3 \, B a^{3} d e^{42}}{{\left(x e + d\right)}^{4}} - \frac{9 \, A a^{2} b d e^{42}}{{\left(x e + d\right)}^{4}} + \frac{3 \, A a^{3} e^{43}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-44\right)}"," ",0,"1/6*(2*B*c^3 - 3*(7*B*c^3*d*e - 3*B*b*c^2*e^2 - A*c^3*e^2)*e^(-1)/(x*e + d) + 18*(7*B*c^3*d^2*e^2 - 6*B*b*c^2*d*e^3 - 2*A*c^3*d*e^3 + B*b^2*c*e^4 + B*a*c^2*e^4 + A*b*c^2*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-8) + (35*B*c^3*d^3 - 45*B*b*c^2*d^2*e - 15*A*c^3*d^2*e + 15*B*b^2*c*d*e^2 + 15*B*a*c^2*d*e^2 + 15*A*b*c^2*d*e^2 - B*b^3*e^3 - 6*B*a*b*c*e^3 - 3*A*b^2*c*e^3 - 3*A*a*c^2*e^3)*e^(-8)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/12*(420*B*c^3*d^4*e^36/(x*e + d) - 126*B*c^3*d^5*e^36/(x*e + d)^2 + 28*B*c^3*d^6*e^36/(x*e + d)^3 - 3*B*c^3*d^7*e^36/(x*e + d)^4 - 720*B*b*c^2*d^3*e^37/(x*e + d) - 240*A*c^3*d^3*e^37/(x*e + d) + 270*B*b*c^2*d^4*e^37/(x*e + d)^2 + 90*A*c^3*d^4*e^37/(x*e + d)^2 - 72*B*b*c^2*d^5*e^37/(x*e + d)^3 - 24*A*c^3*d^5*e^37/(x*e + d)^3 + 9*B*b*c^2*d^6*e^37/(x*e + d)^4 + 3*A*c^3*d^6*e^37/(x*e + d)^4 + 360*B*b^2*c*d^2*e^38/(x*e + d) + 360*B*a*c^2*d^2*e^38/(x*e + d) + 360*A*b*c^2*d^2*e^38/(x*e + d) - 180*B*b^2*c*d^3*e^38/(x*e + d)^2 - 180*B*a*c^2*d^3*e^38/(x*e + d)^2 - 180*A*b*c^2*d^3*e^38/(x*e + d)^2 + 60*B*b^2*c*d^4*e^38/(x*e + d)^3 + 60*B*a*c^2*d^4*e^38/(x*e + d)^3 + 60*A*b*c^2*d^4*e^38/(x*e + d)^3 - 9*B*b^2*c*d^5*e^38/(x*e + d)^4 - 9*B*a*c^2*d^5*e^38/(x*e + d)^4 - 9*A*b*c^2*d^5*e^38/(x*e + d)^4 - 48*B*b^3*d*e^39/(x*e + d) - 288*B*a*b*c*d*e^39/(x*e + d) - 144*A*b^2*c*d*e^39/(x*e + d) - 144*A*a*c^2*d*e^39/(x*e + d) + 36*B*b^3*d^2*e^39/(x*e + d)^2 + 216*B*a*b*c*d^2*e^39/(x*e + d)^2 + 108*A*b^2*c*d^2*e^39/(x*e + d)^2 + 108*A*a*c^2*d^2*e^39/(x*e + d)^2 - 16*B*b^3*d^3*e^39/(x*e + d)^3 - 96*B*a*b*c*d^3*e^39/(x*e + d)^3 - 48*A*b^2*c*d^3*e^39/(x*e + d)^3 - 48*A*a*c^2*d^3*e^39/(x*e + d)^3 + 3*B*b^3*d^4*e^39/(x*e + d)^4 + 18*B*a*b*c*d^4*e^39/(x*e + d)^4 + 9*A*b^2*c*d^4*e^39/(x*e + d)^4 + 9*A*a*c^2*d^4*e^39/(x*e + d)^4 + 36*B*a*b^2*e^40/(x*e + d) + 12*A*b^3*e^40/(x*e + d) + 36*B*a^2*c*e^40/(x*e + d) + 72*A*a*b*c*e^40/(x*e + d) - 54*B*a*b^2*d*e^40/(x*e + d)^2 - 18*A*b^3*d*e^40/(x*e + d)^2 - 54*B*a^2*c*d*e^40/(x*e + d)^2 - 108*A*a*b*c*d*e^40/(x*e + d)^2 + 36*B*a*b^2*d^2*e^40/(x*e + d)^3 + 12*A*b^3*d^2*e^40/(x*e + d)^3 + 36*B*a^2*c*d^2*e^40/(x*e + d)^3 + 72*A*a*b*c*d^2*e^40/(x*e + d)^3 - 9*B*a*b^2*d^3*e^40/(x*e + d)^4 - 3*A*b^3*d^3*e^40/(x*e + d)^4 - 9*B*a^2*c*d^3*e^40/(x*e + d)^4 - 18*A*a*b*c*d^3*e^40/(x*e + d)^4 + 18*B*a^2*b*e^41/(x*e + d)^2 + 18*A*a*b^2*e^41/(x*e + d)^2 + 18*A*a^2*c*e^41/(x*e + d)^2 - 24*B*a^2*b*d*e^41/(x*e + d)^3 - 24*A*a*b^2*d*e^41/(x*e + d)^3 - 24*A*a^2*c*d*e^41/(x*e + d)^3 + 9*B*a^2*b*d^2*e^41/(x*e + d)^4 + 9*A*a*b^2*d^2*e^41/(x*e + d)^4 + 9*A*a^2*c*d^2*e^41/(x*e + d)^4 + 4*B*a^3*e^42/(x*e + d)^3 + 12*A*a^2*b*e^42/(x*e + d)^3 - 3*B*a^3*d*e^42/(x*e + d)^4 - 9*A*a^2*b*d*e^42/(x*e + d)^4 + 3*A*a^3*e^43/(x*e + d)^4)*e^(-44)","B",0
2344,1,998,0,0.179363," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^6,x, algorithm=""giac"")","3 \, {\left(7 \, B c^{3} d^{2} - 6 \, B b c^{2} d e - 2 \, A c^{3} d e + B b^{2} c e^{2} + B a c^{2} e^{2} + A b c^{2} e^{2}\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(B c^{3} x^{2} e^{6} - 12 \, B c^{3} d x e^{5} + 6 \, B b c^{2} x e^{6} + 2 \, A c^{3} x e^{6}\right)} e^{\left(-12\right)} + \frac{{\left(459 \, B c^{3} d^{7} - 522 \, B b c^{2} d^{6} e - 174 \, A c^{3} d^{6} e + 137 \, B b^{2} c d^{5} e^{2} + 137 \, B a c^{2} d^{5} e^{2} + 137 \, A b c^{2} d^{5} e^{2} - 4 \, B b^{3} d^{4} e^{3} - 24 \, B a b c d^{4} e^{3} - 12 \, A b^{2} c d^{4} e^{3} - 12 \, A a c^{2} d^{4} e^{3} - 3 \, B a b^{2} d^{3} e^{4} - A b^{3} d^{3} e^{4} - 3 \, B a^{2} c d^{3} e^{4} - 6 \, A a b c d^{3} e^{4} - 2 \, B a^{2} b d^{2} e^{5} - 2 \, A a b^{2} d^{2} e^{5} - 2 \, A a^{2} c d^{2} e^{5} - B a^{3} d e^{6} - 3 \, A a^{2} b d e^{6} + 20 \, {\left(35 \, B c^{3} d^{3} e^{4} - 45 \, B b c^{2} d^{2} e^{5} - 15 \, A c^{3} d^{2} e^{5} + 15 \, B b^{2} c d e^{6} + 15 \, B a c^{2} d e^{6} + 15 \, A b c^{2} d e^{6} - B b^{3} e^{7} - 6 \, B a b c e^{7} - 3 \, A b^{2} c e^{7} - 3 \, A a c^{2} e^{7}\right)} x^{4} - 4 \, A a^{3} e^{7} + 10 \, {\left(245 \, B c^{3} d^{4} e^{3} - 300 \, B b c^{2} d^{3} e^{4} - 100 \, A c^{3} d^{3} e^{4} + 90 \, B b^{2} c d^{2} e^{5} + 90 \, B a c^{2} d^{2} e^{5} + 90 \, A b c^{2} d^{2} e^{5} - 4 \, B b^{3} d e^{6} - 24 \, B a b c d e^{6} - 12 \, A b^{2} c d e^{6} - 12 \, A a c^{2} d e^{6} - 3 \, B a b^{2} e^{7} - A b^{3} e^{7} - 3 \, B a^{2} c e^{7} - 6 \, A a b c e^{7}\right)} x^{3} + 10 \, {\left(329 \, B c^{3} d^{5} e^{2} - 390 \, B b c^{2} d^{4} e^{3} - 130 \, A c^{3} d^{4} e^{3} + 110 \, B b^{2} c d^{3} e^{4} + 110 \, B a c^{2} d^{3} e^{4} + 110 \, A b c^{2} d^{3} e^{4} - 4 \, B b^{3} d^{2} e^{5} - 24 \, B a b c d^{2} e^{5} - 12 \, A b^{2} c d^{2} e^{5} - 12 \, A a c^{2} d^{2} e^{5} - 3 \, B a b^{2} d e^{6} - A b^{3} d e^{6} - 3 \, B a^{2} c d e^{6} - 6 \, A a b c d e^{6} - 2 \, B a^{2} b e^{7} - 2 \, A a b^{2} e^{7} - 2 \, A a^{2} c e^{7}\right)} x^{2} + 5 \, {\left(399 \, B c^{3} d^{6} e - 462 \, B b c^{2} d^{5} e^{2} - 154 \, A c^{3} d^{5} e^{2} + 125 \, B b^{2} c d^{4} e^{3} + 125 \, B a c^{2} d^{4} e^{3} + 125 \, A b c^{2} d^{4} e^{3} - 4 \, B b^{3} d^{3} e^{4} - 24 \, B a b c d^{3} e^{4} - 12 \, A b^{2} c d^{3} e^{4} - 12 \, A a c^{2} d^{3} e^{4} - 3 \, B a b^{2} d^{2} e^{5} - A b^{3} d^{2} e^{5} - 3 \, B a^{2} c d^{2} e^{5} - 6 \, A a b c d^{2} e^{5} - 2 \, B a^{2} b d e^{6} - 2 \, A a b^{2} d e^{6} - 2 \, A a^{2} c d e^{6} - B a^{3} e^{7} - 3 \, A a^{2} b e^{7}\right)} x\right)} e^{\left(-8\right)}}{20 \, {\left(x e + d\right)}^{5}}"," ",0,"3*(7*B*c^3*d^2 - 6*B*b*c^2*d*e - 2*A*c^3*d*e + B*b^2*c*e^2 + B*a*c^2*e^2 + A*b*c^2*e^2)*e^(-8)*log(abs(x*e + d)) + 1/2*(B*c^3*x^2*e^6 - 12*B*c^3*d*x*e^5 + 6*B*b*c^2*x*e^6 + 2*A*c^3*x*e^6)*e^(-12) + 1/20*(459*B*c^3*d^7 - 522*B*b*c^2*d^6*e - 174*A*c^3*d^6*e + 137*B*b^2*c*d^5*e^2 + 137*B*a*c^2*d^5*e^2 + 137*A*b*c^2*d^5*e^2 - 4*B*b^3*d^4*e^3 - 24*B*a*b*c*d^4*e^3 - 12*A*b^2*c*d^4*e^3 - 12*A*a*c^2*d^4*e^3 - 3*B*a*b^2*d^3*e^4 - A*b^3*d^3*e^4 - 3*B*a^2*c*d^3*e^4 - 6*A*a*b*c*d^3*e^4 - 2*B*a^2*b*d^2*e^5 - 2*A*a*b^2*d^2*e^5 - 2*A*a^2*c*d^2*e^5 - B*a^3*d*e^6 - 3*A*a^2*b*d*e^6 + 20*(35*B*c^3*d^3*e^4 - 45*B*b*c^2*d^2*e^5 - 15*A*c^3*d^2*e^5 + 15*B*b^2*c*d*e^6 + 15*B*a*c^2*d*e^6 + 15*A*b*c^2*d*e^6 - B*b^3*e^7 - 6*B*a*b*c*e^7 - 3*A*b^2*c*e^7 - 3*A*a*c^2*e^7)*x^4 - 4*A*a^3*e^7 + 10*(245*B*c^3*d^4*e^3 - 300*B*b*c^2*d^3*e^4 - 100*A*c^3*d^3*e^4 + 90*B*b^2*c*d^2*e^5 + 90*B*a*c^2*d^2*e^5 + 90*A*b*c^2*d^2*e^5 - 4*B*b^3*d*e^6 - 24*B*a*b*c*d*e^6 - 12*A*b^2*c*d*e^6 - 12*A*a*c^2*d*e^6 - 3*B*a*b^2*e^7 - A*b^3*e^7 - 3*B*a^2*c*e^7 - 6*A*a*b*c*e^7)*x^3 + 10*(329*B*c^3*d^5*e^2 - 390*B*b*c^2*d^4*e^3 - 130*A*c^3*d^4*e^3 + 110*B*b^2*c*d^3*e^4 + 110*B*a*c^2*d^3*e^4 + 110*A*b*c^2*d^3*e^4 - 4*B*b^3*d^2*e^5 - 24*B*a*b*c*d^2*e^5 - 12*A*b^2*c*d^2*e^5 - 12*A*a*c^2*d^2*e^5 - 3*B*a*b^2*d*e^6 - A*b^3*d*e^6 - 3*B*a^2*c*d*e^6 - 6*A*a*b*c*d*e^6 - 2*B*a^2*b*e^7 - 2*A*a*b^2*e^7 - 2*A*a^2*c*e^7)*x^2 + 5*(399*B*c^3*d^6*e - 462*B*b*c^2*d^5*e^2 - 154*A*c^3*d^5*e^2 + 125*B*b^2*c*d^4*e^3 + 125*B*a*c^2*d^4*e^3 + 125*A*b*c^2*d^4*e^3 - 4*B*b^3*d^3*e^4 - 24*B*a*b*c*d^3*e^4 - 12*A*b^2*c*d^3*e^4 - 12*A*a*c^2*d^3*e^4 - 3*B*a*b^2*d^2*e^5 - A*b^3*d^2*e^5 - 3*B*a^2*c*d^2*e^5 - 6*A*a*b*c*d^2*e^5 - 2*B*a^2*b*d*e^6 - 2*A*a*b^2*d*e^6 - 2*A*a^2*c*d*e^6 - B*a^3*e^7 - 3*A*a^2*b*e^7)*x)*e^(-8)/(x*e + d)^5","A",0
2345,1,989,0,0.227067," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^7,x, algorithm=""giac"")","B c^{3} x e^{\left(-7\right)} - {\left(7 \, B c^{3} d - 3 \, B b c^{2} e - A c^{3} e\right)} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(669 \, B c^{3} d^{7} - 441 \, B b c^{2} d^{6} e - 147 \, A c^{3} d^{6} e + 30 \, B b^{2} c d^{5} e^{2} + 30 \, B a c^{2} d^{5} e^{2} + 30 \, A b c^{2} d^{5} e^{2} + 2 \, B b^{3} d^{4} e^{3} + 12 \, B a b c d^{4} e^{3} + 6 \, A b^{2} c d^{4} e^{3} + 6 \, A a c^{2} d^{4} e^{3} + 3 \, B a b^{2} d^{3} e^{4} + A b^{3} d^{3} e^{4} + 3 \, B a^{2} c d^{3} e^{4} + 6 \, A a b c d^{3} e^{4} + 3 \, B a^{2} b d^{2} e^{5} + 3 \, A a b^{2} d^{2} e^{5} + 3 \, A a^{2} c d^{2} e^{5} + 180 \, {\left(7 \, B c^{3} d^{2} e^{5} - 6 \, B b c^{2} d e^{6} - 2 \, A c^{3} d e^{6} + B b^{2} c e^{7} + B a c^{2} e^{7} + A b c^{2} e^{7}\right)} x^{5} + 2 \, B a^{3} d e^{6} + 6 \, A a^{2} b d e^{6} + 30 \, {\left(175 \, B c^{3} d^{3} e^{4} - 135 \, B b c^{2} d^{2} e^{5} - 45 \, A c^{3} d^{2} e^{5} + 15 \, B b^{2} c d e^{6} + 15 \, B a c^{2} d e^{6} + 15 \, A b c^{2} d e^{6} + B b^{3} e^{7} + 6 \, B a b c e^{7} + 3 \, A b^{2} c e^{7} + 3 \, A a c^{2} e^{7}\right)} x^{4} + 10 \, A a^{3} e^{7} + 20 \, {\left(455 \, B c^{3} d^{4} e^{3} - 330 \, B b c^{2} d^{3} e^{4} - 110 \, A c^{3} d^{3} e^{4} + 30 \, B b^{2} c d^{2} e^{5} + 30 \, B a c^{2} d^{2} e^{5} + 30 \, A b c^{2} d^{2} e^{5} + 2 \, B b^{3} d e^{6} + 12 \, B a b c d e^{6} + 6 \, A b^{2} c d e^{6} + 6 \, A a c^{2} d e^{6} + 3 \, B a b^{2} e^{7} + A b^{3} e^{7} + 3 \, B a^{2} c e^{7} + 6 \, A a b c e^{7}\right)} x^{3} + 15 \, {\left(539 \, B c^{3} d^{5} e^{2} - 375 \, B b c^{2} d^{4} e^{3} - 125 \, A c^{3} d^{4} e^{3} + 30 \, B b^{2} c d^{3} e^{4} + 30 \, B a c^{2} d^{3} e^{4} + 30 \, A b c^{2} d^{3} e^{4} + 2 \, B b^{3} d^{2} e^{5} + 12 \, B a b c d^{2} e^{5} + 6 \, A b^{2} c d^{2} e^{5} + 6 \, A a c^{2} d^{2} e^{5} + 3 \, B a b^{2} d e^{6} + A b^{3} d e^{6} + 3 \, B a^{2} c d e^{6} + 6 \, A a b c d e^{6} + 3 \, B a^{2} b e^{7} + 3 \, A a b^{2} e^{7} + 3 \, A a^{2} c e^{7}\right)} x^{2} + 6 \, {\left(609 \, B c^{3} d^{6} e - 411 \, B b c^{2} d^{5} e^{2} - 137 \, A c^{3} d^{5} e^{2} + 30 \, B b^{2} c d^{4} e^{3} + 30 \, B a c^{2} d^{4} e^{3} + 30 \, A b c^{2} d^{4} e^{3} + 2 \, B b^{3} d^{3} e^{4} + 12 \, B a b c d^{3} e^{4} + 6 \, A b^{2} c d^{3} e^{4} + 6 \, A a c^{2} d^{3} e^{4} + 3 \, B a b^{2} d^{2} e^{5} + A b^{3} d^{2} e^{5} + 3 \, B a^{2} c d^{2} e^{5} + 6 \, A a b c d^{2} e^{5} + 3 \, B a^{2} b d e^{6} + 3 \, A a b^{2} d e^{6} + 3 \, A a^{2} c d e^{6} + 2 \, B a^{3} e^{7} + 6 \, A a^{2} b e^{7}\right)} x\right)} e^{\left(-8\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"B*c^3*x*e^(-7) - (7*B*c^3*d - 3*B*b*c^2*e - A*c^3*e)*e^(-8)*log(abs(x*e + d)) - 1/60*(669*B*c^3*d^7 - 441*B*b*c^2*d^6*e - 147*A*c^3*d^6*e + 30*B*b^2*c*d^5*e^2 + 30*B*a*c^2*d^5*e^2 + 30*A*b*c^2*d^5*e^2 + 2*B*b^3*d^4*e^3 + 12*B*a*b*c*d^4*e^3 + 6*A*b^2*c*d^4*e^3 + 6*A*a*c^2*d^4*e^3 + 3*B*a*b^2*d^3*e^4 + A*b^3*d^3*e^4 + 3*B*a^2*c*d^3*e^4 + 6*A*a*b*c*d^3*e^4 + 3*B*a^2*b*d^2*e^5 + 3*A*a*b^2*d^2*e^5 + 3*A*a^2*c*d^2*e^5 + 180*(7*B*c^3*d^2*e^5 - 6*B*b*c^2*d*e^6 - 2*A*c^3*d*e^6 + B*b^2*c*e^7 + B*a*c^2*e^7 + A*b*c^2*e^7)*x^5 + 2*B*a^3*d*e^6 + 6*A*a^2*b*d*e^6 + 30*(175*B*c^3*d^3*e^4 - 135*B*b*c^2*d^2*e^5 - 45*A*c^3*d^2*e^5 + 15*B*b^2*c*d*e^6 + 15*B*a*c^2*d*e^6 + 15*A*b*c^2*d*e^6 + B*b^3*e^7 + 6*B*a*b*c*e^7 + 3*A*b^2*c*e^7 + 3*A*a*c^2*e^7)*x^4 + 10*A*a^3*e^7 + 20*(455*B*c^3*d^4*e^3 - 330*B*b*c^2*d^3*e^4 - 110*A*c^3*d^3*e^4 + 30*B*b^2*c*d^2*e^5 + 30*B*a*c^2*d^2*e^5 + 30*A*b*c^2*d^2*e^5 + 2*B*b^3*d*e^6 + 12*B*a*b*c*d*e^6 + 6*A*b^2*c*d*e^6 + 6*A*a*c^2*d*e^6 + 3*B*a*b^2*e^7 + A*b^3*e^7 + 3*B*a^2*c*e^7 + 6*A*a*b*c*e^7)*x^3 + 15*(539*B*c^3*d^5*e^2 - 375*B*b*c^2*d^4*e^3 - 125*A*c^3*d^4*e^3 + 30*B*b^2*c*d^3*e^4 + 30*B*a*c^2*d^3*e^4 + 30*A*b*c^2*d^3*e^4 + 2*B*b^3*d^2*e^5 + 12*B*a*b*c*d^2*e^5 + 6*A*b^2*c*d^2*e^5 + 6*A*a*c^2*d^2*e^5 + 3*B*a*b^2*d*e^6 + A*b^3*d*e^6 + 3*B*a^2*c*d*e^6 + 6*A*a*b*c*d*e^6 + 3*B*a^2*b*e^7 + 3*A*a*b^2*e^7 + 3*A*a^2*c*e^7)*x^2 + 6*(609*B*c^3*d^6*e - 411*B*b*c^2*d^5*e^2 - 137*A*c^3*d^5*e^2 + 30*B*b^2*c*d^4*e^3 + 30*B*a*c^2*d^4*e^3 + 30*A*b*c^2*d^4*e^3 + 2*B*b^3*d^3*e^4 + 12*B*a*b*c*d^3*e^4 + 6*A*b^2*c*d^3*e^4 + 6*A*a*c^2*d^3*e^4 + 3*B*a*b^2*d^2*e^5 + A*b^3*d^2*e^5 + 3*B*a^2*c*d^2*e^5 + 6*A*a*b*c*d^2*e^5 + 3*B*a^2*b*d*e^6 + 3*A*a*b^2*d*e^6 + 3*A*a^2*c*d*e^6 + 2*B*a^3*e^7 + 6*A*a^2*b*e^7)*x)*e^(-8)/(x*e + d)^6","A",0
2346,1,1001,0,0.183006," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^8,x, algorithm=""giac"")","B c^{3} e^{\left(-8\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(420 \, {\left(7 \, B c^{3} d e^{5} - 3 \, B b c^{2} e^{6} - A c^{3} e^{6}\right)} x^{6} + 630 \, {\left(21 \, B c^{3} d^{2} e^{4} - 6 \, B b c^{2} d e^{5} - 2 \, A c^{3} d e^{5} - B b^{2} c e^{6} - B a c^{2} e^{6} - A b c^{2} e^{6}\right)} x^{5} + 70 \, {\left(385 \, B c^{3} d^{3} e^{3} - 90 \, B b c^{2} d^{2} e^{4} - 30 \, A c^{3} d^{2} e^{4} - 15 \, B b^{2} c d e^{5} - 15 \, B a c^{2} d e^{5} - 15 \, A b c^{2} d e^{5} - 2 \, B b^{3} e^{6} - 12 \, B a b c e^{6} - 6 \, A b^{2} c e^{6} - 6 \, A a c^{2} e^{6}\right)} x^{4} + 35 \, {\left(875 \, B c^{3} d^{4} e^{2} - 180 \, B b c^{2} d^{3} e^{3} - 60 \, A c^{3} d^{3} e^{3} - 30 \, B b^{2} c d^{2} e^{4} - 30 \, B a c^{2} d^{2} e^{4} - 30 \, A b c^{2} d^{2} e^{4} - 4 \, B b^{3} d e^{5} - 24 \, B a b c d e^{5} - 12 \, A b^{2} c d e^{5} - 12 \, A a c^{2} d e^{5} - 9 \, B a b^{2} e^{6} - 3 \, A b^{3} e^{6} - 9 \, B a^{2} c e^{6} - 18 \, A a b c e^{6}\right)} x^{3} + 21 \, {\left(959 \, B c^{3} d^{5} e - 180 \, B b c^{2} d^{4} e^{2} - 60 \, A c^{3} d^{4} e^{2} - 30 \, B b^{2} c d^{3} e^{3} - 30 \, B a c^{2} d^{3} e^{3} - 30 \, A b c^{2} d^{3} e^{3} - 4 \, B b^{3} d^{2} e^{4} - 24 \, B a b c d^{2} e^{4} - 12 \, A b^{2} c d^{2} e^{4} - 12 \, A a c^{2} d^{2} e^{4} - 9 \, B a b^{2} d e^{5} - 3 \, A b^{3} d e^{5} - 9 \, B a^{2} c d e^{5} - 18 \, A a b c d e^{5} - 12 \, B a^{2} b e^{6} - 12 \, A a b^{2} e^{6} - 12 \, A a^{2} c e^{6}\right)} x^{2} + 7 \, {\left(1029 \, B c^{3} d^{6} - 180 \, B b c^{2} d^{5} e - 60 \, A c^{3} d^{5} e - 30 \, B b^{2} c d^{4} e^{2} - 30 \, B a c^{2} d^{4} e^{2} - 30 \, A b c^{2} d^{4} e^{2} - 4 \, B b^{3} d^{3} e^{3} - 24 \, B a b c d^{3} e^{3} - 12 \, A b^{2} c d^{3} e^{3} - 12 \, A a c^{2} d^{3} e^{3} - 9 \, B a b^{2} d^{2} e^{4} - 3 \, A b^{3} d^{2} e^{4} - 9 \, B a^{2} c d^{2} e^{4} - 18 \, A a b c d^{2} e^{4} - 12 \, B a^{2} b d e^{5} - 12 \, A a b^{2} d e^{5} - 12 \, A a^{2} c d e^{5} - 10 \, B a^{3} e^{6} - 30 \, A a^{2} b e^{6}\right)} x + {\left(1089 \, B c^{3} d^{7} - 180 \, B b c^{2} d^{6} e - 60 \, A c^{3} d^{6} e - 30 \, B b^{2} c d^{5} e^{2} - 30 \, B a c^{2} d^{5} e^{2} - 30 \, A b c^{2} d^{5} e^{2} - 4 \, B b^{3} d^{4} e^{3} - 24 \, B a b c d^{4} e^{3} - 12 \, A b^{2} c d^{4} e^{3} - 12 \, A a c^{2} d^{4} e^{3} - 9 \, B a b^{2} d^{3} e^{4} - 3 \, A b^{3} d^{3} e^{4} - 9 \, B a^{2} c d^{3} e^{4} - 18 \, A a b c d^{3} e^{4} - 12 \, B a^{2} b d^{2} e^{5} - 12 \, A a b^{2} d^{2} e^{5} - 12 \, A a^{2} c d^{2} e^{5} - 10 \, B a^{3} d e^{6} - 30 \, A a^{2} b d e^{6} - 60 \, A a^{3} e^{7}\right)} e^{\left(-1\right)}\right)} e^{\left(-7\right)}}{420 \, {\left(x e + d\right)}^{7}}"," ",0,"B*c^3*e^(-8)*log(abs(x*e + d)) + 1/420*(420*(7*B*c^3*d*e^5 - 3*B*b*c^2*e^6 - A*c^3*e^6)*x^6 + 630*(21*B*c^3*d^2*e^4 - 6*B*b*c^2*d*e^5 - 2*A*c^3*d*e^5 - B*b^2*c*e^6 - B*a*c^2*e^6 - A*b*c^2*e^6)*x^5 + 70*(385*B*c^3*d^3*e^3 - 90*B*b*c^2*d^2*e^4 - 30*A*c^3*d^2*e^4 - 15*B*b^2*c*d*e^5 - 15*B*a*c^2*d*e^5 - 15*A*b*c^2*d*e^5 - 2*B*b^3*e^6 - 12*B*a*b*c*e^6 - 6*A*b^2*c*e^6 - 6*A*a*c^2*e^6)*x^4 + 35*(875*B*c^3*d^4*e^2 - 180*B*b*c^2*d^3*e^3 - 60*A*c^3*d^3*e^3 - 30*B*b^2*c*d^2*e^4 - 30*B*a*c^2*d^2*e^4 - 30*A*b*c^2*d^2*e^4 - 4*B*b^3*d*e^5 - 24*B*a*b*c*d*e^5 - 12*A*b^2*c*d*e^5 - 12*A*a*c^2*d*e^5 - 9*B*a*b^2*e^6 - 3*A*b^3*e^6 - 9*B*a^2*c*e^6 - 18*A*a*b*c*e^6)*x^3 + 21*(959*B*c^3*d^5*e - 180*B*b*c^2*d^4*e^2 - 60*A*c^3*d^4*e^2 - 30*B*b^2*c*d^3*e^3 - 30*B*a*c^2*d^3*e^3 - 30*A*b*c^2*d^3*e^3 - 4*B*b^3*d^2*e^4 - 24*B*a*b*c*d^2*e^4 - 12*A*b^2*c*d^2*e^4 - 12*A*a*c^2*d^2*e^4 - 9*B*a*b^2*d*e^5 - 3*A*b^3*d*e^5 - 9*B*a^2*c*d*e^5 - 18*A*a*b*c*d*e^5 - 12*B*a^2*b*e^6 - 12*A*a*b^2*e^6 - 12*A*a^2*c*e^6)*x^2 + 7*(1029*B*c^3*d^6 - 180*B*b*c^2*d^5*e - 60*A*c^3*d^5*e - 30*B*b^2*c*d^4*e^2 - 30*B*a*c^2*d^4*e^2 - 30*A*b*c^2*d^4*e^2 - 4*B*b^3*d^3*e^3 - 24*B*a*b*c*d^3*e^3 - 12*A*b^2*c*d^3*e^3 - 12*A*a*c^2*d^3*e^3 - 9*B*a*b^2*d^2*e^4 - 3*A*b^3*d^2*e^4 - 9*B*a^2*c*d^2*e^4 - 18*A*a*b*c*d^2*e^4 - 12*B*a^2*b*d*e^5 - 12*A*a*b^2*d*e^5 - 12*A*a^2*c*d*e^5 - 10*B*a^3*e^6 - 30*A*a^2*b*e^6)*x + (1089*B*c^3*d^7 - 180*B*b*c^2*d^6*e - 60*A*c^3*d^6*e - 30*B*b^2*c*d^5*e^2 - 30*B*a*c^2*d^5*e^2 - 30*A*b*c^2*d^5*e^2 - 4*B*b^3*d^4*e^3 - 24*B*a*b*c*d^4*e^3 - 12*A*b^2*c*d^4*e^3 - 12*A*a*c^2*d^4*e^3 - 9*B*a*b^2*d^3*e^4 - 3*A*b^3*d^3*e^4 - 9*B*a^2*c*d^3*e^4 - 18*A*a*b*c*d^3*e^4 - 12*B*a^2*b*d^2*e^5 - 12*A*a*b^2*d^2*e^5 - 12*A*a^2*c*d^2*e^5 - 10*B*a^3*d*e^6 - 30*A*a^2*b*d*e^6 - 60*A*a^3*e^7)*e^(-1))*e^(-7)/(x*e + d)^7","A",0
2347,1,1127,0,0.184305," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(280 \, B c^{3} x^{7} e^{7} + 980 \, B c^{3} d x^{6} e^{6} + 1960 \, B c^{3} d^{2} x^{5} e^{5} + 2450 \, B c^{3} d^{3} x^{4} e^{4} + 1960 \, B c^{3} d^{4} x^{3} e^{3} + 980 \, B c^{3} d^{5} x^{2} e^{2} + 280 \, B c^{3} d^{6} x e + 35 \, B c^{3} d^{7} + 420 \, B b c^{2} x^{6} e^{7} + 140 \, A c^{3} x^{6} e^{7} + 840 \, B b c^{2} d x^{5} e^{6} + 280 \, A c^{3} d x^{5} e^{6} + 1050 \, B b c^{2} d^{2} x^{4} e^{5} + 350 \, A c^{3} d^{2} x^{4} e^{5} + 840 \, B b c^{2} d^{3} x^{3} e^{4} + 280 \, A c^{3} d^{3} x^{3} e^{4} + 420 \, B b c^{2} d^{4} x^{2} e^{3} + 140 \, A c^{3} d^{4} x^{2} e^{3} + 120 \, B b c^{2} d^{5} x e^{2} + 40 \, A c^{3} d^{5} x e^{2} + 15 \, B b c^{2} d^{6} e + 5 \, A c^{3} d^{6} e + 280 \, B b^{2} c x^{5} e^{7} + 280 \, B a c^{2} x^{5} e^{7} + 280 \, A b c^{2} x^{5} e^{7} + 350 \, B b^{2} c d x^{4} e^{6} + 350 \, B a c^{2} d x^{4} e^{6} + 350 \, A b c^{2} d x^{4} e^{6} + 280 \, B b^{2} c d^{2} x^{3} e^{5} + 280 \, B a c^{2} d^{2} x^{3} e^{5} + 280 \, A b c^{2} d^{2} x^{3} e^{5} + 140 \, B b^{2} c d^{3} x^{2} e^{4} + 140 \, B a c^{2} d^{3} x^{2} e^{4} + 140 \, A b c^{2} d^{3} x^{2} e^{4} + 40 \, B b^{2} c d^{4} x e^{3} + 40 \, B a c^{2} d^{4} x e^{3} + 40 \, A b c^{2} d^{4} x e^{3} + 5 \, B b^{2} c d^{5} e^{2} + 5 \, B a c^{2} d^{5} e^{2} + 5 \, A b c^{2} d^{5} e^{2} + 70 \, B b^{3} x^{4} e^{7} + 420 \, B a b c x^{4} e^{7} + 210 \, A b^{2} c x^{4} e^{7} + 210 \, A a c^{2} x^{4} e^{7} + 56 \, B b^{3} d x^{3} e^{6} + 336 \, B a b c d x^{3} e^{6} + 168 \, A b^{2} c d x^{3} e^{6} + 168 \, A a c^{2} d x^{3} e^{6} + 28 \, B b^{3} d^{2} x^{2} e^{5} + 168 \, B a b c d^{2} x^{2} e^{5} + 84 \, A b^{2} c d^{2} x^{2} e^{5} + 84 \, A a c^{2} d^{2} x^{2} e^{5} + 8 \, B b^{3} d^{3} x e^{4} + 48 \, B a b c d^{3} x e^{4} + 24 \, A b^{2} c d^{3} x e^{4} + 24 \, A a c^{2} d^{3} x e^{4} + B b^{3} d^{4} e^{3} + 6 \, B a b c d^{4} e^{3} + 3 \, A b^{2} c d^{4} e^{3} + 3 \, A a c^{2} d^{4} e^{3} + 168 \, B a b^{2} x^{3} e^{7} + 56 \, A b^{3} x^{3} e^{7} + 168 \, B a^{2} c x^{3} e^{7} + 336 \, A a b c x^{3} e^{7} + 84 \, B a b^{2} d x^{2} e^{6} + 28 \, A b^{3} d x^{2} e^{6} + 84 \, B a^{2} c d x^{2} e^{6} + 168 \, A a b c d x^{2} e^{6} + 24 \, B a b^{2} d^{2} x e^{5} + 8 \, A b^{3} d^{2} x e^{5} + 24 \, B a^{2} c d^{2} x e^{5} + 48 \, A a b c d^{2} x e^{5} + 3 \, B a b^{2} d^{3} e^{4} + A b^{3} d^{3} e^{4} + 3 \, B a^{2} c d^{3} e^{4} + 6 \, A a b c d^{3} e^{4} + 140 \, B a^{2} b x^{2} e^{7} + 140 \, A a b^{2} x^{2} e^{7} + 140 \, A a^{2} c x^{2} e^{7} + 40 \, B a^{2} b d x e^{6} + 40 \, A a b^{2} d x e^{6} + 40 \, A a^{2} c d x e^{6} + 5 \, B a^{2} b d^{2} e^{5} + 5 \, A a b^{2} d^{2} e^{5} + 5 \, A a^{2} c d^{2} e^{5} + 40 \, B a^{3} x e^{7} + 120 \, A a^{2} b x e^{7} + 5 \, B a^{3} d e^{6} + 15 \, A a^{2} b d e^{6} + 35 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(280*B*c^3*x^7*e^7 + 980*B*c^3*d*x^6*e^6 + 1960*B*c^3*d^2*x^5*e^5 + 2450*B*c^3*d^3*x^4*e^4 + 1960*B*c^3*d^4*x^3*e^3 + 980*B*c^3*d^5*x^2*e^2 + 280*B*c^3*d^6*x*e + 35*B*c^3*d^7 + 420*B*b*c^2*x^6*e^7 + 140*A*c^3*x^6*e^7 + 840*B*b*c^2*d*x^5*e^6 + 280*A*c^3*d*x^5*e^6 + 1050*B*b*c^2*d^2*x^4*e^5 + 350*A*c^3*d^2*x^4*e^5 + 840*B*b*c^2*d^3*x^3*e^4 + 280*A*c^3*d^3*x^3*e^4 + 420*B*b*c^2*d^4*x^2*e^3 + 140*A*c^3*d^4*x^2*e^3 + 120*B*b*c^2*d^5*x*e^2 + 40*A*c^3*d^5*x*e^2 + 15*B*b*c^2*d^6*e + 5*A*c^3*d^6*e + 280*B*b^2*c*x^5*e^7 + 280*B*a*c^2*x^5*e^7 + 280*A*b*c^2*x^5*e^7 + 350*B*b^2*c*d*x^4*e^6 + 350*B*a*c^2*d*x^4*e^6 + 350*A*b*c^2*d*x^4*e^6 + 280*B*b^2*c*d^2*x^3*e^5 + 280*B*a*c^2*d^2*x^3*e^5 + 280*A*b*c^2*d^2*x^3*e^5 + 140*B*b^2*c*d^3*x^2*e^4 + 140*B*a*c^2*d^3*x^2*e^4 + 140*A*b*c^2*d^3*x^2*e^4 + 40*B*b^2*c*d^4*x*e^3 + 40*B*a*c^2*d^4*x*e^3 + 40*A*b*c^2*d^4*x*e^3 + 5*B*b^2*c*d^5*e^2 + 5*B*a*c^2*d^5*e^2 + 5*A*b*c^2*d^5*e^2 + 70*B*b^3*x^4*e^7 + 420*B*a*b*c*x^4*e^7 + 210*A*b^2*c*x^4*e^7 + 210*A*a*c^2*x^4*e^7 + 56*B*b^3*d*x^3*e^6 + 336*B*a*b*c*d*x^3*e^6 + 168*A*b^2*c*d*x^3*e^6 + 168*A*a*c^2*d*x^3*e^6 + 28*B*b^3*d^2*x^2*e^5 + 168*B*a*b*c*d^2*x^2*e^5 + 84*A*b^2*c*d^2*x^2*e^5 + 84*A*a*c^2*d^2*x^2*e^5 + 8*B*b^3*d^3*x*e^4 + 48*B*a*b*c*d^3*x*e^4 + 24*A*b^2*c*d^3*x*e^4 + 24*A*a*c^2*d^3*x*e^4 + B*b^3*d^4*e^3 + 6*B*a*b*c*d^4*e^3 + 3*A*b^2*c*d^4*e^3 + 3*A*a*c^2*d^4*e^3 + 168*B*a*b^2*x^3*e^7 + 56*A*b^3*x^3*e^7 + 168*B*a^2*c*x^3*e^7 + 336*A*a*b*c*x^3*e^7 + 84*B*a*b^2*d*x^2*e^6 + 28*A*b^3*d*x^2*e^6 + 84*B*a^2*c*d*x^2*e^6 + 168*A*a*b*c*d*x^2*e^6 + 24*B*a*b^2*d^2*x*e^5 + 8*A*b^3*d^2*x*e^5 + 24*B*a^2*c*d^2*x*e^5 + 48*A*a*b*c*d^2*x*e^5 + 3*B*a*b^2*d^3*e^4 + A*b^3*d^3*e^4 + 3*B*a^2*c*d^3*e^4 + 6*A*a*b*c*d^3*e^4 + 140*B*a^2*b*x^2*e^7 + 140*A*a*b^2*x^2*e^7 + 140*A*a^2*c*x^2*e^7 + 40*B*a^2*b*d*x*e^6 + 40*A*a*b^2*d*x*e^6 + 40*A*a^2*c*d*x*e^6 + 5*B*a^2*b*d^2*e^5 + 5*A*a*b^2*d^2*e^5 + 5*A*a^2*c*d^2*e^5 + 40*B*a^3*x*e^7 + 120*A*a^2*b*x*e^7 + 5*B*a^3*d*e^6 + 15*A*a^2*b*d*e^6 + 35*A*a^3*e^7)*e^(-8)/(x*e + d)^8","B",0
2348,1,1129,0,0.205470," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(1260 \, B c^{3} x^{7} e^{7} + 2940 \, B c^{3} d x^{6} e^{6} + 4410 \, B c^{3} d^{2} x^{5} e^{5} + 4410 \, B c^{3} d^{3} x^{4} e^{4} + 2940 \, B c^{3} d^{4} x^{3} e^{3} + 1260 \, B c^{3} d^{5} x^{2} e^{2} + 315 \, B c^{3} d^{6} x e + 35 \, B c^{3} d^{7} + 2520 \, B b c^{2} x^{6} e^{7} + 840 \, A c^{3} x^{6} e^{7} + 3780 \, B b c^{2} d x^{5} e^{6} + 1260 \, A c^{3} d x^{5} e^{6} + 3780 \, B b c^{2} d^{2} x^{4} e^{5} + 1260 \, A c^{3} d^{2} x^{4} e^{5} + 2520 \, B b c^{2} d^{3} x^{3} e^{4} + 840 \, A c^{3} d^{3} x^{3} e^{4} + 1080 \, B b c^{2} d^{4} x^{2} e^{3} + 360 \, A c^{3} d^{4} x^{2} e^{3} + 270 \, B b c^{2} d^{5} x e^{2} + 90 \, A c^{3} d^{5} x e^{2} + 30 \, B b c^{2} d^{6} e + 10 \, A c^{3} d^{6} e + 1890 \, B b^{2} c x^{5} e^{7} + 1890 \, B a c^{2} x^{5} e^{7} + 1890 \, A b c^{2} x^{5} e^{7} + 1890 \, B b^{2} c d x^{4} e^{6} + 1890 \, B a c^{2} d x^{4} e^{6} + 1890 \, A b c^{2} d x^{4} e^{6} + 1260 \, B b^{2} c d^{2} x^{3} e^{5} + 1260 \, B a c^{2} d^{2} x^{3} e^{5} + 1260 \, A b c^{2} d^{2} x^{3} e^{5} + 540 \, B b^{2} c d^{3} x^{2} e^{4} + 540 \, B a c^{2} d^{3} x^{2} e^{4} + 540 \, A b c^{2} d^{3} x^{2} e^{4} + 135 \, B b^{2} c d^{4} x e^{3} + 135 \, B a c^{2} d^{4} x e^{3} + 135 \, A b c^{2} d^{4} x e^{3} + 15 \, B b^{2} c d^{5} e^{2} + 15 \, B a c^{2} d^{5} e^{2} + 15 \, A b c^{2} d^{5} e^{2} + 504 \, B b^{3} x^{4} e^{7} + 3024 \, B a b c x^{4} e^{7} + 1512 \, A b^{2} c x^{4} e^{7} + 1512 \, A a c^{2} x^{4} e^{7} + 336 \, B b^{3} d x^{3} e^{6} + 2016 \, B a b c d x^{3} e^{6} + 1008 \, A b^{2} c d x^{3} e^{6} + 1008 \, A a c^{2} d x^{3} e^{6} + 144 \, B b^{3} d^{2} x^{2} e^{5} + 864 \, B a b c d^{2} x^{2} e^{5} + 432 \, A b^{2} c d^{2} x^{2} e^{5} + 432 \, A a c^{2} d^{2} x^{2} e^{5} + 36 \, B b^{3} d^{3} x e^{4} + 216 \, B a b c d^{3} x e^{4} + 108 \, A b^{2} c d^{3} x e^{4} + 108 \, A a c^{2} d^{3} x e^{4} + 4 \, B b^{3} d^{4} e^{3} + 24 \, B a b c d^{4} e^{3} + 12 \, A b^{2} c d^{4} e^{3} + 12 \, A a c^{2} d^{4} e^{3} + 1260 \, B a b^{2} x^{3} e^{7} + 420 \, A b^{3} x^{3} e^{7} + 1260 \, B a^{2} c x^{3} e^{7} + 2520 \, A a b c x^{3} e^{7} + 540 \, B a b^{2} d x^{2} e^{6} + 180 \, A b^{3} d x^{2} e^{6} + 540 \, B a^{2} c d x^{2} e^{6} + 1080 \, A a b c d x^{2} e^{6} + 135 \, B a b^{2} d^{2} x e^{5} + 45 \, A b^{3} d^{2} x e^{5} + 135 \, B a^{2} c d^{2} x e^{5} + 270 \, A a b c d^{2} x e^{5} + 15 \, B a b^{2} d^{3} e^{4} + 5 \, A b^{3} d^{3} e^{4} + 15 \, B a^{2} c d^{3} e^{4} + 30 \, A a b c d^{3} e^{4} + 1080 \, B a^{2} b x^{2} e^{7} + 1080 \, A a b^{2} x^{2} e^{7} + 1080 \, A a^{2} c x^{2} e^{7} + 270 \, B a^{2} b d x e^{6} + 270 \, A a b^{2} d x e^{6} + 270 \, A a^{2} c d x e^{6} + 30 \, B a^{2} b d^{2} e^{5} + 30 \, A a b^{2} d^{2} e^{5} + 30 \, A a^{2} c d^{2} e^{5} + 315 \, B a^{3} x e^{7} + 945 \, A a^{2} b x e^{7} + 35 \, B a^{3} d e^{6} + 105 \, A a^{2} b d e^{6} + 280 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{2520 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/2520*(1260*B*c^3*x^7*e^7 + 2940*B*c^3*d*x^6*e^6 + 4410*B*c^3*d^2*x^5*e^5 + 4410*B*c^3*d^3*x^4*e^4 + 2940*B*c^3*d^4*x^3*e^3 + 1260*B*c^3*d^5*x^2*e^2 + 315*B*c^3*d^6*x*e + 35*B*c^3*d^7 + 2520*B*b*c^2*x^6*e^7 + 840*A*c^3*x^6*e^7 + 3780*B*b*c^2*d*x^5*e^6 + 1260*A*c^3*d*x^5*e^6 + 3780*B*b*c^2*d^2*x^4*e^5 + 1260*A*c^3*d^2*x^4*e^5 + 2520*B*b*c^2*d^3*x^3*e^4 + 840*A*c^3*d^3*x^3*e^4 + 1080*B*b*c^2*d^4*x^2*e^3 + 360*A*c^3*d^4*x^2*e^3 + 270*B*b*c^2*d^5*x*e^2 + 90*A*c^3*d^5*x*e^2 + 30*B*b*c^2*d^6*e + 10*A*c^3*d^6*e + 1890*B*b^2*c*x^5*e^7 + 1890*B*a*c^2*x^5*e^7 + 1890*A*b*c^2*x^5*e^7 + 1890*B*b^2*c*d*x^4*e^6 + 1890*B*a*c^2*d*x^4*e^6 + 1890*A*b*c^2*d*x^4*e^6 + 1260*B*b^2*c*d^2*x^3*e^5 + 1260*B*a*c^2*d^2*x^3*e^5 + 1260*A*b*c^2*d^2*x^3*e^5 + 540*B*b^2*c*d^3*x^2*e^4 + 540*B*a*c^2*d^3*x^2*e^4 + 540*A*b*c^2*d^3*x^2*e^4 + 135*B*b^2*c*d^4*x*e^3 + 135*B*a*c^2*d^4*x*e^3 + 135*A*b*c^2*d^4*x*e^3 + 15*B*b^2*c*d^5*e^2 + 15*B*a*c^2*d^5*e^2 + 15*A*b*c^2*d^5*e^2 + 504*B*b^3*x^4*e^7 + 3024*B*a*b*c*x^4*e^7 + 1512*A*b^2*c*x^4*e^7 + 1512*A*a*c^2*x^4*e^7 + 336*B*b^3*d*x^3*e^6 + 2016*B*a*b*c*d*x^3*e^6 + 1008*A*b^2*c*d*x^3*e^6 + 1008*A*a*c^2*d*x^3*e^6 + 144*B*b^3*d^2*x^2*e^5 + 864*B*a*b*c*d^2*x^2*e^5 + 432*A*b^2*c*d^2*x^2*e^5 + 432*A*a*c^2*d^2*x^2*e^5 + 36*B*b^3*d^3*x*e^4 + 216*B*a*b*c*d^3*x*e^4 + 108*A*b^2*c*d^3*x*e^4 + 108*A*a*c^2*d^3*x*e^4 + 4*B*b^3*d^4*e^3 + 24*B*a*b*c*d^4*e^3 + 12*A*b^2*c*d^4*e^3 + 12*A*a*c^2*d^4*e^3 + 1260*B*a*b^2*x^3*e^7 + 420*A*b^3*x^3*e^7 + 1260*B*a^2*c*x^3*e^7 + 2520*A*a*b*c*x^3*e^7 + 540*B*a*b^2*d*x^2*e^6 + 180*A*b^3*d*x^2*e^6 + 540*B*a^2*c*d*x^2*e^6 + 1080*A*a*b*c*d*x^2*e^6 + 135*B*a*b^2*d^2*x*e^5 + 45*A*b^3*d^2*x*e^5 + 135*B*a^2*c*d^2*x*e^5 + 270*A*a*b*c*d^2*x*e^5 + 15*B*a*b^2*d^3*e^4 + 5*A*b^3*d^3*e^4 + 15*B*a^2*c*d^3*e^4 + 30*A*a*b*c*d^3*e^4 + 1080*B*a^2*b*x^2*e^7 + 1080*A*a*b^2*x^2*e^7 + 1080*A*a^2*c*x^2*e^7 + 270*B*a^2*b*d*x*e^6 + 270*A*a*b^2*d*x*e^6 + 270*A*a^2*c*d*x*e^6 + 30*B*a^2*b*d^2*e^5 + 30*A*a*b^2*d^2*e^5 + 30*A*a^2*c*d^2*e^5 + 315*B*a^3*x*e^7 + 945*A*a^2*b*x*e^7 + 35*B*a^3*d*e^6 + 105*A*a^2*b*d*e^6 + 280*A*a^3*e^7)*e^(-8)/(x*e + d)^9","B",0
2349,1,1129,0,0.183314," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(840 \, B c^{3} x^{7} e^{7} + 1470 \, B c^{3} d x^{6} e^{6} + 1764 \, B c^{3} d^{2} x^{5} e^{5} + 1470 \, B c^{3} d^{3} x^{4} e^{4} + 840 \, B c^{3} d^{4} x^{3} e^{3} + 315 \, B c^{3} d^{5} x^{2} e^{2} + 70 \, B c^{3} d^{6} x e + 7 \, B c^{3} d^{7} + 1890 \, B b c^{2} x^{6} e^{7} + 630 \, A c^{3} x^{6} e^{7} + 2268 \, B b c^{2} d x^{5} e^{6} + 756 \, A c^{3} d x^{5} e^{6} + 1890 \, B b c^{2} d^{2} x^{4} e^{5} + 630 \, A c^{3} d^{2} x^{4} e^{5} + 1080 \, B b c^{2} d^{3} x^{3} e^{4} + 360 \, A c^{3} d^{3} x^{3} e^{4} + 405 \, B b c^{2} d^{4} x^{2} e^{3} + 135 \, A c^{3} d^{4} x^{2} e^{3} + 90 \, B b c^{2} d^{5} x e^{2} + 30 \, A c^{3} d^{5} x e^{2} + 9 \, B b c^{2} d^{6} e + 3 \, A c^{3} d^{6} e + 1512 \, B b^{2} c x^{5} e^{7} + 1512 \, B a c^{2} x^{5} e^{7} + 1512 \, A b c^{2} x^{5} e^{7} + 1260 \, B b^{2} c d x^{4} e^{6} + 1260 \, B a c^{2} d x^{4} e^{6} + 1260 \, A b c^{2} d x^{4} e^{6} + 720 \, B b^{2} c d^{2} x^{3} e^{5} + 720 \, B a c^{2} d^{2} x^{3} e^{5} + 720 \, A b c^{2} d^{2} x^{3} e^{5} + 270 \, B b^{2} c d^{3} x^{2} e^{4} + 270 \, B a c^{2} d^{3} x^{2} e^{4} + 270 \, A b c^{2} d^{3} x^{2} e^{4} + 60 \, B b^{2} c d^{4} x e^{3} + 60 \, B a c^{2} d^{4} x e^{3} + 60 \, A b c^{2} d^{4} x e^{3} + 6 \, B b^{2} c d^{5} e^{2} + 6 \, B a c^{2} d^{5} e^{2} + 6 \, A b c^{2} d^{5} e^{2} + 420 \, B b^{3} x^{4} e^{7} + 2520 \, B a b c x^{4} e^{7} + 1260 \, A b^{2} c x^{4} e^{7} + 1260 \, A a c^{2} x^{4} e^{7} + 240 \, B b^{3} d x^{3} e^{6} + 1440 \, B a b c d x^{3} e^{6} + 720 \, A b^{2} c d x^{3} e^{6} + 720 \, A a c^{2} d x^{3} e^{6} + 90 \, B b^{3} d^{2} x^{2} e^{5} + 540 \, B a b c d^{2} x^{2} e^{5} + 270 \, A b^{2} c d^{2} x^{2} e^{5} + 270 \, A a c^{2} d^{2} x^{2} e^{5} + 20 \, B b^{3} d^{3} x e^{4} + 120 \, B a b c d^{3} x e^{4} + 60 \, A b^{2} c d^{3} x e^{4} + 60 \, A a c^{2} d^{3} x e^{4} + 2 \, B b^{3} d^{4} e^{3} + 12 \, B a b c d^{4} e^{3} + 6 \, A b^{2} c d^{4} e^{3} + 6 \, A a c^{2} d^{4} e^{3} + 1080 \, B a b^{2} x^{3} e^{7} + 360 \, A b^{3} x^{3} e^{7} + 1080 \, B a^{2} c x^{3} e^{7} + 2160 \, A a b c x^{3} e^{7} + 405 \, B a b^{2} d x^{2} e^{6} + 135 \, A b^{3} d x^{2} e^{6} + 405 \, B a^{2} c d x^{2} e^{6} + 810 \, A a b c d x^{2} e^{6} + 90 \, B a b^{2} d^{2} x e^{5} + 30 \, A b^{3} d^{2} x e^{5} + 90 \, B a^{2} c d^{2} x e^{5} + 180 \, A a b c d^{2} x e^{5} + 9 \, B a b^{2} d^{3} e^{4} + 3 \, A b^{3} d^{3} e^{4} + 9 \, B a^{2} c d^{3} e^{4} + 18 \, A a b c d^{3} e^{4} + 945 \, B a^{2} b x^{2} e^{7} + 945 \, A a b^{2} x^{2} e^{7} + 945 \, A a^{2} c x^{2} e^{7} + 210 \, B a^{2} b d x e^{6} + 210 \, A a b^{2} d x e^{6} + 210 \, A a^{2} c d x e^{6} + 21 \, B a^{2} b d^{2} e^{5} + 21 \, A a b^{2} d^{2} e^{5} + 21 \, A a^{2} c d^{2} e^{5} + 280 \, B a^{3} x e^{7} + 840 \, A a^{2} b x e^{7} + 28 \, B a^{3} d e^{6} + 84 \, A a^{2} b d e^{6} + 252 \, A a^{3} e^{7}\right)} e^{\left(-8\right)}}{2520 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/2520*(840*B*c^3*x^7*e^7 + 1470*B*c^3*d*x^6*e^6 + 1764*B*c^3*d^2*x^5*e^5 + 1470*B*c^3*d^3*x^4*e^4 + 840*B*c^3*d^4*x^3*e^3 + 315*B*c^3*d^5*x^2*e^2 + 70*B*c^3*d^6*x*e + 7*B*c^3*d^7 + 1890*B*b*c^2*x^6*e^7 + 630*A*c^3*x^6*e^7 + 2268*B*b*c^2*d*x^5*e^6 + 756*A*c^3*d*x^5*e^6 + 1890*B*b*c^2*d^2*x^4*e^5 + 630*A*c^3*d^2*x^4*e^5 + 1080*B*b*c^2*d^3*x^3*e^4 + 360*A*c^3*d^3*x^3*e^4 + 405*B*b*c^2*d^4*x^2*e^3 + 135*A*c^3*d^4*x^2*e^3 + 90*B*b*c^2*d^5*x*e^2 + 30*A*c^3*d^5*x*e^2 + 9*B*b*c^2*d^6*e + 3*A*c^3*d^6*e + 1512*B*b^2*c*x^5*e^7 + 1512*B*a*c^2*x^5*e^7 + 1512*A*b*c^2*x^5*e^7 + 1260*B*b^2*c*d*x^4*e^6 + 1260*B*a*c^2*d*x^4*e^6 + 1260*A*b*c^2*d*x^4*e^6 + 720*B*b^2*c*d^2*x^3*e^5 + 720*B*a*c^2*d^2*x^3*e^5 + 720*A*b*c^2*d^2*x^3*e^5 + 270*B*b^2*c*d^3*x^2*e^4 + 270*B*a*c^2*d^3*x^2*e^4 + 270*A*b*c^2*d^3*x^2*e^4 + 60*B*b^2*c*d^4*x*e^3 + 60*B*a*c^2*d^4*x*e^3 + 60*A*b*c^2*d^4*x*e^3 + 6*B*b^2*c*d^5*e^2 + 6*B*a*c^2*d^5*e^2 + 6*A*b*c^2*d^5*e^2 + 420*B*b^3*x^4*e^7 + 2520*B*a*b*c*x^4*e^7 + 1260*A*b^2*c*x^4*e^7 + 1260*A*a*c^2*x^4*e^7 + 240*B*b^3*d*x^3*e^6 + 1440*B*a*b*c*d*x^3*e^6 + 720*A*b^2*c*d*x^3*e^6 + 720*A*a*c^2*d*x^3*e^6 + 90*B*b^3*d^2*x^2*e^5 + 540*B*a*b*c*d^2*x^2*e^5 + 270*A*b^2*c*d^2*x^2*e^5 + 270*A*a*c^2*d^2*x^2*e^5 + 20*B*b^3*d^3*x*e^4 + 120*B*a*b*c*d^3*x*e^4 + 60*A*b^2*c*d^3*x*e^4 + 60*A*a*c^2*d^3*x*e^4 + 2*B*b^3*d^4*e^3 + 12*B*a*b*c*d^4*e^3 + 6*A*b^2*c*d^4*e^3 + 6*A*a*c^2*d^4*e^3 + 1080*B*a*b^2*x^3*e^7 + 360*A*b^3*x^3*e^7 + 1080*B*a^2*c*x^3*e^7 + 2160*A*a*b*c*x^3*e^7 + 405*B*a*b^2*d*x^2*e^6 + 135*A*b^3*d*x^2*e^6 + 405*B*a^2*c*d*x^2*e^6 + 810*A*a*b*c*d*x^2*e^6 + 90*B*a*b^2*d^2*x*e^5 + 30*A*b^3*d^2*x*e^5 + 90*B*a^2*c*d^2*x*e^5 + 180*A*a*b*c*d^2*x*e^5 + 9*B*a*b^2*d^3*e^4 + 3*A*b^3*d^3*e^4 + 9*B*a^2*c*d^3*e^4 + 18*A*a*b*c*d^3*e^4 + 945*B*a^2*b*x^2*e^7 + 945*A*a*b^2*x^2*e^7 + 945*A*a^2*c*x^2*e^7 + 210*B*a^2*b*d*x*e^6 + 210*A*a*b^2*d*x*e^6 + 210*A*a^2*c*d*x*e^6 + 21*B*a^2*b*d^2*e^5 + 21*A*a*b^2*d^2*e^5 + 21*A*a^2*c*d^2*e^5 + 280*B*a^3*x*e^7 + 840*A*a^2*b*x*e^7 + 28*B*a^3*d*e^6 + 84*A*a^2*b*d*e^6 + 252*A*a^3*e^7)*e^(-8)/(x*e + d)^10","B",0
2350,1,606,0,0.197991," ","integrate(x*(e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} c d m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} b m^{3} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} c m^{2} x^{4} e^{4} + {\left(x e + d\right)}^{m} b d m^{3} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} c d m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} c d^{2} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} a m^{3} x^{2} e^{4} + 7 \, {\left(x e + d\right)}^{m} b m^{2} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} c m x^{4} e^{4} + {\left(x e + d\right)}^{m} a d m^{3} x e^{3} + 5 \, {\left(x e + d\right)}^{m} b d m^{2} x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} c d m x^{3} e^{3} - 2 \, {\left(x e + d\right)}^{m} b d^{2} m^{2} x e^{2} - 3 \, {\left(x e + d\right)}^{m} c d^{2} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} c d^{3} m x e + 8 \, {\left(x e + d\right)}^{m} a m^{2} x^{2} e^{4} + 14 \, {\left(x e + d\right)}^{m} b m x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} c x^{4} e^{4} + 7 \, {\left(x e + d\right)}^{m} a d m^{2} x e^{3} + 4 \, {\left(x e + d\right)}^{m} b d m x^{2} e^{3} - {\left(x e + d\right)}^{m} a d^{2} m^{2} e^{2} - 8 \, {\left(x e + d\right)}^{m} b d^{2} m x e^{2} + 2 \, {\left(x e + d\right)}^{m} b d^{3} m e - 6 \, {\left(x e + d\right)}^{m} c d^{4} + 19 \, {\left(x e + d\right)}^{m} a m x^{2} e^{4} + 8 \, {\left(x e + d\right)}^{m} b x^{3} e^{4} + 12 \, {\left(x e + d\right)}^{m} a d m x e^{3} - 7 \, {\left(x e + d\right)}^{m} a d^{2} m e^{2} + 8 \, {\left(x e + d\right)}^{m} b d^{3} e + 12 \, {\left(x e + d\right)}^{m} a x^{2} e^{4} - 12 \, {\left(x e + d\right)}^{m} a d^{2} e^{2}}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"((x*e + d)^m*c*m^3*x^4*e^4 + (x*e + d)^m*c*d*m^3*x^3*e^3 + (x*e + d)^m*b*m^3*x^3*e^4 + 6*(x*e + d)^m*c*m^2*x^4*e^4 + (x*e + d)^m*b*d*m^3*x^2*e^3 + 3*(x*e + d)^m*c*d*m^2*x^3*e^3 - 3*(x*e + d)^m*c*d^2*m^2*x^2*e^2 + (x*e + d)^m*a*m^3*x^2*e^4 + 7*(x*e + d)^m*b*m^2*x^3*e^4 + 11*(x*e + d)^m*c*m*x^4*e^4 + (x*e + d)^m*a*d*m^3*x*e^3 + 5*(x*e + d)^m*b*d*m^2*x^2*e^3 + 2*(x*e + d)^m*c*d*m*x^3*e^3 - 2*(x*e + d)^m*b*d^2*m^2*x*e^2 - 3*(x*e + d)^m*c*d^2*m*x^2*e^2 + 6*(x*e + d)^m*c*d^3*m*x*e + 8*(x*e + d)^m*a*m^2*x^2*e^4 + 14*(x*e + d)^m*b*m*x^3*e^4 + 6*(x*e + d)^m*c*x^4*e^4 + 7*(x*e + d)^m*a*d*m^2*x*e^3 + 4*(x*e + d)^m*b*d*m*x^2*e^3 - (x*e + d)^m*a*d^2*m^2*e^2 - 8*(x*e + d)^m*b*d^2*m*x*e^2 + 2*(x*e + d)^m*b*d^3*m*e - 6*(x*e + d)^m*c*d^4 + 19*(x*e + d)^m*a*m*x^2*e^4 + 8*(x*e + d)^m*b*x^3*e^4 + 12*(x*e + d)^m*a*d*m*x*e^3 - 7*(x*e + d)^m*a*d^2*m*e^2 + 8*(x*e + d)^m*b*d^3*e + 12*(x*e + d)^m*a*x^2*e^4 - 12*(x*e + d)^m*a*d^2*e^2)/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
2351,1,177,0,0.150620," ","integrate(x*(e*x+d)^5*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{9} \, c x^{9} e^{5} + \frac{5}{8} \, c d x^{8} e^{4} + \frac{10}{7} \, c d^{2} x^{7} e^{3} + \frac{5}{3} \, c d^{3} x^{6} e^{2} + c d^{4} x^{5} e + \frac{1}{4} \, c d^{5} x^{4} + \frac{1}{8} \, b x^{8} e^{5} + \frac{5}{7} \, b d x^{7} e^{4} + \frac{5}{3} \, b d^{2} x^{6} e^{3} + 2 \, b d^{3} x^{5} e^{2} + \frac{5}{4} \, b d^{4} x^{4} e + \frac{1}{3} \, b d^{5} x^{3} + \frac{1}{7} \, a x^{7} e^{5} + \frac{5}{6} \, a d x^{6} e^{4} + 2 \, a d^{2} x^{5} e^{3} + \frac{5}{2} \, a d^{3} x^{4} e^{2} + \frac{5}{3} \, a d^{4} x^{3} e + \frac{1}{2} \, a d^{5} x^{2}"," ",0,"1/9*c*x^9*e^5 + 5/8*c*d*x^8*e^4 + 10/7*c*d^2*x^7*e^3 + 5/3*c*d^3*x^6*e^2 + c*d^4*x^5*e + 1/4*c*d^5*x^4 + 1/8*b*x^8*e^5 + 5/7*b*d*x^7*e^4 + 5/3*b*d^2*x^6*e^3 + 2*b*d^3*x^5*e^2 + 5/4*b*d^4*x^4*e + 1/3*b*d^5*x^3 + 1/7*a*x^7*e^5 + 5/6*a*d*x^6*e^4 + 2*a*d^2*x^5*e^3 + 5/2*a*d^3*x^4*e^2 + 5/3*a*d^4*x^3*e + 1/2*a*d^5*x^2","A",0
2352,1,143,0,0.164151," ","integrate(x*(e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{8} \, c x^{8} e^{4} + \frac{4}{7} \, c d x^{7} e^{3} + c d^{2} x^{6} e^{2} + \frac{4}{5} \, c d^{3} x^{5} e + \frac{1}{4} \, c d^{4} x^{4} + \frac{1}{7} \, b x^{7} e^{4} + \frac{2}{3} \, b d x^{6} e^{3} + \frac{6}{5} \, b d^{2} x^{5} e^{2} + b d^{3} x^{4} e + \frac{1}{3} \, b d^{4} x^{3} + \frac{1}{6} \, a x^{6} e^{4} + \frac{4}{5} \, a d x^{5} e^{3} + \frac{3}{2} \, a d^{2} x^{4} e^{2} + \frac{4}{3} \, a d^{3} x^{3} e + \frac{1}{2} \, a d^{4} x^{2}"," ",0,"1/8*c*x^8*e^4 + 4/7*c*d*x^7*e^3 + c*d^2*x^6*e^2 + 4/5*c*d^3*x^5*e + 1/4*c*d^4*x^4 + 1/7*b*x^7*e^4 + 2/3*b*d*x^6*e^3 + 6/5*b*d^2*x^5*e^2 + b*d^3*x^4*e + 1/3*b*d^4*x^3 + 1/6*a*x^6*e^4 + 4/5*a*d*x^5*e^3 + 3/2*a*d^2*x^4*e^2 + 4/3*a*d^3*x^3*e + 1/2*a*d^4*x^2","A",0
2353,1,111,0,0.173044," ","integrate(x*(e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} e^{3} + \frac{1}{2} \, c d x^{6} e^{2} + \frac{3}{5} \, c d^{2} x^{5} e + \frac{1}{4} \, c d^{3} x^{4} + \frac{1}{6} \, b x^{6} e^{3} + \frac{3}{5} \, b d x^{5} e^{2} + \frac{3}{4} \, b d^{2} x^{4} e + \frac{1}{3} \, b d^{3} x^{3} + \frac{1}{5} \, a x^{5} e^{3} + \frac{3}{4} \, a d x^{4} e^{2} + a d^{2} x^{3} e + \frac{1}{2} \, a d^{3} x^{2}"," ",0,"1/7*c*x^7*e^3 + 1/2*c*d*x^6*e^2 + 3/5*c*d^2*x^5*e + 1/4*c*d^3*x^4 + 1/6*b*x^6*e^3 + 3/5*b*d*x^5*e^2 + 3/4*b*d^2*x^4*e + 1/3*b*d^3*x^3 + 1/5*a*x^5*e^3 + 3/4*a*d*x^4*e^2 + a*d^2*x^3*e + 1/2*a*d^3*x^2","A",0
2354,1,79,0,0.151019," ","integrate(x*(e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{6} \, c x^{6} e^{2} + \frac{2}{5} \, c d x^{5} e + \frac{1}{4} \, c d^{2} x^{4} + \frac{1}{5} \, b x^{5} e^{2} + \frac{1}{2} \, b d x^{4} e + \frac{1}{3} \, b d^{2} x^{3} + \frac{1}{4} \, a x^{4} e^{2} + \frac{2}{3} \, a d x^{3} e + \frac{1}{2} \, a d^{2} x^{2}"," ",0,"1/6*c*x^6*e^2 + 2/5*c*d*x^5*e + 1/4*c*d^2*x^4 + 1/5*b*x^5*e^2 + 1/2*b*d*x^4*e + 1/3*b*d^2*x^3 + 1/4*a*x^4*e^2 + 2/3*a*d*x^3*e + 1/2*a*d^2*x^2","A",0
2355,1,46,0,0.166352," ","integrate(x*(e*x+d)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{5} \, c x^{5} e + \frac{1}{4} \, c d x^{4} + \frac{1}{4} \, b x^{4} e + \frac{1}{3} \, b d x^{3} + \frac{1}{3} \, a x^{3} e + \frac{1}{2} \, a d x^{2}"," ",0,"1/5*c*x^5*e + 1/4*c*d*x^4 + 1/4*b*x^4*e + 1/3*b*d*x^3 + 1/3*a*x^3*e + 1/2*a*d*x^2","A",0
2356,1,19,0,0.151140," ","integrate(x*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{4} \, c x^{4} + \frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2}"," ",0,"1/4*c*x^4 + 1/3*b*x^3 + 1/2*a*x^2","A",0
2357,1,82,0,0.182278," ","integrate(x*(c*x^2+b*x+a)/(e*x+d),x, algorithm=""giac"")","-{\left(c d^{3} - b d^{2} e + a d e^{2}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, c x^{3} e^{2} - 3 \, c d x^{2} e + 6 \, c d^{2} x + 3 \, b x^{2} e^{2} - 6 \, b d x e + 6 \, a x e^{2}\right)} e^{\left(-3\right)}"," ",0,"-(c*d^3 - b*d^2*e + a*d*e^2)*e^(-4)*log(abs(x*e + d)) + 1/6*(2*c*x^3*e^2 - 3*c*d*x^2*e + 6*c*d^2*x + 3*b*x^2*e^2 - 6*b*d*x*e + 6*a*x*e^2)*e^(-3)","A",0
2358,1,131,0,0.199454," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left({\left(x e + d\right)}^{2} {\left(c - \frac{2 \, {\left(3 \, c d e - b e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} e^{\left(-3\right)} - 2 \, {\left(3 \, c d^{2} - 2 \, b d e + a e^{2}\right)} e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + 2 \, {\left(\frac{c d^{3} e^{2}}{x e + d} - \frac{b d^{2} e^{3}}{x e + d} + \frac{a d e^{4}}{x e + d}\right)} e^{\left(-5\right)}\right)} e^{\left(-1\right)}"," ",0,"1/2*((x*e + d)^2*(c - 2*(3*c*d*e - b*e^2)*e^(-1)/(x*e + d))*e^(-3) - 2*(3*c*d^2 - 2*b*d*e + a*e^2)*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 2*(c*d^3*e^2/(x*e + d) - b*d^2*e^3/(x*e + d) + a*d*e^4/(x*e + d))*e^(-5))*e^(-1)","A",0
2359,1,82,0,0.154774," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""giac"")","c x e^{\left(-3\right)} - {\left(3 \, c d - b e\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, c d^{3} - 3 \, b d^{2} e + a d e^{2} + 2 \, {\left(3 \, c d^{2} e - 2 \, b d e^{2} + a e^{3}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"c*x*e^(-3) - (3*c*d - b*e)*e^(-4)*log(abs(x*e + d)) - 1/2*(5*c*d^3 - 3*b*d^2*e + a*d*e^2 + 2*(3*c*d^2*e - 2*b*d*e^2 + a*e^3)*x)*e^(-4)/(x*e + d)^2","A",0
2360,1,88,0,0.156873," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""giac"")","c e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(6 \, {\left(3 \, c d e - b e^{2}\right)} x^{2} + 3 \, {\left(9 \, c d^{2} - 2 \, b d e - a e^{2}\right)} x + {\left(11 \, c d^{3} - 2 \, b d^{2} e - a d e^{2}\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"c*e^(-4)*log(abs(x*e + d)) + 1/6*(6*(3*c*d*e - b*e^2)*x^2 + 3*(9*c*d^2 - 2*b*d*e - a*e^2)*x + (11*c*d^3 - 2*b*d^2*e - a*d*e^2)*e^(-1))*e^(-3)/(x*e + d)^3","A",0
2361,1,128,0,0.158950," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{12 \, c e^{\left(-1\right)}}{x e + d} - \frac{18 \, c d e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}} + \frac{12 \, c d^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, c d^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{6 \, b}{{\left(x e + d\right)}^{2}} - \frac{8 \, b d}{{\left(x e + d\right)}^{3}} + \frac{3 \, b d^{2}}{{\left(x e + d\right)}^{4}} + \frac{4 \, a e}{{\left(x e + d\right)}^{3}} - \frac{3 \, a d e}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-3\right)}"," ",0,"-1/12*(12*c*e^(-1)/(x*e + d) - 18*c*d*e^(-1)/(x*e + d)^2 + 12*c*d^2*e^(-1)/(x*e + d)^3 - 3*c*d^3*e^(-1)/(x*e + d)^4 + 6*b/(x*e + d)^2 - 8*b*d/(x*e + d)^3 + 3*b*d^2/(x*e + d)^4 + 4*a*e/(x*e + d)^3 - 3*a*d*e/(x*e + d)^4)*e^(-3)","A",0
2362,1,80,0,0.174031," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(30 \, c x^{3} e^{3} + 30 \, c d x^{2} e^{2} + 15 \, c d^{2} x e + 3 \, c d^{3} + 20 \, b x^{2} e^{3} + 10 \, b d x e^{2} + 2 \, b d^{2} e + 15 \, a x e^{3} + 3 \, a d e^{2}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/60*(30*c*x^3*e^3 + 30*c*d*x^2*e^2 + 15*c*d^2*x*e + 3*c*d^3 + 20*b*x^2*e^3 + 10*b*d*x*e^2 + 2*b*d^2*e + 15*a*x*e^3 + 3*a*d*e^2)*e^(-4)/(x*e + d)^5","A",0
2363,1,78,0,0.152243," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(20 \, c x^{3} e^{3} + 15 \, c d x^{2} e^{2} + 6 \, c d^{2} x e + c d^{3} + 15 \, b x^{2} e^{3} + 6 \, b d x e^{2} + b d^{2} e + 12 \, a x e^{3} + 2 \, a d e^{2}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(20*c*x^3*e^3 + 15*c*d*x^2*e^2 + 6*c*d^2*x*e + c*d^3 + 15*b*x^2*e^3 + 6*b*d*x*e^2 + b*d^2*e + 12*a*x*e^3 + 2*a*d*e^2)*e^(-4)/(x*e + d)^6","A",0
2364,1,402,0,0.177888," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, B c^{2} x^{3} e^{3} + 9 \, B c^{2} d x^{2} e^{2} + 18 \, B c^{2} d^{2} x e - 3 \, B b c x^{2} e^{3} + 3 \, A c^{2} x^{2} e^{3} - 18 \, B b c d x e^{2} + 18 \, A c^{2} d x e^{2} + 6 \, B b^{2} x e^{3} - 6 \, B a c x e^{3} - 6 \, A b c x e^{3}}{6 \, c^{3}} + \frac{{\left(B c^{3} d^{3} - 3 \, B b c^{2} d^{2} e + 3 \, A c^{3} d^{2} e + 3 \, B b^{2} c d e^{2} - 3 \, B a c^{2} d e^{2} - 3 \, A b c^{2} d e^{2} - B b^{3} e^{3} + 2 \, B a b c e^{3} + A b^{2} c e^{3} - A a c^{2} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} - \frac{{\left(B b c^{3} d^{3} - 2 \, A c^{4} d^{3} - 3 \, B b^{2} c^{2} d^{2} e + 6 \, B a c^{3} d^{2} e + 3 \, A b c^{3} d^{2} e + 3 \, B b^{3} c d e^{2} - 9 \, B a b c^{2} d e^{2} - 3 \, A b^{2} c^{2} d e^{2} + 6 \, A a c^{3} d e^{2} - B b^{4} e^{3} + 4 \, B a b^{2} c e^{3} + A b^{3} c e^{3} - 2 \, B a^{2} c^{2} e^{3} - 3 \, A a b c^{2} e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{4}}"," ",0,"1/6*(2*B*c^2*x^3*e^3 + 9*B*c^2*d*x^2*e^2 + 18*B*c^2*d^2*x*e - 3*B*b*c*x^2*e^3 + 3*A*c^2*x^2*e^3 - 18*B*b*c*d*x*e^2 + 18*A*c^2*d*x*e^2 + 6*B*b^2*x*e^3 - 6*B*a*c*x*e^3 - 6*A*b*c*x*e^3)/c^3 + 1/2*(B*c^3*d^3 - 3*B*b*c^2*d^2*e + 3*A*c^3*d^2*e + 3*B*b^2*c*d*e^2 - 3*B*a*c^2*d*e^2 - 3*A*b*c^2*d*e^2 - B*b^3*e^3 + 2*B*a*b*c*e^3 + A*b^2*c*e^3 - A*a*c^2*e^3)*log(c*x^2 + b*x + a)/c^4 - (B*b*c^3*d^3 - 2*A*c^4*d^3 - 3*B*b^2*c^2*d^2*e + 6*B*a*c^3*d^2*e + 3*A*b*c^3*d^2*e + 3*B*b^3*c*d*e^2 - 9*B*a*b*c^2*d*e^2 - 3*A*b^2*c^2*d*e^2 + 6*A*a*c^3*d*e^2 - B*b^4*e^3 + 4*B*a*b^2*c*e^3 + A*b^3*c*e^3 - 2*B*a^2*c^2*e^3 - 3*A*a*b*c^2*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4)","A",0
2365,1,219,0,0.161088," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{B c x^{2} e^{2} + 4 \, B c d x e - 2 \, B b x e^{2} + 2 \, A c x e^{2}}{2 \, c^{2}} + \frac{{\left(B c^{2} d^{2} - 2 \, B b c d e + 2 \, A c^{2} d e + B b^{2} e^{2} - B a c e^{2} - A b c e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} - \frac{{\left(B b c^{2} d^{2} - 2 \, A c^{3} d^{2} - 2 \, B b^{2} c d e + 4 \, B a c^{2} d e + 2 \, A b c^{2} d e + B b^{3} e^{2} - 3 \, B a b c e^{2} - A b^{2} c e^{2} + 2 \, A a c^{2} e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/2*(B*c*x^2*e^2 + 4*B*c*d*x*e - 2*B*b*x*e^2 + 2*A*c*x*e^2)/c^2 + 1/2*(B*c^2*d^2 - 2*B*b*c*d*e + 2*A*c^2*d*e + B*b^2*e^2 - B*a*c*e^2 - A*b*c*e^2)*log(c*x^2 + b*x + a)/c^3 - (B*b*c^2*d^2 - 2*A*c^3*d^2 - 2*B*b^2*c*d*e + 4*B*a*c^2*d*e + 2*A*b*c^2*d*e + B*b^3*e^2 - 3*B*a*b*c*e^2 - A*b^2*c*e^2 + 2*A*a*c^2*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
2366,1,112,0,0.157482," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{B x e}{c} + \frac{{\left(B c d - B b e + A c e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} - \frac{{\left(B b c d - 2 \, A c^{2} d - B b^{2} e + 2 \, B a c e + A b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"B*x*e/c + 1/2*(B*c*d - B*b*e + A*c*e)*log(c*x^2 + b*x + a)/c^2 - (B*b*c*d - 2*A*c^2*d - B*b^2*e + 2*B*a*c*e + A*b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
2367,1,63,0,0.183255," ","integrate((B*x+A)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{B \log\left(c x^{2} + b x + a\right)}{2 \, c} - \frac{{\left(B b - 2 \, A c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c}"," ",0,"1/2*B*log(c*x^2 + b*x + a)/c - (B*b - 2*A*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c)","A",0
2368,1,155,0,0.157923," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(B d - A e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}} - \frac{{\left(B d e - A e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{c d^{2} e - b d e^{2} + a e^{3}} - \frac{{\left(B b d - 2 \, A c d - 2 \, B a e + A b e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"1/2*(B*d - A*e)*log(c*x^2 + b*x + a)/(c*d^2 - b*d*e + a*e^2) - (B*d*e - A*e^2)*log(abs(x*e + d))/(c*d^2*e - b*d*e^2 + a*e^3) - (B*b*d - 2*A*c*d - 2*B*a*e + A*b*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c*d^2 - b*d*e + a*e^2)*sqrt(-b^2 + 4*a*c))","A",0
2369,1,383,0,0.173799," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{{\left(B b c d^{2} e^{2} - 2 \, A c^{2} d^{2} e^{2} - 4 \, B a c d e^{3} + 2 \, A b c d e^{3} + B a b e^{4} - A b^{2} e^{4} + 2 \, A a c e^{4}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(B c d^{2} - 2 \, A c d e - B a e^{2} + A b e^{2}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}} + \frac{\frac{B d e^{2}}{x e + d} - \frac{A e^{3}}{x e + d}}{c d^{2} e^{2} - b d e^{3} + a e^{4}}"," ",0,"-(B*b*c*d^2*e^2 - 2*A*c^2*d^2*e^2 - 4*B*a*c*d*e^3 + 2*A*b*c*d*e^3 + B*a*b*e^4 - A*b^2*e^4 + 2*A*a*c*e^4)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-b^2 + 4*a*c)) + 1/2*(B*c*d^2 - 2*A*c*d*e - B*a*e^2 + A*b*e^2)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) + (B*d*e^2/(x*e + d) - A*e^3/(x*e + d))/(c*d^2*e^2 - b*d*e^3 + a*e^4)","A",0
2370,1,797,0,0.185025," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(B c^{2} d^{3} - 3 \, A c^{2} d^{2} e - 3 \, B a c d e^{2} + 3 \, A b c d e^{2} + B a b e^{3} - A b^{2} e^{3} + A a c e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} - \frac{{\left(B c^{2} d^{3} e - 3 \, A c^{2} d^{2} e^{2} - 3 \, B a c d e^{3} + 3 \, A b c d e^{3} + B a b e^{4} - A b^{2} e^{4} + A a c e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}} - \frac{{\left(B b c^{2} d^{3} - 2 \, A c^{3} d^{3} - 6 \, B a c^{2} d^{2} e + 3 \, A b c^{2} d^{2} e + 3 \, B a b c d e^{2} - 3 \, A b^{2} c d e^{2} + 6 \, A a c^{2} d e^{2} - B a b^{2} e^{3} + A b^{3} e^{3} + 2 \, B a^{2} c e^{3} - 3 \, A a b c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, B c^{2} d^{5} - 4 \, B b c d^{4} e - 5 \, A c^{2} d^{4} e + B b^{2} d^{3} e^{2} + 2 \, B a c d^{3} e^{2} + 8 \, A b c d^{3} e^{2} - 3 \, A b^{2} d^{2} e^{3} - 6 \, A a c d^{2} e^{3} - B a^{2} d e^{4} + 4 \, A a b d e^{4} - A a^{2} e^{5} + 2 \, {\left(B c^{2} d^{4} e - B b c d^{3} e^{2} - 2 \, A c^{2} d^{3} e^{2} + 3 \, A b c d^{2} e^{3} + B a b d e^{4} - A b^{2} d e^{4} - 2 \, A a c d e^{4} - B a^{2} e^{5} + A a b e^{5}\right)} x}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"1/2*(B*c^2*d^3 - 3*A*c^2*d^2*e - 3*B*a*c*d*e^2 + 3*A*b*c*d*e^2 + B*a*b*e^3 - A*b^2*e^3 + A*a*c*e^3)*log(c*x^2 + b*x + a)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) - (B*c^2*d^3*e - 3*A*c^2*d^2*e^2 - 3*B*a*c*d*e^3 + 3*A*b*c*d*e^3 + B*a*b*e^4 - A*b^2*e^4 + A*a*c*e^4)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7) - (B*b*c^2*d^3 - 2*A*c^3*d^3 - 6*B*a*c^2*d^2*e + 3*A*b*c^2*d^2*e + 3*B*a*b*c*d*e^2 - 3*A*b^2*c*d*e^2 + 6*A*a*c^2*d*e^2 - B*a*b^2*e^3 + A*b^3*e^3 + 2*B*a^2*c*e^3 - 3*A*a*b*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-b^2 + 4*a*c)) + 1/2*(3*B*c^2*d^5 - 4*B*b*c*d^4*e - 5*A*c^2*d^4*e + B*b^2*d^3*e^2 + 2*B*a*c*d^3*e^2 + 8*A*b*c*d^3*e^2 - 3*A*b^2*d^2*e^3 - 6*A*a*c*d^2*e^3 - B*a^2*d*e^4 + 4*A*a*b*d*e^4 - A*a^2*e^5 + 2*(B*c^2*d^4*e - B*b*c*d^3*e^2 - 2*A*c^2*d^3*e^2 + 3*A*b*c*d^2*e^3 + B*a*b*d*e^4 - A*b^2*d*e^4 - 2*A*a*c*d*e^4 - B*a^2*e^5 + A*a*b*e^5)*x)/((c*d^2 - b*d*e + a*e^2)^3*(x*e + d)^2)","A",0
2371,1,1316,0,0.254207," ","integrate((e*x+d)^4*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(12 \, c^{5} d^{4} f - 6 \, b c^{4} d^{4} g - 24 \, b c^{4} d^{3} f e + 8 \, b^{2} c^{3} d^{3} g e + 16 \, a c^{4} d^{3} g e + 12 \, b^{2} c^{3} d^{2} f e^{2} + 24 \, a c^{4} d^{2} f e^{2} - 36 \, a b c^{3} d^{2} g e^{2} - 24 \, a b c^{3} d f e^{3} + 48 \, a^{2} c^{3} d g e^{3} + 12 \, a^{2} c^{3} f e^{4} - b^{5} g e^{4} + 10 \, a b^{3} c g e^{4} - 30 \, a^{2} b c^{2} g e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{g e^{4} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} - \frac{b^{3} c^{3} d^{4} f - 10 \, a b c^{4} d^{4} f + a b^{2} c^{3} d^{4} g + 8 \, a^{2} c^{4} d^{4} g + 4 \, a b^{2} c^{3} d^{3} f e + 32 \, a^{2} c^{4} d^{3} f e - 24 \, a^{2} b c^{3} d^{3} g e - 36 \, a^{2} b c^{3} d^{2} f e^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g e^{2} + 48 \, a^{3} c^{3} d^{2} g e^{2} + 4 \, a^{2} b^{2} c^{2} d f e^{3} + 32 \, a^{3} c^{3} d f e^{3} + 4 \, a^{2} b^{3} c d g e^{3} - 40 \, a^{3} b c^{2} d g e^{3} + a^{2} b^{3} c f e^{4} - 10 \, a^{3} b c^{2} f e^{4} - 3 \, a^{2} b^{4} g e^{4} + 21 \, a^{3} b^{2} c g e^{4} - 24 \, a^{4} c^{2} g e^{4} - 2 \, {\left(6 \, c^{6} d^{4} f - 3 \, b c^{5} d^{4} g - 12 \, b c^{5} d^{3} f e + 4 \, b^{2} c^{4} d^{3} g e + 8 \, a c^{5} d^{3} g e + 6 \, b^{2} c^{4} d^{2} f e^{2} + 12 \, a c^{5} d^{2} f e^{2} - 18 \, a b c^{4} d^{2} g e^{2} - 12 \, a b c^{4} d f e^{3} - 4 \, b^{4} c^{2} d g e^{3} + 32 \, a b^{2} c^{3} d g e^{3} - 40 \, a^{2} c^{4} d g e^{3} - b^{4} c^{2} f e^{4} + 8 \, a b^{2} c^{3} f e^{4} - 10 \, a^{2} c^{4} f e^{4} + 2 \, b^{5} c g e^{4} - 15 \, a b^{3} c^{2} g e^{4} + 25 \, a^{2} b c^{3} g e^{4}\right)} x^{3} - {\left(18 \, b c^{5} d^{4} f - 9 \, b^{2} c^{4} d^{4} g - 36 \, b^{2} c^{4} d^{3} f e + 12 \, b^{3} c^{3} d^{3} g e + 24 \, a b c^{4} d^{3} g e + 18 \, b^{3} c^{3} d^{2} f e^{2} + 36 \, a b c^{4} d^{2} f e^{2} - 6 \, b^{4} c^{2} d^{2} g e^{2} - 6 \, a b^{2} c^{3} d^{2} g e^{2} - 96 \, a^{2} c^{4} d^{2} g e^{2} - 4 \, b^{4} c^{2} d f e^{3} - 4 \, a b^{2} c^{3} d f e^{3} - 64 \, a^{2} c^{4} d f e^{3} - 4 \, b^{5} c d g e^{3} + 32 \, a b^{3} c^{2} d g e^{3} + 8 \, a^{2} b c^{3} d g e^{3} - b^{5} c f e^{4} + 8 \, a b^{3} c^{2} f e^{4} + 2 \, a^{2} b c^{3} f e^{4} + 3 \, b^{6} g e^{4} - 19 \, a b^{4} c g e^{4} + 11 \, a^{2} b^{2} c^{2} g e^{4} + 32 \, a^{3} c^{3} g e^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{4} d^{4} f + 10 \, a c^{5} d^{4} f - b^{3} c^{3} d^{4} g - 5 \, a b c^{4} d^{4} g - 4 \, b^{3} c^{3} d^{3} f e - 20 \, a b c^{4} d^{3} f e + 20 \, a b^{2} c^{3} d^{3} g e - 8 \, a^{2} c^{4} d^{3} g e + 30 \, a b^{2} c^{3} d^{2} f e^{2} - 12 \, a^{2} c^{4} d^{2} f e^{2} - 6 \, a b^{3} c^{2} d^{2} g e^{2} - 30 \, a^{2} b c^{3} d^{2} g e^{2} - 4 \, a b^{3} c^{2} d f e^{3} - 20 \, a^{2} b c^{3} d f e^{3} - 4 \, a b^{4} c d g e^{3} + 40 \, a^{2} b^{2} c^{2} d g e^{3} - 24 \, a^{3} c^{3} d g e^{3} - a b^{4} c f e^{4} + 10 \, a^{2} b^{2} c^{2} f e^{4} - 6 \, a^{3} c^{3} f e^{4} + 3 \, a b^{5} g e^{4} - 22 \, a^{2} b^{3} c g e^{4} + 31 \, a^{3} b c^{2} g e^{4}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} c^{3}}"," ",0,"(12*c^5*d^4*f - 6*b*c^4*d^4*g - 24*b*c^4*d^3*f*e + 8*b^2*c^3*d^3*g*e + 16*a*c^4*d^3*g*e + 12*b^2*c^3*d^2*f*e^2 + 24*a*c^4*d^2*f*e^2 - 36*a*b*c^3*d^2*g*e^2 - 24*a*b*c^3*d*f*e^3 + 48*a^2*c^3*d*g*e^3 + 12*a^2*c^3*f*e^4 - b^5*g*e^4 + 10*a*b^3*c*g*e^4 - 30*a^2*b*c^2*g*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(-b^2 + 4*a*c)) + 1/2*g*e^4*log(c*x^2 + b*x + a)/c^3 - 1/2*(b^3*c^3*d^4*f - 10*a*b*c^4*d^4*f + a*b^2*c^3*d^4*g + 8*a^2*c^4*d^4*g + 4*a*b^2*c^3*d^3*f*e + 32*a^2*c^4*d^3*f*e - 24*a^2*b*c^3*d^3*g*e - 36*a^2*b*c^3*d^2*f*e^2 + 6*a^2*b^2*c^2*d^2*g*e^2 + 48*a^3*c^3*d^2*g*e^2 + 4*a^2*b^2*c^2*d*f*e^3 + 32*a^3*c^3*d*f*e^3 + 4*a^2*b^3*c*d*g*e^3 - 40*a^3*b*c^2*d*g*e^3 + a^2*b^3*c*f*e^4 - 10*a^3*b*c^2*f*e^4 - 3*a^2*b^4*g*e^4 + 21*a^3*b^2*c*g*e^4 - 24*a^4*c^2*g*e^4 - 2*(6*c^6*d^4*f - 3*b*c^5*d^4*g - 12*b*c^5*d^3*f*e + 4*b^2*c^4*d^3*g*e + 8*a*c^5*d^3*g*e + 6*b^2*c^4*d^2*f*e^2 + 12*a*c^5*d^2*f*e^2 - 18*a*b*c^4*d^2*g*e^2 - 12*a*b*c^4*d*f*e^3 - 4*b^4*c^2*d*g*e^3 + 32*a*b^2*c^3*d*g*e^3 - 40*a^2*c^4*d*g*e^3 - b^4*c^2*f*e^4 + 8*a*b^2*c^3*f*e^4 - 10*a^2*c^4*f*e^4 + 2*b^5*c*g*e^4 - 15*a*b^3*c^2*g*e^4 + 25*a^2*b*c^3*g*e^4)*x^3 - (18*b*c^5*d^4*f - 9*b^2*c^4*d^4*g - 36*b^2*c^4*d^3*f*e + 12*b^3*c^3*d^3*g*e + 24*a*b*c^4*d^3*g*e + 18*b^3*c^3*d^2*f*e^2 + 36*a*b*c^4*d^2*f*e^2 - 6*b^4*c^2*d^2*g*e^2 - 6*a*b^2*c^3*d^2*g*e^2 - 96*a^2*c^4*d^2*g*e^2 - 4*b^4*c^2*d*f*e^3 - 4*a*b^2*c^3*d*f*e^3 - 64*a^2*c^4*d*f*e^3 - 4*b^5*c*d*g*e^3 + 32*a*b^3*c^2*d*g*e^3 + 8*a^2*b*c^3*d*g*e^3 - b^5*c*f*e^4 + 8*a*b^3*c^2*f*e^4 + 2*a^2*b*c^3*f*e^4 + 3*b^6*g*e^4 - 19*a*b^4*c*g*e^4 + 11*a^2*b^2*c^2*g*e^4 + 32*a^3*c^3*g*e^4)*x^2 - 2*(2*b^2*c^4*d^4*f + 10*a*c^5*d^4*f - b^3*c^3*d^4*g - 5*a*b*c^4*d^4*g - 4*b^3*c^3*d^3*f*e - 20*a*b*c^4*d^3*f*e + 20*a*b^2*c^3*d^3*g*e - 8*a^2*c^4*d^3*g*e + 30*a*b^2*c^3*d^2*f*e^2 - 12*a^2*c^4*d^2*f*e^2 - 6*a*b^3*c^2*d^2*g*e^2 - 30*a^2*b*c^3*d^2*g*e^2 - 4*a*b^3*c^2*d*f*e^3 - 20*a^2*b*c^3*d*f*e^3 - 4*a*b^4*c*d*g*e^3 + 40*a^2*b^2*c^2*d*g*e^3 - 24*a^3*c^3*d*g*e^3 - a*b^4*c*f*e^4 + 10*a^2*b^2*c^2*f*e^4 - 6*a^3*c^3*f*e^4 + 3*a*b^5*g*e^4 - 22*a^2*b^3*c*g*e^4 + 31*a^3*b*c^2*g*e^4)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*c^3)","B",0
2372,1,979,0,0.205824," ","integrate((e*x+d)^3*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{6 \, {\left(2 \, c^{2} d^{3} f - b c d^{3} g - 3 \, b c d^{2} f e + b^{2} d^{2} g e + 2 \, a c d^{2} g e + b^{2} d f e^{2} + 2 \, a c d f e^{2} - 3 \, a b d g e^{2} - a b f e^{3} + 2 \, a^{2} g e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{5} d^{3} f x^{3} - 6 \, b c^{4} d^{3} g x^{3} - 18 \, b c^{4} d^{2} f x^{3} e + 6 \, b^{2} c^{3} d^{2} g x^{3} e + 12 \, a c^{4} d^{2} g x^{3} e + 18 \, b c^{4} d^{3} f x^{2} - 9 \, b^{2} c^{3} d^{3} g x^{2} + 6 \, b^{2} c^{3} d f x^{3} e^{2} + 12 \, a c^{4} d f x^{3} e^{2} - 18 \, a b c^{3} d g x^{3} e^{2} - 27 \, b^{2} c^{3} d^{2} f x^{2} e + 9 \, b^{3} c^{2} d^{2} g x^{2} e + 18 \, a b c^{3} d^{2} g x^{2} e + 4 \, b^{2} c^{3} d^{3} f x + 20 \, a c^{4} d^{3} f x - 2 \, b^{3} c^{2} d^{3} g x - 10 \, a b c^{3} d^{3} g x - 6 \, a b c^{3} f x^{3} e^{3} - 2 \, b^{4} c g x^{3} e^{3} + 16 \, a b^{2} c^{2} g x^{3} e^{3} - 20 \, a^{2} c^{3} g x^{3} e^{3} + 9 \, b^{3} c^{2} d f x^{2} e^{2} + 18 \, a b c^{3} d f x^{2} e^{2} - 3 \, b^{4} c d g x^{2} e^{2} - 3 \, a b^{2} c^{2} d g x^{2} e^{2} - 48 \, a^{2} c^{3} d g x^{2} e^{2} - 6 \, b^{3} c^{2} d^{2} f x e - 30 \, a b c^{3} d^{2} f x e + 30 \, a b^{2} c^{2} d^{2} g x e - 12 \, a^{2} c^{3} d^{2} g x e - b^{3} c^{2} d^{3} f + 10 \, a b c^{3} d^{3} f - a b^{2} c^{2} d^{3} g - 8 \, a^{2} c^{3} d^{3} g - b^{4} c f x^{2} e^{3} - a b^{2} c^{2} f x^{2} e^{3} - 16 \, a^{2} c^{3} f x^{2} e^{3} - b^{5} g x^{2} e^{3} + 8 \, a b^{3} c g x^{2} e^{3} + 2 \, a^{2} b c^{2} g x^{2} e^{3} + 30 \, a b^{2} c^{2} d f x e^{2} - 12 \, a^{2} c^{3} d f x e^{2} - 6 \, a b^{3} c d g x e^{2} - 30 \, a^{2} b c^{2} d g x e^{2} - 3 \, a b^{2} c^{2} d^{2} f e - 24 \, a^{2} c^{3} d^{2} f e + 18 \, a^{2} b c^{2} d^{2} g e - 2 \, a b^{3} c f x e^{3} - 10 \, a^{2} b c^{2} f x e^{3} - 2 \, a b^{4} g x e^{3} + 20 \, a^{2} b^{2} c g x e^{3} - 12 \, a^{3} c^{2} g x e^{3} + 18 \, a^{2} b c^{2} d f e^{2} - 3 \, a^{2} b^{2} c d g e^{2} - 24 \, a^{3} c^{2} d g e^{2} - a^{2} b^{2} c f e^{3} - 8 \, a^{3} c^{2} f e^{3} - a^{2} b^{3} g e^{3} + 10 \, a^{3} b c g e^{3}}{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"6*(2*c^2*d^3*f - b*c*d^3*g - 3*b*c*d^2*f*e + b^2*d^2*g*e + 2*a*c*d^2*g*e + b^2*d*f*e^2 + 2*a*c*d*f*e^2 - 3*a*b*d*g*e^2 - a*b*f*e^3 + 2*a^2*g*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^5*d^3*f*x^3 - 6*b*c^4*d^3*g*x^3 - 18*b*c^4*d^2*f*x^3*e + 6*b^2*c^3*d^2*g*x^3*e + 12*a*c^4*d^2*g*x^3*e + 18*b*c^4*d^3*f*x^2 - 9*b^2*c^3*d^3*g*x^2 + 6*b^2*c^3*d*f*x^3*e^2 + 12*a*c^4*d*f*x^3*e^2 - 18*a*b*c^3*d*g*x^3*e^2 - 27*b^2*c^3*d^2*f*x^2*e + 9*b^3*c^2*d^2*g*x^2*e + 18*a*b*c^3*d^2*g*x^2*e + 4*b^2*c^3*d^3*f*x + 20*a*c^4*d^3*f*x - 2*b^3*c^2*d^3*g*x - 10*a*b*c^3*d^3*g*x - 6*a*b*c^3*f*x^3*e^3 - 2*b^4*c*g*x^3*e^3 + 16*a*b^2*c^2*g*x^3*e^3 - 20*a^2*c^3*g*x^3*e^3 + 9*b^3*c^2*d*f*x^2*e^2 + 18*a*b*c^3*d*f*x^2*e^2 - 3*b^4*c*d*g*x^2*e^2 - 3*a*b^2*c^2*d*g*x^2*e^2 - 48*a^2*c^3*d*g*x^2*e^2 - 6*b^3*c^2*d^2*f*x*e - 30*a*b*c^3*d^2*f*x*e + 30*a*b^2*c^2*d^2*g*x*e - 12*a^2*c^3*d^2*g*x*e - b^3*c^2*d^3*f + 10*a*b*c^3*d^3*f - a*b^2*c^2*d^3*g - 8*a^2*c^3*d^3*g - b^4*c*f*x^2*e^3 - a*b^2*c^2*f*x^2*e^3 - 16*a^2*c^3*f*x^2*e^3 - b^5*g*x^2*e^3 + 8*a*b^3*c*g*x^2*e^3 + 2*a^2*b*c^2*g*x^2*e^3 + 30*a*b^2*c^2*d*f*x*e^2 - 12*a^2*c^3*d*f*x*e^2 - 6*a*b^3*c*d*g*x*e^2 - 30*a^2*b*c^2*d*g*x*e^2 - 3*a*b^2*c^2*d^2*f*e - 24*a^2*c^3*d^2*f*e + 18*a^2*b*c^2*d^2*g*e - 2*a*b^3*c*f*x*e^3 - 10*a^2*b*c^2*f*x*e^3 - 2*a*b^4*g*x*e^3 + 20*a^2*b^2*c*g*x*e^3 - 12*a^3*c^2*g*x*e^3 + 18*a^2*b*c^2*d*f*e^2 - 3*a^2*b^2*c*d*g*e^2 - 24*a^3*c^2*d*g*e^2 - a^2*b^2*c*f*e^3 - 8*a^3*c^2*f*e^3 - a^2*b^3*g*e^3 + 10*a^3*b*c*g*e^3)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^2 + b*x + a)^2)","B",0
2373,1,645,0,0.179524," ","integrate((e*x+d)^2*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2 \, {\left(6 \, c^{2} d^{2} f - 3 \, b c d^{2} g - 6 \, b c d f e + 2 \, b^{2} d g e + 4 \, a c d g e + b^{2} f e^{2} + 2 \, a c f e^{2} - 3 \, a b g e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{4} d^{2} f x^{3} - 6 \, b c^{3} d^{2} g x^{3} - 12 \, b c^{3} d f x^{3} e + 4 \, b^{2} c^{2} d g x^{3} e + 8 \, a c^{3} d g x^{3} e + 18 \, b c^{3} d^{2} f x^{2} - 9 \, b^{2} c^{2} d^{2} g x^{2} + 2 \, b^{2} c^{2} f x^{3} e^{2} + 4 \, a c^{3} f x^{3} e^{2} - 6 \, a b c^{2} g x^{3} e^{2} - 18 \, b^{2} c^{2} d f x^{2} e + 6 \, b^{3} c d g x^{2} e + 12 \, a b c^{2} d g x^{2} e + 4 \, b^{2} c^{2} d^{2} f x + 20 \, a c^{3} d^{2} f x - 2 \, b^{3} c d^{2} g x - 10 \, a b c^{2} d^{2} g x + 3 \, b^{3} c f x^{2} e^{2} + 6 \, a b c^{2} f x^{2} e^{2} - b^{4} g x^{2} e^{2} - a b^{2} c g x^{2} e^{2} - 16 \, a^{2} c^{2} g x^{2} e^{2} - 4 \, b^{3} c d f x e - 20 \, a b c^{2} d f x e + 20 \, a b^{2} c d g x e - 8 \, a^{2} c^{2} d g x e - b^{3} c d^{2} f + 10 \, a b c^{2} d^{2} f - a b^{2} c d^{2} g - 8 \, a^{2} c^{2} d^{2} g + 10 \, a b^{2} c f x e^{2} - 4 \, a^{2} c^{2} f x e^{2} - 2 \, a b^{3} g x e^{2} - 10 \, a^{2} b c g x e^{2} - 2 \, a b^{2} c d f e - 16 \, a^{2} c^{2} d f e + 12 \, a^{2} b c d g e + 6 \, a^{2} b c f e^{2} - a^{2} b^{2} g e^{2} - 8 \, a^{3} c g e^{2}}{2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"2*(6*c^2*d^2*f - 3*b*c*d^2*g - 6*b*c*d*f*e + 2*b^2*d*g*e + 4*a*c*d*g*e + b^2*f*e^2 + 2*a*c*f*e^2 - 3*a*b*g*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^4*d^2*f*x^3 - 6*b*c^3*d^2*g*x^3 - 12*b*c^3*d*f*x^3*e + 4*b^2*c^2*d*g*x^3*e + 8*a*c^3*d*g*x^3*e + 18*b*c^3*d^2*f*x^2 - 9*b^2*c^2*d^2*g*x^2 + 2*b^2*c^2*f*x^3*e^2 + 4*a*c^3*f*x^3*e^2 - 6*a*b*c^2*g*x^3*e^2 - 18*b^2*c^2*d*f*x^2*e + 6*b^3*c*d*g*x^2*e + 12*a*b*c^2*d*g*x^2*e + 4*b^2*c^2*d^2*f*x + 20*a*c^3*d^2*f*x - 2*b^3*c*d^2*g*x - 10*a*b*c^2*d^2*g*x + 3*b^3*c*f*x^2*e^2 + 6*a*b*c^2*f*x^2*e^2 - b^4*g*x^2*e^2 - a*b^2*c*g*x^2*e^2 - 16*a^2*c^2*g*x^2*e^2 - 4*b^3*c*d*f*x*e - 20*a*b*c^2*d*f*x*e + 20*a*b^2*c*d*g*x*e - 8*a^2*c^2*d*g*x*e - b^3*c*d^2*f + 10*a*b*c^2*d^2*f - a*b^2*c*d^2*g - 8*a^2*c^2*d^2*g + 10*a*b^2*c*f*x*e^2 - 4*a^2*c^2*f*x*e^2 - 2*a*b^3*g*x*e^2 - 10*a^2*b*c*g*x*e^2 - 2*a*b^2*c*d*f*e - 16*a^2*c^2*d*f*e + 12*a^2*b*c*d*g*e + 6*a^2*b*c*f*e^2 - a^2*b^2*g*e^2 - 8*a^3*c*g*e^2)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^2 + b*x + a)^2)","B",0
2374,1,369,0,0.214903," ","integrate((e*x+d)*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2 \, {\left(6 \, c^{2} d f - 3 \, b c d g - 3 \, b c f e + b^{2} g e + 2 \, a c g e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} d f x^{3} - 6 \, b c^{2} d g x^{3} - 6 \, b c^{2} f x^{3} e + 2 \, b^{2} c g x^{3} e + 4 \, a c^{2} g x^{3} e + 18 \, b c^{2} d f x^{2} - 9 \, b^{2} c d g x^{2} - 9 \, b^{2} c f x^{2} e + 3 \, b^{3} g x^{2} e + 6 \, a b c g x^{2} e + 4 \, b^{2} c d f x + 20 \, a c^{2} d f x - 2 \, b^{3} d g x - 10 \, a b c d g x - 2 \, b^{3} f x e - 10 \, a b c f x e + 10 \, a b^{2} g x e - 4 \, a^{2} c g x e - b^{3} d f + 10 \, a b c d f - a b^{2} d g - 8 \, a^{2} c d g - a b^{2} f e - 8 \, a^{2} c f e + 6 \, a^{2} b g e}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"2*(6*c^2*d*f - 3*b*c*d*g - 3*b*c*f*e + b^2*g*e + 2*a*c*g*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*d*f*x^3 - 6*b*c^2*d*g*x^3 - 6*b*c^2*f*x^3*e + 2*b^2*c*g*x^3*e + 4*a*c^2*g*x^3*e + 18*b*c^2*d*f*x^2 - 9*b^2*c*d*g*x^2 - 9*b^2*c*f*x^2*e + 3*b^3*g*x^2*e + 6*a*b*c*g*x^2*e + 4*b^2*c*d*f*x + 20*a*c^2*d*f*x - 2*b^3*d*g*x - 10*a*b*c*d*g*x - 2*b^3*f*x*e - 10*a*b*c*f*x*e + 10*a*b^2*g*x*e - 4*a^2*c*g*x*e - b^3*d*f + 10*a*b*c*d*f - a*b^2*d*g - 8*a^2*c*d*g - a*b^2*f*e - 8*a^2*c*f*e + 6*a^2*b*g*e)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
2375,1,199,0,0.169582," ","integrate((g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{6 \, {\left(2 \, c^{2} f - b c g\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} f x^{3} - 6 \, b c^{2} g x^{3} + 18 \, b c^{2} f x^{2} - 9 \, b^{2} c g x^{2} + 4 \, b^{2} c f x + 20 \, a c^{2} f x - 2 \, b^{3} g x - 10 \, a b c g x - b^{3} f + 10 \, a b c f - a b^{2} g - 8 \, a^{2} c g}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"6*(2*c^2*f - b*c*g)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*f*x^3 - 6*b*c^2*g*x^3 + 18*b*c^2*f*x^2 - 9*b^2*c*g*x^2 + 4*b^2*c*f*x + 20*a*c^2*f*x - 2*b^3*g*x - 10*a*b*c*g*x - b^3*f + 10*a*b*c*f - a*b^2*g - 8*a^2*c*g)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
2376,1,2288,0,0.266379," ","integrate((g*x+f)/(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(d g e^{4} - f e^{5}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} - \frac{{\left(d g e^{5} - f e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}} + \frac{{\left(12 \, c^{5} d^{5} f - 6 \, b c^{4} d^{5} g - 30 \, b c^{4} d^{4} f e + 16 \, b^{2} c^{3} d^{4} g e - 4 \, a c^{4} d^{4} g e + 20 \, b^{2} c^{3} d^{3} f e^{2} + 40 \, a c^{4} d^{3} f e^{2} - 12 \, b^{3} c^{2} d^{3} g e^{2} - 12 \, a b c^{3} d^{3} g e^{2} - 60 \, a b c^{3} d^{2} f e^{3} + 36 \, a b^{2} c^{2} d^{2} g e^{3} - 24 \, a^{2} c^{3} d^{2} g e^{3} + 60 \, a^{2} c^{3} d f e^{4} + b^{5} d g e^{4} - 10 \, a b^{3} c d g e^{4} - 6 \, a^{2} b c^{2} d g e^{4} - b^{5} f e^{5} + 10 \, a b^{3} c f e^{5} - 30 \, a^{2} b c^{2} f e^{5} + 12 \, a^{3} c^{2} g e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{3} d^{6} - 8 \, a b^{2} c^{4} d^{6} + 16 \, a^{2} c^{5} d^{6} - 3 \, b^{5} c^{2} d^{5} e + 24 \, a b^{3} c^{3} d^{5} e - 48 \, a^{2} b c^{4} d^{5} e + 3 \, b^{6} c d^{4} e^{2} - 21 \, a b^{4} c^{2} d^{4} e^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{2} + 48 \, a^{3} c^{4} d^{4} e^{2} - b^{7} d^{3} e^{3} + 2 \, a b^{5} c d^{3} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{3} - 96 \, a^{3} b c^{3} d^{3} e^{3} + 3 \, a b^{6} d^{2} e^{4} - 21 \, a^{2} b^{4} c d^{2} e^{4} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{4} + 48 \, a^{4} c^{3} d^{2} e^{4} - 3 \, a^{2} b^{5} d e^{5} + 24 \, a^{3} b^{3} c d e^{5} - 48 \, a^{4} b c^{2} d e^{5} + a^{3} b^{4} e^{6} - 8 \, a^{4} b^{2} c e^{6} + 16 \, a^{5} c^{2} e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b^{3} c^{3} d^{5} f - 10 \, a b c^{4} d^{5} f + a b^{2} c^{3} d^{5} g + 8 \, a^{2} c^{4} d^{5} g - 3 \, b^{4} c^{2} d^{4} f e + 29 \, a b^{2} c^{3} d^{4} f e - 8 \, a^{2} c^{4} d^{4} f e - 3 \, a b^{3} c^{2} d^{4} g e - 18 \, a^{2} b c^{3} d^{4} g e + 3 \, b^{5} c d^{3} f e^{2} - 24 \, a b^{3} c^{2} d^{3} f e^{2} - 12 \, a^{2} b c^{3} d^{3} f e^{2} + 3 \, a b^{4} c d^{3} g e^{2} + 10 \, a^{2} b^{2} c^{2} d^{3} g e^{2} + 32 \, a^{3} c^{3} d^{3} g e^{2} - b^{6} d^{2} f e^{3} + a b^{4} c d^{2} f e^{3} + 50 \, a^{2} b^{2} c^{2} d^{2} f e^{3} - 32 \, a^{3} c^{3} d^{2} f e^{3} - a b^{5} d^{2} g e^{3} - 44 \, a^{3} b c^{2} d^{2} g e^{3} + 4 \, a b^{5} d f e^{4} - 27 \, a^{2} b^{3} c d f e^{4} + 14 \, a^{3} b c^{2} d f e^{4} + 9 \, a^{3} b^{2} c d g e^{4} + 24 \, a^{4} c^{2} d g e^{4} - 3 \, a^{2} b^{4} f e^{5} + 21 \, a^{3} b^{2} c f e^{5} - 24 \, a^{4} c^{2} f e^{5} + a^{3} b^{3} g e^{5} - 10 \, a^{4} b c g e^{5} - 2 \, {\left(6 \, c^{6} d^{5} f - 3 \, b c^{5} d^{5} g - 15 \, b c^{5} d^{4} f e + 8 \, b^{2} c^{4} d^{4} g e - 2 \, a c^{5} d^{4} g e + 10 \, b^{2} c^{4} d^{3} f e^{2} + 20 \, a c^{5} d^{3} f e^{2} - 6 \, b^{3} c^{3} d^{3} g e^{2} - 6 \, a b c^{4} d^{3} g e^{2} - 30 \, a b c^{4} d^{2} f e^{3} + b^{4} c^{2} d^{2} g e^{3} + 10 \, a b^{2} c^{3} d^{2} g e^{3} + 4 \, a^{2} c^{4} d^{2} g e^{3} - b^{4} c^{2} d f e^{4} + 8 \, a b^{2} c^{3} d f e^{4} + 14 \, a^{2} c^{4} d f e^{4} - a b^{3} c^{2} d g e^{4} - 11 \, a^{2} b c^{3} d g e^{4} + a b^{3} c^{2} f e^{5} - 7 \, a^{2} b c^{3} f e^{5} + 6 \, a^{3} c^{3} g e^{5}\right)} x^{3} - {\left(18 \, b c^{5} d^{5} f - 9 \, b^{2} c^{4} d^{5} g - 45 \, b^{2} c^{4} d^{4} f e + 24 \, b^{3} c^{3} d^{4} g e - 6 \, a b c^{4} d^{4} g e + 30 \, b^{3} c^{3} d^{3} f e^{2} + 60 \, a b c^{4} d^{3} f e^{2} - 19 \, b^{4} c^{2} d^{3} g e^{2} - 10 \, a b^{2} c^{3} d^{3} g e^{2} - 16 \, a^{2} c^{4} d^{3} g e^{2} + b^{4} c^{2} d^{2} f e^{3} - 98 \, a b^{2} c^{3} d^{2} f e^{3} + 16 \, a^{2} c^{4} d^{2} f e^{3} + 4 \, b^{5} c d^{2} g e^{3} + 22 \, a b^{3} c^{2} d^{2} g e^{3} + 28 \, a^{2} b c^{3} d^{2} g e^{3} - 4 \, b^{5} c d f e^{4} + 32 \, a b^{3} c^{2} d f e^{4} + 26 \, a^{2} b c^{3} d f e^{4} - 4 \, a b^{4} c d g e^{4} - 25 \, a^{2} b^{2} c^{2} d g e^{4} - 16 \, a^{3} c^{3} d g e^{4} + 4 \, a b^{4} c f e^{5} - 29 \, a^{2} b^{2} c^{2} f e^{5} + 16 \, a^{3} c^{3} f e^{5} + 18 \, a^{3} b c^{2} g e^{5}\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{4} d^{5} f + 10 \, a c^{5} d^{5} f - b^{3} c^{3} d^{5} g - 5 \, a b c^{4} d^{5} g - 5 \, b^{3} c^{3} d^{4} f e - 25 \, a b c^{4} d^{4} f e + 3 \, b^{4} c^{2} d^{4} g e + 10 \, a b^{2} c^{3} d^{4} g e + 2 \, a^{2} c^{4} d^{4} g e + 3 \, b^{4} c^{2} d^{3} f e^{2} + 26 \, a b^{2} c^{3} d^{3} f e^{2} + 28 \, a^{2} c^{4} d^{3} f e^{2} - 3 \, b^{5} c d^{3} g e^{2} - 4 \, a b^{3} c^{2} d^{3} g e^{2} - 26 \, a^{2} b c^{3} d^{3} g e^{2} + b^{5} c d^{2} f e^{3} - 18 \, a b^{3} c^{2} d^{2} f e^{3} - 34 \, a^{2} b c^{3} d^{2} f e^{3} + b^{6} d^{2} g e^{3} + 26 \, a^{2} b^{2} c^{2} d^{2} g e^{3} + 12 \, a^{3} c^{3} d^{2} g e^{3} - b^{6} d f e^{4} + 6 \, a b^{4} c d f e^{4} + 10 \, a^{2} b^{2} c^{2} d f e^{4} + 18 \, a^{3} c^{3} d f e^{4} - a b^{5} d g e^{4} - 29 \, a^{3} b c^{2} d g e^{4} + a b^{5} f e^{5} - 6 \, a^{2} b^{3} c f e^{5} - a^{3} b c^{2} f e^{5} + 2 \, a^{3} b^{2} c g e^{5} + 10 \, a^{4} c^{2} g e^{5}\right)} x}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{3} {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2}}"," ",0,"1/2*(d*g*e^4 - f*e^5)*log(c*x^2 + b*x + a)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) - (d*g*e^5 - f*e^6)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7) + (12*c^5*d^5*f - 6*b*c^4*d^5*g - 30*b*c^4*d^4*f*e + 16*b^2*c^3*d^4*g*e - 4*a*c^4*d^4*g*e + 20*b^2*c^3*d^3*f*e^2 + 40*a*c^4*d^3*f*e^2 - 12*b^3*c^2*d^3*g*e^2 - 12*a*b*c^3*d^3*g*e^2 - 60*a*b*c^3*d^2*f*e^3 + 36*a*b^2*c^2*d^2*g*e^3 - 24*a^2*c^3*d^2*g*e^3 + 60*a^2*c^3*d*f*e^4 + b^5*d*g*e^4 - 10*a*b^3*c*d*g*e^4 - 6*a^2*b*c^2*d*g*e^4 - b^5*f*e^5 + 10*a*b^3*c*f*e^5 - 30*a^2*b*c^2*f*e^5 + 12*a^3*c^2*g*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3*d^6 - 8*a*b^2*c^4*d^6 + 16*a^2*c^5*d^6 - 3*b^5*c^2*d^5*e + 24*a*b^3*c^3*d^5*e - 48*a^2*b*c^4*d^5*e + 3*b^6*c*d^4*e^2 - 21*a*b^4*c^2*d^4*e^2 + 24*a^2*b^2*c^3*d^4*e^2 + 48*a^3*c^4*d^4*e^2 - b^7*d^3*e^3 + 2*a*b^5*c*d^3*e^3 + 32*a^2*b^3*c^2*d^3*e^3 - 96*a^3*b*c^3*d^3*e^3 + 3*a*b^6*d^2*e^4 - 21*a^2*b^4*c*d^2*e^4 + 24*a^3*b^2*c^2*d^2*e^4 + 48*a^4*c^3*d^2*e^4 - 3*a^2*b^5*d*e^5 + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 + a^3*b^4*e^6 - 8*a^4*b^2*c*e^6 + 16*a^5*c^2*e^6)*sqrt(-b^2 + 4*a*c)) - 1/2*(b^3*c^3*d^5*f - 10*a*b*c^4*d^5*f + a*b^2*c^3*d^5*g + 8*a^2*c^4*d^5*g - 3*b^4*c^2*d^4*f*e + 29*a*b^2*c^3*d^4*f*e - 8*a^2*c^4*d^4*f*e - 3*a*b^3*c^2*d^4*g*e - 18*a^2*b*c^3*d^4*g*e + 3*b^5*c*d^3*f*e^2 - 24*a*b^3*c^2*d^3*f*e^2 - 12*a^2*b*c^3*d^3*f*e^2 + 3*a*b^4*c*d^3*g*e^2 + 10*a^2*b^2*c^2*d^3*g*e^2 + 32*a^3*c^3*d^3*g*e^2 - b^6*d^2*f*e^3 + a*b^4*c*d^2*f*e^3 + 50*a^2*b^2*c^2*d^2*f*e^3 - 32*a^3*c^3*d^2*f*e^3 - a*b^5*d^2*g*e^3 - 44*a^3*b*c^2*d^2*g*e^3 + 4*a*b^5*d*f*e^4 - 27*a^2*b^3*c*d*f*e^4 + 14*a^3*b*c^2*d*f*e^4 + 9*a^3*b^2*c*d*g*e^4 + 24*a^4*c^2*d*g*e^4 - 3*a^2*b^4*f*e^5 + 21*a^3*b^2*c*f*e^5 - 24*a^4*c^2*f*e^5 + a^3*b^3*g*e^5 - 10*a^4*b*c*g*e^5 - 2*(6*c^6*d^5*f - 3*b*c^5*d^5*g - 15*b*c^5*d^4*f*e + 8*b^2*c^4*d^4*g*e - 2*a*c^5*d^4*g*e + 10*b^2*c^4*d^3*f*e^2 + 20*a*c^5*d^3*f*e^2 - 6*b^3*c^3*d^3*g*e^2 - 6*a*b*c^4*d^3*g*e^2 - 30*a*b*c^4*d^2*f*e^3 + b^4*c^2*d^2*g*e^3 + 10*a*b^2*c^3*d^2*g*e^3 + 4*a^2*c^4*d^2*g*e^3 - b^4*c^2*d*f*e^4 + 8*a*b^2*c^3*d*f*e^4 + 14*a^2*c^4*d*f*e^4 - a*b^3*c^2*d*g*e^4 - 11*a^2*b*c^3*d*g*e^4 + a*b^3*c^2*f*e^5 - 7*a^2*b*c^3*f*e^5 + 6*a^3*c^3*g*e^5)*x^3 - (18*b*c^5*d^5*f - 9*b^2*c^4*d^5*g - 45*b^2*c^4*d^4*f*e + 24*b^3*c^3*d^4*g*e - 6*a*b*c^4*d^4*g*e + 30*b^3*c^3*d^3*f*e^2 + 60*a*b*c^4*d^3*f*e^2 - 19*b^4*c^2*d^3*g*e^2 - 10*a*b^2*c^3*d^3*g*e^2 - 16*a^2*c^4*d^3*g*e^2 + b^4*c^2*d^2*f*e^3 - 98*a*b^2*c^3*d^2*f*e^3 + 16*a^2*c^4*d^2*f*e^3 + 4*b^5*c*d^2*g*e^3 + 22*a*b^3*c^2*d^2*g*e^3 + 28*a^2*b*c^3*d^2*g*e^3 - 4*b^5*c*d*f*e^4 + 32*a*b^3*c^2*d*f*e^4 + 26*a^2*b*c^3*d*f*e^4 - 4*a*b^4*c*d*g*e^4 - 25*a^2*b^2*c^2*d*g*e^4 - 16*a^3*c^3*d*g*e^4 + 4*a*b^4*c*f*e^5 - 29*a^2*b^2*c^2*f*e^5 + 16*a^3*c^3*f*e^5 + 18*a^3*b*c^2*g*e^5)*x^2 - 2*(2*b^2*c^4*d^5*f + 10*a*c^5*d^5*f - b^3*c^3*d^5*g - 5*a*b*c^4*d^5*g - 5*b^3*c^3*d^4*f*e - 25*a*b*c^4*d^4*f*e + 3*b^4*c^2*d^4*g*e + 10*a*b^2*c^3*d^4*g*e + 2*a^2*c^4*d^4*g*e + 3*b^4*c^2*d^3*f*e^2 + 26*a*b^2*c^3*d^3*f*e^2 + 28*a^2*c^4*d^3*f*e^2 - 3*b^5*c*d^3*g*e^2 - 4*a*b^3*c^2*d^3*g*e^2 - 26*a^2*b*c^3*d^3*g*e^2 + b^5*c*d^2*f*e^3 - 18*a*b^3*c^2*d^2*f*e^3 - 34*a^2*b*c^3*d^2*f*e^3 + b^6*d^2*g*e^3 + 26*a^2*b^2*c^2*d^2*g*e^3 + 12*a^3*c^3*d^2*g*e^3 - b^6*d*f*e^4 + 6*a*b^4*c*d*f*e^4 + 10*a^2*b^2*c^2*d*f*e^4 + 18*a^3*c^3*d*f*e^4 - a*b^5*d*g*e^4 - 29*a^3*b*c^2*d*g*e^4 + a*b^5*f*e^5 - 6*a^2*b^3*c*f*e^5 - a^3*b*c^2*f*e^5 + 2*a^3*b^2*c*g*e^5 + 10*a^4*c^2*g*e^5)*x)/((c*d^2 - b*d*e + a*e^2)^3*(c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2)","B",0
2377,1,3417,0,2.138917," ","integrate((g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(12 \, c^{6} d^{6} f e^{2} - 6 \, b c^{5} d^{6} g e^{2} - 36 \, b c^{5} d^{5} f e^{3} + 20 \, b^{2} c^{4} d^{5} g e^{3} - 8 \, a c^{5} d^{5} g e^{3} + 30 \, b^{2} c^{4} d^{4} f e^{4} + 60 \, a c^{5} d^{4} f e^{4} - 20 \, b^{3} c^{3} d^{4} g e^{4} - 10 \, a b c^{4} d^{4} g e^{4} - 120 \, a b c^{4} d^{3} f e^{5} + 80 \, a b^{2} c^{3} d^{3} g e^{5} - 80 \, a^{2} c^{4} d^{3} g e^{5} + 180 \, a^{2} c^{4} d^{2} f e^{6} + 5 \, b^{5} c d^{2} g e^{6} - 50 \, a b^{3} c^{2} d^{2} g e^{6} + 30 \, a^{2} b c^{3} d^{2} g e^{6} - 6 \, b^{5} c d f e^{7} + 60 \, a b^{3} c^{2} d f e^{7} - 180 \, a^{2} b c^{3} d f e^{7} - 2 \, b^{6} d g e^{7} + 20 \, a b^{4} c d g e^{7} - 60 \, a^{2} b^{2} c^{2} d g e^{7} + 120 \, a^{3} c^{3} d g e^{7} + 3 \, b^{6} f e^{8} - 30 \, a b^{4} c f e^{8} + 90 \, a^{2} b^{2} c^{2} f e^{8} - 60 \, a^{3} c^{3} f e^{8} - a b^{5} g e^{8} + 10 \, a^{2} b^{3} c g e^{8} - 30 \, a^{3} b c^{2} g e^{8}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(b^{4} c^{4} d^{8} - 8 \, a b^{2} c^{5} d^{8} + 16 \, a^{2} c^{6} d^{8} - 4 \, b^{5} c^{3} d^{7} e + 32 \, a b^{3} c^{4} d^{7} e - 64 \, a^{2} b c^{5} d^{7} e + 6 \, b^{6} c^{2} d^{6} e^{2} - 44 \, a b^{4} c^{3} d^{6} e^{2} + 64 \, a^{2} b^{2} c^{4} d^{6} e^{2} + 64 \, a^{3} c^{5} d^{6} e^{2} - 4 \, b^{7} c d^{5} e^{3} + 20 \, a b^{5} c^{2} d^{5} e^{3} + 32 \, a^{2} b^{3} c^{3} d^{5} e^{3} - 192 \, a^{3} b c^{4} d^{5} e^{3} + b^{8} d^{4} e^{4} + 4 \, a b^{6} c d^{4} e^{4} - 74 \, a^{2} b^{4} c^{2} d^{4} e^{4} + 144 \, a^{3} b^{2} c^{3} d^{4} e^{4} + 96 \, a^{4} c^{4} d^{4} e^{4} - 4 \, a b^{7} d^{3} e^{5} + 20 \, a^{2} b^{5} c d^{3} e^{5} + 32 \, a^{3} b^{3} c^{2} d^{3} e^{5} - 192 \, a^{4} b c^{3} d^{3} e^{5} + 6 \, a^{2} b^{6} d^{2} e^{6} - 44 \, a^{3} b^{4} c d^{2} e^{6} + 64 \, a^{4} b^{2} c^{2} d^{2} e^{6} + 64 \, a^{5} c^{3} d^{2} e^{6} - 4 \, a^{3} b^{5} d e^{7} + 32 \, a^{4} b^{3} c d e^{7} - 64 \, a^{5} b c^{2} d e^{7} + a^{4} b^{4} e^{8} - 8 \, a^{5} b^{2} c e^{8} + 16 \, a^{6} c^{2} e^{8}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(5 \, c d^{2} g e^{4} - 6 \, c d f e^{5} - 2 \, b d g e^{5} + 3 \, b f e^{6} - a g e^{6}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)}} + \frac{\frac{d g e^{10}}{x e + d} - \frac{f e^{11}}{x e + d}}{c^{3} d^{6} e^{6} - 3 \, b c^{2} d^{5} e^{7} + 3 \, b^{2} c d^{4} e^{8} + 3 \, a c^{2} d^{4} e^{8} - b^{3} d^{3} e^{9} - 6 \, a b c d^{3} e^{9} + 3 \, a b^{2} d^{2} e^{10} + 3 \, a^{2} c d^{2} e^{10} - 3 \, a^{2} b d e^{11} + a^{3} e^{12}} + \frac{12 \, c^{7} d^{5} f e - 6 \, b c^{6} d^{5} g e - 30 \, b c^{6} d^{4} f e^{2} + 17 \, b^{2} c^{5} d^{4} g e^{2} - 8 \, a c^{6} d^{4} g e^{2} + 16 \, b^{2} c^{5} d^{3} f e^{3} + 56 \, a c^{6} d^{3} f e^{3} - 12 \, b^{3} c^{4} d^{3} g e^{3} - 12 \, a b c^{5} d^{3} g e^{3} + 6 \, b^{3} c^{4} d^{2} f e^{4} - 84 \, a b c^{5} d^{2} f e^{4} + 8 \, b^{4} c^{3} d^{2} g e^{4} - 34 \, a b^{2} c^{4} d^{2} g e^{4} + 128 \, a^{2} c^{5} d^{2} g e^{4} - 14 \, b^{4} c^{3} d f e^{5} + 100 \, a b^{2} c^{4} d f e^{5} - 116 \, a^{2} c^{5} d f e^{5} - 2 \, b^{5} c^{2} d g e^{5} + 18 \, a b^{3} c^{3} d g e^{5} - 70 \, a^{2} b c^{4} d g e^{5} + 5 \, b^{5} c^{2} f e^{6} - 36 \, a b^{3} c^{3} f e^{6} + 58 \, a^{2} b c^{4} f e^{6} - 3 \, a b^{4} c^{2} g e^{6} + 21 \, a^{2} b^{2} c^{3} g e^{6} - 24 \, a^{3} c^{4} g e^{6} - \frac{2 \, {\left(18 \, c^{7} d^{6} f e^{2} - 9 \, b c^{6} d^{6} g e^{2} - 54 \, b c^{6} d^{5} f e^{3} + 30 \, b^{2} c^{5} d^{5} g e^{3} - 12 \, a c^{6} d^{5} g e^{3} + 47 \, b^{2} c^{5} d^{4} f e^{4} + 82 \, a c^{6} d^{4} f e^{4} - 31 \, b^{3} c^{4} d^{4} g e^{4} - 11 \, a b c^{5} d^{4} g e^{4} - 4 \, b^{3} c^{4} d^{3} f e^{5} - 164 \, a b c^{5} d^{3} f e^{5} + 24 \, b^{4} c^{3} d^{3} g e^{5} - 64 \, a b^{2} c^{4} d^{3} g e^{5} + 232 \, a^{2} c^{5} d^{3} g e^{5} - 29 \, b^{4} c^{3} d^{2} f e^{6} + 244 \, a b^{2} c^{4} d^{2} f e^{6} - 242 \, a^{2} c^{5} d^{2} f e^{6} - 11 \, b^{5} c^{2} d^{2} g e^{6} + 67 \, a b^{3} c^{3} d^{2} g e^{6} - 227 \, a^{2} b c^{4} d^{2} g e^{6} + 22 \, b^{5} c^{2} d f e^{7} - 162 \, a b^{3} c^{3} d f e^{7} + 242 \, a^{2} b c^{4} d f e^{7} + 2 \, b^{6} c d g e^{7} - 24 \, a b^{4} c^{2} d g e^{7} + 110 \, a^{2} b^{2} c^{3} d g e^{7} - 76 \, a^{3} c^{4} d g e^{7} - 5 \, b^{6} c f e^{8} + 38 \, a b^{4} c^{2} f e^{8} - 71 \, a^{2} b^{2} c^{3} f e^{8} + 14 \, a^{3} c^{4} f e^{8} + 3 \, a b^{5} c g e^{8} - 22 \, a^{2} b^{3} c^{2} g e^{8} + 31 \, a^{3} b c^{3} g e^{8}\right)} e^{\left(-1\right)}}{x e + d} + \frac{{\left(36 \, c^{7} d^{7} f e^{3} - 18 \, b c^{6} d^{7} g e^{3} - 126 \, b c^{6} d^{6} f e^{4} + 69 \, b^{2} c^{5} d^{6} g e^{4} - 24 \, a c^{6} d^{6} g e^{4} + 144 \, b^{2} c^{5} d^{5} f e^{5} + 180 \, a c^{6} d^{5} f e^{5} - 90 \, b^{3} c^{4} d^{5} g e^{5} - 18 \, a b c^{5} d^{5} g e^{5} - 45 \, b^{3} c^{4} d^{4} f e^{6} - 450 \, a b c^{5} d^{4} f e^{6} + 80 \, b^{4} c^{3} d^{4} g e^{6} - 145 \, a b^{2} c^{4} d^{4} g e^{6} + 560 \, a^{2} c^{5} d^{4} g e^{6} - 70 \, b^{4} c^{3} d^{3} f e^{7} + 740 \, a b^{2} c^{4} d^{3} f e^{7} - 580 \, a^{2} c^{5} d^{3} f e^{7} - 50 \, b^{5} c^{2} d^{3} g e^{7} + 250 \, a b^{3} c^{3} d^{3} g e^{7} - 830 \, a^{2} b c^{4} d^{3} g e^{7} + 87 \, b^{5} c^{2} d^{2} f e^{8} - 660 \, a b^{3} c^{3} d^{2} f e^{8} + 870 \, a^{2} b c^{4} d^{2} f e^{8} + 16 \, b^{6} c d^{2} g e^{8} - 129 \, a b^{4} c^{2} d^{2} g e^{8} + 471 \, a^{2} b^{2} c^{3} d^{2} g e^{8} - 88 \, a^{3} c^{4} d^{2} g e^{8} - 36 \, b^{6} c d f e^{9} + 258 \, a b^{4} c^{2} d f e^{9} - 372 \, a^{2} b^{2} c^{3} d f e^{9} - 84 \, a^{3} c^{4} d f e^{9} - 2 \, b^{7} d g e^{9} + 32 \, a b^{5} c d g e^{9} - 160 \, a^{2} b^{3} c^{2} d g e^{9} + 130 \, a^{3} b c^{3} d g e^{9} + 5 \, b^{7} f e^{10} - 34 \, a b^{5} c f e^{10} + 41 \, a^{2} b^{3} c^{2} f e^{10} + 42 \, a^{3} b c^{3} f e^{10} - 3 \, a b^{6} g e^{10} + 19 \, a^{2} b^{4} c g e^{10} - 11 \, a^{3} b^{2} c^{2} g e^{10} - 32 \, a^{4} c^{3} g e^{10}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{2 \, {\left(6 \, c^{7} d^{8} f e^{4} - 3 \, b c^{6} d^{8} g e^{4} - 24 \, b c^{6} d^{7} f e^{5} + 13 \, b^{2} c^{5} d^{7} g e^{5} - 4 \, a c^{6} d^{7} g e^{5} + 33 \, b^{2} c^{5} d^{6} f e^{6} + 36 \, a c^{6} d^{6} f e^{6} - 20 \, b^{3} c^{4} d^{6} g e^{6} - 4 \, a b c^{5} d^{6} g e^{6} - 15 \, b^{3} c^{4} d^{5} f e^{7} - 108 \, a b c^{5} d^{5} f e^{7} + 20 \, b^{4} c^{3} d^{5} g e^{7} - 25 \, a b^{2} c^{4} d^{5} g e^{7} + 116 \, a^{2} c^{5} d^{5} g e^{7} - 15 \, b^{4} c^{3} d^{4} f e^{8} + 195 \, a b^{2} c^{4} d^{4} f e^{8} - 120 \, a^{2} c^{5} d^{4} f e^{8} - 15 \, b^{5} c^{2} d^{4} g e^{8} + 65 \, a b^{3} c^{3} d^{4} g e^{8} - 230 \, a^{2} b c^{4} d^{4} g e^{8} + 27 \, b^{5} c^{2} d^{3} f e^{9} - 210 \, a b^{3} c^{3} d^{3} f e^{9} + 240 \, a^{2} b c^{4} d^{3} f e^{9} + 6 \, b^{6} c d^{3} g e^{9} - 39 \, a b^{4} c^{2} d^{3} g e^{9} + 131 \, a^{2} b^{2} c^{3} d^{3} g e^{9} + 52 \, a^{3} c^{4} d^{3} g e^{9} - 15 \, b^{6} c d^{2} f e^{10} + 99 \, a b^{4} c^{2} d^{2} f e^{10} - 81 \, a^{2} b^{2} c^{3} d^{2} f e^{10} - 132 \, a^{3} c^{4} d^{2} f e^{10} - b^{7} d^{2} g e^{10} + 11 \, a b^{5} c d^{2} g e^{10} - 46 \, a^{2} b^{3} c^{2} d^{2} g e^{10} - 12 \, a^{3} b c^{3} d^{2} g e^{10} + 3 \, b^{7} d f e^{11} - 12 \, a b^{5} c d f e^{11} - 39 \, a^{2} b^{3} c^{2} d f e^{11} + 132 \, a^{3} b c^{3} d f e^{11} - a b^{6} d g e^{11} + a^{2} b^{4} c d g e^{11} + 41 \, a^{3} b^{2} c^{2} d g e^{11} - 68 \, a^{4} c^{3} d g e^{11} - 3 \, a b^{6} f e^{12} + 24 \, a^{2} b^{4} c f e^{12} - 51 \, a^{3} b^{2} c^{2} f e^{12} + 18 \, a^{4} c^{3} f e^{12} + 2 \, a^{2} b^{5} g e^{12} - 15 \, a^{3} b^{3} c g e^{12} + 25 \, a^{4} b c^{2} g e^{12}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{4} {\left(b^{2} - 4 \, a c\right)}^{2} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{2}}"," ",0,"(12*c^6*d^6*f*e^2 - 6*b*c^5*d^6*g*e^2 - 36*b*c^5*d^5*f*e^3 + 20*b^2*c^4*d^5*g*e^3 - 8*a*c^5*d^5*g*e^3 + 30*b^2*c^4*d^4*f*e^4 + 60*a*c^5*d^4*f*e^4 - 20*b^3*c^3*d^4*g*e^4 - 10*a*b*c^4*d^4*g*e^4 - 120*a*b*c^4*d^3*f*e^5 + 80*a*b^2*c^3*d^3*g*e^5 - 80*a^2*c^4*d^3*g*e^5 + 180*a^2*c^4*d^2*f*e^6 + 5*b^5*c*d^2*g*e^6 - 50*a*b^3*c^2*d^2*g*e^6 + 30*a^2*b*c^3*d^2*g*e^6 - 6*b^5*c*d*f*e^7 + 60*a*b^3*c^2*d*f*e^7 - 180*a^2*b*c^3*d*f*e^7 - 2*b^6*d*g*e^7 + 20*a*b^4*c*d*g*e^7 - 60*a^2*b^2*c^2*d*g*e^7 + 120*a^3*c^3*d*g*e^7 + 3*b^6*f*e^8 - 30*a*b^4*c*f*e^8 + 90*a^2*b^2*c^2*f*e^8 - 60*a^3*c^3*f*e^8 - a*b^5*g*e^8 + 10*a^2*b^3*c*g*e^8 - 30*a^3*b*c^2*g*e^8)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((b^4*c^4*d^8 - 8*a*b^2*c^5*d^8 + 16*a^2*c^6*d^8 - 4*b^5*c^3*d^7*e + 32*a*b^3*c^4*d^7*e - 64*a^2*b*c^5*d^7*e + 6*b^6*c^2*d^6*e^2 - 44*a*b^4*c^3*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 64*a^3*c^5*d^6*e^2 - 4*b^7*c*d^5*e^3 + 20*a*b^5*c^2*d^5*e^3 + 32*a^2*b^3*c^3*d^5*e^3 - 192*a^3*b*c^4*d^5*e^3 + b^8*d^4*e^4 + 4*a*b^6*c*d^4*e^4 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 96*a^4*c^4*d^4*e^4 - 4*a*b^7*d^3*e^5 + 20*a^2*b^5*c*d^3*e^5 + 32*a^3*b^3*c^2*d^3*e^5 - 192*a^4*b*c^3*d^3*e^5 + 6*a^2*b^6*d^2*e^6 - 44*a^3*b^4*c*d^2*e^6 + 64*a^4*b^2*c^2*d^2*e^6 + 64*a^5*c^3*d^2*e^6 - 4*a^3*b^5*d*e^7 + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 + a^4*b^4*e^8 - 8*a^5*b^2*c*e^8 + 16*a^6*c^2*e^8)*sqrt(-b^2 + 4*a*c)) + 1/2*(5*c*d^2*g*e^4 - 6*c*d*f*e^5 - 2*b*d*g*e^5 + 3*b*f*e^6 - a*g*e^6)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8) + (d*g*e^10/(x*e + d) - f*e^11/(x*e + d))/(c^3*d^6*e^6 - 3*b*c^2*d^5*e^7 + 3*b^2*c*d^4*e^8 + 3*a*c^2*d^4*e^8 - b^3*d^3*e^9 - 6*a*b*c*d^3*e^9 + 3*a*b^2*d^2*e^10 + 3*a^2*c*d^2*e^10 - 3*a^2*b*d*e^11 + a^3*e^12) + 1/2*(12*c^7*d^5*f*e - 6*b*c^6*d^5*g*e - 30*b*c^6*d^4*f*e^2 + 17*b^2*c^5*d^4*g*e^2 - 8*a*c^6*d^4*g*e^2 + 16*b^2*c^5*d^3*f*e^3 + 56*a*c^6*d^3*f*e^3 - 12*b^3*c^4*d^3*g*e^3 - 12*a*b*c^5*d^3*g*e^3 + 6*b^3*c^4*d^2*f*e^4 - 84*a*b*c^5*d^2*f*e^4 + 8*b^4*c^3*d^2*g*e^4 - 34*a*b^2*c^4*d^2*g*e^4 + 128*a^2*c^5*d^2*g*e^4 - 14*b^4*c^3*d*f*e^5 + 100*a*b^2*c^4*d*f*e^5 - 116*a^2*c^5*d*f*e^5 - 2*b^5*c^2*d*g*e^5 + 18*a*b^3*c^3*d*g*e^5 - 70*a^2*b*c^4*d*g*e^5 + 5*b^5*c^2*f*e^6 - 36*a*b^3*c^3*f*e^6 + 58*a^2*b*c^4*f*e^6 - 3*a*b^4*c^2*g*e^6 + 21*a^2*b^2*c^3*g*e^6 - 24*a^3*c^4*g*e^6 - 2*(18*c^7*d^6*f*e^2 - 9*b*c^6*d^6*g*e^2 - 54*b*c^6*d^5*f*e^3 + 30*b^2*c^5*d^5*g*e^3 - 12*a*c^6*d^5*g*e^3 + 47*b^2*c^5*d^4*f*e^4 + 82*a*c^6*d^4*f*e^4 - 31*b^3*c^4*d^4*g*e^4 - 11*a*b*c^5*d^4*g*e^4 - 4*b^3*c^4*d^3*f*e^5 - 164*a*b*c^5*d^3*f*e^5 + 24*b^4*c^3*d^3*g*e^5 - 64*a*b^2*c^4*d^3*g*e^5 + 232*a^2*c^5*d^3*g*e^5 - 29*b^4*c^3*d^2*f*e^6 + 244*a*b^2*c^4*d^2*f*e^6 - 242*a^2*c^5*d^2*f*e^6 - 11*b^5*c^2*d^2*g*e^6 + 67*a*b^3*c^3*d^2*g*e^6 - 227*a^2*b*c^4*d^2*g*e^6 + 22*b^5*c^2*d*f*e^7 - 162*a*b^3*c^3*d*f*e^7 + 242*a^2*b*c^4*d*f*e^7 + 2*b^6*c*d*g*e^7 - 24*a*b^4*c^2*d*g*e^7 + 110*a^2*b^2*c^3*d*g*e^7 - 76*a^3*c^4*d*g*e^7 - 5*b^6*c*f*e^8 + 38*a*b^4*c^2*f*e^8 - 71*a^2*b^2*c^3*f*e^8 + 14*a^3*c^4*f*e^8 + 3*a*b^5*c*g*e^8 - 22*a^2*b^3*c^2*g*e^8 + 31*a^3*b*c^3*g*e^8)*e^(-1)/(x*e + d) + (36*c^7*d^7*f*e^3 - 18*b*c^6*d^7*g*e^3 - 126*b*c^6*d^6*f*e^4 + 69*b^2*c^5*d^6*g*e^4 - 24*a*c^6*d^6*g*e^4 + 144*b^2*c^5*d^5*f*e^5 + 180*a*c^6*d^5*f*e^5 - 90*b^3*c^4*d^5*g*e^5 - 18*a*b*c^5*d^5*g*e^5 - 45*b^3*c^4*d^4*f*e^6 - 450*a*b*c^5*d^4*f*e^6 + 80*b^4*c^3*d^4*g*e^6 - 145*a*b^2*c^4*d^4*g*e^6 + 560*a^2*c^5*d^4*g*e^6 - 70*b^4*c^3*d^3*f*e^7 + 740*a*b^2*c^4*d^3*f*e^7 - 580*a^2*c^5*d^3*f*e^7 - 50*b^5*c^2*d^3*g*e^7 + 250*a*b^3*c^3*d^3*g*e^7 - 830*a^2*b*c^4*d^3*g*e^7 + 87*b^5*c^2*d^2*f*e^8 - 660*a*b^3*c^3*d^2*f*e^8 + 870*a^2*b*c^4*d^2*f*e^8 + 16*b^6*c*d^2*g*e^8 - 129*a*b^4*c^2*d^2*g*e^8 + 471*a^2*b^2*c^3*d^2*g*e^8 - 88*a^3*c^4*d^2*g*e^8 - 36*b^6*c*d*f*e^9 + 258*a*b^4*c^2*d*f*e^9 - 372*a^2*b^2*c^3*d*f*e^9 - 84*a^3*c^4*d*f*e^9 - 2*b^7*d*g*e^9 + 32*a*b^5*c*d*g*e^9 - 160*a^2*b^3*c^2*d*g*e^9 + 130*a^3*b*c^3*d*g*e^9 + 5*b^7*f*e^10 - 34*a*b^5*c*f*e^10 + 41*a^2*b^3*c^2*f*e^10 + 42*a^3*b*c^3*f*e^10 - 3*a*b^6*g*e^10 + 19*a^2*b^4*c*g*e^10 - 11*a^3*b^2*c^2*g*e^10 - 32*a^4*c^3*g*e^10)*e^(-2)/(x*e + d)^2 - 2*(6*c^7*d^8*f*e^4 - 3*b*c^6*d^8*g*e^4 - 24*b*c^6*d^7*f*e^5 + 13*b^2*c^5*d^7*g*e^5 - 4*a*c^6*d^7*g*e^5 + 33*b^2*c^5*d^6*f*e^6 + 36*a*c^6*d^6*f*e^6 - 20*b^3*c^4*d^6*g*e^6 - 4*a*b*c^5*d^6*g*e^6 - 15*b^3*c^4*d^5*f*e^7 - 108*a*b*c^5*d^5*f*e^7 + 20*b^4*c^3*d^5*g*e^7 - 25*a*b^2*c^4*d^5*g*e^7 + 116*a^2*c^5*d^5*g*e^7 - 15*b^4*c^3*d^4*f*e^8 + 195*a*b^2*c^4*d^4*f*e^8 - 120*a^2*c^5*d^4*f*e^8 - 15*b^5*c^2*d^4*g*e^8 + 65*a*b^3*c^3*d^4*g*e^8 - 230*a^2*b*c^4*d^4*g*e^8 + 27*b^5*c^2*d^3*f*e^9 - 210*a*b^3*c^3*d^3*f*e^9 + 240*a^2*b*c^4*d^3*f*e^9 + 6*b^6*c*d^3*g*e^9 - 39*a*b^4*c^2*d^3*g*e^9 + 131*a^2*b^2*c^3*d^3*g*e^9 + 52*a^3*c^4*d^3*g*e^9 - 15*b^6*c*d^2*f*e^10 + 99*a*b^4*c^2*d^2*f*e^10 - 81*a^2*b^2*c^3*d^2*f*e^10 - 132*a^3*c^4*d^2*f*e^10 - b^7*d^2*g*e^10 + 11*a*b^5*c*d^2*g*e^10 - 46*a^2*b^3*c^2*d^2*g*e^10 - 12*a^3*b*c^3*d^2*g*e^10 + 3*b^7*d*f*e^11 - 12*a*b^5*c*d*f*e^11 - 39*a^2*b^3*c^2*d*f*e^11 + 132*a^3*b*c^3*d*f*e^11 - a*b^6*d*g*e^11 + a^2*b^4*c*d*g*e^11 + 41*a^3*b^2*c^2*d*g*e^11 - 68*a^4*c^3*d*g*e^11 - 3*a*b^6*f*e^12 + 24*a^2*b^4*c*f*e^12 - 51*a^3*b^2*c^2*f*e^12 + 18*a^4*c^3*f*e^12 + 2*a^2*b^5*g*e^12 - 15*a^3*b^3*c*g*e^12 + 25*a^4*b*c^2*g*e^12)*e^(-3)/(x*e + d)^3)/((c*d^2 - b*d*e + a*e^2)^4*(b^2 - 4*a*c)^2*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)^2)","B",0
2378,1,35,0,0.161445," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{4}{3} \, x^{4} + \frac{32}{27} \, x^{3} + \frac{1156}{27} \, x^{2} + \frac{11576}{81} \, x + \frac{10625}{243} \, \log\left({\left| 3 \, x + 2 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-4/3*x^4 + 32/27*x^3 + 1156/27*x^2 + 11576/81*x + 10625/243*log(abs(3*x + 2)) - 6*log(abs(x + 1))","A",0
2379,1,30,0,0.150422," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \, \log\left({\left| 3 \, x + 2 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-8/9*x^3 + 26/9*x^2 + 922/27*x + 2125/81*log(abs(3*x + 2)) - 6*log(abs(x + 1))","A",0
2380,1,25,0,0.170608," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{2}{3} \, x^{2} + \frac{44}{9} \, x + \frac{425}{27} \, \log\left({\left| 3 \, x + 2 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-2/3*x^2 + 44/9*x + 425/27*log(abs(3*x + 2)) - 6*log(abs(x + 1))","A",0
2381,1,20,0,0.212540," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{2}{3} \, x + \frac{85}{9} \, \log\left({\left| 3 \, x + 2 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-2/3*x + 85/9*log(abs(3*x + 2)) - 6*log(abs(x + 1))","A",0
2382,1,17,0,0.149604," ","integrate((5-x)/(3*x^2+5*x+2),x, algorithm=""giac"")","\frac{17}{3} \, \log\left({\left| 3 \, x + 2 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"17/3*log(abs(3*x + 2)) - 6*log(abs(x + 1))","A",0
2383,1,26,0,0.147619," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2),x, algorithm=""giac"")","\frac{17}{5} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{13}{5} \, \log\left({\left| 2 \, x + 3 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"17/5*log(abs(3*x + 2)) + 13/5*log(abs(2*x + 3)) - 6*log(abs(x + 1))","A",0
2384,1,40,0,0.187360," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{13}{5 \, {\left(2 \, x + 3\right)}} - 6 \, \log\left({\left| -\frac{1}{2 \, x + 3} + 1 \right|}\right) + \frac{51}{25} \, \log\left({\left| -\frac{5}{2 \, x + 3} + 3 \right|}\right)"," ",0,"-13/5/(2*x + 3) - 6*log(abs(-1/(2*x + 3) + 1)) + 51/25*log(abs(-5/(2*x + 3) + 3))","A",0
2385,1,40,0,0.163929," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{396 \, x + 659}{50 \, {\left(2 \, x + 3\right)}^{2}} + \frac{153}{125} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{597}{125} \, \log\left({\left| 2 \, x + 3 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/50*(396*x + 659)/(2*x + 3)^2 + 153/125*log(abs(3*x + 2)) + 597/125*log(abs(2*x + 3)) - 6*log(abs(x + 1))","A",0
2386,1,45,0,0.170241," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{14328 \, x^{2} + 45954 \, x + 37343}{750 \, {\left(2 \, x + 3\right)}^{3}} + \frac{459}{625} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{3291}{625} \, \log\left({\left| 2 \, x + 3 \right|}\right) - 6 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/750*(14328*x^2 + 45954*x + 37343)/(2*x + 3)^3 + 459/625*log(abs(3*x + 2)) + 3291/625*log(abs(2*x + 3)) - 6*log(abs(x + 1))","A",0
2387,1,44,0,0.155377," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{8}{9} \, x^{2} + \frac{112}{27} \, x - \frac{12083 \, x + 11597}{81 \, {\left(3 \, x + 2\right)} {\left(x + 1\right)}} - \frac{1625}{27} \, \log\left({\left| 3 \, x + 2 \right|}\right) + 83 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-8/9*x^2 + 112/27*x - 1/81*(12083*x + 11597)/((3*x + 2)*(x + 1)) - 1625/27*log(abs(3*x + 2)) + 83*log(abs(x + 1))","A",0
2388,1,39,0,0.193424," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{8}{9} \, x - \frac{2611 \, x + 2449}{27 \, {\left(3 \, x + 2\right)} {\left(x + 1\right)}} - \frac{1825}{27} \, \log\left({\left| 3 \, x + 2 \right|}\right) + 71 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-8/9*x - 1/27*(2611*x + 2449)/((3*x + 2)*(x + 1)) - 1825/27*log(abs(3*x + 2)) + 71*log(abs(x + 1))","A",0
2389,1,36,0,0.194350," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{587 \, x + 533}{9 \, {\left(3 \, x + 2\right)} {\left(x + 1\right)}} - \frac{535}{9} \, \log\left({\left| 3 \, x + 2 \right|}\right) + 59 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/9*(587*x + 533)/((3*x + 2)*(x + 1)) - 535/9*log(abs(3*x + 2)) + 59*log(abs(x + 1))","A",0
2390,1,36,0,0.159896," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{139 \, x + 121}{3 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}} - 47 \, \log\left({\left| 3 \, x + 2 \right|}\right) + 47 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/3*(139*x + 121)/(3*x^2 + 5*x + 2) - 47*log(abs(3*x + 2)) + 47*log(abs(x + 1))","A",0
2391,1,36,0,0.148581," ","integrate((5-x)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{35 \, x + 29}{3 \, x^{2} + 5 \, x + 2} - 35 \, \log\left({\left| 3 \, x + 2 \right|}\right) + 35 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-(35*x + 29)/(3*x^2 + 5*x + 2) - 35*log(abs(3*x + 2)) + 35*log(abs(x + 1))","A",0
2392,1,45,0,0.152150," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{3 \, {\left(47 \, x + 37\right)}}{5 \, {\left(3 \, x + 2\right)} {\left(x + 1\right)}} - \frac{627}{25} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{52}{25} \, \log\left({\left| 2 \, x + 3 \right|}\right) + 23 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-3/5*(47*x + 37)/((3*x + 2)*(x + 1)) - 627/25*log(abs(3*x + 2)) + 52/25*log(abs(2*x + 3)) + 23*log(abs(x + 1))","A",0
2393,1,77,0,0.169475," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{52}{25 \, {\left(2 \, x + 3\right)}} + \frac{6 \, {\left(\frac{1403}{2 \, x + 3} - 903\right)}}{125 \, {\left(\frac{5}{2 \, x + 3} - 3\right)} {\left(\frac{1}{2 \, x + 3} - 1\right)}} + 11 \, \log\left({\left| -\frac{1}{2 \, x + 3} + 1 \right|}\right) - \frac{2187}{125} \, \log\left({\left| -\frac{5}{2 \, x + 3} + 3 \right|}\right)"," ",0,"-52/25/(2*x + 3) + 6/125*(1403/(2*x + 3) - 903)/((5/(2*x + 3) - 3)*(1/(2*x + 3) - 1)) + 11*log(abs(-1/(2*x + 3) + 1)) - 2187/125*log(abs(-5/(2*x + 3) + 3))","A",0
2394,1,62,0,0.150606," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{15708 \, x^{3} + 56162 \, x^{2} + 63967 \, x + 22763}{125 \, {\left(3 \, x + 2\right)} {\left(2 \, x + 3\right)}^{2} {\left(x + 1\right)}} - \frac{7479}{625} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{8104}{625} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/125*(15708*x^3 + 56162*x^2 + 63967*x + 22763)/((3*x + 2)*(2*x + 3)^2*(x + 1)) - 7479/625*log(abs(3*x + 2)) + 8104/625*log(abs(2*x + 3)) - log(abs(x + 1))","A",0
2395,1,67,0,0.173667," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{594792 \, x^{4} + 2974776 \, x^{3} + 5433540 \, x^{2} + 4260599 \, x + 1195793}{1875 \, {\left(3 \, x + 2\right)} {\left(2 \, x + 3\right)}^{3} {\left(x + 1\right)}} - \frac{25191}{3125} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{65816}{3125} \, \log\left({\left| 2 \, x + 3 \right|}\right) - 13 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/1875*(594792*x^4 + 2974776*x^3 + 5433540*x^2 + 4260599*x + 1195793)/((3*x + 2)*(2*x + 3)^3*(x + 1)) - 25191/3125*log(abs(3*x + 2)) + 65816/3125*log(abs(2*x + 3)) - 13*log(abs(x + 1))","A",0
2396,1,49,0,0.153414," ","integrate((5-x)*(3+2*x)^5/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","-\frac{32}{27} \, x + \frac{502254 \, x^{3} + 1235675 \, x^{2} + 979978 \, x + 247043}{162 \, {\left(3 \, x + 2\right)}^{2} {\left(x + 1\right)}^{2}} + \frac{29375}{27} \, \log\left({\left| 3 \, x + 2 \right|}\right) - 1085 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-32/27*x + 1/162*(502254*x^3 + 1235675*x^2 + 979978*x + 247043)/((3*x + 2)^2*(x + 1)^2) + 29375/27*log(abs(3*x + 2)) - 1085*log(abs(x + 1))","A",0
2397,1,46,0,0.165086," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{47362 \, x^{3} + 117789 \, x^{2} + 94986 \, x + 24613}{18 \, {\left(3 \, x + 2\right)}^{2} {\left(x + 1\right)}^{2}} + \frac{23825}{27} \, \log\left({\left| 3 \, x + 2 \right|}\right) - 883 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/18*(47362*x^3 + 117789*x^2 + 94986*x + 24613)/((3*x + 2)^2*(x + 1)^2) + 23825/27*log(abs(3*x + 2)) - 883*log(abs(x + 1))","A",0
2398,1,46,0,0.178361," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{38118 \, x^{3} + 95203 \, x^{2} + 77330 \, x + 20299}{18 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{2}} + 705 \, \log\left({\left| 3 \, x + 2 \right|}\right) - 705 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/18*(38118*x^3 + 95203*x^2 + 77330*x + 20299)/(3*x^2 + 5*x + 2)^2 + 705*log(abs(3*x + 2)) - 705*log(abs(x + 1))","A",0
2399,1,46,0,0.156538," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{9918 \, x^{3} + 24799 \, x^{2} + 20198 \, x + 5335}{6 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{2}} + 551 \, \log\left({\left| 3 \, x + 2 \right|}\right) - 551 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/6*(9918*x^3 + 24799*x^2 + 20198*x + 5335)/(3*x^2 + 5*x + 2)^2 + 551*log(abs(3*x + 2)) - 551*log(abs(x + 1))","A",0
2400,1,46,0,0.199794," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{2526 \, x^{3} + 6315 \, x^{2} + 5146 \, x + 1363}{2 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{2}} + 421 \, \log\left({\left| 3 \, x + 2 \right|}\right) - 421 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*(2526*x^3 + 6315*x^2 + 5146*x + 1363)/(3*x^2 + 5*x + 2)^2 + 421*log(abs(3*x + 2)) - 421*log(abs(x + 1))","A",0
2401,1,46,0,0.156173," ","integrate((5-x)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{1890 \, x^{3} + 4725 \, x^{2} + 3850 \, x + 1021}{2 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{2}} + 315 \, \log\left({\left| 3 \, x + 2 \right|}\right) - 315 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*(1890*x^3 + 4725*x^2 + 3850*x + 1021)/(3*x^2 + 5*x + 2)^2 + 315*log(abs(3*x + 2)) - 315*log(abs(x + 1))","A",0
2402,1,55,0,0.152455," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{34326 \, x^{3} + 85971 \, x^{2} + 70114 \, x + 18619}{50 \, {\left(3 \, x + 2\right)}^{2} {\left(x + 1\right)}^{2}} + \frac{28917}{125} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{208}{125} \, \log\left({\left| 2 \, x + 3 \right|}\right) - 233 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/50*(34326*x^3 + 85971*x^2 + 70114*x + 18619)/((3*x + 2)^2*(x + 1)^2) + 28917/125*log(abs(3*x + 2)) + 208/125*log(abs(2*x + 3)) - 233*log(abs(x + 1))","A",0
2403,1,95,0,0.157519," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","-\frac{208}{125 \, {\left(2 \, x + 3\right)}} - \frac{2 \, {\left(\frac{168231}{2 \, x + 3} - \frac{211036}{{\left(2 \, x + 3\right)}^{2}} + \frac{82447}{{\left(2 \, x + 3\right)}^{3}} - 42642\right)}}{125 \, {\left(\frac{5}{2 \, x + 3} - 3\right)}^{2} {\left(\frac{1}{2 \, x + 3} - 1\right)}^{2}} - 175 \, \log\left({\left| -\frac{1}{2 \, x + 3} + 1 \right|}\right) + \frac{104463}{625} \, \log\left({\left| -\frac{5}{2 \, x + 3} + 3 \right|}\right)"," ",0,"-208/125/(2*x + 3) - 2/125*(168231/(2*x + 3) - 211036/(2*x + 3)^2 + 82447/(2*x + 3)^3 - 42642)/((5/(2*x + 3) - 3)^2*(1/(2*x + 3) - 1)^2) - 175*log(abs(-1/(2*x + 3) + 1)) + 104463/625*log(abs(-5/(2*x + 3) + 3))","A",0
2404,1,70,0,0.161309," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{1291896 \, x^{5} + 7311204 \, x^{4} + 16096458 \, x^{3} + 17180967 \, x^{2} + 8871646 \, x + 1771579}{1250 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)}^{2}} + \frac{372033}{3125} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{68592}{3125} \, \log\left({\left| 2 \, x + 3 \right|}\right) - 141 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/1250*(1291896*x^5 + 7311204*x^4 + 16096458*x^3 + 17180967*x^2 + 8871646*x + 1771579)/(6*x^3 + 19*x^2 + 19*x + 6)^2 + 372033/3125*log(abs(3*x + 2)) + 68592/3125*log(abs(2*x + 3)) - 141*log(abs(x + 1))","A",0
2405,1,20,0,0.149954," ","integrate(x*(1+x)^2/(x^2+x+1)^3,x, algorithm=""giac"")","-\frac{3 \, x^{2} + 4 \, x + 2}{6 \, {\left(x^{2} + x + 1\right)}^{2}}"," ",0,"-1/6*(3*x^2 + 4*x + 2)/(x^2 + x + 1)^2","A",0
2406,1,79,0,0.195870," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{544320} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(30 \, {\left(36 \, x + 47\right)} x - 24869\right)} x - 858565\right)} x - 8691731\right)} x - 80957725\right)} x - 47009103\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{25969}{93312} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/544320*(2*(12*(6*(8*(30*(36*x + 47)*x - 24869)*x - 858565)*x - 8691731)*x - 80957725)*x - 47009103)*sqrt(3*x^2 + 5*x + 2) + 25969/93312*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2407,1,74,0,0.203942," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{25920} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(30 \, x - 13\right)} x - 5735\right)} x - 96577\right)} x - 1216175\right)} x - 859701\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{6221}{31104} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/25920*(2*(12*(6*(8*(30*x - 13)*x - 5735)*x - 96577)*x - 1216175)*x - 859701)*sqrt(3*x^2 + 5*x + 2) + 6221/31104*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2408,1,69,0,0.188769," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{12960} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(24 \, x - 55\right)} x - 9559\right)} x - 187625\right)} x - 168627\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{2267}{15552} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/12960*(2*(12*(18*(24*x - 55)*x - 9559)*x - 187625)*x - 168627)*sqrt(3*x^2 + 5*x + 2) + 2267/15552*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2409,1,64,0,0.249989," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{864} \, {\left(2 \, {\left(12 \, {\left(18 \, x - 79\right)} x - 3713\right)} x - 4539\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{559}{5184} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/864*(2*(12*(18*x - 79)*x - 3713)*x - 4539)*sqrt(3*x^2 + 5*x + 2) + 559/5184*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2410,1,59,0,0.177769," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{72} \, {\left(2 \, {\left(12 \, x - 85\right)} x - 159\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{35}{432} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/72*(2*(12*x - 85)*x - 159)*sqrt(3*x^2 + 5*x + 2) + 35/432*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2411,1,126,0,0.292289," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x),x, algorithm=""giac"")","-\frac{1}{24} \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x - 73\right)} + \frac{13}{8} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{311}{144} \, \sqrt{3} \log\left({\left| -6 \, \sqrt{3} x - 5 \, \sqrt{3} + 6 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}\right)"," ",0,"-1/24*sqrt(3*x^2 + 5*x + 2)*(6*x - 73) + 13/8*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 311/144*sqrt(3)*log(abs(-6*sqrt(3)*x - 5*sqrt(3) + 6*sqrt(3*x^2 + 5*x + 2)))","A",0
2412,1,291,0,0.745034," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^2,x, algorithm=""giac"")","-\frac{43}{24} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}{{\left| 2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{57}{40} \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{13}{8} \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{4 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 3 \, \sqrt{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{4 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} - 3\right)}}"," ",0,"-43/24*sqrt(3)*log(abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3))/abs(2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3)))*sgn(1/(2*x + 3)) + 57/40*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))*sgn(1/(2*x + 3)) - 13/8*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3)*sgn(1/(2*x + 3)) + 1/4*(4*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))*sgn(1/(2*x + 3)) - 3*sqrt(5)*sgn(1/(2*x + 3)))/((sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2 - 3)","B",0
2413,1,240,0,0.311240," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^3,x, algorithm=""giac"")","\frac{27}{400} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{1}{8} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{886 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 2897 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 9039 \, \sqrt{3} x + 3037 \, \sqrt{3} - 9039 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{40 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{2}}"," ",0,"27/400*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 1/8*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 1/40*(886*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 2897*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 9039*sqrt(3)*x + 3037*sqrt(3) - 9039*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^2","B",0
2414,1,257,0,0.317893," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^4,x, algorithm=""giac"")","-\frac{47}{2000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{1236 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 4830 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 90290 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 144945 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 287985 \, \sqrt{3} x - 69339 \, \sqrt{3} + 287985 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{600 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{3}}"," ",0,"-47/2000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/600*(1236*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 4830*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 90290*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 144945*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 287985*sqrt(3)*x - 69339*sqrt(3) + 287985*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^3","B",0
2415,1,183,0,0.268266," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^5,x, algorithm=""giac"")","-\frac{3}{8000} \, \sqrt{5} {\left(44 \, \sqrt{5} \sqrt{3} + 51 \, \log\left(-\sqrt{5} \sqrt{3} + 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{153}{8000} \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1}{1600} \, {\left(\frac{5 \, {\left(\frac{2 \, {\left(\frac{65 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 24 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} - 25 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} - 132 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)} \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3}"," ",0,"-3/8000*sqrt(5)*(44*sqrt(5)*sqrt(3) + 51*log(-sqrt(5)*sqrt(3) + 4))*sgn(1/(2*x + 3)) + 153/8000*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))*sgn(1/(2*x + 3)) - 1/1600*(5*(2*(65*sgn(1/(2*x + 3))/(2*x + 3) - 24*sgn(1/(2*x + 3)))/(2*x + 3) - 25*sgn(1/(2*x + 3)))/(2*x + 3) - 132*sgn(1/(2*x + 3)))*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3)","A",0
2416,1,363,0,0.409325," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^6,x, algorithm=""giac"")","-\frac{3159}{200000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{\sqrt{3} {\left(50544 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 2047032 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 11747352 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 121295556 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 269183136 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 1164571962 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 1077361162 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 1845838971 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 592102521 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 244862928\right)}}{60000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{5}}"," ",0,"-3159/200000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 1/60000*sqrt(3)*(50544*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 2047032*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 11747352*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 121295556*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 269183136*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 1164571962*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 1077361162*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 1845838971*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 592102521*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 244862928)/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^5","B",0
2417,1,410,0,0.339846," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^7,x, algorithm=""giac"")","-\frac{26453}{2000000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{2539488 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 41901552 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 924796880 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 3988893600 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 33933192480 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 66530947296 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 275158218192 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 265623867480 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 526452161650 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 226453420305 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 171288605499 \, \sqrt{3} x + 19197814536 \, \sqrt{3} - 171288605499 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{600000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{6}}"," ",0,"-26453/2000000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 1/600000*(2539488*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 41901552*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 924796880*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 3988893600*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 33933192480*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 66530947296*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 275158218192*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 265623867480*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 526452161650*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 226453420305*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 171288605499*sqrt(3)*x + 19197814536*sqrt(3) - 171288605499*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^6","B",0
2418,1,89,0,0.212724," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{22394880} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(30 \, {\left(36 \, {\left(2 \, {\left(48 \, x + 149\right)} x - 1723\right)} x - 428573\right)} x - 32346133\right)} x - 346648445\right)} x - 1568778787\right)} x - 7524649325\right)} x - 2471988351\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{454969}{26873856} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/22394880*(2*(12*(6*(8*(30*(36*(2*(48*x + 149)*x - 1723)*x - 428573)*x - 32346133)*x - 346648445)*x - 1568778787)*x - 7524649325)*x - 2471988351)*sqrt(3*x^2 + 5*x + 2) - 454969/26873856*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2419,1,84,0,0.213665," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{5806080} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(30 \, {\left(12 \, {\left(42 \, x + 61\right)} x - 10655\right)} x - 1432423\right)} x - 20785055\right)} x - 115100737\right)} x - 638056175\right)} x - 233137461\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{12277}{995328} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/5806080*(2*(12*(6*(8*(30*(12*(42*x + 61)*x - 10655)*x - 1432423)*x - 20785055)*x - 115100737)*x - 638056175)*x - 233137461)*sqrt(3*x^2 + 5*x + 2) - 12277/995328*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2420,1,79,0,0.212306," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{725760} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(90 \, {\left(4 \, x - 1\right)} x - 7837\right)} x - 182985\right)} x - 3952549\right)} x - 25985675\right)} x - 10669737\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{1129}{124416} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/725760*(2*(12*(18*(8*(90*(4*x - 1)*x - 7837)*x - 182985)*x - 3952549)*x - 25985675)*x - 10669737)*sqrt(3*x^2 + 5*x + 2) - 1129/124416*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2421,1,74,0,0.240972," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{103680} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(30 \, x - 61\right)} x - 4705\right)} x - 148637\right)} x - 1203475\right)} x - 561921\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{839}{124416} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/103680*(2*(12*(18*(8*(30*x - 61)*x - 4705)*x - 148637)*x - 1203475)*x - 561921)*sqrt(3*x^2 + 5*x + 2) - 839/124416*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2422,1,69,0,0.192893," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{5760} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(24 \, x - 95\right)} x - 2033\right)} x - 21535\right)} x - 11589\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{35}{6912} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/5760*(2*(12*(6*(24*x - 95)*x - 2033)*x - 21535)*x - 11589)*sqrt(3*x^2 + 5*x + 2) - 35/6912*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2423,1,136,0,0.303026," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x),x, algorithm=""giac"")","-\frac{1}{384} \, {\left(2 \, {\left(12 \, {\left(6 \, x - 37\right)} x - 271\right)} x - 1277\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{65}{32} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{2011}{768} \, \sqrt{3} \log\left({\left| -6 \, \sqrt{3} x - 5 \, \sqrt{3} + 6 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}\right)"," ",0,"-1/384*(2*(12*(6*x - 37)*x - 271)*x - 1277)*sqrt(3*x^2 + 5*x + 2) + 65/32*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 2011/768*sqrt(3)*log(abs(-6*sqrt(3)*x - 5*sqrt(3) + 6*sqrt(3*x^2 + 5*x + 2)))","A",0
2424,1,481,0,1.131503," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^2,x, algorithm=""giac"")","-\frac{3743}{576} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}{{\left| 2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{161}{32} \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{65}{32} \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{4069 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 4308 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 14464 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 17388 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 12627 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 17928 \, \sqrt{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{96 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} - 3\right)}^{3}}"," ",0,"-3743/576*sqrt(3)*log(abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3))/abs(2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3)))*sgn(1/(2*x + 3)) + 161/32*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))*sgn(1/(2*x + 3)) - 65/32*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3)*sgn(1/(2*x + 3)) + 1/96*(4069*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^5*sgn(1/(2*x + 3)) - 4308*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^4*sgn(1/(2*x + 3)) - 14464*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^3*sgn(1/(2*x + 3)) + 17388*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2*sgn(1/(2*x + 3)) + 12627*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))*sgn(1/(2*x + 3)) - 17928*sqrt(5)*sgn(1/(2*x + 3)))/((sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2 - 3)^3","B",0
2425,1,259,0,0.340277," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^3,x, algorithm=""giac"")","-\frac{1}{32} \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x - 89\right)} + \frac{1329}{320} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{343}{64} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{5 \, {\left(510 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 1869 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6259 \, \sqrt{3} x + 2209 \, \sqrt{3} - 6259 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{32 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{2}}"," ",0,"-1/32*sqrt(3*x^2 + 5*x + 2)*(6*x - 89) + 1329/320*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 343/64*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 5/32*(510*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 1869*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6259*sqrt(3)*x + 2209*sqrt(3) - 6259*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^2","B",0
2426,1,305,0,0.342505," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^4,x, algorithm=""giac"")","-\frac{1973}{1600} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{51}{32} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{3}{16} \, \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{62484 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 390510 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 2835190 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 3307455 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 5598195 \, \sqrt{3} x + 1227924 \, \sqrt{3} - 5598195 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{480 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{3}}"," ",0,"-1973/1600*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 51/32*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 3/16*sqrt(3*x^2 + 5*x + 2) - 1/480*(62484*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 390510*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 2835190*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 3307455*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 5598195*sqrt(3)*x + 1227924*sqrt(3) - 5598195*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^3","B",0
2427,1,106,0,0.286401," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^5,x, algorithm=""giac"")","-\frac{1}{19200} \, {\left(\frac{5 \, {\left(\frac{10 \, {\left(\frac{195 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 488 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} + 4109 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} - 7572 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)} \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} - \frac{631}{1600} \, \sqrt{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)"," ",0,"-1/19200*(5*(10*(195*sgn(1/(2*x + 3))/(2*x + 3) - 488*sgn(1/(2*x + 3)))/(2*x + 3) + 4109*sgn(1/(2*x + 3)))/(2*x + 3) - 7572*sgn(1/(2*x + 3)))*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) - 631/1600*sqrt(3)*sgn(1/(2*x + 3))","A",0
2428,1,359,0,0.309610," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^6,x, algorithm=""giac"")","\frac{141}{160000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{146256 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 654456 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 415048 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 15455452 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 140042336 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 207568854 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 544555762 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 286352757 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 252454821 \, \sqrt{3} x - 31985676 \, \sqrt{3} + 252454821 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{16000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{5}}"," ",0,"141/160000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/16000*(146256*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 654456*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 415048*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 15455452*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 140042336*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 207568854*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 544555762*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 286352757*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 252454821*sqrt(3)*x - 31985676*sqrt(3) + 252454821*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^5","B",0
2429,1,410,0,0.357103," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^7,x, algorithm=""giac"")","\frac{1141}{1600000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{109536 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 6127344 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 70129360 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} - 83080800 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} - 3334681440 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 9802137888 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 47432214576 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 48106882440 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 94851959950 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 39436262415 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 28403540997 \, \sqrt{3} x - 3009604608 \, \sqrt{3} + 28403540997 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{480000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{6}}"," ",0,"1141/1600000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/480000*(109536*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 6127344*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 70129360*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 - 83080800*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 - 3334681440*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 9802137888*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 47432214576*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 48106882440*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 94851959950*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 39436262415*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 28403540997*sqrt(3)*x - 3009604608*sqrt(3) + 28403540997*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^6","B",0
2430,1,461,0,0.325411," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^8,x, algorithm=""giac"")","\frac{4663}{8000000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{6267072 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 122207904 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 3852187808 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 18344551344 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 131374293680 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 134399090784 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} - 264419126976 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 1446858601104 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 6675760646156 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 5954681858370 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 10149146991914 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 3640765552263 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 2268672558411 \, \sqrt{3} x - 208833935688 \, \sqrt{3} + 2268672558411 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{16800000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{7}}"," ",0,"4663/8000000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/16800000*(6267072*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 122207904*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 3852187808*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 18344551344*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 131374293680*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 134399090784*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 - 264419126976*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 1446858601104*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 6675760646156*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 5954681858370*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 10149146991914*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 3640765552263*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 2268672558411*sqrt(3)*x - 208833935688*sqrt(3) + 2268672558411*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^7","B",0
2431,1,512,0,0.350704," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^9,x, algorithm=""giac"")","\frac{153927}{320000000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{19702656 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} + 443309760 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} + 13775440320 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 88813739520 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 1135723030560 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 3326100961968 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 20795205897360 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 31719485197440 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 108381222834920 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 93303707056820 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 182905948708404 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 90199904722080 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 98616726439110 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 25302796273485 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 12323187970155 \, \sqrt{3} x + 954490882968 \, \sqrt{3} - 12323187970155 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{32000000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{8}}"," ",0,"153927/320000000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/32000000*(19702656*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 + 443309760*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 + 13775440320*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 88813739520*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 1135723030560*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 3326100961968*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 20795205897360*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 31719485197440*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 108381222834920*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 93303707056820*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 182905948708404*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 90199904722080*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 98616726439110*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 25302796273485*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 12323187970155*sqrt(3)*x + 954490882968*sqrt(3) - 12323187970155*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^8","B",0
2432,1,99,0,0.219517," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{13795246080} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(14 \, {\left(48 \, {\left(54 \, {\left(20 \, x + 97\right)} x - 11555\right)} x - 7394353\right)} x - 362075335\right)} x - 24952744049\right)} x - 177825630725\right)} x - 1077467853325\right)} x - 3044577502355\right)} x - 9760850180605\right)} x - 2261297826735\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{249299}{214990848} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/13795246080*(2*(12*(6*(8*(6*(36*(14*(48*(54*(20*x + 97)*x - 11555)*x - 7394353)*x - 362075335)*x - 24952744049)*x - 177825630725)*x - 1077467853325)*x - 3044577502355)*x - 9760850180605)*x - 2261297826735)*sqrt(3*x^2 + 5*x + 2) + 249299/214990848*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2433,1,94,0,0.239142," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{1254113280} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(14 \, {\left(48 \, {\left(54 \, x + 175\right)} x - 42469\right)} x - 4367155\right)} x - 418553957\right)} x - 3692650505\right)} x - 26130182065\right)} x - 83163094895\right)} x - 292874708065\right)} x - 73178684475\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{182917}{214990848} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/1254113280*(2*(12*(6*(8*(6*(36*(14*(48*(54*x + 175)*x - 42469)*x - 4367155)*x - 418553957)*x - 3692650505)*x - 26130182065)*x - 83163094895)*x - 292874708065)*x - 73178684475)*sqrt(3*x^2 + 5*x + 2) + 182917/214990848*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2434,1,89,0,0.435090," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{41803776} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(14 \, {\left(48 \, x + 77\right)} x - 13165\right)} x - 2236091\right)} x - 26350487\right)} x - 225527791\right)} x - 823423217\right)} x - 3217468735\right)} x - 871825317\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{22535}{35831808} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/41803776*(2*(12*(6*(8*(6*(36*(14*(48*x + 77)*x - 13165)*x - 2236091)*x - 26350487)*x - 225527791)*x - 823423217)*x - 3217468735)*x - 871825317)*sqrt(3*x^2 + 5*x + 2) + 22535/35831808*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2435,1,84,0,0.219420," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{4644864} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(14 \, x - 1\right)} x - 10183\right)} x - 189587\right)} x - 2078283\right)} x - 26791487\right)} x - 117611665\right)} x - 34777419\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{1865}{3981312} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/4644864*(2*(12*(18*(8*(6*(36*(14*x - 1)*x - 10183)*x - 189587)*x - 2078283)*x - 26791487)*x - 117611665)*x - 34777419)*sqrt(3*x^2 + 5*x + 2) + 1865/3981312*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2436,1,79,0,0.231451," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{580608} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(6 \, {\left(36 \, x - 65\right)} x - 3893\right)} x - 61085\right)} x - 962953\right)} x - 4825895\right)} x - 1568541\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{175}{497664} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/580608*(2*(12*(18*(8*(6*(36*x - 65)*x - 3893)*x - 61085)*x - 962953)*x - 4825895)*x - 1568541)*sqrt(3*x^2 + 5*x + 2) + 175/497664*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2437,1,146,0,0.333227," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x),x, algorithm=""giac"")","-\frac{1}{138240} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(30 \, x - 109\right)} x - 3035\right)} x - 67703\right)} x - 291745\right)} x - 580299\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{325}{128} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{543811}{165888} \, \sqrt{3} \log\left({\left| -6 \, \sqrt{3} x - 5 \, \sqrt{3} + 6 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}\right)"," ",0,"-1/138240*(2*(12*(18*(8*(30*x - 109)*x - 3035)*x - 67703)*x - 291745)*x - 580299)*sqrt(3*x^2 + 5*x + 2) + 325/128*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 543811/165888*sqrt(3)*log(abs(-6*sqrt(3)*x - 5*sqrt(3) + 6*sqrt(3*x^2 + 5*x + 2)))","A",0
2438,1,671,0,1.168216," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^2,x, algorithm=""giac"")","-\frac{41053}{3072} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}{{\left| 2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{1325}{128} \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{325}{128} \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{1304805 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{9} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 2064120 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{8} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 4382950 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 10490640 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 19083456 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 33372000 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 42760170 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 60102000 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 21448395 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 36498600 \, \sqrt{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{7680 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} - 3\right)}^{5}}"," ",0,"-41053/3072*sqrt(3)*log(abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3))/abs(2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3)))*sgn(1/(2*x + 3)) + 1325/128*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))*sgn(1/(2*x + 3)) - 325/128*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3)*sgn(1/(2*x + 3)) + 1/7680*(1304805*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^9*sgn(1/(2*x + 3)) - 2064120*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^8*sgn(1/(2*x + 3)) - 4382950*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^7*sgn(1/(2*x + 3)) + 10490640*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^6*sgn(1/(2*x + 3)) + 19083456*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^5*sgn(1/(2*x + 3)) - 33372000*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^4*sgn(1/(2*x + 3)) - 42760170*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^3*sgn(1/(2*x + 3)) + 60102000*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2*sgn(1/(2*x + 3)) + 21448395*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))*sgn(1/(2*x + 3)) - 36498600*sqrt(5)*sgn(1/(2*x + 3)))/((sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2 - 3)^5","B",0
2439,1,269,0,0.336066," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^3,x, algorithm=""giac"")","-\frac{1}{1536} \, {\left(2 \, {\left(12 \, {\left(18 \, x - 143\right)} x + 2855\right)} x - 23731\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{4295}{256} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{199615}{9216} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{5 \, {\left(4214 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 15793 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 53551 \, \sqrt{3} x + 19053 \, \sqrt{3} - 53551 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{128 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{2}}"," ",0,"-1/1536*(2*(12*(18*x - 143)*x + 2855)*x - 23731)*sqrt(3*x^2 + 5*x + 2) + 4295/256*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 199615/9216*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 5/128*(4214*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 15793*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 53551*sqrt(3)*x + 19053*sqrt(3) - 53551*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^2","B",0
2440,1,315,0,0.339010," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^4,x, algorithm=""giac"")","-\frac{1}{128} \, {\left(2 \, {\left(12 \, x - 133\right)} x + 1197\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{3487}{256} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{13505}{768} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{203604 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 1334970 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 10053790 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 12051375 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 20819415 \, \sqrt{3} x + 4639299 \, \sqrt{3} - 20819415 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{384 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{3}}"," ",0,"-1/128*(2*(12*x - 133)*x + 1197)*sqrt(3*x^2 + 5*x + 2) - 3487/256*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 13505/768*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 1/384*(203604*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 1334970*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 10053790*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 12051375*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 20819415*sqrt(3)*x + 4639299*sqrt(3) - 20819415*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^3","B",0
2441,1,445,0,1.055481," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^5,x, algorithm=""giac"")","\frac{1875}{256} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}{{\left| 2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{29047}{5120} \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1}{3072} \, {\left(\frac{\frac{10 \, {\left(\frac{195 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 904 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} + 18577 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 27132 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)} \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} - \frac{9 \, {\left(157 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 126 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 409 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 330 \, \sqrt{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{128 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} - 3\right)}^{2}}"," ",0,"1875/256*sqrt(3)*log(abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3))/abs(2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3)))*sgn(1/(2*x + 3)) - 29047/5120*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))*sgn(1/(2*x + 3)) - 1/3072*((10*(195*sgn(1/(2*x + 3))/(2*x + 3) - 904*sgn(1/(2*x + 3)))/(2*x + 3) + 18577*sgn(1/(2*x + 3)))/(2*x + 3) - 27132*sgn(1/(2*x + 3)))*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) - 9/128*(157*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^3*sgn(1/(2*x + 3)) - 126*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2*sgn(1/(2*x + 3)) - 409*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))*sgn(1/(2*x + 3)) + 330*sqrt(5)*sgn(1/(2*x + 3)))/((sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2 - 3)^2","B",0
2442,1,407,0,0.400777," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^6,x, algorithm=""giac"")","-\frac{137111}{128000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{177}{128} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{9}{64} \, \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{27201072 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 316934472 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 4873277176 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 14374341276 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 80473660448 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 98380998102 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 236231795506 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 119385279741 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 103767800973 \, \sqrt{3} x + 13144069068 \, \sqrt{3} - 103767800973 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{38400 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{5}}"," ",0,"-137111/128000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 177/128*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 9/64*sqrt(3*x^2 + 5*x + 2) - 1/38400*(27201072*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 316934472*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 4873277176*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 14374341276*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 80473660448*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 98380998102*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 236231795506*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 119385279741*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 103767800973*sqrt(3)*x + 13144069068*sqrt(3) - 103767800973*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^5","B",0
2443,1,444,0,0.370507," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^7,x, algorithm=""giac"")","\frac{13931}{256000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{9}{128} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{20435424 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 269619696 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 4893810640 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 17834042400 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 129909086880 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 219870810528 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 791797675536 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 672745449240 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 1187868124850 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 460902113505 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 318216938187 \, \sqrt{3} x + 32907940848 \, \sqrt{3} - 318216938187 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{76800 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{6}}"," ",0,"13931/256000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 9/128*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 1/76800*(20435424*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 269619696*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 4893810640*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 17834042400*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 129909086880*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 219870810528*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 791797675536*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 672745449240*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 1187868124850*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 460902113505*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 318216938187*sqrt(3)*x + 32907940848*sqrt(3) - 318216938187*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^6","B",0
2444,1,461,0,0.330185," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^8,x, algorithm=""giac"")","-\frac{47}{1280000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{72512832 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 651952224 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 6898276448 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 8494566864 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} - 58878767920 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} - 326450774496 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} - 2207907445056 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 3147944405424 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 9314774279636 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 6492162811470 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 9472821206534 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 3070624865553 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 1792565462541 \, \sqrt{3} x - 158637115728 \, \sqrt{3} + 1792565462541 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{2688000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{7}}"," ",0,"-47/1280000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/2688000*(72512832*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 651952224*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 6898276448*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 8494566864*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 - 58878767920*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 - 326450774496*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 - 2207907445056*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 3147944405424*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 9314774279636*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 6492162811470*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 9472821206534*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 3070624865553*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 1792565462541*sqrt(3)*x - 158637115728*sqrt(3) + 1792565462541*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^7","B",0
2445,1,512,0,0.347822," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^9,x, algorithm=""giac"")","-\frac{1517}{51200000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{4077696 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} - 2811291840 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} - 54242130880 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 23829496320 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 4407279220960 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 22617729467088 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 195051199819760 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 377875254407040 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 1580087388997720 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 1627784736400620 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 3742975645158764 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 2115026806109280 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 2573382759804010 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 709918795444635 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 358308332266605 \, \sqrt{3} x + 27766562618088 \, \sqrt{3} - 358308332266605 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{107520000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{8}}"," ",0,"-1517/51200000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 1/107520000*(4077696*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 - 2811291840*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 - 54242130880*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 23829496320*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 4407279220960*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 22617729467088*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 195051199819760*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 377875254407040*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 1580087388997720*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 1627784736400620*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 3742975645158764*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 2115026806109280*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 2573382759804010*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 709918795444635*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 358308332266605*sqrt(3)*x + 27766562618088*sqrt(3) - 358308332266605*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^8","B",0
2446,1,563,0,0.347440," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^10,x, algorithm=""giac"")","-\frac{6167}{256000000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{99461376 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{17} + 2536265088 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{16} - 83954355072 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} - 341000936640 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} + 17778066768000 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 177356386111968 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 2399974462831392 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 6844601123556624 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 41172892580130560 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 60936872688585000 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 204498063708405624 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 174436297943297292 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 339439601929212792 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 164994557892929730 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 174936772514694750 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 42504221165006223 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 19065836258759367 \, \sqrt{3} x + 1323473153587704 \, \sqrt{3} - 19065836258759367 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{1612800000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{9}}"," ",0,"-6167/256000000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 1/1612800000*(99461376*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^17 + 2536265088*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^16 - 83954355072*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 - 341000936640*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 + 17778066768000*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 177356386111968*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 2399974462831392*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 6844601123556624*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 41172892580130560*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 60936872688585000*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 204498063708405624*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 174436297943297292*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 339439601929212792*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 164994557892929730*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 174936772514694750*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 42504221165006223*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 19065836258759367*sqrt(3)*x + 1323473153587704*sqrt(3) - 19065836258759367*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^9","B",0
2447,1,109,0,0.233299," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(7/2),x, algorithm=""giac"")","-\frac{1}{67077144576} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(2 \, {\left(48 \, {\left(54 \, {\left(4 \, {\left(6 \, {\left(72 \, x + 473\right)} x - 409\right)} x - 258889\right)} x - 66586273\right)} x - 8082617507\right)} x - 26220538883\right)} x - 1042194858901\right)} x - 4773502588153\right)} x - 19901779363361\right)} x - 40629353336575\right)} x - 97720614817745\right)} x - 17510968283403\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{2595845}{30958682112} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/67077144576*(2*(12*(6*(8*(6*(36*(2*(48*(54*(4*(6*(72*x + 473)*x - 409)*x - 258889)*x - 66586273)*x - 8082617507)*x - 26220538883)*x - 1042194858901)*x - 4773502588153)*x - 19901779363361)*x - 40629353336575)*x - 97720614817745)*x - 17510968283403)*sqrt(3*x^2 + 5*x + 2) - 2595845/30958682112*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2448,1,104,0,0.333284," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(7/2),x, algorithm=""giac"")","-\frac{1}{94595973120} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(2 \, {\left(48 \, {\left(54 \, {\left(20 \, {\left(66 \, x + 329\right)} x - 12087\right)} x - 9872495\right)} x - 1740351757\right)} x - 7097898925\right)} x - 332597328443\right)} x - 1729442810135\right)} x - 7981449547375\right)} x - 17709832699505\right)} x - 45659361023935\right)} x - 8675936123685\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{637609}{10319560704} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/94595973120*(2*(12*(6*(8*(6*(36*(2*(48*(54*(20*(66*x + 329)*x - 12087)*x - 9872495)*x - 1740351757)*x - 7097898925)*x - 332597328443)*x - 1729442810135)*x - 7981449547375)*x - 17709832699505)*x - 45659361023935)*x - 8675936123685)*sqrt(3*x^2 + 5*x + 2) - 637609/10319560704*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2449,1,99,0,0.224815," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(7/2),x, algorithm=""giac"")","-\frac{1}{7882997760} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(2 \, {\left(48 \, {\left(54 \, {\left(60 \, x + 203\right)} x - 48415\right)} x - 18318737\right)} x - 103376945\right)} x - 5959290583\right)} x - 36000278755\right)} x - 186438341915\right)} x - 453432637765\right)} x - 1259771377835\right)} x - 254668717065\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{39389}{859963392} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/7882997760*(2*(12*(6*(8*(6*(36*(2*(48*(54*(60*x + 203)*x - 48415)*x - 18318737)*x - 103376945)*x - 5959290583)*x - 36000278755)*x - 186438341915)*x - 453432637765)*x - 1259771377835)*x - 254668717065)*sqrt(3*x^2 + 5*x + 2) - 39389/859963392*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2450,1,94,0,0.229305," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(7/2),x, algorithm=""giac"")","-\frac{1}{238878720} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(2 \, {\left(48 \, {\left(54 \, x + 95\right)} x - 47279\right)} x - 473615\right)} x - 36201961\right)} x - 262936285\right)} x - 1556234405\right)} x - 4192200955\right)} x - 12628922645\right)} x - 2726071095\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{9793}{286654464} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/238878720*(2*(12*(6*(8*(6*(36*(2*(48*(54*x + 95)*x - 47279)*x - 473615)*x - 36201961)*x - 262936285)*x - 1556234405)*x - 4192200955)*x - 12628922645)*x - 2726071095)*sqrt(3*x^2 + 5*x + 2) - 9793/286654464*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2451,1,89,0,0.218016," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2),x, algorithm=""giac"")","-\frac{1}{7962624} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(2 \, {\left(48 \, x + 5\right)} x - 1819\right)} x - 218045\right)} x - 2014529\right)} x - 13983145\right)} x - 42283127\right)} x - 139128025\right)} x - 32198883\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{1225}{47775744} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/7962624*(2*(12*(6*(8*(6*(36*(2*(48*x + 5)*x - 1819)*x - 218045)*x - 2014529)*x - 13983145)*x - 42283127)*x - 139128025)*x - 32198883)*sqrt(3*x^2 + 5*x + 2) - 1225/47775744*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2452,1,156,0,0.357447," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x),x, algorithm=""giac"")","-\frac{1}{18579456} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(42 \, x - 67\right)} x - 25549\right)} x - 337921\right)} x - 2835289\right)} x - 30119573\right)} x - 92990875\right)} x - 101435865\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{1625}{512} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{65251715}{15925248} \, \sqrt{3} \log\left({\left| -6 \, \sqrt{3} x - 5 \, \sqrt{3} + 6 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}\right)"," ",0,"-1/18579456*(2*(12*(18*(8*(6*(36*(42*x - 67)*x - 25549)*x - 337921)*x - 2835289)*x - 30119573)*x - 92990875)*x - 101435865)*sqrt(3*x^2 + 5*x + 2) + 1625/512*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 65251715/15925248*sqrt(3)*log(abs(-6*sqrt(3)*x - 5*sqrt(3) + 6*sqrt(3*x^2 + 5*x + 2)))","A",0
2453,1,861,0,1.453107," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^2,x, algorithm=""giac"")","-\frac{15434623}{663552} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}{{\left| 2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{9225}{512} \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1625}{512} \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{1702084195 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{13} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 3595838400 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{12} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 462583100 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{11} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 12803555520 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{10} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 91554292599 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{9} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 132950643840 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{8} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 221215739904 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 432202780800 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 252015304401 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 680038027200 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 506502404100 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 786343723200 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 178876045845 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 339366412800 \, \sqrt{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{3870720 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} - 3\right)}^{7}}"," ",0,"-15434623/663552*sqrt(3)*log(abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3))/abs(2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3)))*sgn(1/(2*x + 3)) + 9225/512*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))*sgn(1/(2*x + 3)) - 1625/512*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3)*sgn(1/(2*x + 3)) + 1/3870720*(1702084195*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^13*sgn(1/(2*x + 3)) - 3595838400*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^12*sgn(1/(2*x + 3)) - 462583100*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^11*sgn(1/(2*x + 3)) + 12803555520*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^10*sgn(1/(2*x + 3)) + 91554292599*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^9*sgn(1/(2*x + 3)) - 132950643840*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^8*sgn(1/(2*x + 3)) - 221215739904*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^7*sgn(1/(2*x + 3)) + 432202780800*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^6*sgn(1/(2*x + 3)) + 252015304401*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^5*sgn(1/(2*x + 3)) - 680038027200*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^4*sgn(1/(2*x + 3)) - 506502404100*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^3*sgn(1/(2*x + 3)) + 786343723200*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2*sgn(1/(2*x + 3)) + 178876045845*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))*sgn(1/(2*x + 3)) - 339366412800*sqrt(5)*sgn(1/(2*x + 3)))/((sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2 - 3)^7","B",0
2454,1,279,0,0.381210," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^3,x, algorithm=""giac"")","-\frac{1}{184320} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(30 \, x - 157\right)} x - 725\right)} x - 67409\right)} x + 1173065\right)} x - 8219517\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{44625}{1024} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{12443893}{221184} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{25 \, {\left(5878 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 22241 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 75807 \, \sqrt{3} x + 27061 \, \sqrt{3} - 75807 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{512 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{2}}"," ",0,"-1/184320*(2*(12*(18*(8*(30*x - 157)*x - 725)*x - 67409)*x + 1173065)*x - 8219517)*sqrt(3*x^2 + 5*x + 2) + 44625/1024*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 12443893/221184*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 25/512*(5878*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 22241*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 75807*sqrt(3)*x + 27061*sqrt(3) - 75807*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^2","A",0
2455,1,325,0,0.483125," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^4,x, algorithm=""giac"")","-\frac{1}{30720} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(24 \, x - 175\right)} x + 4661\right)} x - 218885\right)} x + 1563313\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{59745}{1024} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{2776697}{36864} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{5 \, {\left(424596 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 2828550 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 21565510 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 26086815 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 45375675 \, \sqrt{3} x + 10164786 \, \sqrt{3} - 45375675 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{1536 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{3}}"," ",0,"-1/30720*(2*(12*(18*(24*x - 175)*x + 4661)*x - 218885)*x + 1563313)*sqrt(3*x^2 + 5*x + 2) - 59745/1024*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 2776697/36864*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 5/1536*(424596*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 2828550*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 21565510*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 26086815*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 45375675*sqrt(3)*x + 10164786*sqrt(3) - 45375675*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^3","B",0
2456,1,636,0,1.309166," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^5,x, algorithm=""giac"")","\frac{744275}{12288} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}{{\left| 2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{2 \, \sqrt{5}}{2 \, x + 3} \right|}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{192171}{4096} \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1}{4096} \, {\left(\frac{5 \, {\left(\frac{50 \, {\left(\frac{13 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2 \, x + 3} - 88 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} + 14343 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)}}{2 \, x + 3} - 181996 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)\right)} \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} - \frac{479709 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 499296 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 3133183 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 3365712 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 7550211 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 8139744 \, \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - 6574257 \, {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + 6966000 \, \sqrt{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}{2048 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)}^{2} - 3\right)}^{4}}"," ",0,"744275/12288*sqrt(3)*log(abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3))/abs(2*sqrt(3) + 2*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + 2*sqrt(5)/(2*x + 3)))*sgn(1/(2*x + 3)) - 192171/4096*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))*sgn(1/(2*x + 3)) - 1/4096*(5*(50*(13*sgn(1/(2*x + 3))/(2*x + 3) - 88*sgn(1/(2*x + 3)))/(2*x + 3) + 14343*sgn(1/(2*x + 3)))/(2*x + 3) - 181996*sgn(1/(2*x + 3)))*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) - 1/2048*(479709*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^7*sgn(1/(2*x + 3)) - 499296*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^6*sgn(1/(2*x + 3)) - 3133183*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^5*sgn(1/(2*x + 3)) + 3365712*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^4*sgn(1/(2*x + 3)) + 7550211*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^3*sgn(1/(2*x + 3)) - 8139744*sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2*sgn(1/(2*x + 3)) - 6574257*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))*sgn(1/(2*x + 3)) + 6966000*sqrt(5)*sgn(1/(2*x + 3)))/((sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3))^2 - 3)^4","B",0
2457,1,417,0,0.366596," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^6,x, algorithm=""giac"")","-\frac{3}{512} \, {\left(2 \, {\left(12 \, x - 157\right)} x + 2067\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{2345091}{102400} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{30275}{1024} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{60397264 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 739203704 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 11836231432 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 36096211012 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 207702455456 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 259725515674 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 635418284542 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 326158305587 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 287216072451 \, \sqrt{3} x + 36785380096 \, \sqrt{3} - 287216072451 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{10240 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{5}}"," ",0,"-3/512*(2*(12*x - 157)*x + 2067)*sqrt(3*x^2 + 5*x + 2) - 2345091/102400*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 30275/1024*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 1/10240*(60397264*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 739203704*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 11836231432*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 36096211012*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 207702455456*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 259725515674*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 635418284542*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 326158305587*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 287216072451*sqrt(3)*x + 36785380096*sqrt(3) - 287216072451*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^5","B",0
2458,1,467,0,0.387098," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^7,x, algorithm=""giac"")","-\frac{9}{512} \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x - 121\right)} + \frac{6620481}{1024000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{8547}{1024} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{\sqrt{3} {\left(1761054624 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 78359519088 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 522182992240 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 6180007168800 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 16013156565600 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 85756996584864 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 107556795368496 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 284279833881720 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 172447244925750 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 205883289380025 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 48408731804817 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 15295619190024\right)}}{921600 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{6}}"," ",0,"-9/512*sqrt(3*x^2 + 5*x + 2)*(6*x - 121) + 6620481/1024000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 8547/1024*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 1/921600*sqrt(3)*(1761054624*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 78359519088*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 522182992240*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 6180007168800*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 16013156565600*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 85756996584864*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 107556795368496*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 284279833881720*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 172447244925750*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 205883289380025*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 48408731804817*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 15295619190024)/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^6","B",0
2459,1,509,0,0.410872," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^8,x, algorithm=""giac"")","-\frac{934161}{1024000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{603}{512} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{27}{256} \, \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{2310353472 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 39459777504 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 930047331808 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 4439192854544 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 42996771835920 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 98991221694624 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 500967391220544 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 626374342937616 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 1740466332835804 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 1179088946690970 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 1703610278292706 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 552456024942507 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 324453464706399 \, \sqrt{3} x + 28970271150072 \, \sqrt{3} - 324453464706399 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{716800 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{7}}"," ",0,"-934161/1024000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 603/512*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 27/256*sqrt(3*x^2 + 5*x + 2) - 1/716800*(2310353472*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 39459777504*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 930047331808*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 4439192854544*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 42996771835920*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 98991221694624*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 500967391220544*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 626374342937616*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 1740466332835804*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 1179088946690970*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 1703610278292706*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 552456024942507*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 324453464706399*sqrt(3)*x + 28970271150072*sqrt(3) - 324453464706399*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^7","B",0
2460,1,546,0,0.508811," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^9,x, algorithm=""giac"")","\frac{1673211}{40960000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{27}{512} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{25982914944 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} + 475461282240 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} + 12329944383680 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 66497191380480 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 747738478510240 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 2056338758898032 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} + 12823219634258640 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 20470141041874560 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 75774797457107080 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 72179382871515780 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 157788604924552196 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 86325470670757920 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 102935771527447390 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 28057073003987265 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 14067886443441495 \, \sqrt{3} x + 1086949713645432 \, \sqrt{3} - 14067886443441495 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{28672000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{8}}"," ",0,"1673211/40960000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 27/512*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 1/28672000*(25982914944*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 + 475461282240*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 + 12329944383680*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 66497191380480*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 747738478510240*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 2056338758898032*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 12823219634258640*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 20470141041874560*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 75774797457107080*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 72179382871515780*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 157788604924552196*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 86325470670757920*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 102935771527447390*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 28057073003987265*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 14067886443441495*sqrt(3)*x + 1086949713645432*sqrt(3) - 14067886443441495*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^8","B",0
2461,1,563,0,0.376115," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^10,x, algorithm=""giac"")","\frac{329}{204800000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{14930678016 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{17} + 204061569408 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{16} + 3866707486848 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} + 14840812733760 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} + 114102022608000 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} + 198779998219488 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} + 649357338634272 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} + 207317438979984 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} - 2217334591351040 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} - 5247913396815000 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} - 20151247122371016 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 17924557725783828 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 35125577732048328 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 16953161853593070 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 17752204726475250 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 4253745315948057 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 1882391465118753 \, \sqrt{3} x - 129047626217736 \, \sqrt{3} + 1882391465118753 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{184320000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{9}}"," ",0,"329/204800000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/184320000*(14930678016*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^17 + 204061569408*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^16 + 3866707486848*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 + 14840812733760*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 + 114102022608000*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 198779998219488*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 649357338634272*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 + 207317438979984*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 - 2217334591351040*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 - 5247913396815000*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 - 20151247122371016*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 17924557725783828*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 35125577732048328*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 16953161853593070*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 17752204726475250*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 4253745315948057*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 1882391465118753*sqrt(3)*x - 129047626217736*sqrt(3) + 1882391465118753*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^9","B",0
2462,1,614,0,0.406760," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^11,x, algorithm=""giac"")","\frac{13251}{10240000000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{6784512 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{19} + 83137358592 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{18} + 2689605043456 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{17} + 9174489217536 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{16} - 53080570863872 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} - 898783135722624 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} - 13174687008250752 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} - 40507172795248512 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} - 270169596727110016 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} - 458790099197766656 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} - 1833183533173743552 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} - 1939024456450048032 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} - 4903074367120921776 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 3280073192617110456 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 5164856211259534888 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 2082844158764403144 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 1869656136275991262 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 391066159205340747 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 153124376229353121 \, \sqrt{3} x - 9387541838830536 \, \sqrt{3} + 153124376229353121 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{1024000000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{10}}"," ",0,"13251/10240000000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/1024000000*(6784512*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^19 + 83137358592*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^18 + 2689605043456*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^17 + 9174489217536*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^16 - 53080570863872*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 - 898783135722624*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 - 13174687008250752*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 - 40507172795248512*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 - 270169596727110016*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 - 458790099197766656*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 - 1833183533173743552*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 - 1939024456450048032*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 - 4903074367120921776*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 3280073192617110456*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 5164856211259534888*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 2082844158764403144*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 1869656136275991262*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 391066159205340747*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 153124376229353121*sqrt(3)*x - 9387541838830536*sqrt(3) + 153124376229353121*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^10","B",0
2463,1,665,0,0.381456," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^12,x, algorithm=""giac"")","\frac{53697}{51200000000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{1814529024 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{21} + 57157664256 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{20} + 57290941171200 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{19} + 557490020440320 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{18} + 3116590396465920 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{17} - 40571342658595584 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{16} - 1098653419392131328 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} - 4929229513296950400 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} - 44860439685628251520 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} - 101067124429527527040 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} - 530008429621517017088 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} - 735944911884403670592 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} - 2465807894359584887200 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} - 2226326899649908579920 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} - 4870616002552398497520 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 2849658548882889760632 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 3959763769847021107884 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 1420163541040959876150 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 1141537424727199856070 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 215130617786249721765 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 76323347715579462729 \, \sqrt{3} x - 4261520459402725896 \, \sqrt{3} + 76323347715579462729 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{168960000000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{11}}"," ",0,"53697/51200000000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/168960000000*(1814529024*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^21 + 57157664256*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^20 + 57290941171200*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^19 + 557490020440320*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^18 + 3116590396465920*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^17 - 40571342658595584*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^16 - 1098653419392131328*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 - 4929229513296950400*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 - 44860439685628251520*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 - 101067124429527527040*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 - 530008429621517017088*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 - 735944911884403670592*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 - 2465807894359584887200*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 - 2226326899649908579920*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 - 4870616002552398497520*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 2849658548882889760632*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 3959763769847021107884*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 1420163541040959876150*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 1141537424727199856070*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 215130617786249721765*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 76323347715579462729*sqrt(3)*x - 4261520459402725896*sqrt(3) + 76323347715579462729*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^11","B",0
2464,1,716,0,0.543051," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^13,x, algorithm=""giac"")","\frac{175119}{204800000000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{11835242496 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{23} + 408315866112 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{22} + 20039038086144 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{21} + 535243596890112 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{20} + 13859706456921600 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{19} + 31535346744025344 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{18} - 789031961976842496 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{17} - 7977976824329385984 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{16} - 113078650509677476096 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{15} - 358779889050339715200 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{14} - 2538162771649151164032 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{13} - 4660243350382625915904 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{12} - 20499122524155108829248 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{11} - 24347916060701730772704 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{10} - 70788415443572756925600 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} - 56076083911431114398208 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} - 108598043564223524909928 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} - 56663550021725424101412 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} - 70668287639831997261828 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} - 22876037084903247115200 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} - 16680770211437743348146 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} - 2864949797863813201587 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} - 930278306769206446269 \, \sqrt{3} x - 47729262032858665512 \, \sqrt{3} + 930278306769206446269 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{675840000000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{12}}"," ",0,"175119/204800000000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/675840000000*(11835242496*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^23 + 408315866112*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^22 + 20039038086144*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^21 + 535243596890112*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^20 + 13859706456921600*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^19 + 31535346744025344*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^18 - 789031961976842496*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^17 - 7977976824329385984*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^16 - 113078650509677476096*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^15 - 358779889050339715200*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^14 - 2538162771649151164032*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 - 4660243350382625915904*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 - 20499122524155108829248*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^11 - 24347916060701730772704*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 - 70788415443572756925600*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 - 56076083911431114398208*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 - 108598043564223524909928*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 - 56663550021725424101412*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 70668287639831997261828*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 22876037084903247115200*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 - 16680770211437743348146*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 2864949797863813201587*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 930278306769206446269*sqrt(3)*x - 47729262032858665512*sqrt(3) + 930278306769206446269*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^12","B",0
2465,1,412,0,0.295253," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(\frac{6 \, B x e^{3}}{c} + \frac{24 \, B c^{3} d e^{2} - 7 \, B b c^{2} e^{3} + 8 \, A c^{3} e^{3}}{c^{4}}\right)} x + \frac{144 \, B c^{3} d^{2} e - 120 \, B b c^{2} d e^{2} + 144 \, A c^{3} d e^{2} + 35 \, B b^{2} c e^{3} - 36 \, B a c^{2} e^{3} - 40 \, A b c^{2} e^{3}}{c^{4}}\right)} x + \frac{192 \, B c^{3} d^{3} - 432 \, B b c^{2} d^{2} e + 576 \, A c^{3} d^{2} e + 360 \, B b^{2} c d e^{2} - 384 \, B a c^{2} d e^{2} - 432 \, A b c^{2} d e^{2} - 105 \, B b^{3} e^{3} + 220 \, B a b c e^{3} + 120 \, A b^{2} c e^{3} - 128 \, A a c^{2} e^{3}}{c^{4}}\right)} + \frac{{\left(64 \, B b c^{3} d^{3} - 128 \, A c^{4} d^{3} - 144 \, B b^{2} c^{2} d^{2} e + 192 \, B a c^{3} d^{2} e + 192 \, A b c^{3} d^{2} e + 120 \, B b^{3} c d e^{2} - 288 \, B a b c^{2} d e^{2} - 144 \, A b^{2} c^{2} d e^{2} + 192 \, A a c^{3} d e^{2} - 35 \, B b^{4} e^{3} + 120 \, B a b^{2} c e^{3} + 40 \, A b^{3} c e^{3} - 48 \, B a^{2} c^{2} e^{3} - 96 \, A a b c^{2} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*B*x*e^3/c + (24*B*c^3*d*e^2 - 7*B*b*c^2*e^3 + 8*A*c^3*e^3)/c^4)*x + (144*B*c^3*d^2*e - 120*B*b*c^2*d*e^2 + 144*A*c^3*d*e^2 + 35*B*b^2*c*e^3 - 36*B*a*c^2*e^3 - 40*A*b*c^2*e^3)/c^4)*x + (192*B*c^3*d^3 - 432*B*b*c^2*d^2*e + 576*A*c^3*d^2*e + 360*B*b^2*c*d*e^2 - 384*B*a*c^2*d*e^2 - 432*A*b*c^2*d*e^2 - 105*B*b^3*e^3 + 220*B*a*b*c*e^3 + 120*A*b^2*c*e^3 - 128*A*a*c^2*e^3)/c^4) + 1/128*(64*B*b*c^3*d^3 - 128*A*c^4*d^3 - 144*B*b^2*c^2*d^2*e + 192*B*a*c^3*d^2*e + 192*A*b*c^3*d^2*e + 120*B*b^3*c*d*e^2 - 288*B*a*b*c^2*d*e^2 - 144*A*b^2*c^2*d*e^2 + 192*A*a*c^3*d*e^2 - 35*B*b^4*e^3 + 120*B*a*b^2*c*e^3 + 40*A*b^3*c*e^3 - 48*B*a^2*c^2*e^3 - 96*A*a*b*c^2*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
2466,1,231,0,0.262671," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(\frac{4 \, B x e^{2}}{c} + \frac{12 \, B c^{2} d e - 5 \, B b c e^{2} + 6 \, A c^{2} e^{2}}{c^{3}}\right)} x + \frac{24 \, B c^{2} d^{2} - 36 \, B b c d e + 48 \, A c^{2} d e + 15 \, B b^{2} e^{2} - 16 \, B a c e^{2} - 18 \, A b c e^{2}}{c^{3}}\right)} + \frac{{\left(8 \, B b c^{2} d^{2} - 16 \, A c^{3} d^{2} - 12 \, B b^{2} c d e + 16 \, B a c^{2} d e + 16 \, A b c^{2} d e + 5 \, B b^{3} e^{2} - 12 \, B a b c e^{2} - 6 \, A b^{2} c e^{2} + 8 \, A a c^{2} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*(4*B*x*e^2/c + (12*B*c^2*d*e - 5*B*b*c*e^2 + 6*A*c^2*e^2)/c^3)*x + (24*B*c^2*d^2 - 36*B*b*c*d*e + 48*A*c^2*d*e + 15*B*b^2*e^2 - 16*B*a*c*e^2 - 18*A*b*c*e^2)/c^3) + 1/16*(8*B*b*c^2*d^2 - 16*A*c^3*d^2 - 12*B*b^2*c*d*e + 16*B*a*c^2*d*e + 16*A*b*c^2*d*e + 5*B*b^3*e^2 - 12*B*a*b*c*e^2 - 6*A*b^2*c*e^2 + 8*A*a*c^2*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
2467,1,119,0,0.248527," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(\frac{2 \, B x e}{c} + \frac{4 \, B c d - 3 \, B b e + 4 \, A c e}{c^{2}}\right)} + \frac{{\left(4 \, B b c d - 8 \, A c^{2} d - 3 \, B b^{2} e + 4 \, B a c e + 4 \, A b c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*B*x*e/c + (4*B*c*d - 3*B*b*e + 4*A*c*e)/c^2) + 1/8*(4*B*b*c*d - 8*A*c^2*d - 3*B*b^2*e + 4*B*a*c*e + 4*A*b*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
2468,1,62,0,0.236760," ","integrate((B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x + a} B}{c} + \frac{{\left(B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"sqrt(c*x^2 + b*x + a)*B/c + 1/2*(B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
2469,-2,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2470,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2471,1,1476,0,0.392158," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, B b c d^{2} - 8 \, A c^{2} d^{2} - B b^{2} d e - 12 \, B a c d e + 8 \, A b c d e + 4 \, B a b e^{2} - 3 \, A b^{2} e^{2} + 4 \, A a c e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B c^{\frac{5}{2}} d^{4} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b c^{\frac{3}{2}} d^{3} e - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A c^{\frac{5}{2}} d^{3} e + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b c^{2} d^{4} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b c d^{2} e^{2} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A c^{2} d^{2} e^{2} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a c^{2} d^{3} e - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b c^{2} d^{3} e + 2 \, B b^{2} c^{\frac{3}{2}} d^{4} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b^{2} \sqrt{c} d^{2} e^{2} - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a c^{\frac{3}{2}} d^{2} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b c^{\frac{3}{2}} d^{2} e^{2} + B b^{3} \sqrt{c} d^{3} e - 8 \, B a b c^{\frac{3}{2}} d^{3} e - 6 \, A b^{2} c^{\frac{3}{2}} d^{3} e - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b^{2} d e^{3} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a c d e^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b c d e^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b^{3} d^{2} e^{2} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b c d^{2} e^{2} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{2} c d^{2} e^{2} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a c^{2} d^{2} e^{2} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a b \sqrt{c} d e^{3} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b^{2} \sqrt{c} d e^{3} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a c^{\frac{3}{2}} d e^{3} - 5 \, B a b^{2} \sqrt{c} d^{2} e^{2} + 3 \, A b^{3} \sqrt{c} d^{2} e^{2} + 4 \, B a^{2} c^{\frac{3}{2}} d^{2} e^{2} + 20 \, A a b c^{\frac{3}{2}} d^{2} e^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b e^{4} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} e^{4} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c e^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b^{2} d e^{3} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{3} d e^{3} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} c d e^{3} - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b c d e^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} \sqrt{c} e^{4} + 12 \, B a^{2} b \sqrt{c} d e^{3} - 11 \, A a b^{2} \sqrt{c} d e^{3} - 12 \, A a^{2} c^{\frac{3}{2}} d e^{3} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b e^{4} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} e^{4} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c e^{4} - 8 \, B a^{3} \sqrt{c} e^{4} + 8 \, A a^{2} b \sqrt{c} e^{4}}{4 \, {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3} + 2 \, a c d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{2}}"," ",0,"-1/4*(4*B*b*c*d^2 - 8*A*c^2*d^2 - B*b^2*d*e - 12*B*a*c*d*e + 8*A*b*c*d*e + 4*B*a*b*e^2 - 3*A*b^2*e^2 + 4*A*a*c*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*c^(5/2)*d^4 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b*c^(3/2)*d^3*e - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*c^(5/2)*d^3*e + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b*c^2*d^4 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b*c*d^2*e^2 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*c^2*d^2*e^2 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*c^2*d^3*e - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b*c^2*d^3*e + 2*B*b^2*c^(3/2)*d^4 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b^2*sqrt(c)*d^2*e^2 - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*c^(3/2)*d^2*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b*c^(3/2)*d^2*e^2 + B*b^3*sqrt(c)*d^3*e - 8*B*a*b*c^(3/2)*d^3*e - 6*A*b^2*c^(3/2)*d^3*e - (sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b^2*d*e^3 - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*c*d*e^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b*c*d*e^3 + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b^3*d^2*e^2 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b*c*d^2*e^2 + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^2*c*d^2*e^2 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*c^2*d^2*e^2 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*b*sqrt(c)*d*e^3 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b^2*sqrt(c)*d*e^3 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*c^(3/2)*d*e^3 - 5*B*a*b^2*sqrt(c)*d^2*e^2 + 3*A*b^3*sqrt(c)*d^2*e^2 + 4*B*a^2*c^(3/2)*d^2*e^2 + 20*A*a*b*c^(3/2)*d^2*e^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b*e^4 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2*e^4 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c*e^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b^2*d*e^3 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^3*d*e^3 + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*c*d*e^3 - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b*c*d*e^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*sqrt(c)*e^4 + 12*B*a^2*b*sqrt(c)*d*e^3 - 11*A*a*b^2*sqrt(c)*d*e^3 - 12*A*a^2*c^(3/2)*d*e^3 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b*e^4 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2*e^4 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c*e^4 - 8*B*a^3*sqrt(c)*e^4 + 8*A*a^2*b*sqrt(c)*e^4)/((c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3 + 2*a*c*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^2)","B",0
2472,1,4249,0,0.744154," ","integrate((B*x+A)/(e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(8 \, B b c^{2} d^{3} - 16 \, A c^{3} d^{3} - 4 \, B b^{2} c d^{2} e - 32 \, B a c^{2} d^{2} e + 24 \, A b c^{2} d^{2} e + B b^{3} d e^{2} + 20 \, B a b c d e^{2} - 18 \, A b^{2} c d e^{2} + 24 \, A a c^{2} d e^{2} - 6 \, B a b^{2} e^{3} + 5 \, A b^{3} e^{3} + 8 \, B a^{2} c e^{3} - 12 \, A a b c e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{8 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B c^{4} d^{6} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b c^{3} d^{5} e - 352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A c^{4} d^{5} e + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b c^{\frac{7}{2}} d^{6} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B b c^{\frac{5}{2}} d^{4} e^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A c^{\frac{7}{2}} d^{4} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b^{2} c^{\frac{5}{2}} d^{5} e - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a c^{\frac{7}{2}} d^{5} e - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b c^{\frac{7}{2}} d^{5} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b^{2} c^{3} d^{6} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B b c^{2} d^{3} e^{3} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A c^{3} d^{3} e^{3} + 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b^{2} c^{2} d^{4} e^{2} - 512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a c^{3} d^{4} e^{2} + 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b c^{3} d^{4} e^{2} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b^{3} c^{2} d^{5} e - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b c^{3} d^{5} e - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{2} c^{3} d^{5} e + 8 \, B b^{3} c^{\frac{5}{2}} d^{6} - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B b^{2} c^{\frac{3}{2}} d^{3} e^{3} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a c^{\frac{5}{2}} d^{3} e^{3} + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A b c^{\frac{5}{2}} d^{3} e^{3} + 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b^{3} c^{\frac{3}{2}} d^{4} e^{2} - 696 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a b c^{\frac{5}{2}} d^{4} e^{2} + 756 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b^{2} c^{\frac{5}{2}} d^{4} e^{2} + 816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a c^{\frac{7}{2}} d^{4} e^{2} + 10 \, B b^{4} c^{\frac{3}{2}} d^{5} e - 48 \, B a b^{2} c^{\frac{5}{2}} d^{5} e - 44 \, A b^{3} c^{\frac{5}{2}} d^{5} e - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B b^{2} c d^{2} e^{4} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a c^{2} d^{2} e^{4} + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b c^{2} d^{2} e^{4} - 74 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b^{3} c d^{3} e^{3} - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b c^{2} d^{3} e^{3} - 204 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} c^{2} d^{3} e^{3} + 656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c^{3} d^{3} e^{3} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b^{4} c d^{4} e^{2} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b^{2} c^{2} d^{4} e^{2} + 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{3} c^{2} d^{4} e^{2} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} c^{3} d^{4} e^{2} + 816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b c^{3} d^{4} e^{2} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B b^{3} \sqrt{c} d^{2} e^{4} + 300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a b c^{\frac{3}{2}} d^{2} e^{4} - 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A b^{2} c^{\frac{3}{2}} d^{2} e^{4} + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a c^{\frac{5}{2}} d^{2} e^{4} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b^{4} \sqrt{c} d^{3} e^{3} + 252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a b^{2} c^{\frac{3}{2}} d^{3} e^{3} - 498 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b^{3} c^{\frac{3}{2}} d^{3} e^{3} + 816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} c^{\frac{5}{2}} d^{3} e^{3} - 648 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b c^{\frac{5}{2}} d^{3} e^{3} - 3 \, B b^{5} \sqrt{c} d^{4} e^{2} - 70 \, B a b^{3} c^{\frac{3}{2}} d^{4} e^{2} + 44 \, A b^{4} c^{\frac{3}{2}} d^{4} e^{2} + 48 \, B a^{2} b c^{\frac{5}{2}} d^{4} e^{2} + 204 \, A a b^{2} c^{\frac{5}{2}} d^{4} e^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B b^{3} d e^{5} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a b c d e^{5} - 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b^{2} c d e^{5} + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a c^{2} d e^{5} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b^{4} d^{2} e^{4} + 252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b^{2} c d^{2} e^{4} - 34 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{3} c d^{2} e^{4} + 624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} c^{2} d^{2} e^{4} - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b c^{2} d^{2} e^{4} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b^{5} d^{3} e^{3} + 186 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b^{3} c d^{3} e^{3} - 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{4} c d^{3} e^{3} + 864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b c^{2} d^{3} e^{3} - 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} c^{2} d^{3} e^{3} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c^{3} d^{3} e^{3} - 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a b^{2} \sqrt{c} d e^{5} + 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A b^{3} \sqrt{c} d e^{5} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} B a^{2} c^{\frac{3}{2}} d e^{5} - 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} A a b c^{\frac{3}{2}} d e^{5} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a b^{3} \sqrt{c} d^{2} e^{4} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b^{4} \sqrt{c} d^{2} e^{4} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} b c^{\frac{3}{2}} d^{2} e^{4} + 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b^{2} c^{\frac{3}{2}} d^{2} e^{4} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{2} c^{\frac{5}{2}} d^{2} e^{4} + 24 \, B a b^{4} \sqrt{c} d^{3} e^{3} - 15 \, A b^{5} \sqrt{c} d^{3} e^{3} + 240 \, B a^{2} b^{2} c^{\frac{3}{2}} d^{3} e^{3} - 206 \, A a b^{3} c^{\frac{3}{2}} d^{3} e^{3} - 16 \, B a^{3} c^{\frac{5}{2}} d^{3} e^{3} - 240 \, A a^{2} b c^{\frac{5}{2}} d^{3} e^{3} - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a b^{2} e^{6} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A b^{3} e^{6} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} B a^{2} c e^{6} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} A a b c e^{6} - 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b^{3} d e^{5} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{4} d e^{5} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} b c d e^{5} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{2} c d e^{5} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} c^{2} d e^{5} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b^{4} d^{2} e^{4} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{5} d^{2} e^{4} - 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b^{2} c d^{2} e^{4} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{3} c d^{2} e^{4} - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} c^{2} d^{2} e^{4} + 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b c^{2} d^{2} e^{4} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b^{3} \sqrt{c} d e^{5} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} c^{\frac{3}{2}} d e^{5} - 87 \, B a^{2} b^{3} \sqrt{c} d^{2} e^{4} + 78 \, A a b^{4} \sqrt{c} d^{2} e^{4} - 284 \, B a^{3} b c^{\frac{3}{2}} d^{2} e^{4} + 222 \, A a^{2} b^{2} c^{\frac{3}{2}} d^{2} e^{4} + 88 \, A a^{3} c^{\frac{5}{2}} d^{2} e^{4} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a^{2} b^{2} e^{6} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a b^{3} e^{6} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a^{2} b c e^{6} + 57 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b^{3} d e^{5} - 66 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{4} d e^{5} + 276 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b c d e^{5} - 306 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{2} c d e^{5} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} c^{2} d e^{5} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{3} b \sqrt{c} e^{6} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a^{3} c^{\frac{3}{2}} e^{6} + 114 \, B a^{3} b^{2} \sqrt{c} d e^{5} - 111 \, A a^{2} b^{3} \sqrt{c} d e^{5} + 104 \, B a^{4} c^{\frac{3}{2}} d e^{5} - 28 \, A a^{3} b c^{\frac{3}{2}} d e^{5} - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{3} b^{2} e^{6} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} b^{3} e^{6} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{4} c e^{6} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{3} b c e^{6} - 48 \, B a^{4} b \sqrt{c} e^{6} + 48 \, A a^{3} b^{2} \sqrt{c} e^{6} - 32 \, A a^{4} c^{\frac{3}{2}} e^{6}}{24 \, {\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{3}}"," ",0,"-1/8*(8*B*b*c^2*d^3 - 16*A*c^3*d^3 - 4*B*b^2*c*d^2*e - 32*B*a*c^2*d^2*e + 24*A*b*c^2*d^2*e + B*b^3*d*e^2 + 20*B*a*b*c*d*e^2 - 18*A*b^2*c*d*e^2 + 24*A*a*c^2*d*e^2 - 6*B*a*b^2*e^3 + 5*A*b^3*e^3 + 8*B*a^2*c*e^3 - 12*A*a*b*c*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/24*(64*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*c^4*d^6 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b*c^3*d^5*e - 352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*c^4*d^5*e + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b*c^(7/2)*d^6 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*b*c^(5/2)*d^4*e^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*c^(7/2)*d^4*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b^2*c^(5/2)*d^5*e - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*c^(7/2)*d^5*e - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b*c^(7/2)*d^5*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b^2*c^3*d^6 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*b*c^2*d^3*e^3 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*c^3*d^3*e^3 + 168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b^2*c^2*d^4*e^2 - 512*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*c^3*d^4*e^2 + 400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b*c^3*d^4*e^2 + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b^3*c^2*d^5*e - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b*c^3*d^5*e - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^2*c^3*d^5*e + 8*B*b^3*c^(5/2)*d^6 - 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*b^2*c^(3/2)*d^3*e^3 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a*c^(5/2)*d^3*e^3 + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*b*c^(5/2)*d^3*e^3 + 54*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b^3*c^(3/2)*d^4*e^2 - 696*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*b*c^(5/2)*d^4*e^2 + 756*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b^2*c^(5/2)*d^4*e^2 + 816*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*c^(7/2)*d^4*e^2 + 10*B*b^4*c^(3/2)*d^5*e - 48*B*a*b^2*c^(5/2)*d^5*e - 44*A*b^3*c^(5/2)*d^5*e - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*b^2*c*d^2*e^4 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*c^2*d^2*e^4 + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b*c^2*d^2*e^4 - 74*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b^3*c*d^3*e^3 - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b*c^2*d^3*e^3 - 204*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2*c^2*d^3*e^3 + 656*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c^3*d^3*e^3 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b^4*c*d^4*e^2 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b^2*c^2*d^4*e^2 + 336*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^3*c^2*d^4*e^2 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*c^3*d^4*e^2 + 816*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b*c^3*d^4*e^2 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*b^3*sqrt(c)*d^2*e^4 + 300*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a*b*c^(3/2)*d^2*e^4 - 270*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*b^2*c^(3/2)*d^2*e^4 + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a*c^(5/2)*d^2*e^4 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b^4*sqrt(c)*d^3*e^3 + 252*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*b^2*c^(3/2)*d^3*e^3 - 498*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b^3*c^(3/2)*d^3*e^3 + 816*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*c^(5/2)*d^3*e^3 - 648*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b*c^(5/2)*d^3*e^3 - 3*B*b^5*sqrt(c)*d^4*e^2 - 70*B*a*b^3*c^(3/2)*d^4*e^2 + 44*A*b^4*c^(3/2)*d^4*e^2 + 48*B*a^2*b*c^(5/2)*d^4*e^2 + 204*A*a*b^2*c^(5/2)*d^4*e^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*b^3*d*e^5 + 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*b*c*d*e^5 - 54*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b^2*c*d*e^5 + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*c^2*d*e^5 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b^4*d^2*e^4 + 252*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b^2*c*d^2*e^4 - 34*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^3*c*d^2*e^4 + 624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*c^2*d^2*e^4 - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b*c^2*d^2*e^4 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b^5*d^3*e^3 + 186*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b^3*c*d^3*e^3 - 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^4*c*d^3*e^3 + 864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b*c^2*d^3*e^3 - 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2*c^2*d^3*e^3 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c^3*d^3*e^3 - 90*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a*b^2*sqrt(c)*d*e^5 + 75*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*b^3*sqrt(c)*d*e^5 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*B*a^2*c^(3/2)*d*e^5 - 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*A*a*b*c^(3/2)*d*e^5 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*b^3*sqrt(c)*d^2*e^4 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b^4*sqrt(c)*d^2*e^4 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*b*c^(3/2)*d^2*e^4 + 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b^2*c^(3/2)*d^2*e^4 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^2*c^(5/2)*d^2*e^4 + 24*B*a*b^4*sqrt(c)*d^3*e^3 - 15*A*b^5*sqrt(c)*d^3*e^3 + 240*B*a^2*b^2*c^(3/2)*d^3*e^3 - 206*A*a*b^3*c^(3/2)*d^3*e^3 - 16*B*a^3*c^(5/2)*d^3*e^3 - 240*A*a^2*b*c^(5/2)*d^3*e^3 - 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a*b^2*e^6 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*b^3*e^6 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*B*a^2*c*e^6 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*A*a*b*c*e^6 - 56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b^3*d*e^5 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^4*d*e^5 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*b*c*d*e^5 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^2*c*d*e^5 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*c^2*d*e^5 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b^4*d^2*e^4 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^5*d^2*e^4 - 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b^2*c*d^2*e^4 + 450*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^3*c*d^2*e^4 - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*c^2*d^2*e^4 + 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b*c^2*d^2*e^4 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b^3*sqrt(c)*d*e^5 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*c^(3/2)*d*e^5 - 87*B*a^2*b^3*sqrt(c)*d^2*e^4 + 78*A*a*b^4*sqrt(c)*d^2*e^4 - 284*B*a^3*b*c^(3/2)*d^2*e^4 + 222*A*a^2*b^2*c^(3/2)*d^2*e^4 + 88*A*a^3*c^(5/2)*d^2*e^4 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a^2*b^2*e^6 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*b^3*e^6 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a^2*b*c*e^6 + 57*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b^3*d*e^5 - 66*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^4*d*e^5 + 276*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b*c*d*e^5 - 306*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^2*c*d*e^5 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*c^2*d*e^5 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^3*b*sqrt(c)*e^6 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a^3*c^(3/2)*e^6 + 114*B*a^3*b^2*sqrt(c)*d*e^5 - 111*A*a^2*b^3*sqrt(c)*d*e^5 + 104*B*a^4*c^(3/2)*d*e^5 - 28*A*a^3*b*c^(3/2)*d*e^5 - 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^3*b^2*e^6 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*b^3*e^6 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^4*c*e^6 + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^3*b*c*e^6 - 48*B*a^4*b*sqrt(c)*e^6 + 48*A*a^3*b^2*sqrt(c)*e^6 - 32*A*a^4*c^(3/2)*e^6)/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^3)","B",0
2473,1,530,0,0.328955," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, {\left(B b^{2} c^{2} e^{3} - 4 \, B a c^{3} e^{3}\right)} x}{b^{2} c^{3} - 4 \, a c^{4}} + \frac{12 \, B b^{2} c^{2} d e^{2} - 48 \, B a c^{3} d e^{2} - 5 \, B b^{3} c e^{3} + 20 \, B a b c^{2} e^{3} + 4 \, A b^{2} c^{2} e^{3} - 16 \, A a c^{3} e^{3}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x + \frac{8 \, B b c^{3} d^{3} - 16 \, A c^{4} d^{3} - 24 \, B b^{2} c^{2} d^{2} e + 48 \, B a c^{3} d^{2} e + 24 \, A b c^{3} d^{2} e + 36 \, B b^{3} c d e^{2} - 120 \, B a b c^{2} d e^{2} - 24 \, A b^{2} c^{2} d e^{2} + 48 \, A a c^{3} d e^{2} - 15 \, B b^{4} e^{3} + 62 \, B a b^{2} c e^{3} + 12 \, A b^{3} c e^{3} - 24 \, B a^{2} c^{2} e^{3} - 40 \, A a b c^{2} e^{3}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x + \frac{16 \, B a c^{3} d^{3} - 8 \, A b c^{3} d^{3} - 24 \, B a b c^{2} d^{2} e + 48 \, A a c^{3} d^{2} e + 36 \, B a b^{2} c d e^{2} - 96 \, B a^{2} c^{2} d e^{2} - 24 \, A a b c^{2} d e^{2} - 15 \, B a b^{3} e^{3} + 52 \, B a^{2} b c e^{3} + 12 \, A a b^{2} c e^{3} - 32 \, A a^{2} c^{2} e^{3}}{b^{2} c^{3} - 4 \, a c^{4}}}{4 \, \sqrt{c x^{2} + b x + a}} - \frac{3 \, {\left(8 \, B c^{2} d^{2} e - 12 \, B b c d e^{2} + 8 \, A c^{2} d e^{2} + 5 \, B b^{2} e^{3} - 4 \, B a c e^{3} - 4 \, A b c e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{7}{2}}}"," ",0,"1/4*(((2*(B*b^2*c^2*e^3 - 4*B*a*c^3*e^3)*x/(b^2*c^3 - 4*a*c^4) + (12*B*b^2*c^2*d*e^2 - 48*B*a*c^3*d*e^2 - 5*B*b^3*c*e^3 + 20*B*a*b*c^2*e^3 + 4*A*b^2*c^2*e^3 - 16*A*a*c^3*e^3)/(b^2*c^3 - 4*a*c^4))*x + (8*B*b*c^3*d^3 - 16*A*c^4*d^3 - 24*B*b^2*c^2*d^2*e + 48*B*a*c^3*d^2*e + 24*A*b*c^3*d^2*e + 36*B*b^3*c*d*e^2 - 120*B*a*b*c^2*d*e^2 - 24*A*b^2*c^2*d*e^2 + 48*A*a*c^3*d*e^2 - 15*B*b^4*e^3 + 62*B*a*b^2*c*e^3 + 12*A*b^3*c*e^3 - 24*B*a^2*c^2*e^3 - 40*A*a*b*c^2*e^3)/(b^2*c^3 - 4*a*c^4))*x + (16*B*a*c^3*d^3 - 8*A*b*c^3*d^3 - 24*B*a*b*c^2*d^2*e + 48*A*a*c^3*d^2*e + 36*B*a*b^2*c*d*e^2 - 96*B*a^2*c^2*d*e^2 - 24*A*a*b*c^2*d*e^2 - 15*B*a*b^3*e^3 + 52*B*a^2*b*c*e^3 + 12*A*a*b^2*c*e^3 - 32*A*a^2*c^2*e^3)/(b^2*c^3 - 4*a*c^4))/sqrt(c*x^2 + b*x + a) - 3/8*(8*B*c^2*d^2*e - 12*B*b*c*d*e^2 + 8*A*c^2*d*e^2 + 5*B*b^2*e^3 - 4*B*a*c*e^3 - 4*A*b*c*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
2474,1,294,0,0.305515," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{{\left(B b^{2} c e^{2} - 4 \, B a c^{2} e^{2}\right)} x}{b^{2} c^{2} - 4 \, a c^{3}} + \frac{2 \, B b c^{2} d^{2} - 4 \, A c^{3} d^{2} - 4 \, B b^{2} c d e + 8 \, B a c^{2} d e + 4 \, A b c^{2} d e + 3 \, B b^{3} e^{2} - 10 \, B a b c e^{2} - 2 \, A b^{2} c e^{2} + 4 \, A a c^{2} e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x + \frac{4 \, B a c^{2} d^{2} - 2 \, A b c^{2} d^{2} - 4 \, B a b c d e + 8 \, A a c^{2} d e + 3 \, B a b^{2} e^{2} - 8 \, B a^{2} c e^{2} - 2 \, A a b c e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}{\sqrt{c x^{2} + b x + a}} - \frac{{\left(4 \, B c d e - 3 \, B b e^{2} + 2 \, A c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"(((B*b^2*c*e^2 - 4*B*a*c^2*e^2)*x/(b^2*c^2 - 4*a*c^3) + (2*B*b*c^2*d^2 - 4*A*c^3*d^2 - 4*B*b^2*c*d*e + 8*B*a*c^2*d*e + 4*A*b*c^2*d*e + 3*B*b^3*e^2 - 10*B*a*b*c*e^2 - 2*A*b^2*c*e^2 + 4*A*a*c^2*e^2)/(b^2*c^2 - 4*a*c^3))*x + (4*B*a*c^2*d^2 - 2*A*b*c^2*d^2 - 4*B*a*b*c*d*e + 8*A*a*c^2*d*e + 3*B*a*b^2*e^2 - 8*B*a^2*c*e^2 - 2*A*a*b*c*e^2)/(b^2*c^2 - 4*a*c^3))/sqrt(c*x^2 + b*x + a) - 1/2*(4*B*c*d*e - 3*B*b*e^2 + 2*A*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
2475,1,147,0,0.318894," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{B e \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}} + \frac{2 \, {\left(\frac{{\left(B b c d - 2 \, A c^{2} d - B b^{2} e + 2 \, B a c e + A b c e\right)} x}{b^{2} c - 4 \, a c^{2}} + \frac{2 \, B a c d - A b c d - B a b e + 2 \, A a c e}{b^{2} c - 4 \, a c^{2}}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"-B*e*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2) + 2*((B*b*c*d - 2*A*c^2*d - B*b^2*e + 2*B*a*c*e + A*b*c*e)*x/(b^2*c - 4*a*c^2) + (2*B*a*c*d - A*b*c*d - B*a*b*e + 2*A*a*c*e)/(b^2*c - 4*a*c^2))/sqrt(c*x^2 + b*x + a)","A",0
2476,1,55,0,0.288189," ","integrate((B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B b - 2 \, A c\right)} x}{b^{2} - 4 \, a c} + \frac{2 \, B a - A b}{b^{2} - 4 \, a c}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"2*((B*b - 2*A*c)*x/(b^2 - 4*a*c) + (2*B*a - A*b)/(b^2 - 4*a*c))/sqrt(c*x^2 + b*x + a)","A",0
2477,1,568,0,0.306705," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B b c^{2} d^{3} - 2 \, A c^{3} d^{3} - B b^{2} c d^{2} e - 2 \, B a c^{2} d^{2} e + 3 \, A b c^{2} d^{2} e + 3 \, B a b c d e^{2} - A b^{2} c d e^{2} - 2 \, A a c^{2} d e^{2} - 2 \, B a^{2} c e^{3} + A a b c e^{3}\right)} x}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}} + \frac{2 \, B a c^{2} d^{3} - A b c^{2} d^{3} - 3 \, B a b c d^{2} e + 2 \, A b^{2} c d^{2} e - 2 \, A a c^{2} d^{2} e + B a b^{2} d e^{2} - A b^{3} d e^{2} + 2 \, B a^{2} c d e^{2} + A a b c d e^{2} - B a^{2} b e^{3} + A a b^{2} e^{3} - 2 \, A a^{2} c e^{3}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{2 \, {\left(B d e - A e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}}"," ",0,"2*((B*b*c^2*d^3 - 2*A*c^3*d^3 - B*b^2*c*d^2*e - 2*B*a*c^2*d^2*e + 3*A*b*c^2*d^2*e + 3*B*a*b*c*d*e^2 - A*b^2*c*d*e^2 - 2*A*a*c^2*d*e^2 - 2*B*a^2*c*e^3 + A*a*b*c*e^3)*x/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4) + (2*B*a*c^2*d^3 - A*b*c^2*d^3 - 3*B*a*b*c*d^2*e + 2*A*b^2*c*d^2*e - 2*A*a*c^2*d^2*e + B*a*b^2*d*e^2 - A*b^3*d*e^2 + 2*B*a^2*c*d*e^2 + A*a*b*c*d*e^2 - B*a^2*b*e^3 + A*a*b^2*e^3 - 2*A*a^2*c*e^3)/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4))/sqrt(c*x^2 + b*x + a) - 2*(B*d*e - A*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c*d^2 - b*d*e + a*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2))","B",0
2478,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2479,1,4002,0,0.858755," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(B b c^{6} d^{9} - 2 \, A c^{7} d^{9} - 3 \, B b^{2} c^{5} d^{8} e - 6 \, B a c^{6} d^{8} e + 9 \, A b c^{6} d^{8} e + 3 \, B b^{3} c^{4} d^{7} e^{2} + 24 \, B a b c^{5} d^{7} e^{2} - 18 \, A b^{2} c^{5} d^{7} e^{2} - B b^{4} c^{3} d^{6} e^{3} - 34 \, B a b^{2} c^{4} d^{6} e^{3} + 21 \, A b^{3} c^{4} d^{6} e^{3} - 16 \, B a^{2} c^{5} d^{6} e^{3} + 21 \, B a b^{3} c^{3} d^{5} e^{4} - 15 \, A b^{4} c^{3} d^{5} e^{4} + 42 \, B a^{2} b c^{4} d^{5} e^{4} - 6 \, A a b^{2} c^{4} d^{5} e^{4} + 12 \, A a^{2} c^{5} d^{5} e^{4} - 6 \, B a b^{4} c^{2} d^{4} e^{5} + 6 \, A b^{5} c^{2} d^{4} e^{5} - 36 \, B a^{2} b^{2} c^{3} d^{4} e^{5} + 15 \, A a b^{3} c^{3} d^{4} e^{5} - 12 \, B a^{3} c^{4} d^{4} e^{5} - 30 \, A a^{2} b c^{4} d^{4} e^{5} + B a b^{5} c d^{3} e^{6} - A b^{6} c d^{3} e^{6} + 13 \, B a^{2} b^{3} c^{2} d^{3} e^{6} - 12 \, A a b^{4} c^{2} d^{3} e^{6} + 16 \, B a^{3} b c^{3} d^{3} e^{6} + 18 \, A a^{2} b^{2} c^{3} d^{3} e^{6} + 16 \, A a^{3} c^{4} d^{3} e^{6} - 3 \, B a^{2} b^{4} c d^{2} e^{7} + 3 \, A a b^{5} c d^{2} e^{7} - 6 \, B a^{3} b^{2} c^{2} d^{2} e^{7} + 3 \, A a^{2} b^{3} c^{2} d^{2} e^{7} - 24 \, A a^{3} b c^{3} d^{2} e^{7} + 3 \, B a^{3} b^{3} c d e^{8} - 3 \, A a^{2} b^{4} c d e^{8} - 3 \, B a^{4} b c^{2} d e^{8} + 6 \, A a^{3} b^{2} c^{2} d e^{8} + 6 \, A a^{4} c^{3} d e^{8} - B a^{4} b^{2} c e^{9} + A a^{3} b^{3} c e^{9} + 2 \, B a^{5} c^{2} e^{9} - 3 \, A a^{4} b c^{2} e^{9}\right)} x}{b^{2} c^{6} d^{12} - 4 \, a c^{7} d^{12} - 6 \, b^{3} c^{5} d^{11} e + 24 \, a b c^{6} d^{11} e + 15 \, b^{4} c^{4} d^{10} e^{2} - 54 \, a b^{2} c^{5} d^{10} e^{2} - 24 \, a^{2} c^{6} d^{10} e^{2} - 20 \, b^{5} c^{3} d^{9} e^{3} + 50 \, a b^{3} c^{4} d^{9} e^{3} + 120 \, a^{2} b c^{5} d^{9} e^{3} + 15 \, b^{6} c^{2} d^{8} e^{4} - 225 \, a^{2} b^{2} c^{4} d^{8} e^{4} - 60 \, a^{3} c^{5} d^{8} e^{4} - 6 \, b^{7} c d^{7} e^{5} - 36 \, a b^{5} c^{2} d^{7} e^{5} + 180 \, a^{2} b^{3} c^{3} d^{7} e^{5} + 240 \, a^{3} b c^{4} d^{7} e^{5} + b^{8} d^{6} e^{6} + 26 \, a b^{6} c d^{6} e^{6} - 30 \, a^{2} b^{4} c^{2} d^{6} e^{6} - 340 \, a^{3} b^{2} c^{3} d^{6} e^{6} - 80 \, a^{4} c^{4} d^{6} e^{6} - 6 \, a b^{7} d^{5} e^{7} - 36 \, a^{2} b^{5} c d^{5} e^{7} + 180 \, a^{3} b^{3} c^{2} d^{5} e^{7} + 240 \, a^{4} b c^{3} d^{5} e^{7} + 15 \, a^{2} b^{6} d^{4} e^{8} - 225 \, a^{4} b^{2} c^{2} d^{4} e^{8} - 60 \, a^{5} c^{3} d^{4} e^{8} - 20 \, a^{3} b^{5} d^{3} e^{9} + 50 \, a^{4} b^{3} c d^{3} e^{9} + 120 \, a^{5} b c^{2} d^{3} e^{9} + 15 \, a^{4} b^{4} d^{2} e^{10} - 54 \, a^{5} b^{2} c d^{2} e^{10} - 24 \, a^{6} c^{2} d^{2} e^{10} - 6 \, a^{5} b^{3} d e^{11} + 24 \, a^{6} b c d e^{11} + a^{6} b^{2} e^{12} - 4 \, a^{7} c e^{12}} + \frac{2 \, B a c^{6} d^{9} - A b c^{6} d^{9} - 9 \, B a b c^{5} d^{8} e + 6 \, A b^{2} c^{5} d^{8} e - 6 \, A a c^{6} d^{8} e + 18 \, B a b^{2} c^{4} d^{7} e^{2} - 15 \, A b^{3} c^{4} d^{7} e^{2} + 24 \, A a b c^{5} d^{7} e^{2} - 21 \, B a b^{3} c^{3} d^{6} e^{3} + 20 \, A b^{4} c^{3} d^{6} e^{3} - 34 \, A a b^{2} c^{4} d^{6} e^{3} - 16 \, A a^{2} c^{5} d^{6} e^{3} + 15 \, B a b^{4} c^{2} d^{5} e^{4} - 15 \, A b^{5} c^{2} d^{5} e^{4} + 6 \, B a^{2} b^{2} c^{3} d^{5} e^{4} + 15 \, A a b^{3} c^{3} d^{5} e^{4} - 12 \, B a^{3} c^{4} d^{5} e^{4} + 54 \, A a^{2} b c^{4} d^{5} e^{4} - 6 \, B a b^{5} c d^{4} e^{5} + 6 \, A b^{6} c d^{4} e^{5} - 15 \, B a^{2} b^{3} c^{2} d^{4} e^{5} + 9 \, A a b^{4} c^{2} d^{4} e^{5} + 30 \, B a^{3} b c^{3} d^{4} e^{5} - 66 \, A a^{2} b^{2} c^{3} d^{4} e^{5} - 12 \, A a^{3} c^{4} d^{4} e^{5} + B a b^{6} d^{3} e^{6} - A b^{7} d^{3} e^{6} + 12 \, B a^{2} b^{4} c d^{3} e^{6} - 11 \, A a b^{5} c d^{3} e^{6} - 18 \, B a^{3} b^{2} c^{2} d^{3} e^{6} + 31 \, A a^{2} b^{3} c^{2} d^{3} e^{6} - 16 \, B a^{4} c^{3} d^{3} e^{6} + 32 \, A a^{3} b c^{3} d^{3} e^{6} - 3 \, B a^{2} b^{5} d^{2} e^{7} + 3 \, A a b^{6} d^{2} e^{7} - 3 \, B a^{3} b^{3} c d^{2} e^{7} + 24 \, B a^{4} b c^{2} d^{2} e^{7} - 30 \, A a^{3} b^{2} c^{2} d^{2} e^{7} + 3 \, B a^{3} b^{4} d e^{8} - 3 \, A a^{2} b^{5} d e^{8} - 6 \, B a^{4} b^{2} c d e^{8} + 9 \, A a^{3} b^{3} c d e^{8} - 6 \, B a^{5} c^{2} d e^{8} + 3 \, A a^{4} b c^{2} d e^{8} - B a^{4} b^{3} e^{9} + A a^{3} b^{4} e^{9} + 3 \, B a^{5} b c e^{9} - 4 \, A a^{4} b^{2} c e^{9} + 2 \, A a^{5} c^{2} e^{9}}{b^{2} c^{6} d^{12} - 4 \, a c^{7} d^{12} - 6 \, b^{3} c^{5} d^{11} e + 24 \, a b c^{6} d^{11} e + 15 \, b^{4} c^{4} d^{10} e^{2} - 54 \, a b^{2} c^{5} d^{10} e^{2} - 24 \, a^{2} c^{6} d^{10} e^{2} - 20 \, b^{5} c^{3} d^{9} e^{3} + 50 \, a b^{3} c^{4} d^{9} e^{3} + 120 \, a^{2} b c^{5} d^{9} e^{3} + 15 \, b^{6} c^{2} d^{8} e^{4} - 225 \, a^{2} b^{2} c^{4} d^{8} e^{4} - 60 \, a^{3} c^{5} d^{8} e^{4} - 6 \, b^{7} c d^{7} e^{5} - 36 \, a b^{5} c^{2} d^{7} e^{5} + 180 \, a^{2} b^{3} c^{3} d^{7} e^{5} + 240 \, a^{3} b c^{4} d^{7} e^{5} + b^{8} d^{6} e^{6} + 26 \, a b^{6} c d^{6} e^{6} - 30 \, a^{2} b^{4} c^{2} d^{6} e^{6} - 340 \, a^{3} b^{2} c^{3} d^{6} e^{6} - 80 \, a^{4} c^{4} d^{6} e^{6} - 6 \, a b^{7} d^{5} e^{7} - 36 \, a^{2} b^{5} c d^{5} e^{7} + 180 \, a^{3} b^{3} c^{2} d^{5} e^{7} + 240 \, a^{4} b c^{3} d^{5} e^{7} + 15 \, a^{2} b^{6} d^{4} e^{8} - 225 \, a^{4} b^{2} c^{2} d^{4} e^{8} - 60 \, a^{5} c^{3} d^{4} e^{8} - 20 \, a^{3} b^{5} d^{3} e^{9} + 50 \, a^{4} b^{3} c d^{3} e^{9} + 120 \, a^{5} b c^{2} d^{3} e^{9} + 15 \, a^{4} b^{4} d^{2} e^{10} - 54 \, a^{5} b^{2} c d^{2} e^{10} - 24 \, a^{6} c^{2} d^{2} e^{10} - 6 \, a^{5} b^{3} d e^{11} + 24 \, a^{6} b c d e^{11} + a^{6} b^{2} e^{12} - 4 \, a^{7} c e^{12}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{3 \, {\left(8 \, B c^{2} d^{3} e - 4 \, B b c d^{2} e^{2} - 16 \, A c^{2} d^{2} e^{2} + B b^{2} d e^{3} - 12 \, B a c d e^{3} + 16 \, A b c d e^{3} + 4 \, B a b e^{4} - 5 \, A b^{2} e^{4} + 4 \, A a c e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B c^{\frac{5}{2}} d^{4} e + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B c^{2} d^{3} e^{2} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b c^{2} d^{4} e - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b c^{\frac{3}{2}} d^{3} e^{2} - 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A c^{\frac{5}{2}} d^{3} e^{2} + 10 \, B b^{2} c^{\frac{3}{2}} d^{4} e - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b c d^{2} e^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A c^{2} d^{2} e^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b^{2} c d^{3} e^{2} - 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a c^{2} d^{3} e^{2} - 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b c^{2} d^{3} e^{2} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B b^{2} \sqrt{c} d^{2} e^{3} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a c^{\frac{3}{2}} d^{2} e^{3} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b c^{\frac{3}{2}} d^{2} e^{3} - 3 \, B b^{3} \sqrt{c} d^{3} e^{2} - 32 \, B a b c^{\frac{3}{2}} d^{3} e^{2} - 14 \, A b^{2} c^{\frac{3}{2}} d^{3} e^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B b^{2} d e^{4} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a c d e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b c d e^{4} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B b^{3} d^{2} e^{3} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b c d^{2} e^{3} + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{2} c d^{2} e^{3} + 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a c^{2} d^{2} e^{3} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a b \sqrt{c} d e^{4} - 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A b^{2} \sqrt{c} d e^{4} + 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a c^{\frac{3}{2}} d e^{4} + 7 \, B a b^{2} \sqrt{c} d^{2} e^{3} + 7 \, A b^{3} \sqrt{c} d^{2} e^{3} + 20 \, B a^{2} c^{\frac{3}{2}} d^{2} e^{3} + 44 \, A a b c^{\frac{3}{2}} d^{2} e^{3} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} B a b e^{5} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A b^{2} e^{5} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} A a c e^{5} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a b^{2} d e^{4} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A b^{3} d e^{4} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} c d e^{4} - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b c d e^{4} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} B a^{2} \sqrt{c} e^{5} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} A a b \sqrt{c} e^{5} + 4 \, B a^{2} b \sqrt{c} d e^{4} - 23 \, A a b^{2} \sqrt{c} d e^{4} - 28 \, A a^{2} c^{\frac{3}{2}} d e^{4} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} B a^{2} b e^{5} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a b^{2} e^{5} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} A a^{2} c e^{5} - 8 \, B a^{3} \sqrt{c} e^{5} + 16 \, A a^{2} b \sqrt{c} e^{5}}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{2}}"," ",0,"2*((B*b*c^6*d^9 - 2*A*c^7*d^9 - 3*B*b^2*c^5*d^8*e - 6*B*a*c^6*d^8*e + 9*A*b*c^6*d^8*e + 3*B*b^3*c^4*d^7*e^2 + 24*B*a*b*c^5*d^7*e^2 - 18*A*b^2*c^5*d^7*e^2 - B*b^4*c^3*d^6*e^3 - 34*B*a*b^2*c^4*d^6*e^3 + 21*A*b^3*c^4*d^6*e^3 - 16*B*a^2*c^5*d^6*e^3 + 21*B*a*b^3*c^3*d^5*e^4 - 15*A*b^4*c^3*d^5*e^4 + 42*B*a^2*b*c^4*d^5*e^4 - 6*A*a*b^2*c^4*d^5*e^4 + 12*A*a^2*c^5*d^5*e^4 - 6*B*a*b^4*c^2*d^4*e^5 + 6*A*b^5*c^2*d^4*e^5 - 36*B*a^2*b^2*c^3*d^4*e^5 + 15*A*a*b^3*c^3*d^4*e^5 - 12*B*a^3*c^4*d^4*e^5 - 30*A*a^2*b*c^4*d^4*e^5 + B*a*b^5*c*d^3*e^6 - A*b^6*c*d^3*e^6 + 13*B*a^2*b^3*c^2*d^3*e^6 - 12*A*a*b^4*c^2*d^3*e^6 + 16*B*a^3*b*c^3*d^3*e^6 + 18*A*a^2*b^2*c^3*d^3*e^6 + 16*A*a^3*c^4*d^3*e^6 - 3*B*a^2*b^4*c*d^2*e^7 + 3*A*a*b^5*c*d^2*e^7 - 6*B*a^3*b^2*c^2*d^2*e^7 + 3*A*a^2*b^3*c^2*d^2*e^7 - 24*A*a^3*b*c^3*d^2*e^7 + 3*B*a^3*b^3*c*d*e^8 - 3*A*a^2*b^4*c*d*e^8 - 3*B*a^4*b*c^2*d*e^8 + 6*A*a^3*b^2*c^2*d*e^8 + 6*A*a^4*c^3*d*e^8 - B*a^4*b^2*c*e^9 + A*a^3*b^3*c*e^9 + 2*B*a^5*c^2*e^9 - 3*A*a^4*b*c^2*e^9)*x/(b^2*c^6*d^12 - 4*a*c^7*d^12 - 6*b^3*c^5*d^11*e + 24*a*b*c^6*d^11*e + 15*b^4*c^4*d^10*e^2 - 54*a*b^2*c^5*d^10*e^2 - 24*a^2*c^6*d^10*e^2 - 20*b^5*c^3*d^9*e^3 + 50*a*b^3*c^4*d^9*e^3 + 120*a^2*b*c^5*d^9*e^3 + 15*b^6*c^2*d^8*e^4 - 225*a^2*b^2*c^4*d^8*e^4 - 60*a^3*c^5*d^8*e^4 - 6*b^7*c*d^7*e^5 - 36*a*b^5*c^2*d^7*e^5 + 180*a^2*b^3*c^3*d^7*e^5 + 240*a^3*b*c^4*d^7*e^5 + b^8*d^6*e^6 + 26*a*b^6*c*d^6*e^6 - 30*a^2*b^4*c^2*d^6*e^6 - 340*a^3*b^2*c^3*d^6*e^6 - 80*a^4*c^4*d^6*e^6 - 6*a*b^7*d^5*e^7 - 36*a^2*b^5*c*d^5*e^7 + 180*a^3*b^3*c^2*d^5*e^7 + 240*a^4*b*c^3*d^5*e^7 + 15*a^2*b^6*d^4*e^8 - 225*a^4*b^2*c^2*d^4*e^8 - 60*a^5*c^3*d^4*e^8 - 20*a^3*b^5*d^3*e^9 + 50*a^4*b^3*c*d^3*e^9 + 120*a^5*b*c^2*d^3*e^9 + 15*a^4*b^4*d^2*e^10 - 54*a^5*b^2*c*d^2*e^10 - 24*a^6*c^2*d^2*e^10 - 6*a^5*b^3*d*e^11 + 24*a^6*b*c*d*e^11 + a^6*b^2*e^12 - 4*a^7*c*e^12) + (2*B*a*c^6*d^9 - A*b*c^6*d^9 - 9*B*a*b*c^5*d^8*e + 6*A*b^2*c^5*d^8*e - 6*A*a*c^6*d^8*e + 18*B*a*b^2*c^4*d^7*e^2 - 15*A*b^3*c^4*d^7*e^2 + 24*A*a*b*c^5*d^7*e^2 - 21*B*a*b^3*c^3*d^6*e^3 + 20*A*b^4*c^3*d^6*e^3 - 34*A*a*b^2*c^4*d^6*e^3 - 16*A*a^2*c^5*d^6*e^3 + 15*B*a*b^4*c^2*d^5*e^4 - 15*A*b^5*c^2*d^5*e^4 + 6*B*a^2*b^2*c^3*d^5*e^4 + 15*A*a*b^3*c^3*d^5*e^4 - 12*B*a^3*c^4*d^5*e^4 + 54*A*a^2*b*c^4*d^5*e^4 - 6*B*a*b^5*c*d^4*e^5 + 6*A*b^6*c*d^4*e^5 - 15*B*a^2*b^3*c^2*d^4*e^5 + 9*A*a*b^4*c^2*d^4*e^5 + 30*B*a^3*b*c^3*d^4*e^5 - 66*A*a^2*b^2*c^3*d^4*e^5 - 12*A*a^3*c^4*d^4*e^5 + B*a*b^6*d^3*e^6 - A*b^7*d^3*e^6 + 12*B*a^2*b^4*c*d^3*e^6 - 11*A*a*b^5*c*d^3*e^6 - 18*B*a^3*b^2*c^2*d^3*e^6 + 31*A*a^2*b^3*c^2*d^3*e^6 - 16*B*a^4*c^3*d^3*e^6 + 32*A*a^3*b*c^3*d^3*e^6 - 3*B*a^2*b^5*d^2*e^7 + 3*A*a*b^6*d^2*e^7 - 3*B*a^3*b^3*c*d^2*e^7 + 24*B*a^4*b*c^2*d^2*e^7 - 30*A*a^3*b^2*c^2*d^2*e^7 + 3*B*a^3*b^4*d*e^8 - 3*A*a^2*b^5*d*e^8 - 6*B*a^4*b^2*c*d*e^8 + 9*A*a^3*b^3*c*d*e^8 - 6*B*a^5*c^2*d*e^8 + 3*A*a^4*b*c^2*d*e^8 - B*a^4*b^3*e^9 + A*a^3*b^4*e^9 + 3*B*a^5*b*c*e^9 - 4*A*a^4*b^2*c*e^9 + 2*A*a^5*c^2*e^9)/(b^2*c^6*d^12 - 4*a*c^7*d^12 - 6*b^3*c^5*d^11*e + 24*a*b*c^6*d^11*e + 15*b^4*c^4*d^10*e^2 - 54*a*b^2*c^5*d^10*e^2 - 24*a^2*c^6*d^10*e^2 - 20*b^5*c^3*d^9*e^3 + 50*a*b^3*c^4*d^9*e^3 + 120*a^2*b*c^5*d^9*e^3 + 15*b^6*c^2*d^8*e^4 - 225*a^2*b^2*c^4*d^8*e^4 - 60*a^3*c^5*d^8*e^4 - 6*b^7*c*d^7*e^5 - 36*a*b^5*c^2*d^7*e^5 + 180*a^2*b^3*c^3*d^7*e^5 + 240*a^3*b*c^4*d^7*e^5 + b^8*d^6*e^6 + 26*a*b^6*c*d^6*e^6 - 30*a^2*b^4*c^2*d^6*e^6 - 340*a^3*b^2*c^3*d^6*e^6 - 80*a^4*c^4*d^6*e^6 - 6*a*b^7*d^5*e^7 - 36*a^2*b^5*c*d^5*e^7 + 180*a^3*b^3*c^2*d^5*e^7 + 240*a^4*b*c^3*d^5*e^7 + 15*a^2*b^6*d^4*e^8 - 225*a^4*b^2*c^2*d^4*e^8 - 60*a^5*c^3*d^4*e^8 - 20*a^3*b^5*d^3*e^9 + 50*a^4*b^3*c*d^3*e^9 + 120*a^5*b*c^2*d^3*e^9 + 15*a^4*b^4*d^2*e^10 - 54*a^5*b^2*c*d^2*e^10 - 24*a^6*c^2*d^2*e^10 - 6*a^5*b^3*d*e^11 + 24*a^6*b*c*d*e^11 + a^6*b^2*e^12 - 4*a^7*c*e^12))/sqrt(c*x^2 + b*x + a) - 3/4*(8*B*c^2*d^3*e - 4*B*b*c*d^2*e^2 - 16*A*c^2*d^2*e^2 + B*b^2*d*e^3 - 12*B*a*c*d*e^3 + 16*A*b*c*d*e^3 + 4*B*a*b*e^4 - 5*A*b^2*e^4 + 4*A*a*c*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/4*(40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*c^(5/2)*d^4*e + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*c^2*d^3*e^2 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b*c^2*d^4*e - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b*c^(3/2)*d^3*e^2 - 56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*c^(5/2)*d^3*e^2 + 10*B*b^2*c^(3/2)*d^4*e - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b*c*d^2*e^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*c^2*d^2*e^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b^2*c*d^3*e^2 - 64*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*c^2*d^3*e^2 - 56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b*c^2*d^3*e^2 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*b^2*sqrt(c)*d^2*e^3 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*c^(3/2)*d^2*e^3 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b*c^(3/2)*d^2*e^3 - 3*B*b^3*sqrt(c)*d^3*e^2 - 32*B*a*b*c^(3/2)*d^3*e^2 - 14*A*b^2*c^(3/2)*d^3*e^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*b^2*d*e^4 - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*c*d*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b*c*d*e^4 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*b^3*d^2*e^3 + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b*c*d^2*e^3 + 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^2*c*d^2*e^3 + 88*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*c^2*d^2*e^3 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a*b*sqrt(c)*d*e^4 - 13*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*b^2*sqrt(c)*d*e^4 + 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*c^(3/2)*d*e^4 + 7*B*a*b^2*sqrt(c)*d^2*e^3 + 7*A*b^3*sqrt(c)*d^2*e^3 + 20*B*a^2*c^(3/2)*d^2*e^3 + 44*A*a*b*c^(3/2)*d^2*e^3 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*B*a*b*e^5 - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*b^2*e^5 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*A*a*c*e^5 - (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a*b^2*d*e^4 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*b^3*d*e^4 + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*c*d*e^4 - 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b*c*d*e^4 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*B*a^2*sqrt(c)*e^5 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*A*a*b*sqrt(c)*e^5 + 4*B*a^2*b*sqrt(c)*d*e^4 - 23*A*a*b^2*sqrt(c)*d*e^4 - 28*A*a^2*c^(3/2)*d*e^4 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*B*a^2*b*e^5 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a*b^2*e^5 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*A*a^2*c*e^5 - 8*B*a^3*sqrt(c)*e^5 + 16*A*a^2*b*sqrt(c)*e^5)/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^2)","B",0
2480,1,1185,0,0.401469," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(\frac{3 \, {\left(B b^{4} c^{2} e^{4} - 8 \, B a b^{2} c^{3} e^{4} + 16 \, B a^{2} c^{4} e^{4}\right)} x}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}} - \frac{4 \, {\left(4 \, B b c^{5} d^{4} - 8 \, A c^{6} d^{4} - 4 \, B b^{2} c^{4} d^{3} e - 16 \, B a c^{5} d^{3} e + 16 \, A b c^{5} d^{3} e - 3 \, B b^{3} c^{3} d^{2} e^{2} + 36 \, B a b c^{4} d^{2} e^{2} - 6 \, A b^{2} c^{4} d^{2} e^{2} - 24 \, A a c^{5} d^{2} e^{2} + 8 \, B b^{4} c^{2} d e^{3} - 56 \, B a b^{2} c^{3} d e^{3} - 2 \, A b^{3} c^{3} d e^{3} + 64 \, B a^{2} c^{4} d e^{3} + 24 \, A a b c^{4} d e^{3} - 5 \, B b^{5} c e^{4} + 37 \, B a b^{3} c^{2} e^{4} + 2 \, A b^{4} c^{2} e^{4} - 64 \, B a^{2} b c^{3} e^{4} - 14 \, A a b^{2} c^{3} e^{4} + 16 \, A a^{2} c^{4} e^{4}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x - \frac{3 \, {\left(8 \, B b^{2} c^{4} d^{4} - 16 \, A b c^{5} d^{4} - 8 \, B b^{3} c^{3} d^{3} e - 32 \, B a b c^{4} d^{3} e + 32 \, A b^{2} c^{4} d^{3} e + 24 \, B a b^{2} c^{3} d^{2} e^{2} - 12 \, A b^{3} c^{3} d^{2} e^{2} + 96 \, B a^{2} c^{4} d^{2} e^{2} - 48 \, A a b c^{4} d^{2} e^{2} + 8 \, B b^{5} c d e^{3} - 48 \, B a b^{3} c^{2} d e^{3} + 16 \, A a b^{2} c^{3} d e^{3} + 64 \, A a^{2} c^{4} d e^{3} - 5 \, B b^{6} e^{4} + 30 \, B a b^{4} c e^{4} + 2 \, A b^{5} c e^{4} - 16 \, B a^{2} b^{2} c^{2} e^{4} - 12 \, A a b^{3} c^{2} e^{4} - 64 \, B a^{3} c^{3} e^{4}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x - \frac{6 \, {\left(B b^{3} c^{3} d^{4} + 4 \, B a b c^{4} d^{4} - 2 \, A b^{2} c^{4} d^{4} - 8 \, A a c^{5} d^{4} - 16 \, B a b^{2} c^{3} d^{3} e + 4 \, A b^{3} c^{3} d^{3} e + 16 \, A a b c^{4} d^{3} e + 48 \, B a^{2} b c^{3} d^{2} e^{2} - 24 \, A a b^{2} c^{3} d^{2} e^{2} + 8 \, B a b^{4} c d e^{3} - 56 \, B a^{2} b^{2} c^{2} d e^{3} + 32 \, B a^{3} c^{3} d e^{3} + 32 \, A a^{2} b c^{3} d e^{3} - 5 \, B a b^{5} e^{4} + 35 \, B a^{2} b^{3} c e^{4} + 2 \, A a b^{4} c e^{4} - 52 \, B a^{3} b c^{2} e^{4} - 14 \, A a^{2} b^{2} c^{2} e^{4} + 8 \, A a^{3} c^{3} e^{4}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x - \frac{4 \, B a b^{2} c^{3} d^{4} + 2 \, A b^{3} c^{3} d^{4} + 16 \, B a^{2} c^{4} d^{4} - 24 \, A a b c^{4} d^{4} - 64 \, B a^{2} b c^{3} d^{3} e + 16 \, A a b^{2} c^{3} d^{3} e + 64 \, A a^{2} c^{4} d^{3} e + 192 \, B a^{3} c^{3} d^{2} e^{2} - 96 \, A a^{2} b c^{3} d^{2} e^{2} + 24 \, B a^{2} b^{3} c d e^{3} - 160 \, B a^{3} b c^{2} d e^{3} + 128 \, A a^{3} c^{3} d e^{3} - 15 \, B a^{2} b^{4} e^{4} + 100 \, B a^{3} b^{2} c e^{4} + 6 \, A a^{2} b^{3} c e^{4} - 128 \, B a^{4} c^{2} e^{4} - 40 \, A a^{3} b c^{2} e^{4}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} - \frac{{\left(8 \, B c d e^{3} - 5 \, B b e^{4} + 2 \, A c e^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{7}{2}}}"," ",0,"1/3*((((3*(B*b^4*c^2*e^4 - 8*B*a*b^2*c^3*e^4 + 16*B*a^2*c^4*e^4)*x/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5) - 4*(4*B*b*c^5*d^4 - 8*A*c^6*d^4 - 4*B*b^2*c^4*d^3*e - 16*B*a*c^5*d^3*e + 16*A*b*c^5*d^3*e - 3*B*b^3*c^3*d^2*e^2 + 36*B*a*b*c^4*d^2*e^2 - 6*A*b^2*c^4*d^2*e^2 - 24*A*a*c^5*d^2*e^2 + 8*B*b^4*c^2*d*e^3 - 56*B*a*b^2*c^3*d*e^3 - 2*A*b^3*c^3*d*e^3 + 64*B*a^2*c^4*d*e^3 + 24*A*a*b*c^4*d*e^3 - 5*B*b^5*c*e^4 + 37*B*a*b^3*c^2*e^4 + 2*A*b^4*c^2*e^4 - 64*B*a^2*b*c^3*e^4 - 14*A*a*b^2*c^3*e^4 + 16*A*a^2*c^4*e^4)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x - 3*(8*B*b^2*c^4*d^4 - 16*A*b*c^5*d^4 - 8*B*b^3*c^3*d^3*e - 32*B*a*b*c^4*d^3*e + 32*A*b^2*c^4*d^3*e + 24*B*a*b^2*c^3*d^2*e^2 - 12*A*b^3*c^3*d^2*e^2 + 96*B*a^2*c^4*d^2*e^2 - 48*A*a*b*c^4*d^2*e^2 + 8*B*b^5*c*d*e^3 - 48*B*a*b^3*c^2*d*e^3 + 16*A*a*b^2*c^3*d*e^3 + 64*A*a^2*c^4*d*e^3 - 5*B*b^6*e^4 + 30*B*a*b^4*c*e^4 + 2*A*b^5*c*e^4 - 16*B*a^2*b^2*c^2*e^4 - 12*A*a*b^3*c^2*e^4 - 64*B*a^3*c^3*e^4)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x - 6*(B*b^3*c^3*d^4 + 4*B*a*b*c^4*d^4 - 2*A*b^2*c^4*d^4 - 8*A*a*c^5*d^4 - 16*B*a*b^2*c^3*d^3*e + 4*A*b^3*c^3*d^3*e + 16*A*a*b*c^4*d^3*e + 48*B*a^2*b*c^3*d^2*e^2 - 24*A*a*b^2*c^3*d^2*e^2 + 8*B*a*b^4*c*d*e^3 - 56*B*a^2*b^2*c^2*d*e^3 + 32*B*a^3*c^3*d*e^3 + 32*A*a^2*b*c^3*d*e^3 - 5*B*a*b^5*e^4 + 35*B*a^2*b^3*c*e^4 + 2*A*a*b^4*c*e^4 - 52*B*a^3*b*c^2*e^4 - 14*A*a^2*b^2*c^2*e^4 + 8*A*a^3*c^3*e^4)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x - (4*B*a*b^2*c^3*d^4 + 2*A*b^3*c^3*d^4 + 16*B*a^2*c^4*d^4 - 24*A*a*b*c^4*d^4 - 64*B*a^2*b*c^3*d^3*e + 16*A*a*b^2*c^3*d^3*e + 64*A*a^2*c^4*d^3*e + 192*B*a^3*c^3*d^2*e^2 - 96*A*a^2*b*c^3*d^2*e^2 + 24*B*a^2*b^3*c*d*e^3 - 160*B*a^3*b*c^2*d*e^3 + 128*A*a^3*c^3*d*e^3 - 15*B*a^2*b^4*e^4 + 100*B*a^3*b^2*c*e^4 + 6*A*a^2*b^3*c*e^4 - 128*B*a^4*c^2*e^4 - 40*A*a^3*b*c^2*e^4)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))/(c*x^2 + b*x + a)^(3/2) - 1/2*(8*B*c*d*e^3 - 5*B*b*e^4 + 2*A*c*e^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","B",0
2481,1,790,0,0.387355," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{B e^{3} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}} - \frac{2 \, {\left({\left({\left(\frac{{\left(8 \, B b c^{4} d^{3} - 16 \, A c^{5} d^{3} - 6 \, B b^{2} c^{3} d^{2} e - 24 \, B a c^{4} d^{2} e + 24 \, A b c^{4} d^{2} e - 3 \, B b^{3} c^{2} d e^{2} + 36 \, B a b c^{3} d e^{2} - 6 \, A b^{2} c^{3} d e^{2} - 24 \, A a c^{4} d e^{2} + 4 \, B b^{4} c e^{3} - 28 \, B a b^{2} c^{2} e^{3} - A b^{3} c^{2} e^{3} + 32 \, B a^{2} c^{3} e^{3} + 12 \, A a b c^{3} e^{3}\right)} x}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}} + \frac{3 \, {\left(4 \, B b^{2} c^{3} d^{3} - 8 \, A b c^{4} d^{3} - 3 \, B b^{3} c^{2} d^{2} e - 12 \, B a b c^{3} d^{2} e + 12 \, A b^{2} c^{3} d^{2} e + 6 \, B a b^{2} c^{2} d e^{2} - 3 \, A b^{3} c^{2} d e^{2} + 24 \, B a^{2} c^{3} d e^{2} - 12 \, A a b c^{3} d e^{2} + B b^{5} e^{3} - 6 \, B a b^{3} c e^{3} + 2 \, A a b^{2} c^{2} e^{3} + 8 \, A a^{2} c^{3} e^{3}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{3 \, {\left(B b^{3} c^{2} d^{3} + 4 \, B a b c^{3} d^{3} - 2 \, A b^{2} c^{3} d^{3} - 8 \, A a c^{4} d^{3} - 12 \, B a b^{2} c^{2} d^{2} e + 3 \, A b^{3} c^{2} d^{2} e + 12 \, A a b c^{3} d^{2} e + 24 \, B a^{2} b c^{2} d e^{2} - 12 \, A a b^{2} c^{2} d e^{2} + 2 \, B a b^{4} e^{3} - 14 \, B a^{2} b^{2} c e^{3} + 8 \, B a^{3} c^{2} e^{3} + 8 \, A a^{2} b c^{2} e^{3}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{2 \, B a b^{2} c^{2} d^{3} + A b^{3} c^{2} d^{3} + 8 \, B a^{2} c^{3} d^{3} - 12 \, A a b c^{3} d^{3} - 24 \, B a^{2} b c^{2} d^{2} e + 6 \, A a b^{2} c^{2} d^{2} e + 24 \, A a^{2} c^{3} d^{2} e + 48 \, B a^{3} c^{2} d e^{2} - 24 \, A a^{2} b c^{2} d e^{2} + 3 \, B a^{2} b^{3} e^{3} - 20 \, B a^{3} b c e^{3} + 16 \, A a^{3} c^{2} e^{3}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-B*e^3*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2) - 2/3*((((8*B*b*c^4*d^3 - 16*A*c^5*d^3 - 6*B*b^2*c^3*d^2*e - 24*B*a*c^4*d^2*e + 24*A*b*c^4*d^2*e - 3*B*b^3*c^2*d*e^2 + 36*B*a*b*c^3*d*e^2 - 6*A*b^2*c^3*d*e^2 - 24*A*a*c^4*d*e^2 + 4*B*b^4*c*e^3 - 28*B*a*b^2*c^2*e^3 - A*b^3*c^2*e^3 + 32*B*a^2*c^3*e^3 + 12*A*a*b*c^3*e^3)*x/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4) + 3*(4*B*b^2*c^3*d^3 - 8*A*b*c^4*d^3 - 3*B*b^3*c^2*d^2*e - 12*B*a*b*c^3*d^2*e + 12*A*b^2*c^3*d^2*e + 6*B*a*b^2*c^2*d*e^2 - 3*A*b^3*c^2*d*e^2 + 24*B*a^2*c^3*d*e^2 - 12*A*a*b*c^3*d*e^2 + B*b^5*e^3 - 6*B*a*b^3*c*e^3 + 2*A*a*b^2*c^2*e^3 + 8*A*a^2*c^3*e^3)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x + 3*(B*b^3*c^2*d^3 + 4*B*a*b*c^3*d^3 - 2*A*b^2*c^3*d^3 - 8*A*a*c^4*d^3 - 12*B*a*b^2*c^2*d^2*e + 3*A*b^3*c^2*d^2*e + 12*A*a*b*c^3*d^2*e + 24*B*a^2*b*c^2*d*e^2 - 12*A*a*b^2*c^2*d*e^2 + 2*B*a*b^4*e^3 - 14*B*a^2*b^2*c*e^3 + 8*B*a^3*c^2*e^3 + 8*A*a^2*b*c^2*e^3)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x + (2*B*a*b^2*c^2*d^3 + A*b^3*c^2*d^3 + 8*B*a^2*c^3*d^3 - 12*A*a*b*c^3*d^3 - 24*B*a^2*b*c^2*d^2*e + 6*A*a*b^2*c^2*d^2*e + 24*A*a^2*c^3*d^2*e + 48*B*a^3*c^2*d*e^2 - 24*A*a^2*b*c^2*d*e^2 + 3*B*a^2*b^3*e^3 - 20*B*a^3*b*c*e^3 + 16*A*a^3*c^2*e^3)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))/(c*x^2 + b*x + a)^(3/2)","B",0
2482,1,448,0,0.333850," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(\frac{{\left(8 \, B b c^{2} d^{2} - 16 \, A c^{3} d^{2} - 4 \, B b^{2} c d e - 16 \, B a c^{2} d e + 16 \, A b c^{2} d e - B b^{3} e^{2} + 12 \, B a b c e^{2} - 2 \, A b^{2} c e^{2} - 8 \, A a c^{2} e^{2}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(4 \, B b^{2} c d^{2} - 8 \, A b c^{2} d^{2} - 2 \, B b^{3} d e - 8 \, B a b c d e + 8 \, A b^{2} c d e + 2 \, B a b^{2} e^{2} - A b^{3} e^{2} + 8 \, B a^{2} c e^{2} - 4 \, A a b c e^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(B b^{3} d^{2} + 4 \, B a b c d^{2} - 2 \, A b^{2} c d^{2} - 8 \, A a c^{2} d^{2} - 8 \, B a b^{2} d e + 2 \, A b^{3} d e + 8 \, A a b c d e + 8 \, B a^{2} b e^{2} - 4 \, A a b^{2} e^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{2 \, B a b^{2} d^{2} + A b^{3} d^{2} + 8 \, B a^{2} c d^{2} - 12 \, A a b c d^{2} - 16 \, B a^{2} b d e + 4 \, A a b^{2} d e + 16 \, A a^{2} c d e + 16 \, B a^{3} e^{2} - 8 \, A a^{2} b e^{2}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((((8*B*b*c^2*d^2 - 16*A*c^3*d^2 - 4*B*b^2*c*d*e - 16*B*a*c^2*d*e + 16*A*b*c^2*d*e - B*b^3*e^2 + 12*B*a*b*c*e^2 - 2*A*b^2*c*e^2 - 8*A*a*c^2*e^2)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(4*B*b^2*c*d^2 - 8*A*b*c^2*d^2 - 2*B*b^3*d*e - 8*B*a*b*c*d*e + 8*A*b^2*c*d*e + 2*B*a*b^2*e^2 - A*b^3*e^2 + 8*B*a^2*c*e^2 - 4*A*a*b*c*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(B*b^3*d^2 + 4*B*a*b*c*d^2 - 2*A*b^2*c*d^2 - 8*A*a*c^2*d^2 - 8*B*a*b^2*d*e + 2*A*b^3*d*e + 8*A*a*b*c*d*e + 8*B*a^2*b*e^2 - 4*A*a*b^2*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (2*B*a*b^2*d^2 + A*b^3*d^2 + 8*B*a^2*c*d^2 - 12*A*a*b*c*d^2 - 16*B*a^2*b*d*e + 4*A*a*b^2*d*e + 16*A*a^2*c*d*e + 16*B*a^3*e^2 - 8*A*a^2*b*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
2483,1,309,0,0.327068," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(\frac{2 \, {\left(4 \, B b c^{2} d - 8 \, A c^{3} d - B b^{2} c e - 4 \, B a c^{2} e + 4 \, A b c^{2} e\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(4 \, B b^{2} c d - 8 \, A b c^{2} d - B b^{3} e - 4 \, B a b c e + 4 \, A b^{2} c e\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(B b^{3} d + 4 \, B a b c d - 2 \, A b^{2} c d - 8 \, A a c^{2} d - 4 \, B a b^{2} e + A b^{3} e + 4 \, A a b c e\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{2 \, B a b^{2} d + A b^{3} d + 8 \, B a^{2} c d - 12 \, A a b c d - 8 \, B a^{2} b e + 2 \, A a b^{2} e + 8 \, A a^{2} c e}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2/3*(((2*(4*B*b*c^2*d - 8*A*c^3*d - B*b^2*c*e - 4*B*a*c^2*e + 4*A*b*c^2*e)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(4*B*b^2*c*d - 8*A*b*c^2*d - B*b^3*e - 4*B*a*b*c*e + 4*A*b^2*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(B*b^3*d + 4*B*a*b*c*d - 2*A*b^2*c*d - 8*A*a*c^2*d - 4*B*a*b^2*e + A*b^3*e + 4*A*a*b*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (2*B*a*b^2*d + A*b^3*d + 8*B*a^2*c*d - 12*A*a*b*c*d - 8*B*a^2*b*e + 2*A*a*b^2*e + 8*A*a^2*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
2484,1,193,0,0.303777," ","integrate((B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(4 \, {\left(\frac{2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(B b^{3} + 4 \, B a b c - 2 \, A b^{2} c - 8 \, A a c^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{2 \, B a b^{2} + A b^{3} + 8 \, B a^{2} c - 12 \, A a b c}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((4*(2*(B*b*c^2 - 2*A*c^3)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(B*b^2*c - 2*A*b*c^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(B*b^3 + 4*B*a*b*c - 2*A*b^2*c - 8*A*a*c^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (2*B*a*b^2 + A*b^3 + 8*B*a^2*c - 12*A*a*b*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
2485,1,11729,0,0.903061," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(B d e^{3} - A e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{2 \, {\left({\left({\left(\frac{{\left(8 \, B b c^{10} d^{15} - 16 \, A c^{11} d^{15} - 62 \, B b^{2} c^{9} d^{14} e + 8 \, B a c^{10} d^{14} e + 120 \, A b c^{10} d^{14} e + 207 \, B b^{3} c^{8} d^{13} e^{2} + 12 \, B a b c^{9} d^{13} e^{2} - 386 \, A b^{2} c^{9} d^{13} e^{2} - 136 \, A a c^{10} d^{13} e^{2} - 388 \, B b^{4} c^{7} d^{12} e^{3} - 276 \, B a b^{2} c^{8} d^{12} e^{3} + 689 \, A b^{3} c^{8} d^{12} e^{3} + 32 \, B a^{2} c^{9} d^{12} e^{3} + 884 \, A a b c^{9} d^{12} e^{3} + 445 \, B b^{5} c^{6} d^{11} e^{4} + 938 \, B a b^{3} c^{7} d^{11} e^{4} - 732 \, A b^{4} c^{7} d^{11} e^{4} + 48 \, B a^{2} b c^{8} d^{11} e^{4} - 2412 \, A a b^{2} c^{8} d^{11} e^{4} - 480 \, A a^{2} c^{9} d^{11} e^{4} - 318 \, B b^{6} c^{5} d^{10} e^{5} - 1530 \, B a b^{4} c^{6} d^{10} e^{5} + 451 \, A b^{5} c^{6} d^{10} e^{5} - 810 \, B a^{2} b^{2} c^{7} d^{10} e^{5} + 3542 \, A a b^{3} c^{7} d^{10} e^{5} + 24 \, B a^{3} c^{8} d^{10} e^{5} + 2640 \, A a^{2} b c^{8} d^{10} e^{5} + 137 \, B b^{7} c^{4} d^{9} e^{6} + 1392 \, B a b^{5} c^{5} d^{9} e^{6} - 130 \, A b^{6} c^{5} d^{9} e^{6} + 2165 \, B a^{2} b^{3} c^{6} d^{9} e^{6} - 2950 \, A a b^{4} c^{6} d^{9} e^{6} + 340 \, B a^{3} b c^{7} d^{9} e^{6} - 5910 \, A a^{2} b^{2} c^{7} d^{9} e^{6} - 920 \, A a^{3} c^{8} d^{9} e^{6} - 32 \, B b^{8} c^{3} d^{8} e^{7} - 712 \, B a b^{6} c^{4} d^{8} e^{7} - 9 \, A b^{7} c^{4} d^{8} e^{7} - 2640 \, B a^{2} b^{4} c^{5} d^{8} e^{7} + 1296 \, A a b^{5} c^{5} d^{8} e^{7} - 1720 \, B a^{3} b^{2} c^{6} d^{8} e^{7} + 6795 \, A a^{2} b^{3} c^{6} d^{8} e^{7} - 80 \, B a^{4} c^{7} d^{8} e^{7} + 4140 \, A a^{3} b c^{7} d^{8} e^{7} + 3 \, B b^{9} c^{2} d^{7} e^{8} + 186 \, B a b^{7} c^{3} d^{7} e^{8} + 16 \, A b^{8} c^{3} d^{7} e^{8} + 1638 \, B a^{2} b^{5} c^{4} d^{7} e^{8} - 184 \, A a b^{6} c^{4} d^{7} e^{8} + 2940 \, B a^{3} b^{3} c^{5} d^{7} e^{8} - 4080 \, A a^{2} b^{4} c^{5} d^{7} e^{8} + 840 \, B a^{4} b c^{6} d^{7} e^{8} - 7240 \, A a^{3} b^{2} c^{6} d^{7} e^{8} - 1040 \, A a^{4} c^{7} d^{7} e^{8} - 18 \, B a b^{8} c^{2} d^{6} e^{9} - 3 \, A b^{9} c^{2} d^{6} e^{9} - 478 \, B a^{2} b^{6} c^{3} d^{6} e^{9} - 58 \, A a b^{7} c^{3} d^{6} e^{9} - 2260 \, B a^{3} b^{4} c^{4} d^{6} e^{9} + 1050 \, A a^{2} b^{5} c^{4} d^{6} e^{9} - 2130 \, B a^{4} b^{2} c^{5} d^{6} e^{9} + 6020 \, A a^{3} b^{3} c^{5} d^{6} e^{9} - 200 \, B a^{5} c^{6} d^{6} e^{9} + 3640 \, A a^{4} b c^{6} d^{6} e^{9} + 45 \, B a^{2} b^{7} c^{2} d^{5} e^{10} + 18 \, A a b^{8} c^{2} d^{5} e^{10} + 736 \, B a^{3} b^{5} c^{3} d^{5} e^{10} + 30 \, A a^{2} b^{6} c^{3} d^{5} e^{10} + 2105 \, B a^{4} b^{3} c^{4} d^{5} e^{10} - 2220 \, A a^{3} b^{4} c^{4} d^{5} e^{10} + 948 \, B a^{5} b c^{5} d^{5} e^{10} - 4590 \, A a^{4} b^{2} c^{5} d^{5} e^{10} - 696 \, A a^{5} c^{6} d^{5} e^{10} - 60 \, B a^{3} b^{6} c^{2} d^{4} e^{11} - 45 \, A a^{2} b^{7} c^{2} d^{4} e^{11} - 780 \, B a^{4} b^{4} c^{3} d^{4} e^{11} + 160 \, A a^{3} b^{5} c^{3} d^{4} e^{11} - 1332 \, B a^{5} b^{2} c^{4} d^{4} e^{11} + 2375 \, A a^{4} b^{3} c^{4} d^{4} e^{11} - 192 \, B a^{6} c^{5} d^{4} e^{11} + 1740 \, A a^{5} b c^{5} d^{4} e^{11} + 45 \, B a^{4} b^{5} c^{2} d^{3} e^{12} + 60 \, A a^{3} b^{6} c^{2} d^{3} e^{12} + 602 \, B a^{5} b^{3} c^{3} d^{3} e^{12} - 340 \, A a^{4} b^{4} c^{3} d^{3} e^{12} + 512 \, B a^{6} b c^{4} d^{3} e^{12} - 1356 \, A a^{5} b^{2} c^{4} d^{3} e^{12} - 256 \, A a^{6} c^{5} d^{3} e^{12} - 18 \, B a^{5} b^{4} c^{2} d^{2} e^{13} - 45 \, A a^{4} b^{5} c^{2} d^{2} e^{13} - 326 \, B a^{6} b^{2} c^{3} d^{2} e^{13} + 294 \, A a^{5} b^{3} c^{3} d^{2} e^{13} - 88 \, B a^{7} c^{4} d^{2} e^{13} + 384 \, A a^{6} b c^{4} d^{2} e^{13} + 3 \, B a^{6} b^{3} c^{2} d e^{14} + 18 \, A a^{5} b^{4} c^{2} d e^{14} + 108 \, B a^{7} b c^{3} d e^{14} - 122 \, A a^{6} b^{2} c^{3} d e^{14} - 40 \, A a^{7} c^{4} d e^{14} - 3 \, A a^{6} b^{3} c^{2} e^{15} - 16 \, B a^{8} c^{3} e^{15} + 20 \, A a^{7} b c^{3} e^{15}\right)} x}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}} + \frac{3 \, {\left(4 \, B b^{2} c^{9} d^{15} - 8 \, A b c^{10} d^{15} - 31 \, B b^{3} c^{8} d^{14} e + 4 \, B a b c^{9} d^{14} e + 60 \, A b^{2} c^{9} d^{14} e + 104 \, B b^{4} c^{7} d^{13} e^{2} + 2 \, B a b^{2} c^{8} d^{13} e^{2} - 193 \, A b^{3} c^{8} d^{13} e^{2} + 8 \, B a^{2} c^{9} d^{13} e^{2} - 68 \, A a b c^{9} d^{13} e^{2} - 197 \, B b^{5} c^{6} d^{12} e^{3} - 114 \, B a b^{3} c^{7} d^{12} e^{3} + 344 \, A b^{4} c^{7} d^{12} e^{3} - 32 \, B a^{2} b c^{8} d^{12} e^{3} + 446 \, A a b^{2} c^{8} d^{12} e^{3} - 8 \, A a^{2} c^{9} d^{12} e^{3} + 230 \, B b^{6} c^{5} d^{11} e^{4} + 412 \, B a b^{4} c^{6} d^{11} e^{4} - 363 \, A b^{5} c^{6} d^{11} e^{4} + 120 \, B a^{2} b^{2} c^{7} d^{11} e^{4} - 1230 \, A a b^{3} c^{7} d^{11} e^{4} + 48 \, B a^{3} c^{8} d^{11} e^{4} - 192 \, A a^{2} b c^{8} d^{11} e^{4} - 169 \, B b^{7} c^{4} d^{10} e^{5} - 700 \, B a b^{5} c^{5} d^{10} e^{5} + 218 \, A b^{6} c^{5} d^{10} e^{5} - 445 \, B a^{2} b^{3} c^{6} d^{10} e^{5} + 1828 \, A a b^{4} c^{6} d^{10} e^{5} - 228 \, B a^{3} b c^{7} d^{10} e^{5} + 1224 \, A a^{2} b^{2} c^{7} d^{10} e^{5} - 48 \, A a^{3} c^{8} d^{10} e^{5} + 76 \, B b^{8} c^{3} d^{9} e^{6} + 666 \, B a b^{6} c^{4} d^{9} e^{6} - 55 \, A b^{7} c^{4} d^{9} e^{6} + 970 \, B a^{2} b^{4} c^{5} d^{9} e^{6} - 1540 \, A a b^{5} c^{5} d^{9} e^{6} + 590 \, B a^{3} b^{2} c^{6} d^{9} e^{6} - 2915 \, A a^{2} b^{3} c^{6} d^{9} e^{6} + 120 \, B a^{4} c^{7} d^{9} e^{6} - 220 \, A a^{3} b c^{7} d^{9} e^{6} - 19 \, B b^{9} c^{2} d^{8} e^{7} - 362 \, B a b^{7} c^{3} d^{8} e^{7} - 12 \, A b^{8} c^{3} d^{8} e^{7} - 1158 \, B a^{2} b^{5} c^{4} d^{8} e^{7} + 678 \, A a b^{6} c^{4} d^{8} e^{7} - 1100 \, B a^{3} b^{3} c^{5} d^{8} e^{7} + 3510 \, A a^{2} b^{4} c^{5} d^{8} e^{7} - 520 \, B a^{4} b c^{6} d^{8} e^{7} + 1650 \, A a^{3} b^{2} c^{6} d^{8} e^{7} - 120 \, A a^{4} c^{7} d^{8} e^{7} + 2 \, B b^{10} c d^{7} e^{8} + 104 \, B a b^{8} c^{2} d^{7} e^{8} + 11 \, A b^{9} c^{2} d^{7} e^{8} + 752 \, B a^{2} b^{6} c^{3} d^{7} e^{8} - 86 \, A a b^{7} c^{3} d^{7} e^{8} + 1360 \, B a^{3} b^{4} c^{4} d^{7} e^{8} - 2202 \, A a^{2} b^{5} c^{4} d^{7} e^{8} + 1060 \, B a^{4} b^{2} c^{5} d^{7} e^{8} - 3380 \, A a^{3} b^{3} c^{5} d^{7} e^{8} + 160 \, B a^{5} c^{6} d^{7} e^{8} - 40 \, A a^{4} b c^{6} d^{7} e^{8} - 12 \, B a b^{9} c d^{6} e^{9} - 2 \, A b^{10} c d^{6} e^{9} - 245 \, B a^{2} b^{7} c^{2} d^{6} e^{9} - 40 \, A a b^{8} c^{2} d^{6} e^{9} - 968 \, B a^{3} b^{5} c^{3} d^{6} e^{9} + 592 \, A a^{2} b^{6} c^{3} d^{6} e^{9} - 1305 \, B a^{4} b^{3} c^{4} d^{6} e^{9} + 3120 \, A a^{3} b^{4} c^{4} d^{6} e^{9} - 580 \, B a^{5} b c^{5} d^{6} e^{9} + 1180 \, A a^{4} b^{2} c^{5} d^{6} e^{9} - 160 \, A a^{5} c^{6} d^{6} e^{9} + 30 \, B a^{2} b^{8} c d^{5} e^{10} + 12 \, A a b^{9} c d^{5} e^{10} + 338 \, B a^{3} b^{6} c^{2} d^{5} e^{10} + 21 \, A a^{2} b^{7} c^{2} d^{5} e^{10} + 940 \, B a^{4} b^{4} c^{3} d^{5} e^{10} - 1272 \, A a^{3} b^{5} c^{3} d^{5} e^{10} + 894 \, B a^{5} b^{2} c^{4} d^{5} e^{10} - 2055 \, A a^{4} b^{3} c^{4} d^{5} e^{10} + 120 \, B a^{6} c^{5} d^{5} e^{10} + 132 \, A a^{5} b c^{5} d^{5} e^{10} - 40 \, B a^{3} b^{7} c d^{4} e^{11} - 30 \, A a^{2} b^{8} c d^{4} e^{11} - 325 \, B a^{4} b^{5} c^{2} d^{4} e^{11} + 110 \, A a^{3} b^{6} c^{2} d^{4} e^{11} - 706 \, B a^{5} b^{3} c^{3} d^{4} e^{11} + 1300 \, A a^{4} b^{4} c^{3} d^{4} e^{11} - 336 \, B a^{6} b c^{4} d^{4} e^{11} + 450 \, A a^{5} b^{2} c^{4} d^{4} e^{11} - 120 \, A a^{6} c^{5} d^{4} e^{11} + 30 \, B a^{4} b^{6} c d^{3} e^{12} + 40 \, A a^{3} b^{7} c d^{3} e^{12} + 244 \, B a^{5} b^{4} c^{2} d^{3} e^{12} - 235 \, A a^{4} b^{5} c^{2} d^{3} e^{12} + 352 \, B a^{6} b^{2} c^{3} d^{3} e^{12} - 638 \, A a^{5} b^{3} c^{3} d^{3} e^{12} + 48 \, B a^{7} c^{4} d^{3} e^{12} + 112 \, A a^{6} b c^{4} d^{3} e^{12} - 12 \, B a^{5} b^{5} c d^{2} e^{13} - 30 \, A a^{4} b^{6} c d^{2} e^{13} - 139 \, B a^{6} b^{3} c^{2} d^{2} e^{13} + 204 \, A a^{5} b^{4} c^{2} d^{2} e^{13} - 92 \, B a^{7} b c^{3} d^{2} e^{13} + 96 \, A a^{6} b^{2} c^{3} d^{2} e^{13} - 48 \, A a^{7} c^{4} d^{2} e^{13} + 2 \, B a^{6} b^{4} c d e^{14} + 12 \, A a^{5} b^{5} c d e^{14} + 50 \, B a^{7} b^{2} c^{2} d e^{14} - 85 \, A a^{6} b^{3} c^{2} d e^{14} + 8 \, B a^{8} c^{3} d e^{14} + 28 \, A a^{7} b c^{3} d e^{14} - 2 \, A a^{6} b^{4} c e^{15} - 8 \, B a^{8} b c^{2} e^{15} + 14 \, A a^{7} b^{2} c^{2} e^{15} - 8 \, A a^{8} c^{3} e^{15}\right)}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)} x + \frac{3 \, {\left(B b^{3} c^{8} d^{15} + 4 \, B a b c^{9} d^{15} - 2 \, A b^{2} c^{9} d^{15} - 8 \, A a c^{10} d^{15} - 8 \, B b^{4} c^{7} d^{14} e - 28 \, B a b^{2} c^{8} d^{14} e + 15 \, A b^{3} c^{8} d^{14} e + 60 \, A a b c^{9} d^{14} e + 28 \, B b^{5} c^{6} d^{13} e^{2} + 88 \, B a b^{3} c^{7} d^{13} e^{2} - 48 \, A b^{4} c^{7} d^{13} e^{2} + 40 \, B a^{2} b c^{8} d^{13} e^{2} - 212 \, A a b^{2} c^{8} d^{13} e^{2} - 64 \, A a^{2} c^{9} d^{13} e^{2} - 56 \, B b^{6} c^{5} d^{12} e^{3} - 170 \, B a b^{4} c^{6} d^{12} e^{3} + 84 \, A b^{5} c^{6} d^{12} e^{3} - 242 \, B a^{2} b^{2} c^{7} d^{12} e^{3} + 472 \, A a b^{3} c^{7} d^{12} e^{3} - 8 \, B a^{3} c^{8} d^{12} e^{3} + 408 \, A a^{2} b c^{8} d^{12} e^{3} + 70 \, B b^{7} c^{4} d^{11} e^{4} + 236 \, B a b^{5} c^{5} d^{11} e^{4} - 84 \, A b^{6} c^{5} d^{11} e^{4} + 615 \, B a^{2} b^{3} c^{6} d^{11} e^{4} - 726 \, A a b^{4} c^{6} d^{11} e^{4} + 204 \, B a^{3} b c^{7} d^{11} e^{4} - 1158 \, A a^{2} b^{2} c^{7} d^{11} e^{4} - 216 \, A a^{3} c^{8} d^{11} e^{4} - 56 \, B b^{8} c^{3} d^{10} e^{5} - 254 \, B a b^{6} c^{4} d^{10} e^{5} + 42 \, A b^{7} c^{4} d^{10} e^{5} - 860 \, B a^{2} b^{4} c^{5} d^{10} e^{5} + 772 \, A a b^{5} c^{5} d^{10} e^{5} - 912 \, B a^{3} b^{2} c^{6} d^{10} e^{5} + 1961 \, A a^{2} b^{3} c^{6} d^{10} e^{5} - 48 \, B a^{4} c^{7} d^{10} e^{5} + 1140 \, A a^{3} b c^{7} d^{10} e^{5} + 28 \, B b^{9} c^{2} d^{9} e^{6} + 208 \, B a b^{7} c^{3} d^{9} e^{6} + 745 \, B a^{2} b^{5} c^{4} d^{9} e^{6} - 530 \, A a b^{6} c^{4} d^{9} e^{6} + 1770 \, B a^{3} b^{3} c^{5} d^{9} e^{6} - 2220 \, A a^{2} b^{4} c^{5} d^{9} e^{6} + 560 \, B a^{4} b c^{6} d^{9} e^{6} - 2560 \, A a^{3} b^{2} c^{6} d^{9} e^{6} - 400 \, A a^{4} c^{7} d^{9} e^{6} - 8 \, B b^{10} c d^{8} e^{7} - 118 \, B a b^{8} c^{2} d^{8} e^{7} - 12 \, A b^{9} c^{2} d^{8} e^{7} - 450 \, B a^{2} b^{6} c^{3} d^{8} e^{7} + 192 \, A a b^{7} c^{3} d^{8} e^{7} - 1780 \, B a^{3} b^{4} c^{4} d^{8} e^{7} + 1719 \, A a^{2} b^{5} c^{4} d^{8} e^{7} - 1790 \, B a^{4} b^{2} c^{5} d^{8} e^{7} + 3270 \, A a^{3} b^{3} c^{5} d^{8} e^{7} - 120 \, B a^{5} c^{6} d^{8} e^{7} + 1680 \, A a^{4} b c^{6} d^{8} e^{7} + B b^{11} d^{7} e^{8} + 40 \, B a b^{9} c d^{7} e^{8} + 6 \, A b^{10} c d^{7} e^{8} + 217 \, B a^{2} b^{7} c^{2} d^{7} e^{8} - 2 \, A a b^{8} c^{2} d^{7} e^{8} + 968 \, B a^{3} b^{5} c^{3} d^{7} e^{8} - 838 \, A a^{2} b^{6} c^{3} d^{7} e^{8} + 2495 \, B a^{4} b^{3} c^{4} d^{7} e^{8} - 2700 \, A a^{3} b^{4} c^{4} d^{7} e^{8} + 860 \, B a^{5} b c^{5} d^{7} e^{8} - 2830 \, A a^{4} b^{2} c^{5} d^{7} e^{8} - 440 \, A a^{5} c^{6} d^{7} e^{8} - 6 \, B a b^{10} d^{6} e^{9} - A b^{11} d^{6} e^{9} - 80 \, B a^{2} b^{8} c d^{6} e^{9} - 24 \, A a b^{9} c d^{6} e^{9} - 304 \, B a^{3} b^{6} c^{2} d^{6} e^{9} + 183 \, A a^{2} b^{7} c^{2} d^{6} e^{9} - 1640 \, B a^{4} b^{4} c^{3} d^{6} e^{9} + 1496 \, A a^{3} b^{5} c^{3} d^{6} e^{9} - 1900 \, B a^{5} b^{2} c^{4} d^{6} e^{9} + 2545 \, A a^{4} b^{3} c^{4} d^{6} e^{9} - 160 \, B a^{6} c^{5} d^{6} e^{9} + 1380 \, A a^{5} b c^{5} d^{6} e^{9} + 15 \, B a^{2} b^{9} d^{5} e^{10} + 6 \, A a b^{10} d^{5} e^{10} + 82 \, B a^{3} b^{7} c d^{5} e^{10} + 24 \, A a^{2} b^{8} c d^{5} e^{10} + 458 \, B a^{4} b^{5} c^{2} d^{5} e^{10} - 480 \, A a^{3} b^{6} c^{2} d^{5} e^{10} + 1716 \, B a^{5} b^{3} c^{3} d^{5} e^{10} - 1440 \, A a^{4} b^{4} c^{3} d^{5} e^{10} + 744 \, B a^{6} b c^{4} d^{5} e^{10} - 1572 \, A a^{5} b^{2} c^{4} d^{5} e^{10} - 288 \, A a^{6} c^{5} d^{5} e^{10} - 20 \, B a^{3} b^{8} d^{4} e^{11} - 15 \, A a^{2} b^{9} d^{4} e^{11} - 50 \, B a^{4} b^{6} c d^{4} e^{11} + 30 \, A a^{3} b^{7} c d^{4} e^{11} - 578 \, B a^{5} b^{4} c^{2} d^{4} e^{11} + 550 \, A a^{4} b^{5} c^{2} d^{4} e^{11} - 1038 \, B a^{6} b^{2} c^{3} d^{4} e^{11} + 860 \, A a^{5} b^{3} c^{3} d^{4} e^{11} - 120 \, B a^{7} c^{4} d^{4} e^{11} + 600 \, A a^{6} b c^{4} d^{4} e^{11} + 15 \, B a^{4} b^{7} d^{3} e^{12} + 20 \, A a^{3} b^{8} d^{3} e^{12} + 28 \, B a^{5} b^{5} c d^{3} e^{12} - 90 \, A a^{4} b^{6} c d^{3} e^{12} + 473 \, B a^{6} b^{3} c^{2} d^{3} e^{12} - 318 \, A a^{5} b^{4} c^{2} d^{3} e^{12} + 340 \, B a^{7} b c^{3} d^{3} e^{12} - 362 \, A a^{6} b^{2} c^{3} d^{3} e^{12} - 104 \, A a^{7} c^{4} d^{3} e^{12} - 6 \, B a^{5} b^{6} d^{2} e^{13} - 15 \, A a^{4} b^{7} d^{2} e^{13} - 20 \, B a^{6} b^{4} c d^{2} e^{13} + 84 \, A a^{5} b^{5} c d^{2} e^{13} - 232 \, B a^{7} b^{2} c^{2} d^{2} e^{13} + 87 \, A a^{6} b^{3} c^{2} d^{2} e^{13} - 48 \, B a^{8} c^{3} d^{2} e^{13} + 108 \, A a^{7} b c^{3} d^{2} e^{13} + B a^{6} b^{5} d e^{14} + 6 \, A a^{5} b^{6} d e^{14} + 10 \, B a^{7} b^{3} c d e^{14} - 36 \, A a^{6} b^{4} c d e^{14} + 64 \, B a^{8} b c^{2} d e^{14} - 8 \, A a^{7} b^{2} c^{2} d e^{14} - 16 \, A a^{8} c^{3} d e^{14} - A a^{6} b^{5} e^{15} - 2 \, B a^{8} b^{2} c e^{15} + 6 \, A a^{7} b^{3} c e^{15} - 8 \, B a^{9} c^{2} e^{15}\right)}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)} x + \frac{2 \, B a b^{2} c^{8} d^{15} + A b^{3} c^{8} d^{15} + 8 \, B a^{2} c^{9} d^{15} - 12 \, A a b c^{9} d^{15} - 16 \, B a b^{3} c^{7} d^{14} e - 8 \, A b^{4} c^{7} d^{14} e - 56 \, B a^{2} b c^{8} d^{14} e + 94 \, A a b^{2} c^{8} d^{14} e - 8 \, A a^{2} c^{9} d^{14} e + 56 \, B a b^{4} c^{6} d^{13} e^{2} + 28 \, A b^{5} c^{6} d^{13} e^{2} + 176 \, B a^{2} b^{2} c^{7} d^{13} e^{2} - 312 \, A a b^{3} c^{7} d^{13} e^{2} + 80 \, B a^{3} c^{8} d^{13} e^{2} - 40 \, A a^{2} b c^{8} d^{13} e^{2} - 112 \, B a b^{5} c^{5} d^{12} e^{3} - 56 \, A b^{6} c^{5} d^{12} e^{3} - 339 \, B a^{2} b^{3} c^{6} d^{12} e^{3} + 560 \, A a b^{4} c^{6} d^{12} e^{3} - 492 \, B a^{3} b c^{7} d^{12} e^{3} + 496 \, A a^{2} b^{2} c^{7} d^{12} e^{3} - 80 \, A a^{3} c^{8} d^{12} e^{3} + 140 \, B a b^{6} c^{4} d^{11} e^{4} + 70 \, A b^{7} c^{4} d^{11} e^{4} + 466 \, B a^{2} b^{4} c^{5} d^{11} e^{4} - 560 \, A a b^{5} c^{5} d^{11} e^{4} + 1278 \, B a^{3} b^{2} c^{6} d^{11} e^{4} - 1649 \, A a^{2} b^{3} c^{6} d^{11} e^{4} + 312 \, B a^{4} c^{7} d^{11} e^{4} + 156 \, A a^{3} b c^{7} d^{11} e^{4} - 112 \, B a b^{7} c^{3} d^{10} e^{5} - 56 \, A b^{8} c^{3} d^{10} e^{5} - 493 \, B a^{2} b^{5} c^{4} d^{10} e^{5} + 252 \, A a b^{6} c^{4} d^{10} e^{5} - 1834 \, B a^{3} b^{3} c^{5} d^{10} e^{5} + 2726 \, A a^{2} b^{4} c^{5} d^{10} e^{5} - 1632 \, B a^{4} b c^{6} d^{10} e^{5} + 738 \, A a^{3} b^{2} c^{6} d^{10} e^{5} - 312 \, A a^{4} c^{7} d^{10} e^{5} + 56 \, B a b^{8} c^{2} d^{9} e^{6} + 28 \, A b^{9} c^{2} d^{9} e^{6} + 396 \, B a^{2} b^{6} c^{3} d^{9} e^{6} + 56 \, A a b^{7} c^{3} d^{9} e^{6} + 1620 \, B a^{3} b^{4} c^{4} d^{9} e^{6} - 2447 \, A a^{2} b^{5} c^{4} d^{9} e^{6} + 3460 \, B a^{4} b^{2} c^{5} d^{9} e^{6} - 3150 \, A a^{3} b^{3} c^{5} d^{9} e^{6} + 640 \, B a^{5} c^{6} d^{9} e^{6} + 960 \, A a^{4} b c^{6} d^{9} e^{6} - 16 \, B a b^{9} c d^{8} e^{7} - 8 \, A b^{10} c d^{8} e^{7} - 221 \, B a^{2} b^{7} c^{2} d^{8} e^{7} - 128 \, A a b^{8} c^{2} d^{8} e^{7} - 960 \, B a^{3} b^{5} c^{3} d^{8} e^{7} + 1060 \, A a^{2} b^{6} c^{3} d^{8} e^{7} - 3785 \, B a^{4} b^{3} c^{4} d^{8} e^{7} + 4820 \, A a^{3} b^{4} c^{4} d^{8} e^{7} - 2740 \, B a^{5} b c^{5} d^{8} e^{7} - 100 \, A a^{4} b^{2} c^{5} d^{8} e^{7} - 640 \, A a^{5} c^{6} d^{8} e^{7} + 2 \, B a b^{10} d^{7} e^{8} + A b^{11} d^{7} e^{8} + 74 \, B a^{2} b^{8} c d^{7} e^{8} + 60 \, A a b^{9} c d^{7} e^{8} + 422 \, B a^{3} b^{6} c^{2} d^{7} e^{8} - 31 \, A a^{2} b^{7} c^{2} d^{7} e^{8} + 2260 \, B a^{4} b^{4} c^{3} d^{7} e^{8} - 3520 \, A a^{3} b^{5} c^{3} d^{7} e^{8} + 4510 \, B a^{5} b^{2} c^{4} d^{7} e^{8} - 2865 \, A a^{4} b^{3} c^{4} d^{7} e^{8} + 760 \, B a^{6} c^{5} d^{7} e^{8} + 1900 \, A a^{5} b c^{5} d^{7} e^{8} - 11 \, B a^{2} b^{9} d^{6} e^{9} - 10 \, A a b^{10} d^{6} e^{9} - 138 \, B a^{3} b^{7} c d^{6} e^{9} - 146 \, A a^{2} b^{8} c d^{6} e^{9} - 742 \, B a^{4} b^{5} c^{2} d^{6} e^{9} + 1034 \, A a^{3} b^{6} c^{2} d^{6} e^{9} - 3500 \, B a^{5} b^{3} c^{3} d^{6} e^{9} + 4180 \, A a^{4} b^{4} c^{3} d^{6} e^{9} - 2520 \, B a^{6} b c^{4} d^{6} e^{9} - 1150 \, A a^{5} b^{2} c^{4} d^{6} e^{9} - 760 \, A a^{6} c^{5} d^{6} e^{9} + 24 \, B a^{3} b^{8} d^{5} e^{10} + 39 \, A a^{2} b^{9} d^{5} e^{10} + 152 \, B a^{4} b^{6} c d^{5} e^{10} + 82 \, A a^{3} b^{7} c d^{5} e^{10} + 1240 \, B a^{5} b^{4} c^{2} d^{5} e^{10} - 2198 \, A a^{4} b^{5} c^{2} d^{5} e^{10} + 2952 \, B a^{6} b^{2} c^{3} d^{5} e^{10} - 1484 \, A a^{5} b^{3} c^{3} d^{5} e^{10} + 528 \, B a^{7} c^{4} d^{5} e^{10} + 1848 \, A a^{6} b c^{4} d^{5} e^{10} - 25 \, B a^{4} b^{7} d^{4} e^{11} - 80 \, A a^{3} b^{8} d^{4} e^{11} - 160 \, B a^{5} b^{5} c d^{4} e^{11} + 240 \, A a^{4} b^{6} c d^{4} e^{11} - 1381 \, B a^{6} b^{3} c^{2} d^{4} e^{11} + 1952 \, A a^{5} b^{4} c^{2} d^{4} e^{11} - 1236 \, B a^{7} b c^{3} d^{4} e^{11} - 936 \, A a^{6} b^{2} c^{3} d^{4} e^{11} - 528 \, A a^{7} c^{4} d^{4} e^{11} + 10 \, B a^{5} b^{6} d^{3} e^{12} + 95 \, A a^{4} b^{7} d^{3} e^{12} + 186 \, B a^{6} b^{4} c d^{3} e^{12} - 512 \, A a^{5} b^{5} c d^{3} e^{12} + 866 \, B a^{7} b^{2} c^{2} d^{3} e^{12} - 607 \, A a^{6} b^{3} c^{2} d^{3} e^{12} + 200 \, B a^{8} c^{3} d^{3} e^{12} + 900 \, A a^{7} b c^{3} d^{3} e^{12} + 3 \, B a^{6} b^{5} d^{2} e^{13} - 66 \, A a^{5} b^{6} d^{2} e^{13} - 154 \, B a^{7} b^{3} c d^{2} e^{13} + 430 \, A a^{6} b^{4} c d^{2} e^{13} - 272 \, B a^{8} b c^{2} d^{2} e^{13} - 194 \, A a^{7} b^{2} c^{2} d^{2} e^{13} - 200 \, A a^{8} c^{3} d^{2} e^{13} - 4 \, B a^{7} b^{4} d e^{14} + 25 \, A a^{6} b^{5} d e^{14} + 68 \, B a^{8} b^{2} c d e^{14} - 174 \, A a^{7} b^{3} c d e^{14} + 32 \, B a^{9} c^{2} d e^{14} + 176 \, A a^{8} b c^{2} d e^{14} + B a^{8} b^{3} e^{15} - 4 \, A a^{7} b^{4} e^{15} - 12 \, B a^{9} b c e^{15} + 28 \, A a^{8} b^{2} c e^{15} - 32 \, A a^{9} c^{2} e^{15}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2*(B*d*e^3 - A*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) - 2/3*((((8*B*b*c^10*d^15 - 16*A*c^11*d^15 - 62*B*b^2*c^9*d^14*e + 8*B*a*c^10*d^14*e + 120*A*b*c^10*d^14*e + 207*B*b^3*c^8*d^13*e^2 + 12*B*a*b*c^9*d^13*e^2 - 386*A*b^2*c^9*d^13*e^2 - 136*A*a*c^10*d^13*e^2 - 388*B*b^4*c^7*d^12*e^3 - 276*B*a*b^2*c^8*d^12*e^3 + 689*A*b^3*c^8*d^12*e^3 + 32*B*a^2*c^9*d^12*e^3 + 884*A*a*b*c^9*d^12*e^3 + 445*B*b^5*c^6*d^11*e^4 + 938*B*a*b^3*c^7*d^11*e^4 - 732*A*b^4*c^7*d^11*e^4 + 48*B*a^2*b*c^8*d^11*e^4 - 2412*A*a*b^2*c^8*d^11*e^4 - 480*A*a^2*c^9*d^11*e^4 - 318*B*b^6*c^5*d^10*e^5 - 1530*B*a*b^4*c^6*d^10*e^5 + 451*A*b^5*c^6*d^10*e^5 - 810*B*a^2*b^2*c^7*d^10*e^5 + 3542*A*a*b^3*c^7*d^10*e^5 + 24*B*a^3*c^8*d^10*e^5 + 2640*A*a^2*b*c^8*d^10*e^5 + 137*B*b^7*c^4*d^9*e^6 + 1392*B*a*b^5*c^5*d^9*e^6 - 130*A*b^6*c^5*d^9*e^6 + 2165*B*a^2*b^3*c^6*d^9*e^6 - 2950*A*a*b^4*c^6*d^9*e^6 + 340*B*a^3*b*c^7*d^9*e^6 - 5910*A*a^2*b^2*c^7*d^9*e^6 - 920*A*a^3*c^8*d^9*e^6 - 32*B*b^8*c^3*d^8*e^7 - 712*B*a*b^6*c^4*d^8*e^7 - 9*A*b^7*c^4*d^8*e^7 - 2640*B*a^2*b^4*c^5*d^8*e^7 + 1296*A*a*b^5*c^5*d^8*e^7 - 1720*B*a^3*b^2*c^6*d^8*e^7 + 6795*A*a^2*b^3*c^6*d^8*e^7 - 80*B*a^4*c^7*d^8*e^7 + 4140*A*a^3*b*c^7*d^8*e^7 + 3*B*b^9*c^2*d^7*e^8 + 186*B*a*b^7*c^3*d^7*e^8 + 16*A*b^8*c^3*d^7*e^8 + 1638*B*a^2*b^5*c^4*d^7*e^8 - 184*A*a*b^6*c^4*d^7*e^8 + 2940*B*a^3*b^3*c^5*d^7*e^8 - 4080*A*a^2*b^4*c^5*d^7*e^8 + 840*B*a^4*b*c^6*d^7*e^8 - 7240*A*a^3*b^2*c^6*d^7*e^8 - 1040*A*a^4*c^7*d^7*e^8 - 18*B*a*b^8*c^2*d^6*e^9 - 3*A*b^9*c^2*d^6*e^9 - 478*B*a^2*b^6*c^3*d^6*e^9 - 58*A*a*b^7*c^3*d^6*e^9 - 2260*B*a^3*b^4*c^4*d^6*e^9 + 1050*A*a^2*b^5*c^4*d^6*e^9 - 2130*B*a^4*b^2*c^5*d^6*e^9 + 6020*A*a^3*b^3*c^5*d^6*e^9 - 200*B*a^5*c^6*d^6*e^9 + 3640*A*a^4*b*c^6*d^6*e^9 + 45*B*a^2*b^7*c^2*d^5*e^10 + 18*A*a*b^8*c^2*d^5*e^10 + 736*B*a^3*b^5*c^3*d^5*e^10 + 30*A*a^2*b^6*c^3*d^5*e^10 + 2105*B*a^4*b^3*c^4*d^5*e^10 - 2220*A*a^3*b^4*c^4*d^5*e^10 + 948*B*a^5*b*c^5*d^5*e^10 - 4590*A*a^4*b^2*c^5*d^5*e^10 - 696*A*a^5*c^6*d^5*e^10 - 60*B*a^3*b^6*c^2*d^4*e^11 - 45*A*a^2*b^7*c^2*d^4*e^11 - 780*B*a^4*b^4*c^3*d^4*e^11 + 160*A*a^3*b^5*c^3*d^4*e^11 - 1332*B*a^5*b^2*c^4*d^4*e^11 + 2375*A*a^4*b^3*c^4*d^4*e^11 - 192*B*a^6*c^5*d^4*e^11 + 1740*A*a^5*b*c^5*d^4*e^11 + 45*B*a^4*b^5*c^2*d^3*e^12 + 60*A*a^3*b^6*c^2*d^3*e^12 + 602*B*a^5*b^3*c^3*d^3*e^12 - 340*A*a^4*b^4*c^3*d^3*e^12 + 512*B*a^6*b*c^4*d^3*e^12 - 1356*A*a^5*b^2*c^4*d^3*e^12 - 256*A*a^6*c^5*d^3*e^12 - 18*B*a^5*b^4*c^2*d^2*e^13 - 45*A*a^4*b^5*c^2*d^2*e^13 - 326*B*a^6*b^2*c^3*d^2*e^13 + 294*A*a^5*b^3*c^3*d^2*e^13 - 88*B*a^7*c^4*d^2*e^13 + 384*A*a^6*b*c^4*d^2*e^13 + 3*B*a^6*b^3*c^2*d*e^14 + 18*A*a^5*b^4*c^2*d*e^14 + 108*B*a^7*b*c^3*d*e^14 - 122*A*a^6*b^2*c^3*d*e^14 - 40*A*a^7*c^4*d*e^14 - 3*A*a^6*b^3*c^2*e^15 - 16*B*a^8*c^3*e^15 + 20*A*a^7*b*c^3*e^15)*x/(b^4*c^8*d^16 - 8*a*b^2*c^9*d^16 + 16*a^2*c^10*d^16 - 8*b^5*c^7*d^15*e + 64*a*b^3*c^8*d^15*e - 128*a^2*b*c^9*d^15*e + 28*b^6*c^6*d^14*e^2 - 216*a*b^4*c^7*d^14*e^2 + 384*a^2*b^2*c^8*d^14*e^2 + 128*a^3*c^9*d^14*e^2 - 56*b^7*c^5*d^13*e^3 + 392*a*b^5*c^6*d^13*e^3 - 448*a^2*b^3*c^7*d^13*e^3 - 896*a^3*b*c^8*d^13*e^3 + 70*b^8*c^4*d^12*e^4 - 392*a*b^6*c^5*d^12*e^4 - 196*a^2*b^4*c^6*d^12*e^4 + 2464*a^3*b^2*c^7*d^12*e^4 + 448*a^4*c^8*d^12*e^4 - 56*b^9*c^3*d^11*e^5 + 168*a*b^7*c^4*d^11*e^5 + 1176*a^2*b^5*c^5*d^11*e^5 - 3136*a^3*b^3*c^6*d^11*e^5 - 2688*a^4*b*c^7*d^11*e^5 + 28*b^10*c^2*d^10*e^6 + 56*a*b^8*c^3*d^10*e^6 - 1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 12*a^2*b^8*c^2*d^8*e^8 - 1904*a^3*b^6*c^3*d^8*e^8 + 2310*a^4*b^4*c^4*d^8*e^8 + 8400*a^5*b^2*c^5*d^8*e^8 + 1120*a^6*c^6*d^8*e^8 - 8*a*b^11*d^7*e^9 - 104*a^2*b^9*c*d^7*e^9 + 656*a^3*b^7*c^2*d^7*e^9 + 1512*a^4*b^5*c^3*d^7*e^9 - 6720*a^5*b^3*c^4*d^7*e^9 - 4480*a^6*b*c^5*d^7*e^9 + 28*a^2*b^10*d^6*e^10 + 56*a^3*b^8*c*d^6*e^10 - 1372*a^4*b^6*c^2*d^6*e^10 + 1176*a^5*b^4*c^3*d^6*e^10 + 6272*a^6*b^2*c^4*d^6*e^10 + 896*a^7*c^5*d^6*e^10 - 56*a^3*b^9*d^5*e^11 + 168*a^4*b^7*c*d^5*e^11 + 1176*a^5*b^5*c^2*d^5*e^11 - 3136*a^6*b^3*c^3*d^5*e^11 - 2688*a^7*b*c^4*d^5*e^11 + 70*a^4*b^8*d^4*e^12 - 392*a^5*b^6*c*d^4*e^12 - 196*a^6*b^4*c^2*d^4*e^12 + 2464*a^7*b^2*c^3*d^4*e^12 + 448*a^8*c^4*d^4*e^12 - 56*a^5*b^7*d^3*e^13 + 392*a^6*b^5*c*d^3*e^13 - 448*a^7*b^3*c^2*d^3*e^13 - 896*a^8*b*c^3*d^3*e^13 + 28*a^6*b^6*d^2*e^14 - 216*a^7*b^4*c*d^2*e^14 + 384*a^8*b^2*c^2*d^2*e^14 + 128*a^9*c^3*d^2*e^14 - 8*a^7*b^5*d*e^15 + 64*a^8*b^3*c*d*e^15 - 128*a^9*b*c^2*d*e^15 + a^8*b^4*e^16 - 8*a^9*b^2*c*e^16 + 16*a^10*c^2*e^16) + 3*(4*B*b^2*c^9*d^15 - 8*A*b*c^10*d^15 - 31*B*b^3*c^8*d^14*e + 4*B*a*b*c^9*d^14*e + 60*A*b^2*c^9*d^14*e + 104*B*b^4*c^7*d^13*e^2 + 2*B*a*b^2*c^8*d^13*e^2 - 193*A*b^3*c^8*d^13*e^2 + 8*B*a^2*c^9*d^13*e^2 - 68*A*a*b*c^9*d^13*e^2 - 197*B*b^5*c^6*d^12*e^3 - 114*B*a*b^3*c^7*d^12*e^3 + 344*A*b^4*c^7*d^12*e^3 - 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512*A*a^5*b^5*c*d^3*e^12 + 866*B*a^7*b^2*c^2*d^3*e^12 - 607*A*a^6*b^3*c^2*d^3*e^12 + 200*B*a^8*c^3*d^3*e^12 + 900*A*a^7*b*c^3*d^3*e^12 + 3*B*a^6*b^5*d^2*e^13 - 66*A*a^5*b^6*d^2*e^13 - 154*B*a^7*b^3*c*d^2*e^13 + 430*A*a^6*b^4*c*d^2*e^13 - 272*B*a^8*b*c^2*d^2*e^13 - 194*A*a^7*b^2*c^2*d^2*e^13 - 200*A*a^8*c^3*d^2*e^13 - 4*B*a^7*b^4*d*e^14 + 25*A*a^6*b^5*d*e^14 + 68*B*a^8*b^2*c*d*e^14 - 174*A*a^7*b^3*c*d*e^14 + 32*B*a^9*c^2*d*e^14 + 176*A*a^8*b*c^2*d*e^14 + B*a^8*b^3*e^15 - 4*A*a^7*b^4*e^15 - 12*B*a^9*b*c*e^15 + 28*A*a^8*b^2*c*e^15 - 32*A*a^9*c^2*e^15)/(b^4*c^8*d^16 - 8*a*b^2*c^9*d^16 + 16*a^2*c^10*d^16 - 8*b^5*c^7*d^15*e + 64*a*b^3*c^8*d^15*e - 128*a^2*b*c^9*d^15*e + 28*b^6*c^6*d^14*e^2 - 216*a*b^4*c^7*d^14*e^2 + 384*a^2*b^2*c^8*d^14*e^2 + 128*a^3*c^9*d^14*e^2 - 56*b^7*c^5*d^13*e^3 + 392*a*b^5*c^6*d^13*e^3 - 448*a^2*b^3*c^7*d^13*e^3 - 896*a^3*b*c^8*d^13*e^3 + 70*b^8*c^4*d^12*e^4 - 392*a*b^6*c^5*d^12*e^4 - 196*a^2*b^4*c^6*d^12*e^4 + 2464*a^3*b^2*c^7*d^12*e^4 + 448*a^4*c^8*d^12*e^4 - 56*b^9*c^3*d^11*e^5 + 168*a*b^7*c^4*d^11*e^5 + 1176*a^2*b^5*c^5*d^11*e^5 - 3136*a^3*b^3*c^6*d^11*e^5 - 2688*a^4*b*c^7*d^11*e^5 + 28*b^10*c^2*d^10*e^6 + 56*a*b^8*c^3*d^10*e^6 - 1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 12*a^2*b^8*c^2*d^8*e^8 - 1904*a^3*b^6*c^3*d^8*e^8 + 2310*a^4*b^4*c^4*d^8*e^8 + 8400*a^5*b^2*c^5*d^8*e^8 + 1120*a^6*c^6*d^8*e^8 - 8*a*b^11*d^7*e^9 - 104*a^2*b^9*c*d^7*e^9 + 656*a^3*b^7*c^2*d^7*e^9 + 1512*a^4*b^5*c^3*d^7*e^9 - 6720*a^5*b^3*c^4*d^7*e^9 - 4480*a^6*b*c^5*d^7*e^9 + 28*a^2*b^10*d^6*e^10 + 56*a^3*b^8*c*d^6*e^10 - 1372*a^4*b^6*c^2*d^6*e^10 + 1176*a^5*b^4*c^3*d^6*e^10 + 6272*a^6*b^2*c^4*d^6*e^10 + 896*a^7*c^5*d^6*e^10 - 56*a^3*b^9*d^5*e^11 + 168*a^4*b^7*c*d^5*e^11 + 1176*a^5*b^5*c^2*d^5*e^11 - 3136*a^6*b^3*c^3*d^5*e^11 - 2688*a^7*b*c^4*d^5*e^11 + 70*a^4*b^8*d^4*e^12 - 392*a^5*b^6*c*d^4*e^12 - 196*a^6*b^4*c^2*d^4*e^12 + 2464*a^7*b^2*c^3*d^4*e^12 + 448*a^8*c^4*d^4*e^12 - 56*a^5*b^7*d^3*e^13 + 392*a^6*b^5*c*d^3*e^13 - 448*a^7*b^3*c^2*d^3*e^13 - 896*a^8*b*c^3*d^3*e^13 + 28*a^6*b^6*d^2*e^14 - 216*a^7*b^4*c*d^2*e^14 + 384*a^8*b^2*c^2*d^2*e^14 + 128*a^9*c^3*d^2*e^14 - 8*a^7*b^5*d*e^15 + 64*a^8*b^3*c*d*e^15 - 128*a^9*b*c^2*d*e^15 + a^8*b^4*e^16 - 8*a^9*b^2*c*e^16 + 16*a^10*c^2*e^16))/(c*x^2 + b*x + a)^(3/2)","B",0
2486,1,8475,0,3.786712," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{{\left(32 \, \sqrt{c d^{2} - b d e + a e^{2}} B b c^{4} d^{4} e^{2} - 64 \, \sqrt{c d^{2} - b d e + a e^{2}} A c^{5} d^{4} e^{2} - 80 \, \sqrt{c d^{2} - b d e + a e^{2}} B b^{2} c^{3} d^{3} e^{3} + 64 \, \sqrt{c d^{2} - b d e + a e^{2}} B a c^{4} d^{3} e^{3} + 128 \, \sqrt{c d^{2} - b d e + a e^{2}} A b c^{4} d^{3} e^{3} - 24 \, B b^{4} c^{\frac{3}{2}} d^{2} e^{5} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 192 \, B a b^{2} c^{\frac{5}{2}} d^{2} e^{5} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 384 \, B a^{2} c^{\frac{7}{2}} d^{2} e^{5} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 36 \, \sqrt{c d^{2} - b d e + a e^{2}} B b^{3} c^{2} d^{2} e^{4} + 48 \, \sqrt{c d^{2} - b d e + a e^{2}} B a b c^{3} d^{2} e^{4} - 24 \, \sqrt{c d^{2} - b d e + a e^{2}} A b^{2} c^{3} d^{2} e^{4} - 288 \, \sqrt{c d^{2} - b d e + a e^{2}} A a c^{4} d^{2} e^{4} + 9 \, B b^{5} \sqrt{c} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 72 \, B a b^{3} c^{\frac{3}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 30 \, A b^{4} c^{\frac{3}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 144 \, B a^{2} b c^{\frac{5}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 240 \, A a b^{2} c^{\frac{5}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 480 \, A a^{2} c^{\frac{7}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 18 \, \sqrt{c d^{2} - b d e + a e^{2}} B b^{4} c d e^{5} + 112 \, \sqrt{c d^{2} - b d e + a e^{2}} B a b^{2} c^{2} d e^{5} - 40 \, \sqrt{c d^{2} - b d e + a e^{2}} A b^{3} c^{2} d e^{5} - 416 \, \sqrt{c d^{2} - b d e + a e^{2}} B a^{2} c^{3} d e^{5} + 288 \, \sqrt{c d^{2} - b d e + a e^{2}} A a b c^{3} d e^{5} + 6 \, B a b^{4} \sqrt{c} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 15 \, A b^{5} \sqrt{c} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 48 \, B a^{2} b^{2} c^{\frac{3}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 120 \, A a b^{3} c^{\frac{3}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 96 \, B a^{3} c^{\frac{5}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 240 \, A a^{2} b c^{\frac{5}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 12 \, \sqrt{c d^{2} - b d e + a e^{2}} B a b^{3} c e^{6} + 30 \, \sqrt{c d^{2} - b d e + a e^{2}} A b^{4} c e^{6} + 80 \, \sqrt{c d^{2} - b d e + a e^{2}} B a^{2} b c^{2} e^{6} - 200 \, \sqrt{c d^{2} - b d e + a e^{2}} A a b^{2} c^{2} e^{6} + 256 \, \sqrt{c d^{2} - b d e + a e^{2}} A a^{2} c^{3} e^{6}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e + a e^{2}} b^{4} c^{\frac{7}{2}} d^{6} - 8 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{2} c^{\frac{9}{2}} d^{6} + 16 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} c^{\frac{11}{2}} d^{6} - 3 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{5} c^{\frac{5}{2}} d^{5} e + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{3} c^{\frac{7}{2}} d^{5} e - 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b c^{\frac{9}{2}} d^{5} e + 3 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{6} c^{\frac{3}{2}} d^{4} e^{2} - 21 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{4} c^{\frac{5}{2}} d^{4} e^{2} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{2} c^{\frac{7}{2}} d^{4} e^{2} + 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} c^{\frac{9}{2}} d^{4} e^{2} - \sqrt{c d^{2} - b d e + a e^{2}} b^{7} \sqrt{c} d^{3} e^{3} + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{5} c^{\frac{3}{2}} d^{3} e^{3} + 32 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{3} c^{\frac{5}{2}} d^{3} e^{3} - 96 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b c^{\frac{7}{2}} d^{3} e^{3} + 3 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{6} \sqrt{c} d^{2} e^{4} - 21 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{4} c^{\frac{3}{2}} d^{2} e^{4} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b^{2} c^{\frac{5}{2}} d^{2} e^{4} + 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{4} c^{\frac{7}{2}} d^{2} e^{4} - 3 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{5} \sqrt{c} d e^{5} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b^{3} c^{\frac{3}{2}} d e^{5} - 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{4} b c^{\frac{5}{2}} d e^{5} + \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b^{4} \sqrt{c} e^{6} - 8 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{4} b^{2} c^{\frac{3}{2}} e^{6} + 16 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{5} c^{\frac{5}{2}} e^{6}} + \frac{2 \, {\left(\frac{{\left(\frac{{\left(\frac{{\left(\frac{4 \, {\left(4 \, B b c^{5} d^{7} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, A c^{6} d^{7} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, B b^{2} c^{4} d^{6} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 8 \, B a c^{5} d^{6} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 28 \, A b c^{5} d^{6} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 21 \, B b^{3} c^{3} d^{5} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 30 \, A b^{2} c^{4} d^{5} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, A a c^{5} d^{5} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 18 \, B b^{4} c^{2} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 34 \, B a b^{2} c^{3} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, A b^{3} c^{3} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 128 \, B a^{2} c^{4} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 120 \, A a b c^{4} d^{4} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 12 \, B b^{5} c d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 66 \, B a b^{3} c^{2} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 18 \, A b^{4} c^{2} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 212 \, B a^{2} b c^{3} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 164 \, A a b^{2} c^{3} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 88 \, A a^{2} c^{4} d^{3} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, B b^{6} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 18 \, B a b^{4} c d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 18 \, A b^{5} c d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 36 \, B a^{2} b^{2} c^{2} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 126 \, A a b^{3} c^{2} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 120 \, B a^{3} c^{3} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 132 \, A a^{2} b c^{3} d^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + B a b^{5} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, A b^{6} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 11 \, B a^{2} b^{3} c d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, A a b^{4} c d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 56 \, B a^{3} b c^{2} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 30 \, A a^{2} b^{2} c^{2} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 128 \, A a^{3} c^{3} d e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, B a^{2} b^{4} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, A a b^{5} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 14 \, B a^{3} b^{2} c e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 37 \, A a^{2} b^{3} c e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, B a^{4} c^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 64 \, A a^{3} b c^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}} + \frac{3 \, {\left(B b^{4} c^{2} d^{5} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, B a b^{2} c^{3} d^{5} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, B a^{2} c^{4} d^{5} e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, B b^{5} c d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, B a b^{3} c^{2} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A b^{4} c^{2} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, B a^{2} b c^{3} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 8 \, A a b^{2} c^{3} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A a^{2} c^{4} d^{4} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + B b^{6} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 6 \, B a b^{4} c d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, A b^{5} c d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A a b^{3} c^{2} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, B a^{3} c^{3} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, A a^{2} b c^{3} d^{3} e^{22} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, B a b^{5} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A b^{6} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, B a^{2} b^{3} c d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 6 \, A a b^{4} c d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, B a^{3} b c^{2} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, A a^{3} c^{3} d^{2} e^{23} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + B a^{2} b^{4} d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, A a b^{5} d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, B a^{3} b^{2} c d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A a^{2} b^{3} c d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, B a^{4} c^{2} d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, A a^{3} b c^{2} d e^{24} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - A a^{2} b^{4} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 8 \, A a^{3} b^{2} c e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A a^{4} c^{2} e^{25} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{3 \, {\left(16 \, B b c^{5} d^{6} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, A c^{6} d^{6} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 56 \, B b^{2} c^{4} d^{5} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, B a c^{5} d^{5} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 96 \, A b c^{5} d^{5} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 60 \, B b^{3} c^{3} d^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 80 \, A b^{2} c^{4} d^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 160 \, A a c^{5} d^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 42 \, B b^{4} c^{2} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 96 \, B a b^{2} c^{3} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 352 \, B a^{2} c^{4} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 320 \, A a b c^{4} d^{3} e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 20 \, B b^{5} c d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 120 \, B a b^{3} c^{2} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 46 \, A b^{4} c^{2} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 400 \, B a^{2} b c^{3} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 368 \, A a b^{2} c^{3} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 256 \, A a^{2} c^{4} d^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, B b^{6} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 26 \, B a b^{4} c d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 30 \, A b^{5} c d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 88 \, B a^{2} b^{2} c^{2} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 208 \, A a b^{3} c^{2} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 64 \, B a^{3} c^{3} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 256 \, A a^{2} b c^{3} d e^{20} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, B a b^{5} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, A b^{6} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 12 \, B a^{2} b^{3} c e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 30 \, A a b^{4} c e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, A a^{2} b^{2} c^{2} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 64 \, A a^{3} c^{3} e^{21} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(8 \, B b c^{5} d^{5} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, A c^{6} d^{5} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, B b^{2} c^{4} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, B a c^{5} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 40 \, A b c^{5} d^{4} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 19 \, B b^{3} c^{3} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 4 \, B a b c^{4} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 22 \, A b^{2} c^{4} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 72 \, A a c^{5} d^{3} e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 11 \, B b^{4} c^{2} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 38 \, B a b^{2} c^{3} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 7 \, A b^{3} c^{3} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 136 \, B a^{2} c^{4} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 108 \, A a b c^{4} d^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, B b^{5} c d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 23 \, B a b^{3} c^{2} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 15 \, A b^{4} c^{2} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 84 \, B a^{2} b c^{3} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 106 \, A a b^{2} c^{3} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 104 \, A a^{2} c^{4} d e^{18} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, B a b^{4} c e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, A b^{5} c e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 14 \, B a^{2} b^{2} c^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 35 \, A a b^{3} c^{2} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 8 \, B a^{3} c^{3} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 52 \, A a^{2} b c^{3} e^{19} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{16 \, B b c^{5} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 32 \, A c^{6} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 40 \, B b^{2} c^{4} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, B a c^{5} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 64 \, A b c^{5} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 18 \, B b^{3} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, B a b c^{4} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 12 \, A b^{2} c^{4} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 144 \, A a c^{5} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 9 \, B b^{4} c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 56 \, B a b^{2} c^{3} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 20 \, A b^{3} c^{3} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 208 \, B a^{2} c^{4} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 144 \, A a b c^{4} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 6 \, B a b^{3} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 15 \, A b^{4} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 40 \, B a^{2} b c^{3} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 100 \, A a b^{2} c^{3} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 128 \, A a^{2} c^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2} + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)^{2}}\right)}}{{\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{\frac{3}{2}}} + \frac{3 \, {\left(8 \, B c d^{2} e^{6} - 3 \, B b d e^{7} - 10 \, A c d e^{7} - 2 \, B a e^{8} + 5 \, A b e^{8}\right)} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3} + a e^{4}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"1/6*((32*sqrt(c*d^2 - b*d*e + a*e^2)*B*b*c^4*d^4*e^2 - 64*sqrt(c*d^2 - b*d*e + a*e^2)*A*c^5*d^4*e^2 - 80*sqrt(c*d^2 - b*d*e + a*e^2)*B*b^2*c^3*d^3*e^3 + 64*sqrt(c*d^2 - b*d*e + a*e^2)*B*a*c^4*d^3*e^3 + 128*sqrt(c*d^2 - b*d*e + a*e^2)*A*b*c^4*d^3*e^3 - 24*B*b^4*c^(3/2)*d^2*e^5*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 192*B*a*b^2*c^(5/2)*d^2*e^5*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 384*B*a^2*c^(7/2)*d^2*e^5*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 36*sqrt(c*d^2 - b*d*e + a*e^2)*B*b^3*c^2*d^2*e^4 + 48*sqrt(c*d^2 - b*d*e + a*e^2)*B*a*b*c^3*d^2*e^4 - 24*sqrt(c*d^2 - b*d*e + a*e^2)*A*b^2*c^3*d^2*e^4 - 288*sqrt(c*d^2 - b*d*e + a*e^2)*A*a*c^4*d^2*e^4 + 9*B*b^5*sqrt(c)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 72*B*a*b^3*c^(3/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 30*A*b^4*c^(3/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 144*B*a^2*b*c^(5/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 240*A*a*b^2*c^(5/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 480*A*a^2*c^(7/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 18*sqrt(c*d^2 - b*d*e + a*e^2)*B*b^4*c*d*e^5 + 112*sqrt(c*d^2 - b*d*e + a*e^2)*B*a*b^2*c^2*d*e^5 - 40*sqrt(c*d^2 - b*d*e + a*e^2)*A*b^3*c^2*d*e^5 - 416*sqrt(c*d^2 - b*d*e + a*e^2)*B*a^2*c^3*d*e^5 + 288*sqrt(c*d^2 - b*d*e + a*e^2)*A*a*b*c^3*d*e^5 + 6*B*a*b^4*sqrt(c)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 15*A*b^5*sqrt(c)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 48*B*a^2*b^2*c^(3/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 120*A*a*b^3*c^(3/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 96*B*a^3*c^(5/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 240*A*a^2*b*c^(5/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 12*sqrt(c*d^2 - b*d*e + a*e^2)*B*a*b^3*c*e^6 + 30*sqrt(c*d^2 - b*d*e + a*e^2)*A*b^4*c*e^6 + 80*sqrt(c*d^2 - b*d*e + a*e^2)*B*a^2*b*c^2*e^6 - 200*sqrt(c*d^2 - b*d*e + a*e^2)*A*a*b^2*c^2*e^6 + 256*sqrt(c*d^2 - b*d*e + a*e^2)*A*a^2*c^3*e^6)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e + a*e^2)*b^4*c^(7/2)*d^6 - 8*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^2*c^(9/2)*d^6 + 16*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*c^(11/2)*d^6 - 3*sqrt(c*d^2 - b*d*e + a*e^2)*b^5*c^(5/2)*d^5*e + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^3*c^(7/2)*d^5*e - 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b*c^(9/2)*d^5*e + 3*sqrt(c*d^2 - b*d*e + a*e^2)*b^6*c^(3/2)*d^4*e^2 - 21*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^4*c^(5/2)*d^4*e^2 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^2*c^(7/2)*d^4*e^2 + 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*c^(9/2)*d^4*e^2 - sqrt(c*d^2 - b*d*e + a*e^2)*b^7*sqrt(c)*d^3*e^3 + 2*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^5*c^(3/2)*d^3*e^3 + 32*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^3*c^(5/2)*d^3*e^3 - 96*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b*c^(7/2)*d^3*e^3 + 3*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^6*sqrt(c)*d^2*e^4 - 21*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^4*c^(3/2)*d^2*e^4 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b^2*c^(5/2)*d^2*e^4 + 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^4*c^(7/2)*d^2*e^4 - 3*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^5*sqrt(c)*d*e^5 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b^3*c^(3/2)*d*e^5 - 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^4*b*c^(5/2)*d*e^5 + sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b^4*sqrt(c)*e^6 - 8*sqrt(c*d^2 - b*d*e + a*e^2)*a^4*b^2*c^(3/2)*e^6 + 16*sqrt(c*d^2 - b*d*e + a*e^2)*a^5*c^(5/2)*e^6) + 2*((((4*(4*B*b*c^5*d^7*e^16*sgn(1/(x*e + d)) - 8*A*c^6*d^7*e^16*sgn(1/(x*e + d)) - 16*B*b^2*c^4*d^6*e^17*sgn(1/(x*e + d)) + 8*B*a*c^5*d^6*e^17*sgn(1/(x*e + d)) + 28*A*b*c^5*d^6*e^17*sgn(1/(x*e + d)) + 21*B*b^3*c^3*d^5*e^18*sgn(1/(x*e + d)) - 30*A*b^2*c^4*d^5*e^18*sgn(1/(x*e + d)) - 48*A*a*c^5*d^5*e^18*sgn(1/(x*e + d)) - 18*B*b^4*c^2*d^4*e^19*sgn(1/(x*e + d)) + 34*B*a*b^2*c^3*d^4*e^19*sgn(1/(x*e + d)) + 5*A*b^3*c^3*d^4*e^19*sgn(1/(x*e + d)) - 128*B*a^2*c^4*d^4*e^19*sgn(1/(x*e + d)) + 120*A*a*b*c^4*d^4*e^19*sgn(1/(x*e + d)) + 12*B*b^5*c*d^3*e^20*sgn(1/(x*e + d)) - 66*B*a*b^3*c^2*d^3*e^20*sgn(1/(x*e + d)) + 18*A*b^4*c^2*d^3*e^20*sgn(1/(x*e + d)) + 212*B*a^2*b*c^3*d^3*e^20*sgn(1/(x*e + d)) - 164*A*a*b^2*c^3*d^3*e^20*sgn(1/(x*e + d)) + 88*A*a^2*c^4*d^3*e^20*sgn(1/(x*e + d)) - 3*B*b^6*d^2*e^21*sgn(1/(x*e + d)) + 18*B*a*b^4*c*d^2*e^21*sgn(1/(x*e + d)) - 18*A*b^5*c*d^2*e^21*sgn(1/(x*e + d)) - 36*B*a^2*b^2*c^2*d^2*e^21*sgn(1/(x*e + d)) + 126*A*a*b^3*c^2*d^2*e^21*sgn(1/(x*e + d)) - 120*B*a^3*c^3*d^2*e^21*sgn(1/(x*e + d)) - 132*A*a^2*b*c^3*d^2*e^21*sgn(1/(x*e + d)) + B*a*b^5*d*e^22*sgn(1/(x*e + d)) + 5*A*b^6*d*e^22*sgn(1/(x*e + d)) - 11*B*a^2*b^3*c*d*e^22*sgn(1/(x*e + d)) - 24*A*a*b^4*c*d*e^22*sgn(1/(x*e + d)) + 56*B*a^3*b*c^2*d*e^22*sgn(1/(x*e + d)) - 30*A*a^2*b^2*c^2*d*e^22*sgn(1/(x*e + d)) + 128*A*a^3*c^3*d*e^22*sgn(1/(x*e + d)) + 2*B*a^2*b^4*e^23*sgn(1/(x*e + d)) - 5*A*a*b^5*e^23*sgn(1/(x*e + d)) - 14*B*a^3*b^2*c*e^23*sgn(1/(x*e + d)) + 37*A*a^2*b^3*c*e^23*sgn(1/(x*e + d)) + 16*B*a^4*c^2*e^23*sgn(1/(x*e + d)) - 64*A*a^3*b*c^2*e^23*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2) + 3*(B*b^4*c^2*d^5*e^20*sgn(1/(x*e + d)) - 8*B*a*b^2*c^3*d^5*e^20*sgn(1/(x*e + d)) + 16*B*a^2*c^4*d^5*e^20*sgn(1/(x*e + d)) - 2*B*b^5*c*d^4*e^21*sgn(1/(x*e + d)) + 16*B*a*b^3*c^2*d^4*e^21*sgn(1/(x*e + d)) - A*b^4*c^2*d^4*e^21*sgn(1/(x*e + d)) - 32*B*a^2*b*c^3*d^4*e^21*sgn(1/(x*e + d)) + 8*A*a*b^2*c^3*d^4*e^21*sgn(1/(x*e + d)) - 16*A*a^2*c^4*d^4*e^21*sgn(1/(x*e + d)) + B*b^6*d^3*e^22*sgn(1/(x*e + d)) - 6*B*a*b^4*c*d^3*e^22*sgn(1/(x*e + d)) + 2*A*b^5*c*d^3*e^22*sgn(1/(x*e + d)) - 16*A*a*b^3*c^2*d^3*e^22*sgn(1/(x*e + d)) + 32*B*a^3*c^3*d^3*e^22*sgn(1/(x*e + d)) + 32*A*a^2*b*c^3*d^3*e^22*sgn(1/(x*e + d)) - 2*B*a*b^5*d^2*e^23*sgn(1/(x*e + d)) - A*b^6*d^2*e^23*sgn(1/(x*e + d)) + 16*B*a^2*b^3*c*d^2*e^23*sgn(1/(x*e + d)) + 6*A*a*b^4*c*d^2*e^23*sgn(1/(x*e + d)) - 32*B*a^3*b*c^2*d^2*e^23*sgn(1/(x*e + d)) - 32*A*a^3*c^3*d^2*e^23*sgn(1/(x*e + d)) + B*a^2*b^4*d*e^24*sgn(1/(x*e + d)) + 2*A*a*b^5*d*e^24*sgn(1/(x*e + d)) - 8*B*a^3*b^2*c*d*e^24*sgn(1/(x*e + d)) - 16*A*a^2*b^3*c*d*e^24*sgn(1/(x*e + d)) + 16*B*a^4*c^2*d*e^24*sgn(1/(x*e + d)) + 32*A*a^3*b*c^2*d*e^24*sgn(1/(x*e + d)) - A*a^2*b^4*e^25*sgn(1/(x*e + d)) + 8*A*a^3*b^2*c*e^25*sgn(1/(x*e + d)) - 16*A*a^4*c^2*e^25*sgn(1/(x*e + d)))*e^(-1)/((b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2)*(x*e + d)))*e^(-1)/(x*e + d) - 3*(16*B*b*c^5*d^6*e^15*sgn(1/(x*e + d)) - 32*A*c^6*d^6*e^15*sgn(1/(x*e + d)) - 56*B*b^2*c^4*d^5*e^16*sgn(1/(x*e + d)) + 32*B*a*c^5*d^5*e^16*sgn(1/(x*e + d)) + 96*A*b*c^5*d^5*e^16*sgn(1/(x*e + d)) + 60*B*b^3*c^3*d^4*e^17*sgn(1/(x*e + d)) - 80*A*b^2*c^4*d^4*e^17*sgn(1/(x*e + d)) - 160*A*a*c^5*d^4*e^17*sgn(1/(x*e + d)) - 42*B*b^4*c^2*d^3*e^18*sgn(1/(x*e + d)) + 96*B*a*b^2*c^3*d^3*e^18*sgn(1/(x*e + d)) - 352*B*a^2*c^4*d^3*e^18*sgn(1/(x*e + d)) + 320*A*a*b*c^4*d^3*e^18*sgn(1/(x*e + d)) + 20*B*b^5*c*d^2*e^19*sgn(1/(x*e + d)) - 120*B*a*b^3*c^2*d^2*e^19*sgn(1/(x*e + d)) + 46*A*b^4*c^2*d^2*e^19*sgn(1/(x*e + d)) + 400*B*a^2*b*c^3*d^2*e^19*sgn(1/(x*e + d)) - 368*A*a*b^2*c^3*d^2*e^19*sgn(1/(x*e + d)) + 256*A*a^2*c^4*d^2*e^19*sgn(1/(x*e + d)) - 3*B*b^6*d*e^20*sgn(1/(x*e + d)) + 26*B*a*b^4*c*d*e^20*sgn(1/(x*e + d)) - 30*A*b^5*c*d*e^20*sgn(1/(x*e + d)) - 88*B*a^2*b^2*c^2*d*e^20*sgn(1/(x*e + d)) + 208*A*a*b^3*c^2*d*e^20*sgn(1/(x*e + d)) - 64*B*a^3*c^3*d*e^20*sgn(1/(x*e + d)) - 256*A*a^2*b*c^3*d*e^20*sgn(1/(x*e + d)) - 2*B*a*b^5*e^21*sgn(1/(x*e + d)) + 5*A*b^6*e^21*sgn(1/(x*e + d)) + 12*B*a^2*b^3*c*e^21*sgn(1/(x*e + d)) - 30*A*a*b^4*c*e^21*sgn(1/(x*e + d)) + 16*A*a^2*b^2*c^2*e^21*sgn(1/(x*e + d)) + 64*A*a^3*c^3*e^21*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2))*e^(-1)/(x*e + d) + 6*(8*B*b*c^5*d^5*e^14*sgn(1/(x*e + d)) - 16*A*c^6*d^5*e^14*sgn(1/(x*e + d)) - 24*B*b^2*c^4*d^4*e^15*sgn(1/(x*e + d)) + 16*B*a*c^5*d^4*e^15*sgn(1/(x*e + d)) + 40*A*b*c^5*d^4*e^15*sgn(1/(x*e + d)) + 19*B*b^3*c^3*d^3*e^16*sgn(1/(x*e + d)) + 4*B*a*b*c^4*d^3*e^16*sgn(1/(x*e + d)) - 22*A*b^2*c^4*d^3*e^16*sgn(1/(x*e + d)) - 72*A*a*c^5*d^3*e^16*sgn(1/(x*e + d)) - 11*B*b^4*c^2*d^2*e^17*sgn(1/(x*e + d)) + 38*B*a*b^2*c^3*d^2*e^17*sgn(1/(x*e + d)) - 7*A*b^3*c^3*d^2*e^17*sgn(1/(x*e + d)) - 136*B*a^2*c^4*d^2*e^17*sgn(1/(x*e + d)) + 108*A*a*b*c^4*d^2*e^17*sgn(1/(x*e + d)) + 3*B*b^5*c*d*e^18*sgn(1/(x*e + d)) - 23*B*a*b^3*c^2*d*e^18*sgn(1/(x*e + d)) + 15*A*b^4*c^2*d*e^18*sgn(1/(x*e + d)) + 84*B*a^2*b*c^3*d*e^18*sgn(1/(x*e + d)) - 106*A*a*b^2*c^3*d*e^18*sgn(1/(x*e + d)) + 104*A*a^2*c^4*d*e^18*sgn(1/(x*e + d)) + 2*B*a*b^4*c*e^19*sgn(1/(x*e + d)) - 5*A*b^5*c*e^19*sgn(1/(x*e + d)) - 14*B*a^2*b^2*c^2*e^19*sgn(1/(x*e + d)) + 35*A*a*b^3*c^2*e^19*sgn(1/(x*e + d)) + 8*B*a^3*c^3*e^19*sgn(1/(x*e + d)) - 52*A*a^2*b*c^3*e^19*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2))*e^(-1)/(x*e + d) - (16*B*b*c^5*d^4*e^13*sgn(1/(x*e + d)) - 32*A*c^6*d^4*e^13*sgn(1/(x*e + d)) - 40*B*b^2*c^4*d^3*e^14*sgn(1/(x*e + d)) + 32*B*a*c^5*d^3*e^14*sgn(1/(x*e + d)) + 64*A*b*c^5*d^3*e^14*sgn(1/(x*e + d)) + 18*B*b^3*c^3*d^2*e^15*sgn(1/(x*e + d)) + 24*B*a*b*c^4*d^2*e^15*sgn(1/(x*e + d)) - 12*A*b^2*c^4*d^2*e^15*sgn(1/(x*e + d)) - 144*A*a*c^5*d^2*e^15*sgn(1/(x*e + d)) - 9*B*b^4*c^2*d*e^16*sgn(1/(x*e + d)) + 56*B*a*b^2*c^3*d*e^16*sgn(1/(x*e + d)) - 20*A*b^3*c^3*d*e^16*sgn(1/(x*e + d)) - 208*B*a^2*c^4*d*e^16*sgn(1/(x*e + d)) + 144*A*a*b*c^4*d*e^16*sgn(1/(x*e + d)) - 6*B*a*b^3*c^2*e^17*sgn(1/(x*e + d)) + 15*A*b^4*c^2*e^17*sgn(1/(x*e + d)) + 40*B*a^2*b*c^3*e^17*sgn(1/(x*e + d)) - 100*A*a*b^2*c^3*e^17*sgn(1/(x*e + d)) + 128*A*a^2*c^4*e^17*sgn(1/(x*e + d)))/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d))^2 - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d))^2 + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d))^2 - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d))^2 + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d))^2 - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d))^2 + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d))^2 - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d))^2 + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d))^2 + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d))^2 - b^7*d^3*e^14*sgn(1/(x*e + d))^2 + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d))^2 + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d))^2 - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d))^2 + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d))^2 - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d))^2 + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d))^2 + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d))^2 - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d))^2 + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d))^2 - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d))^2 + a^3*b^4*e^17*sgn(1/(x*e + d))^2 - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d))^2 + 16*a^5*c^2*e^17*sgn(1/(x*e + d))^2))/(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)^(3/2) + 3*(8*B*c*d^2*e^6 - 3*B*b*d*e^7 - 10*A*c*d*e^7 - 2*B*a*e^8 + 5*A*b*e^8)*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3 + a*e^4)*e^(-1)/(x*e + d))))/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7)*sqrt(c*d^2 - b*d*e + a*e^2)*sgn(1/(x*e + d))))*e^(-2)","B",0
2487,1,3352,0,0.490294," ","integrate((B*x+A)*(e*x+d)^6/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left({\left(\frac{15 \, {\left(B b^{6} c^{3} e^{6} - 12 \, B a b^{4} c^{4} e^{6} + 48 \, B a^{2} b^{2} c^{5} e^{6} - 64 \, B a^{3} c^{6} e^{6}\right)} x}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}} + \frac{256 \, B b c^{8} d^{6} - 512 \, A c^{9} d^{6} - 576 \, B b^{2} c^{7} d^{5} e - 768 \, B a c^{8} d^{5} e + 1536 \, A b c^{8} d^{5} e + 240 \, B b^{3} c^{6} d^{4} e^{2} + 2880 \, B a b c^{7} d^{4} e^{2} - 1440 \, A b^{2} c^{7} d^{4} e^{2} - 1920 \, A a c^{8} d^{4} e^{2} + 80 \, B b^{4} c^{5} d^{3} e^{3} - 1920 \, B a b^{2} c^{6} d^{3} e^{3} + 320 \, A b^{3} c^{6} d^{3} e^{3} - 3840 \, B a^{2} c^{7} d^{3} e^{3} + 3840 \, A a b c^{7} d^{3} e^{3} + 90 \, B b^{5} c^{4} d^{2} e^{4} - 1200 \, B a b^{3} c^{5} d^{2} e^{4} + 60 \, A b^{4} c^{5} d^{2} e^{4} + 7200 \, B a^{2} b c^{6} d^{2} e^{4} - 1440 \, A a b^{2} c^{6} d^{2} e^{4} - 2880 \, A a^{2} c^{7} d^{2} e^{4} - 276 \, B b^{6} c^{3} d e^{5} + 3096 \, B a b^{4} c^{4} d e^{5} + 36 \, A b^{5} c^{4} d e^{5} - 10944 \, B a^{2} b^{2} c^{5} d e^{5} - 480 \, A a b^{3} c^{5} d e^{5} + 8832 \, B a^{3} c^{6} d e^{5} + 2880 \, A a^{2} b c^{6} d e^{5} + 161 \, B b^{7} c^{2} e^{6} - 1842 \, B a b^{5} c^{3} e^{6} - 46 \, A b^{6} c^{3} e^{6} + 6864 \, B a^{2} b^{3} c^{4} e^{6} + 516 \, A a b^{4} c^{4} e^{6} - 8032 \, B a^{3} b c^{5} e^{6} - 1824 \, A a^{2} b^{2} c^{5} e^{6} + 1472 \, A a^{3} c^{6} e^{6}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}\right)} x + \frac{5 \, {\left(128 \, B b^{2} c^{7} d^{6} - 256 \, A b c^{8} d^{6} - 288 \, B b^{3} c^{6} d^{5} e - 384 \, B a b c^{7} d^{5} e + 768 \, A b^{2} c^{7} d^{5} e + 120 \, B b^{4} c^{5} d^{4} e^{2} + 1440 \, B a b^{2} c^{6} d^{4} e^{2} - 720 \, A b^{3} c^{6} d^{4} e^{2} - 960 \, A a b c^{7} d^{4} e^{2} + 40 \, B b^{5} c^{4} d^{3} e^{3} - 960 \, B a b^{3} c^{5} d^{3} e^{3} + 160 \, A b^{4} c^{5} d^{3} e^{3} - 1920 \, B a^{2} b c^{6} d^{3} e^{3} + 1920 \, A a b^{2} c^{6} d^{3} e^{3} - 60 \, B a b^{4} c^{4} d^{2} e^{4} + 30 \, A b^{5} c^{4} d^{2} e^{4} + 1440 \, B a^{2} b^{2} c^{5} d^{2} e^{4} - 720 \, A a b^{3} c^{5} d^{2} e^{4} + 2880 \, B a^{3} c^{6} d^{2} e^{4} - 1440 \, A a^{2} b c^{6} d^{2} e^{4} - 84 \, B b^{7} c^{2} d e^{5} + 900 \, B a b^{5} c^{3} d e^{5} - 2880 \, B a^{2} b^{3} c^{4} d e^{5} - 24 \, A a b^{4} c^{4} d e^{5} + 960 \, B a^{3} b c^{5} d e^{5} + 576 \, A a^{2} b^{2} c^{5} d e^{5} + 1152 \, A a^{3} c^{6} d e^{5} + 49 \, B b^{8} c e^{6} - 525 \, B a b^{6} c^{2} e^{6} - 14 \, A b^{7} c^{2} e^{6} + 1704 \, B a^{2} b^{4} c^{3} e^{6} + 150 \, A a b^{5} c^{3} e^{6} - 1136 \, B a^{3} b^{2} c^{4} e^{6} - 480 \, A a^{2} b^{3} c^{4} e^{6} - 1152 \, B a^{4} c^{5} e^{6} + 160 \, A a^{3} b c^{5} e^{6}\right)}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}\right)} x + \frac{5 \, {\left(96 \, B b^{3} c^{6} d^{6} + 128 \, B a b c^{7} d^{6} - 192 \, A b^{2} c^{7} d^{6} - 256 \, A a c^{8} d^{6} - 216 \, B b^{4} c^{5} d^{5} e - 576 \, B a b^{2} c^{6} d^{5} e + 576 \, A b^{3} c^{6} d^{5} e - 384 \, B a^{2} c^{7} d^{5} e + 768 \, A a b c^{7} d^{5} e + 90 \, B b^{5} c^{4} d^{4} e^{2} + 1200 \, B a b^{3} c^{5} d^{4} e^{2} - 540 \, A b^{4} c^{5} d^{4} e^{2} + 1440 \, B a^{2} b c^{6} d^{4} e^{2} - 1440 \, A a b^{2} c^{6} d^{4} e^{2} - 960 \, A a^{2} c^{7} d^{4} e^{2} - 320 \, B a b^{4} c^{4} d^{3} e^{3} + 120 \, A b^{5} c^{4} d^{3} e^{3} - 3840 \, B a^{2} b^{2} c^{5} d^{3} e^{3} + 1600 \, A a b^{3} c^{5} d^{3} e^{3} + 1920 \, A a^{2} b c^{6} d^{3} e^{3} + 480 \, B a^{2} b^{3} c^{4} d^{2} e^{4} - 240 \, A a b^{4} c^{4} d^{2} e^{4} + 5760 \, B a^{3} b c^{5} d^{2} e^{4} - 2880 \, A a^{2} b^{2} c^{5} d^{2} e^{4} - 36 \, B b^{8} c d e^{5} + 240 \, B a b^{6} c^{2} d e^{5} + 360 \, B a^{2} b^{4} c^{3} d e^{5} - 5184 \, B a^{3} b^{2} c^{4} d e^{5} + 192 \, A a^{2} b^{3} c^{4} d e^{5} + 2688 \, B a^{4} c^{5} d e^{5} + 2304 \, A a^{3} b c^{5} d e^{5} + 21 \, B b^{9} e^{6} - 140 \, B a b^{7} c e^{6} - 6 \, A b^{8} c e^{6} - 210 \, B a^{2} b^{5} c^{2} e^{6} + 40 \, A a b^{6} c^{2} e^{6} + 2832 \, B a^{3} b^{3} c^{3} e^{6} + 60 \, A a^{2} b^{4} c^{3} e^{6} - 3872 \, B a^{4} b c^{4} e^{6} - 864 \, A a^{3} b^{2} c^{4} e^{6} + 448 \, A a^{4} c^{5} e^{6}\right)}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}\right)} x + \frac{5 \, {\left(16 \, B b^{4} c^{5} d^{6} + 192 \, B a b^{2} c^{6} d^{6} - 32 \, A b^{3} c^{6} d^{6} - 384 \, A a b c^{7} d^{6} - 36 \, B b^{5} c^{4} d^{5} e - 480 \, B a b^{3} c^{5} d^{5} e + 96 \, A b^{4} c^{5} d^{5} e - 576 \, B a^{2} b c^{6} d^{5} e + 1152 \, A a b^{2} c^{6} d^{5} e + 540 \, B a b^{4} c^{4} d^{4} e^{2} - 90 \, A b^{5} c^{4} d^{4} e^{2} + 1440 \, B a^{2} b^{2} c^{5} d^{4} e^{2} - 1200 \, A a b^{3} c^{5} d^{4} e^{2} + 960 \, B a^{3} c^{6} d^{4} e^{2} - 1440 \, A a^{2} b c^{6} d^{4} e^{2} - 1920 \, B a^{2} b^{3} c^{4} d^{3} e^{3} + 720 \, A a b^{4} c^{4} d^{3} e^{3} - 2560 \, B a^{3} b c^{5} d^{3} e^{3} + 1920 \, A a^{2} b^{2} c^{5} d^{3} e^{3} + 1280 \, A a^{3} c^{6} d^{3} e^{3} + 2880 \, B a^{3} b^{2} c^{4} d^{2} e^{4} - 1440 \, A a^{2} b^{3} c^{4} d^{2} e^{4} + 3840 \, B a^{4} c^{5} d^{2} e^{4} - 1920 \, A a^{3} b c^{5} d^{2} e^{4} - 108 \, B a b^{7} c d e^{5} + 1116 \, B a^{2} b^{5} c^{2} d e^{5} - 3360 \, B a^{3} b^{3} c^{3} d e^{5} - 576 \, B a^{4} b c^{4} d e^{5} + 1152 \, A a^{3} b^{2} c^{4} d e^{5} + 1536 \, A a^{4} c^{5} d e^{5} + 63 \, B a b^{8} e^{6} - 651 \, B a^{2} b^{6} c e^{6} - 18 \, A a b^{7} c e^{6} + 1960 \, B a^{3} b^{4} c^{2} e^{6} + 186 \, A a^{2} b^{5} c^{2} e^{6} - 816 \, B a^{4} b^{2} c^{3} e^{6} - 560 \, A a^{3} b^{3} c^{3} e^{6} - 1536 \, B a^{5} c^{4} e^{6} - 96 \, A a^{4} b c^{4} e^{6}\right)}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}\right)} x - \frac{5 \, {\left(2 \, B b^{5} c^{4} d^{6} - 48 \, B a b^{3} c^{5} d^{6} - 4 \, A b^{4} c^{5} d^{6} - 96 \, B a^{2} b c^{6} d^{6} + 96 \, A a b^{2} c^{6} d^{6} + 192 \, A a^{2} c^{7} d^{6} + 48 \, B a b^{4} c^{4} d^{5} e + 12 \, A b^{5} c^{4} d^{5} e + 576 \, B a^{2} b^{2} c^{5} d^{5} e - 288 \, A a b^{3} c^{5} d^{5} e - 576 \, A a^{2} b c^{6} d^{5} e - 720 \, B a^{2} b^{3} c^{4} d^{4} e^{2} + 120 \, A a b^{4} c^{4} d^{4} e^{2} - 960 \, B a^{3} b c^{5} d^{4} e^{2} + 1440 \, A a^{2} b^{2} c^{5} d^{4} e^{2} + 2560 \, B a^{3} b^{2} c^{4} d^{3} e^{3} - 960 \, A a^{2} b^{3} c^{4} d^{3} e^{3} - 1280 \, A a^{3} b c^{5} d^{3} e^{3} - 3840 \, B a^{4} b c^{4} d^{2} e^{4} + 1920 \, A a^{3} b^{2} c^{4} d^{2} e^{4} + 108 \, B a^{2} b^{6} c d e^{5} - 1176 \, B a^{3} b^{4} c^{2} d e^{5} + 4032 \, B a^{4} b^{2} c^{3} d e^{5} - 1152 \, B a^{5} c^{4} d e^{5} - 1536 \, A a^{4} b c^{4} d e^{5} - 63 \, B a^{2} b^{7} e^{6} + 686 \, B a^{3} b^{5} c e^{6} + 18 \, A a^{2} b^{6} c e^{6} - 2352 \, B a^{4} b^{3} c^{2} e^{6} - 196 \, A a^{3} b^{4} c^{2} e^{6} + 2208 \, B a^{5} b c^{3} e^{6} + 672 \, A a^{4} b^{2} c^{3} e^{6} - 192 \, A a^{5} c^{4} e^{6}\right)}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}\right)} x - \frac{4 \, B a b^{4} c^{4} d^{6} + 6 \, A b^{5} c^{4} d^{6} - 96 \, B a^{2} b^{2} c^{5} d^{6} - 80 \, A a b^{3} c^{5} d^{6} - 192 \, B a^{3} c^{6} d^{6} + 480 \, A a^{2} b c^{6} d^{6} + 96 \, B a^{2} b^{3} c^{4} d^{5} e + 24 \, A a b^{4} c^{4} d^{5} e + 1152 \, B a^{3} b c^{5} d^{5} e - 576 \, A a^{2} b^{2} c^{5} d^{5} e - 1152 \, A a^{3} c^{6} d^{5} e - 1440 \, B a^{3} b^{2} c^{4} d^{4} e^{2} + 240 \, A a^{2} b^{3} c^{4} d^{4} e^{2} - 1920 \, B a^{4} c^{5} d^{4} e^{2} + 2880 \, A a^{3} b c^{5} d^{4} e^{2} + 5120 \, B a^{4} b c^{4} d^{3} e^{3} - 1920 \, A a^{3} b^{2} c^{4} d^{3} e^{3} - 2560 \, A a^{4} c^{5} d^{3} e^{3} - 7680 \, B a^{5} c^{4} d^{2} e^{4} + 3840 \, A a^{4} b c^{4} d^{2} e^{4} + 180 \, B a^{3} b^{5} c d e^{5} - 1920 \, B a^{4} b^{3} c^{2} d e^{5} + 6336 \, B a^{5} b c^{3} d e^{5} - 3072 \, A a^{5} c^{4} d e^{5} - 105 \, B a^{3} b^{6} e^{6} + 1120 \, B a^{4} b^{4} c e^{6} + 30 \, A a^{3} b^{5} c e^{6} - 3696 \, B a^{5} b^{2} c^{2} e^{6} - 320 \, A a^{4} b^{3} c^{2} e^{6} + 3072 \, B a^{6} c^{3} e^{6} + 1056 \, A a^{5} b c^{3} e^{6}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}} - \frac{{\left(12 \, B c d e^{5} - 7 \, B b e^{6} + 2 \, A c e^{6}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{9}{2}}}"," ",0,"1/15*((((((15*(B*b^6*c^3*e^6 - 12*B*a*b^4*c^4*e^6 + 48*B*a^2*b^2*c^5*e^6 - 64*B*a^3*c^6*e^6)*x/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7) + (256*B*b*c^8*d^6 - 512*A*c^9*d^6 - 576*B*b^2*c^7*d^5*e - 768*B*a*c^8*d^5*e + 1536*A*b*c^8*d^5*e + 240*B*b^3*c^6*d^4*e^2 + 2880*B*a*b*c^7*d^4*e^2 - 1440*A*b^2*c^7*d^4*e^2 - 1920*A*a*c^8*d^4*e^2 + 80*B*b^4*c^5*d^3*e^3 - 1920*B*a*b^2*c^6*d^3*e^3 + 320*A*b^3*c^6*d^3*e^3 - 3840*B*a^2*c^7*d^3*e^3 + 3840*A*a*b*c^7*d^3*e^3 + 90*B*b^5*c^4*d^2*e^4 - 1200*B*a*b^3*c^5*d^2*e^4 + 60*A*b^4*c^5*d^2*e^4 + 7200*B*a^2*b*c^6*d^2*e^4 - 1440*A*a*b^2*c^6*d^2*e^4 - 2880*A*a^2*c^7*d^2*e^4 - 276*B*b^6*c^3*d*e^5 + 3096*B*a*b^4*c^4*d*e^5 + 36*A*b^5*c^4*d*e^5 - 10944*B*a^2*b^2*c^5*d*e^5 - 480*A*a*b^3*c^5*d*e^5 + 8832*B*a^3*c^6*d*e^5 + 2880*A*a^2*b*c^6*d*e^5 + 161*B*b^7*c^2*e^6 - 1842*B*a*b^5*c^3*e^6 - 46*A*b^6*c^3*e^6 + 6864*B*a^2*b^3*c^4*e^6 + 516*A*a*b^4*c^4*e^6 - 8032*B*a^3*b*c^5*e^6 - 1824*A*a^2*b^2*c^5*e^6 + 1472*A*a^3*c^6*e^6)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*x + 5*(128*B*b^2*c^7*d^6 - 256*A*b*c^8*d^6 - 288*B*b^3*c^6*d^5*e - 384*B*a*b*c^7*d^5*e + 768*A*b^2*c^7*d^5*e + 120*B*b^4*c^5*d^4*e^2 + 1440*B*a*b^2*c^6*d^4*e^2 - 720*A*b^3*c^6*d^4*e^2 - 960*A*a*b*c^7*d^4*e^2 + 40*B*b^5*c^4*d^3*e^3 - 960*B*a*b^3*c^5*d^3*e^3 + 160*A*b^4*c^5*d^3*e^3 - 1920*B*a^2*b*c^6*d^3*e^3 + 1920*A*a*b^2*c^6*d^3*e^3 - 60*B*a*b^4*c^4*d^2*e^4 + 30*A*b^5*c^4*d^2*e^4 + 1440*B*a^2*b^2*c^5*d^2*e^4 - 720*A*a*b^3*c^5*d^2*e^4 + 2880*B*a^3*c^6*d^2*e^4 - 1440*A*a^2*b*c^6*d^2*e^4 - 84*B*b^7*c^2*d*e^5 + 900*B*a*b^5*c^3*d*e^5 - 2880*B*a^2*b^3*c^4*d*e^5 - 24*A*a*b^4*c^4*d*e^5 + 960*B*a^3*b*c^5*d*e^5 + 576*A*a^2*b^2*c^5*d*e^5 + 1152*A*a^3*c^6*d*e^5 + 49*B*b^8*c*e^6 - 525*B*a*b^6*c^2*e^6 - 14*A*b^7*c^2*e^6 + 1704*B*a^2*b^4*c^3*e^6 + 150*A*a*b^5*c^3*e^6 - 1136*B*a^3*b^2*c^4*e^6 - 480*A*a^2*b^3*c^4*e^6 - 1152*B*a^4*c^5*e^6 + 160*A*a^3*b*c^5*e^6)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*x + 5*(96*B*b^3*c^6*d^6 + 128*B*a*b*c^7*d^6 - 192*A*b^2*c^7*d^6 - 256*A*a*c^8*d^6 - 216*B*b^4*c^5*d^5*e - 576*B*a*b^2*c^6*d^5*e + 576*A*b^3*c^6*d^5*e - 384*B*a^2*c^7*d^5*e + 768*A*a*b*c^7*d^5*e + 90*B*b^5*c^4*d^4*e^2 + 1200*B*a*b^3*c^5*d^4*e^2 - 540*A*b^4*c^5*d^4*e^2 + 1440*B*a^2*b*c^6*d^4*e^2 - 1440*A*a*b^2*c^6*d^4*e^2 - 960*A*a^2*c^7*d^4*e^2 - 320*B*a*b^4*c^4*d^3*e^3 + 120*A*b^5*c^4*d^3*e^3 - 3840*B*a^2*b^2*c^5*d^3*e^3 + 1600*A*a*b^3*c^5*d^3*e^3 + 1920*A*a^2*b*c^6*d^3*e^3 + 480*B*a^2*b^3*c^4*d^2*e^4 - 240*A*a*b^4*c^4*d^2*e^4 + 5760*B*a^3*b*c^5*d^2*e^4 - 2880*A*a^2*b^2*c^5*d^2*e^4 - 36*B*b^8*c*d*e^5 + 240*B*a*b^6*c^2*d*e^5 + 360*B*a^2*b^4*c^3*d*e^5 - 5184*B*a^3*b^2*c^4*d*e^5 + 192*A*a^2*b^3*c^4*d*e^5 + 2688*B*a^4*c^5*d*e^5 + 2304*A*a^3*b*c^5*d*e^5 + 21*B*b^9*e^6 - 140*B*a*b^7*c*e^6 - 6*A*b^8*c*e^6 - 210*B*a^2*b^5*c^2*e^6 + 40*A*a*b^6*c^2*e^6 + 2832*B*a^3*b^3*c^3*e^6 + 60*A*a^2*b^4*c^3*e^6 - 3872*B*a^4*b*c^4*e^6 - 864*A*a^3*b^2*c^4*e^6 + 448*A*a^4*c^5*e^6)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*x + 5*(16*B*b^4*c^5*d^6 + 192*B*a*b^2*c^6*d^6 - 32*A*b^3*c^6*d^6 - 384*A*a*b*c^7*d^6 - 36*B*b^5*c^4*d^5*e - 480*B*a*b^3*c^5*d^5*e + 96*A*b^4*c^5*d^5*e - 576*B*a^2*b*c^6*d^5*e + 1152*A*a*b^2*c^6*d^5*e + 540*B*a*b^4*c^4*d^4*e^2 - 90*A*b^5*c^4*d^4*e^2 + 1440*B*a^2*b^2*c^5*d^4*e^2 - 1200*A*a*b^3*c^5*d^4*e^2 + 960*B*a^3*c^6*d^4*e^2 - 1440*A*a^2*b*c^6*d^4*e^2 - 1920*B*a^2*b^3*c^4*d^3*e^3 + 720*A*a*b^4*c^4*d^3*e^3 - 2560*B*a^3*b*c^5*d^3*e^3 + 1920*A*a^2*b^2*c^5*d^3*e^3 + 1280*A*a^3*c^6*d^3*e^3 + 2880*B*a^3*b^2*c^4*d^2*e^4 - 1440*A*a^2*b^3*c^4*d^2*e^4 + 3840*B*a^4*c^5*d^2*e^4 - 1920*A*a^3*b*c^5*d^2*e^4 - 108*B*a*b^7*c*d*e^5 + 1116*B*a^2*b^5*c^2*d*e^5 - 3360*B*a^3*b^3*c^3*d*e^5 - 576*B*a^4*b*c^4*d*e^5 + 1152*A*a^3*b^2*c^4*d*e^5 + 1536*A*a^4*c^5*d*e^5 + 63*B*a*b^8*e^6 - 651*B*a^2*b^6*c*e^6 - 18*A*a*b^7*c*e^6 + 1960*B*a^3*b^4*c^2*e^6 + 186*A*a^2*b^5*c^2*e^6 - 816*B*a^4*b^2*c^3*e^6 - 560*A*a^3*b^3*c^3*e^6 - 1536*B*a^5*c^4*e^6 - 96*A*a^4*b*c^4*e^6)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*x - 5*(2*B*b^5*c^4*d^6 - 48*B*a*b^3*c^5*d^6 - 4*A*b^4*c^5*d^6 - 96*B*a^2*b*c^6*d^6 + 96*A*a*b^2*c^6*d^6 + 192*A*a^2*c^7*d^6 + 48*B*a*b^4*c^4*d^5*e + 12*A*b^5*c^4*d^5*e + 576*B*a^2*b^2*c^5*d^5*e - 288*A*a*b^3*c^5*d^5*e - 576*A*a^2*b*c^6*d^5*e - 720*B*a^2*b^3*c^4*d^4*e^2 + 120*A*a*b^4*c^4*d^4*e^2 - 960*B*a^3*b*c^5*d^4*e^2 + 1440*A*a^2*b^2*c^5*d^4*e^2 + 2560*B*a^3*b^2*c^4*d^3*e^3 - 960*A*a^2*b^3*c^4*d^3*e^3 - 1280*A*a^3*b*c^5*d^3*e^3 - 3840*B*a^4*b*c^4*d^2*e^4 + 1920*A*a^3*b^2*c^4*d^2*e^4 + 108*B*a^2*b^6*c*d*e^5 - 1176*B*a^3*b^4*c^2*d*e^5 + 4032*B*a^4*b^2*c^3*d*e^5 - 1152*B*a^5*c^4*d*e^5 - 1536*A*a^4*b*c^4*d*e^5 - 63*B*a^2*b^7*e^6 + 686*B*a^3*b^5*c*e^6 + 18*A*a^2*b^6*c*e^6 - 2352*B*a^4*b^3*c^2*e^6 - 196*A*a^3*b^4*c^2*e^6 + 2208*B*a^5*b*c^3*e^6 + 672*A*a^4*b^2*c^3*e^6 - 192*A*a^5*c^4*e^6)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*x - (4*B*a*b^4*c^4*d^6 + 6*A*b^5*c^4*d^6 - 96*B*a^2*b^2*c^5*d^6 - 80*A*a*b^3*c^5*d^6 - 192*B*a^3*c^6*d^6 + 480*A*a^2*b*c^6*d^6 + 96*B*a^2*b^3*c^4*d^5*e + 24*A*a*b^4*c^4*d^5*e + 1152*B*a^3*b*c^5*d^5*e - 576*A*a^2*b^2*c^5*d^5*e - 1152*A*a^3*c^6*d^5*e - 1440*B*a^3*b^2*c^4*d^4*e^2 + 240*A*a^2*b^3*c^4*d^4*e^2 - 1920*B*a^4*c^5*d^4*e^2 + 2880*A*a^3*b*c^5*d^4*e^2 + 5120*B*a^4*b*c^4*d^3*e^3 - 1920*A*a^3*b^2*c^4*d^3*e^3 - 2560*A*a^4*c^5*d^3*e^3 - 7680*B*a^5*c^4*d^2*e^4 + 3840*A*a^4*b*c^4*d^2*e^4 + 180*B*a^3*b^5*c*d*e^5 - 1920*B*a^4*b^3*c^2*d*e^5 + 6336*B*a^5*b*c^3*d*e^5 - 3072*A*a^5*c^4*d*e^5 - 105*B*a^3*b^6*e^6 + 1120*B*a^4*b^4*c*e^6 + 30*A*a^3*b^5*c*e^6 - 3696*B*a^5*b^2*c^2*e^6 - 320*A*a^4*b^3*c^2*e^6 + 3072*B*a^6*c^3*e^6 + 1056*A*a^5*b*c^3*e^6)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))/(c*x^2 + b*x + a)^(5/2) - 1/2*(12*B*c*d*e^5 - 7*B*b*e^6 + 2*A*c*e^6)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","B",0
2488,1,2525,0,0.837050," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","-\frac{B e^{5} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{7}{2}}} + \frac{2 \, {\left({\left({\left({\left({\left(\frac{{\left(128 \, B b c^{7} d^{5} - 256 \, A c^{8} d^{5} - 240 \, B b^{2} c^{6} d^{4} e - 320 \, B a c^{7} d^{4} e + 640 \, A b c^{7} d^{4} e + 80 \, B b^{3} c^{5} d^{3} e^{2} + 960 \, B a b c^{6} d^{3} e^{2} - 480 \, A b^{2} c^{6} d^{3} e^{2} - 640 \, A a c^{7} d^{3} e^{2} + 20 \, B b^{4} c^{4} d^{2} e^{3} - 480 \, B a b^{2} c^{5} d^{2} e^{3} + 80 \, A b^{3} c^{5} d^{2} e^{3} - 960 \, B a^{2} c^{6} d^{2} e^{3} + 960 \, A a b c^{6} d^{2} e^{3} + 15 \, B b^{5} c^{3} d e^{4} - 200 \, B a b^{3} c^{4} d e^{4} + 10 \, A b^{4} c^{4} d e^{4} + 1200 \, B a^{2} b c^{5} d e^{4} - 240 \, A a b^{2} c^{5} d e^{4} - 480 \, A a^{2} c^{6} d e^{4} - 23 \, B b^{6} c^{2} e^{5} + 258 \, B a b^{4} c^{3} e^{5} + 3 \, A b^{5} c^{3} e^{5} - 912 \, B a^{2} b^{2} c^{4} e^{5} - 40 \, A a b^{3} c^{4} e^{5} + 736 \, B a^{3} c^{5} e^{5} + 240 \, A a^{2} b c^{5} e^{5}\right)} x}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}} + \frac{5 \, {\left(64 \, B b^{2} c^{6} d^{5} - 128 \, A b c^{7} d^{5} - 120 \, B b^{3} c^{5} d^{4} e - 160 \, B a b c^{6} d^{4} e + 320 \, A b^{2} c^{6} d^{4} e + 40 \, B b^{4} c^{4} d^{3} e^{2} + 480 \, B a b^{2} c^{5} d^{3} e^{2} - 240 \, A b^{3} c^{5} d^{3} e^{2} - 320 \, A a b c^{6} d^{3} e^{2} + 10 \, B b^{5} c^{3} d^{2} e^{3} - 240 \, B a b^{3} c^{4} d^{2} e^{3} + 40 \, A b^{4} c^{4} d^{2} e^{3} - 480 \, B a^{2} b c^{5} d^{2} e^{3} + 480 \, A a b^{2} c^{5} d^{2} e^{3} - 10 \, B a b^{4} c^{3} d e^{4} + 5 \, A b^{5} c^{3} d e^{4} + 240 \, B a^{2} b^{2} c^{4} d e^{4} - 120 \, A a b^{3} c^{4} d e^{4} + 480 \, B a^{3} c^{5} d e^{4} - 240 \, A a^{2} b c^{5} d e^{4} - 7 \, B b^{7} c e^{5} + 75 \, B a b^{5} c^{2} e^{5} - 240 \, B a^{2} b^{3} c^{3} e^{5} - 2 \, A a b^{4} c^{3} e^{5} + 80 \, B a^{3} b c^{4} e^{5} + 48 \, A a^{2} b^{2} c^{4} e^{5} + 96 \, A a^{3} c^{5} e^{5}\right)}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}\right)} x + \frac{5 \, {\left(48 \, B b^{3} c^{5} d^{5} + 64 \, B a b c^{6} d^{5} - 96 \, A b^{2} c^{6} d^{5} - 128 \, A a c^{7} d^{5} - 90 \, B b^{4} c^{4} d^{4} e - 240 \, B a b^{2} c^{5} d^{4} e + 240 \, A b^{3} c^{5} d^{4} e - 160 \, B a^{2} c^{6} d^{4} e + 320 \, A a b c^{6} d^{4} e + 30 \, B b^{5} c^{3} d^{3} e^{2} + 400 \, B a b^{3} c^{4} d^{3} e^{2} - 180 \, A b^{4} c^{4} d^{3} e^{2} + 480 \, B a^{2} b c^{5} d^{3} e^{2} - 480 \, A a b^{2} c^{5} d^{3} e^{2} - 320 \, A a^{2} c^{6} d^{3} e^{2} - 80 \, B a b^{4} c^{3} d^{2} e^{3} + 30 \, A b^{5} c^{3} d^{2} e^{3} - 960 \, B a^{2} b^{2} c^{4} d^{2} e^{3} + 400 \, A a b^{3} c^{4} d^{2} e^{3} + 480 \, A a^{2} b c^{5} d^{2} e^{3} + 80 \, B a^{2} b^{3} c^{3} d e^{4} - 40 \, A a b^{4} c^{3} d e^{4} + 960 \, B a^{3} b c^{4} d e^{4} - 480 \, A a^{2} b^{2} c^{4} d e^{4} - 3 \, B b^{8} e^{5} + 20 \, B a b^{6} c e^{5} + 30 \, B a^{2} b^{4} c^{2} e^{5} - 432 \, B a^{3} b^{2} c^{3} e^{5} + 16 \, A a^{2} b^{3} c^{3} e^{5} + 224 \, B a^{4} c^{4} e^{5} + 192 \, A a^{3} b c^{4} e^{5}\right)}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}\right)} x + \frac{5 \, {\left(8 \, B b^{4} c^{4} d^{5} + 96 \, B a b^{2} c^{5} d^{5} - 16 \, A b^{3} c^{5} d^{5} - 192 \, A a b c^{6} d^{5} - 15 \, B b^{5} c^{3} d^{4} e - 200 \, B a b^{3} c^{4} d^{4} e + 40 \, A b^{4} c^{4} d^{4} e - 240 \, B a^{2} b c^{5} d^{4} e + 480 \, A a b^{2} c^{5} d^{4} e + 180 \, B a b^{4} c^{3} d^{3} e^{2} - 30 \, A b^{5} c^{3} d^{3} e^{2} + 480 \, B a^{2} b^{2} c^{4} d^{3} e^{2} - 400 \, A a b^{3} c^{4} d^{3} e^{2} + 320 \, B a^{3} c^{5} d^{3} e^{2} - 480 \, A a^{2} b c^{5} d^{3} e^{2} - 480 \, B a^{2} b^{3} c^{3} d^{2} e^{3} + 180 \, A a b^{4} c^{3} d^{2} e^{3} - 640 \, B a^{3} b c^{4} d^{2} e^{3} + 480 \, A a^{2} b^{2} c^{4} d^{2} e^{3} + 320 \, A a^{3} c^{5} d^{2} e^{3} + 480 \, B a^{3} b^{2} c^{3} d e^{4} - 240 \, A a^{2} b^{3} c^{3} d e^{4} + 640 \, B a^{4} c^{4} d e^{4} - 320 \, A a^{3} b c^{4} d e^{4} - 9 \, B a b^{7} e^{5} + 93 \, B a^{2} b^{5} c e^{5} - 280 \, B a^{3} b^{3} c^{2} e^{5} - 48 \, B a^{4} b c^{3} e^{5} + 96 \, A a^{3} b^{2} c^{3} e^{5} + 128 \, A a^{4} c^{4} e^{5}\right)}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}\right)} x - \frac{5 \, {\left(B b^{5} c^{3} d^{5} - 24 \, B a b^{3} c^{4} d^{5} - 2 \, A b^{4} c^{4} d^{5} - 48 \, B a^{2} b c^{5} d^{5} + 48 \, A a b^{2} c^{5} d^{5} + 96 \, A a^{2} c^{6} d^{5} + 20 \, B a b^{4} c^{3} d^{4} e + 5 \, A b^{5} c^{3} d^{4} e + 240 \, B a^{2} b^{2} c^{4} d^{4} e - 120 \, A a b^{3} c^{4} d^{4} e - 240 \, A a^{2} b c^{5} d^{4} e - 240 \, B a^{2} b^{3} c^{3} d^{3} e^{2} + 40 \, A a b^{4} c^{3} d^{3} e^{2} - 320 \, B a^{3} b c^{4} d^{3} e^{2} + 480 \, A a^{2} b^{2} c^{4} d^{3} e^{2} + 640 \, B a^{3} b^{2} c^{3} d^{2} e^{3} - 240 \, A a^{2} b^{3} c^{3} d^{2} e^{3} - 320 \, A a^{3} b c^{4} d^{2} e^{3} - 640 \, B a^{4} b c^{3} d e^{4} + 320 \, A a^{3} b^{2} c^{3} d e^{4} + 9 \, B a^{2} b^{6} e^{5} - 98 \, B a^{3} b^{4} c e^{5} + 336 \, B a^{4} b^{2} c^{2} e^{5} - 96 \, B a^{5} c^{3} e^{5} - 128 \, A a^{4} b c^{3} e^{5}\right)}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}\right)} x - \frac{2 \, B a b^{4} c^{3} d^{5} + 3 \, A b^{5} c^{3} d^{5} - 48 \, B a^{2} b^{2} c^{4} d^{5} - 40 \, A a b^{3} c^{4} d^{5} - 96 \, B a^{3} c^{5} d^{5} + 240 \, A a^{2} b c^{5} d^{5} + 40 \, B a^{2} b^{3} c^{3} d^{4} e + 10 \, A a b^{4} c^{3} d^{4} e + 480 \, B a^{3} b c^{4} d^{4} e - 240 \, A a^{2} b^{2} c^{4} d^{4} e - 480 \, A a^{3} c^{5} d^{4} e - 480 \, B a^{3} b^{2} c^{3} d^{3} e^{2} + 80 \, A a^{2} b^{3} c^{3} d^{3} e^{2} - 640 \, B a^{4} c^{4} d^{3} e^{2} + 960 \, A a^{3} b c^{4} d^{3} e^{2} + 1280 \, B a^{4} b c^{3} d^{2} e^{3} - 480 \, A a^{3} b^{2} c^{3} d^{2} e^{3} - 640 \, A a^{4} c^{4} d^{2} e^{3} - 1280 \, B a^{5} c^{3} d e^{4} + 640 \, A a^{4} b c^{3} d e^{4} + 15 \, B a^{3} b^{5} e^{5} - 160 \, B a^{4} b^{3} c e^{5} + 528 \, B a^{5} b c^{2} e^{5} - 256 \, A a^{5} c^{3} e^{5}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"-B*e^5*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2) + 2/15*((((((128*B*b*c^7*d^5 - 256*A*c^8*d^5 - 240*B*b^2*c^6*d^4*e - 320*B*a*c^7*d^4*e + 640*A*b*c^7*d^4*e + 80*B*b^3*c^5*d^3*e^2 + 960*B*a*b*c^6*d^3*e^2 - 480*A*b^2*c^6*d^3*e^2 - 640*A*a*c^7*d^3*e^2 + 20*B*b^4*c^4*d^2*e^3 - 480*B*a*b^2*c^5*d^2*e^3 + 80*A*b^3*c^5*d^2*e^3 - 960*B*a^2*c^6*d^2*e^3 + 960*A*a*b*c^6*d^2*e^3 + 15*B*b^5*c^3*d*e^4 - 200*B*a*b^3*c^4*d*e^4 + 10*A*b^4*c^4*d*e^4 + 1200*B*a^2*b*c^5*d*e^4 - 240*A*a*b^2*c^5*d*e^4 - 480*A*a^2*c^6*d*e^4 - 23*B*b^6*c^2*e^5 + 258*B*a*b^4*c^3*e^5 + 3*A*b^5*c^3*e^5 - 912*B*a^2*b^2*c^4*e^5 - 40*A*a*b^3*c^4*e^5 + 736*B*a^3*c^5*e^5 + 240*A*a^2*b*c^5*e^5)*x/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6) + 5*(64*B*b^2*c^6*d^5 - 128*A*b*c^7*d^5 - 120*B*b^3*c^5*d^4*e - 160*B*a*b*c^6*d^4*e + 320*A*b^2*c^6*d^4*e + 40*B*b^4*c^4*d^3*e^2 + 480*B*a*b^2*c^5*d^3*e^2 - 240*A*b^3*c^5*d^3*e^2 - 320*A*a*b*c^6*d^3*e^2 + 10*B*b^5*c^3*d^2*e^3 - 240*B*a*b^3*c^4*d^2*e^3 + 40*A*b^4*c^4*d^2*e^3 - 480*B*a^2*b*c^5*d^2*e^3 + 480*A*a*b^2*c^5*d^2*e^3 - 10*B*a*b^4*c^3*d*e^4 + 5*A*b^5*c^3*d*e^4 + 240*B*a^2*b^2*c^4*d*e^4 - 120*A*a*b^3*c^4*d*e^4 + 480*B*a^3*c^5*d*e^4 - 240*A*a^2*b*c^5*d*e^4 - 7*B*b^7*c*e^5 + 75*B*a*b^5*c^2*e^5 - 240*B*a^2*b^3*c^3*e^5 - 2*A*a*b^4*c^3*e^5 + 80*B*a^3*b*c^4*e^5 + 48*A*a^2*b^2*c^4*e^5 + 96*A*a^3*c^5*e^5)/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*x + 5*(48*B*b^3*c^5*d^5 + 64*B*a*b*c^6*d^5 - 96*A*b^2*c^6*d^5 - 128*A*a*c^7*d^5 - 90*B*b^4*c^4*d^4*e - 240*B*a*b^2*c^5*d^4*e + 240*A*b^3*c^5*d^4*e - 160*B*a^2*c^6*d^4*e + 320*A*a*b*c^6*d^4*e + 30*B*b^5*c^3*d^3*e^2 + 400*B*a*b^3*c^4*d^3*e^2 - 180*A*b^4*c^4*d^3*e^2 + 480*B*a^2*b*c^5*d^3*e^2 - 480*A*a*b^2*c^5*d^3*e^2 - 320*A*a^2*c^6*d^3*e^2 - 80*B*a*b^4*c^3*d^2*e^3 + 30*A*b^5*c^3*d^2*e^3 - 960*B*a^2*b^2*c^4*d^2*e^3 + 400*A*a*b^3*c^4*d^2*e^3 + 480*A*a^2*b*c^5*d^2*e^3 + 80*B*a^2*b^3*c^3*d*e^4 - 40*A*a*b^4*c^3*d*e^4 + 960*B*a^3*b*c^4*d*e^4 - 480*A*a^2*b^2*c^4*d*e^4 - 3*B*b^8*e^5 + 20*B*a*b^6*c*e^5 + 30*B*a^2*b^4*c^2*e^5 - 432*B*a^3*b^2*c^3*e^5 + 16*A*a^2*b^3*c^3*e^5 + 224*B*a^4*c^4*e^5 + 192*A*a^3*b*c^4*e^5)/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*x + 5*(8*B*b^4*c^4*d^5 + 96*B*a*b^2*c^5*d^5 - 16*A*b^3*c^5*d^5 - 192*A*a*b*c^6*d^5 - 15*B*b^5*c^3*d^4*e - 200*B*a*b^3*c^4*d^4*e + 40*A*b^4*c^4*d^4*e - 240*B*a^2*b*c^5*d^4*e + 480*A*a*b^2*c^5*d^4*e + 180*B*a*b^4*c^3*d^3*e^2 - 30*A*b^5*c^3*d^3*e^2 + 480*B*a^2*b^2*c^4*d^3*e^2 - 400*A*a*b^3*c^4*d^3*e^2 + 320*B*a^3*c^5*d^3*e^2 - 480*A*a^2*b*c^5*d^3*e^2 - 480*B*a^2*b^3*c^3*d^2*e^3 + 180*A*a*b^4*c^3*d^2*e^3 - 640*B*a^3*b*c^4*d^2*e^3 + 480*A*a^2*b^2*c^4*d^2*e^3 + 320*A*a^3*c^5*d^2*e^3 + 480*B*a^3*b^2*c^3*d*e^4 - 240*A*a^2*b^3*c^3*d*e^4 + 640*B*a^4*c^4*d*e^4 - 320*A*a^3*b*c^4*d*e^4 - 9*B*a*b^7*e^5 + 93*B*a^2*b^5*c*e^5 - 280*B*a^3*b^3*c^2*e^5 - 48*B*a^4*b*c^3*e^5 + 96*A*a^3*b^2*c^3*e^5 + 128*A*a^4*c^4*e^5)/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*x - 5*(B*b^5*c^3*d^5 - 24*B*a*b^3*c^4*d^5 - 2*A*b^4*c^4*d^5 - 48*B*a^2*b*c^5*d^5 + 48*A*a*b^2*c^5*d^5 + 96*A*a^2*c^6*d^5 + 20*B*a*b^4*c^3*d^4*e + 5*A*b^5*c^3*d^4*e + 240*B*a^2*b^2*c^4*d^4*e - 120*A*a*b^3*c^4*d^4*e - 240*A*a^2*b*c^5*d^4*e - 240*B*a^2*b^3*c^3*d^3*e^2 + 40*A*a*b^4*c^3*d^3*e^2 - 320*B*a^3*b*c^4*d^3*e^2 + 480*A*a^2*b^2*c^4*d^3*e^2 + 640*B*a^3*b^2*c^3*d^2*e^3 - 240*A*a^2*b^3*c^3*d^2*e^3 - 320*A*a^3*b*c^4*d^2*e^3 - 640*B*a^4*b*c^3*d*e^4 + 320*A*a^3*b^2*c^3*d*e^4 + 9*B*a^2*b^6*e^5 - 98*B*a^3*b^4*c*e^5 + 336*B*a^4*b^2*c^2*e^5 - 96*B*a^5*c^3*e^5 - 128*A*a^4*b*c^3*e^5)/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*x - (2*B*a*b^4*c^3*d^5 + 3*A*b^5*c^3*d^5 - 48*B*a^2*b^2*c^4*d^5 - 40*A*a*b^3*c^4*d^5 - 96*B*a^3*c^5*d^5 + 240*A*a^2*b*c^5*d^5 + 40*B*a^2*b^3*c^3*d^4*e + 10*A*a*b^4*c^3*d^4*e + 480*B*a^3*b*c^4*d^4*e - 240*A*a^2*b^2*c^4*d^4*e - 480*A*a^3*c^5*d^4*e - 480*B*a^3*b^2*c^3*d^3*e^2 + 80*A*a^2*b^3*c^3*d^3*e^2 - 640*B*a^4*c^4*d^3*e^2 + 960*A*a^3*b*c^4*d^3*e^2 + 1280*B*a^4*b*c^3*d^2*e^3 - 480*A*a^3*b^2*c^3*d^2*e^3 - 640*A*a^4*c^4*d^2*e^3 - 1280*B*a^5*c^3*d*e^4 + 640*A*a^4*b*c^3*d*e^4 + 15*B*a^3*b^5*e^5 - 160*B*a^4*b^3*c*e^5 + 528*B*a^5*b*c^2*e^5 - 256*A*a^5*c^3*e^5)/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))/(c*x^2 + b*x + a)^(5/2)","B",0
2489,1,1763,0,0.368387," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left({\left(\frac{{\left(128 \, B b c^{4} d^{4} - 256 \, A c^{5} d^{4} - 192 \, B b^{2} c^{3} d^{3} e - 256 \, B a c^{4} d^{3} e + 512 \, A b c^{4} d^{3} e + 48 \, B b^{3} c^{2} d^{2} e^{2} + 576 \, B a b c^{3} d^{2} e^{2} - 288 \, A b^{2} c^{3} d^{2} e^{2} - 384 \, A a c^{4} d^{2} e^{2} + 8 \, B b^{4} c d e^{3} - 192 \, B a b^{2} c^{2} d e^{3} + 32 \, A b^{3} c^{2} d e^{3} - 384 \, B a^{2} c^{3} d e^{3} + 384 \, A a b c^{3} d e^{3} + 3 \, B b^{5} e^{4} - 40 \, B a b^{3} c e^{4} + 2 \, A b^{4} c e^{4} + 240 \, B a^{2} b c^{2} e^{4} - 48 \, A a b^{2} c^{2} e^{4} - 96 \, A a^{2} c^{3} e^{4}\right)} x}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}} + \frac{5 \, {\left(64 \, B b^{2} c^{3} d^{4} - 128 \, A b c^{4} d^{4} - 96 \, B b^{3} c^{2} d^{3} e - 128 \, B a b c^{3} d^{3} e + 256 \, A b^{2} c^{3} d^{3} e + 24 \, B b^{4} c d^{2} e^{2} + 288 \, B a b^{2} c^{2} d^{2} e^{2} - 144 \, A b^{3} c^{2} d^{2} e^{2} - 192 \, A a b c^{3} d^{2} e^{2} + 4 \, B b^{5} d e^{3} - 96 \, B a b^{3} c d e^{3} + 16 \, A b^{4} c d e^{3} - 192 \, B a^{2} b c^{2} d e^{3} + 192 \, A a b^{2} c^{2} d e^{3} - 2 \, B a b^{4} e^{4} + A b^{5} e^{4} + 48 \, B a^{2} b^{2} c e^{4} - 24 \, A a b^{3} c e^{4} + 96 \, B a^{3} c^{2} e^{4} - 48 \, A a^{2} b c^{2} e^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{10 \, {\left(24 \, B b^{3} c^{2} d^{4} + 32 \, B a b c^{3} d^{4} - 48 \, A b^{2} c^{3} d^{4} - 64 \, A a c^{4} d^{4} - 36 \, B b^{4} c d^{3} e - 96 \, B a b^{2} c^{2} d^{3} e + 96 \, A b^{3} c^{2} d^{3} e - 64 \, B a^{2} c^{3} d^{3} e + 128 \, A a b c^{3} d^{3} e + 9 \, B b^{5} d^{2} e^{2} + 120 \, B a b^{3} c d^{2} e^{2} - 54 \, A b^{4} c d^{2} e^{2} + 144 \, B a^{2} b c^{2} d^{2} e^{2} - 144 \, A a b^{2} c^{2} d^{2} e^{2} - 96 \, A a^{2} c^{3} d^{2} e^{2} - 16 \, B a b^{4} d e^{3} + 6 \, A b^{5} d e^{3} - 192 \, B a^{2} b^{2} c d e^{3} + 80 \, A a b^{3} c d e^{3} + 96 \, A a^{2} b c^{2} d e^{3} + 8 \, B a^{2} b^{3} e^{4} - 4 \, A a b^{4} e^{4} + 96 \, B a^{3} b c e^{4} - 48 \, A a^{2} b^{2} c e^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{10 \, {\left(4 \, B b^{4} c d^{4} + 48 \, B a b^{2} c^{2} d^{4} - 8 \, A b^{3} c^{2} d^{4} - 96 \, A a b c^{3} d^{4} - 6 \, B b^{5} d^{3} e - 80 \, B a b^{3} c d^{3} e + 16 \, A b^{4} c d^{3} e - 96 \, B a^{2} b c^{2} d^{3} e + 192 \, A a b^{2} c^{2} d^{3} e + 54 \, B a b^{4} d^{2} e^{2} - 9 \, A b^{5} d^{2} e^{2} + 144 \, B a^{2} b^{2} c d^{2} e^{2} - 120 \, A a b^{3} c d^{2} e^{2} + 96 \, B a^{3} c^{2} d^{2} e^{2} - 144 \, A a^{2} b c^{2} d^{2} e^{2} - 96 \, B a^{2} b^{3} d e^{3} + 36 \, A a b^{4} d e^{3} - 128 \, B a^{3} b c d e^{3} + 96 \, A a^{2} b^{2} c d e^{3} + 64 \, A a^{3} c^{2} d e^{3} + 48 \, B a^{3} b^{2} e^{4} - 24 \, A a^{2} b^{3} e^{4} + 64 \, B a^{4} c e^{4} - 32 \, A a^{3} b c e^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{5 \, {\left(B b^{5} d^{4} - 24 \, B a b^{3} c d^{4} - 2 \, A b^{4} c d^{4} - 48 \, B a^{2} b c^{2} d^{4} + 48 \, A a b^{2} c^{2} d^{4} + 96 \, A a^{2} c^{3} d^{4} + 16 \, B a b^{4} d^{3} e + 4 \, A b^{5} d^{3} e + 192 \, B a^{2} b^{2} c d^{3} e - 96 \, A a b^{3} c d^{3} e - 192 \, A a^{2} b c^{2} d^{3} e - 144 \, B a^{2} b^{3} d^{2} e^{2} + 24 \, A a b^{4} d^{2} e^{2} - 192 \, B a^{3} b c d^{2} e^{2} + 288 \, A a^{2} b^{2} c d^{2} e^{2} + 256 \, B a^{3} b^{2} d e^{3} - 96 \, A a^{2} b^{3} d e^{3} - 128 \, A a^{3} b c d e^{3} - 128 \, B a^{4} b e^{4} + 64 \, A a^{3} b^{2} e^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{2 \, B a b^{4} d^{4} + 3 \, A b^{5} d^{4} - 48 \, B a^{2} b^{2} c d^{4} - 40 \, A a b^{3} c d^{4} - 96 \, B a^{3} c^{2} d^{4} + 240 \, A a^{2} b c^{2} d^{4} + 32 \, B a^{2} b^{3} d^{3} e + 8 \, A a b^{4} d^{3} e + 384 \, B a^{3} b c d^{3} e - 192 \, A a^{2} b^{2} c d^{3} e - 384 \, A a^{3} c^{2} d^{3} e - 288 \, B a^{3} b^{2} d^{2} e^{2} + 48 \, A a^{2} b^{3} d^{2} e^{2} - 384 \, B a^{4} c d^{2} e^{2} + 576 \, A a^{3} b c d^{2} e^{2} + 512 \, B a^{4} b d e^{3} - 192 \, A a^{3} b^{2} d e^{3} - 256 \, A a^{4} c d e^{3} - 256 \, B a^{5} e^{4} + 128 \, A a^{4} b e^{4}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"2/15*((((((128*B*b*c^4*d^4 - 256*A*c^5*d^4 - 192*B*b^2*c^3*d^3*e - 256*B*a*c^4*d^3*e + 512*A*b*c^4*d^3*e + 48*B*b^3*c^2*d^2*e^2 + 576*B*a*b*c^3*d^2*e^2 - 288*A*b^2*c^3*d^2*e^2 - 384*A*a*c^4*d^2*e^2 + 8*B*b^4*c*d*e^3 - 192*B*a*b^2*c^2*d*e^3 + 32*A*b^3*c^2*d*e^3 - 384*B*a^2*c^3*d*e^3 + 384*A*a*b*c^3*d*e^3 + 3*B*b^5*e^4 - 40*B*a*b^3*c*e^4 + 2*A*b^4*c*e^4 + 240*B*a^2*b*c^2*e^4 - 48*A*a*b^2*c^2*e^4 - 96*A*a^2*c^3*e^4)*x/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3) + 5*(64*B*b^2*c^3*d^4 - 128*A*b*c^4*d^4 - 96*B*b^3*c^2*d^3*e - 128*B*a*b*c^3*d^3*e + 256*A*b^2*c^3*d^3*e + 24*B*b^4*c*d^2*e^2 + 288*B*a*b^2*c^2*d^2*e^2 - 144*A*b^3*c^2*d^2*e^2 - 192*A*a*b*c^3*d^2*e^2 + 4*B*b^5*d*e^3 - 96*B*a*b^3*c*d*e^3 + 16*A*b^4*c*d*e^3 - 192*B*a^2*b*c^2*d*e^3 + 192*A*a*b^2*c^2*d*e^3 - 2*B*a*b^4*e^4 + A*b^5*e^4 + 48*B*a^2*b^2*c*e^4 - 24*A*a*b^3*c*e^4 + 96*B*a^3*c^2*e^4 - 48*A*a^2*b*c^2*e^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 10*(24*B*b^3*c^2*d^4 + 32*B*a*b*c^3*d^4 - 48*A*b^2*c^3*d^4 - 64*A*a*c^4*d^4 - 36*B*b^4*c*d^3*e - 96*B*a*b^2*c^2*d^3*e + 96*A*b^3*c^2*d^3*e - 64*B*a^2*c^3*d^3*e + 128*A*a*b*c^3*d^3*e + 9*B*b^5*d^2*e^2 + 120*B*a*b^3*c*d^2*e^2 - 54*A*b^4*c*d^2*e^2 + 144*B*a^2*b*c^2*d^2*e^2 - 144*A*a*b^2*c^2*d^2*e^2 - 96*A*a^2*c^3*d^2*e^2 - 16*B*a*b^4*d*e^3 + 6*A*b^5*d*e^3 - 192*B*a^2*b^2*c*d*e^3 + 80*A*a*b^3*c*d*e^3 + 96*A*a^2*b*c^2*d*e^3 + 8*B*a^2*b^3*e^4 - 4*A*a*b^4*e^4 + 96*B*a^3*b*c*e^4 - 48*A*a^2*b^2*c*e^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 10*(4*B*b^4*c*d^4 + 48*B*a*b^2*c^2*d^4 - 8*A*b^3*c^2*d^4 - 96*A*a*b*c^3*d^4 - 6*B*b^5*d^3*e - 80*B*a*b^3*c*d^3*e + 16*A*b^4*c*d^3*e - 96*B*a^2*b*c^2*d^3*e + 192*A*a*b^2*c^2*d^3*e + 54*B*a*b^4*d^2*e^2 - 9*A*b^5*d^2*e^2 + 144*B*a^2*b^2*c*d^2*e^2 - 120*A*a*b^3*c*d^2*e^2 + 96*B*a^3*c^2*d^2*e^2 - 144*A*a^2*b*c^2*d^2*e^2 - 96*B*a^2*b^3*d*e^3 + 36*A*a*b^4*d*e^3 - 128*B*a^3*b*c*d*e^3 + 96*A*a^2*b^2*c*d*e^3 + 64*A*a^3*c^2*d*e^3 + 48*B*a^3*b^2*e^4 - 24*A*a^2*b^3*e^4 + 64*B*a^4*c*e^4 - 32*A*a^3*b*c*e^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - 5*(B*b^5*d^4 - 24*B*a*b^3*c*d^4 - 2*A*b^4*c*d^4 - 48*B*a^2*b*c^2*d^4 + 48*A*a*b^2*c^2*d^4 + 96*A*a^2*c^3*d^4 + 16*B*a*b^4*d^3*e + 4*A*b^5*d^3*e + 192*B*a^2*b^2*c*d^3*e - 96*A*a*b^3*c*d^3*e - 192*A*a^2*b*c^2*d^3*e - 144*B*a^2*b^3*d^2*e^2 + 24*A*a*b^4*d^2*e^2 - 192*B*a^3*b*c*d^2*e^2 + 288*A*a^2*b^2*c*d^2*e^2 + 256*B*a^3*b^2*d*e^3 - 96*A*a^2*b^3*d*e^3 - 128*A*a^3*b*c*d*e^3 - 128*B*a^4*b*e^4 + 64*A*a^3*b^2*e^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - (2*B*a*b^4*d^4 + 3*A*b^5*d^4 - 48*B*a^2*b^2*c*d^4 - 40*A*a*b^3*c*d^4 - 96*B*a^3*c^2*d^4 + 240*A*a^2*b*c^2*d^4 + 32*B*a^2*b^3*d^3*e + 8*A*a*b^4*d^3*e + 384*B*a^3*b*c*d^3*e - 192*A*a^2*b^2*c*d^3*e - 384*A*a^3*c^2*d^3*e - 288*B*a^3*b^2*d^2*e^2 + 48*A*a^2*b^3*d^2*e^2 - 384*B*a^4*c*d^2*e^2 + 576*A*a^3*b*c*d^2*e^2 + 512*B*a^4*b*d*e^3 - 192*A*a^3*b^2*d*e^3 - 256*A*a^4*c*d*e^3 - 256*B*a^5*e^4 + 128*A*a^4*b*e^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(c*x^2 + b*x + a)^(5/2)","B",0
2490,1,1437,0,0.359937," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left({\left(\frac{2 \, {\left(64 \, B b c^{4} d^{3} - 128 \, A c^{5} d^{3} - 72 \, B b^{2} c^{3} d^{2} e - 96 \, B a c^{4} d^{2} e + 192 \, A b c^{4} d^{2} e + 12 \, B b^{3} c^{2} d e^{2} + 144 \, B a b c^{3} d e^{2} - 72 \, A b^{2} c^{3} d e^{2} - 96 \, A a c^{4} d e^{2} + B b^{4} c e^{3} - 24 \, B a b^{2} c^{2} e^{3} + 4 \, A b^{3} c^{2} e^{3} - 48 \, B a^{2} c^{3} e^{3} + 48 \, A a b c^{3} e^{3}\right)} x}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}} + \frac{5 \, {\left(64 \, B b^{2} c^{3} d^{3} - 128 \, A b c^{4} d^{3} - 72 \, B b^{3} c^{2} d^{2} e - 96 \, B a b c^{3} d^{2} e + 192 \, A b^{2} c^{3} d^{2} e + 12 \, B b^{4} c d e^{2} + 144 \, B a b^{2} c^{2} d e^{2} - 72 \, A b^{3} c^{2} d e^{2} - 96 \, A a b c^{3} d e^{2} + B b^{5} e^{3} - 24 \, B a b^{3} c e^{3} + 4 \, A b^{4} c e^{3} - 48 \, B a^{2} b c^{2} e^{3} + 48 \, A a b^{2} c^{2} e^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(48 \, B b^{3} c^{2} d^{3} + 64 \, B a b c^{3} d^{3} - 96 \, A b^{2} c^{3} d^{3} - 128 \, A a c^{4} d^{3} - 54 \, B b^{4} c d^{2} e - 144 \, B a b^{2} c^{2} d^{2} e + 144 \, A b^{3} c^{2} d^{2} e - 96 \, B a^{2} c^{3} d^{2} e + 192 \, A a b c^{3} d^{2} e + 9 \, B b^{5} d e^{2} + 120 \, B a b^{3} c d e^{2} - 54 \, A b^{4} c d e^{2} + 144 \, B a^{2} b c^{2} d e^{2} - 144 \, A a b^{2} c^{2} d e^{2} - 96 \, A a^{2} c^{3} d e^{2} - 8 \, B a b^{4} e^{3} + 3 \, A b^{5} e^{3} - 96 \, B a^{2} b^{2} c e^{3} + 40 \, A a b^{3} c e^{3} + 48 \, A a^{2} b c^{2} e^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(8 \, B b^{4} c d^{3} + 96 \, B a b^{2} c^{2} d^{3} - 16 \, A b^{3} c^{2} d^{3} - 192 \, A a b c^{3} d^{3} - 9 \, B b^{5} d^{2} e - 120 \, B a b^{3} c d^{2} e + 24 \, A b^{4} c d^{2} e - 144 \, B a^{2} b c^{2} d^{2} e + 288 \, A a b^{2} c^{2} d^{2} e + 54 \, B a b^{4} d e^{2} - 9 \, A b^{5} d e^{2} + 144 \, B a^{2} b^{2} c d e^{2} - 120 \, A a b^{3} c d e^{2} + 96 \, B a^{3} c^{2} d e^{2} - 144 \, A a^{2} b c^{2} d e^{2} - 48 \, B a^{2} b^{3} e^{3} + 18 \, A a b^{4} e^{3} - 64 \, B a^{3} b c e^{3} + 48 \, A a^{2} b^{2} c e^{3} + 32 \, A a^{3} c^{2} e^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{5 \, {\left(B b^{5} d^{3} - 24 \, B a b^{3} c d^{3} - 2 \, A b^{4} c d^{3} - 48 \, B a^{2} b c^{2} d^{3} + 48 \, A a b^{2} c^{2} d^{3} + 96 \, A a^{2} c^{3} d^{3} + 12 \, B a b^{4} d^{2} e + 3 \, A b^{5} d^{2} e + 144 \, B a^{2} b^{2} c d^{2} e - 72 \, A a b^{3} c d^{2} e - 144 \, A a^{2} b c^{2} d^{2} e - 72 \, B a^{2} b^{3} d e^{2} + 12 \, A a b^{4} d e^{2} - 96 \, B a^{3} b c d e^{2} + 144 \, A a^{2} b^{2} c d e^{2} + 64 \, B a^{3} b^{2} e^{3} - 24 \, A a^{2} b^{3} e^{3} - 32 \, A a^{3} b c e^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{2 \, B a b^{4} d^{3} + 3 \, A b^{5} d^{3} - 48 \, B a^{2} b^{2} c d^{3} - 40 \, A a b^{3} c d^{3} - 96 \, B a^{3} c^{2} d^{3} + 240 \, A a^{2} b c^{2} d^{3} + 24 \, B a^{2} b^{3} d^{2} e + 6 \, A a b^{4} d^{2} e + 288 \, B a^{3} b c d^{2} e - 144 \, A a^{2} b^{2} c d^{2} e - 288 \, A a^{3} c^{2} d^{2} e - 144 \, B a^{3} b^{2} d e^{2} + 24 \, A a^{2} b^{3} d e^{2} - 192 \, B a^{4} c d e^{2} + 288 \, A a^{3} b c d e^{2} + 128 \, B a^{4} b e^{3} - 48 \, A a^{3} b^{2} e^{3} - 64 \, A a^{4} c e^{3}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"2/15*(((((2*(64*B*b*c^4*d^3 - 128*A*c^5*d^3 - 72*B*b^2*c^3*d^2*e - 96*B*a*c^4*d^2*e + 192*A*b*c^4*d^2*e + 12*B*b^3*c^2*d*e^2 + 144*B*a*b*c^3*d*e^2 - 72*A*b^2*c^3*d*e^2 - 96*A*a*c^4*d*e^2 + B*b^4*c*e^3 - 24*B*a*b^2*c^2*e^3 + 4*A*b^3*c^2*e^3 - 48*B*a^2*c^3*e^3 + 48*A*a*b*c^3*e^3)*x/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3) + 5*(64*B*b^2*c^3*d^3 - 128*A*b*c^4*d^3 - 72*B*b^3*c^2*d^2*e - 96*B*a*b*c^3*d^2*e + 192*A*b^2*c^3*d^2*e + 12*B*b^4*c*d*e^2 + 144*B*a*b^2*c^2*d*e^2 - 72*A*b^3*c^2*d*e^2 - 96*A*a*b*c^3*d*e^2 + B*b^5*e^3 - 24*B*a*b^3*c*e^3 + 4*A*b^4*c*e^3 - 48*B*a^2*b*c^2*e^3 + 48*A*a*b^2*c^2*e^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(48*B*b^3*c^2*d^3 + 64*B*a*b*c^3*d^3 - 96*A*b^2*c^3*d^3 - 128*A*a*c^4*d^3 - 54*B*b^4*c*d^2*e - 144*B*a*b^2*c^2*d^2*e + 144*A*b^3*c^2*d^2*e - 96*B*a^2*c^3*d^2*e + 192*A*a*b*c^3*d^2*e + 9*B*b^5*d*e^2 + 120*B*a*b^3*c*d*e^2 - 54*A*b^4*c*d*e^2 + 144*B*a^2*b*c^2*d*e^2 - 144*A*a*b^2*c^2*d*e^2 - 96*A*a^2*c^3*d*e^2 - 8*B*a*b^4*e^3 + 3*A*b^5*e^3 - 96*B*a^2*b^2*c*e^3 + 40*A*a*b^3*c*e^3 + 48*A*a^2*b*c^2*e^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(8*B*b^4*c*d^3 + 96*B*a*b^2*c^2*d^3 - 16*A*b^3*c^2*d^3 - 192*A*a*b*c^3*d^3 - 9*B*b^5*d^2*e - 120*B*a*b^3*c*d^2*e + 24*A*b^4*c*d^2*e - 144*B*a^2*b*c^2*d^2*e + 288*A*a*b^2*c^2*d^2*e + 54*B*a*b^4*d*e^2 - 9*A*b^5*d*e^2 + 144*B*a^2*b^2*c*d*e^2 - 120*A*a*b^3*c*d*e^2 + 96*B*a^3*c^2*d*e^2 - 144*A*a^2*b*c^2*d*e^2 - 48*B*a^2*b^3*e^3 + 18*A*a*b^4*e^3 - 64*B*a^3*b*c*e^3 + 48*A*a^2*b^2*c*e^3 + 32*A*a^3*c^2*e^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - 5*(B*b^5*d^3 - 24*B*a*b^3*c*d^3 - 2*A*b^4*c*d^3 - 48*B*a^2*b*c^2*d^3 + 48*A*a*b^2*c^2*d^3 + 96*A*a^2*c^3*d^3 + 12*B*a*b^4*d^2*e + 3*A*b^5*d^2*e + 144*B*a^2*b^2*c*d^2*e - 72*A*a*b^3*c*d^2*e - 144*A*a^2*b*c^2*d^2*e - 72*B*a^2*b^3*d*e^2 + 12*A*a*b^4*d*e^2 - 96*B*a^3*b*c*d*e^2 + 144*A*a^2*b^2*c*d*e^2 + 64*B*a^3*b^2*e^3 - 24*A*a^2*b^3*e^3 - 32*A*a^3*b*c*e^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - (2*B*a*b^4*d^3 + 3*A*b^5*d^3 - 48*B*a^2*b^2*c*d^3 - 40*A*a*b^3*c*d^3 - 96*B*a^3*c^2*d^3 + 240*A*a^2*b*c^2*d^3 + 24*B*a^2*b^3*d^2*e + 6*A*a*b^4*d^2*e + 288*B*a^3*b*c*d^2*e - 144*A*a^2*b^2*c*d^2*e - 288*A*a^3*c^2*d^2*e - 144*B*a^3*b^2*d*e^2 + 24*A*a^2*b^3*d*e^2 - 192*B*a^4*c*d*e^2 + 288*A*a^3*b*c*d*e^2 + 128*B*a^4*b*e^3 - 48*A*a^3*b^2*e^3 - 64*A*a^4*c*e^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(c*x^2 + b*x + a)^(5/2)","B",0
2491,1,1089,0,0.340513," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left(4 \, {\left(\frac{2 \, {\left(16 \, B b c^{4} d^{2} - 32 \, A c^{5} d^{2} - 12 \, B b^{2} c^{3} d e - 16 \, B a c^{4} d e + 32 \, A b c^{4} d e + B b^{3} c^{2} e^{2} + 12 \, B a b c^{3} e^{2} - 6 \, A b^{2} c^{3} e^{2} - 8 \, A a c^{4} e^{2}\right)} x}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}} + \frac{5 \, {\left(16 \, B b^{2} c^{3} d^{2} - 32 \, A b c^{4} d^{2} - 12 \, B b^{3} c^{2} d e - 16 \, B a b c^{3} d e + 32 \, A b^{2} c^{3} d e + B b^{4} c e^{2} + 12 \, B a b^{2} c^{2} e^{2} - 6 \, A b^{3} c^{2} e^{2} - 8 \, A a b c^{3} e^{2}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(48 \, B b^{3} c^{2} d^{2} + 64 \, B a b c^{3} d^{2} - 96 \, A b^{2} c^{3} d^{2} - 128 \, A a c^{4} d^{2} - 36 \, B b^{4} c d e - 96 \, B a b^{2} c^{2} d e + 96 \, A b^{3} c^{2} d e - 64 \, B a^{2} c^{3} d e + 128 \, A a b c^{3} d e + 3 \, B b^{5} e^{2} + 40 \, B a b^{3} c e^{2} - 18 \, A b^{4} c e^{2} + 48 \, B a^{2} b c^{2} e^{2} - 48 \, A a b^{2} c^{2} e^{2} - 32 \, A a^{2} c^{3} e^{2}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(8 \, B b^{4} c d^{2} + 96 \, B a b^{2} c^{2} d^{2} - 16 \, A b^{3} c^{2} d^{2} - 192 \, A a b c^{3} d^{2} - 6 \, B b^{5} d e - 80 \, B a b^{3} c d e + 16 \, A b^{4} c d e - 96 \, B a^{2} b c^{2} d e + 192 \, A a b^{2} c^{2} d e + 18 \, B a b^{4} e^{2} - 3 \, A b^{5} e^{2} + 48 \, B a^{2} b^{2} c e^{2} - 40 \, A a b^{3} c e^{2} + 32 \, B a^{3} c^{2} e^{2} - 48 \, A a^{2} b c^{2} e^{2}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{5 \, {\left(B b^{5} d^{2} - 24 \, B a b^{3} c d^{2} - 2 \, A b^{4} c d^{2} - 48 \, B a^{2} b c^{2} d^{2} + 48 \, A a b^{2} c^{2} d^{2} + 96 \, A a^{2} c^{3} d^{2} + 8 \, B a b^{4} d e + 2 \, A b^{5} d e + 96 \, B a^{2} b^{2} c d e - 48 \, A a b^{3} c d e - 96 \, A a^{2} b c^{2} d e - 24 \, B a^{2} b^{3} e^{2} + 4 \, A a b^{4} e^{2} - 32 \, B a^{3} b c e^{2} + 48 \, A a^{2} b^{2} c e^{2}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{2 \, B a b^{4} d^{2} + 3 \, A b^{5} d^{2} - 48 \, B a^{2} b^{2} c d^{2} - 40 \, A a b^{3} c d^{2} - 96 \, B a^{3} c^{2} d^{2} + 240 \, A a^{2} b c^{2} d^{2} + 16 \, B a^{2} b^{3} d e + 4 \, A a b^{4} d e + 192 \, B a^{3} b c d e - 96 \, A a^{2} b^{2} c d e - 192 \, A a^{3} c^{2} d e - 48 \, B a^{3} b^{2} e^{2} + 8 \, A a^{2} b^{3} e^{2} - 64 \, B a^{4} c e^{2} + 96 \, A a^{3} b c e^{2}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"2/15*((((4*(2*(16*B*b*c^4*d^2 - 32*A*c^5*d^2 - 12*B*b^2*c^3*d*e - 16*B*a*c^4*d*e + 32*A*b*c^4*d*e + B*b^3*c^2*e^2 + 12*B*a*b*c^3*e^2 - 6*A*b^2*c^3*e^2 - 8*A*a*c^4*e^2)*x/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3) + 5*(16*B*b^2*c^3*d^2 - 32*A*b*c^4*d^2 - 12*B*b^3*c^2*d*e - 16*B*a*b*c^3*d*e + 32*A*b^2*c^3*d*e + B*b^4*c*e^2 + 12*B*a*b^2*c^2*e^2 - 6*A*b^3*c^2*e^2 - 8*A*a*b*c^3*e^2)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(48*B*b^3*c^2*d^2 + 64*B*a*b*c^3*d^2 - 96*A*b^2*c^3*d^2 - 128*A*a*c^4*d^2 - 36*B*b^4*c*d*e - 96*B*a*b^2*c^2*d*e + 96*A*b^3*c^2*d*e - 64*B*a^2*c^3*d*e + 128*A*a*b*c^3*d*e + 3*B*b^5*e^2 + 40*B*a*b^3*c*e^2 - 18*A*b^4*c*e^2 + 48*B*a^2*b*c^2*e^2 - 48*A*a*b^2*c^2*e^2 - 32*A*a^2*c^3*e^2)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(8*B*b^4*c*d^2 + 96*B*a*b^2*c^2*d^2 - 16*A*b^3*c^2*d^2 - 192*A*a*b*c^3*d^2 - 6*B*b^5*d*e - 80*B*a*b^3*c*d*e + 16*A*b^4*c*d*e - 96*B*a^2*b*c^2*d*e + 192*A*a*b^2*c^2*d*e + 18*B*a*b^4*e^2 - 3*A*b^5*e^2 + 48*B*a^2*b^2*c*e^2 - 40*A*a*b^3*c*e^2 + 32*B*a^3*c^2*e^2 - 48*A*a^2*b*c^2*e^2)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - 5*(B*b^5*d^2 - 24*B*a*b^3*c*d^2 - 2*A*b^4*c*d^2 - 48*B*a^2*b*c^2*d^2 + 48*A*a*b^2*c^2*d^2 + 96*A*a^2*c^3*d^2 + 8*B*a*b^4*d*e + 2*A*b^5*d*e + 96*B*a^2*b^2*c*d*e - 48*A*a*b^3*c*d*e - 96*A*a^2*b*c^2*d*e - 24*B*a^2*b^3*e^2 + 4*A*a*b^4*e^2 - 32*B*a^3*b*c*e^2 + 48*A*a^2*b^2*c*e^2)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - (2*B*a*b^4*d^2 + 3*A*b^5*d^2 - 48*B*a^2*b^2*c*d^2 - 40*A*a*b^3*c*d^2 - 96*B*a^3*c^2*d^2 + 240*A*a^2*b*c^2*d^2 + 16*B*a^2*b^3*d*e + 4*A*a*b^4*d*e + 192*B*a^3*b*c*d*e - 96*A*a^2*b^2*c*d*e - 192*A*a^3*c^2*d*e - 48*B*a^3*b^2*e^2 + 8*A*a^2*b^3*e^2 - 64*B*a^4*c*e^2 + 96*A*a^3*b*c*e^2)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(c*x^2 + b*x + a)^(5/2)","B",0
2492,1,727,0,0.313451," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(2 \, {\left(4 \, {\left(\frac{2 \, {\left(8 \, B b c^{4} d - 16 \, A c^{5} d - 3 \, B b^{2} c^{3} e - 4 \, B a c^{4} e + 8 \, A b c^{4} e\right)} x}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}} + \frac{5 \, {\left(8 \, B b^{2} c^{3} d - 16 \, A b c^{4} d - 3 \, B b^{3} c^{2} e - 4 \, B a b c^{3} e + 8 \, A b^{2} c^{3} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(24 \, B b^{3} c^{2} d + 32 \, B a b c^{3} d - 48 \, A b^{2} c^{3} d - 64 \, A a c^{4} d - 9 \, B b^{4} c e - 24 \, B a b^{2} c^{2} e + 24 \, A b^{3} c^{2} e - 16 \, B a^{2} c^{3} e + 32 \, A a b c^{3} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(8 \, B b^{4} c d + 96 \, B a b^{2} c^{2} d - 16 \, A b^{3} c^{2} d - 192 \, A a b c^{3} d - 3 \, B b^{5} e - 40 \, B a b^{3} c e + 8 \, A b^{4} c e - 48 \, B a^{2} b c^{2} e + 96 \, A a b^{2} c^{2} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{5 \, {\left(B b^{5} d - 24 \, B a b^{3} c d - 2 \, A b^{4} c d - 48 \, B a^{2} b c^{2} d + 48 \, A a b^{2} c^{2} d + 96 \, A a^{2} c^{3} d + 4 \, B a b^{4} e + A b^{5} e + 48 \, B a^{2} b^{2} c e - 24 \, A a b^{3} c e - 48 \, A a^{2} b c^{2} e\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{2 \, B a b^{4} d + 3 \, A b^{5} d - 48 \, B a^{2} b^{2} c d - 40 \, A a b^{3} c d - 96 \, B a^{3} c^{2} d + 240 \, A a^{2} b c^{2} d + 8 \, B a^{2} b^{3} e + 2 \, A a b^{4} e + 96 \, B a^{3} b c e - 48 \, A a^{2} b^{2} c e - 96 \, A a^{3} c^{2} e}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"2/15*(((2*(4*(2*(8*B*b*c^4*d - 16*A*c^5*d - 3*B*b^2*c^3*e - 4*B*a*c^4*e + 8*A*b*c^4*e)*x/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3) + 5*(8*B*b^2*c^3*d - 16*A*b*c^4*d - 3*B*b^3*c^2*e - 4*B*a*b*c^3*e + 8*A*b^2*c^3*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(24*B*b^3*c^2*d + 32*B*a*b*c^3*d - 48*A*b^2*c^3*d - 64*A*a*c^4*d - 9*B*b^4*c*e - 24*B*a*b^2*c^2*e + 24*A*b^3*c^2*e - 16*B*a^2*c^3*e + 32*A*a*b*c^3*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(8*B*b^4*c*d + 96*B*a*b^2*c^2*d - 16*A*b^3*c^2*d - 192*A*a*b*c^3*d - 3*B*b^5*e - 40*B*a*b^3*c*e + 8*A*b^4*c*e - 48*B*a^2*b*c^2*e + 96*A*a*b^2*c^2*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - 5*(B*b^5*d - 24*B*a*b^3*c*d - 2*A*b^4*c*d - 48*B*a^2*b*c^2*d + 48*A*a*b^2*c^2*d + 96*A*a^2*c^3*d + 4*B*a*b^4*e + A*b^5*e + 48*B*a^2*b^2*c*e - 24*A*a*b^3*c*e - 48*A*a^2*b*c^2*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - (2*B*a*b^4*d + 3*A*b^5*d - 48*B*a^2*b^2*c*d - 40*A*a*b^3*c*d - 96*B*a^3*c^2*d + 240*A*a^2*b*c^2*d + 8*B*a^2*b^3*e + 2*A*a*b^4*e + 96*B*a^3*b*c*e - 48*A*a^2*b^2*c*e - 96*A*a^3*c^2*e)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(c*x^2 + b*x + a)^(5/2)","B",0
2493,1,433,0,0.279211," ","integrate((B*x+A)/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(8 \, {\left(2 \, {\left(4 \, {\left(\frac{2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} x}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}} + \frac{5 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(3 \, B b^{3} c^{2} + 4 \, B a b c^{3} - 6 \, A b^{2} c^{3} - 8 \, A a c^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(B b^{4} c + 12 \, B a b^{2} c^{2} - 2 \, A b^{3} c^{2} - 24 \, A a b c^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{5 \, {\left(B b^{5} - 24 \, B a b^{3} c - 2 \, A b^{4} c - 48 \, B a^{2} b c^{2} + 48 \, A a b^{2} c^{2} + 96 \, A a^{2} c^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x - \frac{2 \, B a b^{4} + 3 \, A b^{5} - 48 \, B a^{2} b^{2} c - 40 \, A a b^{3} c - 96 \, B a^{3} c^{2} + 240 \, A a^{2} b c^{2}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"2/15*((8*(2*(4*(2*(B*b*c^4 - 2*A*c^5)*x/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3) + 5*(B*b^2*c^3 - 2*A*b*c^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(3*B*b^3*c^2 + 4*B*a*b*c^3 - 6*A*b^2*c^3 - 8*A*a*c^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(B*b^4*c + 12*B*a*b^2*c^2 - 2*A*b^3*c^2 - 24*A*a*b*c^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - 5*(B*b^5 - 24*B*a*b^3*c - 2*A*b^4*c - 48*B*a^2*b*c^2 + 48*A*a*b^2*c^2 + 96*A*a^2*c^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x - (2*B*a*b^4 + 3*A*b^5 - 48*B*a^2*b^2*c - 40*A*a*b^3*c - 96*B*a^3*c^2 + 240*A*a^2*b*c^2)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(c*x^2 + b*x + a)^(5/2)","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2495,1,69,0,0.231256," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{3240} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, x - 5\right)} x - 3913\right)} x - 134375\right)} x - 281829\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{28051}{3888} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/3240*(2*(12*(18*(8*x - 5)*x - 3913)*x - 134375)*x - 281829)*sqrt(3*x^2 + 5*x + 2) - 28051/3888*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2496,1,64,0,0.225546," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{648} \, {\left(2 \, {\left(12 \, {\left(18 \, x - 47\right)} x - 5845\right)} x - 21759\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{19405}{3888} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/648*(2*(12*(18*x - 47)*x - 5845)*x - 21759)*sqrt(3*x^2 + 5*x + 2) - 19405/3888*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2497,1,59,0,0.225543," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{54} \, {\left(2 \, {\left(12 \, x - 61\right)} x - 645\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{1147}{324} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/54*(2*(12*x - 61)*x - 645)*sqrt(3*x^2 + 5*x + 2) - 1147/324*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2498,1,54,0,0.217558," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x - 19\right)} - \frac{31}{12} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right)"," ",0,"-1/6*sqrt(3*x^2 + 5*x + 2)*(2*x - 19) - 31/12*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5))","A",0
2499,1,49,0,0.249098," ","integrate((5-x)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{35}{18} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{1}{3} \, \sqrt{3 \, x^{2} + 5 \, x + 2}"," ",0,"-35/18*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 1/3*sqrt(3*x^2 + 5*x + 2)","A",0
2500,1,107,0,0.292974," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{13}{10} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{1}{6} \, \sqrt{3} \log\left({\left| -6 \, \sqrt{3} x - 5 \, \sqrt{3} + 6 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}\right)"," ",0,"13/10*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 1/6*sqrt(3)*log(abs(-6*sqrt(3)*x - 5*sqrt(3) + 6*sqrt(3*x^2 + 5*x + 2)))","A",0
2501,1,127,0,0.343060," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{50} \, \sqrt{5} {\left(13 \, \sqrt{5} \sqrt{3} + 47 \, \log\left(-\sqrt{5} \sqrt{3} + 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{47 \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right)}{50 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} - \frac{13 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3}}{10 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"1/50*sqrt(5)*(13*sqrt(5)*sqrt(3) + 47*log(-sqrt(5)*sqrt(3) + 4))*sgn(1/(2*x + 3)) - 47/50*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))/sgn(1/(2*x + 3)) - 13/10*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3)/sgn(1/(2*x + 3))","B",0
2502,1,206,0,0.323947," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{389}{500} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{778 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 3551 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 13217 \, \sqrt{3} x + 4971 \, \sqrt{3} - 13217 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{50 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{2}}"," ",0,"389/500*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/50*(778*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 3551*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 13217*sqrt(3)*x + 4971*sqrt(3) - 13217*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^2","B",0
2503,1,257,0,0.314961," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{331}{500} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{3972 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 29790 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 255470 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 338835 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 632175 \, \sqrt{3} x + 149502 \, \sqrt{3} - 632175 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{150 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{3}}"," ",0,"331/500*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/150*(3972*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 29790*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 255470*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 338835*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 632175*sqrt(3)*x + 149502*sqrt(3) - 632175*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^3","B",0
2504,1,193,0,0.368189," ","integrate((5-x)/(3+2*x)^5/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{10000} \, \sqrt{5} {\left(2724 \, \sqrt{5} \sqrt{3} + 5771 \, \log\left(-\sqrt{5} \sqrt{3} + 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{1}{6000} \, {\left(\frac{5 \, {\left(\frac{2 \, {\left(\frac{344}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{195}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} + \frac{1025}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} + \frac{8172}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)} \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} - \frac{5771 \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right)}{10000 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"1/10000*sqrt(5)*(2724*sqrt(5)*sqrt(3) + 5771*log(-sqrt(5)*sqrt(3) + 4))*sgn(1/(2*x + 3)) - 1/6000*(5*(2*(344/sgn(1/(2*x + 3)) + 195/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) + 1025/sgn(1/(2*x + 3)))/(2*x + 3) + 8172/sgn(1/(2*x + 3)))*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) - 5771/10000*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))/sgn(1/(2*x + 3))","A",0
2505,1,359,0,0.555272," ","integrate((5-x)/(3+2*x)^6/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{128381}{250000} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{6162288 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{9} + 83190888 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{8} + 1461489304 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{7} + 4863585804 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{6} + 30365807072 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 40931011758 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 107175203674 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 58461317289 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 54344360217 \, \sqrt{3} x + 7303159752 \, \sqrt{3} - 54344360217 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{75000 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{5}}"," ",0,"128381/250000*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 1/75000*(6162288*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 83190888*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^8 + 1461489304*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7 + 4863585804*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 + 30365807072*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 40931011758*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 107175203674*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 58461317289*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 54344360217*sqrt(3)*x + 7303159752*sqrt(3) - 54344360217*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^5","B",0
2506,1,67,0,0.226378," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\frac{6265}{243} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{2 \, {\left({\left({\left(6 \, {\left(12 \, x - 17\right)} x - 3331\right)} x + 6920\right)} x + 9591\right)}}{81 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}"," ",0,"-6265/243*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 2/81*(((6*(12*x - 17)*x - 3331)*x + 6920)*x + 9591)/sqrt(3*x^2 + 5*x + 2)","A",0
2507,1,62,0,0.226739," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\frac{247}{27} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{2 \, {\left({\left({\left(6 \, x - 31\right)} x + 806\right)} x + 789\right)}}{9 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}"," ",0,"-247/27*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 2/9*(((6*x - 31)*x + 806)*x + 789)/sqrt(3*x^2 + 5*x + 2)","A",0
2508,1,58,0,0.217025," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-2 \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{2 \, {\left({\left(2 \, x + 199\right)} x + 179\right)}}{3 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}"," ",0,"-2*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 2/3*((2*x + 199)*x + 179)/sqrt(3*x^2 + 5*x + 2)","A",0
2509,1,54,0,0.212574," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{2 \, {\left(139 \, x + 121\right)}}{3 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}"," ",0,"2/9*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 2/3*(139*x + 121)/sqrt(3*x^2 + 5*x + 2)","A",0
2510,1,19,0,0.230867," ","integrate((5-x)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","-\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
2511,1,93,0,0.277092," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\frac{26}{25} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{6 \, {\left(47 \, x + 37\right)}}{5 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}"," ",0,"26/25*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 6/5*(47*x + 37)/sqrt(3*x^2 + 5*x + 2)","A",0
2512,1,170,0,0.315076," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\frac{2}{125} \, \sqrt{5} {\left(214 \, \sqrt{5} \sqrt{3} + 151 \, \log\left(-\sqrt{5} \sqrt{3} + 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) + \frac{2 \, {\left(\frac{\frac{1007}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} - \frac{65}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} - \frac{642}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{25 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3}} - \frac{302 \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right)}{125 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"2/125*sqrt(5)*(214*sqrt(5)*sqrt(3) + 151*log(-sqrt(5)*sqrt(3) + 4))*sgn(1/(2*x + 3)) + 2/25*((1007/sgn(1/(2*x + 3)) - 65/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) - 642/sgn(1/(2*x + 3)))/sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) - 302/125*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))/sgn(1/(2*x + 3))","B",0
2513,1,225,0,0.356136," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\frac{483}{125} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{6 \, {\left(903 \, x + 653\right)}}{125 \, \sqrt{3 \, x^{2} + 5 \, x + 2}} - \frac{2 \, {\left(2442 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 9999 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 35473 \, \sqrt{3} x + 12979 \, \sqrt{3} - 35473 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{125 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{2}}"," ",0,"483/125*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 6/125*(903*x + 653)/sqrt(3*x^2 + 5*x + 2) - 2/125*(2442*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 9999*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 35473*sqrt(3)*x + 12979*sqrt(3) - 35473*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^2","B",0
2514,1,276,0,0.321854," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\frac{3289}{625} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) - \frac{6 \, {\left(4209 \, x + 2959\right)}}{625 \, \sqrt{3 \, x^{2} + 5 \, x + 2}} - \frac{2 \, {\left(118356 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 851850 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 6938110 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 8824815 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 15944775 \, \sqrt{3} x + 3678471 \, \sqrt{3} - 15944775 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{1875 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{3}}"," ",0,"3289/625*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) - 6/625*(4209*x + 2959)/sqrt(3*x^2 + 5*x + 2) - 2/1875*(118356*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 851850*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 6938110*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 8824815*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 15944775*sqrt(3)*x + 3678471*sqrt(3) - 15944775*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^3","B",0
2515,1,235,0,0.350362," ","integrate((5-x)/(3+2*x)^5/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\frac{1}{12500} \, \sqrt{5} {\left(50916 \, \sqrt{5} \sqrt{3} + 82039 \, \log\left(-\sqrt{5} \sqrt{3} + 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{\frac{\frac{5 \, {\left(\frac{\frac{10 \, {\left(\frac{448}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{195}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} + \frac{9619}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} + \frac{27724}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} - \frac{857109}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} + \frac{458244}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{7500 \, \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3}} - \frac{82039 \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right)}{12500 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}"," ",0,"1/12500*sqrt(5)*(50916*sqrt(5)*sqrt(3) + 82039*log(-sqrt(5)*sqrt(3) + 4))*sgn(1/(2*x + 3)) - 1/7500*((5*((10*(448/sgn(1/(2*x + 3)) + 195/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) + 9619/sgn(1/(2*x + 3)))/(2*x + 3) + 27724/sgn(1/(2*x + 3)))/(2*x + 3) - 857109/sgn(1/(2*x + 3)))/(2*x + 3) + 458244/sgn(1/(2*x + 3)))/sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) - 82039/12500*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))/sgn(1/(2*x + 3))","A",0
2516,1,68,0,0.230857," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","-\frac{152}{81} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) - \frac{2 \, {\left({\left(4 \, {\left(2 \, {\left(9 \, x - 7340\right)} x - 36545\right)} x - 118153\right)} x - 30819\right)}}{27 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}"," ",0,"-152/81*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) - 2/27*((4*(2*(9*x - 7340)*x - 36545)*x - 118153)*x - 30819)/(3*x^2 + 5*x + 2)^(3/2)","A",0
2517,1,63,0,0.463908," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\frac{8}{27} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{2 \, {\left({\left(2 \, {\left(8224 \, x + 20537\right)} x + 33443\right)} x + 8835\right)}}{9 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}"," ",0,"8/27*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 2/9*((2*(8224*x + 20537)*x + 33443)*x + 8835)/(3*x^2 + 5*x + 2)^(3/2)","A",0
2518,1,28,0,0.218485," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(4 \, {\left(1093 \, x + 2733\right)} x + 8925\right)} x + 2371\right)}}{3 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}"," ",0,"2/3*((4*(1093*x + 2733)*x + 8925)*x + 2371)/(3*x^2 + 5*x + 2)^(3/2)","A",0
2519,1,28,0,0.240099," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(562 \, {\left(2 \, x + 5\right)} x + 2295\right)} x + 611\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}"," ",0,"2*((562*(2*x + 5)*x + 2295)*x + 611)/(3*x^2 + 5*x + 2)^(3/2)","A",0
2520,1,29,0,0.205990," ","integrate((5-x)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(12 \, {\left(2 \, x + 5\right)} x + 49\right)} x + 457\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}"," ",0,"2*(35*(12*(2*x + 5)*x + 49)*x + 457)/(3*x^2 + 5*x + 2)^(3/2)","A",0
2521,1,102,0,0.279808," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\frac{104}{125} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{2 \, {\left({\left(6 \, {\left(2508 \, x + 6283\right)} x + 30827\right)} x + 8227\right)}}{25 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}"," ",0,"104/125*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 2/25*((6*(2508*x + 6283)*x + 30827)*x + 8227)/(3*x^2 + 5*x + 2)^(3/2)","A",0
2522,1,235,0,0.392927," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","-\frac{24}{125} \, \sqrt{5} {\left(92 \, \sqrt{5} \sqrt{3} - 17 \, \log\left(-\sqrt{5} \sqrt{3} + 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right) - \frac{408 \, \sqrt{5} \log\left({\left| \sqrt{5} {\left(\sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3} + \frac{\sqrt{5}}{2 \, x + 3}\right)} - 4 \right|}\right)}{125 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{8 \, {\left(\frac{\frac{\frac{5 \, {\left(\frac{972}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)} + \frac{13}{{\left(2 \, x + 3\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{2 \, x + 3} - \frac{12324}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} + \frac{9783}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}}{2 \, x + 3} - \frac{2484}{\mathrm{sgn}\left(\frac{1}{2 \, x + 3}\right)}\right)}}{25 \, {\left(\frac{8}{2 \, x + 3} - \frac{5}{{\left(2 \, x + 3\right)}^{2}} - 3\right)} \sqrt{-\frac{8}{2 \, x + 3} + \frac{5}{{\left(2 \, x + 3\right)}^{2}} + 3}}"," ",0,"-24/125*sqrt(5)*(92*sqrt(5)*sqrt(3) - 17*log(-sqrt(5)*sqrt(3) + 4))*sgn(1/(2*x + 3)) - 408/125*sqrt(5)*log(abs(sqrt(5)*(sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3) + sqrt(5)/(2*x + 3)) - 4))/sgn(1/(2*x + 3)) + 8/25*(((5*(972/sgn(1/(2*x + 3)) + 13/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) - 12324/sgn(1/(2*x + 3)))/(2*x + 3) + 9783/sgn(1/(2*x + 3)))/(2*x + 3) - 2484/sgn(1/(2*x + 3)))/((8/(2*x + 3) - 5/(2*x + 3)^2 - 3)*sqrt(-8/(2*x + 3) + 5/(2*x + 3)^2 + 3))","B",0
2523,1,234,0,0.320680," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\frac{4884}{625} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{2 \, {\left({\left(6 \, {\left(23826 \, x + 61591\right)} x + 309599\right)} x + 84259\right)}}{625 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}} - \frac{8 \, {\left(4106 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 16447 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 57729 \, \sqrt{3} x + 20987 \, \sqrt{3} - 57729 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{625 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{2}}"," ",0,"4884/625*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 2/625*((6*(23826*x + 61591)*x + 309599)*x + 84259)/(3*x^2 + 5*x + 2)^(3/2) - 8/625*(4106*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 16447*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 57729*sqrt(3)*x + 20987*sqrt(3) - 57729*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^2","A",0
2524,1,285,0,0.335403," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\frac{46108}{3125} \, \sqrt{5} \log\left(\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}{{\left| -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}}\right) + \frac{2 \, {\left({\left(12 \, {\left(19992 \, x + 58207\right)} x + 636631\right)} x + 184301\right)}}{3125 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}} - \frac{8 \, {\left(296724 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{5} + 2103870 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{4} + 16891990 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{3} + 21246975 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 38063715 \, \sqrt{3} x + 8723544 \, \sqrt{3} - 38063715 \, \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{9375 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}^{2} + 6 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} + 11\right)}^{3}}"," ",0,"46108/3125*sqrt(5)*log(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2))) + 2/3125*((12*(19992*x + 58207)*x + 636631)*x + 184301)/(3*x^2 + 5*x + 2)^(3/2) - 8/9375*(296724*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 + 2103870*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^4 + 16891990*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 + 21246975*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 38063715*sqrt(3)*x + 8723544*sqrt(3) - 38063715*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^3","A",0
2525,1,52,0,0.181495," ","integrate((-1+x)/(1+x)/(x^2+x+1)^(1/2),x, algorithm=""giac"")","-\log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right) + 2 \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} \right|}\right) - 2 \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 2 \right|}\right)"," ",0,"-log(-2*x + 2*sqrt(x^2 + x + 1) - 1) + 2*log(abs(-x + sqrt(x^2 + x + 1))) - 2*log(abs(-x + sqrt(x^2 + x + 1) - 2))","A",0
2526,1,37,0,0.157340," ","integrate((5-x)*(3+2*x)^(7/2)*(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{1}{40} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} + \frac{47}{104} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} - \frac{109}{88} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{65}{72} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}}"," ",0,"-1/40*(2*x + 3)^(15/2) + 47/104*(2*x + 3)^(13/2) - 109/88*(2*x + 3)^(11/2) + 65/72*(2*x + 3)^(9/2)","A",0
2527,1,37,0,0.192663," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{3}{104} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} + \frac{47}{88} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} - \frac{109}{72} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{65}{56} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}}"," ",0,"-3/104*(2*x + 3)^(13/2) + 47/88*(2*x + 3)^(11/2) - 109/72*(2*x + 3)^(9/2) + 65/56*(2*x + 3)^(7/2)","A",0
2528,1,37,0,0.209488," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{3}{88} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{47}{72} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} - \frac{109}{56} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{13}{8} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}"," ",0,"-3/88*(2*x + 3)^(11/2) + 47/72*(2*x + 3)^(9/2) - 109/56*(2*x + 3)^(7/2) + 13/8*(2*x + 3)^(5/2)","A",0
2529,1,37,0,0.154134," ","integrate((5-x)*(3*x^2+5*x+2)*(3+2*x)^(1/2),x, algorithm=""giac"")","-\frac{1}{24} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{47}{56} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - \frac{109}{40} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{65}{24} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}"," ",0,"-1/24*(2*x + 3)^(9/2) + 47/56*(2*x + 3)^(7/2) - 109/40*(2*x + 3)^(5/2) + 65/24*(2*x + 3)^(3/2)","A",0
2530,1,37,0,0.158643," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(1/2),x, algorithm=""giac"")","-\frac{3}{56} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{47}{40} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} - \frac{109}{24} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{65}{8} \, \sqrt{2 \, x + 3}"," ",0,"-3/56*(2*x + 3)^(7/2) + 47/40*(2*x + 3)^(5/2) - 109/24*(2*x + 3)^(3/2) + 65/8*sqrt(2*x + 3)","A",0
2531,1,37,0,0.157791," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(3/2),x, algorithm=""giac"")","-\frac{3}{40} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{47}{24} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - \frac{109}{8} \, \sqrt{2 \, x + 3} - \frac{65}{8 \, \sqrt{2 \, x + 3}}"," ",0,"-3/40*(2*x + 3)^(5/2) + 47/24*(2*x + 3)^(3/2) - 109/8*sqrt(2*x + 3) - 65/8/sqrt(2*x + 3)","A",0
2532,1,33,0,0.199232," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(5/2),x, algorithm=""giac"")","-\frac{1}{8} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{47}{8} \, \sqrt{2 \, x + 3} + \frac{327 \, x + 458}{12 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}}"," ",0,"-1/8*(2*x + 3)^(3/2) + 47/8*sqrt(2*x + 3) + 1/12*(327*x + 458)/(2*x + 3)^(3/2)","A",0
2533,1,33,0,0.209812," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(7/2),x, algorithm=""giac"")","-\frac{3}{8} \, \sqrt{2 \, x + 3} - \frac{141 \, {\left(2 \, x + 3\right)}^{2} - 218 \, x - 288}{24 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}}"," ",0,"-3/8*sqrt(2*x + 3) - 1/24*(141*(2*x + 3)^2 - 218*x - 288)/(2*x + 3)^(5/2)","A",0
2534,1,55,0,0.165044," ","integrate((5-x)*(3+2*x)^(7/2)*(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{9}{608} \, {\left(2 \, x + 3\right)}^{\frac{19}{2}} + \frac{165}{544} \, {\left(2 \, x + 3\right)}^{\frac{17}{2}} - \frac{359}{240} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} + \frac{651}{208} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} - \frac{1065}{352} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{325}{288} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}}"," ",0,"-9/608*(2*x + 3)^(19/2) + 165/544*(2*x + 3)^(17/2) - 359/240*(2*x + 3)^(15/2) + 651/208*(2*x + 3)^(13/2) - 1065/352*(2*x + 3)^(11/2) + 325/288*(2*x + 3)^(9/2)","A",0
2535,1,55,0,0.162887," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{9}{544} \, {\left(2 \, x + 3\right)}^{\frac{17}{2}} + \frac{11}{32} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} - \frac{359}{208} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} + \frac{651}{176} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} - \frac{355}{96} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{325}{224} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}}"," ",0,"-9/544*(2*x + 3)^(17/2) + 11/32*(2*x + 3)^(15/2) - 359/208*(2*x + 3)^(13/2) + 651/176*(2*x + 3)^(11/2) - 355/96*(2*x + 3)^(9/2) + 325/224*(2*x + 3)^(7/2)","A",0
2536,1,55,0,0.176305," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{3}{160} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} + \frac{165}{416} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} - \frac{359}{176} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{217}{48} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} - \frac{1065}{224} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{65}{32} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}"," ",0,"-3/160*(2*x + 3)^(15/2) + 165/416*(2*x + 3)^(13/2) - 359/176*(2*x + 3)^(11/2) + 217/48*(2*x + 3)^(9/2) - 1065/224*(2*x + 3)^(7/2) + 65/32*(2*x + 3)^(5/2)","A",0
2537,1,55,0,0.156162," ","integrate((5-x)*(3*x^2+5*x+2)^2*(3+2*x)^(1/2),x, algorithm=""giac"")","-\frac{9}{416} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} + \frac{15}{32} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} - \frac{359}{144} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{93}{16} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - \frac{213}{32} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{325}{96} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}"," ",0,"-9/416*(2*x + 3)^(13/2) + 15/32*(2*x + 3)^(11/2) - 359/144*(2*x + 3)^(9/2) + 93/16*(2*x + 3)^(7/2) - 213/32*(2*x + 3)^(5/2) + 325/96*(2*x + 3)^(3/2)","A",0
2538,1,55,0,0.167362," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(1/2),x, algorithm=""giac"")","-\frac{9}{352} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{55}{96} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} - \frac{359}{112} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{651}{80} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} - \frac{355}{32} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{325}{32} \, \sqrt{2 \, x + 3}"," ",0,"-9/352*(2*x + 3)^(11/2) + 55/96*(2*x + 3)^(9/2) - 359/112*(2*x + 3)^(7/2) + 651/80*(2*x + 3)^(5/2) - 355/32*(2*x + 3)^(3/2) + 325/32*sqrt(2*x + 3)","A",0
2539,1,55,0,0.166584," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(3/2),x, algorithm=""giac"")","-\frac{1}{32} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{165}{224} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - \frac{359}{80} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{217}{16} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - \frac{1065}{32} \, \sqrt{2 \, x + 3} - \frac{325}{32 \, \sqrt{2 \, x + 3}}"," ",0,"-1/32*(2*x + 3)^(9/2) + 165/224*(2*x + 3)^(7/2) - 359/80*(2*x + 3)^(5/2) + 217/16*(2*x + 3)^(3/2) - 1065/32*sqrt(2*x + 3) - 325/32/sqrt(2*x + 3)","A",0
2540,1,51,0,0.175809," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(5/2),x, algorithm=""giac"")","-\frac{9}{224} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{33}{32} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} - \frac{359}{48} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{651}{16} \, \sqrt{2 \, x + 3} + \frac{5 \, {\left(639 \, x + 926\right)}}{48 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}}"," ",0,"-9/224*(2*x + 3)^(7/2) + 33/32*(2*x + 3)^(5/2) - 359/48*(2*x + 3)^(3/2) + 651/16*sqrt(2*x + 3) + 5/48*(639*x + 926)/(2*x + 3)^(3/2)","A",0
2541,1,51,0,0.170100," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(7/2),x, algorithm=""giac"")","-\frac{9}{160} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{55}{32} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - \frac{359}{16} \, \sqrt{2 \, x + 3} - \frac{651 \, {\left(2 \, x + 3\right)}^{2} - 355 \, x - 500}{16 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}}"," ",0,"-9/160*(2*x + 3)^(5/2) + 55/32*(2*x + 3)^(3/2) - 359/16*sqrt(2*x + 3) - 1/16*(651*(2*x + 3)^2 - 355*x - 500)/(2*x + 3)^(5/2)","A",0
2542,1,73,0,0.175996," ","integrate((5-x)*(3+2*x)^(7/2)*(3*x^2+5*x+2)^3,x, algorithm=""giac"")","-\frac{27}{2944} \, {\left(2 \, x + 3\right)}^{\frac{23}{2}} + \frac{27}{128} \, {\left(2 \, x + 3\right)}^{\frac{21}{2}} - \frac{3519}{2432} \, {\left(2 \, x + 3\right)}^{\frac{19}{2}} + \frac{10475}{2176} \, {\left(2 \, x + 3\right)}^{\frac{17}{2}} - \frac{17201}{1920} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} + \frac{16005}{1664} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} - \frac{7925}{1408} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{1625}{1152} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}}"," ",0,"-27/2944*(2*x + 3)^(23/2) + 27/128*(2*x + 3)^(21/2) - 3519/2432*(2*x + 3)^(19/2) + 10475/2176*(2*x + 3)^(17/2) - 17201/1920*(2*x + 3)^(15/2) + 16005/1664*(2*x + 3)^(13/2) - 7925/1408*(2*x + 3)^(11/2) + 1625/1152*(2*x + 3)^(9/2)","A",0
2543,1,73,0,0.171895," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^3,x, algorithm=""giac"")","-\frac{9}{896} \, {\left(2 \, x + 3\right)}^{\frac{21}{2}} + \frac{567}{2432} \, {\left(2 \, x + 3\right)}^{\frac{19}{2}} - \frac{207}{128} \, {\left(2 \, x + 3\right)}^{\frac{17}{2}} + \frac{2095}{384} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} - \frac{17201}{1664} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} + \frac{1455}{128} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} - \frac{7925}{1152} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{1625}{896} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}}"," ",0,"-9/896*(2*x + 3)^(21/2) + 567/2432*(2*x + 3)^(19/2) - 207/128*(2*x + 3)^(17/2) + 2095/384*(2*x + 3)^(15/2) - 17201/1664*(2*x + 3)^(13/2) + 1455/128*(2*x + 3)^(11/2) - 7925/1152*(2*x + 3)^(9/2) + 1625/896*(2*x + 3)^(7/2)","A",0
2544,1,73,0,0.171967," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^3,x, algorithm=""giac"")","-\frac{27}{2432} \, {\left(2 \, x + 3\right)}^{\frac{19}{2}} + \frac{567}{2176} \, {\left(2 \, x + 3\right)}^{\frac{17}{2}} - \frac{1173}{640} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} + \frac{10475}{1664} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} - \frac{17201}{1408} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{5335}{384} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} - \frac{7925}{896} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{325}{128} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}"," ",0,"-27/2432*(2*x + 3)^(19/2) + 567/2176*(2*x + 3)^(17/2) - 1173/640*(2*x + 3)^(15/2) + 10475/1664*(2*x + 3)^(13/2) - 17201/1408*(2*x + 3)^(11/2) + 5335/384*(2*x + 3)^(9/2) - 7925/896*(2*x + 3)^(7/2) + 325/128*(2*x + 3)^(5/2)","A",0
2545,1,73,0,0.211017," ","integrate((5-x)*(3*x^2+5*x+2)^3*(3+2*x)^(1/2),x, algorithm=""giac"")","-\frac{27}{2176} \, {\left(2 \, x + 3\right)}^{\frac{17}{2}} + \frac{189}{640} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} - \frac{3519}{1664} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} + \frac{10475}{1408} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} - \frac{17201}{1152} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{16005}{896} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - \frac{1585}{128} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{1625}{384} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}"," ",0,"-27/2176*(2*x + 3)^(17/2) + 189/640*(2*x + 3)^(15/2) - 3519/1664*(2*x + 3)^(13/2) + 10475/1408*(2*x + 3)^(11/2) - 17201/1152*(2*x + 3)^(9/2) + 16005/896*(2*x + 3)^(7/2) - 1585/128*(2*x + 3)^(5/2) + 1625/384*(2*x + 3)^(3/2)","A",0
2546,1,73,0,0.164946," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(1/2),x, algorithm=""giac"")","-\frac{9}{640} \, {\left(2 \, x + 3\right)}^{\frac{15}{2}} + \frac{567}{1664} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} - \frac{3519}{1408} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{10475}{1152} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} - \frac{17201}{896} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{3201}{128} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} - \frac{7925}{384} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{1625}{128} \, \sqrt{2 \, x + 3}"," ",0,"-9/640*(2*x + 3)^(15/2) + 567/1664*(2*x + 3)^(13/2) - 3519/1408*(2*x + 3)^(11/2) + 10475/1152*(2*x + 3)^(9/2) - 17201/896*(2*x + 3)^(7/2) + 3201/128*(2*x + 3)^(5/2) - 7925/384*(2*x + 3)^(3/2) + 1625/128*sqrt(2*x + 3)","A",0
2547,1,73,0,0.166505," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(3/2),x, algorithm=""giac"")","-\frac{27}{1664} \, {\left(2 \, x + 3\right)}^{\frac{13}{2}} + \frac{567}{1408} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} - \frac{391}{128} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{10475}{896} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - \frac{17201}{640} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{5335}{128} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - \frac{7925}{128} \, \sqrt{2 \, x + 3} - \frac{1625}{128 \, \sqrt{2 \, x + 3}}"," ",0,"-27/1664*(2*x + 3)^(13/2) + 567/1408*(2*x + 3)^(11/2) - 391/128*(2*x + 3)^(9/2) + 10475/896*(2*x + 3)^(7/2) - 17201/640*(2*x + 3)^(5/2) + 5335/128*(2*x + 3)^(3/2) - 7925/128*sqrt(2*x + 3) - 1625/128/sqrt(2*x + 3)","A",0
2548,1,69,0,0.175949," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(5/2),x, algorithm=""giac"")","-\frac{27}{1408} \, {\left(2 \, x + 3\right)}^{\frac{11}{2}} + \frac{63}{128} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} - \frac{3519}{896} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{2095}{128} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} - \frac{17201}{384} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{16005}{128} \, \sqrt{2 \, x + 3} + \frac{25 \, {\left(951 \, x + 1394\right)}}{192 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}}"," ",0,"-27/1408*(2*x + 3)^(11/2) + 63/128*(2*x + 3)^(9/2) - 3519/896*(2*x + 3)^(7/2) + 2095/128*(2*x + 3)^(5/2) - 17201/384*(2*x + 3)^(3/2) + 16005/128*sqrt(2*x + 3) + 25/192*(951*x + 1394)/(2*x + 3)^(3/2)","A",0
2549,1,69,0,0.181639," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(7/2),x, algorithm=""giac"")","-\frac{3}{128} \, {\left(2 \, x + 3\right)}^{\frac{9}{2}} + \frac{81}{128} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - \frac{3519}{640} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{10475}{384} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - \frac{17201}{128} \, \sqrt{2 \, x + 3} - \frac{5 \, {\left(9603 \, {\left(2 \, x + 3\right)}^{2} - 3170 \, x - 4560\right)}}{384 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}}"," ",0,"-3/128*(2*x + 3)^(9/2) + 81/128*(2*x + 3)^(7/2) - 3519/640*(2*x + 3)^(5/2) + 10475/384*(2*x + 3)^(3/2) - 17201/128*sqrt(2*x + 3) - 5/384*(9603*(2*x + 3)^2 - 3170*x - 4560)/(2*x + 3)^(5/2)","A",0
2550,1,101,0,0.216082," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{2}{21} \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} + \frac{62}{45} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{526}{81} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{2125}{243} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{3278}{81} \, \sqrt{2 \, x + 3} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-2/21*(2*x + 3)^(7/2) + 62/45*(2*x + 3)^(5/2) + 526/81*(2*x + 3)^(3/2) + 2125/243*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 3278/81*sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","A",0
2551,1,92,0,0.175208," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{2}{15} \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + \frac{62}{27} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{425}{81} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{526}{27} \, \sqrt{2 \, x + 3} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-2/15*(2*x + 3)^(5/2) + 62/27*(2*x + 3)^(3/2) + 425/81*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 526/27*sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","A",0
2552,1,83,0,0.179029," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2),x, algorithm=""giac"")","-\frac{2}{9} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + \frac{85}{27} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{62}{9} \, \sqrt{2 \, x + 3} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-2/9*(2*x + 3)^(3/2) + 85/27*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 62/9*sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","A",0
2553,1,74,0,0.171242," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2),x, algorithm=""giac"")","\frac{17}{9} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{2}{3} \, \sqrt{2 \, x + 3} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"17/9*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 2/3*sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","A",0
2554,1,65,0,0.166793," ","integrate((5-x)/(3*x^2+5*x+2)/(3+2*x)^(1/2),x, algorithm=""giac"")","\frac{17}{15} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"17/15*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","B",0
2555,1,74,0,0.183656," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2),x, algorithm=""giac"")","\frac{17}{25} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{26}{5 \, \sqrt{2 \, x + 3}} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"17/25*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 26/5/sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","A",0
2556,1,79,0,0.173095," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2),x, algorithm=""giac"")","\frac{51}{125} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{4 \, {\left(297 \, x + 478\right)}}{75 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"51/125*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 4/75*(297*x + 478)/(2*x + 3)^(3/2) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","A",0
2557,1,88,0,0.170412," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2),x, algorithm=""giac"")","\frac{153}{625} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{2 \, {\left(597 \, {\left(2 \, x + 3\right)}^{2} + 330 \, x + 560\right)}}{125 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"153/625*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 2/125*(597*(2*x + 3)^2 + 330*x + 560)/(2*x + 3)^(5/2) + 6*log(sqrt(2*x + 3) + 1) - 6*log(abs(sqrt(2*x + 3) - 1))","A",0
2558,1,120,0,0.184395," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{8}{27} \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - \frac{1400}{81} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{184}{27} \, \sqrt{2 \, x + 3} - \frac{2 \, {\left(2611 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 2935 \, \sqrt{2 \, x + 3}\right)}}{27 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}} - 77 \, \log\left(\sqrt{2 \, x + 3} + 1\right) + 77 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-8/27*(2*x + 3)^(3/2) - 1400/81*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 184/27*sqrt(2*x + 3) - 2/27*(2611*(2*x + 3)^(3/2) - 2935*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19) - 77*log(sqrt(2*x + 3) + 1) + 77*log(abs(sqrt(2*x + 3) - 1))","A",0
2559,1,111,0,0.304697," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{50}{3} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{8}{9} \, \sqrt{2 \, x + 3} - \frac{2 \, {\left(587 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 695 \, \sqrt{2 \, x + 3}\right)}}{9 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}} - 65 \, \log\left(\sqrt{2 \, x + 3} + 1\right) + 65 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-50/3*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 8/9*sqrt(2*x + 3) - 2/9*(587*(2*x + 3)^(3/2) - 695*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19) - 65*log(sqrt(2*x + 3) + 1) + 65*log(abs(sqrt(2*x + 3) - 1))","A",0
2560,1,102,0,0.175120," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{124}{9} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{2 \, {\left(139 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 175 \, \sqrt{2 \, x + 3}\right)}}{3 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}} - 53 \, \log\left(\sqrt{2 \, x + 3} + 1\right) + 53 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-124/9*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 2/3*(139*(2*x + 3)^(3/2) - 175*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19) - 53*log(sqrt(2*x + 3) + 1) + 53*log(abs(sqrt(2*x + 3) - 1))","A",0
2561,1,102,0,0.175131," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{158}{15} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{2 \, {\left(35 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 47 \, \sqrt{2 \, x + 3}\right)}}{3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19} - 41 \, \log\left(\sqrt{2 \, x + 3} + 1\right) + 41 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-158/15*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 2*(35*(2*x + 3)^(3/2) - 47*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19) - 41*log(sqrt(2*x + 3) + 1) + 41*log(abs(sqrt(2*x + 3) - 1))","A",0
2562,1,102,0,0.173894," ","integrate((5-x)/(3*x^2+5*x+2)^2/(3+2*x)^(1/2),x, algorithm=""giac"")","-\frac{192}{25} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{6 \, {\left(47 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 67 \, \sqrt{2 \, x + 3}\right)}}{5 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}} - 29 \, \log\left(\sqrt{2 \, x + 3} + 1\right) + 29 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-192/25*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 6/5*(47*(2*x + 3)^(3/2) - 67*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19) - 29*log(sqrt(2*x + 3) + 1) + 29*log(abs(sqrt(2*x + 3) - 1))","A",0
2563,1,111,0,0.174524," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{678}{125} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{2 \, {\left(759 \, {\left(2 \, x + 3\right)}^{2} - 2638 \, x - 3697\right)}}{25 \, {\left(3 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} - 8 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} + 5 \, \sqrt{2 \, x + 3}\right)}} - 17 \, \log\left(\sqrt{2 \, x + 3} + 1\right) + 17 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-678/125*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 2/25*(759*(2*x + 3)^2 - 2638*x - 3697)/(3*(2*x + 3)^(5/2) - 8*(2*x + 3)^(3/2) + 5*sqrt(2*x + 3)) - 17*log(sqrt(2*x + 3) + 1) + 17*log(abs(sqrt(2*x + 3) - 1))","A",0
2564,1,116,0,0.178308," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{468}{125} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{6 \, {\left(903 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 1403 \, \sqrt{2 \, x + 3}\right)}}{125 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}} - \frac{16 \, {\left(609 \, x + 946\right)}}{375 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}} - 5 \, \log\left(\sqrt{2 \, x + 3} + 1\right) + 5 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-468/125*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 6/125*(903*(2*x + 3)^(3/2) - 1403*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19) - 16/375*(609*x + 946)/(2*x + 3)^(3/2) - 5*log(sqrt(2*x + 3) + 1) + 5*log(abs(sqrt(2*x + 3) - 1))","A",0
2565,1,125,0,0.197225," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^2,x, algorithm=""giac"")","-\frac{7938}{3125} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{6 \, {\left(4209 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 6709 \, \sqrt{2 \, x + 3}\right)}}{625 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}} - \frac{16 \, {\left(3039 \, {\left(2 \, x + 3\right)}^{2} + 1015 \, x + 1620\right)}}{1875 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}} + 7 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 7 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"-7938/3125*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 6/625*(4209*(2*x + 3)^(3/2) - 6709*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19) - 16/1875*(3039*(2*x + 3)^2 + 1015*x + 1620)/(2*x + 3)^(5/2) + 7*log(sqrt(2*x + 3) + 1) - 7*log(abs(sqrt(2*x + 3) - 1))","A",0
2566,1,129,0,0.199755," ","integrate((5-x)*(3+2*x)^(9/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{13675}{54} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{32}{27} \, \sqrt{2 \, x + 3} + \frac{137169 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 554983 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 717035 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 297925 \, \sqrt{2 \, x + 3}}{27 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 981 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 981 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"13675/54*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 32/27*sqrt(2*x + 3) + 1/27*(137169*(2*x + 3)^(7/2) - 554983*(2*x + 3)^(5/2) + 717035*(2*x + 3)^(3/2) - 297925*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 981*log(sqrt(2*x + 3) + 1) - 981*log(abs(sqrt(2*x + 3) - 1))","A",0
2567,1,120,0,0.186258," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{1225}{6} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{12443 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 50029 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 64505 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 26775 \, \sqrt{2 \, x + 3}}{3 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 791 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 791 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"1225/6*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 1/3*(12443*(2*x + 3)^(7/2) - 50029*(2*x + 3)^(5/2) + 64505*(2*x + 3)^(3/2) - 26775*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 791*log(sqrt(2*x + 3) + 1) - 791*log(abs(sqrt(2*x + 3) - 1))","A",0
2568,1,120,0,0.191020," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{2905}{18} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{9825 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 39431 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 50875 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 21125 \, \sqrt{2 \, x + 3}}{3 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 625 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 625 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"2905/18*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 1/3*(9825*(2*x + 3)^(7/2) - 39431*(2*x + 3)^(5/2) + 50875*(2*x + 3)^(3/2) - 21125*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 625*log(sqrt(2*x + 3) + 1) - 625*log(abs(sqrt(2*x + 3) - 1))","A",0
2569,1,119,0,0.182407," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{1247}{10} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{2529 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 10151 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 13115 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 5445 \, \sqrt{2 \, x + 3}}{{\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 483 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 483 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"1247/10*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + (2529*(2*x + 3)^(7/2) - 10151*(2*x + 3)^(5/2) + 13115*(2*x + 3)^(3/2) - 5445*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 483*log(sqrt(2*x + 3) + 1) - 483*log(abs(sqrt(2*x + 3) - 1))","A",0
2570,1,120,0,0.190726," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{4713}{50} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{9567 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 38409 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 49637 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 20555 \, \sqrt{2 \, x + 3}}{5 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 365 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 365 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"4713/50*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 1/5*(9567*(2*x + 3)^(7/2) - 38409*(2*x + 3)^(5/2) + 49637*(2*x + 3)^(3/2) - 20555*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 365*log(sqrt(2*x + 3) + 1) - 365*log(abs(sqrt(2*x + 3) - 1))","A",0
2571,1,120,0,0.176099," ","integrate((5-x)/(3*x^2+5*x+2)^3/(3+2*x)^(1/2),x, algorithm=""giac"")","\frac{17463}{250} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{35217 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 141159 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 181867 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 74725 \, \sqrt{2 \, x + 3}}{25 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 271 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 271 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"17463/250*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 1/25*(35217*(2*x + 3)^(7/2) - 141159*(2*x + 3)^(5/2) + 181867*(2*x + 3)^(3/2) - 74725*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 271*log(sqrt(2*x + 3) + 1) - 271*log(abs(sqrt(2*x + 3) - 1))","A",0
2572,1,129,0,0.183971," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{12717}{250} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{416}{125 \, \sqrt{2 \, x + 3}} + \frac{123759 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 492873 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 628469 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 253355 \, \sqrt{2 \, x + 3}}{125 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 201 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 201 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"12717/250*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 416/125/sqrt(2*x + 3) + 1/125*(123759*(2*x + 3)^(7/2) - 492873*(2*x + 3)^(5/2) + 628469*(2*x + 3)^(3/2) - 253355*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 201*log(sqrt(2*x + 3) + 1) - 201*log(abs(sqrt(2*x + 3) - 1))","A",0
2573,1,134,0,0.182335," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{45603}{1250} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) - \frac{64 \, {\left(921 \, x + 1414\right)}}{1875 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}}} + \frac{396801 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 1551207 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 1922011 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 737605 \, \sqrt{2 \, x + 3}}{625 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} + 155 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 155 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"45603/1250*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) - 64/1875*(921*x + 1414)/(2*x + 3)^(3/2) + 1/625*(396801*(2*x + 3)^(7/2) - 1551207*(2*x + 3)^(5/2) + 1922011*(2*x + 3)^(3/2) - 737605*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 + 155*log(sqrt(2*x + 3) + 1) - 155*log(abs(sqrt(2*x + 3) - 1))","A",0
2574,1,143,0,0.189513," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^3,x, algorithm=""giac"")","\frac{806841}{31250} \, \sqrt{15} \log\left(\frac{{\left| -2 \, \sqrt{15} + 6 \, \sqrt{2 \, x + 3} \right|}}{2 \, {\left(\sqrt{15} + 3 \, \sqrt{2 \, x + 3}\right)}}\right) + \frac{202995 \, {\left(2 \, x + 3\right)}^{\frac{7}{2}} - 745077 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}} + 831169 \, {\left(2 \, x + 3\right)}^{\frac{3}{2}} - 259087 \, \sqrt{2 \, x + 3}}{625 \, {\left(3 \, {\left(2 \, x + 3\right)}^{2} - 16 \, x - 19\right)}^{2}} - \frac{32 \, {\left(12861 \, {\left(2 \, x + 3\right)}^{2} + 3070 \, x + 4800\right)}}{9375 \, {\left(2 \, x + 3\right)}^{\frac{5}{2}}} + 133 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 133 \, \log\left({\left| \sqrt{2 \, x + 3} - 1 \right|}\right)"," ",0,"806841/31250*sqrt(15)*log(1/2*abs(-2*sqrt(15) + 6*sqrt(2*x + 3))/(sqrt(15) + 3*sqrt(2*x + 3))) + 1/625*(202995*(2*x + 3)^(7/2) - 745077*(2*x + 3)^(5/2) + 831169*(2*x + 3)^(3/2) - 259087*sqrt(2*x + 3))/(3*(2*x + 3)^2 - 16*x - 19)^2 - 32/9375*(12861*(2*x + 3)^2 + 3070*x + 4800)/(2*x + 3)^(5/2) + 133*log(sqrt(2*x + 3) + 1) - 133*log(abs(sqrt(2*x + 3) - 1))","A",0
2575,1,313,0,1.012003," ","integrate((5+10*x+35^(1/2))/(5*x^2+3*x+2)/(1+2*x)^(1/2),x, algorithm=""giac"")","\frac{1}{7443100} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 980 \, \sqrt{35} \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 1960 \, \sqrt{35} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{7443100} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 980 \, \sqrt{35} \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 1960 \, \sqrt{35} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right)"," ",0,"1/7443100*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 980*sqrt(35)*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 1960*sqrt(35)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/7443100*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 980*sqrt(35)*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 1960*sqrt(35)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2))","B",0
2576,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x + 3\right)}^{\frac{5}{2}} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(2*x + 3)^(5/2)*(x - 5), x)","F",0
2577,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x + 3\right)}^{\frac{3}{2}} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(2*x + 3)^(3/2)*(x - 5), x)","F",0
2578,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(1/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5), x)","F",0
2579,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(1/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(x - 5\right)}}{\sqrt{2 \, x + 3}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(x - 5)/sqrt(2*x + 3), x)","F",0
2580,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(3/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(x - 5)/(2*x + 3)^(3/2), x)","F",0
2581,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(5/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(x - 5)/(2*x + 3)^(5/2), x)","F",0
2582,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(7/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(x - 5)/(2*x + 3)^(7/2), x)","F",0
2583,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(9/2),x, algorithm=""giac"")","\int -\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(-sqrt(3*x^2 + 5*x + 2)*(x - 5)/(2*x + 3)^(9/2), x)","F",0
2584,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(2 \, x + 3\right)}^{\frac{5}{2}} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(2*x + 3)^(5/2)*(x - 5), x)","F",0
2585,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(2 \, x + 3\right)}^{\frac{3}{2}} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(2*x + 3)^(3/2)*(x - 5), x)","F",0
2586,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)*(3+2*x)^(1/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} \sqrt{2 \, x + 3} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*sqrt(2*x + 3)*(x - 5), x)","F",0
2587,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{\sqrt{2 \, x + 3}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/sqrt(2*x + 3), x)","F",0
2588,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^(3/2), x)","F",0
2589,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^(5/2), x)","F",0
2590,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(7/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^(7/2), x)","F",0
2591,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(9/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^(9/2), x)","F",0
2592,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(11/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^(11/2), x)","F",0
2593,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(13/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^(13/2), x)","F",0
2594,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(2 \, x + 3\right)}^{\frac{5}{2}} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(2*x + 3)^(5/2)*(x - 5), x)","F",0
2595,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(2 \, x + 3\right)}^{\frac{3}{2}} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(2*x + 3)^(3/2)*(x - 5), x)","F",0
2596,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)*(3+2*x)^(1/2),x, algorithm=""giac"")","\int -{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} \sqrt{2 \, x + 3} {\left(x - 5\right)}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*sqrt(2*x + 3)*(x - 5), x)","F",0
2597,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{\sqrt{2 \, x + 3}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/sqrt(2*x + 3), x)","F",0
2598,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(3/2), x)","F",0
2599,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(5/2), x)","F",0
2600,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(7/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(7/2), x)","F",0
2601,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(9/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(9/2), x)","F",0
2602,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(11/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(11/2), x)","F",0
2603,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(13/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(13/2), x)","F",0
2604,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(15/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{15}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(15/2), x)","F",0
2605,0,0,0,0.000000," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(17/2),x, algorithm=""giac"")","\int -\frac{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(2 \, x + 3\right)}^{\frac{17}{2}}}\,{d x}"," ",0,"integrate(-(3*x^2 + 5*x + 2)^(5/2)*(x - 5)/(2*x + 3)^(17/2), x)","F",0
2606,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(5/2)*(x - 5)/sqrt(3*x^2 + 5*x + 2), x)","F",0
2607,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(3/2)*(x - 5)/sqrt(3*x^2 + 5*x + 2), x)","F",0
2608,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{\sqrt{2 \, x + 3} {\left(x - 5\right)}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(-sqrt(2*x + 3)*(x - 5)/sqrt(3*x^2 + 5*x + 2), x)","F",0
2609,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 5}{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}\,{d x}"," ",0,"integrate(-(x - 5)/(sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)), x)","F",0
2610,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 5}{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/(sqrt(3*x^2 + 5*x + 2)*(2*x + 3)^(3/2)), x)","F",0
2611,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 5}{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x + 3\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/(sqrt(3*x^2 + 5*x + 2)*(2*x + 3)^(5/2)), x)","F",0
2612,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 5}{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x + 3\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/(sqrt(3*x^2 + 5*x + 2)*(2*x + 3)^(7/2)), x)","F",0
2613,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{7}{2}} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(7/2)*(x - 5)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
2614,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(5/2)*(x - 5)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
2615,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(3/2)*(x - 5)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
2616,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{\sqrt{2 \, x + 3} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-sqrt(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^(3/2), x)","F",0
2617,0,0,0,0.000000," ","integrate((5-x)/(3*x^2+5*x+2)^(3/2)/(3+2*x)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} \sqrt{2 \, x + 3}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(3/2)*sqrt(2*x + 3)), x)","F",0
2618,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(3/2)*(2*x + 3)^(3/2)), x)","F",0
2619,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(2 \, x + 3\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(3/2)*(2*x + 3)^(5/2)), x)","F",0
2620,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{3}{2}} {\left(2 \, x + 3\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(3/2)*(2*x + 3)^(7/2)), x)","F",0
2621,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(9/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{9}{2}} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(9/2)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
2622,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{7}{2}} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(7/2)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
2623,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{5}{2}} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(5/2)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
2624,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x + 3\right)}^{\frac{3}{2}} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(2*x + 3)^(3/2)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
2625,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{\sqrt{2 \, x + 3} {\left(x - 5\right)}}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-sqrt(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2), x)","F",0
2626,0,0,0,0.000000," ","integrate((5-x)/(3*x^2+5*x+2)^(5/2)/(3+2*x)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} \sqrt{2 \, x + 3}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(5/2)*sqrt(2*x + 3)), x)","F",0
2627,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(5/2)*(2*x + 3)^(3/2)), x)","F",0
2628,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(2 \, x + 3\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(5/2)*(2*x + 3)^(5/2)), x)","F",0
2629,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""giac"")","\int -\frac{x - 5}{{\left(3 \, x^{2} + 5 \, x + 2\right)}^{\frac{5}{2}} {\left(2 \, x + 3\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(x - 5)/((3*x^2 + 5*x + 2)^(5/2)*(2*x + 3)^(7/2)), x)","F",0
2630,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
2631,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
2632,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)), x)","F",0
2633,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2)), x)","F",0
2634,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(5/2)), x)","F",0
2635,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(5/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
2636,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(3/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
2637,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} \sqrt{e x + d}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x + A)*sqrt(e*x + d)/(c*x^2 + b*x + a)^(3/2), x)","F",0
2638,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x + A}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((B*x + A)/((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d)), x)","F",0
2639,-2,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 7.46Unable to transpose Error: Bad Argument Value","F(-2)",0
2640,1,14376,0,0.820508," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c^{3} m^{7} x^{8} e^{8} + {\left(x e + d\right)}^{m} B c^{3} d m^{7} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} B b c^{2} m^{7} x^{7} e^{8} + {\left(x e + d\right)}^{m} A c^{3} m^{7} x^{7} e^{8} + 28 \, {\left(x e + d\right)}^{m} B c^{3} m^{6} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{7} x^{6} e^{7} + {\left(x e + d\right)}^{m} A c^{3} d m^{7} x^{6} e^{7} + 21 \, {\left(x e + d\right)}^{m} B c^{3} d m^{6} x^{7} e^{7} - 7 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{6} x^{6} e^{6} + 3 \, {\left(x e + d\right)}^{m} B b^{2} c m^{7} x^{6} e^{8} + 3 \, {\left(x e + d\right)}^{m} B a c^{2} m^{7} x^{6} e^{8} + 3 \, {\left(x e + d\right)}^{m} A b c^{2} m^{7} x^{6} e^{8} + 87 \, {\left(x e + d\right)}^{m} B b c^{2} m^{6} x^{7} e^{8} + 29 \, {\left(x e + d\right)}^{m} A c^{3} m^{6} x^{7} e^{8} + 322 \, {\left(x e + d\right)}^{m} B c^{3} m^{5} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{7} x^{5} e^{7} + 3 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{7} x^{5} e^{7} + 3 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{7} x^{5} e^{7} + 69 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{6} x^{6} e^{7} + 23 \, {\left(x e + d\right)}^{m} A c^{3} d m^{6} x^{6} e^{7} + 175 \, {\left(x e + d\right)}^{m} B c^{3} d m^{5} x^{7} e^{7} - 18 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{6} x^{5} e^{6} - 6 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{6} x^{5} e^{6} - 105 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{5} x^{6} e^{6} + 42 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{5} x^{5} e^{5} + {\left(x e + d\right)}^{m} B b^{3} m^{7} x^{5} e^{8} + 6 \, {\left(x e + d\right)}^{m} B a b c m^{7} x^{5} e^{8} + 3 \, {\left(x e + d\right)}^{m} A b^{2} c m^{7} x^{5} e^{8} + 3 \, {\left(x e + d\right)}^{m} A a c^{2} m^{7} x^{5} e^{8} + 90 \, {\left(x e + d\right)}^{m} B b^{2} c m^{6} x^{6} e^{8} + 90 \, {\left(x e + d\right)}^{m} B a c^{2} m^{6} x^{6} e^{8} + 90 \, {\left(x e + d\right)}^{m} A b c^{2} m^{6} x^{6} e^{8} + 1029 \, {\left(x e + d\right)}^{m} B b c^{2} m^{5} x^{7} e^{8} + 343 \, {\left(x e + d\right)}^{m} A c^{3} m^{5} x^{7} e^{8} + 1960 \, {\left(x e + d\right)}^{m} B c^{3} m^{4} x^{8} e^{8} + {\left(x e + d\right)}^{m} B b^{3} d m^{7} x^{4} e^{7} + 6 \, {\left(x e + d\right)}^{m} B a b c d m^{7} x^{4} e^{7} + 3 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{7} x^{4} e^{7} + 3 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{7} x^{4} e^{7} + 75 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{6} x^{5} e^{7} + 75 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{6} x^{5} e^{7} + 75 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{6} x^{5} e^{7} + 615 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{5} x^{6} e^{7} + 205 \, {\left(x e + d\right)}^{m} A c^{3} d m^{5} x^{6} e^{7} + 735 \, {\left(x e + d\right)}^{m} B c^{3} d m^{4} x^{7} e^{7} - 15 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{6} x^{4} e^{6} - 15 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{6} x^{4} e^{6} - 15 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{6} x^{4} e^{6} - 324 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{5} x^{5} e^{6} - 108 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{5} x^{5} e^{6} - 595 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{4} x^{6} e^{6} + 90 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{5} x^{4} e^{5} + 30 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{5} x^{4} e^{5} + 420 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{4} x^{5} e^{5} - 210 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{4} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} B a b^{2} m^{7} x^{4} e^{8} + {\left(x e + d\right)}^{m} A b^{3} m^{7} x^{4} e^{8} + 3 \, {\left(x e + d\right)}^{m} B a^{2} c m^{7} x^{4} e^{8} + 6 \, {\left(x e + d\right)}^{m} A a b c m^{7} x^{4} e^{8} + 31 \, {\left(x e + d\right)}^{m} B b^{3} m^{6} x^{5} e^{8} + 186 \, {\left(x e + d\right)}^{m} B a b c m^{6} x^{5} e^{8} + 93 \, {\left(x e + d\right)}^{m} A b^{2} c m^{6} x^{5} e^{8} + 93 \, {\left(x e + d\right)}^{m} A a c^{2} m^{6} x^{5} e^{8} + 1098 \, {\left(x e + d\right)}^{m} B b^{2} c m^{5} x^{6} e^{8} + 1098 \, {\left(x e + d\right)}^{m} B a c^{2} m^{5} x^{6} e^{8} + 1098 \, {\left(x e + d\right)}^{m} A b c^{2} m^{5} x^{6} e^{8} + 6405 \, {\left(x e + d\right)}^{m} B b c^{2} m^{4} x^{7} e^{8} + 2135 \, {\left(x e + d\right)}^{m} A c^{3} m^{4} x^{7} e^{8} + 6769 \, {\left(x e + d\right)}^{m} B c^{3} m^{3} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{7} x^{3} e^{7} + {\left(x e + d\right)}^{m} A b^{3} d m^{7} x^{3} e^{7} + 3 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{7} x^{3} e^{7} + 6 \, {\left(x e + d\right)}^{m} A a b c d m^{7} x^{3} e^{7} + 27 \, {\left(x e + d\right)}^{m} B b^{3} d m^{6} x^{4} e^{7} + 162 \, {\left(x e + d\right)}^{m} B a b c d m^{6} x^{4} e^{7} + 81 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{6} x^{4} e^{7} + 81 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{6} x^{4} e^{7} + 723 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{5} x^{5} e^{7} + 723 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{5} x^{5} e^{7} + 723 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{5} x^{5} e^{7} + 2715 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{4} x^{6} e^{7} + 905 \, {\left(x e + d\right)}^{m} A c^{3} d m^{4} x^{6} e^{7} + 1624 \, {\left(x e + d\right)}^{m} B c^{3} d m^{3} x^{7} e^{7} - 4 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{6} x^{3} e^{6} - 24 \, {\left(x e + d\right)}^{m} B a b c d^{2} m^{6} x^{3} e^{6} - 12 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{6} x^{3} e^{6} - 12 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{6} x^{3} e^{6} - 315 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{5} x^{4} e^{6} - 315 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{5} x^{4} e^{6} - 315 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{5} x^{4} e^{6} - 2070 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{4} x^{5} e^{6} - 690 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{4} x^{5} e^{6} - 1575 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{3} x^{6} e^{6} + 60 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{5} x^{3} e^{5} + 60 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{5} x^{3} e^{5} + 60 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{5} x^{3} e^{5} + 1260 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{4} x^{4} e^{5} + 420 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{4} x^{4} e^{5} + 1470 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{3} x^{5} e^{5} - 360 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m^{4} x^{3} e^{4} - 120 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{4} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{3} x^{4} e^{4} + 840 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m^{3} x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} B a^{2} b m^{7} x^{3} e^{8} + 3 \, {\left(x e + d\right)}^{m} A a b^{2} m^{7} x^{3} e^{8} + 3 \, {\left(x e + d\right)}^{m} A a^{2} c m^{7} x^{3} e^{8} + 96 \, {\left(x e + d\right)}^{m} B a b^{2} m^{6} x^{4} e^{8} + 32 \, {\left(x e + d\right)}^{m} A b^{3} m^{6} x^{4} e^{8} + 96 \, {\left(x e + d\right)}^{m} B a^{2} c m^{6} x^{4} e^{8} + 192 \, {\left(x e + d\right)}^{m} A a b c m^{6} x^{4} e^{8} + 391 \, {\left(x e + d\right)}^{m} B b^{3} m^{5} x^{5} e^{8} + 2346 \, {\left(x e + d\right)}^{m} B a b c m^{5} x^{5} e^{8} + 1173 \, {\left(x e + d\right)}^{m} A b^{2} c m^{5} x^{5} e^{8} + 1173 \, {\left(x e + d\right)}^{m} A a c^{2} m^{5} x^{5} e^{8} + 7020 \, {\left(x e + d\right)}^{m} B b^{2} c m^{4} x^{6} e^{8} + 7020 \, {\left(x e + d\right)}^{m} B a c^{2} m^{4} x^{6} e^{8} + 7020 \, {\left(x e + d\right)}^{m} A b c^{2} m^{4} x^{6} e^{8} + 22512 \, {\left(x e + d\right)}^{m} B b c^{2} m^{3} x^{7} e^{8} + 7504 \, {\left(x e + d\right)}^{m} A c^{3} m^{3} x^{7} e^{8} + 13132 \, {\left(x e + d\right)}^{m} B c^{3} m^{2} x^{8} e^{8} + 3 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{7} x^{2} e^{7} + 3 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{7} x^{2} e^{7} + 3 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{7} x^{2} e^{7} + 87 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{6} x^{3} e^{7} + 29 \, {\left(x e + d\right)}^{m} A b^{3} d m^{6} x^{3} e^{7} + 87 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{6} x^{3} e^{7} + 174 \, {\left(x e + d\right)}^{m} A a b c d m^{6} x^{3} e^{7} + 283 \, {\left(x e + d\right)}^{m} B b^{3} d m^{5} x^{4} e^{7} + 1698 \, {\left(x e + d\right)}^{m} B a b c d m^{5} x^{4} e^{7} + 849 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{5} x^{4} e^{7} + 849 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{5} x^{4} e^{7} + 3405 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{4} x^{5} e^{7} + 3405 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{4} x^{5} e^{7} + 3405 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{4} x^{5} e^{7} + 6222 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{3} x^{6} e^{7} + 2074 \, {\left(x e + d\right)}^{m} A c^{3} d m^{3} x^{6} e^{7} + 1764 \, {\left(x e + d\right)}^{m} B c^{3} d m^{2} x^{7} e^{7} - 9 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m^{6} x^{2} e^{6} - 3 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{6} x^{2} e^{6} - 9 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{6} x^{2} e^{6} - 18 \, {\left(x e + d\right)}^{m} A a b c d^{2} m^{6} x^{2} e^{6} - 96 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{5} x^{3} e^{6} - 576 \, {\left(x e + d\right)}^{m} B a b c d^{2} m^{5} x^{3} e^{6} - 288 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{5} x^{3} e^{6} - 288 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{5} x^{3} e^{6} - 2355 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{4} x^{4} e^{6} - 2355 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{4} x^{4} e^{6} - 2355 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{4} x^{4} e^{6} - 5940 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{3} x^{5} e^{6} - 1980 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{3} x^{5} e^{6} - 1918 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m^{2} x^{6} e^{6} + 12 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{5} x^{2} e^{5} + 72 \, {\left(x e + d\right)}^{m} B a b c d^{3} m^{5} x^{2} e^{5} + 36 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{5} x^{2} e^{5} + 36 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{5} x^{2} e^{5} + 1080 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{4} x^{3} e^{5} + 1080 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{4} x^{3} e^{5} + 1080 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{4} x^{3} e^{5} + 5310 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{3} x^{4} e^{5} + 1770 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{3} x^{4} e^{5} + 2100 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m^{2} x^{5} e^{5} - 180 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m^{4} x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m^{4} x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m^{4} x^{2} e^{4} - 3960 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m^{3} x^{3} e^{4} - 1320 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{3} x^{3} e^{4} - 2310 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m^{2} x^{4} e^{4} + 1080 \, {\left(x e + d\right)}^{m} B b c^{2} d^{5} m^{3} x^{2} e^{3} + 360 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m^{3} x^{2} e^{3} + 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m^{2} x^{3} e^{3} - 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{6} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a^{3} m^{7} x^{2} e^{8} + 3 \, {\left(x e + d\right)}^{m} A a^{2} b m^{7} x^{2} e^{8} + 99 \, {\left(x e + d\right)}^{m} B a^{2} b m^{6} x^{3} e^{8} + 99 \, {\left(x e + d\right)}^{m} A a b^{2} m^{6} x^{3} e^{8} + 99 \, {\left(x e + d\right)}^{m} A a^{2} c m^{6} x^{3} e^{8} + 1254 \, {\left(x e + d\right)}^{m} B a b^{2} m^{5} x^{4} e^{8} + 418 \, {\left(x e + d\right)}^{m} A b^{3} m^{5} x^{4} e^{8} + 1254 \, {\left(x e + d\right)}^{m} B a^{2} c m^{5} x^{4} e^{8} + 2508 \, {\left(x e + d\right)}^{m} A a b c m^{5} x^{4} e^{8} + 2581 \, {\left(x e + d\right)}^{m} B b^{3} m^{4} x^{5} e^{8} + 15486 \, {\left(x e + d\right)}^{m} B a b c m^{4} x^{5} e^{8} + 7743 \, {\left(x e + d\right)}^{m} A b^{2} c m^{4} x^{5} e^{8} + 7743 \, {\left(x e + d\right)}^{m} A a c^{2} m^{4} x^{5} e^{8} + 25227 \, {\left(x e + d\right)}^{m} B b^{2} c m^{3} x^{6} e^{8} + 25227 \, {\left(x e + d\right)}^{m} B a c^{2} m^{3} x^{6} e^{8} + 25227 \, {\left(x e + d\right)}^{m} A b c^{2} m^{3} x^{6} e^{8} + 44268 \, {\left(x e + d\right)}^{m} B b c^{2} m^{2} x^{7} e^{8} + 14756 \, {\left(x e + d\right)}^{m} A c^{3} m^{2} x^{7} e^{8} + 13068 \, {\left(x e + d\right)}^{m} B c^{3} m x^{8} e^{8} + {\left(x e + d\right)}^{m} B a^{3} d m^{7} x e^{7} + 3 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{7} x e^{7} + 93 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{6} x^{2} e^{7} + 93 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{6} x^{2} e^{7} + 93 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{6} x^{2} e^{7} + 993 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{5} x^{3} e^{7} + 331 \, {\left(x e + d\right)}^{m} A b^{3} d m^{5} x^{3} e^{7} + 993 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{5} x^{3} e^{7} + 1986 \, {\left(x e + d\right)}^{m} A a b c d m^{5} x^{3} e^{7} + 1449 \, {\left(x e + d\right)}^{m} B b^{3} d m^{4} x^{4} e^{7} + 8694 \, {\left(x e + d\right)}^{m} B a b c d m^{4} x^{4} e^{7} + 4347 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{4} x^{4} e^{7} + 4347 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{4} x^{4} e^{7} + 8202 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{3} x^{5} e^{7} + 8202 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{3} x^{5} e^{7} + 8202 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{3} x^{5} e^{7} + 6936 \, {\left(x e + d\right)}^{m} B b c^{2} d m^{2} x^{6} e^{7} + 2312 \, {\left(x e + d\right)}^{m} A c^{3} d m^{2} x^{6} e^{7} + 720 \, {\left(x e + d\right)}^{m} B c^{3} d m x^{7} e^{7} - 6 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m^{6} x e^{6} - 6 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m^{6} x e^{6} - 6 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{6} x e^{6} - 243 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m^{5} x^{2} e^{6} - 81 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{5} x^{2} e^{6} - 243 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{5} x^{2} e^{6} - 486 \, {\left(x e + d\right)}^{m} A a b c d^{2} m^{5} x^{2} e^{6} - 844 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{4} x^{3} e^{6} - 5064 \, {\left(x e + d\right)}^{m} B a b c d^{2} m^{4} x^{3} e^{6} - 2532 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{4} x^{3} e^{6} - 2532 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{4} x^{3} e^{6} - 7605 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{3} x^{4} e^{6} - 7605 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{3} x^{4} e^{6} - 7605 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{3} x^{4} e^{6} - 7632 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m^{2} x^{5} e^{6} - 2544 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m^{2} x^{5} e^{6} - 840 \, {\left(x e + d\right)}^{m} B c^{3} d^{2} m x^{6} e^{6} + 18 \, {\left(x e + d\right)}^{m} B a b^{2} d^{3} m^{5} x e^{5} + 6 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{5} x e^{5} + 18 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{5} x e^{5} + 36 \, {\left(x e + d\right)}^{m} A a b c d^{3} m^{5} x e^{5} + 264 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{4} x^{2} e^{5} + 1584 \, {\left(x e + d\right)}^{m} B a b c d^{3} m^{4} x^{2} e^{5} + 792 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{4} x^{2} e^{5} + 792 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{4} x^{2} e^{5} + 6180 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{3} x^{3} e^{5} + 6180 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{3} x^{3} e^{5} + 6180 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{3} x^{3} e^{5} + 8460 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m^{2} x^{4} e^{5} + 2820 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m^{2} x^{4} e^{5} + 1008 \, {\left(x e + d\right)}^{m} B c^{3} d^{3} m x^{5} e^{5} - 24 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m^{4} x e^{4} - 144 \, {\left(x e + d\right)}^{m} B a b c d^{4} m^{4} x e^{4} - 72 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m^{4} x e^{4} - 72 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m^{4} x e^{4} - 2880 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m^{3} x^{2} e^{4} - 2880 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m^{3} x^{2} e^{4} - 2880 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m^{3} x^{2} e^{4} - 9360 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m^{2} x^{3} e^{4} - 3120 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m^{2} x^{3} e^{4} - 1260 \, {\left(x e + d\right)}^{m} B c^{3} d^{4} m x^{4} e^{4} + 360 \, {\left(x e + d\right)}^{m} B b^{2} c d^{5} m^{3} x e^{3} + 360 \, {\left(x e + d\right)}^{m} B a c^{2} d^{5} m^{3} x e^{3} + 360 \, {\left(x e + d\right)}^{m} A b c^{2} d^{5} m^{3} x e^{3} + 9720 \, {\left(x e + d\right)}^{m} B b c^{2} d^{5} m^{2} x^{2} e^{3} + 3240 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m^{2} x^{2} e^{3} + 1680 \, {\left(x e + d\right)}^{m} B c^{3} d^{5} m x^{3} e^{3} - 2160 \, {\left(x e + d\right)}^{m} B b c^{2} d^{6} m^{2} x e^{2} - 720 \, {\left(x e + d\right)}^{m} A c^{3} d^{6} m^{2} x e^{2} - 2520 \, {\left(x e + d\right)}^{m} B c^{3} d^{6} m x^{2} e^{2} + 5040 \, {\left(x e + d\right)}^{m} B c^{3} d^{7} m x e + {\left(x e + d\right)}^{m} A a^{3} m^{7} x e^{8} + 34 \, {\left(x e + d\right)}^{m} B a^{3} m^{6} x^{2} e^{8} + 102 \, {\left(x e + d\right)}^{m} A a^{2} b m^{6} x^{2} e^{8} + 1341 \, {\left(x e + d\right)}^{m} B a^{2} b m^{5} x^{3} e^{8} + 1341 \, {\left(x e + d\right)}^{m} A a b^{2} m^{5} x^{3} e^{8} + 1341 \, {\left(x e + d\right)}^{m} A a^{2} c m^{5} x^{3} e^{8} + 8592 \, {\left(x e + d\right)}^{m} B a b^{2} m^{4} x^{4} e^{8} + 2864 \, {\left(x e + d\right)}^{m} A b^{3} m^{4} x^{4} e^{8} + 8592 \, {\left(x e + d\right)}^{m} B a^{2} c m^{4} x^{4} e^{8} + 17184 \, {\left(x e + d\right)}^{m} A a b c m^{4} x^{4} e^{8} + 9544 \, {\left(x e + d\right)}^{m} B b^{3} m^{3} x^{5} e^{8} + 57264 \, {\left(x e + d\right)}^{m} B a b c m^{3} x^{5} e^{8} + 28632 \, {\left(x e + d\right)}^{m} A b^{2} c m^{3} x^{5} e^{8} + 28632 \, {\left(x e + d\right)}^{m} A a c^{2} m^{3} x^{5} e^{8} + 50490 \, {\left(x e + d\right)}^{m} B b^{2} c m^{2} x^{6} e^{8} + 50490 \, {\left(x e + d\right)}^{m} B a c^{2} m^{2} x^{6} e^{8} + 50490 \, {\left(x e + d\right)}^{m} A b c^{2} m^{2} x^{6} e^{8} + 44496 \, {\left(x e + d\right)}^{m} B b c^{2} m x^{7} e^{8} + 14832 \, {\left(x e + d\right)}^{m} A c^{3} m x^{7} e^{8} + 5040 \, {\left(x e + d\right)}^{m} B c^{3} x^{8} e^{8} + {\left(x e + d\right)}^{m} A a^{3} d m^{7} e^{7} + 33 \, {\left(x e + d\right)}^{m} B a^{3} d m^{6} x e^{7} + 99 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{6} x e^{7} + 1155 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{5} x^{2} e^{7} + 1155 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{5} x^{2} e^{7} + 1155 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{5} x^{2} e^{7} + 5613 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{4} x^{3} e^{7} + 1871 \, {\left(x e + d\right)}^{m} A b^{3} d m^{4} x^{3} e^{7} + 5613 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{4} x^{3} e^{7} + 11226 \, {\left(x e + d\right)}^{m} A a b c d m^{4} x^{3} e^{7} + 3748 \, {\left(x e + d\right)}^{m} B b^{3} d m^{3} x^{4} e^{7} + 22488 \, {\left(x e + d\right)}^{m} B a b c d m^{3} x^{4} e^{7} + 11244 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{3} x^{4} e^{7} + 11244 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{3} x^{4} e^{7} + 9480 \, {\left(x e + d\right)}^{m} B b^{2} c d m^{2} x^{5} e^{7} + 9480 \, {\left(x e + d\right)}^{m} B a c^{2} d m^{2} x^{5} e^{7} + 9480 \, {\left(x e + d\right)}^{m} A b c^{2} d m^{2} x^{5} e^{7} + 2880 \, {\left(x e + d\right)}^{m} B b c^{2} d m x^{6} e^{7} + 960 \, {\left(x e + d\right)}^{m} A c^{3} d m x^{6} e^{7} - {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{6} e^{6} - 3 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m^{6} e^{6} - 180 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m^{5} x e^{6} - 180 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m^{5} x e^{6} - 180 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{5} x e^{6} - 2493 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m^{4} x^{2} e^{6} - 831 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{4} x^{2} e^{6} - 2493 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{4} x^{2} e^{6} - 4986 \, {\left(x e + d\right)}^{m} A a b c d^{2} m^{4} x^{2} e^{6} - 3264 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{3} x^{3} e^{6} - 19584 \, {\left(x e + d\right)}^{m} B a b c d^{2} m^{3} x^{3} e^{6} - 9792 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{3} x^{3} e^{6} - 9792 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{3} x^{3} e^{6} - 10590 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m^{2} x^{4} e^{6} - 10590 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m^{2} x^{4} e^{6} - 10590 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m^{2} x^{4} e^{6} - 3456 \, {\left(x e + d\right)}^{m} B b c^{2} d^{2} m x^{5} e^{6} - 1152 \, {\left(x e + d\right)}^{m} A c^{3} d^{2} m x^{5} e^{6} + 6 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} m^{5} e^{5} + 6 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} m^{5} e^{5} + 6 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{5} e^{5} + 468 \, {\left(x e + d\right)}^{m} B a b^{2} d^{3} m^{4} x e^{5} + 156 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{4} x e^{5} + 468 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{4} x e^{5} + 936 \, {\left(x e + d\right)}^{m} A a b c d^{3} m^{4} x e^{5} + 2004 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{3} x^{2} e^{5} + 12024 \, {\left(x e + d\right)}^{m} B a b c d^{3} m^{3} x^{2} e^{5} + 6012 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{3} x^{2} e^{5} + 6012 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{3} x^{2} e^{5} + 11880 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m^{2} x^{3} e^{5} + 11880 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m^{2} x^{3} e^{5} + 11880 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m^{2} x^{3} e^{5} + 4320 \, {\left(x e + d\right)}^{m} B b c^{2} d^{3} m x^{4} e^{5} + 1440 \, {\left(x e + d\right)}^{m} A c^{3} d^{3} m x^{4} e^{5} - 18 \, {\left(x e + d\right)}^{m} B a b^{2} d^{4} m^{4} e^{4} - 6 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m^{4} e^{4} - 18 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m^{4} e^{4} - 36 \, {\left(x e + d\right)}^{m} A a b c d^{4} m^{4} e^{4} - 504 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m^{3} x e^{4} - 3024 \, {\left(x e + d\right)}^{m} B a b c d^{4} m^{3} x e^{4} - 1512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m^{3} x e^{4} - 1512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m^{3} x e^{4} - 12780 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m^{2} x^{2} e^{4} - 12780 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m^{2} x^{2} e^{4} - 12780 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m^{2} x^{2} e^{4} - 5760 \, {\left(x e + d\right)}^{m} B b c^{2} d^{4} m x^{3} e^{4} - 1920 \, {\left(x e + d\right)}^{m} A c^{3} d^{4} m x^{3} e^{4} + 24 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} m^{3} e^{3} + 144 \, {\left(x e + d\right)}^{m} B a b c d^{5} m^{3} e^{3} + 72 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} m^{3} e^{3} + 72 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} m^{3} e^{3} + 5400 \, {\left(x e + d\right)}^{m} B b^{2} c d^{5} m^{2} x e^{3} + 5400 \, {\left(x e + d\right)}^{m} B a c^{2} d^{5} m^{2} x e^{3} + 5400 \, {\left(x e + d\right)}^{m} A b c^{2} d^{5} m^{2} x e^{3} + 8640 \, {\left(x e + d\right)}^{m} B b c^{2} d^{5} m x^{2} e^{3} + 2880 \, {\left(x e + d\right)}^{m} A c^{3} d^{5} m x^{2} e^{3} - 360 \, {\left(x e + d\right)}^{m} B b^{2} c d^{6} m^{2} e^{2} - 360 \, {\left(x e + d\right)}^{m} B a c^{2} d^{6} m^{2} e^{2} - 360 \, {\left(x e + d\right)}^{m} A b c^{2} d^{6} m^{2} e^{2} - 17280 \, {\left(x e + d\right)}^{m} B b c^{2} d^{6} m x e^{2} - 5760 \, {\left(x e + d\right)}^{m} A c^{3} d^{6} m x e^{2} + 2160 \, {\left(x e + d\right)}^{m} B b c^{2} d^{7} m e + 720 \, {\left(x e + d\right)}^{m} A c^{3} d^{7} m e - 5040 \, {\left(x e + d\right)}^{m} B c^{3} d^{8} + 35 \, {\left(x e + d\right)}^{m} A a^{3} m^{6} x e^{8} + 478 \, {\left(x e + d\right)}^{m} B a^{3} m^{5} x^{2} e^{8} + 1434 \, {\left(x e + d\right)}^{m} A a^{2} b m^{5} x^{2} e^{8} + 9585 \, {\left(x e + d\right)}^{m} B a^{2} b m^{4} x^{3} e^{8} + 9585 \, {\left(x e + d\right)}^{m} A a b^{2} m^{4} x^{3} e^{8} + 9585 \, {\left(x e + d\right)}^{m} A a^{2} c m^{4} x^{3} e^{8} + 32979 \, {\left(x e + d\right)}^{m} B a b^{2} m^{3} x^{4} e^{8} + 10993 \, {\left(x e + d\right)}^{m} A b^{3} m^{3} x^{4} e^{8} + 32979 \, {\left(x e + d\right)}^{m} B a^{2} c m^{3} x^{4} e^{8} + 65958 \, {\left(x e + d\right)}^{m} A a b c m^{3} x^{4} e^{8} + 19564 \, {\left(x e + d\right)}^{m} B b^{3} m^{2} x^{5} e^{8} + 117384 \, {\left(x e + d\right)}^{m} B a b c m^{2} x^{5} e^{8} + 58692 \, {\left(x e + d\right)}^{m} A b^{2} c m^{2} x^{5} e^{8} + 58692 \, {\left(x e + d\right)}^{m} A a c^{2} m^{2} x^{5} e^{8} + 51432 \, {\left(x e + d\right)}^{m} B b^{2} c m x^{6} e^{8} + 51432 \, {\left(x e + d\right)}^{m} B a c^{2} m x^{6} e^{8} + 51432 \, {\left(x e + d\right)}^{m} A b c^{2} m x^{6} e^{8} + 17280 \, {\left(x e + d\right)}^{m} B b c^{2} x^{7} e^{8} + 5760 \, {\left(x e + d\right)}^{m} A c^{3} x^{7} e^{8} + 35 \, {\left(x e + d\right)}^{m} A a^{3} d m^{6} e^{7} + 445 \, {\left(x e + d\right)}^{m} B a^{3} d m^{5} x e^{7} + 1335 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{5} x e^{7} + 7275 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{4} x^{2} e^{7} + 7275 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{4} x^{2} e^{7} + 7275 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{4} x^{2} e^{7} + 16140 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{3} x^{3} e^{7} + 5380 \, {\left(x e + d\right)}^{m} A b^{3} d m^{3} x^{3} e^{7} + 16140 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{3} x^{3} e^{7} + 32280 \, {\left(x e + d\right)}^{m} A a b c d m^{3} x^{3} e^{7} + 4572 \, {\left(x e + d\right)}^{m} B b^{3} d m^{2} x^{4} e^{7} + 27432 \, {\left(x e + d\right)}^{m} B a b c d m^{2} x^{4} e^{7} + 13716 \, {\left(x e + d\right)}^{m} A b^{2} c d m^{2} x^{4} e^{7} + 13716 \, {\left(x e + d\right)}^{m} A a c^{2} d m^{2} x^{4} e^{7} + 4032 \, {\left(x e + d\right)}^{m} B b^{2} c d m x^{5} e^{7} + 4032 \, {\left(x e + d\right)}^{m} B a c^{2} d m x^{5} e^{7} + 4032 \, {\left(x e + d\right)}^{m} A b c^{2} d m x^{5} e^{7} - 33 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{5} e^{6} - 99 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m^{5} e^{6} - 2130 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m^{4} x e^{6} - 2130 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m^{4} x e^{6} - 2130 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{4} x e^{6} - 11853 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m^{3} x^{2} e^{6} - 3951 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{3} x^{2} e^{6} - 11853 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{3} x^{2} e^{6} - 23706 \, {\left(x e + d\right)}^{m} A a b c d^{2} m^{3} x^{2} e^{6} - 5200 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m^{2} x^{3} e^{6} - 31200 \, {\left(x e + d\right)}^{m} B a b c d^{2} m^{2} x^{3} e^{6} - 15600 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m^{2} x^{3} e^{6} - 15600 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m^{2} x^{3} e^{6} - 5040 \, {\left(x e + d\right)}^{m} B b^{2} c d^{2} m x^{4} e^{6} - 5040 \, {\left(x e + d\right)}^{m} B a c^{2} d^{2} m x^{4} e^{6} - 5040 \, {\left(x e + d\right)}^{m} A b c^{2} d^{2} m x^{4} e^{6} + 180 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} m^{4} e^{5} + 180 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} m^{4} e^{5} + 180 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{4} e^{5} + 4518 \, {\left(x e + d\right)}^{m} B a b^{2} d^{3} m^{3} x e^{5} + 1506 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{3} x e^{5} + 4518 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{3} x e^{5} + 9036 \, {\left(x e + d\right)}^{m} A a b c d^{3} m^{3} x e^{5} + 5784 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m^{2} x^{2} e^{5} + 34704 \, {\left(x e + d\right)}^{m} B a b c d^{3} m^{2} x^{2} e^{5} + 17352 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m^{2} x^{2} e^{5} + 17352 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m^{2} x^{2} e^{5} + 6720 \, {\left(x e + d\right)}^{m} B b^{2} c d^{3} m x^{3} e^{5} + 6720 \, {\left(x e + d\right)}^{m} B a c^{2} d^{3} m x^{3} e^{5} + 6720 \, {\left(x e + d\right)}^{m} A b c^{2} d^{3} m x^{3} e^{5} - 468 \, {\left(x e + d\right)}^{m} B a b^{2} d^{4} m^{3} e^{4} - 156 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m^{3} e^{4} - 468 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m^{3} e^{4} - 936 \, {\left(x e + d\right)}^{m} A a b c d^{4} m^{3} e^{4} - 3504 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m^{2} x e^{4} - 21024 \, {\left(x e + d\right)}^{m} B a b c d^{4} m^{2} x e^{4} - 10512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m^{2} x e^{4} - 10512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m^{2} x e^{4} - 10080 \, {\left(x e + d\right)}^{m} B b^{2} c d^{4} m x^{2} e^{4} - 10080 \, {\left(x e + d\right)}^{m} B a c^{2} d^{4} m x^{2} e^{4} - 10080 \, {\left(x e + d\right)}^{m} A b c^{2} d^{4} m x^{2} e^{4} + 504 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} m^{2} e^{3} + 3024 \, {\left(x e + d\right)}^{m} B a b c d^{5} m^{2} e^{3} + 1512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} m^{2} e^{3} + 1512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} m^{2} e^{3} + 20160 \, {\left(x e + d\right)}^{m} B b^{2} c d^{5} m x e^{3} + 20160 \, {\left(x e + d\right)}^{m} B a c^{2} d^{5} m x e^{3} + 20160 \, {\left(x e + d\right)}^{m} A b c^{2} d^{5} m x e^{3} - 5400 \, {\left(x e + d\right)}^{m} B b^{2} c d^{6} m e^{2} - 5400 \, {\left(x e + d\right)}^{m} B a c^{2} d^{6} m e^{2} - 5400 \, {\left(x e + d\right)}^{m} A b c^{2} d^{6} m e^{2} + 17280 \, {\left(x e + d\right)}^{m} B b c^{2} d^{7} e + 5760 \, {\left(x e + d\right)}^{m} A c^{3} d^{7} e + 511 \, {\left(x e + d\right)}^{m} A a^{3} m^{5} x e^{8} + 3580 \, {\left(x e + d\right)}^{m} B a^{3} m^{4} x^{2} e^{8} + 10740 \, {\left(x e + d\right)}^{m} A a^{2} b m^{4} x^{2} e^{8} + 38592 \, {\left(x e + d\right)}^{m} B a^{2} b m^{3} x^{3} e^{8} + 38592 \, {\left(x e + d\right)}^{m} A a b^{2} m^{3} x^{3} e^{8} + 38592 \, {\left(x e + d\right)}^{m} A a^{2} c m^{3} x^{3} e^{8} + 69936 \, {\left(x e + d\right)}^{m} B a b^{2} m^{2} x^{4} e^{8} + 23312 \, {\left(x e + d\right)}^{m} A b^{3} m^{2} x^{4} e^{8} + 69936 \, {\left(x e + d\right)}^{m} B a^{2} c m^{2} x^{4} e^{8} + 139872 \, {\left(x e + d\right)}^{m} A a b c m^{2} x^{4} e^{8} + 20304 \, {\left(x e + d\right)}^{m} B b^{3} m x^{5} e^{8} + 121824 \, {\left(x e + d\right)}^{m} B a b c m x^{5} e^{8} + 60912 \, {\left(x e + d\right)}^{m} A b^{2} c m x^{5} e^{8} + 60912 \, {\left(x e + d\right)}^{m} A a c^{2} m x^{5} e^{8} + 20160 \, {\left(x e + d\right)}^{m} B b^{2} c x^{6} e^{8} + 20160 \, {\left(x e + d\right)}^{m} B a c^{2} x^{6} e^{8} + 20160 \, {\left(x e + d\right)}^{m} A b c^{2} x^{6} e^{8} + 511 \, {\left(x e + d\right)}^{m} A a^{3} d m^{5} e^{7} + 3135 \, {\left(x e + d\right)}^{m} B a^{3} d m^{4} x e^{7} + 9405 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{4} x e^{7} + 24042 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{3} x^{2} e^{7} + 24042 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{3} x^{2} e^{7} + 24042 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{3} x^{2} e^{7} + 21516 \, {\left(x e + d\right)}^{m} B a b^{2} d m^{2} x^{3} e^{7} + 7172 \, {\left(x e + d\right)}^{m} A b^{3} d m^{2} x^{3} e^{7} + 21516 \, {\left(x e + d\right)}^{m} B a^{2} c d m^{2} x^{3} e^{7} + 43032 \, {\left(x e + d\right)}^{m} A a b c d m^{2} x^{3} e^{7} + 2016 \, {\left(x e + d\right)}^{m} B b^{3} d m x^{4} e^{7} + 12096 \, {\left(x e + d\right)}^{m} B a b c d m x^{4} e^{7} + 6048 \, {\left(x e + d\right)}^{m} A b^{2} c d m x^{4} e^{7} + 6048 \, {\left(x e + d\right)}^{m} A a c^{2} d m x^{4} e^{7} - 445 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{4} e^{6} - 1335 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m^{4} e^{6} - 12420 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m^{3} x e^{6} - 12420 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m^{3} x e^{6} - 12420 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{3} x e^{6} - 24714 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m^{2} x^{2} e^{6} - 8238 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m^{2} x^{2} e^{6} - 24714 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m^{2} x^{2} e^{6} - 49428 \, {\left(x e + d\right)}^{m} A a b c d^{2} m^{2} x^{2} e^{6} - 2688 \, {\left(x e + d\right)}^{m} B b^{3} d^{2} m x^{3} e^{6} - 16128 \, {\left(x e + d\right)}^{m} B a b c d^{2} m x^{3} e^{6} - 8064 \, {\left(x e + d\right)}^{m} A b^{2} c d^{2} m x^{3} e^{6} - 8064 \, {\left(x e + d\right)}^{m} A a c^{2} d^{2} m x^{3} e^{6} + 2130 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} m^{3} e^{5} + 2130 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} m^{3} e^{5} + 2130 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{3} e^{5} + 19188 \, {\left(x e + d\right)}^{m} B a b^{2} d^{3} m^{2} x e^{5} + 6396 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m^{2} x e^{5} + 19188 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m^{2} x e^{5} + 38376 \, {\left(x e + d\right)}^{m} A a b c d^{3} m^{2} x e^{5} + 4032 \, {\left(x e + d\right)}^{m} B b^{3} d^{3} m x^{2} e^{5} + 24192 \, {\left(x e + d\right)}^{m} B a b c d^{3} m x^{2} e^{5} + 12096 \, {\left(x e + d\right)}^{m} A b^{2} c d^{3} m x^{2} e^{5} + 12096 \, {\left(x e + d\right)}^{m} A a c^{2} d^{3} m x^{2} e^{5} - 4518 \, {\left(x e + d\right)}^{m} B a b^{2} d^{4} m^{2} e^{4} - 1506 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m^{2} e^{4} - 4518 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m^{2} e^{4} - 9036 \, {\left(x e + d\right)}^{m} A a b c d^{4} m^{2} e^{4} - 8064 \, {\left(x e + d\right)}^{m} B b^{3} d^{4} m x e^{4} - 48384 \, {\left(x e + d\right)}^{m} B a b c d^{4} m x e^{4} - 24192 \, {\left(x e + d\right)}^{m} A b^{2} c d^{4} m x e^{4} - 24192 \, {\left(x e + d\right)}^{m} A a c^{2} d^{4} m x e^{4} + 3504 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} m e^{3} + 21024 \, {\left(x e + d\right)}^{m} B a b c d^{5} m e^{3} + 10512 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} m e^{3} + 10512 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} m e^{3} - 20160 \, {\left(x e + d\right)}^{m} B b^{2} c d^{6} e^{2} - 20160 \, {\left(x e + d\right)}^{m} B a c^{2} d^{6} e^{2} - 20160 \, {\left(x e + d\right)}^{m} A b c^{2} d^{6} e^{2} + 4025 \, {\left(x e + d\right)}^{m} A a^{3} m^{4} x e^{8} + 15289 \, {\left(x e + d\right)}^{m} B a^{3} m^{3} x^{2} e^{8} + 45867 \, {\left(x e + d\right)}^{m} A a^{2} b m^{3} x^{2} e^{8} + 86076 \, {\left(x e + d\right)}^{m} B a^{2} b m^{2} x^{3} e^{8} + 86076 \, {\left(x e + d\right)}^{m} A a b^{2} m^{2} x^{3} e^{8} + 86076 \, {\left(x e + d\right)}^{m} A a^{2} c m^{2} x^{3} e^{8} + 74628 \, {\left(x e + d\right)}^{m} B a b^{2} m x^{4} e^{8} + 24876 \, {\left(x e + d\right)}^{m} A b^{3} m x^{4} e^{8} + 74628 \, {\left(x e + d\right)}^{m} B a^{2} c m x^{4} e^{8} + 149256 \, {\left(x e + d\right)}^{m} A a b c m x^{4} e^{8} + 8064 \, {\left(x e + d\right)}^{m} B b^{3} x^{5} e^{8} + 48384 \, {\left(x e + d\right)}^{m} B a b c x^{5} e^{8} + 24192 \, {\left(x e + d\right)}^{m} A b^{2} c x^{5} e^{8} + 24192 \, {\left(x e + d\right)}^{m} A a c^{2} x^{5} e^{8} + 4025 \, {\left(x e + d\right)}^{m} A a^{3} d m^{4} e^{7} + 12154 \, {\left(x e + d\right)}^{m} B a^{3} d m^{3} x e^{7} + 36462 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{3} x e^{7} + 37992 \, {\left(x e + d\right)}^{m} B a^{2} b d m^{2} x^{2} e^{7} + 37992 \, {\left(x e + d\right)}^{m} A a b^{2} d m^{2} x^{2} e^{7} + 37992 \, {\left(x e + d\right)}^{m} A a^{2} c d m^{2} x^{2} e^{7} + 10080 \, {\left(x e + d\right)}^{m} B a b^{2} d m x^{3} e^{7} + 3360 \, {\left(x e + d\right)}^{m} A b^{3} d m x^{3} e^{7} + 10080 \, {\left(x e + d\right)}^{m} B a^{2} c d m x^{3} e^{7} + 20160 \, {\left(x e + d\right)}^{m} A a b c d m x^{3} e^{7} - 3135 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{3} e^{6} - 9405 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m^{3} e^{6} - 35664 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m^{2} x e^{6} - 35664 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m^{2} x e^{6} - 35664 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m^{2} x e^{6} - 15120 \, {\left(x e + d\right)}^{m} B a b^{2} d^{2} m x^{2} e^{6} - 5040 \, {\left(x e + d\right)}^{m} A b^{3} d^{2} m x^{2} e^{6} - 15120 \, {\left(x e + d\right)}^{m} B a^{2} c d^{2} m x^{2} e^{6} - 30240 \, {\left(x e + d\right)}^{m} A a b c d^{2} m x^{2} e^{6} + 12420 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} m^{2} e^{5} + 12420 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} m^{2} e^{5} + 12420 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m^{2} e^{5} + 30240 \, {\left(x e + d\right)}^{m} B a b^{2} d^{3} m x e^{5} + 10080 \, {\left(x e + d\right)}^{m} A b^{3} d^{3} m x e^{5} + 30240 \, {\left(x e + d\right)}^{m} B a^{2} c d^{3} m x e^{5} + 60480 \, {\left(x e + d\right)}^{m} A a b c d^{3} m x e^{5} - 19188 \, {\left(x e + d\right)}^{m} B a b^{2} d^{4} m e^{4} - 6396 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} m e^{4} - 19188 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} m e^{4} - 38376 \, {\left(x e + d\right)}^{m} A a b c d^{4} m e^{4} + 8064 \, {\left(x e + d\right)}^{m} B b^{3} d^{5} e^{3} + 48384 \, {\left(x e + d\right)}^{m} B a b c d^{5} e^{3} + 24192 \, {\left(x e + d\right)}^{m} A b^{2} c d^{5} e^{3} + 24192 \, {\left(x e + d\right)}^{m} A a c^{2} d^{5} e^{3} + 18424 \, {\left(x e + d\right)}^{m} A a^{3} m^{3} x e^{8} + 36706 \, {\left(x e + d\right)}^{m} B a^{3} m^{2} x^{2} e^{8} + 110118 \, {\left(x e + d\right)}^{m} A a^{2} b m^{2} x^{2} e^{8} + 96144 \, {\left(x e + d\right)}^{m} B a^{2} b m x^{3} e^{8} + 96144 \, {\left(x e + d\right)}^{m} A a b^{2} m x^{3} e^{8} + 96144 \, {\left(x e + d\right)}^{m} A a^{2} c m x^{3} e^{8} + 30240 \, {\left(x e + d\right)}^{m} B a b^{2} x^{4} e^{8} + 10080 \, {\left(x e + d\right)}^{m} A b^{3} x^{4} e^{8} + 30240 \, {\left(x e + d\right)}^{m} B a^{2} c x^{4} e^{8} + 60480 \, {\left(x e + d\right)}^{m} A a b c x^{4} e^{8} + 18424 \, {\left(x e + d\right)}^{m} A a^{3} d m^{3} e^{7} + 24552 \, {\left(x e + d\right)}^{m} B a^{3} d m^{2} x e^{7} + 73656 \, {\left(x e + d\right)}^{m} A a^{2} b d m^{2} x e^{7} + 20160 \, {\left(x e + d\right)}^{m} B a^{2} b d m x^{2} e^{7} + 20160 \, {\left(x e + d\right)}^{m} A a b^{2} d m x^{2} e^{7} + 20160 \, {\left(x e + d\right)}^{m} A a^{2} c d m x^{2} e^{7} - 12154 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m^{2} e^{6} - 36462 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m^{2} e^{6} - 40320 \, {\left(x e + d\right)}^{m} B a^{2} b d^{2} m x e^{6} - 40320 \, {\left(x e + d\right)}^{m} A a b^{2} d^{2} m x e^{6} - 40320 \, {\left(x e + d\right)}^{m} A a^{2} c d^{2} m x e^{6} + 35664 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} m e^{5} + 35664 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} m e^{5} + 35664 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} m e^{5} - 30240 \, {\left(x e + d\right)}^{m} B a b^{2} d^{4} e^{4} - 10080 \, {\left(x e + d\right)}^{m} A b^{3} d^{4} e^{4} - 30240 \, {\left(x e + d\right)}^{m} B a^{2} c d^{4} e^{4} - 60480 \, {\left(x e + d\right)}^{m} A a b c d^{4} e^{4} + 48860 \, {\left(x e + d\right)}^{m} A a^{3} m^{2} x e^{8} + 44712 \, {\left(x e + d\right)}^{m} B a^{3} m x^{2} e^{8} + 134136 \, {\left(x e + d\right)}^{m} A a^{2} b m x^{2} e^{8} + 40320 \, {\left(x e + d\right)}^{m} B a^{2} b x^{3} e^{8} + 40320 \, {\left(x e + d\right)}^{m} A a b^{2} x^{3} e^{8} + 40320 \, {\left(x e + d\right)}^{m} A a^{2} c x^{3} e^{8} + 48860 \, {\left(x e + d\right)}^{m} A a^{3} d m^{2} e^{7} + 20160 \, {\left(x e + d\right)}^{m} B a^{3} d m x e^{7} + 60480 \, {\left(x e + d\right)}^{m} A a^{2} b d m x e^{7} - 24552 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} m e^{6} - 73656 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} m e^{6} + 40320 \, {\left(x e + d\right)}^{m} B a^{2} b d^{3} e^{5} + 40320 \, {\left(x e + d\right)}^{m} A a b^{2} d^{3} e^{5} + 40320 \, {\left(x e + d\right)}^{m} A a^{2} c d^{3} e^{5} + 69264 \, {\left(x e + d\right)}^{m} A a^{3} m x e^{8} + 20160 \, {\left(x e + d\right)}^{m} B a^{3} x^{2} e^{8} + 60480 \, {\left(x e + d\right)}^{m} A a^{2} b x^{2} e^{8} + 69264 \, {\left(x e + d\right)}^{m} A a^{3} d m e^{7} - 20160 \, {\left(x e + d\right)}^{m} B a^{3} d^{2} e^{6} - 60480 \, {\left(x e + d\right)}^{m} A a^{2} b d^{2} e^{6} + 40320 \, {\left(x e + d\right)}^{m} A a^{3} x e^{8} + 40320 \, {\left(x e + d\right)}^{m} A a^{3} d e^{7}}{m^{8} e^{8} + 36 \, m^{7} e^{8} + 546 \, m^{6} e^{8} + 4536 \, m^{5} e^{8} + 22449 \, m^{4} e^{8} + 67284 \, m^{3} e^{8} + 118124 \, m^{2} e^{8} + 109584 \, m e^{8} + 40320 \, e^{8}}"," ",0,"((x*e + d)^m*B*c^3*m^7*x^8*e^8 + (x*e + d)^m*B*c^3*d*m^7*x^7*e^7 + 3*(x*e + d)^m*B*b*c^2*m^7*x^7*e^8 + (x*e + d)^m*A*c^3*m^7*x^7*e^8 + 28*(x*e + d)^m*B*c^3*m^6*x^8*e^8 + 3*(x*e + d)^m*B*b*c^2*d*m^7*x^6*e^7 + (x*e + d)^m*A*c^3*d*m^7*x^6*e^7 + 21*(x*e + d)^m*B*c^3*d*m^6*x^7*e^7 - 7*(x*e + d)^m*B*c^3*d^2*m^6*x^6*e^6 + 3*(x*e + d)^m*B*b^2*c*m^7*x^6*e^8 + 3*(x*e + d)^m*B*a*c^2*m^7*x^6*e^8 + 3*(x*e + d)^m*A*b*c^2*m^7*x^6*e^8 + 87*(x*e + d)^m*B*b*c^2*m^6*x^7*e^8 + 29*(x*e + d)^m*A*c^3*m^6*x^7*e^8 + 322*(x*e + d)^m*B*c^3*m^5*x^8*e^8 + 3*(x*e + d)^m*B*b^2*c*d*m^7*x^5*e^7 + 3*(x*e + d)^m*B*a*c^2*d*m^7*x^5*e^7 + 3*(x*e + d)^m*A*b*c^2*d*m^7*x^5*e^7 + 69*(x*e + d)^m*B*b*c^2*d*m^6*x^6*e^7 + 23*(x*e + d)^m*A*c^3*d*m^6*x^6*e^7 + 175*(x*e + d)^m*B*c^3*d*m^5*x^7*e^7 - 18*(x*e + d)^m*B*b*c^2*d^2*m^6*x^5*e^6 - 6*(x*e + d)^m*A*c^3*d^2*m^6*x^5*e^6 - 105*(x*e + d)^m*B*c^3*d^2*m^5*x^6*e^6 + 42*(x*e + d)^m*B*c^3*d^3*m^5*x^5*e^5 + (x*e + d)^m*B*b^3*m^7*x^5*e^8 + 6*(x*e + d)^m*B*a*b*c*m^7*x^5*e^8 + 3*(x*e + d)^m*A*b^2*c*m^7*x^5*e^8 + 3*(x*e + d)^m*A*a*c^2*m^7*x^5*e^8 + 90*(x*e + d)^m*B*b^2*c*m^6*x^6*e^8 + 90*(x*e + d)^m*B*a*c^2*m^6*x^6*e^8 + 90*(x*e + d)^m*A*b*c^2*m^6*x^6*e^8 + 1029*(x*e + d)^m*B*b*c^2*m^5*x^7*e^8 + 343*(x*e + d)^m*A*c^3*m^5*x^7*e^8 + 1960*(x*e + d)^m*B*c^3*m^4*x^8*e^8 + (x*e + d)^m*B*b^3*d*m^7*x^4*e^7 + 6*(x*e + d)^m*B*a*b*c*d*m^7*x^4*e^7 + 3*(x*e + d)^m*A*b^2*c*d*m^7*x^4*e^7 + 3*(x*e + d)^m*A*a*c^2*d*m^7*x^4*e^7 + 75*(x*e + d)^m*B*b^2*c*d*m^6*x^5*e^7 + 75*(x*e + d)^m*B*a*c^2*d*m^6*x^5*e^7 + 75*(x*e + d)^m*A*b*c^2*d*m^6*x^5*e^7 + 615*(x*e + d)^m*B*b*c^2*d*m^5*x^6*e^7 + 205*(x*e + d)^m*A*c^3*d*m^5*x^6*e^7 + 735*(x*e + d)^m*B*c^3*d*m^4*x^7*e^7 - 15*(x*e + d)^m*B*b^2*c*d^2*m^6*x^4*e^6 - 15*(x*e + d)^m*B*a*c^2*d^2*m^6*x^4*e^6 - 15*(x*e + d)^m*A*b*c^2*d^2*m^6*x^4*e^6 - 324*(x*e + d)^m*B*b*c^2*d^2*m^5*x^5*e^6 - 108*(x*e + d)^m*A*c^3*d^2*m^5*x^5*e^6 - 595*(x*e + d)^m*B*c^3*d^2*m^4*x^6*e^6 + 90*(x*e + d)^m*B*b*c^2*d^3*m^5*x^4*e^5 + 30*(x*e + d)^m*A*c^3*d^3*m^5*x^4*e^5 + 420*(x*e + d)^m*B*c^3*d^3*m^4*x^5*e^5 - 210*(x*e + d)^m*B*c^3*d^4*m^4*x^4*e^4 + 3*(x*e + d)^m*B*a*b^2*m^7*x^4*e^8 + (x*e + d)^m*A*b^3*m^7*x^4*e^8 + 3*(x*e + d)^m*B*a^2*c*m^7*x^4*e^8 + 6*(x*e + d)^m*A*a*b*c*m^7*x^4*e^8 + 31*(x*e + d)^m*B*b^3*m^6*x^5*e^8 + 186*(x*e + d)^m*B*a*b*c*m^6*x^5*e^8 + 93*(x*e + d)^m*A*b^2*c*m^6*x^5*e^8 + 93*(x*e + d)^m*A*a*c^2*m^6*x^5*e^8 + 1098*(x*e + d)^m*B*b^2*c*m^5*x^6*e^8 + 1098*(x*e + d)^m*B*a*c^2*m^5*x^6*e^8 + 1098*(x*e + d)^m*A*b*c^2*m^5*x^6*e^8 + 6405*(x*e + d)^m*B*b*c^2*m^4*x^7*e^8 + 2135*(x*e + d)^m*A*c^3*m^4*x^7*e^8 + 6769*(x*e + d)^m*B*c^3*m^3*x^8*e^8 + 3*(x*e + d)^m*B*a*b^2*d*m^7*x^3*e^7 + (x*e + d)^m*A*b^3*d*m^7*x^3*e^7 + 3*(x*e + d)^m*B*a^2*c*d*m^7*x^3*e^7 + 6*(x*e + d)^m*A*a*b*c*d*m^7*x^3*e^7 + 27*(x*e + d)^m*B*b^3*d*m^6*x^4*e^7 + 162*(x*e + d)^m*B*a*b*c*d*m^6*x^4*e^7 + 81*(x*e + d)^m*A*b^2*c*d*m^6*x^4*e^7 + 81*(x*e + d)^m*A*a*c^2*d*m^6*x^4*e^7 + 723*(x*e + d)^m*B*b^2*c*d*m^5*x^5*e^7 + 723*(x*e + d)^m*B*a*c^2*d*m^5*x^5*e^7 + 723*(x*e + d)^m*A*b*c^2*d*m^5*x^5*e^7 + 2715*(x*e + d)^m*B*b*c^2*d*m^4*x^6*e^7 + 905*(x*e + d)^m*A*c^3*d*m^4*x^6*e^7 + 1624*(x*e + d)^m*B*c^3*d*m^3*x^7*e^7 - 4*(x*e + d)^m*B*b^3*d^2*m^6*x^3*e^6 - 24*(x*e + d)^m*B*a*b*c*d^2*m^6*x^3*e^6 - 12*(x*e + d)^m*A*b^2*c*d^2*m^6*x^3*e^6 - 12*(x*e + d)^m*A*a*c^2*d^2*m^6*x^3*e^6 - 315*(x*e + d)^m*B*b^2*c*d^2*m^5*x^4*e^6 - 315*(x*e + d)^m*B*a*c^2*d^2*m^5*x^4*e^6 - 315*(x*e + d)^m*A*b*c^2*d^2*m^5*x^4*e^6 - 2070*(x*e + d)^m*B*b*c^2*d^2*m^4*x^5*e^6 - 690*(x*e + d)^m*A*c^3*d^2*m^4*x^5*e^6 - 1575*(x*e + d)^m*B*c^3*d^2*m^3*x^6*e^6 + 60*(x*e + d)^m*B*b^2*c*d^3*m^5*x^3*e^5 + 60*(x*e + d)^m*B*a*c^2*d^3*m^5*x^3*e^5 + 60*(x*e + d)^m*A*b*c^2*d^3*m^5*x^3*e^5 + 1260*(x*e + d)^m*B*b*c^2*d^3*m^4*x^4*e^5 + 420*(x*e + d)^m*A*c^3*d^3*m^4*x^4*e^5 + 1470*(x*e + d)^m*B*c^3*d^3*m^3*x^5*e^5 - 360*(x*e + d)^m*B*b*c^2*d^4*m^4*x^3*e^4 - 120*(x*e + d)^m*A*c^3*d^4*m^4*x^3*e^4 - 1260*(x*e + d)^m*B*c^3*d^4*m^3*x^4*e^4 + 840*(x*e + d)^m*B*c^3*d^5*m^3*x^3*e^3 + 3*(x*e + d)^m*B*a^2*b*m^7*x^3*e^8 + 3*(x*e + d)^m*A*a*b^2*m^7*x^3*e^8 + 3*(x*e + d)^m*A*a^2*c*m^7*x^3*e^8 + 96*(x*e + d)^m*B*a*b^2*m^6*x^4*e^8 + 32*(x*e + d)^m*A*b^3*m^6*x^4*e^8 + 96*(x*e + d)^m*B*a^2*c*m^6*x^4*e^8 + 192*(x*e + d)^m*A*a*b*c*m^6*x^4*e^8 + 391*(x*e + d)^m*B*b^3*m^5*x^5*e^8 + 2346*(x*e + d)^m*B*a*b*c*m^5*x^5*e^8 + 1173*(x*e + d)^m*A*b^2*c*m^5*x^5*e^8 + 1173*(x*e + d)^m*A*a*c^2*m^5*x^5*e^8 + 7020*(x*e + d)^m*B*b^2*c*m^4*x^6*e^8 + 7020*(x*e + d)^m*B*a*c^2*m^4*x^6*e^8 + 7020*(x*e + d)^m*A*b*c^2*m^4*x^6*e^8 + 22512*(x*e + d)^m*B*b*c^2*m^3*x^7*e^8 + 7504*(x*e + d)^m*A*c^3*m^3*x^7*e^8 + 13132*(x*e + d)^m*B*c^3*m^2*x^8*e^8 + 3*(x*e + d)^m*B*a^2*b*d*m^7*x^2*e^7 + 3*(x*e + d)^m*A*a*b^2*d*m^7*x^2*e^7 + 3*(x*e + d)^m*A*a^2*c*d*m^7*x^2*e^7 + 87*(x*e + d)^m*B*a*b^2*d*m^6*x^3*e^7 + 29*(x*e + d)^m*A*b^3*d*m^6*x^3*e^7 + 87*(x*e + d)^m*B*a^2*c*d*m^6*x^3*e^7 + 174*(x*e + d)^m*A*a*b*c*d*m^6*x^3*e^7 + 283*(x*e + d)^m*B*b^3*d*m^5*x^4*e^7 + 1698*(x*e + d)^m*B*a*b*c*d*m^5*x^4*e^7 + 849*(x*e + d)^m*A*b^2*c*d*m^5*x^4*e^7 + 849*(x*e + d)^m*A*a*c^2*d*m^5*x^4*e^7 + 3405*(x*e + d)^m*B*b^2*c*d*m^4*x^5*e^7 + 3405*(x*e + d)^m*B*a*c^2*d*m^4*x^5*e^7 + 3405*(x*e + d)^m*A*b*c^2*d*m^4*x^5*e^7 + 6222*(x*e + d)^m*B*b*c^2*d*m^3*x^6*e^7 + 2074*(x*e + d)^m*A*c^3*d*m^3*x^6*e^7 + 1764*(x*e + d)^m*B*c^3*d*m^2*x^7*e^7 - 9*(x*e + d)^m*B*a*b^2*d^2*m^6*x^2*e^6 - 3*(x*e + d)^m*A*b^3*d^2*m^6*x^2*e^6 - 9*(x*e + d)^m*B*a^2*c*d^2*m^6*x^2*e^6 - 18*(x*e + d)^m*A*a*b*c*d^2*m^6*x^2*e^6 - 96*(x*e + d)^m*B*b^3*d^2*m^5*x^3*e^6 - 576*(x*e + d)^m*B*a*b*c*d^2*m^5*x^3*e^6 - 288*(x*e + d)^m*A*b^2*c*d^2*m^5*x^3*e^6 - 288*(x*e + d)^m*A*a*c^2*d^2*m^5*x^3*e^6 - 2355*(x*e + d)^m*B*b^2*c*d^2*m^4*x^4*e^6 - 2355*(x*e + d)^m*B*a*c^2*d^2*m^4*x^4*e^6 - 2355*(x*e + d)^m*A*b*c^2*d^2*m^4*x^4*e^6 - 5940*(x*e + d)^m*B*b*c^2*d^2*m^3*x^5*e^6 - 1980*(x*e + d)^m*A*c^3*d^2*m^3*x^5*e^6 - 1918*(x*e + d)^m*B*c^3*d^2*m^2*x^6*e^6 + 12*(x*e + d)^m*B*b^3*d^3*m^5*x^2*e^5 + 72*(x*e + d)^m*B*a*b*c*d^3*m^5*x^2*e^5 + 36*(x*e + d)^m*A*b^2*c*d^3*m^5*x^2*e^5 + 36*(x*e + d)^m*A*a*c^2*d^3*m^5*x^2*e^5 + 1080*(x*e + d)^m*B*b^2*c*d^3*m^4*x^3*e^5 + 1080*(x*e + d)^m*B*a*c^2*d^3*m^4*x^3*e^5 + 1080*(x*e + d)^m*A*b*c^2*d^3*m^4*x^3*e^5 + 5310*(x*e + d)^m*B*b*c^2*d^3*m^3*x^4*e^5 + 1770*(x*e + d)^m*A*c^3*d^3*m^3*x^4*e^5 + 2100*(x*e + d)^m*B*c^3*d^3*m^2*x^5*e^5 - 180*(x*e + d)^m*B*b^2*c*d^4*m^4*x^2*e^4 - 180*(x*e + d)^m*B*a*c^2*d^4*m^4*x^2*e^4 - 180*(x*e + d)^m*A*b*c^2*d^4*m^4*x^2*e^4 - 3960*(x*e + d)^m*B*b*c^2*d^4*m^3*x^3*e^4 - 1320*(x*e + d)^m*A*c^3*d^4*m^3*x^3*e^4 - 2310*(x*e + d)^m*B*c^3*d^4*m^2*x^4*e^4 + 1080*(x*e + d)^m*B*b*c^2*d^5*m^3*x^2*e^3 + 360*(x*e + d)^m*A*c^3*d^5*m^3*x^2*e^3 + 2520*(x*e + d)^m*B*c^3*d^5*m^2*x^3*e^3 - 2520*(x*e + d)^m*B*c^3*d^6*m^2*x^2*e^2 + (x*e + d)^m*B*a^3*m^7*x^2*e^8 + 3*(x*e + d)^m*A*a^2*b*m^7*x^2*e^8 + 99*(x*e + d)^m*B*a^2*b*m^6*x^3*e^8 + 99*(x*e + d)^m*A*a*b^2*m^6*x^3*e^8 + 99*(x*e + d)^m*A*a^2*c*m^6*x^3*e^8 + 1254*(x*e + d)^m*B*a*b^2*m^5*x^4*e^8 + 418*(x*e + d)^m*A*b^3*m^5*x^4*e^8 + 1254*(x*e + d)^m*B*a^2*c*m^5*x^4*e^8 + 2508*(x*e + d)^m*A*a*b*c*m^5*x^4*e^8 + 2581*(x*e + d)^m*B*b^3*m^4*x^5*e^8 + 15486*(x*e + d)^m*B*a*b*c*m^4*x^5*e^8 + 7743*(x*e + d)^m*A*b^2*c*m^4*x^5*e^8 + 7743*(x*e + d)^m*A*a*c^2*m^4*x^5*e^8 + 25227*(x*e + d)^m*B*b^2*c*m^3*x^6*e^8 + 25227*(x*e + d)^m*B*a*c^2*m^3*x^6*e^8 + 25227*(x*e + d)^m*A*b*c^2*m^3*x^6*e^8 + 44268*(x*e + d)^m*B*b*c^2*m^2*x^7*e^8 + 14756*(x*e + d)^m*A*c^3*m^2*x^7*e^8 + 13068*(x*e + d)^m*B*c^3*m*x^8*e^8 + (x*e + d)^m*B*a^3*d*m^7*x*e^7 + 3*(x*e + d)^m*A*a^2*b*d*m^7*x*e^7 + 93*(x*e + d)^m*B*a^2*b*d*m^6*x^2*e^7 + 93*(x*e + d)^m*A*a*b^2*d*m^6*x^2*e^7 + 93*(x*e + d)^m*A*a^2*c*d*m^6*x^2*e^7 + 993*(x*e + d)^m*B*a*b^2*d*m^5*x^3*e^7 + 331*(x*e + d)^m*A*b^3*d*m^5*x^3*e^7 + 993*(x*e + d)^m*B*a^2*c*d*m^5*x^3*e^7 + 1986*(x*e + d)^m*A*a*b*c*d*m^5*x^3*e^7 + 1449*(x*e + d)^m*B*b^3*d*m^4*x^4*e^7 + 8694*(x*e + d)^m*B*a*b*c*d*m^4*x^4*e^7 + 4347*(x*e + d)^m*A*b^2*c*d*m^4*x^4*e^7 + 4347*(x*e + d)^m*A*a*c^2*d*m^4*x^4*e^7 + 8202*(x*e + d)^m*B*b^2*c*d*m^3*x^5*e^7 + 8202*(x*e + d)^m*B*a*c^2*d*m^3*x^5*e^7 + 8202*(x*e + d)^m*A*b*c^2*d*m^3*x^5*e^7 + 6936*(x*e + d)^m*B*b*c^2*d*m^2*x^6*e^7 + 2312*(x*e + d)^m*A*c^3*d*m^2*x^6*e^7 + 720*(x*e + d)^m*B*c^3*d*m*x^7*e^7 - 6*(x*e + d)^m*B*a^2*b*d^2*m^6*x*e^6 - 6*(x*e + d)^m*A*a*b^2*d^2*m^6*x*e^6 - 6*(x*e + d)^m*A*a^2*c*d^2*m^6*x*e^6 - 243*(x*e + d)^m*B*a*b^2*d^2*m^5*x^2*e^6 - 81*(x*e + d)^m*A*b^3*d^2*m^5*x^2*e^6 - 243*(x*e + d)^m*B*a^2*c*d^2*m^5*x^2*e^6 - 486*(x*e + d)^m*A*a*b*c*d^2*m^5*x^2*e^6 - 844*(x*e + d)^m*B*b^3*d^2*m^4*x^3*e^6 - 5064*(x*e + d)^m*B*a*b*c*d^2*m^4*x^3*e^6 - 2532*(x*e + d)^m*A*b^2*c*d^2*m^4*x^3*e^6 - 2532*(x*e + d)^m*A*a*c^2*d^2*m^4*x^3*e^6 - 7605*(x*e + d)^m*B*b^2*c*d^2*m^3*x^4*e^6 - 7605*(x*e + d)^m*B*a*c^2*d^2*m^3*x^4*e^6 - 7605*(x*e + d)^m*A*b*c^2*d^2*m^3*x^4*e^6 - 7632*(x*e + d)^m*B*b*c^2*d^2*m^2*x^5*e^6 - 2544*(x*e + d)^m*A*c^3*d^2*m^2*x^5*e^6 - 840*(x*e + d)^m*B*c^3*d^2*m*x^6*e^6 + 18*(x*e + d)^m*B*a*b^2*d^3*m^5*x*e^5 + 6*(x*e + d)^m*A*b^3*d^3*m^5*x*e^5 + 18*(x*e + d)^m*B*a^2*c*d^3*m^5*x*e^5 + 36*(x*e + d)^m*A*a*b*c*d^3*m^5*x*e^5 + 264*(x*e + d)^m*B*b^3*d^3*m^4*x^2*e^5 + 1584*(x*e + d)^m*B*a*b*c*d^3*m^4*x^2*e^5 + 792*(x*e + d)^m*A*b^2*c*d^3*m^4*x^2*e^5 + 792*(x*e + d)^m*A*a*c^2*d^3*m^4*x^2*e^5 + 6180*(x*e + d)^m*B*b^2*c*d^3*m^3*x^3*e^5 + 6180*(x*e + d)^m*B*a*c^2*d^3*m^3*x^3*e^5 + 6180*(x*e + d)^m*A*b*c^2*d^3*m^3*x^3*e^5 + 8460*(x*e + d)^m*B*b*c^2*d^3*m^2*x^4*e^5 + 2820*(x*e + d)^m*A*c^3*d^3*m^2*x^4*e^5 + 1008*(x*e + d)^m*B*c^3*d^3*m*x^5*e^5 - 24*(x*e + d)^m*B*b^3*d^4*m^4*x*e^4 - 144*(x*e + d)^m*B*a*b*c*d^4*m^4*x*e^4 - 72*(x*e + d)^m*A*b^2*c*d^4*m^4*x*e^4 - 72*(x*e + d)^m*A*a*c^2*d^4*m^4*x*e^4 - 2880*(x*e + d)^m*B*b^2*c*d^4*m^3*x^2*e^4 - 2880*(x*e + d)^m*B*a*c^2*d^4*m^3*x^2*e^4 - 2880*(x*e + d)^m*A*b*c^2*d^4*m^3*x^2*e^4 - 9360*(x*e + d)^m*B*b*c^2*d^4*m^2*x^3*e^4 - 3120*(x*e + d)^m*A*c^3*d^4*m^2*x^3*e^4 - 1260*(x*e + d)^m*B*c^3*d^4*m*x^4*e^4 + 360*(x*e + d)^m*B*b^2*c*d^5*m^3*x*e^3 + 360*(x*e + d)^m*B*a*c^2*d^5*m^3*x*e^3 + 360*(x*e + d)^m*A*b*c^2*d^5*m^3*x*e^3 + 9720*(x*e + d)^m*B*b*c^2*d^5*m^2*x^2*e^3 + 3240*(x*e + d)^m*A*c^3*d^5*m^2*x^2*e^3 + 1680*(x*e + d)^m*B*c^3*d^5*m*x^3*e^3 - 2160*(x*e + d)^m*B*b*c^2*d^6*m^2*x*e^2 - 720*(x*e + d)^m*A*c^3*d^6*m^2*x*e^2 - 2520*(x*e + d)^m*B*c^3*d^6*m*x^2*e^2 + 5040*(x*e + d)^m*B*c^3*d^7*m*x*e + (x*e + d)^m*A*a^3*m^7*x*e^8 + 34*(x*e + d)^m*B*a^3*m^6*x^2*e^8 + 102*(x*e + d)^m*A*a^2*b*m^6*x^2*e^8 + 1341*(x*e + d)^m*B*a^2*b*m^5*x^3*e^8 + 1341*(x*e + d)^m*A*a*b^2*m^5*x^3*e^8 + 1341*(x*e + d)^m*A*a^2*c*m^5*x^3*e^8 + 8592*(x*e + d)^m*B*a*b^2*m^4*x^4*e^8 + 2864*(x*e + d)^m*A*b^3*m^4*x^4*e^8 + 8592*(x*e + d)^m*B*a^2*c*m^4*x^4*e^8 + 17184*(x*e + d)^m*A*a*b*c*m^4*x^4*e^8 + 9544*(x*e + d)^m*B*b^3*m^3*x^5*e^8 + 57264*(x*e + d)^m*B*a*b*c*m^3*x^5*e^8 + 28632*(x*e + d)^m*A*b^2*c*m^3*x^5*e^8 + 28632*(x*e + d)^m*A*a*c^2*m^3*x^5*e^8 + 50490*(x*e + d)^m*B*b^2*c*m^2*x^6*e^8 + 50490*(x*e + d)^m*B*a*c^2*m^2*x^6*e^8 + 50490*(x*e + d)^m*A*b*c^2*m^2*x^6*e^8 + 44496*(x*e + d)^m*B*b*c^2*m*x^7*e^8 + 14832*(x*e + d)^m*A*c^3*m*x^7*e^8 + 5040*(x*e + d)^m*B*c^3*x^8*e^8 + (x*e + d)^m*A*a^3*d*m^7*e^7 + 33*(x*e + d)^m*B*a^3*d*m^6*x*e^7 + 99*(x*e + d)^m*A*a^2*b*d*m^6*x*e^7 + 1155*(x*e + d)^m*B*a^2*b*d*m^5*x^2*e^7 + 1155*(x*e + d)^m*A*a*b^2*d*m^5*x^2*e^7 + 1155*(x*e + d)^m*A*a^2*c*d*m^5*x^2*e^7 + 5613*(x*e + d)^m*B*a*b^2*d*m^4*x^3*e^7 + 1871*(x*e + d)^m*A*b^3*d*m^4*x^3*e^7 + 5613*(x*e + d)^m*B*a^2*c*d*m^4*x^3*e^7 + 11226*(x*e + d)^m*A*a*b*c*d*m^4*x^3*e^7 + 3748*(x*e + d)^m*B*b^3*d*m^3*x^4*e^7 + 22488*(x*e + d)^m*B*a*b*c*d*m^3*x^4*e^7 + 11244*(x*e + d)^m*A*b^2*c*d*m^3*x^4*e^7 + 11244*(x*e + d)^m*A*a*c^2*d*m^3*x^4*e^7 + 9480*(x*e + d)^m*B*b^2*c*d*m^2*x^5*e^7 + 9480*(x*e + d)^m*B*a*c^2*d*m^2*x^5*e^7 + 9480*(x*e + d)^m*A*b*c^2*d*m^2*x^5*e^7 + 2880*(x*e + d)^m*B*b*c^2*d*m*x^6*e^7 + 960*(x*e + d)^m*A*c^3*d*m*x^6*e^7 - (x*e + d)^m*B*a^3*d^2*m^6*e^6 - 3*(x*e + d)^m*A*a^2*b*d^2*m^6*e^6 - 180*(x*e + d)^m*B*a^2*b*d^2*m^5*x*e^6 - 180*(x*e + d)^m*A*a*b^2*d^2*m^5*x*e^6 - 180*(x*e + d)^m*A*a^2*c*d^2*m^5*x*e^6 - 2493*(x*e + d)^m*B*a*b^2*d^2*m^4*x^2*e^6 - 831*(x*e + d)^m*A*b^3*d^2*m^4*x^2*e^6 - 2493*(x*e + d)^m*B*a^2*c*d^2*m^4*x^2*e^6 - 4986*(x*e + d)^m*A*a*b*c*d^2*m^4*x^2*e^6 - 3264*(x*e + d)^m*B*b^3*d^2*m^3*x^3*e^6 - 19584*(x*e + d)^m*B*a*b*c*d^2*m^3*x^3*e^6 - 9792*(x*e + d)^m*A*b^2*c*d^2*m^3*x^3*e^6 - 9792*(x*e + d)^m*A*a*c^2*d^2*m^3*x^3*e^6 - 10590*(x*e + d)^m*B*b^2*c*d^2*m^2*x^4*e^6 - 10590*(x*e + d)^m*B*a*c^2*d^2*m^2*x^4*e^6 - 10590*(x*e + d)^m*A*b*c^2*d^2*m^2*x^4*e^6 - 3456*(x*e + d)^m*B*b*c^2*d^2*m*x^5*e^6 - 1152*(x*e + d)^m*A*c^3*d^2*m*x^5*e^6 + 6*(x*e + d)^m*B*a^2*b*d^3*m^5*e^5 + 6*(x*e + d)^m*A*a*b^2*d^3*m^5*e^5 + 6*(x*e + d)^m*A*a^2*c*d^3*m^5*e^5 + 468*(x*e + d)^m*B*a*b^2*d^3*m^4*x*e^5 + 156*(x*e + d)^m*A*b^3*d^3*m^4*x*e^5 + 468*(x*e + d)^m*B*a^2*c*d^3*m^4*x*e^5 + 936*(x*e + d)^m*A*a*b*c*d^3*m^4*x*e^5 + 2004*(x*e + d)^m*B*b^3*d^3*m^3*x^2*e^5 + 12024*(x*e + d)^m*B*a*b*c*d^3*m^3*x^2*e^5 + 6012*(x*e + d)^m*A*b^2*c*d^3*m^3*x^2*e^5 + 6012*(x*e + d)^m*A*a*c^2*d^3*m^3*x^2*e^5 + 11880*(x*e + d)^m*B*b^2*c*d^3*m^2*x^3*e^5 + 11880*(x*e + d)^m*B*a*c^2*d^3*m^2*x^3*e^5 + 11880*(x*e + d)^m*A*b*c^2*d^3*m^2*x^3*e^5 + 4320*(x*e + d)^m*B*b*c^2*d^3*m*x^4*e^5 + 1440*(x*e + d)^m*A*c^3*d^3*m*x^4*e^5 - 18*(x*e + d)^m*B*a*b^2*d^4*m^4*e^4 - 6*(x*e + d)^m*A*b^3*d^4*m^4*e^4 - 18*(x*e + d)^m*B*a^2*c*d^4*m^4*e^4 - 36*(x*e + d)^m*A*a*b*c*d^4*m^4*e^4 - 504*(x*e + d)^m*B*b^3*d^4*m^3*x*e^4 - 3024*(x*e + d)^m*B*a*b*c*d^4*m^3*x*e^4 - 1512*(x*e + d)^m*A*b^2*c*d^4*m^3*x*e^4 - 1512*(x*e + d)^m*A*a*c^2*d^4*m^3*x*e^4 - 12780*(x*e + d)^m*B*b^2*c*d^4*m^2*x^2*e^4 - 12780*(x*e + d)^m*B*a*c^2*d^4*m^2*x^2*e^4 - 12780*(x*e + d)^m*A*b*c^2*d^4*m^2*x^2*e^4 - 5760*(x*e + d)^m*B*b*c^2*d^4*m*x^3*e^4 - 1920*(x*e + d)^m*A*c^3*d^4*m*x^3*e^4 + 24*(x*e + d)^m*B*b^3*d^5*m^3*e^3 + 144*(x*e + d)^m*B*a*b*c*d^5*m^3*e^3 + 72*(x*e + d)^m*A*b^2*c*d^5*m^3*e^3 + 72*(x*e + d)^m*A*a*c^2*d^5*m^3*e^3 + 5400*(x*e + d)^m*B*b^2*c*d^5*m^2*x*e^3 + 5400*(x*e + d)^m*B*a*c^2*d^5*m^2*x*e^3 + 5400*(x*e + d)^m*A*b*c^2*d^5*m^2*x*e^3 + 8640*(x*e + d)^m*B*b*c^2*d^5*m*x^2*e^3 + 2880*(x*e + d)^m*A*c^3*d^5*m*x^2*e^3 - 360*(x*e + d)^m*B*b^2*c*d^6*m^2*e^2 - 360*(x*e + d)^m*B*a*c^2*d^6*m^2*e^2 - 360*(x*e + d)^m*A*b*c^2*d^6*m^2*e^2 - 17280*(x*e + d)^m*B*b*c^2*d^6*m*x*e^2 - 5760*(x*e + d)^m*A*c^3*d^6*m*x*e^2 + 2160*(x*e + d)^m*B*b*c^2*d^7*m*e + 720*(x*e + d)^m*A*c^3*d^7*m*e - 5040*(x*e + d)^m*B*c^3*d^8 + 35*(x*e + d)^m*A*a^3*m^6*x*e^8 + 478*(x*e + d)^m*B*a^3*m^5*x^2*e^8 + 1434*(x*e + d)^m*A*a^2*b*m^5*x^2*e^8 + 9585*(x*e + d)^m*B*a^2*b*m^4*x^3*e^8 + 9585*(x*e + d)^m*A*a*b^2*m^4*x^3*e^8 + 9585*(x*e + d)^m*A*a^2*c*m^4*x^3*e^8 + 32979*(x*e + d)^m*B*a*b^2*m^3*x^4*e^8 + 10993*(x*e + d)^m*A*b^3*m^3*x^4*e^8 + 32979*(x*e + d)^m*B*a^2*c*m^3*x^4*e^8 + 65958*(x*e + d)^m*A*a*b*c*m^3*x^4*e^8 + 19564*(x*e + d)^m*B*b^3*m^2*x^5*e^8 + 117384*(x*e + d)^m*B*a*b*c*m^2*x^5*e^8 + 58692*(x*e + d)^m*A*b^2*c*m^2*x^5*e^8 + 58692*(x*e + d)^m*A*a*c^2*m^2*x^5*e^8 + 51432*(x*e + d)^m*B*b^2*c*m*x^6*e^8 + 51432*(x*e + d)^m*B*a*c^2*m*x^6*e^8 + 51432*(x*e + d)^m*A*b*c^2*m*x^6*e^8 + 17280*(x*e + d)^m*B*b*c^2*x^7*e^8 + 5760*(x*e + d)^m*A*c^3*x^7*e^8 + 35*(x*e + d)^m*A*a^3*d*m^6*e^7 + 445*(x*e + d)^m*B*a^3*d*m^5*x*e^7 + 1335*(x*e + d)^m*A*a^2*b*d*m^5*x*e^7 + 7275*(x*e + d)^m*B*a^2*b*d*m^4*x^2*e^7 + 7275*(x*e + d)^m*A*a*b^2*d*m^4*x^2*e^7 + 7275*(x*e + d)^m*A*a^2*c*d*m^4*x^2*e^7 + 16140*(x*e + d)^m*B*a*b^2*d*m^3*x^3*e^7 + 5380*(x*e + d)^m*A*b^3*d*m^3*x^3*e^7 + 16140*(x*e + d)^m*B*a^2*c*d*m^3*x^3*e^7 + 32280*(x*e + d)^m*A*a*b*c*d*m^3*x^3*e^7 + 4572*(x*e + d)^m*B*b^3*d*m^2*x^4*e^7 + 27432*(x*e + d)^m*B*a*b*c*d*m^2*x^4*e^7 + 13716*(x*e + d)^m*A*b^2*c*d*m^2*x^4*e^7 + 13716*(x*e + d)^m*A*a*c^2*d*m^2*x^4*e^7 + 4032*(x*e + d)^m*B*b^2*c*d*m*x^5*e^7 + 4032*(x*e + d)^m*B*a*c^2*d*m*x^5*e^7 + 4032*(x*e + d)^m*A*b*c^2*d*m*x^5*e^7 - 33*(x*e + d)^m*B*a^3*d^2*m^5*e^6 - 99*(x*e + d)^m*A*a^2*b*d^2*m^5*e^6 - 2130*(x*e + d)^m*B*a^2*b*d^2*m^4*x*e^6 - 2130*(x*e + d)^m*A*a*b^2*d^2*m^4*x*e^6 - 2130*(x*e + d)^m*A*a^2*c*d^2*m^4*x*e^6 - 11853*(x*e + d)^m*B*a*b^2*d^2*m^3*x^2*e^6 - 3951*(x*e + d)^m*A*b^3*d^2*m^3*x^2*e^6 - 11853*(x*e + d)^m*B*a^2*c*d^2*m^3*x^2*e^6 - 23706*(x*e + d)^m*A*a*b*c*d^2*m^3*x^2*e^6 - 5200*(x*e + d)^m*B*b^3*d^2*m^2*x^3*e^6 - 31200*(x*e + d)^m*B*a*b*c*d^2*m^2*x^3*e^6 - 15600*(x*e + d)^m*A*b^2*c*d^2*m^2*x^3*e^6 - 15600*(x*e + d)^m*A*a*c^2*d^2*m^2*x^3*e^6 - 5040*(x*e + d)^m*B*b^2*c*d^2*m*x^4*e^6 - 5040*(x*e + d)^m*B*a*c^2*d^2*m*x^4*e^6 - 5040*(x*e + d)^m*A*b*c^2*d^2*m*x^4*e^6 + 180*(x*e + d)^m*B*a^2*b*d^3*m^4*e^5 + 180*(x*e + d)^m*A*a*b^2*d^3*m^4*e^5 + 180*(x*e + d)^m*A*a^2*c*d^3*m^4*e^5 + 4518*(x*e + d)^m*B*a*b^2*d^3*m^3*x*e^5 + 1506*(x*e + d)^m*A*b^3*d^3*m^3*x*e^5 + 4518*(x*e + d)^m*B*a^2*c*d^3*m^3*x*e^5 + 9036*(x*e + d)^m*A*a*b*c*d^3*m^3*x*e^5 + 5784*(x*e + d)^m*B*b^3*d^3*m^2*x^2*e^5 + 34704*(x*e + d)^m*B*a*b*c*d^3*m^2*x^2*e^5 + 17352*(x*e + d)^m*A*b^2*c*d^3*m^2*x^2*e^5 + 17352*(x*e + d)^m*A*a*c^2*d^3*m^2*x^2*e^5 + 6720*(x*e + d)^m*B*b^2*c*d^3*m*x^3*e^5 + 6720*(x*e + d)^m*B*a*c^2*d^3*m*x^3*e^5 + 6720*(x*e + d)^m*A*b*c^2*d^3*m*x^3*e^5 - 468*(x*e + d)^m*B*a*b^2*d^4*m^3*e^4 - 156*(x*e + d)^m*A*b^3*d^4*m^3*e^4 - 468*(x*e + d)^m*B*a^2*c*d^4*m^3*e^4 - 936*(x*e + d)^m*A*a*b*c*d^4*m^3*e^4 - 3504*(x*e + d)^m*B*b^3*d^4*m^2*x*e^4 - 21024*(x*e + d)^m*B*a*b*c*d^4*m^2*x*e^4 - 10512*(x*e + d)^m*A*b^2*c*d^4*m^2*x*e^4 - 10512*(x*e + d)^m*A*a*c^2*d^4*m^2*x*e^4 - 10080*(x*e + d)^m*B*b^2*c*d^4*m*x^2*e^4 - 10080*(x*e + d)^m*B*a*c^2*d^4*m*x^2*e^4 - 10080*(x*e + d)^m*A*b*c^2*d^4*m*x^2*e^4 + 504*(x*e + d)^m*B*b^3*d^5*m^2*e^3 + 3024*(x*e + d)^m*B*a*b*c*d^5*m^2*e^3 + 1512*(x*e + d)^m*A*b^2*c*d^5*m^2*e^3 + 1512*(x*e + d)^m*A*a*c^2*d^5*m^2*e^3 + 20160*(x*e + d)^m*B*b^2*c*d^5*m*x*e^3 + 20160*(x*e + d)^m*B*a*c^2*d^5*m*x*e^3 + 20160*(x*e + d)^m*A*b*c^2*d^5*m*x*e^3 - 5400*(x*e + d)^m*B*b^2*c*d^6*m*e^2 - 5400*(x*e + d)^m*B*a*c^2*d^6*m*e^2 - 5400*(x*e + d)^m*A*b*c^2*d^6*m*e^2 + 17280*(x*e + d)^m*B*b*c^2*d^7*e + 5760*(x*e + d)^m*A*c^3*d^7*e + 511*(x*e + d)^m*A*a^3*m^5*x*e^8 + 3580*(x*e + d)^m*B*a^3*m^4*x^2*e^8 + 10740*(x*e + d)^m*A*a^2*b*m^4*x^2*e^8 + 38592*(x*e + d)^m*B*a^2*b*m^3*x^3*e^8 + 38592*(x*e + d)^m*A*a*b^2*m^3*x^3*e^8 + 38592*(x*e + d)^m*A*a^2*c*m^3*x^3*e^8 + 69936*(x*e + d)^m*B*a*b^2*m^2*x^4*e^8 + 23312*(x*e + d)^m*A*b^3*m^2*x^4*e^8 + 69936*(x*e + d)^m*B*a^2*c*m^2*x^4*e^8 + 139872*(x*e + d)^m*A*a*b*c*m^2*x^4*e^8 + 20304*(x*e + d)^m*B*b^3*m*x^5*e^8 + 121824*(x*e + d)^m*B*a*b*c*m*x^5*e^8 + 60912*(x*e + d)^m*A*b^2*c*m*x^5*e^8 + 60912*(x*e + d)^m*A*a*c^2*m*x^5*e^8 + 20160*(x*e + d)^m*B*b^2*c*x^6*e^8 + 20160*(x*e + d)^m*B*a*c^2*x^6*e^8 + 20160*(x*e + d)^m*A*b*c^2*x^6*e^8 + 511*(x*e + d)^m*A*a^3*d*m^5*e^7 + 3135*(x*e + d)^m*B*a^3*d*m^4*x*e^7 + 9405*(x*e + d)^m*A*a^2*b*d*m^4*x*e^7 + 24042*(x*e + d)^m*B*a^2*b*d*m^3*x^2*e^7 + 24042*(x*e + d)^m*A*a*b^2*d*m^3*x^2*e^7 + 24042*(x*e + d)^m*A*a^2*c*d*m^3*x^2*e^7 + 21516*(x*e + d)^m*B*a*b^2*d*m^2*x^3*e^7 + 7172*(x*e + d)^m*A*b^3*d*m^2*x^3*e^7 + 21516*(x*e + d)^m*B*a^2*c*d*m^2*x^3*e^7 + 43032*(x*e + d)^m*A*a*b*c*d*m^2*x^3*e^7 + 2016*(x*e + d)^m*B*b^3*d*m*x^4*e^7 + 12096*(x*e + d)^m*B*a*b*c*d*m*x^4*e^7 + 6048*(x*e + d)^m*A*b^2*c*d*m*x^4*e^7 + 6048*(x*e + d)^m*A*a*c^2*d*m*x^4*e^7 - 445*(x*e + d)^m*B*a^3*d^2*m^4*e^6 - 1335*(x*e + d)^m*A*a^2*b*d^2*m^4*e^6 - 12420*(x*e + d)^m*B*a^2*b*d^2*m^3*x*e^6 - 12420*(x*e + d)^m*A*a*b^2*d^2*m^3*x*e^6 - 12420*(x*e + d)^m*A*a^2*c*d^2*m^3*x*e^6 - 24714*(x*e + d)^m*B*a*b^2*d^2*m^2*x^2*e^6 - 8238*(x*e + d)^m*A*b^3*d^2*m^2*x^2*e^6 - 24714*(x*e + d)^m*B*a^2*c*d^2*m^2*x^2*e^6 - 49428*(x*e + d)^m*A*a*b*c*d^2*m^2*x^2*e^6 - 2688*(x*e + d)^m*B*b^3*d^2*m*x^3*e^6 - 16128*(x*e + d)^m*B*a*b*c*d^2*m*x^3*e^6 - 8064*(x*e + d)^m*A*b^2*c*d^2*m*x^3*e^6 - 8064*(x*e + d)^m*A*a*c^2*d^2*m*x^3*e^6 + 2130*(x*e + d)^m*B*a^2*b*d^3*m^3*e^5 + 2130*(x*e + d)^m*A*a*b^2*d^3*m^3*e^5 + 2130*(x*e + d)^m*A*a^2*c*d^3*m^3*e^5 + 19188*(x*e + d)^m*B*a*b^2*d^3*m^2*x*e^5 + 6396*(x*e + d)^m*A*b^3*d^3*m^2*x*e^5 + 19188*(x*e + d)^m*B*a^2*c*d^3*m^2*x*e^5 + 38376*(x*e + d)^m*A*a*b*c*d^3*m^2*x*e^5 + 4032*(x*e + d)^m*B*b^3*d^3*m*x^2*e^5 + 24192*(x*e + d)^m*B*a*b*c*d^3*m*x^2*e^5 + 12096*(x*e + d)^m*A*b^2*c*d^3*m*x^2*e^5 + 12096*(x*e + d)^m*A*a*c^2*d^3*m*x^2*e^5 - 4518*(x*e + d)^m*B*a*b^2*d^4*m^2*e^4 - 1506*(x*e + d)^m*A*b^3*d^4*m^2*e^4 - 4518*(x*e + d)^m*B*a^2*c*d^4*m^2*e^4 - 9036*(x*e + d)^m*A*a*b*c*d^4*m^2*e^4 - 8064*(x*e + d)^m*B*b^3*d^4*m*x*e^4 - 48384*(x*e + d)^m*B*a*b*c*d^4*m*x*e^4 - 24192*(x*e + d)^m*A*b^2*c*d^4*m*x*e^4 - 24192*(x*e + d)^m*A*a*c^2*d^4*m*x*e^4 + 3504*(x*e + d)^m*B*b^3*d^5*m*e^3 + 21024*(x*e + d)^m*B*a*b*c*d^5*m*e^3 + 10512*(x*e + d)^m*A*b^2*c*d^5*m*e^3 + 10512*(x*e + d)^m*A*a*c^2*d^5*m*e^3 - 20160*(x*e + d)^m*B*b^2*c*d^6*e^2 - 20160*(x*e + d)^m*B*a*c^2*d^6*e^2 - 20160*(x*e + d)^m*A*b*c^2*d^6*e^2 + 4025*(x*e + d)^m*A*a^3*m^4*x*e^8 + 15289*(x*e + d)^m*B*a^3*m^3*x^2*e^8 + 45867*(x*e + d)^m*A*a^2*b*m^3*x^2*e^8 + 86076*(x*e + d)^m*B*a^2*b*m^2*x^3*e^8 + 86076*(x*e + d)^m*A*a*b^2*m^2*x^3*e^8 + 86076*(x*e + d)^m*A*a^2*c*m^2*x^3*e^8 + 74628*(x*e + d)^m*B*a*b^2*m*x^4*e^8 + 24876*(x*e + d)^m*A*b^3*m*x^4*e^8 + 74628*(x*e + d)^m*B*a^2*c*m*x^4*e^8 + 149256*(x*e + d)^m*A*a*b*c*m*x^4*e^8 + 8064*(x*e + d)^m*B*b^3*x^5*e^8 + 48384*(x*e + d)^m*B*a*b*c*x^5*e^8 + 24192*(x*e + d)^m*A*b^2*c*x^5*e^8 + 24192*(x*e + d)^m*A*a*c^2*x^5*e^8 + 4025*(x*e + d)^m*A*a^3*d*m^4*e^7 + 12154*(x*e + d)^m*B*a^3*d*m^3*x*e^7 + 36462*(x*e + d)^m*A*a^2*b*d*m^3*x*e^7 + 37992*(x*e + d)^m*B*a^2*b*d*m^2*x^2*e^7 + 37992*(x*e + d)^m*A*a*b^2*d*m^2*x^2*e^7 + 37992*(x*e + d)^m*A*a^2*c*d*m^2*x^2*e^7 + 10080*(x*e + d)^m*B*a*b^2*d*m*x^3*e^7 + 3360*(x*e + d)^m*A*b^3*d*m*x^3*e^7 + 10080*(x*e + d)^m*B*a^2*c*d*m*x^3*e^7 + 20160*(x*e + d)^m*A*a*b*c*d*m*x^3*e^7 - 3135*(x*e + d)^m*B*a^3*d^2*m^3*e^6 - 9405*(x*e + d)^m*A*a^2*b*d^2*m^3*e^6 - 35664*(x*e + d)^m*B*a^2*b*d^2*m^2*x*e^6 - 35664*(x*e + d)^m*A*a*b^2*d^2*m^2*x*e^6 - 35664*(x*e + d)^m*A*a^2*c*d^2*m^2*x*e^6 - 15120*(x*e + d)^m*B*a*b^2*d^2*m*x^2*e^6 - 5040*(x*e + d)^m*A*b^3*d^2*m*x^2*e^6 - 15120*(x*e + d)^m*B*a^2*c*d^2*m*x^2*e^6 - 30240*(x*e + d)^m*A*a*b*c*d^2*m*x^2*e^6 + 12420*(x*e + d)^m*B*a^2*b*d^3*m^2*e^5 + 12420*(x*e + d)^m*A*a*b^2*d^3*m^2*e^5 + 12420*(x*e + d)^m*A*a^2*c*d^3*m^2*e^5 + 30240*(x*e + d)^m*B*a*b^2*d^3*m*x*e^5 + 10080*(x*e + d)^m*A*b^3*d^3*m*x*e^5 + 30240*(x*e + d)^m*B*a^2*c*d^3*m*x*e^5 + 60480*(x*e + d)^m*A*a*b*c*d^3*m*x*e^5 - 19188*(x*e + d)^m*B*a*b^2*d^4*m*e^4 - 6396*(x*e + d)^m*A*b^3*d^4*m*e^4 - 19188*(x*e + d)^m*B*a^2*c*d^4*m*e^4 - 38376*(x*e + d)^m*A*a*b*c*d^4*m*e^4 + 8064*(x*e + d)^m*B*b^3*d^5*e^3 + 48384*(x*e + d)^m*B*a*b*c*d^5*e^3 + 24192*(x*e + d)^m*A*b^2*c*d^5*e^3 + 24192*(x*e + d)^m*A*a*c^2*d^5*e^3 + 18424*(x*e + d)^m*A*a^3*m^3*x*e^8 + 36706*(x*e + d)^m*B*a^3*m^2*x^2*e^8 + 110118*(x*e + d)^m*A*a^2*b*m^2*x^2*e^8 + 96144*(x*e + d)^m*B*a^2*b*m*x^3*e^8 + 96144*(x*e + d)^m*A*a*b^2*m*x^3*e^8 + 96144*(x*e + d)^m*A*a^2*c*m*x^3*e^8 + 30240*(x*e + d)^m*B*a*b^2*x^4*e^8 + 10080*(x*e + d)^m*A*b^3*x^4*e^8 + 30240*(x*e + d)^m*B*a^2*c*x^4*e^8 + 60480*(x*e + d)^m*A*a*b*c*x^4*e^8 + 18424*(x*e + d)^m*A*a^3*d*m^3*e^7 + 24552*(x*e + d)^m*B*a^3*d*m^2*x*e^7 + 73656*(x*e + d)^m*A*a^2*b*d*m^2*x*e^7 + 20160*(x*e + d)^m*B*a^2*b*d*m*x^2*e^7 + 20160*(x*e + d)^m*A*a*b^2*d*m*x^2*e^7 + 20160*(x*e + d)^m*A*a^2*c*d*m*x^2*e^7 - 12154*(x*e + d)^m*B*a^3*d^2*m^2*e^6 - 36462*(x*e + d)^m*A*a^2*b*d^2*m^2*e^6 - 40320*(x*e + d)^m*B*a^2*b*d^2*m*x*e^6 - 40320*(x*e + d)^m*A*a*b^2*d^2*m*x*e^6 - 40320*(x*e + d)^m*A*a^2*c*d^2*m*x*e^6 + 35664*(x*e + d)^m*B*a^2*b*d^3*m*e^5 + 35664*(x*e + d)^m*A*a*b^2*d^3*m*e^5 + 35664*(x*e + d)^m*A*a^2*c*d^3*m*e^5 - 30240*(x*e + d)^m*B*a*b^2*d^4*e^4 - 10080*(x*e + d)^m*A*b^3*d^4*e^4 - 30240*(x*e + d)^m*B*a^2*c*d^4*e^4 - 60480*(x*e + d)^m*A*a*b*c*d^4*e^4 + 48860*(x*e + d)^m*A*a^3*m^2*x*e^8 + 44712*(x*e + d)^m*B*a^3*m*x^2*e^8 + 134136*(x*e + d)^m*A*a^2*b*m*x^2*e^8 + 40320*(x*e + d)^m*B*a^2*b*x^3*e^8 + 40320*(x*e + d)^m*A*a*b^2*x^3*e^8 + 40320*(x*e + d)^m*A*a^2*c*x^3*e^8 + 48860*(x*e + d)^m*A*a^3*d*m^2*e^7 + 20160*(x*e + d)^m*B*a^3*d*m*x*e^7 + 60480*(x*e + d)^m*A*a^2*b*d*m*x*e^7 - 24552*(x*e + d)^m*B*a^3*d^2*m*e^6 - 73656*(x*e + d)^m*A*a^2*b*d^2*m*e^6 + 40320*(x*e + d)^m*B*a^2*b*d^3*e^5 + 40320*(x*e + d)^m*A*a*b^2*d^3*e^5 + 40320*(x*e + d)^m*A*a^2*c*d^3*e^5 + 69264*(x*e + d)^m*A*a^3*m*x*e^8 + 20160*(x*e + d)^m*B*a^3*x^2*e^8 + 60480*(x*e + d)^m*A*a^2*b*x^2*e^8 + 69264*(x*e + d)^m*A*a^3*d*m*e^7 - 20160*(x*e + d)^m*B*a^3*d^2*e^6 - 60480*(x*e + d)^m*A*a^2*b*d^2*e^6 + 40320*(x*e + d)^m*A*a^3*x*e^8 + 40320*(x*e + d)^m*A*a^3*d*e^7)/(m^8*e^8 + 36*m^7*e^8 + 546*m^6*e^8 + 4536*m^5*e^8 + 22449*m^4*e^8 + 67284*m^3*e^8 + 118124*m^2*e^8 + 109584*m*e^8 + 40320*e^8)","B",0
2641,1,4940,0,0.335511," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c^{2} m^{5} x^{6} e^{6} + {\left(x e + d\right)}^{m} B c^{2} d m^{5} x^{5} e^{5} + 2 \, {\left(x e + d\right)}^{m} B b c m^{5} x^{5} e^{6} + {\left(x e + d\right)}^{m} A c^{2} m^{5} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} B c^{2} m^{4} x^{6} e^{6} + 2 \, {\left(x e + d\right)}^{m} B b c d m^{5} x^{4} e^{5} + {\left(x e + d\right)}^{m} A c^{2} d m^{5} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} B c^{2} d m^{4} x^{5} e^{5} - 5 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{4} x^{4} e^{4} + {\left(x e + d\right)}^{m} B b^{2} m^{5} x^{4} e^{6} + 2 \, {\left(x e + d\right)}^{m} B a c m^{5} x^{4} e^{6} + 2 \, {\left(x e + d\right)}^{m} A b c m^{5} x^{4} e^{6} + 32 \, {\left(x e + d\right)}^{m} B b c m^{4} x^{5} e^{6} + 16 \, {\left(x e + d\right)}^{m} A c^{2} m^{4} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} B c^{2} m^{3} x^{6} e^{6} + {\left(x e + d\right)}^{m} B b^{2} d m^{5} x^{3} e^{5} + 2 \, {\left(x e + d\right)}^{m} B a c d m^{5} x^{3} e^{5} + 2 \, {\left(x e + d\right)}^{m} A b c d m^{5} x^{3} e^{5} + 24 \, {\left(x e + d\right)}^{m} B b c d m^{4} x^{4} e^{5} + 12 \, {\left(x e + d\right)}^{m} A c^{2} d m^{4} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} B c^{2} d m^{3} x^{5} e^{5} - 8 \, {\left(x e + d\right)}^{m} B b c d^{2} m^{4} x^{3} e^{4} - 4 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{4} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{3} x^{4} e^{4} + 20 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m^{3} x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} B a b m^{5} x^{3} e^{6} + {\left(x e + d\right)}^{m} A b^{2} m^{5} x^{3} e^{6} + 2 \, {\left(x e + d\right)}^{m} A a c m^{5} x^{3} e^{6} + 17 \, {\left(x e + d\right)}^{m} B b^{2} m^{4} x^{4} e^{6} + 34 \, {\left(x e + d\right)}^{m} B a c m^{4} x^{4} e^{6} + 34 \, {\left(x e + d\right)}^{m} A b c m^{4} x^{4} e^{6} + 190 \, {\left(x e + d\right)}^{m} B b c m^{3} x^{5} e^{6} + 95 \, {\left(x e + d\right)}^{m} A c^{2} m^{3} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} B c^{2} m^{2} x^{6} e^{6} + 2 \, {\left(x e + d\right)}^{m} B a b d m^{5} x^{2} e^{5} + {\left(x e + d\right)}^{m} A b^{2} d m^{5} x^{2} e^{5} + 2 \, {\left(x e + d\right)}^{m} A a c d m^{5} x^{2} e^{5} + 14 \, {\left(x e + d\right)}^{m} B b^{2} d m^{4} x^{3} e^{5} + 28 \, {\left(x e + d\right)}^{m} B a c d m^{4} x^{3} e^{5} + 28 \, {\left(x e + d\right)}^{m} A b c d m^{4} x^{3} e^{5} + 94 \, {\left(x e + d\right)}^{m} B b c d m^{3} x^{4} e^{5} + 47 \, {\left(x e + d\right)}^{m} A c^{2} d m^{3} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} B c^{2} d m^{2} x^{5} e^{5} - 3 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m^{4} x^{2} e^{4} - 6 \, {\left(x e + d\right)}^{m} B a c d^{2} m^{4} x^{2} e^{4} - 6 \, {\left(x e + d\right)}^{m} A b c d^{2} m^{4} x^{2} e^{4} - 72 \, {\left(x e + d\right)}^{m} B b c d^{2} m^{3} x^{3} e^{4} - 36 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{3} x^{3} e^{4} - 55 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m^{2} x^{4} e^{4} + 24 \, {\left(x e + d\right)}^{m} B b c d^{3} m^{3} x^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m^{3} x^{2} e^{3} + 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m^{2} x^{3} e^{3} - 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{4} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a^{2} m^{5} x^{2} e^{6} + 2 \, {\left(x e + d\right)}^{m} A a b m^{5} x^{2} e^{6} + 36 \, {\left(x e + d\right)}^{m} B a b m^{4} x^{3} e^{6} + 18 \, {\left(x e + d\right)}^{m} A b^{2} m^{4} x^{3} e^{6} + 36 \, {\left(x e + d\right)}^{m} A a c m^{4} x^{3} e^{6} + 107 \, {\left(x e + d\right)}^{m} B b^{2} m^{3} x^{4} e^{6} + 214 \, {\left(x e + d\right)}^{m} B a c m^{3} x^{4} e^{6} + 214 \, {\left(x e + d\right)}^{m} A b c m^{3} x^{4} e^{6} + 520 \, {\left(x e + d\right)}^{m} B b c m^{2} x^{5} e^{6} + 260 \, {\left(x e + d\right)}^{m} A c^{2} m^{2} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} B c^{2} m x^{6} e^{6} + {\left(x e + d\right)}^{m} B a^{2} d m^{5} x e^{5} + 2 \, {\left(x e + d\right)}^{m} A a b d m^{5} x e^{5} + 32 \, {\left(x e + d\right)}^{m} B a b d m^{4} x^{2} e^{5} + 16 \, {\left(x e + d\right)}^{m} A b^{2} d m^{4} x^{2} e^{5} + 32 \, {\left(x e + d\right)}^{m} A a c d m^{4} x^{2} e^{5} + 65 \, {\left(x e + d\right)}^{m} B b^{2} d m^{3} x^{3} e^{5} + 130 \, {\left(x e + d\right)}^{m} B a c d m^{3} x^{3} e^{5} + 130 \, {\left(x e + d\right)}^{m} A b c d m^{3} x^{3} e^{5} + 144 \, {\left(x e + d\right)}^{m} B b c d m^{2} x^{4} e^{5} + 72 \, {\left(x e + d\right)}^{m} A c^{2} d m^{2} x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} B c^{2} d m x^{5} e^{5} - 4 \, {\left(x e + d\right)}^{m} B a b d^{2} m^{4} x e^{4} - 2 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m^{4} x e^{4} - 4 \, {\left(x e + d\right)}^{m} A a c d^{2} m^{4} x e^{4} - 36 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m^{3} x^{2} e^{4} - 72 \, {\left(x e + d\right)}^{m} B a c d^{2} m^{3} x^{2} e^{4} - 72 \, {\left(x e + d\right)}^{m} A b c d^{2} m^{3} x^{2} e^{4} - 160 \, {\left(x e + d\right)}^{m} B b c d^{2} m^{2} x^{3} e^{4} - 80 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m^{2} x^{3} e^{4} - 30 \, {\left(x e + d\right)}^{m} B c^{2} d^{2} m x^{4} e^{4} + 6 \, {\left(x e + d\right)}^{m} B b^{2} d^{3} m^{3} x e^{3} + 12 \, {\left(x e + d\right)}^{m} B a c d^{3} m^{3} x e^{3} + 12 \, {\left(x e + d\right)}^{m} A b c d^{3} m^{3} x e^{3} + 168 \, {\left(x e + d\right)}^{m} B b c d^{3} m^{2} x^{2} e^{3} + 84 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m^{2} x^{2} e^{3} + 40 \, {\left(x e + d\right)}^{m} B c^{2} d^{3} m x^{3} e^{3} - 48 \, {\left(x e + d\right)}^{m} B b c d^{4} m^{2} x e^{2} - 24 \, {\left(x e + d\right)}^{m} A c^{2} d^{4} m^{2} x e^{2} - 60 \, {\left(x e + d\right)}^{m} B c^{2} d^{4} m x^{2} e^{2} + 120 \, {\left(x e + d\right)}^{m} B c^{2} d^{5} m x e + {\left(x e + d\right)}^{m} A a^{2} m^{5} x e^{6} + 19 \, {\left(x e + d\right)}^{m} B a^{2} m^{4} x^{2} e^{6} + 38 \, {\left(x e + d\right)}^{m} A a b m^{4} x^{2} e^{6} + 242 \, {\left(x e + d\right)}^{m} B a b m^{3} x^{3} e^{6} + 121 \, {\left(x e + d\right)}^{m} A b^{2} m^{3} x^{3} e^{6} + 242 \, {\left(x e + d\right)}^{m} A a c m^{3} x^{3} e^{6} + 307 \, {\left(x e + d\right)}^{m} B b^{2} m^{2} x^{4} e^{6} + 614 \, {\left(x e + d\right)}^{m} B a c m^{2} x^{4} e^{6} + 614 \, {\left(x e + d\right)}^{m} A b c m^{2} x^{4} e^{6} + 648 \, {\left(x e + d\right)}^{m} B b c m x^{5} e^{6} + 324 \, {\left(x e + d\right)}^{m} A c^{2} m x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} B c^{2} x^{6} e^{6} + {\left(x e + d\right)}^{m} A a^{2} d m^{5} e^{5} + 18 \, {\left(x e + d\right)}^{m} B a^{2} d m^{4} x e^{5} + 36 \, {\left(x e + d\right)}^{m} A a b d m^{4} x e^{5} + 178 \, {\left(x e + d\right)}^{m} B a b d m^{3} x^{2} e^{5} + 89 \, {\left(x e + d\right)}^{m} A b^{2} d m^{3} x^{2} e^{5} + 178 \, {\left(x e + d\right)}^{m} A a c d m^{3} x^{2} e^{5} + 112 \, {\left(x e + d\right)}^{m} B b^{2} d m^{2} x^{3} e^{5} + 224 \, {\left(x e + d\right)}^{m} B a c d m^{2} x^{3} e^{5} + 224 \, {\left(x e + d\right)}^{m} A b c d m^{2} x^{3} e^{5} + 72 \, {\left(x e + d\right)}^{m} B b c d m x^{4} e^{5} + 36 \, {\left(x e + d\right)}^{m} A c^{2} d m x^{4} e^{5} - {\left(x e + d\right)}^{m} B a^{2} d^{2} m^{4} e^{4} - 2 \, {\left(x e + d\right)}^{m} A a b d^{2} m^{4} e^{4} - 60 \, {\left(x e + d\right)}^{m} B a b d^{2} m^{3} x e^{4} - 30 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m^{3} x e^{4} - 60 \, {\left(x e + d\right)}^{m} A a c d^{2} m^{3} x e^{4} - 123 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m^{2} x^{2} e^{4} - 246 \, {\left(x e + d\right)}^{m} B a c d^{2} m^{2} x^{2} e^{4} - 246 \, {\left(x e + d\right)}^{m} A b c d^{2} m^{2} x^{2} e^{4} - 96 \, {\left(x e + d\right)}^{m} B b c d^{2} m x^{3} e^{4} - 48 \, {\left(x e + d\right)}^{m} A c^{2} d^{2} m x^{3} e^{4} + 4 \, {\left(x e + d\right)}^{m} B a b d^{3} m^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} m^{3} e^{3} + 4 \, {\left(x e + d\right)}^{m} A a c d^{3} m^{3} e^{3} + 66 \, {\left(x e + d\right)}^{m} B b^{2} d^{3} m^{2} x e^{3} + 132 \, {\left(x e + d\right)}^{m} B a c d^{3} m^{2} x e^{3} + 132 \, {\left(x e + d\right)}^{m} A b c d^{3} m^{2} x e^{3} + 144 \, {\left(x e + d\right)}^{m} B b c d^{3} m x^{2} e^{3} + 72 \, {\left(x e + d\right)}^{m} A c^{2} d^{3} m x^{2} e^{3} - 6 \, {\left(x e + d\right)}^{m} B b^{2} d^{4} m^{2} e^{2} - 12 \, {\left(x e + d\right)}^{m} B a c d^{4} m^{2} e^{2} - 12 \, {\left(x e + d\right)}^{m} A b c d^{4} m^{2} e^{2} - 288 \, {\left(x e + d\right)}^{m} B b c d^{4} m x e^{2} - 144 \, {\left(x e + d\right)}^{m} A c^{2} d^{4} m x e^{2} + 48 \, {\left(x e + d\right)}^{m} B b c d^{5} m e + 24 \, {\left(x e + d\right)}^{m} A c^{2} d^{5} m e - 120 \, {\left(x e + d\right)}^{m} B c^{2} d^{6} + 20 \, {\left(x e + d\right)}^{m} A a^{2} m^{4} x e^{6} + 137 \, {\left(x e + d\right)}^{m} B a^{2} m^{3} x^{2} e^{6} + 274 \, {\left(x e + d\right)}^{m} A a b m^{3} x^{2} e^{6} + 744 \, {\left(x e + d\right)}^{m} B a b m^{2} x^{3} e^{6} + 372 \, {\left(x e + d\right)}^{m} A b^{2} m^{2} x^{3} e^{6} + 744 \, {\left(x e + d\right)}^{m} A a c m^{2} x^{3} e^{6} + 396 \, {\left(x e + d\right)}^{m} B b^{2} m x^{4} e^{6} + 792 \, {\left(x e + d\right)}^{m} B a c m x^{4} e^{6} + 792 \, {\left(x e + d\right)}^{m} A b c m x^{4} e^{6} + 288 \, {\left(x e + d\right)}^{m} B b c x^{5} e^{6} + 144 \, {\left(x e + d\right)}^{m} A c^{2} x^{5} e^{6} + 20 \, {\left(x e + d\right)}^{m} A a^{2} d m^{4} e^{5} + 119 \, {\left(x e + d\right)}^{m} B a^{2} d m^{3} x e^{5} + 238 \, {\left(x e + d\right)}^{m} A a b d m^{3} x e^{5} + 388 \, {\left(x e + d\right)}^{m} B a b d m^{2} x^{2} e^{5} + 194 \, {\left(x e + d\right)}^{m} A b^{2} d m^{2} x^{2} e^{5} + 388 \, {\left(x e + d\right)}^{m} A a c d m^{2} x^{2} e^{5} + 60 \, {\left(x e + d\right)}^{m} B b^{2} d m x^{3} e^{5} + 120 \, {\left(x e + d\right)}^{m} B a c d m x^{3} e^{5} + 120 \, {\left(x e + d\right)}^{m} A b c d m x^{3} e^{5} - 18 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} m^{3} e^{4} - 36 \, {\left(x e + d\right)}^{m} A a b d^{2} m^{3} e^{4} - 296 \, {\left(x e + d\right)}^{m} B a b d^{2} m^{2} x e^{4} - 148 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m^{2} x e^{4} - 296 \, {\left(x e + d\right)}^{m} A a c d^{2} m^{2} x e^{4} - 90 \, {\left(x e + d\right)}^{m} B b^{2} d^{2} m x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} B a c d^{2} m x^{2} e^{4} - 180 \, {\left(x e + d\right)}^{m} A b c d^{2} m x^{2} e^{4} + 60 \, {\left(x e + d\right)}^{m} B a b d^{3} m^{2} e^{3} + 30 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} m^{2} e^{3} + 60 \, {\left(x e + d\right)}^{m} A a c d^{3} m^{2} e^{3} + 180 \, {\left(x e + d\right)}^{m} B b^{2} d^{3} m x e^{3} + 360 \, {\left(x e + d\right)}^{m} B a c d^{3} m x e^{3} + 360 \, {\left(x e + d\right)}^{m} A b c d^{3} m x e^{3} - 66 \, {\left(x e + d\right)}^{m} B b^{2} d^{4} m e^{2} - 132 \, {\left(x e + d\right)}^{m} B a c d^{4} m e^{2} - 132 \, {\left(x e + d\right)}^{m} A b c d^{4} m e^{2} + 288 \, {\left(x e + d\right)}^{m} B b c d^{5} e + 144 \, {\left(x e + d\right)}^{m} A c^{2} d^{5} e + 155 \, {\left(x e + d\right)}^{m} A a^{2} m^{3} x e^{6} + 461 \, {\left(x e + d\right)}^{m} B a^{2} m^{2} x^{2} e^{6} + 922 \, {\left(x e + d\right)}^{m} A a b m^{2} x^{2} e^{6} + 1016 \, {\left(x e + d\right)}^{m} B a b m x^{3} e^{6} + 508 \, {\left(x e + d\right)}^{m} A b^{2} m x^{3} e^{6} + 1016 \, {\left(x e + d\right)}^{m} A a c m x^{3} e^{6} + 180 \, {\left(x e + d\right)}^{m} B b^{2} x^{4} e^{6} + 360 \, {\left(x e + d\right)}^{m} B a c x^{4} e^{6} + 360 \, {\left(x e + d\right)}^{m} A b c x^{4} e^{6} + 155 \, {\left(x e + d\right)}^{m} A a^{2} d m^{3} e^{5} + 342 \, {\left(x e + d\right)}^{m} B a^{2} d m^{2} x e^{5} + 684 \, {\left(x e + d\right)}^{m} A a b d m^{2} x e^{5} + 240 \, {\left(x e + d\right)}^{m} B a b d m x^{2} e^{5} + 120 \, {\left(x e + d\right)}^{m} A b^{2} d m x^{2} e^{5} + 240 \, {\left(x e + d\right)}^{m} A a c d m x^{2} e^{5} - 119 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} m^{2} e^{4} - 238 \, {\left(x e + d\right)}^{m} A a b d^{2} m^{2} e^{4} - 480 \, {\left(x e + d\right)}^{m} B a b d^{2} m x e^{4} - 240 \, {\left(x e + d\right)}^{m} A b^{2} d^{2} m x e^{4} - 480 \, {\left(x e + d\right)}^{m} A a c d^{2} m x e^{4} + 296 \, {\left(x e + d\right)}^{m} B a b d^{3} m e^{3} + 148 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} m e^{3} + 296 \, {\left(x e + d\right)}^{m} A a c d^{3} m e^{3} - 180 \, {\left(x e + d\right)}^{m} B b^{2} d^{4} e^{2} - 360 \, {\left(x e + d\right)}^{m} B a c d^{4} e^{2} - 360 \, {\left(x e + d\right)}^{m} A b c d^{4} e^{2} + 580 \, {\left(x e + d\right)}^{m} A a^{2} m^{2} x e^{6} + 702 \, {\left(x e + d\right)}^{m} B a^{2} m x^{2} e^{6} + 1404 \, {\left(x e + d\right)}^{m} A a b m x^{2} e^{6} + 480 \, {\left(x e + d\right)}^{m} B a b x^{3} e^{6} + 240 \, {\left(x e + d\right)}^{m} A b^{2} x^{3} e^{6} + 480 \, {\left(x e + d\right)}^{m} A a c x^{3} e^{6} + 580 \, {\left(x e + d\right)}^{m} A a^{2} d m^{2} e^{5} + 360 \, {\left(x e + d\right)}^{m} B a^{2} d m x e^{5} + 720 \, {\left(x e + d\right)}^{m} A a b d m x e^{5} - 342 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} m e^{4} - 684 \, {\left(x e + d\right)}^{m} A a b d^{2} m e^{4} + 480 \, {\left(x e + d\right)}^{m} B a b d^{3} e^{3} + 240 \, {\left(x e + d\right)}^{m} A b^{2} d^{3} e^{3} + 480 \, {\left(x e + d\right)}^{m} A a c d^{3} e^{3} + 1044 \, {\left(x e + d\right)}^{m} A a^{2} m x e^{6} + 360 \, {\left(x e + d\right)}^{m} B a^{2} x^{2} e^{6} + 720 \, {\left(x e + d\right)}^{m} A a b x^{2} e^{6} + 1044 \, {\left(x e + d\right)}^{m} A a^{2} d m e^{5} - 360 \, {\left(x e + d\right)}^{m} B a^{2} d^{2} e^{4} - 720 \, {\left(x e + d\right)}^{m} A a b d^{2} e^{4} + 720 \, {\left(x e + d\right)}^{m} A a^{2} x e^{6} + 720 \, {\left(x e + d\right)}^{m} A a^{2} d e^{5}}{m^{6} e^{6} + 21 \, m^{5} e^{6} + 175 \, m^{4} e^{6} + 735 \, m^{3} e^{6} + 1624 \, m^{2} e^{6} + 1764 \, m e^{6} + 720 \, e^{6}}"," ",0,"((x*e + d)^m*B*c^2*m^5*x^6*e^6 + (x*e + d)^m*B*c^2*d*m^5*x^5*e^5 + 2*(x*e + d)^m*B*b*c*m^5*x^5*e^6 + (x*e + d)^m*A*c^2*m^5*x^5*e^6 + 15*(x*e + d)^m*B*c^2*m^4*x^6*e^6 + 2*(x*e + d)^m*B*b*c*d*m^5*x^4*e^5 + (x*e + d)^m*A*c^2*d*m^5*x^4*e^5 + 10*(x*e + d)^m*B*c^2*d*m^4*x^5*e^5 - 5*(x*e + d)^m*B*c^2*d^2*m^4*x^4*e^4 + (x*e + d)^m*B*b^2*m^5*x^4*e^6 + 2*(x*e + d)^m*B*a*c*m^5*x^4*e^6 + 2*(x*e + d)^m*A*b*c*m^5*x^4*e^6 + 32*(x*e + d)^m*B*b*c*m^4*x^5*e^6 + 16*(x*e + d)^m*A*c^2*m^4*x^5*e^6 + 85*(x*e + d)^m*B*c^2*m^3*x^6*e^6 + (x*e + d)^m*B*b^2*d*m^5*x^3*e^5 + 2*(x*e + d)^m*B*a*c*d*m^5*x^3*e^5 + 2*(x*e + d)^m*A*b*c*d*m^5*x^3*e^5 + 24*(x*e + d)^m*B*b*c*d*m^4*x^4*e^5 + 12*(x*e + d)^m*A*c^2*d*m^4*x^4*e^5 + 35*(x*e + d)^m*B*c^2*d*m^3*x^5*e^5 - 8*(x*e + d)^m*B*b*c*d^2*m^4*x^3*e^4 - 4*(x*e + d)^m*A*c^2*d^2*m^4*x^3*e^4 - 30*(x*e + d)^m*B*c^2*d^2*m^3*x^4*e^4 + 20*(x*e + d)^m*B*c^2*d^3*m^3*x^3*e^3 + 2*(x*e + d)^m*B*a*b*m^5*x^3*e^6 + (x*e + d)^m*A*b^2*m^5*x^3*e^6 + 2*(x*e + d)^m*A*a*c*m^5*x^3*e^6 + 17*(x*e + d)^m*B*b^2*m^4*x^4*e^6 + 34*(x*e + d)^m*B*a*c*m^4*x^4*e^6 + 34*(x*e + d)^m*A*b*c*m^4*x^4*e^6 + 190*(x*e + d)^m*B*b*c*m^3*x^5*e^6 + 95*(x*e + d)^m*A*c^2*m^3*x^5*e^6 + 225*(x*e + d)^m*B*c^2*m^2*x^6*e^6 + 2*(x*e + d)^m*B*a*b*d*m^5*x^2*e^5 + (x*e + d)^m*A*b^2*d*m^5*x^2*e^5 + 2*(x*e + d)^m*A*a*c*d*m^5*x^2*e^5 + 14*(x*e + d)^m*B*b^2*d*m^4*x^3*e^5 + 28*(x*e + d)^m*B*a*c*d*m^4*x^3*e^5 + 28*(x*e + d)^m*A*b*c*d*m^4*x^3*e^5 + 94*(x*e + d)^m*B*b*c*d*m^3*x^4*e^5 + 47*(x*e + d)^m*A*c^2*d*m^3*x^4*e^5 + 50*(x*e + d)^m*B*c^2*d*m^2*x^5*e^5 - 3*(x*e + d)^m*B*b^2*d^2*m^4*x^2*e^4 - 6*(x*e + d)^m*B*a*c*d^2*m^4*x^2*e^4 - 6*(x*e + d)^m*A*b*c*d^2*m^4*x^2*e^4 - 72*(x*e + d)^m*B*b*c*d^2*m^3*x^3*e^4 - 36*(x*e + d)^m*A*c^2*d^2*m^3*x^3*e^4 - 55*(x*e + d)^m*B*c^2*d^2*m^2*x^4*e^4 + 24*(x*e + d)^m*B*b*c*d^3*m^3*x^2*e^3 + 12*(x*e + d)^m*A*c^2*d^3*m^3*x^2*e^3 + 60*(x*e + d)^m*B*c^2*d^3*m^2*x^3*e^3 - 60*(x*e + d)^m*B*c^2*d^4*m^2*x^2*e^2 + (x*e + d)^m*B*a^2*m^5*x^2*e^6 + 2*(x*e + d)^m*A*a*b*m^5*x^2*e^6 + 36*(x*e + d)^m*B*a*b*m^4*x^3*e^6 + 18*(x*e + d)^m*A*b^2*m^4*x^3*e^6 + 36*(x*e + d)^m*A*a*c*m^4*x^3*e^6 + 107*(x*e + d)^m*B*b^2*m^3*x^4*e^6 + 214*(x*e + d)^m*B*a*c*m^3*x^4*e^6 + 214*(x*e + d)^m*A*b*c*m^3*x^4*e^6 + 520*(x*e + d)^m*B*b*c*m^2*x^5*e^6 + 260*(x*e + d)^m*A*c^2*m^2*x^5*e^6 + 274*(x*e + d)^m*B*c^2*m*x^6*e^6 + (x*e + d)^m*B*a^2*d*m^5*x*e^5 + 2*(x*e + d)^m*A*a*b*d*m^5*x*e^5 + 32*(x*e + d)^m*B*a*b*d*m^4*x^2*e^5 + 16*(x*e + d)^m*A*b^2*d*m^4*x^2*e^5 + 32*(x*e + d)^m*A*a*c*d*m^4*x^2*e^5 + 65*(x*e + d)^m*B*b^2*d*m^3*x^3*e^5 + 130*(x*e + d)^m*B*a*c*d*m^3*x^3*e^5 + 130*(x*e + d)^m*A*b*c*d*m^3*x^3*e^5 + 144*(x*e + d)^m*B*b*c*d*m^2*x^4*e^5 + 72*(x*e + d)^m*A*c^2*d*m^2*x^4*e^5 + 24*(x*e + d)^m*B*c^2*d*m*x^5*e^5 - 4*(x*e + d)^m*B*a*b*d^2*m^4*x*e^4 - 2*(x*e + d)^m*A*b^2*d^2*m^4*x*e^4 - 4*(x*e + d)^m*A*a*c*d^2*m^4*x*e^4 - 36*(x*e + d)^m*B*b^2*d^2*m^3*x^2*e^4 - 72*(x*e + d)^m*B*a*c*d^2*m^3*x^2*e^4 - 72*(x*e + d)^m*A*b*c*d^2*m^3*x^2*e^4 - 160*(x*e + d)^m*B*b*c*d^2*m^2*x^3*e^4 - 80*(x*e + d)^m*A*c^2*d^2*m^2*x^3*e^4 - 30*(x*e + d)^m*B*c^2*d^2*m*x^4*e^4 + 6*(x*e + d)^m*B*b^2*d^3*m^3*x*e^3 + 12*(x*e + d)^m*B*a*c*d^3*m^3*x*e^3 + 12*(x*e + d)^m*A*b*c*d^3*m^3*x*e^3 + 168*(x*e + d)^m*B*b*c*d^3*m^2*x^2*e^3 + 84*(x*e + d)^m*A*c^2*d^3*m^2*x^2*e^3 + 40*(x*e + d)^m*B*c^2*d^3*m*x^3*e^3 - 48*(x*e + d)^m*B*b*c*d^4*m^2*x*e^2 - 24*(x*e + d)^m*A*c^2*d^4*m^2*x*e^2 - 60*(x*e + d)^m*B*c^2*d^4*m*x^2*e^2 + 120*(x*e + d)^m*B*c^2*d^5*m*x*e + (x*e + d)^m*A*a^2*m^5*x*e^6 + 19*(x*e + d)^m*B*a^2*m^4*x^2*e^6 + 38*(x*e + d)^m*A*a*b*m^4*x^2*e^6 + 242*(x*e + d)^m*B*a*b*m^3*x^3*e^6 + 121*(x*e + d)^m*A*b^2*m^3*x^3*e^6 + 242*(x*e + d)^m*A*a*c*m^3*x^3*e^6 + 307*(x*e + d)^m*B*b^2*m^2*x^4*e^6 + 614*(x*e + d)^m*B*a*c*m^2*x^4*e^6 + 614*(x*e + d)^m*A*b*c*m^2*x^4*e^6 + 648*(x*e + d)^m*B*b*c*m*x^5*e^6 + 324*(x*e + d)^m*A*c^2*m*x^5*e^6 + 120*(x*e + d)^m*B*c^2*x^6*e^6 + (x*e + d)^m*A*a^2*d*m^5*e^5 + 18*(x*e + d)^m*B*a^2*d*m^4*x*e^5 + 36*(x*e + d)^m*A*a*b*d*m^4*x*e^5 + 178*(x*e + d)^m*B*a*b*d*m^3*x^2*e^5 + 89*(x*e + d)^m*A*b^2*d*m^3*x^2*e^5 + 178*(x*e + d)^m*A*a*c*d*m^3*x^2*e^5 + 112*(x*e + d)^m*B*b^2*d*m^2*x^3*e^5 + 224*(x*e + d)^m*B*a*c*d*m^2*x^3*e^5 + 224*(x*e + d)^m*A*b*c*d*m^2*x^3*e^5 + 72*(x*e + d)^m*B*b*c*d*m*x^4*e^5 + 36*(x*e + d)^m*A*c^2*d*m*x^4*e^5 - (x*e + d)^m*B*a^2*d^2*m^4*e^4 - 2*(x*e + d)^m*A*a*b*d^2*m^4*e^4 - 60*(x*e + d)^m*B*a*b*d^2*m^3*x*e^4 - 30*(x*e + d)^m*A*b^2*d^2*m^3*x*e^4 - 60*(x*e + d)^m*A*a*c*d^2*m^3*x*e^4 - 123*(x*e + d)^m*B*b^2*d^2*m^2*x^2*e^4 - 246*(x*e + d)^m*B*a*c*d^2*m^2*x^2*e^4 - 246*(x*e + d)^m*A*b*c*d^2*m^2*x^2*e^4 - 96*(x*e + d)^m*B*b*c*d^2*m*x^3*e^4 - 48*(x*e + d)^m*A*c^2*d^2*m*x^3*e^4 + 4*(x*e + d)^m*B*a*b*d^3*m^3*e^3 + 2*(x*e + d)^m*A*b^2*d^3*m^3*e^3 + 4*(x*e + d)^m*A*a*c*d^3*m^3*e^3 + 66*(x*e + d)^m*B*b^2*d^3*m^2*x*e^3 + 132*(x*e + d)^m*B*a*c*d^3*m^2*x*e^3 + 132*(x*e + d)^m*A*b*c*d^3*m^2*x*e^3 + 144*(x*e + d)^m*B*b*c*d^3*m*x^2*e^3 + 72*(x*e + d)^m*A*c^2*d^3*m*x^2*e^3 - 6*(x*e + d)^m*B*b^2*d^4*m^2*e^2 - 12*(x*e + d)^m*B*a*c*d^4*m^2*e^2 - 12*(x*e + d)^m*A*b*c*d^4*m^2*e^2 - 288*(x*e + d)^m*B*b*c*d^4*m*x*e^2 - 144*(x*e + d)^m*A*c^2*d^4*m*x*e^2 + 48*(x*e + d)^m*B*b*c*d^5*m*e + 24*(x*e + d)^m*A*c^2*d^5*m*e - 120*(x*e + d)^m*B*c^2*d^6 + 20*(x*e + d)^m*A*a^2*m^4*x*e^6 + 137*(x*e + d)^m*B*a^2*m^3*x^2*e^6 + 274*(x*e + d)^m*A*a*b*m^3*x^2*e^6 + 744*(x*e + d)^m*B*a*b*m^2*x^3*e^6 + 372*(x*e + d)^m*A*b^2*m^2*x^3*e^6 + 744*(x*e + d)^m*A*a*c*m^2*x^3*e^6 + 396*(x*e + d)^m*B*b^2*m*x^4*e^6 + 792*(x*e + d)^m*B*a*c*m*x^4*e^6 + 792*(x*e + d)^m*A*b*c*m*x^4*e^6 + 288*(x*e + d)^m*B*b*c*x^5*e^6 + 144*(x*e + d)^m*A*c^2*x^5*e^6 + 20*(x*e + d)^m*A*a^2*d*m^4*e^5 + 119*(x*e + d)^m*B*a^2*d*m^3*x*e^5 + 238*(x*e + d)^m*A*a*b*d*m^3*x*e^5 + 388*(x*e + d)^m*B*a*b*d*m^2*x^2*e^5 + 194*(x*e + d)^m*A*b^2*d*m^2*x^2*e^5 + 388*(x*e + d)^m*A*a*c*d*m^2*x^2*e^5 + 60*(x*e + d)^m*B*b^2*d*m*x^3*e^5 + 120*(x*e + d)^m*B*a*c*d*m*x^3*e^5 + 120*(x*e + d)^m*A*b*c*d*m*x^3*e^5 - 18*(x*e + d)^m*B*a^2*d^2*m^3*e^4 - 36*(x*e + d)^m*A*a*b*d^2*m^3*e^4 - 296*(x*e + d)^m*B*a*b*d^2*m^2*x*e^4 - 148*(x*e + d)^m*A*b^2*d^2*m^2*x*e^4 - 296*(x*e + d)^m*A*a*c*d^2*m^2*x*e^4 - 90*(x*e + d)^m*B*b^2*d^2*m*x^2*e^4 - 180*(x*e + d)^m*B*a*c*d^2*m*x^2*e^4 - 180*(x*e + d)^m*A*b*c*d^2*m*x^2*e^4 + 60*(x*e + d)^m*B*a*b*d^3*m^2*e^3 + 30*(x*e + d)^m*A*b^2*d^3*m^2*e^3 + 60*(x*e + d)^m*A*a*c*d^3*m^2*e^3 + 180*(x*e + d)^m*B*b^2*d^3*m*x*e^3 + 360*(x*e + d)^m*B*a*c*d^3*m*x*e^3 + 360*(x*e + d)^m*A*b*c*d^3*m*x*e^3 - 66*(x*e + d)^m*B*b^2*d^4*m*e^2 - 132*(x*e + d)^m*B*a*c*d^4*m*e^2 - 132*(x*e + d)^m*A*b*c*d^4*m*e^2 + 288*(x*e + d)^m*B*b*c*d^5*e + 144*(x*e + d)^m*A*c^2*d^5*e + 155*(x*e + d)^m*A*a^2*m^3*x*e^6 + 461*(x*e + d)^m*B*a^2*m^2*x^2*e^6 + 922*(x*e + d)^m*A*a*b*m^2*x^2*e^6 + 1016*(x*e + d)^m*B*a*b*m*x^3*e^6 + 508*(x*e + d)^m*A*b^2*m*x^3*e^6 + 1016*(x*e + d)^m*A*a*c*m*x^3*e^6 + 180*(x*e + d)^m*B*b^2*x^4*e^6 + 360*(x*e + d)^m*B*a*c*x^4*e^6 + 360*(x*e + d)^m*A*b*c*x^4*e^6 + 155*(x*e + d)^m*A*a^2*d*m^3*e^5 + 342*(x*e + d)^m*B*a^2*d*m^2*x*e^5 + 684*(x*e + d)^m*A*a*b*d*m^2*x*e^5 + 240*(x*e + d)^m*B*a*b*d*m*x^2*e^5 + 120*(x*e + d)^m*A*b^2*d*m*x^2*e^5 + 240*(x*e + d)^m*A*a*c*d*m*x^2*e^5 - 119*(x*e + d)^m*B*a^2*d^2*m^2*e^4 - 238*(x*e + d)^m*A*a*b*d^2*m^2*e^4 - 480*(x*e + d)^m*B*a*b*d^2*m*x*e^4 - 240*(x*e + d)^m*A*b^2*d^2*m*x*e^4 - 480*(x*e + d)^m*A*a*c*d^2*m*x*e^4 + 296*(x*e + d)^m*B*a*b*d^3*m*e^3 + 148*(x*e + d)^m*A*b^2*d^3*m*e^3 + 296*(x*e + d)^m*A*a*c*d^3*m*e^3 - 180*(x*e + d)^m*B*b^2*d^4*e^2 - 360*(x*e + d)^m*B*a*c*d^4*e^2 - 360*(x*e + d)^m*A*b*c*d^4*e^2 + 580*(x*e + d)^m*A*a^2*m^2*x*e^6 + 702*(x*e + d)^m*B*a^2*m*x^2*e^6 + 1404*(x*e + d)^m*A*a*b*m*x^2*e^6 + 480*(x*e + d)^m*B*a*b*x^3*e^6 + 240*(x*e + d)^m*A*b^2*x^3*e^6 + 480*(x*e + d)^m*A*a*c*x^3*e^6 + 580*(x*e + d)^m*A*a^2*d*m^2*e^5 + 360*(x*e + d)^m*B*a^2*d*m*x*e^5 + 720*(x*e + d)^m*A*a*b*d*m*x*e^5 - 342*(x*e + d)^m*B*a^2*d^2*m*e^4 - 684*(x*e + d)^m*A*a*b*d^2*m*e^4 + 480*(x*e + d)^m*B*a*b*d^3*e^3 + 240*(x*e + d)^m*A*b^2*d^3*e^3 + 480*(x*e + d)^m*A*a*c*d^3*e^3 + 1044*(x*e + d)^m*A*a^2*m*x*e^6 + 360*(x*e + d)^m*B*a^2*x^2*e^6 + 720*(x*e + d)^m*A*a*b*x^2*e^6 + 1044*(x*e + d)^m*A*a^2*d*m*e^5 - 360*(x*e + d)^m*B*a^2*d^2*e^4 - 720*(x*e + d)^m*A*a*b*d^2*e^4 + 720*(x*e + d)^m*A*a^2*x*e^6 + 720*(x*e + d)^m*A*a^2*d*e^5)/(m^6*e^6 + 21*m^5*e^6 + 175*m^4*e^6 + 735*m^3*e^6 + 1624*m^2*e^6 + 1764*m*e^6 + 720*e^6)","B",0
2642,1,1162,0,0.223894," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} B c m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} B c d m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} B b m^{3} x^{3} e^{4} + {\left(x e + d\right)}^{m} A c m^{3} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B c m^{2} x^{4} e^{4} + {\left(x e + d\right)}^{m} B b d m^{3} x^{2} e^{3} + {\left(x e + d\right)}^{m} A c d m^{3} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} B c d m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} B c d^{2} m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} B a m^{3} x^{2} e^{4} + {\left(x e + d\right)}^{m} A b m^{3} x^{2} e^{4} + 7 \, {\left(x e + d\right)}^{m} B b m^{2} x^{3} e^{4} + 7 \, {\left(x e + d\right)}^{m} A c m^{2} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} B c m x^{4} e^{4} + {\left(x e + d\right)}^{m} B a d m^{3} x e^{3} + {\left(x e + d\right)}^{m} A b d m^{3} x e^{3} + 5 \, {\left(x e + d\right)}^{m} B b d m^{2} x^{2} e^{3} + 5 \, {\left(x e + d\right)}^{m} A c d m^{2} x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} B c d m x^{3} e^{3} - 2 \, {\left(x e + d\right)}^{m} B b d^{2} m^{2} x e^{2} - 2 \, {\left(x e + d\right)}^{m} A c d^{2} m^{2} x e^{2} - 3 \, {\left(x e + d\right)}^{m} B c d^{2} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} B c d^{3} m x e + {\left(x e + d\right)}^{m} A a m^{3} x e^{4} + 8 \, {\left(x e + d\right)}^{m} B a m^{2} x^{2} e^{4} + 8 \, {\left(x e + d\right)}^{m} A b m^{2} x^{2} e^{4} + 14 \, {\left(x e + d\right)}^{m} B b m x^{3} e^{4} + 14 \, {\left(x e + d\right)}^{m} A c m x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} B c x^{4} e^{4} + {\left(x e + d\right)}^{m} A a d m^{3} e^{3} + 7 \, {\left(x e + d\right)}^{m} B a d m^{2} x e^{3} + 7 \, {\left(x e + d\right)}^{m} A b d m^{2} x e^{3} + 4 \, {\left(x e + d\right)}^{m} B b d m x^{2} e^{3} + 4 \, {\left(x e + d\right)}^{m} A c d m x^{2} e^{3} - {\left(x e + d\right)}^{m} B a d^{2} m^{2} e^{2} - {\left(x e + d\right)}^{m} A b d^{2} m^{2} e^{2} - 8 \, {\left(x e + d\right)}^{m} B b d^{2} m x e^{2} - 8 \, {\left(x e + d\right)}^{m} A c d^{2} m x e^{2} + 2 \, {\left(x e + d\right)}^{m} B b d^{3} m e + 2 \, {\left(x e + d\right)}^{m} A c d^{3} m e - 6 \, {\left(x e + d\right)}^{m} B c d^{4} + 9 \, {\left(x e + d\right)}^{m} A a m^{2} x e^{4} + 19 \, {\left(x e + d\right)}^{m} B a m x^{2} e^{4} + 19 \, {\left(x e + d\right)}^{m} A b m x^{2} e^{4} + 8 \, {\left(x e + d\right)}^{m} B b x^{3} e^{4} + 8 \, {\left(x e + d\right)}^{m} A c x^{3} e^{4} + 9 \, {\left(x e + d\right)}^{m} A a d m^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} B a d m x e^{3} + 12 \, {\left(x e + d\right)}^{m} A b d m x e^{3} - 7 \, {\left(x e + d\right)}^{m} B a d^{2} m e^{2} - 7 \, {\left(x e + d\right)}^{m} A b d^{2} m e^{2} + 8 \, {\left(x e + d\right)}^{m} B b d^{3} e + 8 \, {\left(x e + d\right)}^{m} A c d^{3} e + 26 \, {\left(x e + d\right)}^{m} A a m x e^{4} + 12 \, {\left(x e + d\right)}^{m} B a x^{2} e^{4} + 12 \, {\left(x e + d\right)}^{m} A b x^{2} e^{4} + 26 \, {\left(x e + d\right)}^{m} A a d m e^{3} - 12 \, {\left(x e + d\right)}^{m} B a d^{2} e^{2} - 12 \, {\left(x e + d\right)}^{m} A b d^{2} e^{2} + 24 \, {\left(x e + d\right)}^{m} A a x e^{4} + 24 \, {\left(x e + d\right)}^{m} A a d e^{3}}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"((x*e + d)^m*B*c*m^3*x^4*e^4 + (x*e + d)^m*B*c*d*m^3*x^3*e^3 + (x*e + d)^m*B*b*m^3*x^3*e^4 + (x*e + d)^m*A*c*m^3*x^3*e^4 + 6*(x*e + d)^m*B*c*m^2*x^4*e^4 + (x*e + d)^m*B*b*d*m^3*x^2*e^3 + (x*e + d)^m*A*c*d*m^3*x^2*e^3 + 3*(x*e + d)^m*B*c*d*m^2*x^3*e^3 - 3*(x*e + d)^m*B*c*d^2*m^2*x^2*e^2 + (x*e + d)^m*B*a*m^3*x^2*e^4 + (x*e + d)^m*A*b*m^3*x^2*e^4 + 7*(x*e + d)^m*B*b*m^2*x^3*e^4 + 7*(x*e + d)^m*A*c*m^2*x^3*e^4 + 11*(x*e + d)^m*B*c*m*x^4*e^4 + (x*e + d)^m*B*a*d*m^3*x*e^3 + (x*e + d)^m*A*b*d*m^3*x*e^3 + 5*(x*e + d)^m*B*b*d*m^2*x^2*e^3 + 5*(x*e + d)^m*A*c*d*m^2*x^2*e^3 + 2*(x*e + d)^m*B*c*d*m*x^3*e^3 - 2*(x*e + d)^m*B*b*d^2*m^2*x*e^2 - 2*(x*e + d)^m*A*c*d^2*m^2*x*e^2 - 3*(x*e + d)^m*B*c*d^2*m*x^2*e^2 + 6*(x*e + d)^m*B*c*d^3*m*x*e + (x*e + d)^m*A*a*m^3*x*e^4 + 8*(x*e + d)^m*B*a*m^2*x^2*e^4 + 8*(x*e + d)^m*A*b*m^2*x^2*e^4 + 14*(x*e + d)^m*B*b*m*x^3*e^4 + 14*(x*e + d)^m*A*c*m*x^3*e^4 + 6*(x*e + d)^m*B*c*x^4*e^4 + (x*e + d)^m*A*a*d*m^3*e^3 + 7*(x*e + d)^m*B*a*d*m^2*x*e^3 + 7*(x*e + d)^m*A*b*d*m^2*x*e^3 + 4*(x*e + d)^m*B*b*d*m*x^2*e^3 + 4*(x*e + d)^m*A*c*d*m*x^2*e^3 - (x*e + d)^m*B*a*d^2*m^2*e^2 - (x*e + d)^m*A*b*d^2*m^2*e^2 - 8*(x*e + d)^m*B*b*d^2*m*x*e^2 - 8*(x*e + d)^m*A*c*d^2*m*x*e^2 + 2*(x*e + d)^m*B*b*d^3*m*e + 2*(x*e + d)^m*A*c*d^3*m*e - 6*(x*e + d)^m*B*c*d^4 + 9*(x*e + d)^m*A*a*m^2*x*e^4 + 19*(x*e + d)^m*B*a*m*x^2*e^4 + 19*(x*e + d)^m*A*b*m*x^2*e^4 + 8*(x*e + d)^m*B*b*x^3*e^4 + 8*(x*e + d)^m*A*c*x^3*e^4 + 9*(x*e + d)^m*A*a*d*m^2*e^3 + 12*(x*e + d)^m*B*a*d*m*x*e^3 + 12*(x*e + d)^m*A*b*d*m*x*e^3 - 7*(x*e + d)^m*B*a*d^2*m*e^2 - 7*(x*e + d)^m*A*b*d^2*m*e^2 + 8*(x*e + d)^m*B*b*d^3*e + 8*(x*e + d)^m*A*c*d^3*e + 26*(x*e + d)^m*A*a*m*x*e^4 + 12*(x*e + d)^m*B*a*x^2*e^4 + 12*(x*e + d)^m*A*b*x^2*e^4 + 26*(x*e + d)^m*A*a*d*m*e^3 - 12*(x*e + d)^m*B*a*d^2*e^2 - 12*(x*e + d)^m*A*b*d^2*e^2 + 24*(x*e + d)^m*A*a*x*e^4 + 24*(x*e + d)^m*A*a*d*e^3)/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
2643,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/(c*x^2 + b*x + a), x)","F",0
2644,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^m/(c*x^2 + b*x + a)^2, x)","F",0
2645,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(1+m)/(c*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m + 1}}{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((B*x + A)*(e*x + d)^(m + 1)/(c*x^2 + b*x + a), x)","F",0
2646,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(-3-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 3), x)","F",0
