1,1,29,0,0.356443," ","integrate(x^2*(B*x^2+A)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{1}{9} x^{9} c B + \frac{1}{7} x^{7} b B + \frac{1}{7} x^{7} c A + \frac{1}{5} x^{5} b A"," ",0,"1/9*x^9*c*B + 1/7*x^7*b*B + 1/7*x^7*c*A + 1/5*x^5*b*A","A",0
2,1,29,0,0.349221," ","integrate(x*(B*x^2+A)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{1}{8} x^{8} c B + \frac{1}{6} x^{6} b B + \frac{1}{6} x^{6} c A + \frac{1}{4} x^{4} b A"," ",0,"1/8*x^8*c*B + 1/6*x^6*b*B + 1/6*x^6*c*A + 1/4*x^4*b*A","A",0
3,1,29,0,0.336421," ","integrate((B*x^2+A)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c B + \frac{1}{5} x^{5} b B + \frac{1}{5} x^{5} c A + \frac{1}{3} x^{3} b A"," ",0,"1/7*x^7*c*B + 1/5*x^5*b*B + 1/5*x^5*c*A + 1/3*x^3*b*A","A",0
4,1,27,0,0.374190," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x,x, algorithm=""fricas"")","\frac{1}{6} \, B c x^{6} + \frac{1}{4} \, {\left(B b + A c\right)} x^{4} + \frac{1}{2} \, A b x^{2}"," ",0,"1/6*B*c*x^6 + 1/4*(B*b + A*c)*x^4 + 1/2*A*b*x^2","A",0
5,1,24,0,0.383401," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^2,x, algorithm=""fricas"")","\frac{1}{5} \, B c x^{5} + \frac{1}{3} \, {\left(B b + A c\right)} x^{3} + A b x"," ",0,"1/5*B*c*x^5 + 1/3*(B*b + A*c)*x^3 + A*b*x","A",0
6,1,25,0,0.398401," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^3,x, algorithm=""fricas"")","\frac{1}{4} \, B c x^{4} + \frac{1}{2} \, {\left(B b + A c\right)} x^{2} + A b \log\left(x\right)"," ",0,"1/4*B*c*x^4 + 1/2*(B*b + A*c)*x^2 + A*b*log(x)","A",0
7,1,28,0,0.361472," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^4,x, algorithm=""fricas"")","\frac{B c x^{4} + 3 \, {\left(B b + A c\right)} x^{2} - 3 \, A b}{3 \, x}"," ",0,"1/3*(B*c*x^4 + 3*(B*b + A*c)*x^2 - 3*A*b)/x","A",0
8,1,30,0,0.376321," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^5,x, algorithm=""fricas"")","\frac{B c x^{4} + 2 \, {\left(B b + A c\right)} x^{2} \log\left(x\right) - A b}{2 \, x^{2}}"," ",0,"1/2*(B*c*x^4 + 2*(B*b + A*c)*x^2*log(x) - A*b)/x^2","A",0
9,1,29,0,0.365149," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^6,x, algorithm=""fricas"")","\frac{3 \, B c x^{4} - 3 \, {\left(B b + A c\right)} x^{2} - A b}{3 \, x^{3}}"," ",0,"1/3*(3*B*c*x^4 - 3*(B*b + A*c)*x^2 - A*b)/x^3","A",0
10,1,31,0,0.389176," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^7,x, algorithm=""fricas"")","\frac{4 \, B c x^{4} \log\left(x\right) - 2 \, {\left(B b + A c\right)} x^{2} - A b}{4 \, x^{4}}"," ",0,"1/4*(4*B*c*x^4*log(x) - 2*(B*b + A*c)*x^2 - A*b)/x^4","A",0
11,1,29,0,0.383747," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^8,x, algorithm=""fricas"")","-\frac{15 \, B c x^{4} + 5 \, {\left(B b + A c\right)} x^{2} + 3 \, A b}{15 \, x^{5}}"," ",0,"-1/15*(15*B*c*x^4 + 5*(B*b + A*c)*x^2 + 3*A*b)/x^5","A",0
12,1,53,0,0.339135," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} c^{2} B + \frac{2}{9} x^{9} c b B + \frac{1}{9} x^{9} c^{2} A + \frac{1}{7} x^{7} b^{2} B + \frac{2}{7} x^{7} c b A + \frac{1}{5} x^{5} b^{2} A"," ",0,"1/11*x^11*c^2*B + 2/9*x^9*c*b*B + 1/9*x^9*c^2*A + 1/7*x^7*b^2*B + 2/7*x^7*c*b*A + 1/5*x^5*b^2*A","A",0
13,1,51,0,0.382009," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x,x, algorithm=""fricas"")","\frac{1}{10} \, B c^{2} x^{10} + \frac{1}{8} \, {\left(2 \, B b c + A c^{2}\right)} x^{8} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{6} \, {\left(B b^{2} + 2 \, A b c\right)} x^{6}"," ",0,"1/10*B*c^2*x^10 + 1/8*(2*B*b*c + A*c^2)*x^8 + 1/4*A*b^2*x^4 + 1/6*(B*b^2 + 2*A*b*c)*x^6","A",0
14,1,51,0,0.369460," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^2,x, algorithm=""fricas"")","\frac{1}{9} \, B c^{2} x^{9} + \frac{1}{7} \, {\left(2 \, B b c + A c^{2}\right)} x^{7} + \frac{1}{3} \, A b^{2} x^{3} + \frac{1}{5} \, {\left(B b^{2} + 2 \, A b c\right)} x^{5}"," ",0,"1/9*B*c^2*x^9 + 1/7*(2*B*b*c + A*c^2)*x^7 + 1/3*A*b^2*x^3 + 1/5*(B*b^2 + 2*A*b*c)*x^5","A",0
15,1,51,0,0.367916," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^3,x, algorithm=""fricas"")","\frac{1}{8} \, B c^{2} x^{8} + \frac{1}{6} \, {\left(2 \, B b c + A c^{2}\right)} x^{6} + \frac{1}{2} \, A b^{2} x^{2} + \frac{1}{4} \, {\left(B b^{2} + 2 \, A b c\right)} x^{4}"," ",0,"1/8*B*c^2*x^8 + 1/6*(2*B*b*c + A*c^2)*x^6 + 1/2*A*b^2*x^2 + 1/4*(B*b^2 + 2*A*b*c)*x^4","A",0
16,1,48,0,0.368488," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^4,x, algorithm=""fricas"")","\frac{1}{7} \, B c^{2} x^{7} + \frac{1}{5} \, {\left(2 \, B b c + A c^{2}\right)} x^{5} + A b^{2} x + \frac{1}{3} \, {\left(B b^{2} + 2 \, A b c\right)} x^{3}"," ",0,"1/7*B*c^2*x^7 + 1/5*(2*B*b*c + A*c^2)*x^5 + A*b^2*x + 1/3*(B*b^2 + 2*A*b*c)*x^3","A",0
17,1,49,0,0.394900," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^5,x, algorithm=""fricas"")","\frac{1}{6} \, B c^{2} x^{6} + \frac{1}{4} \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + A b^{2} \log\left(x\right) + \frac{1}{2} \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}"," ",0,"1/6*B*c^2*x^6 + 1/4*(2*B*b*c + A*c^2)*x^4 + A*b^2*log(x) + 1/2*(B*b^2 + 2*A*b*c)*x^2","A",0
18,1,53,0,0.382653," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^6,x, algorithm=""fricas"")","\frac{3 \, B c^{2} x^{6} + 5 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} - 15 \, A b^{2} + 15 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}}{15 \, x}"," ",0,"1/15*(3*B*c^2*x^6 + 5*(2*B*b*c + A*c^2)*x^4 - 15*A*b^2 + 15*(B*b^2 + 2*A*b*c)*x^2)/x","A",0
19,1,54,0,0.393401," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^7,x, algorithm=""fricas"")","\frac{B c^{2} x^{6} + 2 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 4 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2} \log\left(x\right) - 2 \, A b^{2}}{4 \, x^{2}}"," ",0,"1/4*(B*c^2*x^6 + 2*(2*B*b*c + A*c^2)*x^4 + 4*(B*b^2 + 2*A*b*c)*x^2*log(x) - 2*A*b^2)/x^2","A",0
20,1,52,0,0.378983," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^8,x, algorithm=""fricas"")","\frac{B c^{2} x^{6} + 3 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} - A b^{2} - 3 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/3*(B*c^2*x^6 + 3*(2*B*b*c + A*c^2)*x^4 - A*b^2 - 3*(B*b^2 + 2*A*b*c)*x^2)/x^3","A",0
21,1,55,0,0.397308," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^9,x, algorithm=""fricas"")","\frac{2 \, B c^{2} x^{6} + 4 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} \log\left(x\right) - A b^{2} - 2 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}}{4 \, x^{4}}"," ",0,"1/4*(2*B*c^2*x^6 + 4*(2*B*b*c + A*c^2)*x^4*log(x) - A*b^2 - 2*(B*b^2 + 2*A*b*c)*x^2)/x^4","A",0
22,1,53,0,0.366107," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^10,x, algorithm=""fricas"")","\frac{15 \, B c^{2} x^{6} - 15 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} - 3 \, A b^{2} - 5 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}}{15 \, x^{5}}"," ",0,"1/15*(15*B*c^2*x^6 - 15*(2*B*b*c + A*c^2)*x^4 - 3*A*b^2 - 5*(B*b^2 + 2*A*b*c)*x^2)/x^5","A",0
23,1,55,0,0.387348," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^11,x, algorithm=""fricas"")","\frac{12 \, B c^{2} x^{6} \log\left(x\right) - 6 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} - 2 \, A b^{2} - 3 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}}{12 \, x^{6}}"," ",0,"1/12*(12*B*c^2*x^6*log(x) - 6*(2*B*b*c + A*c^2)*x^4 - 2*A*b^2 - 3*(B*b^2 + 2*A*b*c)*x^2)/x^6","A",0
24,1,53,0,0.384128," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^12,x, algorithm=""fricas"")","-\frac{105 \, B c^{2} x^{6} + 35 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 15 \, A b^{2} + 21 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}}{105 \, x^{7}}"," ",0,"-1/105*(105*B*c^2*x^6 + 35*(2*B*b*c + A*c^2)*x^4 + 15*A*b^2 + 21*(B*b^2 + 2*A*b*c)*x^2)/x^7","A",0
25,1,73,0,0.379603," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^2,x, algorithm=""fricas"")","\frac{1}{13} \, B c^{3} x^{13} + \frac{1}{11} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{11} + \frac{1}{3} \, {\left(B b^{2} c + A b c^{2}\right)} x^{9} + \frac{1}{5} \, A b^{3} x^{5} + \frac{1}{7} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{7}"," ",0,"1/13*B*c^3*x^13 + 1/11*(3*B*b*c^2 + A*c^3)*x^11 + 1/3*(B*b^2*c + A*b*c^2)*x^9 + 1/5*A*b^3*x^5 + 1/7*(B*b^3 + 3*A*b^2*c)*x^7","A",0
26,1,73,0,0.380665," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^3,x, algorithm=""fricas"")","\frac{1}{12} \, B c^{3} x^{12} + \frac{1}{10} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{10} + \frac{3}{8} \, {\left(B b^{2} c + A b c^{2}\right)} x^{8} + \frac{1}{4} \, A b^{3} x^{4} + \frac{1}{6} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{6}"," ",0,"1/12*B*c^3*x^12 + 1/10*(3*B*b*c^2 + A*c^3)*x^10 + 3/8*(B*b^2*c + A*b*c^2)*x^8 + 1/4*A*b^3*x^4 + 1/6*(B*b^3 + 3*A*b^2*c)*x^6","A",0
27,1,73,0,0.370662," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^4,x, algorithm=""fricas"")","\frac{1}{11} \, B c^{3} x^{11} + \frac{1}{9} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{9} + \frac{3}{7} \, {\left(B b^{2} c + A b c^{2}\right)} x^{7} + \frac{1}{3} \, A b^{3} x^{3} + \frac{1}{5} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{5}"," ",0,"1/11*B*c^3*x^11 + 1/9*(3*B*b*c^2 + A*c^3)*x^9 + 3/7*(B*b^2*c + A*b*c^2)*x^7 + 1/3*A*b^3*x^3 + 1/5*(B*b^3 + 3*A*b^2*c)*x^5","A",0
28,1,73,0,0.377238," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^5,x, algorithm=""fricas"")","\frac{1}{10} \, B c^{3} x^{10} + \frac{1}{8} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{8} + \frac{1}{2} \, {\left(B b^{2} c + A b c^{2}\right)} x^{6} + \frac{1}{2} \, A b^{3} x^{2} + \frac{1}{4} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{4}"," ",0,"1/10*B*c^3*x^10 + 1/8*(3*B*b*c^2 + A*c^3)*x^8 + 1/2*(B*b^2*c + A*b*c^2)*x^6 + 1/2*A*b^3*x^2 + 1/4*(B*b^3 + 3*A*b^2*c)*x^4","A",0
29,1,70,0,0.364782," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^6,x, algorithm=""fricas"")","\frac{1}{9} \, B c^{3} x^{9} + \frac{1}{7} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{7} + \frac{3}{5} \, {\left(B b^{2} c + A b c^{2}\right)} x^{5} + A b^{3} x + \frac{1}{3} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{3}"," ",0,"1/9*B*c^3*x^9 + 1/7*(3*B*b*c^2 + A*c^3)*x^7 + 3/5*(B*b^2*c + A*b*c^2)*x^5 + A*b^3*x + 1/3*(B*b^3 + 3*A*b^2*c)*x^3","A",0
30,1,71,0,0.382373," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^7,x, algorithm=""fricas"")","\frac{1}{8} \, B c^{3} x^{8} + \frac{1}{6} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + \frac{3}{4} \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} + A b^{3} \log\left(x\right) + \frac{1}{2} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}"," ",0,"1/8*B*c^3*x^8 + 1/6*(3*B*b*c^2 + A*c^3)*x^6 + 3/4*(B*b^2*c + A*b*c^2)*x^4 + A*b^3*log(x) + 1/2*(B*b^3 + 3*A*b^2*c)*x^2","A",0
31,1,75,0,0.386592," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^8,x, algorithm=""fricas"")","\frac{5 \, B c^{3} x^{8} + 7 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 35 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} - 35 \, A b^{3} + 35 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{35 \, x}"," ",0,"1/35*(5*B*c^3*x^8 + 7*(3*B*b*c^2 + A*c^3)*x^6 + 35*(B*b^2*c + A*b*c^2)*x^4 - 35*A*b^3 + 35*(B*b^3 + 3*A*b^2*c)*x^2)/x","A",0
32,1,77,0,0.386332," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^9,x, algorithm=""fricas"")","\frac{2 \, B c^{3} x^{8} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 18 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} - 6 \, A b^{3} + 12 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2} \log\left(x\right)}{12 \, x^{2}}"," ",0,"1/12*(2*B*c^3*x^8 + 3*(3*B*b*c^2 + A*c^3)*x^6 + 18*(B*b^2*c + A*b*c^2)*x^4 - 6*A*b^3 + 12*(B*b^3 + 3*A*b^2*c)*x^2*log(x))/x^2","A",0
33,1,75,0,0.370688," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^10,x, algorithm=""fricas"")","\frac{3 \, B c^{3} x^{8} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 45 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} - 5 \, A b^{3} - 15 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{15 \, x^{3}}"," ",0,"1/15*(3*B*c^3*x^8 + 5*(3*B*b*c^2 + A*c^3)*x^6 + 45*(B*b^2*c + A*b*c^2)*x^4 - 5*A*b^3 - 15*(B*b^3 + 3*A*b^2*c)*x^2)/x^3","A",0
34,1,76,0,0.393573," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^11,x, algorithm=""fricas"")","\frac{B c^{3} x^{8} + 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 12 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} \log\left(x\right) - A b^{3} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{4 \, x^{4}}"," ",0,"1/4*(B*c^3*x^8 + 2*(3*B*b*c^2 + A*c^3)*x^6 + 12*(B*b^2*c + A*b*c^2)*x^4*log(x) - A*b^3 - 2*(B*b^3 + 3*A*b^2*c)*x^2)/x^4","A",0
35,1,75,0,0.384470," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^12,x, algorithm=""fricas"")","\frac{5 \, B c^{3} x^{8} + 15 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} - 45 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} - 3 \, A b^{3} - 5 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{15 \, x^{5}}"," ",0,"1/15*(5*B*c^3*x^8 + 15*(3*B*b*c^2 + A*c^3)*x^6 - 45*(B*b^2*c + A*b*c^2)*x^4 - 3*A*b^3 - 5*(B*b^3 + 3*A*b^2*c)*x^2)/x^5","A",0
36,1,77,0,0.403389," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^13,x, algorithm=""fricas"")","\frac{6 \, B c^{3} x^{8} + 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} \log\left(x\right) - 18 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} - 2 \, A b^{3} - 3 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{12 \, x^{6}}"," ",0,"1/12*(6*B*c^3*x^8 + 12*(3*B*b*c^2 + A*c^3)*x^6*log(x) - 18*(B*b^2*c + A*b*c^2)*x^4 - 2*A*b^3 - 3*(B*b^3 + 3*A*b^2*c)*x^2)/x^6","A",0
37,1,75,0,0.389269," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^14,x, algorithm=""fricas"")","\frac{35 \, B c^{3} x^{8} - 35 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} - 35 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} - 5 \, A b^{3} - 7 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{35 \, x^{7}}"," ",0,"1/35*(35*B*c^3*x^8 - 35*(3*B*b*c^2 + A*c^3)*x^6 - 35*(B*b^2*c + A*b*c^2)*x^4 - 5*A*b^3 - 7*(B*b^3 + 3*A*b^2*c)*x^2)/x^7","A",0
38,1,77,0,0.398734," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^15,x, algorithm=""fricas"")","\frac{24 \, B c^{3} x^{8} \log\left(x\right) - 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} - 18 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} - 3 \, A b^{3} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{24 \, x^{8}}"," ",0,"1/24*(24*B*c^3*x^8*log(x) - 12*(3*B*b*c^2 + A*c^3)*x^6 - 18*(B*b^2*c + A*b*c^2)*x^4 - 3*A*b^3 - 4*(B*b^3 + 3*A*b^2*c)*x^2)/x^8","A",0
39,1,75,0,0.392617," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^16,x, algorithm=""fricas"")","-\frac{315 \, B c^{3} x^{8} + 105 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 189 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} + 35 \, A b^{3} + 45 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{315 \, x^{9}}"," ",0,"-1/315*(315*B*c^3*x^8 + 105*(3*B*b*c^2 + A*c^3)*x^6 + 189*(B*b^2*c + A*b*c^2)*x^4 + 35*A*b^3 + 45*(B*b^3 + 3*A*b^2*c)*x^2)/x^9","A",0
40,1,75,0,0.381520," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^17,x, algorithm=""fricas"")","-\frac{20 \, B c^{3} x^{8} + 10 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 20 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} + 4 \, A b^{3} + 5 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}}{40 \, x^{10}}"," ",0,"-1/40*(20*B*c^3*x^8 + 10*(3*B*b*c^2 + A*c^3)*x^6 + 20*(B*b^2*c + A*b*c^2)*x^4 + 4*A*b^3 + 5*(B*b^3 + 3*A*b^2*c)*x^2)/x^10","A",0
41,1,274,0,0.407645," ","integrate(x^10*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{70 \, B c^{4} x^{9} - 90 \, {\left(B b c^{3} - A c^{4}\right)} x^{7} + 126 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} x^{5} - 210 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} x^{3} - 315 \, {\left(B b^{4} - A b^{3} c\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) + 630 \, {\left(B b^{4} - A b^{3} c\right)} x}{630 \, c^{5}}, \frac{35 \, B c^{4} x^{9} - 45 \, {\left(B b c^{3} - A c^{4}\right)} x^{7} + 63 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} x^{5} - 105 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} x^{3} - 315 \, {\left(B b^{4} - A b^{3} c\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) + 315 \, {\left(B b^{4} - A b^{3} c\right)} x}{315 \, c^{5}}\right]"," ",0,"[1/630*(70*B*c^4*x^9 - 90*(B*b*c^3 - A*c^4)*x^7 + 126*(B*b^2*c^2 - A*b*c^3)*x^5 - 210*(B*b^3*c - A*b^2*c^2)*x^3 - 315*(B*b^4 - A*b^3*c)*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) + 630*(B*b^4 - A*b^3*c)*x)/c^5, 1/315*(35*B*c^4*x^9 - 45*(B*b*c^3 - A*c^4)*x^7 + 63*(B*b^2*c^2 - A*b*c^3)*x^5 - 105*(B*b^3*c - A*b^2*c^2)*x^3 - 315*(B*b^4 - A*b^3*c)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) + 315*(B*b^4 - A*b^3*c)*x)/c^5]","A",0
42,1,98,0,0.387786," ","integrate(x^9*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{3 \, B c^{4} x^{8} - 4 \, {\left(B b c^{3} - A c^{4}\right)} x^{6} + 6 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} x^{4} - 12 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} x^{2} + 12 \, {\left(B b^{4} - A b^{3} c\right)} \log\left(c x^{2} + b\right)}{24 \, c^{5}}"," ",0,"1/24*(3*B*c^4*x^8 - 4*(B*b*c^3 - A*c^4)*x^6 + 6*(B*b^2*c^2 - A*b*c^3)*x^4 - 12*(B*b^3*c - A*b^2*c^2)*x^2 + 12*(B*b^4 - A*b^3*c)*log(c*x^2 + b))/c^5","A",0
43,1,228,0,0.404541," ","integrate(x^8*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{30 \, B c^{3} x^{7} - 42 \, {\left(B b c^{2} - A c^{3}\right)} x^{5} + 70 \, {\left(B b^{2} c - A b c^{2}\right)} x^{3} - 105 \, {\left(B b^{3} - A b^{2} c\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) - 210 \, {\left(B b^{3} - A b^{2} c\right)} x}{210 \, c^{4}}, \frac{15 \, B c^{3} x^{7} - 21 \, {\left(B b c^{2} - A c^{3}\right)} x^{5} + 35 \, {\left(B b^{2} c - A b c^{2}\right)} x^{3} + 105 \, {\left(B b^{3} - A b^{2} c\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - 105 \, {\left(B b^{3} - A b^{2} c\right)} x}{105 \, c^{4}}\right]"," ",0,"[1/210*(30*B*c^3*x^7 - 42*(B*b*c^2 - A*c^3)*x^5 + 70*(B*b^2*c - A*b*c^2)*x^3 - 105*(B*b^3 - A*b^2*c)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) - 210*(B*b^3 - A*b^2*c)*x)/c^4, 1/105*(15*B*c^3*x^7 - 21*(B*b*c^2 - A*c^3)*x^5 + 35*(B*b^2*c - A*b*c^2)*x^3 + 105*(B*b^3 - A*b^2*c)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - 105*(B*b^3 - A*b^2*c)*x)/c^4]","A",0
44,1,75,0,0.392524," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2 \, B c^{3} x^{6} - 3 \, {\left(B b c^{2} - A c^{3}\right)} x^{4} + 6 \, {\left(B b^{2} c - A b c^{2}\right)} x^{2} - 6 \, {\left(B b^{3} - A b^{2} c\right)} \log\left(c x^{2} + b\right)}{12 \, c^{4}}"," ",0,"1/12*(2*B*c^3*x^6 - 3*(B*b*c^2 - A*c^3)*x^4 + 6*(B*b^2*c - A*b*c^2)*x^2 - 6*(B*b^3 - A*b^2*c)*log(c*x^2 + b))/c^4","A",0
45,1,178,0,0.411743," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{6 \, B c^{2} x^{5} - 10 \, {\left(B b c - A c^{2}\right)} x^{3} - 15 \, {\left(B b^{2} - A b c\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) + 30 \, {\left(B b^{2} - A b c\right)} x}{30 \, c^{3}}, \frac{3 \, B c^{2} x^{5} - 5 \, {\left(B b c - A c^{2}\right)} x^{3} - 15 \, {\left(B b^{2} - A b c\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) + 15 \, {\left(B b^{2} - A b c\right)} x}{15 \, c^{3}}\right]"," ",0,"[1/30*(6*B*c^2*x^5 - 10*(B*b*c - A*c^2)*x^3 - 15*(B*b^2 - A*b*c)*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) + 30*(B*b^2 - A*b*c)*x)/c^3, 1/15*(3*B*c^2*x^5 - 5*(B*b*c - A*c^2)*x^3 - 15*(B*b^2 - A*b*c)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) + 15*(B*b^2 - A*b*c)*x)/c^3]","A",0
46,1,51,0,0.391333," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{B c^{2} x^{4} - 2 \, {\left(B b c - A c^{2}\right)} x^{2} + 2 \, {\left(B b^{2} - A b c\right)} \log\left(c x^{2} + b\right)}{4 \, c^{3}}"," ",0,"1/4*(B*c^2*x^4 - 2*(B*b*c - A*c^2)*x^2 + 2*(B*b^2 - A*b*c)*log(c*x^2 + b))/c^3","A",0
47,1,129,0,0.398081," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{2 \, B c x^{3} - 3 \, {\left(B b - A c\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) - 6 \, {\left(B b - A c\right)} x}{6 \, c^{2}}, \frac{B c x^{3} + 3 \, {\left(B b - A c\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - 3 \, {\left(B b - A c\right)} x}{3 \, c^{2}}\right]"," ",0,"[1/6*(2*B*c*x^3 - 3*(B*b - A*c)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) - 6*(B*b - A*c)*x)/c^2, 1/3*(B*c*x^3 + 3*(B*b - A*c)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - 3*(B*b - A*c)*x)/c^2]","A",0
48,1,30,0,0.386460," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{B c x^{2} - {\left(B b - A c\right)} \log\left(c x^{2} + b\right)}{2 \, c^{2}}"," ",0,"1/2*(B*c*x^2 - (B*b - A*c)*log(c*x^2 + b))/c^2","A",0
49,1,99,0,0.408187," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{2 \, B b c x + {\left(B b - A c\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{2 \, b c^{2}}, \frac{B b c x - {\left(B b - A c\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{b c^{2}}\right]"," ",0,"[1/2*(2*B*b*c*x + (B*b - A*c)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b*c^2), (B*b*c*x - (B*b - A*c)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b*c^2)]","A",0
50,1,32,0,0.392051," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2 \, A c \log\left(x\right) + {\left(B b - A c\right)} \log\left(c x^{2} + b\right)}{2 \, b c}"," ",0,"1/2*(2*A*c*log(x) + (B*b - A*c)*log(c*x^2 + b))/(b*c)","A",0
51,1,105,0,0.397194," ","integrate((B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{{\left(B b - A c\right)} \sqrt{-b c} x \log\left(\frac{c x^{2} + 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right) - 2 \, A b c}{2 \, b^{2} c x}, \frac{{\left(B b - A c\right)} \sqrt{b c} x \arctan\left(\frac{\sqrt{b c} x}{b}\right) - A b c}{b^{2} c x}\right]"," ",0,"[1/2*((B*b - A*c)*sqrt(-b*c)*x*log((c*x^2 + 2*sqrt(-b*c)*x - b)/(c*x^2 + b)) - 2*A*b*c)/(b^2*c*x), ((B*b - A*c)*sqrt(b*c)*x*arctan(sqrt(b*c)*x/b) - A*b*c)/(b^2*c*x)]","A",0
52,1,103,0,0.419268," ","integrate((B*x^2+A)/(-c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{{\left(B b + A c\right)} \sqrt{b c} x \log\left(\frac{c x^{2} + 2 \, \sqrt{b c} x + b}{c x^{2} - b}\right) - 2 \, A b c}{2 \, b^{2} c x}, -\frac{{\left(B b + A c\right)} \sqrt{-b c} x \arctan\left(\frac{\sqrt{-b c} x}{b}\right) + A b c}{b^{2} c x}\right]"," ",0,"[1/2*((B*b + A*c)*sqrt(b*c)*x*log((c*x^2 + 2*sqrt(b*c)*x + b)/(c*x^2 - b)) - 2*A*b*c)/(b^2*c*x), -((B*b + A*c)*sqrt(-b*c)*x*arctan(sqrt(-b*c)*x/b) + A*b*c)/(b^2*c*x)]","A",0
53,1,47,0,0.400688," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{{\left(B b - A c\right)} x^{2} \log\left(c x^{2} + b\right) - 2 \, {\left(B b - A c\right)} x^{2} \log\left(x\right) + A b}{2 \, b^{2} x^{2}}"," ",0,"-1/2*((B*b - A*c)*x^2*log(c*x^2 + b) - 2*(B*b - A*c)*x^2*log(x) + A*b)/(b^2*x^2)","A",0
54,1,135,0,0.406725," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b - A c\right)} x^{3} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} + 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) + 6 \, {\left(B b - A c\right)} x^{2} + 2 \, A b}{6 \, b^{2} x^{3}}, -\frac{3 \, {\left(B b - A c\right)} x^{3} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) + 3 \, {\left(B b - A c\right)} x^{2} + A b}{3 \, b^{2} x^{3}}\right]"," ",0,"[-1/6*(3*(B*b - A*c)*x^3*sqrt(-c/b)*log((c*x^2 + 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) + 6*(B*b - A*c)*x^2 + 2*A*b)/(b^2*x^3), -1/3*(3*(B*b - A*c)*x^3*sqrt(c/b)*arctan(x*sqrt(c/b)) + 3*(B*b - A*c)*x^2 + A*b)/(b^2*x^3)]","A",0
55,1,73,0,0.408757," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b c - A c^{2}\right)} x^{4} \log\left(c x^{2} + b\right) - 4 \, {\left(B b c - A c^{2}\right)} x^{4} \log\left(x\right) - A b^{2} - 2 \, {\left(B b^{2} - A b c\right)} x^{2}}{4 \, b^{3} x^{4}}"," ",0,"1/4*(2*(B*b*c - A*c^2)*x^4*log(c*x^2 + b) - 4*(B*b*c - A*c^2)*x^4*log(x) - A*b^2 - 2*(B*b^2 - A*b*c)*x^2)/(b^3*x^4)","A",0
56,1,184,0,0.405596," ","integrate((B*x^2+A)/x^4/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b c - A c^{2}\right)} x^{5} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) - 30 \, {\left(B b c - A c^{2}\right)} x^{4} + 6 \, A b^{2} + 10 \, {\left(B b^{2} - A b c\right)} x^{2}}{30 \, b^{3} x^{5}}, \frac{15 \, {\left(B b c - A c^{2}\right)} x^{5} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) + 15 \, {\left(B b c - A c^{2}\right)} x^{4} - 3 \, A b^{2} - 5 \, {\left(B b^{2} - A b c\right)} x^{2}}{15 \, b^{3} x^{5}}\right]"," ",0,"[-1/30*(15*(B*b*c - A*c^2)*x^5*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) - 30*(B*b*c - A*c^2)*x^4 + 6*A*b^2 + 10*(B*b^2 - A*b*c)*x^2)/(b^3*x^5), 1/15*(15*(B*b*c - A*c^2)*x^5*sqrt(c/b)*arctan(x*sqrt(c/b)) + 15*(B*b*c - A*c^2)*x^4 - 3*A*b^2 - 5*(B*b^2 - A*b*c)*x^2)/(b^3*x^5)]","A",0
57,1,98,0,0.394521," ","integrate((B*x^2+A)/x^5/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{6 \, {\left(B b c^{2} - A c^{3}\right)} x^{6} \log\left(c x^{2} + b\right) - 12 \, {\left(B b c^{2} - A c^{3}\right)} x^{6} \log\left(x\right) - 6 \, {\left(B b^{2} c - A b c^{2}\right)} x^{4} + 2 \, A b^{3} + 3 \, {\left(B b^{3} - A b^{2} c\right)} x^{2}}{12 \, b^{4} x^{6}}"," ",0,"-1/12*(6*(B*b*c^2 - A*c^3)*x^6*log(c*x^2 + b) - 12*(B*b*c^2 - A*c^3)*x^6*log(x) - 6*(B*b^2*c - A*b*c^2)*x^4 + 2*A*b^3 + 3*(B*b^3 - A*b^2*c)*x^2)/(b^4*x^6)","A",0
58,1,350,0,0.400011," ","integrate(x^12*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{60 \, B c^{4} x^{9} - 12 \, {\left(9 \, B b c^{3} - 7 \, A c^{4}\right)} x^{7} + 28 \, {\left(9 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{5} - 140 \, {\left(9 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{3} - 105 \, {\left(9 \, B b^{4} - 7 \, A b^{3} c + {\left(9 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) - 210 \, {\left(9 \, B b^{4} - 7 \, A b^{3} c\right)} x}{420 \, {\left(c^{6} x^{2} + b c^{5}\right)}}, \frac{30 \, B c^{4} x^{9} - 6 \, {\left(9 \, B b c^{3} - 7 \, A c^{4}\right)} x^{7} + 14 \, {\left(9 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{5} - 70 \, {\left(9 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{3} + 105 \, {\left(9 \, B b^{4} - 7 \, A b^{3} c + {\left(9 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - 105 \, {\left(9 \, B b^{4} - 7 \, A b^{3} c\right)} x}{210 \, {\left(c^{6} x^{2} + b c^{5}\right)}}\right]"," ",0,"[1/420*(60*B*c^4*x^9 - 12*(9*B*b*c^3 - 7*A*c^4)*x^7 + 28*(9*B*b^2*c^2 - 7*A*b*c^3)*x^5 - 140*(9*B*b^3*c - 7*A*b^2*c^2)*x^3 - 105*(9*B*b^4 - 7*A*b^3*c + (9*B*b^3*c - 7*A*b^2*c^2)*x^2)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) - 210*(9*B*b^4 - 7*A*b^3*c)*x)/(c^6*x^2 + b*c^5), 1/210*(30*B*c^4*x^9 - 6*(9*B*b*c^3 - 7*A*c^4)*x^7 + 14*(9*B*b^2*c^2 - 7*A*b*c^3)*x^5 - 70*(9*B*b^3*c - 7*A*b^2*c^2)*x^3 + 105*(9*B*b^4 - 7*A*b^3*c + (9*B*b^3*c - 7*A*b^2*c^2)*x^2)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - 105*(9*B*b^4 - 7*A*b^3*c)*x)/(c^6*x^2 + b*c^5)]","A",0
59,1,148,0,0.383524," ","integrate(x^11*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2 \, B c^{4} x^{8} - {\left(4 \, B b c^{3} - 3 \, A c^{4}\right)} x^{6} - 6 \, B b^{4} + 6 \, A b^{3} c + 3 \, {\left(4 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} x^{4} + 6 \, {\left(3 \, B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{2} - 6 \, {\left(4 \, B b^{4} - 3 \, A b^{3} c + {\left(4 \, B b^{3} c - 3 \, A b^{2} c^{2}\right)} x^{2}\right)} \log\left(c x^{2} + b\right)}{12 \, {\left(c^{6} x^{2} + b c^{5}\right)}}"," ",0,"1/12*(2*B*c^4*x^8 - (4*B*b*c^3 - 3*A*c^4)*x^6 - 6*B*b^4 + 6*A*b^3*c + 3*(4*B*b^2*c^2 - 3*A*b*c^3)*x^4 + 6*(3*B*b^3*c - 2*A*b^2*c^2)*x^2 - 6*(4*B*b^4 - 3*A*b^3*c + (4*B*b^3*c - 3*A*b^2*c^2)*x^2)*log(c*x^2 + b))/(c^6*x^2 + b*c^5)","A",0
60,1,298,0,0.410050," ","integrate(x^10*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, B c^{3} x^{7} - 4 \, {\left(7 \, B b c^{2} - 5 \, A c^{3}\right)} x^{5} + 20 \, {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{3} - 15 \, {\left(7 \, B b^{3} - 5 \, A b^{2} c + {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) + 30 \, {\left(7 \, B b^{3} - 5 \, A b^{2} c\right)} x}{60 \, {\left(c^{5} x^{2} + b c^{4}\right)}}, \frac{6 \, B c^{3} x^{7} - 2 \, {\left(7 \, B b c^{2} - 5 \, A c^{3}\right)} x^{5} + 10 \, {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{3} - 15 \, {\left(7 \, B b^{3} - 5 \, A b^{2} c + {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) + 15 \, {\left(7 \, B b^{3} - 5 \, A b^{2} c\right)} x}{30 \, {\left(c^{5} x^{2} + b c^{4}\right)}}\right]"," ",0,"[1/60*(12*B*c^3*x^7 - 4*(7*B*b*c^2 - 5*A*c^3)*x^5 + 20*(7*B*b^2*c - 5*A*b*c^2)*x^3 - 15*(7*B*b^3 - 5*A*b^2*c + (7*B*b^2*c - 5*A*b*c^2)*x^2)*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) + 30*(7*B*b^3 - 5*A*b^2*c)*x)/(c^5*x^2 + b*c^4), 1/30*(6*B*c^3*x^7 - 2*(7*B*b*c^2 - 5*A*c^3)*x^5 + 10*(7*B*b^2*c - 5*A*b*c^2)*x^3 - 15*(7*B*b^3 - 5*A*b^2*c + (7*B*b^2*c - 5*A*b*c^2)*x^2)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) + 15*(7*B*b^3 - 5*A*b^2*c)*x)/(c^5*x^2 + b*c^4)]","A",0
61,1,121,0,0.382937," ","integrate(x^9*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{B c^{3} x^{6} - {\left(3 \, B b c^{2} - 2 \, A c^{3}\right)} x^{4} + 2 \, B b^{3} - 2 \, A b^{2} c - 2 \, {\left(2 \, B b^{2} c - A b c^{2}\right)} x^{2} + 2 \, {\left(3 \, B b^{3} - 2 \, A b^{2} c + {\left(3 \, B b^{2} c - 2 \, A b c^{2}\right)} x^{2}\right)} \log\left(c x^{2} + b\right)}{4 \, {\left(c^{5} x^{2} + b c^{4}\right)}}"," ",0,"1/4*(B*c^3*x^6 - (3*B*b*c^2 - 2*A*c^3)*x^4 + 2*B*b^3 - 2*A*b^2*c - 2*(2*B*b^2*c - A*b*c^2)*x^2 + 2*(3*B*b^3 - 2*A*b^2*c + (3*B*b^2*c - 2*A*b*c^2)*x^2)*log(c*x^2 + b))/(c^5*x^2 + b*c^4)","A",0
62,1,240,0,0.408856," ","integrate(x^8*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, B c^{2} x^{5} - 4 \, {\left(5 \, B b c - 3 \, A c^{2}\right)} x^{3} - 3 \, {\left(5 \, B b^{2} - 3 \, A b c + {\left(5 \, B b c - 3 \, A c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) - 6 \, {\left(5 \, B b^{2} - 3 \, A b c\right)} x}{12 \, {\left(c^{4} x^{2} + b c^{3}\right)}}, \frac{2 \, B c^{2} x^{5} - 2 \, {\left(5 \, B b c - 3 \, A c^{2}\right)} x^{3} + 3 \, {\left(5 \, B b^{2} - 3 \, A b c + {\left(5 \, B b c - 3 \, A c^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - 3 \, {\left(5 \, B b^{2} - 3 \, A b c\right)} x}{6 \, {\left(c^{4} x^{2} + b c^{3}\right)}}\right]"," ",0,"[1/12*(4*B*c^2*x^5 - 4*(5*B*b*c - 3*A*c^2)*x^3 - 3*(5*B*b^2 - 3*A*b*c + (5*B*b*c - 3*A*c^2)*x^2)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) - 6*(5*B*b^2 - 3*A*b*c)*x)/(c^4*x^2 + b*c^3), 1/6*(2*B*c^2*x^5 - 2*(5*B*b*c - 3*A*c^2)*x^3 + 3*(5*B*b^2 - 3*A*b*c + (5*B*b*c - 3*A*c^2)*x^2)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - 3*(5*B*b^2 - 3*A*b*c)*x)/(c^4*x^2 + b*c^3)]","A",0
63,1,81,0,0.394930," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{B c^{2} x^{4} + B b c x^{2} - B b^{2} + A b c - {\left(2 \, B b^{2} - A b c + {\left(2 \, B b c - A c^{2}\right)} x^{2}\right)} \log\left(c x^{2} + b\right)}{2 \, {\left(c^{4} x^{2} + b c^{3}\right)}}"," ",0,"1/2*(B*c^2*x^4 + B*b*c*x^2 - B*b^2 + A*b*c - (2*B*b^2 - A*b*c + (2*B*b*c - A*c^2)*x^2)*log(c*x^2 + b))/(c^4*x^2 + b*c^3)","A",0
64,1,208,0,0.421504," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, B b c^{2} x^{3} + {\left(3 \, B b^{2} - A b c + {\left(3 \, B b c - A c^{2}\right)} x^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right) + 2 \, {\left(3 \, B b^{2} c - A b c^{2}\right)} x}{4 \, {\left(b c^{4} x^{2} + b^{2} c^{3}\right)}}, \frac{2 \, B b c^{2} x^{3} - {\left(3 \, B b^{2} - A b c + {\left(3 \, B b c - A c^{2}\right)} x^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right) + {\left(3 \, B b^{2} c - A b c^{2}\right)} x}{2 \, {\left(b c^{4} x^{2} + b^{2} c^{3}\right)}}\right]"," ",0,"[1/4*(4*B*b*c^2*x^3 + (3*B*b^2 - A*b*c + (3*B*b*c - A*c^2)*x^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)) + 2*(3*B*b^2*c - A*b*c^2)*x)/(b*c^4*x^2 + b^2*c^3), 1/2*(2*B*b*c^2*x^3 - (3*B*b^2 - A*b*c + (3*B*b*c - A*c^2)*x^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b) + (3*B*b^2*c - A*b*c^2)*x)/(b*c^4*x^2 + b^2*c^3)]","A",0
65,1,44,0,0.388911," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{B b - A c + {\left(B c x^{2} + B b\right)} \log\left(c x^{2} + b\right)}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}}"," ",0,"1/2*(B*b - A*c + (B*c*x^2 + B*b)*log(c*x^2 + b))/(c^3*x^2 + b*c^2)","A",0
66,1,182,0,0.395164," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(B b^{2} + A b c + {\left(B b c + A c^{2}\right)} x^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right) + 2 \, {\left(B b^{2} c - A b c^{2}\right)} x}{4 \, {\left(b^{2} c^{3} x^{2} + b^{3} c^{2}\right)}}, \frac{{\left(B b^{2} + A b c + {\left(B b c + A c^{2}\right)} x^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right) - {\left(B b^{2} c - A b c^{2}\right)} x}{2 \, {\left(b^{2} c^{3} x^{2} + b^{3} c^{2}\right)}}\right]"," ",0,"[-1/4*((B*b^2 + A*b*c + (B*b*c + A*c^2)*x^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)) + 2*(B*b^2*c - A*b*c^2)*x)/(b^2*c^3*x^2 + b^3*c^2), 1/2*((B*b^2 + A*b*c + (B*b*c + A*c^2)*x^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b) - (B*b^2*c - A*b*c^2)*x)/(b^2*c^3*x^2 + b^3*c^2)]","A",0
67,1,70,0,0.382776," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{B b^{2} - A b c + {\left(A c^{2} x^{2} + A b c\right)} \log\left(c x^{2} + b\right) - 2 \, {\left(A c^{2} x^{2} + A b c\right)} \log\left(x\right)}{2 \, {\left(b^{2} c^{2} x^{2} + b^{3} c\right)}}"," ",0,"-1/2*(B*b^2 - A*b*c + (A*c^2*x^2 + A*b*c)*log(c*x^2 + b) - 2*(A*c^2*x^2 + A*b*c)*log(x))/(b^2*c^2*x^2 + b^3*c)","A",0
68,1,210,0,0.409061," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, A b^{2} c - 2 \, {\left(B b^{2} c - 3 \, A b c^{2}\right)} x^{2} - {\left({\left(B b c - 3 \, A c^{2}\right)} x^{3} + {\left(B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{4 \, {\left(b^{3} c^{2} x^{3} + b^{4} c x\right)}}, -\frac{2 \, A b^{2} c - {\left(B b^{2} c - 3 \, A b c^{2}\right)} x^{2} - {\left({\left(B b c - 3 \, A c^{2}\right)} x^{3} + {\left(B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{2 \, {\left(b^{3} c^{2} x^{3} + b^{4} c x\right)}}\right]"," ",0,"[-1/4*(4*A*b^2*c - 2*(B*b^2*c - 3*A*b*c^2)*x^2 - ((B*b*c - 3*A*c^2)*x^3 + (B*b^2 - 3*A*b*c)*x)*sqrt(-b*c)*log((c*x^2 + 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b^3*c^2*x^3 + b^4*c*x), -1/2*(2*A*b^2*c - (B*b^2*c - 3*A*b*c^2)*x^2 - ((B*b*c - 3*A*c^2)*x^3 + (B*b^2 - 3*A*b*c)*x)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b^3*c^2*x^3 + b^4*c*x)]","A",0
69,1,117,0,0.379449," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{A b^{2} - {\left(B b^{2} - 2 \, A b c\right)} x^{2} + {\left({\left(B b c - 2 \, A c^{2}\right)} x^{4} + {\left(B b^{2} - 2 \, A b c\right)} x^{2}\right)} \log\left(c x^{2} + b\right) - 2 \, {\left({\left(B b c - 2 \, A c^{2}\right)} x^{4} + {\left(B b^{2} - 2 \, A b c\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{3} c x^{4} + b^{4} x^{2}\right)}}"," ",0,"-1/2*(A*b^2 - (B*b^2 - 2*A*b*c)*x^2 + ((B*b*c - 2*A*c^2)*x^4 + (B*b^2 - 2*A*b*c)*x^2)*log(c*x^2 + b) - 2*((B*b*c - 2*A*c^2)*x^4 + (B*b^2 - 2*A*b*c)*x^2)*log(x))/(b^3*c*x^4 + b^4*x^2)","A",0
70,1,250,0,0.406926," ","integrate((B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(3 \, B b c - 5 \, A c^{2}\right)} x^{4} + 4 \, A b^{2} + 4 \, {\left(3 \, B b^{2} - 5 \, A b c\right)} x^{2} + 3 \, {\left({\left(3 \, B b c - 5 \, A c^{2}\right)} x^{5} + {\left(3 \, B b^{2} - 5 \, A b c\right)} x^{3}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} + 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right)}{12 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}, -\frac{3 \, {\left(3 \, B b c - 5 \, A c^{2}\right)} x^{4} + 2 \, A b^{2} + 2 \, {\left(3 \, B b^{2} - 5 \, A b c\right)} x^{2} + 3 \, {\left({\left(3 \, B b c - 5 \, A c^{2}\right)} x^{5} + {\left(3 \, B b^{2} - 5 \, A b c\right)} x^{3}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right)}{6 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}\right]"," ",0,"[-1/12*(6*(3*B*b*c - 5*A*c^2)*x^4 + 4*A*b^2 + 4*(3*B*b^2 - 5*A*b*c)*x^2 + 3*((3*B*b*c - 5*A*c^2)*x^5 + (3*B*b^2 - 5*A*b*c)*x^3)*sqrt(-c/b)*log((c*x^2 + 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)))/(b^3*c*x^5 + b^4*x^3), -1/6*(3*(3*B*b*c - 5*A*c^2)*x^4 + 2*A*b^2 + 2*(3*B*b^2 - 5*A*b*c)*x^2 + 3*((3*B*b*c - 5*A*c^2)*x^5 + (3*B*b^2 - 5*A*b*c)*x^3)*sqrt(c/b)*arctan(x*sqrt(c/b)))/(b^3*c*x^5 + b^4*x^3)]","A",0
71,1,154,0,0.399166," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, B b^{2} c - 3 \, A b c^{2}\right)} x^{4} + A b^{3} + {\left(2 \, B b^{3} - 3 \, A b^{2} c\right)} x^{2} - 2 \, {\left({\left(2 \, B b c^{2} - 3 \, A c^{3}\right)} x^{6} + {\left(2 \, B b^{2} c - 3 \, A b c^{2}\right)} x^{4}\right)} \log\left(c x^{2} + b\right) + 4 \, {\left({\left(2 \, B b c^{2} - 3 \, A c^{3}\right)} x^{6} + {\left(2 \, B b^{2} c - 3 \, A b c^{2}\right)} x^{4}\right)} \log\left(x\right)}{4 \, {\left(b^{4} c x^{6} + b^{5} x^{4}\right)}}"," ",0,"-1/4*(2*(2*B*b^2*c - 3*A*b*c^2)*x^4 + A*b^3 + (2*B*b^3 - 3*A*b^2*c)*x^2 - 2*((2*B*b*c^2 - 3*A*c^3)*x^6 + (2*B*b^2*c - 3*A*b*c^2)*x^4)*log(c*x^2 + b) + 4*((2*B*b*c^2 - 3*A*c^3)*x^6 + (2*B*b^2*c - 3*A*b*c^2)*x^4)*log(x))/(b^4*c*x^6 + b^5*x^4)","A",0
72,1,308,0,0.422307," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{30 \, {\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{6} + 20 \, {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{4} - 12 \, A b^{3} - 4 \, {\left(5 \, B b^{3} - 7 \, A b^{2} c\right)} x^{2} - 15 \, {\left({\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{7} + {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{5}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right)}{60 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}, \frac{15 \, {\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{6} + 10 \, {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{4} - 6 \, A b^{3} - 2 \, {\left(5 \, B b^{3} - 7 \, A b^{2} c\right)} x^{2} + 15 \, {\left({\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{7} + {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{5}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right)}{30 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}\right]"," ",0,"[1/60*(30*(5*B*b*c^2 - 7*A*c^3)*x^6 + 20*(5*B*b^2*c - 7*A*b*c^2)*x^4 - 12*A*b^3 - 4*(5*B*b^3 - 7*A*b^2*c)*x^2 - 15*((5*B*b*c^2 - 7*A*c^3)*x^7 + (5*B*b^2*c - 7*A*b*c^2)*x^5)*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)))/(b^4*c*x^7 + b^5*x^5), 1/30*(15*(5*B*b*c^2 - 7*A*c^3)*x^6 + 10*(5*B*b^2*c - 7*A*b*c^2)*x^4 - 6*A*b^3 - 2*(5*B*b^3 - 7*A*b^2*c)*x^2 + 15*((5*B*b*c^2 - 7*A*c^3)*x^7 + (5*B*b^2*c - 7*A*b*c^2)*x^5)*sqrt(c/b)*arctan(x*sqrt(c/b)))/(b^4*c*x^7 + b^5*x^5)]","A",0
73,1,416,0,0.400964," ","integrate(x^14*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{48 \, B c^{4} x^{9} - 16 \, {\left(9 \, B b c^{3} - 5 \, A c^{4}\right)} x^{7} + 112 \, {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{5} + 350 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x^{3} - 105 \, {\left(9 \, B b^{4} - 5 \, A b^{3} c + {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{4} + 2 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) + 210 \, {\left(9 \, B b^{4} - 5 \, A b^{3} c\right)} x}{240 \, {\left(c^{7} x^{4} + 2 \, b c^{6} x^{2} + b^{2} c^{5}\right)}}, \frac{24 \, B c^{4} x^{9} - 8 \, {\left(9 \, B b c^{3} - 5 \, A c^{4}\right)} x^{7} + 56 \, {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{5} + 175 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x^{3} - 105 \, {\left(9 \, B b^{4} - 5 \, A b^{3} c + {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{4} + 2 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) + 105 \, {\left(9 \, B b^{4} - 5 \, A b^{3} c\right)} x}{120 \, {\left(c^{7} x^{4} + 2 \, b c^{6} x^{2} + b^{2} c^{5}\right)}}\right]"," ",0,"[1/240*(48*B*c^4*x^9 - 16*(9*B*b*c^3 - 5*A*c^4)*x^7 + 112*(9*B*b^2*c^2 - 5*A*b*c^3)*x^5 + 350*(9*B*b^3*c - 5*A*b^2*c^2)*x^3 - 105*(9*B*b^4 - 5*A*b^3*c + (9*B*b^2*c^2 - 5*A*b*c^3)*x^4 + 2*(9*B*b^3*c - 5*A*b^2*c^2)*x^2)*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) + 210*(9*B*b^4 - 5*A*b^3*c)*x)/(c^7*x^4 + 2*b*c^6*x^2 + b^2*c^5), 1/120*(24*B*c^4*x^9 - 8*(9*B*b*c^3 - 5*A*c^4)*x^7 + 56*(9*B*b^2*c^2 - 5*A*b*c^3)*x^5 + 175*(9*B*b^3*c - 5*A*b^2*c^2)*x^3 - 105*(9*B*b^4 - 5*A*b^3*c + (9*B*b^2*c^2 - 5*A*b*c^3)*x^4 + 2*(9*B*b^3*c - 5*A*b^2*c^2)*x^2)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) + 105*(9*B*b^4 - 5*A*b^3*c)*x)/(c^7*x^4 + 2*b*c^6*x^2 + b^2*c^5)]","A",0
74,1,179,0,0.374475," ","integrate(x^13*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{B c^{4} x^{8} - 2 \, {\left(2 \, B b c^{3} - A c^{4}\right)} x^{6} + 7 \, B b^{4} - 5 \, A b^{3} c - {\left(11 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} x^{4} + 2 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{2} + 6 \, {\left(2 \, B b^{4} - A b^{3} c + {\left(2 \, B b^{2} c^{2} - A b c^{3}\right)} x^{4} + 2 \, {\left(2 \, B b^{3} c - A b^{2} c^{2}\right)} x^{2}\right)} \log\left(c x^{2} + b\right)}{4 \, {\left(c^{7} x^{4} + 2 \, b c^{6} x^{2} + b^{2} c^{5}\right)}}"," ",0,"1/4*(B*c^4*x^8 - 2*(2*B*b*c^3 - A*c^4)*x^6 + 7*B*b^4 - 5*A*b^3*c - (11*B*b^2*c^2 - 4*A*b*c^3)*x^4 + 2*(B*b^3*c - 2*A*b^2*c^2)*x^2 + 6*(2*B*b^4 - A*b^3*c + (2*B*b^2*c^2 - A*b*c^3)*x^4 + 2*(2*B*b^3*c - A*b^2*c^2)*x^2)*log(c*x^2 + b))/(c^7*x^4 + 2*b*c^6*x^2 + b^2*c^5)","A",0
75,1,358,0,0.409584," ","integrate(x^12*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, B c^{3} x^{7} - 16 \, {\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{5} - 50 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x^{3} - 15 \, {\left({\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{4} + 7 \, B b^{3} - 3 \, A b^{2} c + 2 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) - 30 \, {\left(7 \, B b^{3} - 3 \, A b^{2} c\right)} x}{48 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}}, \frac{8 \, B c^{3} x^{7} - 8 \, {\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{5} - 25 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x^{3} + 15 \, {\left({\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{4} + 7 \, B b^{3} - 3 \, A b^{2} c + 2 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - 15 \, {\left(7 \, B b^{3} - 3 \, A b^{2} c\right)} x}{24 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}}\right]"," ",0,"[1/48*(16*B*c^3*x^7 - 16*(7*B*b*c^2 - 3*A*c^3)*x^5 - 50*(7*B*b^2*c - 3*A*b*c^2)*x^3 - 15*((7*B*b*c^2 - 3*A*c^3)*x^4 + 7*B*b^3 - 3*A*b^2*c + 2*(7*B*b^2*c - 3*A*b*c^2)*x^2)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) - 30*(7*B*b^3 - 3*A*b^2*c)*x)/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4), 1/24*(8*B*c^3*x^7 - 8*(7*B*b*c^2 - 3*A*c^3)*x^5 - 25*(7*B*b^2*c - 3*A*b*c^2)*x^3 + 15*((7*B*b*c^2 - 3*A*c^3)*x^4 + 7*B*b^3 - 3*A*b^2*c + 2*(7*B*b^2*c - 3*A*b*c^2)*x^2)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - 15*(7*B*b^3 - 3*A*b^2*c)*x)/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)]","A",0
76,1,142,0,0.396925," ","integrate(x^11*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, B c^{3} x^{6} + 4 \, B b c^{2} x^{4} - 5 \, B b^{3} + 3 \, A b^{2} c - 4 \, {\left(B b^{2} c - A b c^{2}\right)} x^{2} - 2 \, {\left({\left(3 \, B b c^{2} - A c^{3}\right)} x^{4} + 3 \, B b^{3} - A b^{2} c + 2 \, {\left(3 \, B b^{2} c - A b c^{2}\right)} x^{2}\right)} \log\left(c x^{2} + b\right)}{4 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}}"," ",0,"1/4*(2*B*c^3*x^6 + 4*B*b*c^2*x^4 - 5*B*b^3 + 3*A*b^2*c - 4*(B*b^2*c - A*b*c^2)*x^2 - 2*((3*B*b*c^2 - A*c^3)*x^4 + 3*B*b^3 - A*b^2*c + 2*(3*B*b^2*c - A*b*c^2)*x^2)*log(c*x^2 + b))/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)","A",0
77,1,328,0,0.426092," ","integrate(x^10*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, B b c^{3} x^{5} + 10 \, {\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x^{3} + 3 \, {\left({\left(5 \, B b c^{2} - A c^{3}\right)} x^{4} + 5 \, B b^{3} - A b^{2} c + 2 \, {\left(5 \, B b^{2} c - A b c^{2}\right)} x^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right) + 6 \, {\left(5 \, B b^{3} c - A b^{2} c^{2}\right)} x}{16 \, {\left(b c^{6} x^{4} + 2 \, b^{2} c^{5} x^{2} + b^{3} c^{4}\right)}}, \frac{8 \, B b c^{3} x^{5} + 5 \, {\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x^{3} - 3 \, {\left({\left(5 \, B b c^{2} - A c^{3}\right)} x^{4} + 5 \, B b^{3} - A b^{2} c + 2 \, {\left(5 \, B b^{2} c - A b c^{2}\right)} x^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right) + 3 \, {\left(5 \, B b^{3} c - A b^{2} c^{2}\right)} x}{8 \, {\left(b c^{6} x^{4} + 2 \, b^{2} c^{5} x^{2} + b^{3} c^{4}\right)}}\right]"," ",0,"[1/16*(16*B*b*c^3*x^5 + 10*(5*B*b^2*c^2 - A*b*c^3)*x^3 + 3*((5*B*b*c^2 - A*c^3)*x^4 + 5*B*b^3 - A*b^2*c + 2*(5*B*b^2*c - A*b*c^2)*x^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)) + 6*(5*B*b^3*c - A*b^2*c^2)*x)/(b*c^6*x^4 + 2*b^2*c^5*x^2 + b^3*c^4), 1/8*(8*B*b*c^3*x^5 + 5*(5*B*b^2*c^2 - A*b*c^3)*x^3 - 3*((5*B*b*c^2 - A*c^3)*x^4 + 5*B*b^3 - A*b^2*c + 2*(5*B*b^2*c - A*b*c^2)*x^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b) + 3*(5*B*b^3*c - A*b^2*c^2)*x)/(b*c^6*x^4 + 2*b^2*c^5*x^2 + b^3*c^4)]","A",0
78,1,89,0,0.388211," ","integrate(x^9*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{3 \, B b^{2} - A b c + 2 \, {\left(2 \, B b c - A c^{2}\right)} x^{2} + 2 \, {\left(B c^{2} x^{4} + 2 \, B b c x^{2} + B b^{2}\right)} \log\left(c x^{2} + b\right)}{4 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}}"," ",0,"1/4*(3*B*b^2 - A*b*c + 2*(2*B*b*c - A*c^2)*x^2 + 2*(B*c^2*x^4 + 2*B*b*c*x^2 + B*b^2)*log(c*x^2 + b))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)","A",0
79,1,301,0,0.411259," ","integrate(x^8*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x^{3} + {\left({\left(3 \, B b c^{2} + A c^{3}\right)} x^{4} + 3 \, B b^{3} + A b^{2} c + 2 \, {\left(3 \, B b^{2} c + A b c^{2}\right)} x^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right) + 2 \, {\left(3 \, B b^{3} c + A b^{2} c^{2}\right)} x}{16 \, {\left(b^{2} c^{5} x^{4} + 2 \, b^{3} c^{4} x^{2} + b^{4} c^{3}\right)}}, -\frac{{\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x^{3} - {\left({\left(3 \, B b c^{2} + A c^{3}\right)} x^{4} + 3 \, B b^{3} + A b^{2} c + 2 \, {\left(3 \, B b^{2} c + A b c^{2}\right)} x^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right) + {\left(3 \, B b^{3} c + A b^{2} c^{2}\right)} x}{8 \, {\left(b^{2} c^{5} x^{4} + 2 \, b^{3} c^{4} x^{2} + b^{4} c^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*B*b^2*c^2 - A*b*c^3)*x^3 + ((3*B*b*c^2 + A*c^3)*x^4 + 3*B*b^3 + A*b^2*c + 2*(3*B*b^2*c + A*b*c^2)*x^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)) + 2*(3*B*b^3*c + A*b^2*c^2)*x)/(b^2*c^5*x^4 + 2*b^3*c^4*x^2 + b^4*c^3), -1/8*((5*B*b^2*c^2 - A*b*c^3)*x^3 - ((3*B*b*c^2 + A*c^3)*x^4 + 3*B*b^3 + A*b^2*c + 2*(3*B*b^2*c + A*b*c^2)*x^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b) + (3*B*b^3*c + A*b^2*c^2)*x)/(b^2*c^5*x^4 + 2*b^3*c^4*x^2 + b^4*c^3)]","A",0
80,1,42,0,0.385025," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{2 \, B c x^{2} + B b + A c}{4 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}}"," ",0,"-1/4*(2*B*c*x^2 + B*b + A*c)/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)","A",0
81,1,300,0,0.419702," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} x^{3} - {\left({\left(B b c^{2} + 3 \, A c^{3}\right)} x^{4} + B b^{3} + 3 \, A b^{2} c + 2 \, {\left(B b^{2} c + 3 \, A b c^{2}\right)} x^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right) - 2 \, {\left(B b^{3} c - 5 \, A b^{2} c^{2}\right)} x}{16 \, {\left(b^{3} c^{4} x^{4} + 2 \, b^{4} c^{3} x^{2} + b^{5} c^{2}\right)}}, \frac{{\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} x^{3} + {\left({\left(B b c^{2} + 3 \, A c^{3}\right)} x^{4} + B b^{3} + 3 \, A b^{2} c + 2 \, {\left(B b^{2} c + 3 \, A b c^{2}\right)} x^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right) - {\left(B b^{3} c - 5 \, A b^{2} c^{2}\right)} x}{8 \, {\left(b^{3} c^{4} x^{4} + 2 \, b^{4} c^{3} x^{2} + b^{5} c^{2}\right)}}\right]"," ",0,"[1/16*(2*(B*b^2*c^2 + 3*A*b*c^3)*x^3 - ((B*b*c^2 + 3*A*c^3)*x^4 + B*b^3 + 3*A*b^2*c + 2*(B*b^2*c + 3*A*b*c^2)*x^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)) - 2*(B*b^3*c - 5*A*b^2*c^2)*x)/(b^3*c^4*x^4 + 2*b^4*c^3*x^2 + b^5*c^2), 1/8*((B*b^2*c^2 + 3*A*b*c^3)*x^3 + ((B*b*c^2 + 3*A*c^3)*x^4 + B*b^3 + 3*A*b^2*c + 2*(B*b^2*c + 3*A*b*c^2)*x^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b) - (B*b^3*c - 5*A*b^2*c^2)*x)/(b^3*c^4*x^4 + 2*b^4*c^3*x^2 + b^5*c^2)]","A",0
82,1,119,0,0.403737," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, A b c^{2} x^{2} - B b^{3} + 3 \, A b^{2} c - 2 \, {\left(A c^{3} x^{4} + 2 \, A b c^{2} x^{2} + A b^{2} c\right)} \log\left(c x^{2} + b\right) + 4 \, {\left(A c^{3} x^{4} + 2 \, A b c^{2} x^{2} + A b^{2} c\right)} \log\left(x\right)}{4 \, {\left(b^{3} c^{3} x^{4} + 2 \, b^{4} c^{2} x^{2} + b^{5} c\right)}}"," ",0,"1/4*(2*A*b*c^2*x^2 - B*b^3 + 3*A*b^2*c - 2*(A*c^3*x^4 + 2*A*b*c^2*x^2 + A*b^2*c)*log(c*x^2 + b) + 4*(A*c^3*x^4 + 2*A*b*c^2*x^2 + A*b^2*c)*log(x))/(b^3*c^3*x^4 + 2*b^4*c^2*x^2 + b^5*c)","A",0
83,1,324,0,0.423532," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, A b^{3} c - 6 \, {\left(B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{4} - 10 \, {\left(B b^{3} c - 5 \, A b^{2} c^{2}\right)} x^{2} - 3 \, {\left({\left(B b c^{2} - 5 \, A c^{3}\right)} x^{5} + 2 \, {\left(B b^{2} c - 5 \, A b c^{2}\right)} x^{3} + {\left(B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{16 \, {\left(b^{4} c^{3} x^{5} + 2 \, b^{5} c^{2} x^{3} + b^{6} c x\right)}}, -\frac{8 \, A b^{3} c - 3 \, {\left(B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{4} - 5 \, {\left(B b^{3} c - 5 \, A b^{2} c^{2}\right)} x^{2} - 3 \, {\left({\left(B b c^{2} - 5 \, A c^{3}\right)} x^{5} + 2 \, {\left(B b^{2} c - 5 \, A b c^{2}\right)} x^{3} + {\left(B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{8 \, {\left(b^{4} c^{3} x^{5} + 2 \, b^{5} c^{2} x^{3} + b^{6} c x\right)}}\right]"," ",0,"[-1/16*(16*A*b^3*c - 6*(B*b^2*c^2 - 5*A*b*c^3)*x^4 - 10*(B*b^3*c - 5*A*b^2*c^2)*x^2 - 3*((B*b*c^2 - 5*A*c^3)*x^5 + 2*(B*b^2*c - 5*A*b*c^2)*x^3 + (B*b^3 - 5*A*b^2*c)*x)*sqrt(-b*c)*log((c*x^2 + 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b^4*c^3*x^5 + 2*b^5*c^2*x^3 + b^6*c*x), -1/8*(8*A*b^3*c - 3*(B*b^2*c^2 - 5*A*b*c^3)*x^4 - 5*(B*b^3*c - 5*A*b^2*c^2)*x^2 - 3*((B*b*c^2 - 5*A*c^3)*x^5 + 2*(B*b^2*c - 5*A*b*c^2)*x^3 + (B*b^3 - 5*A*b^2*c)*x)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b^4*c^3*x^5 + 2*b^5*c^2*x^3 + b^6*c*x)]","A",0
84,1,197,0,0.395567," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{2} c - 3 \, A b c^{2}\right)} x^{4} - 2 \, A b^{3} + 3 \, {\left(B b^{3} - 3 \, A b^{2} c\right)} x^{2} - 2 \, {\left({\left(B b c^{2} - 3 \, A c^{3}\right)} x^{6} + 2 \, {\left(B b^{2} c - 3 \, A b c^{2}\right)} x^{4} + {\left(B b^{3} - 3 \, A b^{2} c\right)} x^{2}\right)} \log\left(c x^{2} + b\right) + 4 \, {\left({\left(B b c^{2} - 3 \, A c^{3}\right)} x^{6} + 2 \, {\left(B b^{2} c - 3 \, A b c^{2}\right)} x^{4} + {\left(B b^{3} - 3 \, A b^{2} c\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(b^{4} c^{2} x^{6} + 2 \, b^{5} c x^{4} + b^{6} x^{2}\right)}}"," ",0,"1/4*(2*(B*b^2*c - 3*A*b*c^2)*x^4 - 2*A*b^3 + 3*(B*b^3 - 3*A*b^2*c)*x^2 - 2*((B*b*c^2 - 3*A*c^3)*x^6 + 2*(B*b^2*c - 3*A*b*c^2)*x^4 + (B*b^3 - 3*A*b^2*c)*x^2)*log(c*x^2 + b) + 4*((B*b*c^2 - 3*A*c^3)*x^6 + 2*(B*b^2*c - 3*A*b*c^2)*x^4 + (B*b^3 - 3*A*b^2*c)*x^2)*log(x))/(b^4*c^2*x^6 + 2*b^5*c*x^4 + b^6*x^2)","B",0
85,1,368,0,0.414173," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[-\frac{30 \, {\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{6} + 50 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{4} + 16 \, A b^{3} + 16 \, {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x^{2} + 15 \, {\left({\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{7} + 2 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{5} + {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x^{3}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} + 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right)}{48 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)}}, -\frac{15 \, {\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{6} + 25 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{4} + 8 \, A b^{3} + 8 \, {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x^{2} + 15 \, {\left({\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{7} + 2 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{5} + {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x^{3}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right)}{24 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)}}\right]"," ",0,"[-1/48*(30*(3*B*b*c^2 - 7*A*c^3)*x^6 + 50*(3*B*b^2*c - 7*A*b*c^2)*x^4 + 16*A*b^3 + 16*(3*B*b^3 - 7*A*b^2*c)*x^2 + 15*((3*B*b*c^2 - 7*A*c^3)*x^7 + 2*(3*B*b^2*c - 7*A*b*c^2)*x^5 + (3*B*b^3 - 7*A*b^2*c)*x^3)*sqrt(-c/b)*log((c*x^2 + 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)))/(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3), -1/24*(15*(3*B*b*c^2 - 7*A*c^3)*x^6 + 25*(3*B*b^2*c - 7*A*b*c^2)*x^4 + 8*A*b^3 + 8*(3*B*b^3 - 7*A*b^2*c)*x^2 + 15*((3*B*b*c^2 - 7*A*c^3)*x^7 + 2*(3*B*b^2*c - 7*A*b*c^2)*x^5 + (3*B*b^3 - 7*A*b^2*c)*x^3)*sqrt(c/b)*arctan(x*sqrt(c/b)))/(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)]","A",0
86,1,229,0,0.413246," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{6} + A b^{4} + 9 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{4} + 2 \, {\left(B b^{4} - 2 \, A b^{3} c\right)} x^{2} - 6 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} x^{8} + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{6} + {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{4}\right)} \log\left(c x^{2} + b\right) + 12 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} x^{8} + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{6} + {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{4}\right)} \log\left(x\right)}{4 \, {\left(b^{5} c^{2} x^{8} + 2 \, b^{6} c x^{6} + b^{7} x^{4}\right)}}"," ",0,"-1/4*(6*(B*b^2*c^2 - 2*A*b*c^3)*x^6 + A*b^4 + 9*(B*b^3*c - 2*A*b^2*c^2)*x^4 + 2*(B*b^4 - 2*A*b^3*c)*x^2 - 6*((B*b*c^3 - 2*A*c^4)*x^8 + 2*(B*b^2*c^2 - 2*A*b*c^3)*x^6 + (B*b^3*c - 2*A*b^2*c^2)*x^4)*log(c*x^2 + b) + 12*((B*b*c^3 - 2*A*c^4)*x^8 + 2*(B*b^2*c^2 - 2*A*b*c^3)*x^6 + (B*b^3*c - 2*A*b^2*c^2)*x^4)*log(x))/(b^5*c^2*x^8 + 2*b^6*c*x^6 + b^7*x^4)","B",0
87,1,426,0,0.427322," ","integrate((B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{210 \, {\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{8} + 350 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{6} - 48 \, A b^{4} + 112 \, {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{4} - 16 \, {\left(5 \, B b^{4} - 9 \, A b^{3} c\right)} x^{2} - 105 \, {\left({\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{9} + 2 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{7} + {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{5}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right)}{240 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)}}, \frac{105 \, {\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{8} + 175 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{6} - 24 \, A b^{4} + 56 \, {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{4} - 8 \, {\left(5 \, B b^{4} - 9 \, A b^{3} c\right)} x^{2} + 105 \, {\left({\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{9} + 2 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{7} + {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{5}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right)}{120 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)}}\right]"," ",0,"[1/240*(210*(5*B*b*c^3 - 9*A*c^4)*x^8 + 350*(5*B*b^2*c^2 - 9*A*b*c^3)*x^6 - 48*A*b^4 + 112*(5*B*b^3*c - 9*A*b^2*c^2)*x^4 - 16*(5*B*b^4 - 9*A*b^3*c)*x^2 - 105*((5*B*b*c^3 - 9*A*c^4)*x^9 + 2*(5*B*b^2*c^2 - 9*A*b*c^3)*x^7 + (5*B*b^3*c - 9*A*b^2*c^2)*x^5)*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)))/(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5), 1/120*(105*(5*B*b*c^3 - 9*A*c^4)*x^8 + 175*(5*B*b^2*c^2 - 9*A*b*c^3)*x^6 - 24*A*b^4 + 56*(5*B*b^3*c - 9*A*b^2*c^2)*x^4 - 8*(5*B*b^4 - 9*A*b^3*c)*x^2 + 105*((5*B*b*c^3 - 9*A*c^4)*x^9 + 2*(5*B*b^2*c^2 - 9*A*b*c^3)*x^7 + (5*B*b^3*c - 9*A*b^2*c^2)*x^5)*sqrt(c/b)*arctan(x*sqrt(c/b)))/(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)]","A",0
88,1,267,0,0.406632," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{12 \, {\left(3 \, B b^{2} c^{3} - 5 \, A b c^{4}\right)} x^{8} + 18 \, {\left(3 \, B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} x^{6} - 2 \, A b^{5} + 4 \, {\left(3 \, B b^{4} c - 5 \, A b^{3} c^{2}\right)} x^{4} - {\left(3 \, B b^{5} - 5 \, A b^{4} c\right)} x^{2} - 12 \, {\left({\left(3 \, B b c^{4} - 5 \, A c^{5}\right)} x^{10} + 2 \, {\left(3 \, B b^{2} c^{3} - 5 \, A b c^{4}\right)} x^{8} + {\left(3 \, B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} x^{6}\right)} \log\left(c x^{2} + b\right) + 24 \, {\left({\left(3 \, B b c^{4} - 5 \, A c^{5}\right)} x^{10} + 2 \, {\left(3 \, B b^{2} c^{3} - 5 \, A b c^{4}\right)} x^{8} + {\left(3 \, B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} x^{6}\right)} \log\left(x\right)}{12 \, {\left(b^{6} c^{2} x^{10} + 2 \, b^{7} c x^{8} + b^{8} x^{6}\right)}}"," ",0,"1/12*(12*(3*B*b^2*c^3 - 5*A*b*c^4)*x^8 + 18*(3*B*b^3*c^2 - 5*A*b^2*c^3)*x^6 - 2*A*b^5 + 4*(3*B*b^4*c - 5*A*b^3*c^2)*x^4 - (3*B*b^5 - 5*A*b^4*c)*x^2 - 12*((3*B*b*c^4 - 5*A*c^5)*x^10 + 2*(3*B*b^2*c^3 - 5*A*b*c^4)*x^8 + (3*B*b^3*c^2 - 5*A*b^2*c^3)*x^6)*log(c*x^2 + b) + 24*((3*B*b*c^4 - 5*A*c^5)*x^10 + 2*(3*B*b^2*c^3 - 5*A*b*c^4)*x^8 + (3*B*b^3*c^2 - 5*A*b^2*c^3)*x^6)*log(x))/(b^6*c^2*x^10 + 2*b^7*c*x^8 + b^8*x^6)","A",0
89,1,368,0,0.572948," ","integrate(x^7*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(1280 \, B c^{6} x^{10} + 128 \, {\left(B b c^{5} + 12 \, A c^{6}\right)} x^{8} + 315 \, B b^{5} c - 420 \, A b^{4} c^{2} - 48 \, {\left(3 \, B b^{2} c^{4} - 4 \, A b c^{5}\right)} x^{6} + 56 \, {\left(3 \, B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} x^{4} - 70 \, {\left(3 \, B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{30720 \, c^{6}}, \frac{105 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(1280 \, B c^{6} x^{10} + 128 \, {\left(B b c^{5} + 12 \, A c^{6}\right)} x^{8} + 315 \, B b^{5} c - 420 \, A b^{4} c^{2} - 48 \, {\left(3 \, B b^{2} c^{4} - 4 \, A b c^{5}\right)} x^{6} + 56 \, {\left(3 \, B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} x^{4} - 70 \, {\left(3 \, B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15360 \, c^{6}}\right]"," ",0,"[-1/30720*(105*(3*B*b^6 - 4*A*b^5*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(1280*B*c^6*x^10 + 128*(B*b*c^5 + 12*A*c^6)*x^8 + 315*B*b^5*c - 420*A*b^4*c^2 - 48*(3*B*b^2*c^4 - 4*A*b*c^5)*x^6 + 56*(3*B*b^3*c^3 - 4*A*b^2*c^4)*x^4 - 70*(3*B*b^4*c^2 - 4*A*b^3*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^6, 1/15360*(105*(3*B*b^6 - 4*A*b^5*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (1280*B*c^6*x^10 + 128*(B*b*c^5 + 12*A*c^6)*x^8 + 315*B*b^5*c - 420*A*b^4*c^2 - 48*(3*B*b^2*c^4 - 4*A*b*c^5)*x^6 + 56*(3*B*b^3*c^3 - 4*A*b^2*c^4)*x^4 - 70*(3*B*b^4*c^2 - 4*A*b^3*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^6]","A",0
90,1,321,0,0.486602," ","integrate(x^5*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(384 \, B c^{5} x^{8} + 48 \, {\left(B b c^{4} + 10 \, A c^{5}\right)} x^{6} - 105 \, B b^{4} c + 150 \, A b^{3} c^{2} - 8 \, {\left(7 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{4} + 10 \, {\left(7 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{7680 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(384 \, B c^{5} x^{8} + 48 \, {\left(B b c^{4} + 10 \, A c^{5}\right)} x^{6} - 105 \, B b^{4} c + 150 \, A b^{3} c^{2} - 8 \, {\left(7 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{4} + 10 \, {\left(7 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{3840 \, c^{5}}\right]"," ",0,"[-1/7680*(15*(7*B*b^5 - 10*A*b^4*c)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(384*B*c^5*x^8 + 48*(B*b*c^4 + 10*A*c^5)*x^6 - 105*B*b^4*c + 150*A*b^3*c^2 - 8*(7*B*b^2*c^3 - 10*A*b*c^4)*x^4 + 10*(7*B*b^3*c^2 - 10*A*b^2*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^5, -1/3840*(15*(7*B*b^5 - 10*A*b^4*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (384*B*c^5*x^8 + 48*(B*b*c^4 + 10*A*c^5)*x^6 - 105*B*b^4*c + 150*A*b^3*c^2 - 8*(7*B*b^2*c^3 - 10*A*b*c^4)*x^4 + 10*(7*B*b^3*c^2 - 10*A*b^2*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^5]","A",0
91,1,272,0,0.460581," ","integrate(x^3*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} x^{6} + 15 \, B b^{3} c - 24 \, A b^{2} c^{2} + 8 \, {\left(B b c^{3} + 8 \, A c^{4}\right)} x^{4} - 2 \, {\left(5 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{768 \, c^{4}}, \frac{3 \, {\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(48 \, B c^{4} x^{6} + 15 \, B b^{3} c - 24 \, A b^{2} c^{2} + 8 \, {\left(B b c^{3} + 8 \, A c^{4}\right)} x^{4} - 2 \, {\left(5 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{384 \, c^{4}}\right]"," ",0,"[-1/768*(3*(5*B*b^4 - 8*A*b^3*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(48*B*c^4*x^6 + 15*B*b^3*c - 24*A*b^2*c^2 + 8*(B*b*c^3 + 8*A*c^4)*x^4 - 2*(5*B*b^2*c^2 - 8*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^4, 1/384*(3*(5*B*b^4 - 8*A*b^3*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (48*B*c^4*x^6 + 15*B*b^3*c - 24*A*b^2*c^2 + 8*(B*b*c^3 + 8*A*c^4)*x^4 - 2*(5*B*b^2*c^2 - 8*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^4]","A",0
92,1,223,0,0.427365," ","integrate(x*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} x^{4} - 3 \, B b^{2} c + 6 \, A b c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, c^{3}}, -\frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(8 \, B c^{3} x^{4} - 3 \, B b^{2} c + 6 \, A b c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, c^{3}}\right]"," ",0,"[-1/96*(3*(B*b^3 - 2*A*b^2*c)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(8*B*c^3*x^4 - 3*B*b^2*c + 6*A*b*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^3, -1/48*(3*(B*b^3 - 2*A*b^2*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (8*B*c^3*x^4 - 3*B*b^2*c + 6*A*b*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^3]","A",0
93,1,172,0,0.437373," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x,x, algorithm=""fricas"")","\left[-\frac{{\left(B b^{2} - 4 \, A b c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(2 \, B c^{2} x^{2} + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, c^{2}}, \frac{{\left(B b^{2} - 4 \, A b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(2 \, B c^{2} x^{2} + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, c^{2}}\right]"," ",0,"[-1/16*((B*b^2 - 4*A*b*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(2*B*c^2*x^2 + B*b*c + 4*A*c^2)*sqrt(c*x^4 + b*x^2))/c^2, 1/8*((B*b^2 - 4*A*b*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (2*B*c^2*x^2 + B*b*c + 4*A*c^2)*sqrt(c*x^4 + b*x^2))/c^2]","A",0
94,1,161,0,0.415200," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{{\left(B b + 2 \, A c\right)} \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(B c x^{2} - 2 \, A c\right)}}{4 \, c x^{2}}, -\frac{{\left(B b + 2 \, A c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - \sqrt{c x^{4} + b x^{2}} {\left(B c x^{2} - 2 \, A c\right)}}{2 \, c x^{2}}\right]"," ",0,"[1/4*((B*b + 2*A*c)*sqrt(c)*x^2*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*(B*c*x^2 - 2*A*c))/(c*x^2), -1/2*((B*b + 2*A*c)*sqrt(-c)*x^2*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - sqrt(c*x^4 + b*x^2)*(B*c*x^2 - 2*A*c))/(c*x^2)]","A",0
95,1,160,0,0.442362," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, B b \sqrt{c} x^{4} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} {\left({\left(3 \, B b + A c\right)} x^{2} + A b\right)}}{6 \, b x^{4}}, -\frac{3 \, B b \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} {\left({\left(3 \, B b + A c\right)} x^{2} + A b\right)}}{3 \, b x^{4}}\right]"," ",0,"[1/6*(3*B*b*sqrt(c)*x^4*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*sqrt(c*x^4 + b*x^2)*((3*B*b + A*c)*x^2 + A*b))/(b*x^4), -1/3*(3*B*b*sqrt(-c)*x^4*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*((3*B*b + A*c)*x^2 + A*b))/(b*x^4)]","A",0
96,1,59,0,0.409570," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{{\left({\left(5 \, B b c - 2 \, A c^{2}\right)} x^{4} + 3 \, A b^{2} + {\left(5 \, B b^{2} + A b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, b^{2} x^{6}}"," ",0,"-1/15*((5*B*b*c - 2*A*c^2)*x^4 + 3*A*b^2 + (5*B*b^2 + A*b*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^2*x^6)","A",0
97,1,85,0,0.434181," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^9,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(7 \, B b c^{2} - 4 \, A c^{3}\right)} x^{6} - {\left(7 \, B b^{2} c - 4 \, A b c^{2}\right)} x^{4} - 15 \, A b^{3} - 3 \, {\left(7 \, B b^{3} + A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{105 \, b^{3} x^{8}}"," ",0,"1/105*(2*(7*B*b*c^2 - 4*A*c^3)*x^6 - (7*B*b^2*c - 4*A*b*c^2)*x^4 - 15*A*b^3 - 3*(7*B*b^3 + A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^3*x^8)","A",0
98,1,109,0,0.468970," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^11,x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(3 \, B b c^{3} - 2 \, A c^{4}\right)} x^{8} - 4 \, {\left(3 \, B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{6} + 35 \, A b^{4} + 3 \, {\left(3 \, B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{4} + 5 \, {\left(9 \, B b^{4} + A b^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, b^{4} x^{10}}"," ",0,"-1/315*(8*(3*B*b*c^3 - 2*A*c^4)*x^8 - 4*(3*B*b^2*c^2 - 2*A*b*c^3)*x^6 + 35*A*b^4 + 3*(3*B*b^3*c - 2*A*b^2*c^2)*x^4 + 5*(9*B*b^4 + A*b^3*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^4*x^10)","A",0
99,1,133,0,0.503755," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^13,x, algorithm=""fricas"")","\frac{{\left(16 \, {\left(11 \, B b c^{4} - 8 \, A c^{5}\right)} x^{10} - 8 \, {\left(11 \, B b^{2} c^{3} - 8 \, A b c^{4}\right)} x^{8} + 6 \, {\left(11 \, B b^{3} c^{2} - 8 \, A b^{2} c^{3}\right)} x^{6} - 315 \, A b^{5} - 5 \, {\left(11 \, B b^{4} c - 8 \, A b^{3} c^{2}\right)} x^{4} - 35 \, {\left(11 \, B b^{5} + A b^{4} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{3465 \, b^{5} x^{12}}"," ",0,"1/3465*(16*(11*B*b*c^4 - 8*A*c^5)*x^10 - 8*(11*B*b^2*c^3 - 8*A*b*c^4)*x^8 + 6*(11*B*b^3*c^2 - 8*A*b^2*c^3)*x^6 - 315*A*b^5 - 5*(11*B*b^4*c - 8*A*b^3*c^2)*x^4 - 35*(11*B*b^5 + A*b^4*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^5*x^12)","A",0
100,1,106,0,0.408952," ","integrate(x^4*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(35 \, B c^{4} x^{8} + 5 \, {\left(B b c^{3} + 9 \, A c^{4}\right)} x^{6} - 16 \, B b^{4} + 24 \, A b^{3} c - 3 \, {\left(2 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} x^{4} + 4 \, {\left(2 \, B b^{3} c - 3 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, c^{4} x}"," ",0,"1/315*(35*B*c^4*x^8 + 5*(B*b*c^3 + 9*A*c^4)*x^6 - 16*B*b^4 + 24*A*b^3*c - 3*(2*B*b^2*c^2 - 3*A*b*c^3)*x^4 + 4*(2*B*b^3*c - 3*A*b^2*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^4*x)","A",0
101,1,82,0,0.410529," ","integrate(x^2*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, B c^{3} x^{6} + 3 \, {\left(B b c^{2} + 7 \, A c^{3}\right)} x^{4} + 8 \, B b^{3} - 14 \, A b^{2} c - {\left(4 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{105 \, c^{3} x}"," ",0,"1/105*(15*B*c^3*x^6 + 3*(B*b*c^2 + 7*A*c^3)*x^4 + 8*B*b^3 - 14*A*b^2*c - (4*B*b^2*c - 7*A*b*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^3*x)","A",0
102,1,57,0,0.411624," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B c^{2} x^{4} - 2 \, B b^{2} + 5 \, A b c + {\left(B b c + 5 \, A c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, c^{2} x}"," ",0,"1/15*(3*B*c^2*x^4 - 2*B*b^2 + 5*A*b*c + (B*b*c + 5*A*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^2*x)","A",0
103,1,159,0,0.411141," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{b} c x \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(B c x^{2} + B b + 3 \, A c\right)}}{6 \, c x}, \frac{3 \, A \sqrt{-b} c x \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(B c x^{2} + B b + 3 \, A c\right)}}{3 \, c x}\right]"," ",0,"[1/6*(3*A*sqrt(b)*c*x*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(B*c*x^2 + B*b + 3*A*c))/(c*x), 1/3*(3*A*sqrt(-b)*c*x*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(B*c*x^2 + B*b + 3*A*c))/(c*x)]","A",0
104,1,169,0,0.430842," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B b + A c\right)} \sqrt{b} x^{3} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, B b x^{2} - A b\right)}}{4 \, b x^{3}}, \frac{{\left(2 \, B b + A c\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(2 \, B b x^{2} - A b\right)}}{2 \, b x^{3}}\right]"," ",0,"[1/4*((2*B*b + A*c)*sqrt(b)*x^3*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(2*B*b*x^2 - A*b))/(b*x^3), 1/2*((2*B*b + A*c)*sqrt(-b)*x^3*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(2*B*b*x^2 - A*b))/(b*x^3)]","A",0
105,1,198,0,0.430892," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B b c - A c^{2}\right)} \sqrt{b} x^{5} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, A b^{2} + {\left(4 \, B b^{2} + A b c\right)} x^{2}\right)}}{16 \, b^{2} x^{5}}, \frac{{\left(4 \, B b c - A c^{2}\right)} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) - \sqrt{c x^{4} + b x^{2}} {\left(2 \, A b^{2} + {\left(4 \, B b^{2} + A b c\right)} x^{2}\right)}}{8 \, b^{2} x^{5}}\right]"," ",0,"[-1/16*((4*B*b*c - A*c^2)*sqrt(b)*x^5*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(2*A*b^2 + (4*B*b^2 + A*b*c)*x^2))/(b^2*x^5), 1/8*((4*B*b*c - A*c^2)*sqrt(-b)*x^5*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) - sqrt(c*x^4 + b*x^2)*(2*A*b^2 + (4*B*b^2 + A*b*c)*x^2))/(b^2*x^5)]","A",0
106,1,418,0,0.694293," ","integrate(x^5*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B b^{7} - 14 \, A b^{6} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(15360 \, B c^{7} x^{12} + 1280 \, {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} x^{10} + 128 \, {\left(3 \, B b^{2} c^{5} + 182 \, A b c^{6}\right)} x^{8} + 945 \, B b^{6} c - 1470 \, A b^{5} c^{2} - 48 \, {\left(9 \, B b^{3} c^{4} - 14 \, A b^{2} c^{5}\right)} x^{6} + 56 \, {\left(9 \, B b^{4} c^{3} - 14 \, A b^{3} c^{4}\right)} x^{4} - 70 \, {\left(9 \, B b^{5} c^{2} - 14 \, A b^{4} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{430080 \, c^{6}}, \frac{105 \, {\left(9 \, B b^{7} - 14 \, A b^{6} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(15360 \, B c^{7} x^{12} + 1280 \, {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} x^{10} + 128 \, {\left(3 \, B b^{2} c^{5} + 182 \, A b c^{6}\right)} x^{8} + 945 \, B b^{6} c - 1470 \, A b^{5} c^{2} - 48 \, {\left(9 \, B b^{3} c^{4} - 14 \, A b^{2} c^{5}\right)} x^{6} + 56 \, {\left(9 \, B b^{4} c^{3} - 14 \, A b^{3} c^{4}\right)} x^{4} - 70 \, {\left(9 \, B b^{5} c^{2} - 14 \, A b^{4} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{215040 \, c^{6}}\right]"," ",0,"[-1/430080*(105*(9*B*b^7 - 14*A*b^6*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(15360*B*c^7*x^12 + 1280*(15*B*b*c^6 + 14*A*c^7)*x^10 + 128*(3*B*b^2*c^5 + 182*A*b*c^6)*x^8 + 945*B*b^6*c - 1470*A*b^5*c^2 - 48*(9*B*b^3*c^4 - 14*A*b^2*c^5)*x^6 + 56*(9*B*b^4*c^3 - 14*A*b^3*c^4)*x^4 - 70*(9*B*b^5*c^2 - 14*A*b^4*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^6, 1/215040*(105*(9*B*b^7 - 14*A*b^6*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (15360*B*c^7*x^12 + 1280*(15*B*b*c^6 + 14*A*c^7)*x^10 + 128*(3*B*b^2*c^5 + 182*A*b*c^6)*x^8 + 945*B*b^6*c - 1470*A*b^5*c^2 - 48*(9*B*b^3*c^4 - 14*A*b^2*c^5)*x^6 + 56*(9*B*b^4*c^3 - 14*A*b^3*c^4)*x^4 - 70*(9*B*b^5*c^2 - 14*A*b^4*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^6]","A",0
107,1,369,0,0.556633," ","integrate(x^3*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{6} - 12 \, A b^{5} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(1280 \, B c^{6} x^{10} + 128 \, {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} x^{8} - 105 \, B b^{5} c + 180 \, A b^{4} c^{2} + 48 \, {\left(B b^{2} c^{4} + 44 \, A b c^{5}\right)} x^{6} - 8 \, {\left(7 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} x^{4} + 10 \, {\left(7 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{30720 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{6} - 12 \, A b^{5} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(1280 \, B c^{6} x^{10} + 128 \, {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} x^{8} - 105 \, B b^{5} c + 180 \, A b^{4} c^{2} + 48 \, {\left(B b^{2} c^{4} + 44 \, A b c^{5}\right)} x^{6} - 8 \, {\left(7 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} x^{4} + 10 \, {\left(7 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15360 \, c^{5}}\right]"," ",0,"[-1/30720*(15*(7*B*b^6 - 12*A*b^5*c)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(1280*B*c^6*x^10 + 128*(13*B*b*c^5 + 12*A*c^6)*x^8 - 105*B*b^5*c + 180*A*b^4*c^2 + 48*(B*b^2*c^4 + 44*A*b*c^5)*x^6 - 8*(7*B*b^3*c^3 - 12*A*b^2*c^4)*x^4 + 10*(7*B*b^4*c^2 - 12*A*b^3*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^5, -1/15360*(15*(7*B*b^6 - 12*A*b^5*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (1280*B*c^6*x^10 + 128*(13*B*b*c^5 + 12*A*c^6)*x^8 - 105*B*b^5*c + 180*A*b^4*c^2 + 48*(B*b^2*c^4 + 44*A*b*c^5)*x^6 - 8*(7*B*b^3*c^3 - 12*A*b^2*c^4)*x^4 + 10*(7*B*b^4*c^2 - 12*A*b^3*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^5]","A",0
108,1,316,0,0.484559," ","integrate(x*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(128 \, B c^{5} x^{8} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{6} + 15 \, B b^{4} c - 30 \, A b^{3} c^{2} + 8 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} x^{4} - 10 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{2560 \, c^{4}}, \frac{15 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(128 \, B c^{5} x^{8} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{6} + 15 \, B b^{4} c - 30 \, A b^{3} c^{2} + 8 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} x^{4} - 10 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{1280 \, c^{4}}\right]"," ",0,"[-1/2560*(15*(B*b^5 - 2*A*b^4*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(128*B*c^5*x^8 + 16*(11*B*b*c^4 + 10*A*c^5)*x^6 + 15*B*b^4*c - 30*A*b^3*c^2 + 8*(B*b^2*c^3 + 30*A*b*c^4)*x^4 - 10*(B*b^3*c^2 - 2*A*b^2*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^4, 1/1280*(15*(B*b^5 - 2*A*b^4*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (128*B*c^5*x^8 + 16*(11*B*b*c^4 + 10*A*c^5)*x^6 + 15*B*b^4*c - 30*A*b^3*c^2 + 8*(B*b^2*c^3 + 30*A*b*c^4)*x^4 - 10*(B*b^3*c^2 - 2*A*b^2*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^4]","A",0
109,1,275,0,0.471338," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} x^{6} - 9 \, B b^{3} c + 24 \, A b^{2} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{4} + 2 \, {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{768 \, c^{3}}, -\frac{3 \, {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(48 \, B c^{4} x^{6} - 9 \, B b^{3} c + 24 \, A b^{2} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{4} + 2 \, {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{384 \, c^{3}}\right]"," ",0,"[-1/768*(3*(3*B*b^4 - 8*A*b^3*c)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(48*B*c^4*x^6 - 9*B*b^3*c + 24*A*b^2*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^4 + 2*(3*B*b^2*c^2 + 56*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^3, -1/384*(3*(3*B*b^4 - 8*A*b^3*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (48*B*c^4*x^6 - 9*B*b^3*c + 24*A*b^2*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^4 + 2*(3*B*b^2*c^2 + 56*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^3]","A",0
110,1,224,0,0.440706," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b^{3} - 6 \, A b^{2} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} x^{4} + 3 \, B b^{2} c + 30 \, A b c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, c^{2}}, \frac{3 \, {\left(B b^{3} - 6 \, A b^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(8 \, B c^{3} x^{4} + 3 \, B b^{2} c + 30 \, A b c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, c^{2}}\right]"," ",0,"[-1/96*(3*(B*b^3 - 6*A*b^2*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(8*B*c^3*x^4 + 3*B*b^2*c + 30*A*b*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^2, 1/48*(3*(B*b^3 - 6*A*b^2*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (8*B*c^3*x^4 + 3*B*b^2*c + 30*A*b*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^2]","A",0
111,1,209,0,0.437026," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b^{2} + 4 \, A b c\right)} \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(2 \, B c^{2} x^{4} - 8 \, A b c + {\left(5 \, B b c + 4 \, A c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, c x^{2}}, -\frac{3 \, {\left(B b^{2} + 4 \, A b c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(2 \, B c^{2} x^{4} - 8 \, A b c + {\left(5 \, B b c + 4 \, A c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, c x^{2}}\right]"," ",0,"[1/16*(3*(B*b^2 + 4*A*b*c)*sqrt(c)*x^2*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(2*B*c^2*x^4 - 8*A*b*c + (5*B*b*c + 4*A*c^2)*x^2)*sqrt(c*x^4 + b*x^2))/(c*x^2), -1/8*(3*(B*b^2 + 4*A*b*c)*sqrt(-c)*x^2*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (2*B*c^2*x^4 - 8*A*b*c + (5*B*b*c + 4*A*c^2)*x^2)*sqrt(c*x^4 + b*x^2))/(c*x^2)]","A",0
112,1,189,0,0.440094," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, B b + 2 \, A c\right)} \sqrt{c} x^{4} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(3 \, B c x^{4} - 2 \, {\left(3 \, B b + 4 \, A c\right)} x^{2} - 2 \, A b\right)} \sqrt{c x^{4} + b x^{2}}}{12 \, x^{4}}, -\frac{3 \, {\left(3 \, B b + 2 \, A c\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(3 \, B c x^{4} - 2 \, {\left(3 \, B b + 4 \, A c\right)} x^{2} - 2 \, A b\right)} \sqrt{c x^{4} + b x^{2}}}{6 \, x^{4}}\right]"," ",0,"[1/12*(3*(3*B*b + 2*A*c)*sqrt(c)*x^4*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(3*B*c*x^4 - 2*(3*B*b + 4*A*c)*x^2 - 2*A*b)*sqrt(c*x^4 + b*x^2))/x^4, -1/6*(3*(3*B*b + 2*A*c)*sqrt(-c)*x^4*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (3*B*c*x^4 - 2*(3*B*b + 4*A*c)*x^2 - 2*A*b)*sqrt(c*x^4 + b*x^2))/x^4]","A",0
113,1,207,0,0.445840," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^9,x, algorithm=""fricas"")","\left[\frac{15 \, B b c^{\frac{3}{2}} x^{6} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left({\left(20 \, B b c + 3 \, A c^{2}\right)} x^{4} + 3 \, A b^{2} + {\left(5 \, B b^{2} + 6 \, A b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{30 \, b x^{6}}, -\frac{15 \, B b \sqrt{-c} c x^{6} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left({\left(20 \, B b c + 3 \, A c^{2}\right)} x^{4} + 3 \, A b^{2} + {\left(5 \, B b^{2} + 6 \, A b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, b x^{6}}\right]"," ",0,"[1/30*(15*B*b*c^(3/2)*x^6*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*((20*B*b*c + 3*A*c^2)*x^4 + 3*A*b^2 + (5*B*b^2 + 6*A*b*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b*x^6), -1/15*(15*B*b*sqrt(-c)*c*x^6*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + ((20*B*b*c + 3*A*c^2)*x^4 + 3*A*b^2 + (5*B*b^2 + 6*A*b*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b*x^6)]","A",0
114,1,82,0,0.429505," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^11,x, algorithm=""fricas"")","-\frac{{\left({\left(7 \, B b c^{2} - 2 \, A c^{3}\right)} x^{6} + {\left(14 \, B b^{2} c + A b c^{2}\right)} x^{4} + 5 \, A b^{3} + {\left(7 \, B b^{3} + 8 \, A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{35 \, b^{2} x^{8}}"," ",0,"-1/35*((7*B*b*c^2 - 2*A*c^3)*x^6 + (14*B*b^2*c + A*b*c^2)*x^4 + 5*A*b^3 + (7*B*b^3 + 8*A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^2*x^8)","A",0
115,1,109,0,0.465507," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^13,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(9 \, B b c^{3} - 4 \, A c^{4}\right)} x^{8} - {\left(9 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} x^{6} - 35 \, A b^{4} - 3 \, {\left(24 \, B b^{3} c + A b^{2} c^{2}\right)} x^{4} - 5 \, {\left(9 \, B b^{4} + 10 \, A b^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, b^{3} x^{10}}"," ",0,"1/315*(2*(9*B*b*c^3 - 4*A*c^4)*x^8 - (9*B*b^2*c^2 - 4*A*b*c^3)*x^6 - 35*A*b^4 - 3*(24*B*b^3*c + A*b^2*c^2)*x^4 - 5*(9*B*b^4 + 10*A*b^3*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^3*x^10)","A",0
116,1,134,0,0.516556," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^15,x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(11 \, B b c^{4} - 6 \, A c^{5}\right)} x^{10} - 4 \, {\left(11 \, B b^{2} c^{3} - 6 \, A b c^{4}\right)} x^{8} + 3 \, {\left(11 \, B b^{3} c^{2} - 6 \, A b^{2} c^{3}\right)} x^{6} + 315 \, A b^{5} + 5 \, {\left(110 \, B b^{4} c + 3 \, A b^{3} c^{2}\right)} x^{4} + 35 \, {\left(11 \, B b^{5} + 12 \, A b^{4} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{3465 \, b^{4} x^{12}}"," ",0,"-1/3465*(8*(11*B*b*c^4 - 6*A*c^5)*x^10 - 4*(11*B*b^2*c^3 - 6*A*b*c^4)*x^8 + 3*(11*B*b^3*c^2 - 6*A*b^2*c^3)*x^6 + 315*A*b^5 + 5*(110*B*b^4*c + 3*A*b^3*c^2)*x^4 + 35*(11*B*b^5 + 12*A*b^4*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^4*x^12)","A",0
117,1,157,0,0.610768," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^17,x, algorithm=""fricas"")","\frac{{\left(16 \, {\left(13 \, B b c^{5} - 8 \, A c^{6}\right)} x^{12} - 8 \, {\left(13 \, B b^{2} c^{4} - 8 \, A b c^{5}\right)} x^{10} + 6 \, {\left(13 \, B b^{3} c^{3} - 8 \, A b^{2} c^{4}\right)} x^{8} - 1155 \, A b^{6} - 5 \, {\left(13 \, B b^{4} c^{2} - 8 \, A b^{3} c^{3}\right)} x^{6} - 35 \, {\left(52 \, B b^{5} c + A b^{4} c^{2}\right)} x^{4} - 105 \, {\left(13 \, B b^{6} + 14 \, A b^{5} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15015 \, b^{5} x^{14}}"," ",0,"1/15015*(16*(13*B*b*c^5 - 8*A*c^6)*x^12 - 8*(13*B*b^2*c^4 - 8*A*b*c^5)*x^10 + 6*(13*B*b^3*c^3 - 8*A*b^2*c^4)*x^8 - 1155*A*b^6 - 5*(13*B*b^4*c^2 - 8*A*b^3*c^3)*x^6 - 35*(52*B*b^5*c + A*b^4*c^2)*x^4 - 105*(13*B*b^6 + 14*A*b^5*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^5*x^14)","A",0
118,1,181,0,0.748932," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^19,x, algorithm=""fricas"")","-\frac{{\left(128 \, {\left(3 \, B b c^{6} - 2 \, A c^{7}\right)} x^{14} - 64 \, {\left(3 \, B b^{2} c^{5} - 2 \, A b c^{6}\right)} x^{12} + 48 \, {\left(3 \, B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} x^{10} - 40 \, {\left(3 \, B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} x^{8} + 3003 \, A b^{7} + 35 \, {\left(3 \, B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} x^{6} + 63 \, {\left(70 \, B b^{6} c + A b^{5} c^{2}\right)} x^{4} + 231 \, {\left(15 \, B b^{7} + 16 \, A b^{6} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{45045 \, b^{6} x^{16}}"," ",0,"-1/45045*(128*(3*B*b*c^6 - 2*A*c^7)*x^14 - 64*(3*B*b^2*c^5 - 2*A*b*c^6)*x^12 + 48*(3*B*b^3*c^4 - 2*A*b^2*c^5)*x^10 - 40*(3*B*b^4*c^3 - 2*A*b^3*c^4)*x^8 + 3003*A*b^7 + 35*(3*B*b^5*c^2 - 2*A*b^4*c^3)*x^6 + 63*(70*B*b^6*c + A*b^5*c^2)*x^4 + 231*(15*B*b^7 + 16*A*b^6*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^6*x^16)","A",0
119,1,154,0,0.414189," ","integrate(x^4*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(1155 \, B c^{6} x^{12} + 105 \, {\left(14 \, B b c^{5} + 13 \, A c^{6}\right)} x^{10} + 35 \, {\left(B b^{2} c^{4} + 52 \, A b c^{5}\right)} x^{8} + 128 \, B b^{6} - 208 \, A b^{5} c - 5 \, {\left(8 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} x^{6} + 6 \, {\left(8 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} x^{4} - 8 \, {\left(8 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15015 \, c^{5} x}"," ",0,"1/15015*(1155*B*c^6*x^12 + 105*(14*B*b*c^5 + 13*A*c^6)*x^10 + 35*(B*b^2*c^4 + 52*A*b*c^5)*x^8 + 128*B*b^6 - 208*A*b^5*c - 5*(8*B*b^3*c^3 - 13*A*b^2*c^4)*x^6 + 6*(8*B*b^4*c^2 - 13*A*b^3*c^3)*x^4 - 8*(8*B*b^5*c - 13*A*b^4*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^5*x)","A",0
120,1,131,0,0.418453," ","integrate(x^2*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(315 \, B c^{5} x^{10} + 35 \, {\left(12 \, B b c^{4} + 11 \, A c^{5}\right)} x^{8} + 5 \, {\left(3 \, B b^{2} c^{3} + 110 \, A b c^{4}\right)} x^{6} - 48 \, B b^{5} + 88 \, A b^{4} c - 3 \, {\left(6 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} x^{4} + 4 \, {\left(6 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{3465 \, c^{4} x}"," ",0,"1/3465*(315*B*c^5*x^10 + 35*(12*B*b*c^4 + 11*A*c^5)*x^8 + 5*(3*B*b^2*c^3 + 110*A*b*c^4)*x^6 - 48*B*b^5 + 88*A*b^4*c - 3*(6*B*b^3*c^2 - 11*A*b^2*c^3)*x^4 + 4*(6*B*b^4*c - 11*A*b^3*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^4*x)","A",0
121,1,106,0,0.421329," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(35 \, B c^{4} x^{8} + 5 \, {\left(10 \, B b c^{3} + 9 \, A c^{4}\right)} x^{6} + 8 \, B b^{4} - 18 \, A b^{3} c + 3 \, {\left(B b^{2} c^{2} + 24 \, A b c^{3}\right)} x^{4} - {\left(4 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, c^{3} x}"," ",0,"1/315*(35*B*c^4*x^8 + 5*(10*B*b*c^3 + 9*A*c^4)*x^6 + 8*B*b^4 - 18*A*b^3*c + 3*(B*b^2*c^2 + 24*A*b*c^3)*x^4 - (4*B*b^3*c - 9*A*b^2*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^3*x)","A",0
122,1,80,0,0.418491," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{{\left(5 \, B c^{3} x^{6} + {\left(8 \, B b c^{2} + 7 \, A c^{3}\right)} x^{4} - 2 \, B b^{3} + 7 \, A b^{2} c + {\left(B b^{2} c + 14 \, A b c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{35 \, c^{2} x}"," ",0,"1/35*(5*B*c^3*x^6 + (8*B*b*c^2 + 7*A*c^3)*x^4 - 2*B*b^3 + 7*A*b^2*c + (B*b^2*c + 14*A*b*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^2*x)","A",0
123,1,206,0,0.434961," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, A b^{\frac{3}{2}} c x \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(3 \, B c^{2} x^{4} + 3 \, B b^{2} + 20 \, A b c + {\left(6 \, B b c + 5 \, A c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{30 \, c x}, \frac{15 \, A \sqrt{-b} b c x \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(3 \, B c^{2} x^{4} + 3 \, B b^{2} + 20 \, A b c + {\left(6 \, B b c + 5 \, A c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, c x}\right]"," ",0,"[1/30*(15*A*b^(3/2)*c*x*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(3*B*c^2*x^4 + 3*B*b^2 + 20*A*b*c + (6*B*b*c + 5*A*c^2)*x^2)*sqrt(c*x^4 + b*x^2))/(c*x), 1/15*(15*A*sqrt(-b)*b*c*x*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (3*B*c^2*x^4 + 3*B*b^2 + 20*A*b*c + (6*B*b*c + 5*A*c^2)*x^2)*sqrt(c*x^4 + b*x^2))/(c*x)]","A",0
124,1,195,0,0.435871," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B b + 3 \, A c\right)} \sqrt{b} x^{3} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(2 \, B c x^{4} + 2 \, {\left(4 \, B b + 3 \, A c\right)} x^{2} - 3 \, A b\right)} \sqrt{c x^{4} + b x^{2}}}{12 \, x^{3}}, \frac{3 \, {\left(2 \, B b + 3 \, A c\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(2 \, B c x^{4} + 2 \, {\left(4 \, B b + 3 \, A c\right)} x^{2} - 3 \, A b\right)} \sqrt{c x^{4} + b x^{2}}}{6 \, x^{3}}\right]"," ",0,"[1/12*(3*(2*B*b + 3*A*c)*sqrt(b)*x^3*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(2*B*c*x^4 + 2*(4*B*b + 3*A*c)*x^2 - 3*A*b)*sqrt(c*x^4 + b*x^2))/x^3, 1/6*(3*(2*B*b + 3*A*c)*sqrt(-b)*x^3*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (2*B*c*x^4 + 2*(4*B*b + 3*A*c)*x^2 - 3*A*b)*sqrt(c*x^4 + b*x^2))/x^3]","A",0
125,1,217,0,0.448902," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^8,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B b c + A c^{2}\right)} \sqrt{b} x^{5} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(8 \, B b c x^{4} - 2 \, A b^{2} - {\left(4 \, B b^{2} + 5 \, A b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, b x^{5}}, \frac{3 \, {\left(4 \, B b c + A c^{2}\right)} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(8 \, B b c x^{4} - 2 \, A b^{2} - {\left(4 \, B b^{2} + 5 \, A b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, b x^{5}}\right]"," ",0,"[1/16*(3*(4*B*b*c + A*c^2)*sqrt(b)*x^5*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(8*B*b*c*x^4 - 2*A*b^2 - (4*B*b^2 + 5*A*b*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b*x^5), 1/8*(3*(4*B*b*c + A*c^2)*sqrt(-b)*x^5*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (8*B*b*c*x^4 - 2*A*b^2 - (4*B*b^2 + 5*A*b*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b*x^5)]","A",0
126,1,250,0,0.440387," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^10,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, B b c^{2} - A c^{3}\right)} \sqrt{b} x^{7} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(3 \, {\left(10 \, B b^{2} c + A b c^{2}\right)} x^{4} + 8 \, A b^{3} + 2 \, {\left(6 \, B b^{3} + 7 \, A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, b^{2} x^{7}}, \frac{3 \, {\left(6 \, B b c^{2} - A c^{3}\right)} \sqrt{-b} x^{7} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) - {\left(3 \, {\left(10 \, B b^{2} c + A b c^{2}\right)} x^{4} + 8 \, A b^{3} + 2 \, {\left(6 \, B b^{3} + 7 \, A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, b^{2} x^{7}}\right]"," ",0,"[-1/96*(3*(6*B*b*c^2 - A*c^3)*sqrt(b)*x^7*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(3*(10*B*b^2*c + A*b*c^2)*x^4 + 8*A*b^3 + 2*(6*B*b^3 + 7*A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^2*x^7), 1/48*(3*(6*B*b*c^2 - A*c^3)*sqrt(-b)*x^7*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) - (3*(10*B*b^2*c + A*b*c^2)*x^4 + 8*A*b^3 + 2*(6*B*b^3 + 7*A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^2*x^7)]","A",0
127,1,299,0,0.464972," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^12,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B b c^{3} - 3 \, A c^{4}\right)} \sqrt{b} x^{9} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(3 \, {\left(8 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} x^{6} + 48 \, A b^{4} + 2 \, {\left(56 \, B b^{3} c + 3 \, A b^{2} c^{2}\right)} x^{4} + 8 \, {\left(8 \, B b^{4} + 9 \, A b^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{768 \, b^{3} x^{9}}, -\frac{3 \, {\left(8 \, B b c^{3} - 3 \, A c^{4}\right)} \sqrt{-b} x^{9} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(3 \, {\left(8 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} x^{6} + 48 \, A b^{4} + 2 \, {\left(56 \, B b^{3} c + 3 \, A b^{2} c^{2}\right)} x^{4} + 8 \, {\left(8 \, B b^{4} + 9 \, A b^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{384 \, b^{3} x^{9}}\right]"," ",0,"[-1/768*(3*(8*B*b*c^3 - 3*A*c^4)*sqrt(b)*x^9*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(3*(8*B*b^2*c^2 - 3*A*b*c^3)*x^6 + 48*A*b^4 + 2*(56*B*b^3*c + 3*A*b^2*c^2)*x^4 + 8*(8*B*b^4 + 9*A*b^3*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^3*x^9), -1/384*(3*(8*B*b*c^3 - 3*A*c^4)*sqrt(-b)*x^9*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (3*(8*B*b^2*c^2 - 3*A*b*c^3)*x^6 + 48*A*b^4 + 2*(56*B*b^3*c + 3*A*b^2*c^2)*x^4 + 8*(8*B*b^4 + 9*A*b^3*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^3*x^9)]","A",0
128,1,345,0,0.510467," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^14,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B b c^{4} - A c^{5}\right)} \sqrt{b} x^{11} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, {\left(15 \, {\left(2 \, B b^{2} c^{3} - A b c^{4}\right)} x^{8} - 10 \, {\left(2 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} x^{6} - 128 \, A b^{5} - 8 \, {\left(30 \, B b^{4} c + A b^{3} c^{2}\right)} x^{4} - 16 \, {\left(10 \, B b^{5} + 11 \, A b^{4} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{2560 \, b^{4} x^{11}}, \frac{15 \, {\left(2 \, B b c^{4} - A c^{5}\right)} \sqrt{-b} x^{11} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(15 \, {\left(2 \, B b^{2} c^{3} - A b c^{4}\right)} x^{8} - 10 \, {\left(2 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} x^{6} - 128 \, A b^{5} - 8 \, {\left(30 \, B b^{4} c + A b^{3} c^{2}\right)} x^{4} - 16 \, {\left(10 \, B b^{5} + 11 \, A b^{4} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{1280 \, b^{4} x^{11}}\right]"," ",0,"[-1/2560*(15*(2*B*b*c^4 - A*c^5)*sqrt(b)*x^11*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*(15*(2*B*b^2*c^3 - A*b*c^4)*x^8 - 10*(2*B*b^3*c^2 - A*b^2*c^3)*x^6 - 128*A*b^5 - 8*(30*B*b^4*c + A*b^3*c^2)*x^4 - 16*(10*B*b^5 + 11*A*b^4*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^4*x^11), 1/1280*(15*(2*B*b*c^4 - A*c^5)*sqrt(-b)*x^11*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (15*(2*B*b^2*c^3 - A*b*c^4)*x^8 - 10*(2*B*b^3*c^2 - A*b^2*c^3)*x^6 - 128*A*b^5 - 8*(30*B*b^4*c + A*b^3*c^2)*x^4 - 16*(10*B*b^5 + 11*A*b^4*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^4*x^11)]","A",0
129,1,393,0,0.580795," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^16,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(12 \, B b c^{5} - 7 \, A c^{6}\right)} \sqrt{b} x^{13} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(15 \, {\left(12 \, B b^{2} c^{4} - 7 \, A b c^{5}\right)} x^{10} - 10 \, {\left(12 \, B b^{3} c^{3} - 7 \, A b^{2} c^{4}\right)} x^{8} + 1280 \, A b^{6} + 8 \, {\left(12 \, B b^{4} c^{2} - 7 \, A b^{3} c^{3}\right)} x^{6} + 48 \, {\left(44 \, B b^{5} c + A b^{4} c^{2}\right)} x^{4} + 128 \, {\left(12 \, B b^{6} + 13 \, A b^{5} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{30720 \, b^{5} x^{13}}, -\frac{15 \, {\left(12 \, B b c^{5} - 7 \, A c^{6}\right)} \sqrt{-b} x^{13} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(15 \, {\left(12 \, B b^{2} c^{4} - 7 \, A b c^{5}\right)} x^{10} - 10 \, {\left(12 \, B b^{3} c^{3} - 7 \, A b^{2} c^{4}\right)} x^{8} + 1280 \, A b^{6} + 8 \, {\left(12 \, B b^{4} c^{2} - 7 \, A b^{3} c^{3}\right)} x^{6} + 48 \, {\left(44 \, B b^{5} c + A b^{4} c^{2}\right)} x^{4} + 128 \, {\left(12 \, B b^{6} + 13 \, A b^{5} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15360 \, b^{5} x^{13}}\right]"," ",0,"[-1/30720*(15*(12*B*b*c^5 - 7*A*c^6)*sqrt(b)*x^13*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(15*(12*B*b^2*c^4 - 7*A*b*c^5)*x^10 - 10*(12*B*b^3*c^3 - 7*A*b^2*c^4)*x^8 + 1280*A*b^6 + 8*(12*B*b^4*c^2 - 7*A*b^3*c^3)*x^6 + 48*(44*B*b^5*c + A*b^4*c^2)*x^4 + 128*(12*B*b^6 + 13*A*b^5*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^5*x^13), -1/15360*(15*(12*B*b*c^5 - 7*A*c^6)*sqrt(-b)*x^13*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (15*(12*B*b^2*c^4 - 7*A*b*c^5)*x^10 - 10*(12*B*b^3*c^3 - 7*A*b^2*c^4)*x^8 + 1280*A*b^6 + 8*(12*B*b^4*c^2 - 7*A*b^3*c^3)*x^6 + 48*(44*B*b^5*c + A*b^4*c^2)*x^4 + 128*(12*B*b^6 + 13*A*b^5*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^5*x^13)]","A",0
130,1,275,0,0.464255," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} x^{6} - 105 \, B b^{3} c + 120 \, A b^{2} c^{2} - 8 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{4} + 10 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{768 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(48 \, B c^{4} x^{6} - 105 \, B b^{3} c + 120 \, A b^{2} c^{2} - 8 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{4} + 10 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{384 \, c^{5}}\right]"," ",0,"[-1/768*(15*(7*B*b^4 - 8*A*b^3*c)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(48*B*c^4*x^6 - 105*B*b^3*c + 120*A*b^2*c^2 - 8*(7*B*b*c^3 - 8*A*c^4)*x^4 + 10*(7*B*b^2*c^2 - 8*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^5, -1/384*(15*(7*B*b^4 - 8*A*b^3*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (48*B*c^4*x^6 - 105*B*b^3*c + 120*A*b^2*c^2 - 8*(7*B*b*c^3 - 8*A*c^4)*x^4 + 10*(7*B*b^2*c^2 - 8*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^5]","A",0
131,1,226,0,0.445776," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} x^{4} + 15 \, B b^{2} c - 18 \, A b c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, c^{4}}, \frac{3 \, {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(8 \, B c^{3} x^{4} + 15 \, B b^{2} c - 18 \, A b c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, c^{4}}\right]"," ",0,"[-1/96*(3*(5*B*b^3 - 6*A*b^2*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(8*B*c^3*x^4 + 15*B*b^2*c - 18*A*b*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^4, 1/48*(3*(5*B*b^3 - 6*A*b^2*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (8*B*c^3*x^4 + 15*B*b^2*c - 18*A*b*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/c^4]","A",0
132,1,177,0,0.433927," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b^{2} - 4 \, A b c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(2 \, B c^{2} x^{2} - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, c^{3}}, -\frac{{\left(3 \, B b^{2} - 4 \, A b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(2 \, B c^{2} x^{2} - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, c^{3}}\right]"," ",0,"[-1/16*((3*B*b^2 - 4*A*b*c)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(2*B*c^2*x^2 - 3*B*b*c + 4*A*c^2)*sqrt(c*x^4 + b*x^2))/c^3, -1/8*((3*B*b^2 - 4*A*b*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (2*B*c^2*x^2 - 3*B*b*c + 4*A*c^2)*sqrt(c*x^4 + b*x^2))/c^3]","A",0
133,1,131,0,0.431446," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c x^{4} + b x^{2}} B c - {\left(B b - 2 \, A c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{4 \, c^{2}}, \frac{\sqrt{c x^{4} + b x^{2}} B c + {\left(B b - 2 \, A c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right)}{2 \, c^{2}}\right]"," ",0,"[1/4*(2*sqrt(c*x^4 + b*x^2)*B*c - (B*b - 2*A*c)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)))/c^2, 1/2*(sqrt(c*x^4 + b*x^2)*B*c + (B*b - 2*A*c)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)))/c^2]","A",0
134,1,136,0,0.426585," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{B b \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} A c}{2 \, b c x^{2}}, -\frac{B b \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} A c}{b c x^{2}}\right]"," ",0,"[1/2*(B*b*sqrt(c)*x^2*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*sqrt(c*x^4 + b*x^2)*A*c)/(b*c*x^2), -(B*b*sqrt(-c)*x^2*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*A*c)/(b*c*x^2)]","A",0
135,1,38,0,0.405550," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + b x^{2}} {\left({\left(3 \, B b - 2 \, A c\right)} x^{2} + A b\right)}}{3 \, b^{2} x^{4}}"," ",0,"-1/3*sqrt(c*x^4 + b*x^2)*((3*B*b - 2*A*c)*x^2 + A*b)/(b^2*x^4)","A",0
136,1,62,0,0.411537," ","integrate((B*x^2+A)/x^5/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(5 \, B b c - 4 \, A c^{2}\right)} x^{4} - 3 \, A b^{2} - {\left(5 \, B b^{2} - 4 \, A b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, b^{3} x^{6}}"," ",0,"1/15*(2*(5*B*b*c - 4*A*c^2)*x^4 - 3*A*b^2 - (5*B*b^2 - 4*A*b*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^3*x^6)","A",0
137,1,86,0,0.421402," ","integrate((B*x^2+A)/x^7/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(7 \, B b c^{2} - 6 \, A c^{3}\right)} x^{6} - 4 \, {\left(7 \, B b^{2} c - 6 \, A b c^{2}\right)} x^{4} + 15 \, A b^{3} + 3 \, {\left(7 \, B b^{3} - 6 \, A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{105 \, b^{4} x^{8}}"," ",0,"-1/105*(8*(7*B*b*c^2 - 6*A*c^3)*x^6 - 4*(7*B*b^2*c - 6*A*b*c^2)*x^4 + 15*A*b^3 + 3*(7*B*b^3 - 6*A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^4*x^8)","A",0
138,1,110,0,0.469040," ","integrate((B*x^2+A)/x^9/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(16 \, {\left(9 \, B b c^{3} - 8 \, A c^{4}\right)} x^{8} - 8 \, {\left(9 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{6} - 35 \, A b^{4} + 6 \, {\left(9 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} x^{4} - 5 \, {\left(9 \, B b^{4} - 8 \, A b^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, b^{5} x^{10}}"," ",0,"1/315*(16*(9*B*b*c^3 - 8*A*c^4)*x^8 - 8*(9*B*b^2*c^2 - 8*A*b*c^3)*x^6 - 35*A*b^4 + 6*(9*B*b^3*c - 8*A*b^2*c^2)*x^4 - 5*(9*B*b^4 - 8*A*b^3*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^5*x^10)","A",0
139,1,83,0,0.422514," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, B c^{3} x^{6} - 3 \, {\left(6 \, B b c^{2} - 7 \, A c^{3}\right)} x^{4} - 48 \, B b^{3} + 56 \, A b^{2} c + 4 \, {\left(6 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{105 \, c^{4} x}"," ",0,"1/105*(15*B*c^3*x^6 - 3*(6*B*b*c^2 - 7*A*c^3)*x^4 - 48*B*b^3 + 56*A*b^2*c + 4*(6*B*b^2*c - 7*A*b*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^4*x)","A",0
140,1,59,0,0.407587," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B c^{2} x^{4} + 8 \, B b^{2} - 10 \, A b c - {\left(4 \, B b c - 5 \, A c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, c^{3} x}"," ",0,"1/15*(3*B*c^2*x^4 + 8*B*b^2 - 10*A*b*c - (4*B*b*c - 5*A*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^3*x)","A",0
141,1,36,0,0.408516," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(B c x^{2} - 2 \, B b + 3 \, A c\right)}}{3 \, c^{2} x}"," ",0,"1/3*sqrt(c*x^4 + b*x^2)*(B*c*x^2 - 2*B*b + 3*A*c)/(c^2*x)","A",0
142,1,138,0,0.432642," ","integrate((B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{b} c x \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} B b}{2 \, b c x}, \frac{A \sqrt{-b} c x \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} B b}{b c x}\right]"," ",0,"[1/2*(A*sqrt(b)*c*x*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*B*b)/(b*c*x), (A*sqrt(-b)*c*x*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*B*b)/(b*c*x)]","A",0
143,1,152,0,0.440738," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B b - A c\right)} \sqrt{b} x^{3} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} A b}{4 \, b^{2} x^{3}}, \frac{{\left(2 \, B b - A c\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) - \sqrt{c x^{4} + b x^{2}} A b}{2 \, b^{2} x^{3}}\right]"," ",0,"[-1/4*((2*B*b - A*c)*sqrt(b)*x^3*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*A*b)/(b^2*x^3), 1/2*((2*B*b - A*c)*sqrt(-b)*x^3*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) - sqrt(c*x^4 + b*x^2)*A*b)/(b^2*x^3)]","A",0
144,1,199,0,0.436732," ","integrate((B*x^2+A)/x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B b c - 3 \, A c^{2}\right)} \sqrt{b} x^{5} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, A b^{2} + {\left(4 \, B b^{2} - 3 \, A b c\right)} x^{2}\right)}}{16 \, b^{3} x^{5}}, -\frac{{\left(4 \, B b c - 3 \, A c^{2}\right)} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(2 \, A b^{2} + {\left(4 \, B b^{2} - 3 \, A b c\right)} x^{2}\right)}}{8 \, b^{3} x^{5}}\right]"," ",0,"[-1/16*((4*B*b*c - 3*A*c^2)*sqrt(b)*x^5*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(2*A*b^2 + (4*B*b^2 - 3*A*b*c)*x^2))/(b^3*x^5), -1/8*((4*B*b*c - 3*A*c^2)*sqrt(-b)*x^5*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(2*A*b^2 + (4*B*b^2 - 3*A*b*c)*x^2))/(b^3*x^5)]","A",0
145,1,340,0,0.443599," ","integrate(x^9*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{4} - 6 \, A b^{3} c + {\left(7 \, B b^{3} c - 6 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{4} x^{6} + 105 \, B b^{3} c - 90 \, A b^{2} c^{2} - 2 \, {\left(7 \, B b c^{3} - 6 \, A c^{4}\right)} x^{4} + 5 \, {\left(7 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, {\left(c^{6} x^{2} + b c^{5}\right)}}, \frac{15 \, {\left(7 \, B b^{4} - 6 \, A b^{3} c + {\left(7 \, B b^{3} c - 6 \, A b^{2} c^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(8 \, B c^{4} x^{6} + 105 \, B b^{3} c - 90 \, A b^{2} c^{2} - 2 \, {\left(7 \, B b c^{3} - 6 \, A c^{4}\right)} x^{4} + 5 \, {\left(7 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, {\left(c^{6} x^{2} + b c^{5}\right)}}\right]"," ",0,"[-1/96*(15*(7*B*b^4 - 6*A*b^3*c + (7*B*b^3*c - 6*A*b^2*c^2)*x^2)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(8*B*c^4*x^6 + 105*B*b^3*c - 90*A*b^2*c^2 - 2*(7*B*b*c^3 - 6*A*c^4)*x^4 + 5*(7*B*b^2*c^2 - 6*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/(c^6*x^2 + b*c^5), 1/48*(15*(7*B*b^4 - 6*A*b^3*c + (7*B*b^3*c - 6*A*b^2*c^2)*x^2)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (8*B*c^4*x^6 + 105*B*b^3*c - 90*A*b^2*c^2 - 2*(7*B*b*c^3 - 6*A*c^4)*x^4 + 5*(7*B*b^2*c^2 - 6*A*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/(c^6*x^2 + b*c^5)]","A",0
146,1,289,0,0.438072," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{3} - 4 \, A b^{2} c + {\left(5 \, B b^{2} c - 4 \, A b c^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(2 \, B c^{3} x^{4} - 15 \, B b^{2} c + 12 \, A b c^{2} - {\left(5 \, B b c^{2} - 4 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, {\left(c^{5} x^{2} + b c^{4}\right)}}, -\frac{3 \, {\left(5 \, B b^{3} - 4 \, A b^{2} c + {\left(5 \, B b^{2} c - 4 \, A b c^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(2 \, B c^{3} x^{4} - 15 \, B b^{2} c + 12 \, A b c^{2} - {\left(5 \, B b c^{2} - 4 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, {\left(c^{5} x^{2} + b c^{4}\right)}}\right]"," ",0,"[-1/16*(3*(5*B*b^3 - 4*A*b^2*c + (5*B*b^2*c - 4*A*b*c^2)*x^2)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(2*B*c^3*x^4 - 15*B*b^2*c + 12*A*b*c^2 - (5*B*b*c^2 - 4*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/(c^5*x^2 + b*c^4), -1/8*(3*(5*B*b^3 - 4*A*b^2*c + (5*B*b^2*c - 4*A*b*c^2)*x^2)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (2*B*c^3*x^4 - 15*B*b^2*c + 12*A*b*c^2 - (5*B*b*c^2 - 4*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2))/(c^5*x^2 + b*c^4)]","A",0
147,1,230,0,0.426378," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b^{2} - 2 \, A b c + {\left(3 \, B b c - 2 \, A c^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, {\left(B c^{2} x^{2} + 3 \, B b c - 2 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{4 \, {\left(c^{4} x^{2} + b c^{3}\right)}}, \frac{{\left(3 \, B b^{2} - 2 \, A b c + {\left(3 \, B b c - 2 \, A c^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(B c^{2} x^{2} + 3 \, B b c - 2 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{2 \, {\left(c^{4} x^{2} + b c^{3}\right)}}\right]"," ",0,"[-1/4*((3*B*b^2 - 2*A*b*c + (3*B*b*c - 2*A*c^2)*x^2)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*(B*c^2*x^2 + 3*B*b*c - 2*A*c^2)*sqrt(c*x^4 + b*x^2))/(c^4*x^2 + b*c^3), 1/2*((3*B*b^2 - 2*A*b*c + (3*B*b*c - 2*A*c^2)*x^2)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (B*c^2*x^2 + 3*B*b*c - 2*A*c^2)*sqrt(c*x^4 + b*x^2))/(c^4*x^2 + b*c^3)]","A",0
148,1,188,0,0.428960," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B b c x^{2} + B b^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} {\left(B b c - A c^{2}\right)}}{2 \, {\left(b c^{3} x^{2} + b^{2} c^{2}\right)}}, -\frac{{\left(B b c x^{2} + B b^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} {\left(B b c - A c^{2}\right)}}{b c^{3} x^{2} + b^{2} c^{2}}\right]"," ",0,"[1/2*((B*b*c*x^2 + B*b^2)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*sqrt(c*x^4 + b*x^2)*(B*b*c - A*c^2))/(b*c^3*x^2 + b^2*c^2), -((B*b*c*x^2 + B*b^2)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*(B*b*c - A*c^2))/(b*c^3*x^2 + b^2*c^2)]","A",0
149,1,49,0,0.411102," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left({\left(B b - 2 \, A c\right)} x^{2} - A b\right)}}{b^{2} c x^{4} + b^{3} x^{2}}"," ",0,"sqrt(c*x^4 + b*x^2)*((B*b - 2*A*c)*x^2 - A*b)/(b^2*c*x^4 + b^3*x^2)","A",0
150,1,72,0,0.418622," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(3 \, B b c - 4 \, A c^{2}\right)} x^{4} + A b^{2} + {\left(3 \, B b^{2} - 4 \, A b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{3 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)}}"," ",0,"-1/3*(2*(3*B*b*c - 4*A*c^2)*x^4 + A*b^2 + (3*B*b^2 - 4*A*b*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^3*c*x^6 + b^4*x^4)","A",0
151,1,98,0,0.421140," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x^{6} + 4 \, {\left(5 \, B b^{2} c - 6 \, A b c^{2}\right)} x^{4} - 3 \, A b^{3} - {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, {\left(b^{4} c x^{8} + b^{5} x^{6}\right)}}"," ",0,"1/15*(8*(5*B*b*c^2 - 6*A*c^3)*x^6 + 4*(5*B*b^2*c - 6*A*b*c^2)*x^4 - 3*A*b^3 - (5*B*b^3 - 6*A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^4*c*x^8 + b^5*x^6)","A",0
152,1,121,0,0.426592," ","integrate((B*x^2+A)/x^5/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(16 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{8} + 8 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{6} + 5 \, A b^{4} - 2 \, {\left(7 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} x^{4} + {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{35 \, {\left(b^{5} c x^{10} + b^{6} x^{8}\right)}}"," ",0,"-1/35*(16*(7*B*b*c^3 - 8*A*c^4)*x^8 + 8*(7*B*b^2*c^2 - 8*A*b*c^3)*x^6 + 5*A*b^4 - 2*(7*B*b^3*c - 8*A*b^2*c^2)*x^4 + (7*B*b^4 - 8*A*b^3*c)*x^2)*sqrt(c*x^4 + b*x^2)/(b^5*c*x^10 + b^6*x^8)","A",0
153,1,93,0,0.415917," ","integrate(x^8*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B c^{3} x^{6} - {\left(6 \, B b c^{2} - 5 \, A c^{3}\right)} x^{4} + 48 \, B b^{3} - 40 \, A b^{2} c + 4 \, {\left(6 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, {\left(c^{5} x^{3} + b c^{4} x\right)}}"," ",0,"1/15*(3*B*c^3*x^6 - (6*B*b*c^2 - 5*A*c^3)*x^4 + 48*B*b^3 - 40*A*b^2*c + 4*(6*B*b^2*c - 5*A*b*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^5*x^3 + b*c^4*x)","A",0
154,1,68,0,0.396092," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(B c^{2} x^{4} - 8 \, B b^{2} + 6 \, A b c - {\left(4 \, B b c - 3 \, A c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{3 \, {\left(c^{4} x^{3} + b c^{3} x\right)}}"," ",0,"1/3*(B*c^2*x^4 - 8*B*b^2 + 6*A*b*c - (4*B*b*c - 3*A*c^2)*x^2)*sqrt(c*x^4 + b*x^2)/(c^4*x^3 + b*c^3*x)","A",0
155,1,45,0,0.407470," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(B c x^{2} + 2 \, B b - A c\right)}}{c^{3} x^{3} + b c^{2} x}"," ",0,"sqrt(c*x^4 + b*x^2)*(B*c*x^2 + 2*B*b - A*c)/(c^3*x^3 + b*c^2*x)","A",0
156,1,199,0,0.428319," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A c^{2} x^{3} + A b c x\right)} \sqrt{b} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} {\left(B b^{2} - A b c\right)}}{2 \, {\left(b^{2} c^{2} x^{3} + b^{3} c x\right)}}, \frac{{\left(A c^{2} x^{3} + A b c x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) - \sqrt{c x^{4} + b x^{2}} {\left(B b^{2} - A b c\right)}}{b^{2} c^{2} x^{3} + b^{3} c x}\right]"," ",0,"[1/2*((A*c^2*x^3 + A*b*c*x)*sqrt(b)*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*sqrt(c*x^4 + b*x^2)*(B*b^2 - A*b*c))/(b^2*c^2*x^3 + b^3*c*x), ((A*c^2*x^3 + A*b*c*x)*sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) - sqrt(c*x^4 + b*x^2)*(B*b^2 - A*b*c))/(b^2*c^2*x^3 + b^3*c*x)]","A",0
157,1,260,0,0.442483," ","integrate((B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, B b c - 3 \, A c^{2}\right)} x^{5} + {\left(2 \, B b^{2} - 3 \, A b c\right)} x^{3}\right)} \sqrt{b} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(A b^{2} - {\left(2 \, B b^{2} - 3 \, A b c\right)} x^{2}\right)}}{4 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}, \frac{{\left({\left(2 \, B b c - 3 \, A c^{2}\right)} x^{5} + {\left(2 \, B b^{2} - 3 \, A b c\right)} x^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) - \sqrt{c x^{4} + b x^{2}} {\left(A b^{2} - {\left(2 \, B b^{2} - 3 \, A b c\right)} x^{2}\right)}}{2 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}\right]"," ",0,"[-1/4*(((2*B*b*c - 3*A*c^2)*x^5 + (2*B*b^2 - 3*A*b*c)*x^3)*sqrt(b)*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(A*b^2 - (2*B*b^2 - 3*A*b*c)*x^2))/(b^3*c*x^5 + b^4*x^3), 1/2*(((2*B*b*c - 3*A*c^2)*x^5 + (2*B*b^2 - 3*A*b*c)*x^3)*sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) - sqrt(c*x^4 + b*x^2)*(A*b^2 - (2*B*b^2 - 3*A*b*c)*x^2))/(b^3*c*x^5 + b^4*x^3)]","A",0
158,1,315,0,0.449681," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, B b c^{2} - 5 \, A c^{3}\right)} x^{7} + {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{5}\right)} \sqrt{b} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(3 \, {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{4} + 2 \, A b^{3} + {\left(4 \, B b^{3} - 5 \, A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}, -\frac{3 \, {\left({\left(4 \, B b c^{2} - 5 \, A c^{3}\right)} x^{7} + {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{5}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(3 \, {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{4} + 2 \, A b^{3} + {\left(4 \, B b^{3} - 5 \, A b^{2} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}\right]"," ",0,"[-1/16*(3*((4*B*b*c^2 - 5*A*c^3)*x^7 + (4*B*b^2*c - 5*A*b*c^2)*x^5)*sqrt(b)*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(3*(4*B*b^2*c - 5*A*b*c^2)*x^4 + 2*A*b^3 + (4*B*b^3 - 5*A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^4*c*x^7 + b^5*x^5), -1/8*(3*((4*B*b*c^2 - 5*A*c^3)*x^7 + (4*B*b^2*c - 5*A*b*c^2)*x^5)*sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (3*(4*B*b^2*c - 5*A*b*c^2)*x^4 + 2*A*b^3 + (4*B*b^3 - 5*A*b^2*c)*x^2)*sqrt(c*x^4 + b*x^2))/(b^4*c*x^7 + b^5*x^5)]","A",0
159,1,32,0,0.413490," ","integrate(x^(7/2)*(B*x^2+A)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2}{4641} \, {\left(221 \, B c x^{10} + 273 \, {\left(B b + A c\right)} x^{8} + 357 \, A b x^{6}\right)} \sqrt{x}"," ",0,"2/4641*(221*B*c*x^10 + 273*(B*b + A*c)*x^8 + 357*A*b*x^6)*sqrt(x)","A",0
160,1,32,0,0.395164," ","integrate(x^(5/2)*(B*x^2+A)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2}{3135} \, {\left(165 \, B c x^{9} + 209 \, {\left(B b + A c\right)} x^{7} + 285 \, A b x^{5}\right)} \sqrt{x}"," ",0,"2/3135*(165*B*c*x^9 + 209*(B*b + A*c)*x^7 + 285*A*b*x^5)*sqrt(x)","A",0
161,1,32,0,0.396576," ","integrate(x^(3/2)*(B*x^2+A)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2}{1989} \, {\left(117 \, B c x^{8} + 153 \, {\left(B b + A c\right)} x^{6} + 221 \, A b x^{4}\right)} \sqrt{x}"," ",0,"2/1989*(117*B*c*x^8 + 153*(B*b + A*c)*x^6 + 221*A*b*x^4)*sqrt(x)","A",0
162,1,32,0,0.390273," ","integrate((B*x^2+A)*(c*x^4+b*x^2)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, B c x^{7} + 105 \, {\left(B b + A c\right)} x^{5} + 165 \, A b x^{3}\right)} \sqrt{x}"," ",0,"2/1155*(77*B*c*x^7 + 105*(B*b + A*c)*x^5 + 165*A*b*x^3)*sqrt(x)","A",0
163,1,32,0,0.386996," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{585} \, {\left(45 \, B c x^{6} + 65 \, {\left(B b + A c\right)} x^{4} + 117 \, A b x^{2}\right)} \sqrt{x}"," ",0,"2/585*(45*B*c*x^6 + 65*(B*b + A*c)*x^4 + 117*A*b*x^2)*sqrt(x)","A",0
164,1,30,0,0.378318," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^(3/2),x, algorithm=""fricas"")","\frac{2}{231} \, {\left(21 \, B c x^{5} + 33 \, {\left(B b + A c\right)} x^{3} + 77 \, A b x\right)} \sqrt{x}"," ",0,"2/231*(21*B*c*x^5 + 33*(B*b + A*c)*x^3 + 77*A*b*x)*sqrt(x)","A",0
165,1,29,0,0.388023," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^(5/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(5 \, B c x^{4} + 9 \, {\left(B b + A c\right)} x^{2} + 45 \, A b\right)} \sqrt{x}"," ",0,"2/45*(5*B*c*x^4 + 9*(B*b + A*c)*x^2 + 45*A*b)*sqrt(x)","A",0
166,1,29,0,0.379393," ","integrate((B*x^2+A)*(c*x^4+b*x^2)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c x^{4} + 7 \, {\left(B b + A c\right)} x^{2} - 21 \, A b\right)}}{21 \, \sqrt{x}}"," ",0,"2/21*(3*B*c*x^4 + 7*(B*b + A*c)*x^2 - 21*A*b)/sqrt(x)","A",0
167,1,56,0,0.395677," ","integrate(x^(7/2)*(B*x^2+A)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2}{258825} \, {\left(8925 \, B c^{2} x^{14} + 10353 \, {\left(2 \, B b c + A c^{2}\right)} x^{12} + 15225 \, A b^{2} x^{8} + 12325 \, {\left(B b^{2} + 2 \, A b c\right)} x^{10}\right)} \sqrt{x}"," ",0,"2/258825*(8925*B*c^2*x^14 + 10353*(2*B*b*c + A*c^2)*x^12 + 15225*A*b^2*x^8 + 12325*(B*b^2 + 2*A*b*c)*x^10)*sqrt(x)","A",0
168,1,56,0,0.402248," ","integrate(x^(5/2)*(B*x^2+A)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2}{58995} \, {\left(2185 \, B c^{2} x^{13} + 2565 \, {\left(2 \, B b c + A c^{2}\right)} x^{11} + 3933 \, A b^{2} x^{7} + 3105 \, {\left(B b^{2} + 2 \, A b c\right)} x^{9}\right)} \sqrt{x}"," ",0,"2/58995*(2185*B*c^2*x^13 + 2565*(2*B*b*c + A*c^2)*x^11 + 3933*A*b^2*x^7 + 3105*(B*b^2 + 2*A*b*c)*x^9)*sqrt(x)","A",0
169,1,56,0,0.399015," ","integrate(x^(3/2)*(B*x^2+A)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2}{116025} \, {\left(4641 \, B c^{2} x^{12} + 5525 \, {\left(2 \, B b c + A c^{2}\right)} x^{10} + 8925 \, A b^{2} x^{6} + 6825 \, {\left(B b^{2} + 2 \, A b c\right)} x^{8}\right)} \sqrt{x}"," ",0,"2/116025*(4641*B*c^2*x^12 + 5525*(2*B*b*c + A*c^2)*x^10 + 8925*A*b^2*x^6 + 6825*(B*b^2 + 2*A*b*c)*x^8)*sqrt(x)","A",0
170,1,56,0,0.402426," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{72105} \, {\left(3135 \, B c^{2} x^{11} + 3795 \, {\left(2 \, B b c + A c^{2}\right)} x^{9} + 6555 \, A b^{2} x^{5} + 4807 \, {\left(B b^{2} + 2 \, A b c\right)} x^{7}\right)} \sqrt{x}"," ",0,"2/72105*(3135*B*c^2*x^11 + 3795*(2*B*b*c + A*c^2)*x^9 + 6555*A*b^2*x^5 + 4807*(B*b^2 + 2*A*b*c)*x^7)*sqrt(x)","A",0
171,1,56,0,0.389647," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{13923} \, {\left(663 \, B c^{2} x^{10} + 819 \, {\left(2 \, B b c + A c^{2}\right)} x^{8} + 1547 \, A b^{2} x^{4} + 1071 \, {\left(B b^{2} + 2 \, A b c\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/13923*(663*B*c^2*x^10 + 819*(2*B*b*c + A*c^2)*x^8 + 1547*A*b^2*x^4 + 1071*(B*b^2 + 2*A*b*c)*x^6)*sqrt(x)","A",0
172,1,56,0,0.394581," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2}{21945} \, {\left(1155 \, B c^{2} x^{9} + 1463 \, {\left(2 \, B b c + A c^{2}\right)} x^{7} + 3135 \, A b^{2} x^{3} + 1995 \, {\left(B b^{2} + 2 \, A b c\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/21945*(1155*B*c^2*x^9 + 1463*(2*B*b*c + A*c^2)*x^7 + 3135*A*b^2*x^3 + 1995*(B*b^2 + 2*A*b*c)*x^5)*sqrt(x)","A",0
173,1,56,0,0.394521," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2}{9945} \, {\left(585 \, B c^{2} x^{8} + 765 \, {\left(2 \, B b c + A c^{2}\right)} x^{6} + 1989 \, A b^{2} x^{2} + 1105 \, {\left(B b^{2} + 2 \, A b c\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/9945*(585*B*c^2*x^8 + 765*(2*B*b*c + A*c^2)*x^6 + 1989*A*b^2*x^2 + 1105*(B*b^2 + 2*A*b*c)*x^4)*sqrt(x)","A",0
174,1,54,0,0.395149," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, B c^{2} x^{7} + 105 \, {\left(2 \, B b c + A c^{2}\right)} x^{5} + 385 \, A b^{2} x + 165 \, {\left(B b^{2} + 2 \, A b c\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/1155*(77*B*c^2*x^7 + 105*(2*B*b*c + A*c^2)*x^5 + 385*A*b^2*x + 165*(B*b^2 + 2*A*b*c)*x^3)*sqrt(x)","A",0
175,1,78,0,0.395213," ","integrate(x^(7/2)*(B*x^2+A)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2}{6196575} \, {\left(167475 \, B c^{3} x^{18} + 187775 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{16} + 641025 \, {\left(B b^{2} c + A b c^{2}\right)} x^{14} + 295075 \, A b^{3} x^{10} + 247863 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{12}\right)} \sqrt{x}"," ",0,"2/6196575*(167475*B*c^3*x^18 + 187775*(3*B*b*c^2 + A*c^3)*x^16 + 641025*(B*b^2*c + A*b*c^2)*x^14 + 295075*A*b^3*x^10 + 247863*(B*b^3 + 3*A*b^2*c)*x^12)*sqrt(x)","A",0
176,1,78,0,0.395003," ","integrate(x^(5/2)*(B*x^2+A)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2}{4267305} \, {\left(121923 \, B c^{3} x^{17} + 137655 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{15} + 474145 \, {\left(B b^{2} c + A b c^{2}\right)} x^{13} + 224595 \, A b^{3} x^{9} + 185535 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{11}\right)} \sqrt{x}"," ",0,"2/4267305*(121923*B*c^3*x^17 + 137655*(3*B*b*c^2 + A*c^3)*x^15 + 474145*(B*b^2*c + A*b*c^2)*x^13 + 224595*A*b^3*x^9 + 185535*(B*b^3 + 3*A*b^2*c)*x^11)*sqrt(x)","A",0
177,1,78,0,0.402645," ","integrate(x^(3/2)*(B*x^2+A)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2}{2847075} \, {\left(86275 \, B c^{3} x^{16} + 98175 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{14} + 341649 \, {\left(B b^{2} c + A b c^{2}\right)} x^{12} + 167475 \, A b^{3} x^{8} + 135575 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{10}\right)} \sqrt{x}"," ",0,"2/2847075*(86275*B*c^3*x^16 + 98175*(3*B*b*c^2 + A*c^3)*x^14 + 341649*(B*b^2*c + A*b*c^2)*x^12 + 167475*A*b^3*x^8 + 135575*(B*b^3 + 3*A*b^2*c)*x^10)*sqrt(x)","A",0
178,1,78,0,0.389870," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{1828845} \, {\left(58995 \, B c^{3} x^{15} + 67735 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{13} + 238545 \, {\left(B b^{2} c + A b c^{2}\right)} x^{11} + 121923 \, A b^{3} x^{7} + 96255 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{9}\right)} \sqrt{x}"," ",0,"2/1828845*(58995*B*c^3*x^15 + 67735*(3*B*b*c^2 + A*c^3)*x^13 + 238545*(B*b^2*c + A*b*c^2)*x^11 + 121923*A*b^3*x^7 + 96255*(B*b^3 + 3*A*b^2*c)*x^9)*sqrt(x)","A",0
179,1,78,0,0.402698," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{1121575} \, {\left(38675 \, B c^{3} x^{14} + 44863 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{12} + 160225 \, {\left(B b^{2} c + A b c^{2}\right)} x^{10} + 86275 \, A b^{3} x^{6} + 65975 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{8}\right)} \sqrt{x}"," ",0,"2/1121575*(38675*B*c^3*x^14 + 44863*(3*B*b*c^2 + A*c^3)*x^12 + 160225*(B*b^2*c + A*b*c^2)*x^10 + 86275*A*b^3*x^6 + 65975*(B*b^3 + 3*A*b^2*c)*x^8)*sqrt(x)","A",0
180,1,78,0,0.401283," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2}{648945} \, {\left(24035 \, B c^{3} x^{13} + 28215 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{11} + 102465 \, {\left(B b^{2} c + A b c^{2}\right)} x^{9} + 58995 \, A b^{3} x^{5} + 43263 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{7}\right)} \sqrt{x}"," ",0,"2/648945*(24035*B*c^3*x^13 + 28215*(3*B*b*c^2 + A*c^3)*x^11 + 102465*(B*b^2*c + A*b*c^2)*x^9 + 58995*A*b^3*x^5 + 43263*(B*b^3 + 3*A*b^2*c)*x^7)*sqrt(x)","A",0
181,1,78,0,0.397760," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2}{348075} \, {\left(13923 \, B c^{3} x^{12} + 16575 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{10} + 61425 \, {\left(B b^{2} c + A b c^{2}\right)} x^{8} + 38675 \, A b^{3} x^{4} + 26775 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/348075*(13923*B*c^3*x^12 + 16575*(3*B*b*c^2 + A*c^3)*x^10 + 61425*(B*b^2*c + A*b*c^2)*x^8 + 38675*A*b^3*x^4 + 26775*(B*b^3 + 3*A*b^2*c)*x^6)*sqrt(x)","A",0
182,1,78,0,0.404632," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2}{168245} \, {\left(7315 \, B c^{3} x^{11} + 8855 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{9} + 33649 \, {\left(B b^{2} c + A b c^{2}\right)} x^{7} + 24035 \, A b^{3} x^{3} + 15295 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/168245*(7315*B*c^3*x^11 + 8855*(3*B*b*c^2 + A*c^3)*x^9 + 33649*(B*b^2*c + A*b*c^2)*x^7 + 24035*A*b^3*x^3 + 15295*(B*b^3 + 3*A*b^2*c)*x^5)*sqrt(x)","A",0
183,1,920,0,0.453270," ","integrate(x^(13/2)*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{924 \, c^{3} \left(-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{16} - 6 \, A B^{5} b^{15} c + 15 \, A^{2} B^{4} b^{14} c^{2} - 20 \, A^{3} B^{3} b^{13} c^{3} + 15 \, A^{4} B^{2} b^{12} c^{4} - 6 \, A^{5} B b^{11} c^{5} + A^{6} b^{10} c^{6}\right)} x - {\left(B^{4} b^{11} c^{7} - 4 \, A B^{3} b^{10} c^{8} + 6 \, A^{2} B^{2} b^{9} c^{9} - 4 \, A^{3} B b^{8} c^{10} + A^{4} b^{7} c^{11}\right)} \sqrt{-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}}} c^{4} \left(-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{8} c^{4} - 3 \, A B^{2} b^{7} c^{5} + 3 \, A^{2} B b^{6} c^{6} - A^{3} b^{5} c^{7}\right)} \sqrt{x} \left(-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}\right)^{\frac{1}{4}}}{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}\right) - 231 \, c^{3} \left(-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}\right)^{\frac{1}{4}} \log\left(c^{11} \left(-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{8} - 3 \, A B^{2} b^{7} c + 3 \, A^{2} B b^{6} c^{2} - A^{3} b^{5} c^{3}\right)} \sqrt{x}\right) + 231 \, c^{3} \left(-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}\right)^{\frac{1}{4}} \log\left(-c^{11} \left(-\frac{B^{4} b^{11} - 4 \, A B^{3} b^{10} c + 6 \, A^{2} B^{2} b^{9} c^{2} - 4 \, A^{3} B b^{8} c^{3} + A^{4} b^{7} c^{4}}{c^{15}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{8} - 3 \, A B^{2} b^{7} c + 3 \, A^{2} B b^{6} c^{2} - A^{3} b^{5} c^{3}\right)} \sqrt{x}\right) - 4 \, {\left(21 \, B c^{2} x^{5} - 33 \, {\left(B b c - A c^{2}\right)} x^{3} + 77 \, {\left(B b^{2} - A b c\right)} x\right)} \sqrt{x}}{462 \, c^{3}}"," ",0,"-1/462*(924*c^3*(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15)^(1/4)*arctan((sqrt((B^6*b^16 - 6*A*B^5*b^15*c + 15*A^2*B^4*b^14*c^2 - 20*A^3*B^3*b^13*c^3 + 15*A^4*B^2*b^12*c^4 - 6*A^5*B*b^11*c^5 + A^6*b^10*c^6)*x - (B^4*b^11*c^7 - 4*A*B^3*b^10*c^8 + 6*A^2*B^2*b^9*c^9 - 4*A^3*B*b^8*c^10 + A^4*b^7*c^11)*sqrt(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15))*c^4*(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15)^(1/4) + (B^3*b^8*c^4 - 3*A*B^2*b^7*c^5 + 3*A^2*B*b^6*c^6 - A^3*b^5*c^7)*sqrt(x)*(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15)^(1/4))/(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)) - 231*c^3*(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15)^(1/4)*log(c^11*(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15)^(3/4) - (B^3*b^8 - 3*A*B^2*b^7*c + 3*A^2*B*b^6*c^2 - A^3*b^5*c^3)*sqrt(x)) + 231*c^3*(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15)^(1/4)*log(-c^11*(-(B^4*b^11 - 4*A*B^3*b^10*c + 6*A^2*B^2*b^9*c^2 - 4*A^3*B*b^8*c^3 + A^4*b^7*c^4)/c^15)^(3/4) - (B^3*b^8 - 3*A*B^2*b^7*c + 3*A^2*B*b^6*c^2 - A^3*b^5*c^3)*sqrt(x)) - 4*(21*B*c^2*x^5 - 33*(B*b*c - A*c^2)*x^3 + 77*(B*b^2 - A*b*c)*x)*sqrt(x))/c^3","B",0
184,1,714,0,0.432306," ","integrate(x^(11/2)*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{180 \, c^{3} \left(-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{6} \sqrt{-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}} + {\left(B^{2} b^{4} - 2 \, A B b^{3} c + A^{2} b^{2} c^{2}\right)} x} c^{10} \left(-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}\right)^{\frac{3}{4}} + {\left(B b^{2} c^{10} - A b c^{11}\right)} \sqrt{x} \left(-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}\right)^{\frac{3}{4}}}{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}\right) + 45 \, c^{3} \left(-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}\right)^{\frac{1}{4}} \log\left(c^{3} \left(-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}\right)^{\frac{1}{4}} - {\left(B b^{2} - A b c\right)} \sqrt{x}\right) - 45 \, c^{3} \left(-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}\right)^{\frac{1}{4}} \log\left(-c^{3} \left(-\frac{B^{4} b^{9} - 4 \, A B^{3} b^{8} c + 6 \, A^{2} B^{2} b^{7} c^{2} - 4 \, A^{3} B b^{6} c^{3} + A^{4} b^{5} c^{4}}{c^{13}}\right)^{\frac{1}{4}} - {\left(B b^{2} - A b c\right)} \sqrt{x}\right) + 4 \, {\left(5 \, B c^{2} x^{4} + 45 \, B b^{2} - 45 \, A b c - 9 \, {\left(B b c - A c^{2}\right)} x^{2}\right)} \sqrt{x}}{90 \, c^{3}}"," ",0,"1/90*(180*c^3*(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13)^(1/4)*arctan((sqrt(c^6*sqrt(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13) + (B^2*b^4 - 2*A*B*b^3*c + A^2*b^2*c^2)*x)*c^10*(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13)^(3/4) + (B*b^2*c^10 - A*b*c^11)*sqrt(x)*(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13)^(3/4))/(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)) + 45*c^3*(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13)^(1/4)*log(c^3*(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13)^(1/4) - (B*b^2 - A*b*c)*sqrt(x)) - 45*c^3*(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13)^(1/4)*log(-c^3*(-(B^4*b^9 - 4*A*B^3*b^8*c + 6*A^2*B^2*b^7*c^2 - 4*A^3*B*b^6*c^3 + A^4*b^5*c^4)/c^13)^(1/4) - (B*b^2 - A*b*c)*sqrt(x)) + 4*(5*B*c^2*x^4 + 45*B*b^2 - 45*A*b*c - 9*(B*b*c - A*c^2)*x^2)*sqrt(x))/c^3","B",0
185,1,899,0,0.452400," ","integrate(x^(9/2)*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{84 \, c^{2} \left(-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{10} - 6 \, A B^{5} b^{9} c + 15 \, A^{2} B^{4} b^{8} c^{2} - 20 \, A^{3} B^{3} b^{7} c^{3} + 15 \, A^{4} B^{2} b^{6} c^{4} - 6 \, A^{5} B b^{5} c^{5} + A^{6} b^{4} c^{6}\right)} x - {\left(B^{4} b^{7} c^{5} - 4 \, A B^{3} b^{6} c^{6} + 6 \, A^{2} B^{2} b^{5} c^{7} - 4 \, A^{3} B b^{4} c^{8} + A^{4} b^{3} c^{9}\right)} \sqrt{-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}}} c^{3} \left(-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{5} c^{3} - 3 \, A B^{2} b^{4} c^{4} + 3 \, A^{2} B b^{3} c^{5} - A^{3} b^{2} c^{6}\right)} \sqrt{x} \left(-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}\right)^{\frac{1}{4}}}{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}\right) - 21 \, c^{2} \left(-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}\right)^{\frac{1}{4}} \log\left(c^{8} \left(-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{5} - 3 \, A B^{2} b^{4} c + 3 \, A^{2} B b^{3} c^{2} - A^{3} b^{2} c^{3}\right)} \sqrt{x}\right) + 21 \, c^{2} \left(-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}\right)^{\frac{1}{4}} \log\left(-c^{8} \left(-\frac{B^{4} b^{7} - 4 \, A B^{3} b^{6} c + 6 \, A^{2} B^{2} b^{5} c^{2} - 4 \, A^{3} B b^{4} c^{3} + A^{4} b^{3} c^{4}}{c^{11}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{5} - 3 \, A B^{2} b^{4} c + 3 \, A^{2} B b^{3} c^{2} - A^{3} b^{2} c^{3}\right)} \sqrt{x}\right) + 4 \, {\left(3 \, B c x^{3} - 7 \, {\left(B b - A c\right)} x\right)} \sqrt{x}}{42 \, c^{2}}"," ",0,"1/42*(84*c^2*(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11)^(1/4)*arctan((sqrt((B^6*b^10 - 6*A*B^5*b^9*c + 15*A^2*B^4*b^8*c^2 - 20*A^3*B^3*b^7*c^3 + 15*A^4*B^2*b^6*c^4 - 6*A^5*B*b^5*c^5 + A^6*b^4*c^6)*x - (B^4*b^7*c^5 - 4*A*B^3*b^6*c^6 + 6*A^2*B^2*b^5*c^7 - 4*A^3*B*b^4*c^8 + A^4*b^3*c^9)*sqrt(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11))*c^3*(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11)^(1/4) + (B^3*b^5*c^3 - 3*A*B^2*b^4*c^4 + 3*A^2*B*b^3*c^5 - A^3*b^2*c^6)*sqrt(x)*(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11)^(1/4))/(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)) - 21*c^2*(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11)^(1/4)*log(c^8*(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11)^(3/4) - (B^3*b^5 - 3*A*B^2*b^4*c + 3*A^2*B*b^3*c^2 - A^3*b^2*c^3)*sqrt(x)) + 21*c^2*(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11)^(1/4)*log(-c^8*(-(B^4*b^7 - 4*A*B^3*b^6*c + 6*A^2*B^2*b^5*c^2 - 4*A^3*B*b^4*c^3 + A^4*b^3*c^4)/c^11)^(3/4) - (B^3*b^5 - 3*A*B^2*b^4*c + 3*A^2*B*b^3*c^2 - A^3*b^2*c^3)*sqrt(x)) + 4*(3*B*c*x^3 - 7*(B*b - A*c)*x)*sqrt(x))/c^2","B",0
186,1,660,0,0.428613," ","integrate(x^(7/2)*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{20 \, c^{2} \left(-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{4} \sqrt{-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}} + {\left(B^{2} b^{2} - 2 \, A B b c + A^{2} c^{2}\right)} x} c^{7} \left(-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}\right)^{\frac{3}{4}} + {\left(B b c^{7} - A c^{8}\right)} \sqrt{x} \left(-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}\right)^{\frac{3}{4}}}{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}\right) + 5 \, c^{2} \left(-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}\right)^{\frac{1}{4}} \log\left(c^{2} \left(-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}\right)^{\frac{1}{4}} - {\left(B b - A c\right)} \sqrt{x}\right) - 5 \, c^{2} \left(-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}\right)^{\frac{1}{4}} \log\left(-c^{2} \left(-\frac{B^{4} b^{5} - 4 \, A B^{3} b^{4} c + 6 \, A^{2} B^{2} b^{3} c^{2} - 4 \, A^{3} B b^{2} c^{3} + A^{4} b c^{4}}{c^{9}}\right)^{\frac{1}{4}} - {\left(B b - A c\right)} \sqrt{x}\right) - 4 \, {\left(B c x^{2} - 5 \, B b + 5 \, A c\right)} \sqrt{x}}{10 \, c^{2}}"," ",0,"-1/10*(20*c^2*(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9)^(1/4)*arctan((sqrt(c^4*sqrt(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9) + (B^2*b^2 - 2*A*B*b*c + A^2*c^2)*x)*c^7*(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9)^(3/4) + (B*b*c^7 - A*c^8)*sqrt(x)*(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9)^(3/4))/(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)) + 5*c^2*(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9)^(1/4)*log(c^2*(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9)^(1/4) - (B*b - A*c)*sqrt(x)) - 5*c^2*(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9)^(1/4)*log(-c^2*(-(B^4*b^5 - 4*A*B^3*b^4*c + 6*A^2*B^2*b^3*c^2 - 4*A^3*B*b^2*c^3 + A^4*b*c^4)/c^9)^(1/4) - (B*b - A*c)*sqrt(x)) - 4*(B*c*x^2 - 5*B*b + 5*A*c)*sqrt(x))/c^2","B",0
187,1,834,0,0.462701," ","integrate(x^(5/2)*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{4 \, B x^{\frac{3}{2}} - 12 \, c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{6} - 6 \, A B^{5} b^{5} c + 15 \, A^{2} B^{4} b^{4} c^{2} - 20 \, A^{3} B^{3} b^{3} c^{3} + 15 \, A^{4} B^{2} b^{2} c^{4} - 6 \, A^{5} B b c^{5} + A^{6} c^{6}\right)} x - {\left(B^{4} b^{5} c^{3} - 4 \, A B^{3} b^{4} c^{4} + 6 \, A^{2} B^{2} b^{3} c^{5} - 4 \, A^{3} B b^{2} c^{6} + A^{4} b c^{7}\right)} \sqrt{-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}}} c^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{3} c^{2} - 3 \, A B^{2} b^{2} c^{3} + 3 \, A^{2} B b c^{4} - A^{3} c^{5}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}\right)^{\frac{1}{4}}}{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) + 3 \, c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}\right)^{\frac{1}{4}} \log\left(b c^{5} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} - 3 \, A B^{2} b^{2} c + 3 \, A^{2} B b c^{2} - A^{3} c^{3}\right)} \sqrt{x}\right) - 3 \, c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}\right)^{\frac{1}{4}} \log\left(-b c^{5} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b c^{7}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} - 3 \, A B^{2} b^{2} c + 3 \, A^{2} B b c^{2} - A^{3} c^{3}\right)} \sqrt{x}\right)}{6 \, c}"," ",0,"1/6*(4*B*x^(3/2) - 12*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7))^(1/4)*arctan((sqrt((B^6*b^6 - 6*A*B^5*b^5*c + 15*A^2*B^4*b^4*c^2 - 20*A^3*B^3*b^3*c^3 + 15*A^4*B^2*b^2*c^4 - 6*A^5*B*b*c^5 + A^6*c^6)*x - (B^4*b^5*c^3 - 4*A*B^3*b^4*c^4 + 6*A^2*B^2*b^3*c^5 - 4*A^3*B*b^2*c^6 + A^4*b*c^7)*sqrt(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7)))*c^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7))^(1/4) + (B^3*b^3*c^2 - 3*A*B^2*b^2*c^3 + 3*A^2*B*b*c^4 - A^3*c^5)*sqrt(x)*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7))^(1/4))/(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)) + 3*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7))^(1/4)*log(b*c^5*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7))^(3/4) - (B^3*b^3 - 3*A*B^2*b^2*c + 3*A^2*B*b*c^2 - A^3*c^3)*sqrt(x)) - 3*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7))^(1/4)*log(-b*c^5*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b*c^7))^(3/4) - (B^3*b^3 - 3*A*B^2*b^2*c + 3*A^2*B*b*c^2 - A^3*c^3)*sqrt(x)))/c","B",0
188,1,645,0,0.439652," ","integrate(x^(3/2)*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{4 \, c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{2} c^{2} \sqrt{-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}} + {\left(B^{2} b^{2} - 2 \, A B b c + A^{2} c^{2}\right)} x} b^{2} c^{4} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}\right)^{\frac{3}{4}} + {\left(B b^{3} c^{4} - A b^{2} c^{5}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}\right)^{\frac{3}{4}}}{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) + c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(b c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}\right)^{\frac{1}{4}} - {\left(B b - A c\right)} \sqrt{x}\right) - c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(-b c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{5}}\right)^{\frac{1}{4}} - {\left(B b - A c\right)} \sqrt{x}\right) + 4 \, B \sqrt{x}}{2 \, c}"," ",0,"1/2*(4*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5))^(1/4)*arctan((sqrt(b^2*c^2*sqrt(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5)) + (B^2*b^2 - 2*A*B*b*c + A^2*c^2)*x)*b^2*c^4*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5))^(3/4) + (B*b^3*c^4 - A*b^2*c^5)*sqrt(x)*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5))^(3/4))/(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)) + c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5))^(1/4)*log(b*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5))^(1/4) - (B*b - A*c)*sqrt(x)) - c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5))^(1/4)*log(-b*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^5))^(1/4) - (B*b - A*c)*sqrt(x)) + 4*B*sqrt(x))/c","B",0
189,1,843,0,0.453563," ","integrate((B*x^2+A)*x^(1/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{4 \, b x \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{6} - 6 \, A B^{5} b^{5} c + 15 \, A^{2} B^{4} b^{4} c^{2} - 20 \, A^{3} B^{3} b^{3} c^{3} + 15 \, A^{4} B^{2} b^{2} c^{4} - 6 \, A^{5} B b c^{5} + A^{6} c^{6}\right)} x - {\left(B^{4} b^{7} c - 4 \, A B^{3} b^{6} c^{2} + 6 \, A^{2} B^{2} b^{5} c^{3} - 4 \, A^{3} B b^{4} c^{4} + A^{4} b^{3} c^{5}\right)} \sqrt{-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}}} b c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{4} c - 3 \, A B^{2} b^{3} c^{2} + 3 \, A^{2} B b^{2} c^{3} - A^{3} b c^{4}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}\right)^{\frac{1}{4}}}{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) - b x \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}\right)^{\frac{1}{4}} \log\left(b^{4} c^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} - 3 \, A B^{2} b^{2} c + 3 \, A^{2} B b c^{2} - A^{3} c^{3}\right)} \sqrt{x}\right) + b x \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}\right)^{\frac{1}{4}} \log\left(-b^{4} c^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} - 3 \, A B^{2} b^{2} c + 3 \, A^{2} B b c^{2} - A^{3} c^{3}\right)} \sqrt{x}\right) - 4 \, A \sqrt{x}}{2 \, b x}"," ",0,"1/2*(4*b*x*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3))^(1/4)*arctan((sqrt((B^6*b^6 - 6*A*B^5*b^5*c + 15*A^2*B^4*b^4*c^2 - 20*A^3*B^3*b^3*c^3 + 15*A^4*B^2*b^2*c^4 - 6*A^5*B*b*c^5 + A^6*c^6)*x - (B^4*b^7*c - 4*A*B^3*b^6*c^2 + 6*A^2*B^2*b^5*c^3 - 4*A^3*B*b^4*c^4 + A^4*b^3*c^5)*sqrt(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3)))*b*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3))^(1/4) + (B^3*b^4*c - 3*A*B^2*b^3*c^2 + 3*A^2*B*b^2*c^3 - A^3*b*c^4)*sqrt(x)*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3))^(1/4))/(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)) - b*x*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3))^(1/4)*log(b^4*c^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3))^(3/4) - (B^3*b^3 - 3*A*B^2*b^2*c + 3*A^2*B*b*c^2 - A^3*c^3)*sqrt(x)) + b*x*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3))^(1/4)*log(-b^4*c^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^3))^(3/4) - (B^3*b^3 - 3*A*B^2*b^2*c + 3*A^2*B*b*c^2 - A^3*c^3)*sqrt(x)) - 4*A*sqrt(x))/(b*x)","B",0
190,1,653,0,0.439726," ","integrate((B*x^2+A)/(c*x^4+b*x^2)/x^(1/2),x, algorithm=""fricas"")","-\frac{12 \, b x^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{4} \sqrt{-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}} + {\left(B^{2} b^{2} - 2 \, A B b c + A^{2} c^{2}\right)} x} b^{5} c \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}\right)^{\frac{3}{4}} + {\left(B b^{6} c - A b^{5} c^{2}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}\right)^{\frac{3}{4}}}{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) + 3 \, b x^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}\right)^{\frac{1}{4}} \log\left(b^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}\right)^{\frac{1}{4}} - {\left(B b - A c\right)} \sqrt{x}\right) - 3 \, b x^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}\right)^{\frac{1}{4}} \log\left(-b^{2} \left(-\frac{B^{4} b^{4} - 4 \, A B^{3} b^{3} c + 6 \, A^{2} B^{2} b^{2} c^{2} - 4 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{7} c}\right)^{\frac{1}{4}} - {\left(B b - A c\right)} \sqrt{x}\right) + 4 \, A \sqrt{x}}{6 \, b x^{2}}"," ",0,"-1/6*(12*b*x^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c))^(1/4)*arctan((sqrt(b^4*sqrt(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c)) + (B^2*b^2 - 2*A*B*b*c + A^2*c^2)*x)*b^5*c*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c))^(3/4) + (B*b^6*c - A*b^5*c^2)*sqrt(x)*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c))^(3/4))/(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)) + 3*b*x^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c))^(1/4)*log(b^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c))^(1/4) - (B*b - A*c)*sqrt(x)) - 3*b*x^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c))^(1/4)*log(-b^2*(-(B^4*b^4 - 4*A*B^3*b^3*c + 6*A^2*B^2*b^2*c^2 - 4*A^3*B*b*c^3 + A^4*c^4)/(b^7*c))^(1/4) - (B*b - A*c)*sqrt(x)) + 4*A*sqrt(x))/(b*x^2)","B",0
191,1,883,0,0.439947," ","integrate((B*x^2+A)/x^(3/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{20 \, b^{2} x^{3} \left(-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{6} c^{2} - 6 \, A B^{5} b^{5} c^{3} + 15 \, A^{2} B^{4} b^{4} c^{4} - 20 \, A^{3} B^{3} b^{3} c^{5} + 15 \, A^{4} B^{2} b^{2} c^{6} - 6 \, A^{5} B b c^{7} + A^{6} c^{8}\right)} x - {\left(B^{4} b^{9} c - 4 \, A B^{3} b^{8} c^{2} + 6 \, A^{2} B^{2} b^{7} c^{3} - 4 \, A^{3} B b^{6} c^{4} + A^{4} b^{5} c^{5}\right)} \sqrt{-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}}} b^{2} \left(-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{5} c - 3 \, A B^{2} b^{4} c^{2} + 3 \, A^{2} B b^{3} c^{3} - A^{3} b^{2} c^{4}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}\right)^{\frac{1}{4}}}{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}\right) - 5 \, b^{2} x^{3} \left(-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}\right)^{\frac{1}{4}} \log\left(b^{7} \left(-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} c - 3 \, A B^{2} b^{2} c^{2} + 3 \, A^{2} B b c^{3} - A^{3} c^{4}\right)} \sqrt{x}\right) + 5 \, b^{2} x^{3} \left(-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-b^{7} \left(-\frac{B^{4} b^{4} c - 4 \, A B^{3} b^{3} c^{2} + 6 \, A^{2} B^{2} b^{2} c^{3} - 4 \, A^{3} B b c^{4} + A^{4} c^{5}}{b^{9}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} c - 3 \, A B^{2} b^{2} c^{2} + 3 \, A^{2} B b c^{3} - A^{3} c^{4}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, {\left(B b - A c\right)} x^{2} + A b\right)} \sqrt{x}}{10 \, b^{2} x^{3}}"," ",0,"-1/10*(20*b^2*x^3*(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9)^(1/4)*arctan((sqrt((B^6*b^6*c^2 - 6*A*B^5*b^5*c^3 + 15*A^2*B^4*b^4*c^4 - 20*A^3*B^3*b^3*c^5 + 15*A^4*B^2*b^2*c^6 - 6*A^5*B*b*c^7 + A^6*c^8)*x - (B^4*b^9*c - 4*A*B^3*b^8*c^2 + 6*A^2*B^2*b^7*c^3 - 4*A^3*B*b^6*c^4 + A^4*b^5*c^5)*sqrt(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9))*b^2*(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9)^(1/4) + (B^3*b^5*c - 3*A*B^2*b^4*c^2 + 3*A^2*B*b^3*c^3 - A^3*b^2*c^4)*sqrt(x)*(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9)^(1/4))/(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)) - 5*b^2*x^3*(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9)^(1/4)*log(b^7*(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9)^(3/4) - (B^3*b^3*c - 3*A*B^2*b^2*c^2 + 3*A^2*B*b*c^3 - A^3*c^4)*sqrt(x)) + 5*b^2*x^3*(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9)^(1/4)*log(-b^7*(-(B^4*b^4*c - 4*A*B^3*b^3*c^2 + 6*A^2*B^2*b^2*c^3 - 4*A^3*B*b*c^4 + A^4*c^5)/b^9)^(3/4) - (B^3*b^3*c - 3*A*B^2*b^2*c^2 + 3*A^2*B*b*c^3 - A^3*c^4)*sqrt(x)) + 4*(5*(B*b - A*c)*x^2 + A*b)*sqrt(x))/(b^2*x^3)","B",0
192,1,707,0,0.430651," ","integrate((B*x^2+A)/x^(5/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{84 \, b^{2} x^{4} \left(-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{6} \sqrt{-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}} + {\left(B^{2} b^{2} c^{2} - 2 \, A B b c^{3} + A^{2} c^{4}\right)} x} b^{8} \left(-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}\right)^{\frac{3}{4}} + {\left(B b^{9} c - A b^{8} c^{2}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}\right)^{\frac{3}{4}}}{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}\right) + 21 \, b^{2} x^{4} \left(-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}\right)^{\frac{1}{4}} \log\left(b^{3} \left(-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}\right)^{\frac{1}{4}} - {\left(B b c - A c^{2}\right)} \sqrt{x}\right) - 21 \, b^{2} x^{4} \left(-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}\right)^{\frac{1}{4}} \log\left(-b^{3} \left(-\frac{B^{4} b^{4} c^{3} - 4 \, A B^{3} b^{3} c^{4} + 6 \, A^{2} B^{2} b^{2} c^{5} - 4 \, A^{3} B b c^{6} + A^{4} c^{7}}{b^{11}}\right)^{\frac{1}{4}} - {\left(B b c - A c^{2}\right)} \sqrt{x}\right) - 4 \, {\left(7 \, {\left(B b - A c\right)} x^{2} + 3 \, A b\right)} \sqrt{x}}{42 \, b^{2} x^{4}}"," ",0,"1/42*(84*b^2*x^4*(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11)^(1/4)*arctan((sqrt(b^6*sqrt(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11) + (B^2*b^2*c^2 - 2*A*B*b*c^3 + A^2*c^4)*x)*b^8*(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11)^(3/4) + (B*b^9*c - A*b^8*c^2)*sqrt(x)*(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11)^(3/4))/(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)) + 21*b^2*x^4*(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11)^(1/4)*log(b^3*(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11)^(1/4) - (B*b*c - A*c^2)*sqrt(x)) - 21*b^2*x^4*(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11)^(1/4)*log(-b^3*(-(B^4*b^4*c^3 - 4*A*B^3*b^3*c^4 + 6*A^2*B^2*b^2*c^5 - 4*A^3*B*b*c^6 + A^4*c^7)/b^11)^(1/4) - (B*b*c - A*c^2)*sqrt(x)) - 4*(7*(B*b - A*c)*x^2 + 3*A*b)*sqrt(x))/(b^2*x^4)","B",0
193,1,931,0,0.448024," ","integrate((B*x^2+A)/x^(7/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{180 \, b^{3} x^{5} \left(-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{6} c^{8} - 6 \, A B^{5} b^{5} c^{9} + 15 \, A^{2} B^{4} b^{4} c^{10} - 20 \, A^{3} B^{3} b^{3} c^{11} + 15 \, A^{4} B^{2} b^{2} c^{12} - 6 \, A^{5} B b c^{13} + A^{6} c^{14}\right)} x - {\left(B^{4} b^{11} c^{5} - 4 \, A B^{3} b^{10} c^{6} + 6 \, A^{2} B^{2} b^{9} c^{7} - 4 \, A^{3} B b^{8} c^{8} + A^{4} b^{7} c^{9}\right)} \sqrt{-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}}} b^{3} \left(-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{6} c^{4} - 3 \, A B^{2} b^{5} c^{5} + 3 \, A^{2} B b^{4} c^{6} - A^{3} b^{3} c^{7}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}\right)^{\frac{1}{4}}}{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}\right) - 45 \, b^{3} x^{5} \left(-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}\right)^{\frac{1}{4}} \log\left(b^{10} \left(-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} c^{4} - 3 \, A B^{2} b^{2} c^{5} + 3 \, A^{2} B b c^{6} - A^{3} c^{7}\right)} \sqrt{x}\right) + 45 \, b^{3} x^{5} \left(-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-b^{10} \left(-\frac{B^{4} b^{4} c^{5} - 4 \, A B^{3} b^{3} c^{6} + 6 \, A^{2} B^{2} b^{2} c^{7} - 4 \, A^{3} B b c^{8} + A^{4} c^{9}}{b^{13}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} c^{4} - 3 \, A B^{2} b^{2} c^{5} + 3 \, A^{2} B b c^{6} - A^{3} c^{7}\right)} \sqrt{x}\right) + 4 \, {\left(45 \, {\left(B b c - A c^{2}\right)} x^{4} - 5 \, A b^{2} - 9 \, {\left(B b^{2} - A b c\right)} x^{2}\right)} \sqrt{x}}{90 \, b^{3} x^{5}}"," ",0,"1/90*(180*b^3*x^5*(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13)^(1/4)*arctan((sqrt((B^6*b^6*c^8 - 6*A*B^5*b^5*c^9 + 15*A^2*B^4*b^4*c^10 - 20*A^3*B^3*b^3*c^11 + 15*A^4*B^2*b^2*c^12 - 6*A^5*B*b*c^13 + A^6*c^14)*x - (B^4*b^11*c^5 - 4*A*B^3*b^10*c^6 + 6*A^2*B^2*b^9*c^7 - 4*A^3*B*b^8*c^8 + A^4*b^7*c^9)*sqrt(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13))*b^3*(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13)^(1/4) + (B^3*b^6*c^4 - 3*A*B^2*b^5*c^5 + 3*A^2*B*b^4*c^6 - A^3*b^3*c^7)*sqrt(x)*(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13)^(1/4))/(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)) - 45*b^3*x^5*(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13)^(1/4)*log(b^10*(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13)^(3/4) - (B^3*b^3*c^4 - 3*A*B^2*b^2*c^5 + 3*A^2*B*b*c^6 - A^3*c^7)*sqrt(x)) + 45*b^3*x^5*(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13)^(1/4)*log(-b^10*(-(B^4*b^4*c^5 - 4*A*B^3*b^3*c^6 + 6*A^2*B^2*b^2*c^7 - 4*A^3*B*b*c^8 + A^4*c^9)/b^13)^(3/4) - (B^3*b^3*c^4 - 3*A*B^2*b^2*c^5 + 3*A^2*B*b*c^6 - A^3*c^7)*sqrt(x)) + 4*(45*(B*b*c - A*c^2)*x^4 - 5*A*b^2 - 9*(B*b^2 - A*b*c)*x^2)*sqrt(x))/(b^3*x^5)","B",0
194,1,734,0,0.439159," ","integrate((B*x^2+A)/x^(9/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{924 \, b^{3} x^{6} \left(-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{8} \sqrt{-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}} + {\left(B^{2} b^{2} c^{4} - 2 \, A B b c^{5} + A^{2} c^{6}\right)} x} b^{11} \left(-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}\right)^{\frac{3}{4}} + {\left(B b^{12} c^{2} - A b^{11} c^{3}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}\right)^{\frac{3}{4}}}{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}\right) + 231 \, b^{3} x^{6} \left(-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}\right)^{\frac{1}{4}} \log\left(b^{4} \left(-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}\right)^{\frac{1}{4}} - {\left(B b c^{2} - A c^{3}\right)} \sqrt{x}\right) - 231 \, b^{3} x^{6} \left(-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}\right)^{\frac{1}{4}} \log\left(-b^{4} \left(-\frac{B^{4} b^{4} c^{7} - 4 \, A B^{3} b^{3} c^{8} + 6 \, A^{2} B^{2} b^{2} c^{9} - 4 \, A^{3} B b c^{10} + A^{4} c^{11}}{b^{15}}\right)^{\frac{1}{4}} - {\left(B b c^{2} - A c^{3}\right)} \sqrt{x}\right) - 4 \, {\left(77 \, {\left(B b c - A c^{2}\right)} x^{4} - 21 \, A b^{2} - 33 \, {\left(B b^{2} - A b c\right)} x^{2}\right)} \sqrt{x}}{462 \, b^{3} x^{6}}"," ",0,"-1/462*(924*b^3*x^6*(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15)^(1/4)*arctan((sqrt(b^8*sqrt(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15) + (B^2*b^2*c^4 - 2*A*B*b*c^5 + A^2*c^6)*x)*b^11*(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15)^(3/4) + (B*b^12*c^2 - A*b^11*c^3)*sqrt(x)*(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15)^(3/4))/(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)) + 231*b^3*x^6*(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15)^(1/4)*log(b^4*(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15)^(1/4) - (B*b*c^2 - A*c^3)*sqrt(x)) - 231*b^3*x^6*(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15)^(1/4)*log(-b^4*(-(B^4*b^4*c^7 - 4*A*B^3*b^3*c^8 + 6*A^2*B^2*b^2*c^9 - 4*A^3*B*b*c^10 + A^4*c^11)/b^15)^(1/4) - (B*b*c^2 - A*c^3)*sqrt(x)) - 4*(77*(B*b*c - A*c^2)*x^4 - 21*A*b^2 - 33*(B*b^2 - A*b*c)*x^2)*sqrt(x))/(b^3*x^6)","B",0
195,1,804,0,0.459675," ","integrate(x^(19/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{180 \, {\left(c^{5} x^{2} + b c^{4}\right)} \left(-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{8} \sqrt{-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}} + {\left(169 \, B^{2} b^{4} - 234 \, A B b^{3} c + 81 \, A^{2} b^{2} c^{2}\right)} x} c^{13} \left(-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}\right)^{\frac{3}{4}} + {\left(13 \, B b^{2} c^{13} - 9 \, A b c^{14}\right)} \sqrt{x} \left(-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}\right)^{\frac{3}{4}}}{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}\right) + 45 \, {\left(c^{5} x^{2} + b c^{4}\right)} \left(-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}\right)^{\frac{1}{4}} \log\left(c^{4} \left(-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}\right)^{\frac{1}{4}} - {\left(13 \, B b^{2} - 9 \, A b c\right)} \sqrt{x}\right) - 45 \, {\left(c^{5} x^{2} + b c^{4}\right)} \left(-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}\right)^{\frac{1}{4}} \log\left(-c^{4} \left(-\frac{28561 \, B^{4} b^{9} - 79092 \, A B^{3} b^{8} c + 82134 \, A^{2} B^{2} b^{7} c^{2} - 37908 \, A^{3} B b^{6} c^{3} + 6561 \, A^{4} b^{5} c^{4}}{c^{17}}\right)^{\frac{1}{4}} - {\left(13 \, B b^{2} - 9 \, A b c\right)} \sqrt{x}\right) + 4 \, {\left(20 \, B c^{3} x^{6} - 4 \, {\left(13 \, B b c^{2} - 9 \, A c^{3}\right)} x^{4} + 585 \, B b^{3} - 405 \, A b^{2} c + 36 \, {\left(13 \, B b^{2} c - 9 \, A b c^{2}\right)} x^{2}\right)} \sqrt{x}}{360 \, {\left(c^{5} x^{2} + b c^{4}\right)}}"," ",0,"1/360*(180*(c^5*x^2 + b*c^4)*(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17)^(1/4)*arctan((sqrt(c^8*sqrt(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17) + (169*B^2*b^4 - 234*A*B*b^3*c + 81*A^2*b^2*c^2)*x)*c^13*(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17)^(3/4) + (13*B*b^2*c^13 - 9*A*b*c^14)*sqrt(x)*(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17)^(3/4))/(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)) + 45*(c^5*x^2 + b*c^4)*(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17)^(1/4)*log(c^4*(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17)^(1/4) - (13*B*b^2 - 9*A*b*c)*sqrt(x)) - 45*(c^5*x^2 + b*c^4)*(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17)^(1/4)*log(-c^4*(-(28561*B^4*b^9 - 79092*A*B^3*b^8*c + 82134*A^2*B^2*b^7*c^2 - 37908*A^3*B*b^6*c^3 + 6561*A^4*b^5*c^4)/c^17)^(1/4) - (13*B*b^2 - 9*A*b*c)*sqrt(x)) + 4*(20*B*c^3*x^6 - 4*(13*B*b*c^2 - 9*A*c^3)*x^4 + 585*B*b^3 - 405*A*b^2*c + 36*(13*B*b^2*c - 9*A*b*c^2)*x^2)*sqrt(x))/(c^5*x^2 + b*c^4)","B",0
196,1,989,0,0.448926," ","integrate(x^(17/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{84 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(1771561 \, B^{6} b^{10} - 6764142 \, A B^{5} b^{9} c + 10761135 \, A^{2} B^{4} b^{8} c^{2} - 9130660 \, A^{3} B^{3} b^{7} c^{3} + 4357815 \, A^{4} B^{2} b^{6} c^{4} - 1109262 \, A^{5} B b^{5} c^{5} + 117649 \, A^{6} b^{4} c^{6}\right)} x - {\left(14641 \, B^{4} b^{7} c^{7} - 37268 \, A B^{3} b^{6} c^{8} + 35574 \, A^{2} B^{2} b^{5} c^{9} - 15092 \, A^{3} B b^{4} c^{10} + 2401 \, A^{4} b^{3} c^{11}\right)} \sqrt{-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}}} c^{4} \left(-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}\right)^{\frac{1}{4}} + {\left(1331 \, B^{3} b^{5} c^{4} - 2541 \, A B^{2} b^{4} c^{5} + 1617 \, A^{2} B b^{3} c^{6} - 343 \, A^{3} b^{2} c^{7}\right)} \sqrt{x} \left(-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}\right)^{\frac{1}{4}}}{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}\right) - 21 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}\right)^{\frac{1}{4}} \log\left(c^{11} \left(-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}\right)^{\frac{3}{4}} - {\left(1331 \, B^{3} b^{5} - 2541 \, A B^{2} b^{4} c + 1617 \, A^{2} B b^{3} c^{2} - 343 \, A^{3} b^{2} c^{3}\right)} \sqrt{x}\right) + 21 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}\right)^{\frac{1}{4}} \log\left(-c^{11} \left(-\frac{14641 \, B^{4} b^{7} - 37268 \, A B^{3} b^{6} c + 35574 \, A^{2} B^{2} b^{5} c^{2} - 15092 \, A^{3} B b^{4} c^{3} + 2401 \, A^{4} b^{3} c^{4}}{c^{15}}\right)^{\frac{3}{4}} - {\left(1331 \, B^{3} b^{5} - 2541 \, A B^{2} b^{4} c + 1617 \, A^{2} B b^{3} c^{2} - 343 \, A^{3} b^{2} c^{3}\right)} \sqrt{x}\right) + 4 \, {\left(12 \, B c^{2} x^{5} - 4 \, {\left(11 \, B b c - 7 \, A c^{2}\right)} x^{3} - 7 \, {\left(11 \, B b^{2} - 7 \, A b c\right)} x\right)} \sqrt{x}}{168 \, {\left(c^{4} x^{2} + b c^{3}\right)}}"," ",0,"1/168*(84*(c^4*x^2 + b*c^3)*(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15)^(1/4)*arctan((sqrt((1771561*B^6*b^10 - 6764142*A*B^5*b^9*c + 10761135*A^2*B^4*b^8*c^2 - 9130660*A^3*B^3*b^7*c^3 + 4357815*A^4*B^2*b^6*c^4 - 1109262*A^5*B*b^5*c^5 + 117649*A^6*b^4*c^6)*x - (14641*B^4*b^7*c^7 - 37268*A*B^3*b^6*c^8 + 35574*A^2*B^2*b^5*c^9 - 15092*A^3*B*b^4*c^10 + 2401*A^4*b^3*c^11)*sqrt(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15))*c^4*(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15)^(1/4) + (1331*B^3*b^5*c^4 - 2541*A*B^2*b^4*c^5 + 1617*A^2*B*b^3*c^6 - 343*A^3*b^2*c^7)*sqrt(x)*(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15)^(1/4))/(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)) - 21*(c^4*x^2 + b*c^3)*(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15)^(1/4)*log(c^11*(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15)^(3/4) - (1331*B^3*b^5 - 2541*A*B^2*b^4*c + 1617*A^2*B*b^3*c^2 - 343*A^3*b^2*c^3)*sqrt(x)) + 21*(c^4*x^2 + b*c^3)*(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15)^(1/4)*log(-c^11*(-(14641*B^4*b^7 - 37268*A*B^3*b^6*c + 35574*A^2*B^2*b^5*c^2 - 15092*A^3*B*b^4*c^3 + 2401*A^4*b^3*c^4)/c^15)^(3/4) - (1331*B^3*b^5 - 2541*A*B^2*b^4*c + 1617*A^2*B*b^3*c^2 - 343*A^3*b^2*c^3)*sqrt(x)) + 4*(12*B*c^2*x^5 - 4*(11*B*b*c - 7*A*c^2)*x^3 - 7*(11*B*b^2 - 7*A*b*c)*x)*sqrt(x))/(c^4*x^2 + b*c^3)","B",0
197,1,748,0,0.452096," ","integrate(x^(15/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{20 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{6} \sqrt{-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}} + {\left(81 \, B^{2} b^{2} - 90 \, A B b c + 25 \, A^{2} c^{2}\right)} x} c^{10} \left(-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}\right)^{\frac{3}{4}} + {\left(9 \, B b c^{10} - 5 \, A c^{11}\right)} \sqrt{x} \left(-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}\right)^{\frac{3}{4}}}{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}\right) + 5 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}\right)^{\frac{1}{4}} \log\left(c^{3} \left(-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}\right)^{\frac{1}{4}} - {\left(9 \, B b - 5 \, A c\right)} \sqrt{x}\right) - 5 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}\right)^{\frac{1}{4}} \log\left(-c^{3} \left(-\frac{6561 \, B^{4} b^{5} - 14580 \, A B^{3} b^{4} c + 12150 \, A^{2} B^{2} b^{3} c^{2} - 4500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{13}}\right)^{\frac{1}{4}} - {\left(9 \, B b - 5 \, A c\right)} \sqrt{x}\right) - 4 \, {\left(4 \, B c^{2} x^{4} - 45 \, B b^{2} + 25 \, A b c - 4 \, {\left(9 \, B b c - 5 \, A c^{2}\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(c^{4} x^{2} + b c^{3}\right)}}"," ",0,"-1/40*(20*(c^4*x^2 + b*c^3)*(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13)^(1/4)*arctan((sqrt(c^6*sqrt(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13) + (81*B^2*b^2 - 90*A*B*b*c + 25*A^2*c^2)*x)*c^10*(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13)^(3/4) + (9*B*b*c^10 - 5*A*c^11)*sqrt(x)*(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13)^(3/4))/(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)) + 5*(c^4*x^2 + b*c^3)*(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13)^(1/4)*log(c^3*(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13)^(1/4) - (9*B*b - 5*A*c)*sqrt(x)) - 5*(c^4*x^2 + b*c^3)*(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13)^(1/4)*log(-c^3*(-(6561*B^4*b^5 - 14580*A*B^3*b^4*c + 12150*A^2*B^2*b^3*c^2 - 4500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^13)^(1/4) - (9*B*b - 5*A*c)*sqrt(x)) - 4*(4*B*c^2*x^4 - 45*B*b^2 + 25*A*b*c - 4*(9*B*b*c - 5*A*c^2)*x^2)*sqrt(x))/(c^4*x^2 + b*c^3)","B",0
198,1,925,0,0.452039," ","integrate(x^(13/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(117649 \, B^{6} b^{6} - 302526 \, A B^{5} b^{5} c + 324135 \, A^{2} B^{4} b^{4} c^{2} - 185220 \, A^{3} B^{3} b^{3} c^{3} + 59535 \, A^{4} B^{2} b^{2} c^{4} - 10206 \, A^{5} B b c^{5} + 729 \, A^{6} c^{6}\right)} x - {\left(2401 \, B^{4} b^{5} c^{5} - 4116 \, A B^{3} b^{4} c^{6} + 2646 \, A^{2} B^{2} b^{3} c^{7} - 756 \, A^{3} B b^{2} c^{8} + 81 \, A^{4} b c^{9}\right)} \sqrt{-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}}} c^{3} \left(-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}\right)^{\frac{1}{4}} + {\left(343 \, B^{3} b^{3} c^{3} - 441 \, A B^{2} b^{2} c^{4} + 189 \, A^{2} B b c^{5} - 27 \, A^{3} c^{6}\right)} \sqrt{x} \left(-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}\right)^{\frac{1}{4}}}{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}\right) - 3 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}\right)^{\frac{1}{4}} \log\left(b c^{8} \left(-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}\right)^{\frac{3}{4}} - {\left(343 \, B^{3} b^{3} - 441 \, A B^{2} b^{2} c + 189 \, A^{2} B b c^{2} - 27 \, A^{3} c^{3}\right)} \sqrt{x}\right) + 3 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}\right)^{\frac{1}{4}} \log\left(-b c^{8} \left(-\frac{2401 \, B^{4} b^{4} - 4116 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 756 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{11}}\right)^{\frac{3}{4}} - {\left(343 \, B^{3} b^{3} - 441 \, A B^{2} b^{2} c + 189 \, A^{2} B b c^{2} - 27 \, A^{3} c^{3}\right)} \sqrt{x}\right) - 4 \, {\left(4 \, B c x^{3} + {\left(7 \, B b - 3 \, A c\right)} x\right)} \sqrt{x}}{24 \, {\left(c^{3} x^{2} + b c^{2}\right)}}"," ",0,"-1/24*(12*(c^3*x^2 + b*c^2)*(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11))^(1/4)*arctan((sqrt((117649*B^6*b^6 - 302526*A*B^5*b^5*c + 324135*A^2*B^4*b^4*c^2 - 185220*A^3*B^3*b^3*c^3 + 59535*A^4*B^2*b^2*c^4 - 10206*A^5*B*b*c^5 + 729*A^6*c^6)*x - (2401*B^4*b^5*c^5 - 4116*A*B^3*b^4*c^6 + 2646*A^2*B^2*b^3*c^7 - 756*A^3*B*b^2*c^8 + 81*A^4*b*c^9)*sqrt(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11)))*c^3*(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11))^(1/4) + (343*B^3*b^3*c^3 - 441*A*B^2*b^2*c^4 + 189*A^2*B*b*c^5 - 27*A^3*c^6)*sqrt(x)*(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11))^(1/4))/(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)) - 3*(c^3*x^2 + b*c^2)*(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11))^(1/4)*log(b*c^8*(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11))^(3/4) - (343*B^3*b^3 - 441*A*B^2*b^2*c + 189*A^2*B*b*c^2 - 27*A^3*c^3)*sqrt(x)) + 3*(c^3*x^2 + b*c^2)*(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11))^(1/4)*log(-b*c^8*(-(2401*B^4*b^4 - 4116*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 756*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^11))^(3/4) - (343*B^3*b^3 - 441*A*B^2*b^2*c + 189*A^2*B*b*c^2 - 27*A^3*c^3)*sqrt(x)) - 4*(4*B*c*x^3 + (7*B*b - 3*A*c)*x)*sqrt(x))/(c^3*x^2 + b*c^2)","B",0
199,1,725,0,0.450713," ","integrate(x^(11/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{2} c^{4} \sqrt{-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}} + {\left(25 \, B^{2} b^{2} - 10 \, A B b c + A^{2} c^{2}\right)} x} b^{2} c^{7} \left(-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}\right)^{\frac{3}{4}} + {\left(5 \, B b^{3} c^{7} - A b^{2} c^{8}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}\right)^{\frac{3}{4}}}{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) + {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}\right)^{\frac{1}{4}} \log\left(b c^{2} \left(-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}\right)^{\frac{1}{4}} - {\left(5 \, B b - A c\right)} \sqrt{x}\right) - {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}\right)^{\frac{1}{4}} \log\left(-b c^{2} \left(-\frac{625 \, B^{4} b^{4} - 500 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 20 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{9}}\right)^{\frac{1}{4}} - {\left(5 \, B b - A c\right)} \sqrt{x}\right) + 4 \, {\left(4 \, B c x^{2} + 5 \, B b - A c\right)} \sqrt{x}}{8 \, {\left(c^{3} x^{2} + b c^{2}\right)}}"," ",0,"1/8*(4*(c^3*x^2 + b*c^2)*(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9))^(1/4)*arctan((sqrt(b^2*c^4*sqrt(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9)) + (25*B^2*b^2 - 10*A*B*b*c + A^2*c^2)*x)*b^2*c^7*(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9))^(3/4) + (5*B*b^3*c^7 - A*b^2*c^8)*sqrt(x)*(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9))^(3/4))/(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)) + (c^3*x^2 + b*c^2)*(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9))^(1/4)*log(b*c^2*(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9))^(1/4) - (5*B*b - A*c)*sqrt(x)) - (c^3*x^2 + b*c^2)*(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9))^(1/4)*log(-b*c^2*(-(625*B^4*b^4 - 500*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 20*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^9))^(1/4) - (5*B*b - A*c)*sqrt(x)) + 4*(4*B*c*x^2 + 5*B*b - A*c)*sqrt(x))/(c^3*x^2 + b*c^2)","B",0
200,1,912,0,0.450743," ","integrate(x^(9/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(B b - A c\right)} x^{\frac{3}{2}} + 4 \, {\left(b c^{2} x^{2} + b^{2} c\right)} \left(-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(729 \, B^{6} b^{6} + 1458 \, A B^{5} b^{5} c + 1215 \, A^{2} B^{4} b^{4} c^{2} + 540 \, A^{3} B^{3} b^{3} c^{3} + 135 \, A^{4} B^{2} b^{2} c^{4} + 18 \, A^{5} B b c^{5} + A^{6} c^{6}\right)} x - {\left(81 \, B^{4} b^{7} c^{3} + 108 \, A B^{3} b^{6} c^{4} + 54 \, A^{2} B^{2} b^{5} c^{5} + 12 \, A^{3} B b^{4} c^{6} + A^{4} b^{3} c^{7}\right)} \sqrt{-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}}} b c^{2} \left(-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}\right)^{\frac{1}{4}} - {\left(27 \, B^{3} b^{4} c^{2} + 27 \, A B^{2} b^{3} c^{3} + 9 \, A^{2} B b^{2} c^{4} + A^{3} b c^{5}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}\right)^{\frac{1}{4}}}{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) - {\left(b c^{2} x^{2} + b^{2} c\right)} \left(-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}\right)^{\frac{1}{4}} \log\left(b^{4} c^{5} \left(-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} b^{3} + 27 \, A B^{2} b^{2} c + 9 \, A^{2} B b c^{2} + A^{3} c^{3}\right)} \sqrt{x}\right) + {\left(b c^{2} x^{2} + b^{2} c\right)} \left(-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}\right)^{\frac{1}{4}} \log\left(-b^{4} c^{5} \left(-\frac{81 \, B^{4} b^{4} + 108 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 12 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} b^{3} + 27 \, A B^{2} b^{2} c + 9 \, A^{2} B b c^{2} + A^{3} c^{3}\right)} \sqrt{x}\right)}{8 \, {\left(b c^{2} x^{2} + b^{2} c\right)}}"," ",0,"-1/8*(4*(B*b - A*c)*x^(3/2) + 4*(b*c^2*x^2 + b^2*c)*(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7))^(1/4)*arctan((sqrt((729*B^6*b^6 + 1458*A*B^5*b^5*c + 1215*A^2*B^4*b^4*c^2 + 540*A^3*B^3*b^3*c^3 + 135*A^4*B^2*b^2*c^4 + 18*A^5*B*b*c^5 + A^6*c^6)*x - (81*B^4*b^7*c^3 + 108*A*B^3*b^6*c^4 + 54*A^2*B^2*b^5*c^5 + 12*A^3*B*b^4*c^6 + A^4*b^3*c^7)*sqrt(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7)))*b*c^2*(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7))^(1/4) - (27*B^3*b^4*c^2 + 27*A*B^2*b^3*c^3 + 9*A^2*B*b^2*c^4 + A^3*b*c^5)*sqrt(x)*(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7))^(1/4))/(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)) - (b*c^2*x^2 + b^2*c)*(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7))^(1/4)*log(b^4*c^5*(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7))^(3/4) + (27*B^3*b^3 + 27*A*B^2*b^2*c + 9*A^2*B*b*c^2 + A^3*c^3)*sqrt(x)) + (b*c^2*x^2 + b^2*c)*(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7))^(1/4)*log(-b^4*c^5*(-(81*B^4*b^4 + 108*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 12*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^7))^(3/4) + (27*B^3*b^3 + 27*A*B^2*b^2*c + 9*A^2*B*b*c^2 + A^3*c^3)*sqrt(x)))/(b*c^2*x^2 + b^2*c)","B",0
201,1,717,0,0.444255," ","integrate(x^(7/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(b c^{2} x^{2} + b^{2} c\right)} \left(-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{4} c^{2} \sqrt{-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}} + {\left(B^{2} b^{2} + 6 \, A B b c + 9 \, A^{2} c^{2}\right)} x} b^{5} c^{4} \left(-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}\right)^{\frac{3}{4}} - {\left(B b^{6} c^{4} + 3 \, A b^{5} c^{5}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}\right)^{\frac{3}{4}}}{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}\right) + {\left(b c^{2} x^{2} + b^{2} c\right)} \left(-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(b^{2} c \left(-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}\right)^{\frac{1}{4}} + {\left(B b + 3 \, A c\right)} \sqrt{x}\right) - {\left(b c^{2} x^{2} + b^{2} c\right)} \left(-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(-b^{2} c \left(-\frac{B^{4} b^{4} + 12 \, A B^{3} b^{3} c + 54 \, A^{2} B^{2} b^{2} c^{2} + 108 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{5}}\right)^{\frac{1}{4}} + {\left(B b + 3 \, A c\right)} \sqrt{x}\right) - 4 \, {\left(B b - A c\right)} \sqrt{x}}{8 \, {\left(b c^{2} x^{2} + b^{2} c\right)}}"," ",0,"1/8*(4*(b*c^2*x^2 + b^2*c)*(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5))^(1/4)*arctan((sqrt(b^4*c^2*sqrt(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5)) + (B^2*b^2 + 6*A*B*b*c + 9*A^2*c^2)*x)*b^5*c^4*(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5))^(3/4) - (B*b^6*c^4 + 3*A*b^5*c^5)*sqrt(x)*(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5))^(3/4))/(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)) + (b*c^2*x^2 + b^2*c)*(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5))^(1/4)*log(b^2*c*(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5))^(1/4) + (B*b + 3*A*c)*sqrt(x)) - (b*c^2*x^2 + b^2*c)*(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5))^(1/4)*log(-b^2*c*(-(B^4*b^4 + 12*A*B^3*b^3*c + 54*A^2*B^2*b^2*c^2 + 108*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^5))^(1/4) + (B*b + 3*A*c)*sqrt(x)) - 4*(B*b - A*c)*sqrt(x))/(b*c^2*x^2 + b^2*c)","B",0
202,1,920,0,0.461337," ","integrate(x^(5/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{2} c x^{3} + b^{3} x\right)} \left(-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{6} - 30 \, A B^{5} b^{5} c + 375 \, A^{2} B^{4} b^{4} c^{2} - 2500 \, A^{3} B^{3} b^{3} c^{3} + 9375 \, A^{4} B^{2} b^{2} c^{4} - 18750 \, A^{5} B b c^{5} + 15625 \, A^{6} c^{6}\right)} x - {\left(B^{4} b^{9} c - 20 \, A B^{3} b^{8} c^{2} + 150 \, A^{2} B^{2} b^{7} c^{3} - 500 \, A^{3} B b^{6} c^{4} + 625 \, A^{4} b^{5} c^{5}\right)} \sqrt{-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}}} b^{2} c \left(-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{5} c - 15 \, A B^{2} b^{4} c^{2} + 75 \, A^{2} B b^{3} c^{3} - 125 \, A^{3} b^{2} c^{4}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}\right)^{\frac{1}{4}}}{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}\right) - {\left(b^{2} c x^{3} + b^{3} x\right)} \left(-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}\right)^{\frac{1}{4}} \log\left(b^{7} c^{2} \left(-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} - 15 \, A B^{2} b^{2} c + 75 \, A^{2} B b c^{2} - 125 \, A^{3} c^{3}\right)} \sqrt{x}\right) + {\left(b^{2} c x^{3} + b^{3} x\right)} \left(-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}\right)^{\frac{1}{4}} \log\left(-b^{7} c^{2} \left(-\frac{B^{4} b^{4} - 20 \, A B^{3} b^{3} c + 150 \, A^{2} B^{2} b^{2} c^{2} - 500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} b^{3} - 15 \, A B^{2} b^{2} c + 75 \, A^{2} B b c^{2} - 125 \, A^{3} c^{3}\right)} \sqrt{x}\right) + 4 \, {\left({\left(B b - 5 \, A c\right)} x^{2} - 4 \, A b\right)} \sqrt{x}}{8 \, {\left(b^{2} c x^{3} + b^{3} x\right)}}"," ",0,"1/8*(4*(b^2*c*x^3 + b^3*x)*(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3))^(1/4)*arctan((sqrt((B^6*b^6 - 30*A*B^5*b^5*c + 375*A^2*B^4*b^4*c^2 - 2500*A^3*B^3*b^3*c^3 + 9375*A^4*B^2*b^2*c^4 - 18750*A^5*B*b*c^5 + 15625*A^6*c^6)*x - (B^4*b^9*c - 20*A*B^3*b^8*c^2 + 150*A^2*B^2*b^7*c^3 - 500*A^3*B*b^6*c^4 + 625*A^4*b^5*c^5)*sqrt(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3)))*b^2*c*(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3))^(1/4) + (B^3*b^5*c - 15*A*B^2*b^4*c^2 + 75*A^2*B*b^3*c^3 - 125*A^3*b^2*c^4)*sqrt(x)*(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3))^(1/4))/(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)) - (b^2*c*x^3 + b^3*x)*(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3))^(1/4)*log(b^7*c^2*(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3))^(3/4) - (B^3*b^3 - 15*A*B^2*b^2*c + 75*A^2*B*b*c^2 - 125*A^3*c^3)*sqrt(x)) + (b^2*c*x^3 + b^3*x)*(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3))^(1/4)*log(-b^7*c^2*(-(B^4*b^4 - 20*A*B^3*b^3*c + 150*A^2*B^2*b^2*c^2 - 500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^3))^(3/4) - (B^3*b^3 - 15*A*B^2*b^2*c + 75*A^2*B*b*c^2 - 125*A^3*c^3)*sqrt(x)) + 4*((B*b - 5*A*c)*x^2 - 4*A*b)*sqrt(x))/(b^2*c*x^3 + b^3*x)","B",0
203,1,741,0,0.448329," ","integrate(x^(3/2)*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)} \left(-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{6} \sqrt{-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}} + {\left(9 \, B^{2} b^{2} - 42 \, A B b c + 49 \, A^{2} c^{2}\right)} x} b^{8} c \left(-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}\right)^{\frac{3}{4}} + {\left(3 \, B b^{9} c - 7 \, A b^{8} c^{2}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}\right)^{\frac{3}{4}}}{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}\right) + 3 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)} \left(-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}\right)^{\frac{1}{4}} \log\left(b^{3} \left(-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}\right)^{\frac{1}{4}} - {\left(3 \, B b - 7 \, A c\right)} \sqrt{x}\right) - 3 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)} \left(-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}\right)^{\frac{1}{4}} \log\left(-b^{3} \left(-\frac{81 \, B^{4} b^{4} - 756 \, A B^{3} b^{3} c + 2646 \, A^{2} B^{2} b^{2} c^{2} - 4116 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c}\right)^{\frac{1}{4}} - {\left(3 \, B b - 7 \, A c\right)} \sqrt{x}\right) - 4 \, {\left({\left(3 \, B b - 7 \, A c\right)} x^{2} - 4 \, A b\right)} \sqrt{x}}{24 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)}}"," ",0,"-1/24*(12*(b^2*c*x^4 + b^3*x^2)*(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c))^(1/4)*arctan((sqrt(b^6*sqrt(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c)) + (9*B^2*b^2 - 42*A*B*b*c + 49*A^2*c^2)*x)*b^8*c*(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c))^(3/4) + (3*B*b^9*c - 7*A*b^8*c^2)*sqrt(x)*(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c))^(3/4))/(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)) + 3*(b^2*c*x^4 + b^3*x^2)*(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c))^(1/4)*log(b^3*(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c))^(1/4) - (3*B*b - 7*A*c)*sqrt(x)) - 3*(b^2*c*x^4 + b^3*x^2)*(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c))^(1/4)*log(-b^3*(-(81*B^4*b^4 - 756*A*B^3*b^3*c + 2646*A^2*B^2*b^2*c^2 - 4116*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c))^(1/4) - (3*B*b - 7*A*c)*sqrt(x)) - 4*((3*B*b - 7*A*c)*x^2 - 4*A*b)*sqrt(x))/(b^2*c*x^4 + b^3*x^2)","B",0
204,1,974,0,0.457454," ","integrate((B*x^2+A)*x^(1/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{20 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)} \left(-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(15625 \, B^{6} b^{6} c^{2} - 168750 \, A B^{5} b^{5} c^{3} + 759375 \, A^{2} B^{4} b^{4} c^{4} - 1822500 \, A^{3} B^{3} b^{3} c^{5} + 2460375 \, A^{4} B^{2} b^{2} c^{6} - 1771470 \, A^{5} B b c^{7} + 531441 \, A^{6} c^{8}\right)} x - {\left(625 \, B^{4} b^{11} c - 4500 \, A B^{3} b^{10} c^{2} + 12150 \, A^{2} B^{2} b^{9} c^{3} - 14580 \, A^{3} B b^{8} c^{4} + 6561 \, A^{4} b^{7} c^{5}\right)} \sqrt{-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}}} b^{3} \left(-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}\right)^{\frac{1}{4}} + {\left(125 \, B^{3} b^{6} c - 675 \, A B^{2} b^{5} c^{2} + 1215 \, A^{2} B b^{4} c^{3} - 729 \, A^{3} b^{3} c^{4}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}\right)^{\frac{1}{4}}}{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}\right) - 5 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)} \left(-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}\right)^{\frac{1}{4}} \log\left(b^{10} \left(-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}\right)^{\frac{3}{4}} - {\left(125 \, B^{3} b^{3} c - 675 \, A B^{2} b^{2} c^{2} + 1215 \, A^{2} B b c^{3} - 729 \, A^{3} c^{4}\right)} \sqrt{x}\right) + 5 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)} \left(-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-b^{10} \left(-\frac{625 \, B^{4} b^{4} c - 4500 \, A B^{3} b^{3} c^{2} + 12150 \, A^{2} B^{2} b^{2} c^{3} - 14580 \, A^{3} B b c^{4} + 6561 \, A^{4} c^{5}}{b^{13}}\right)^{\frac{3}{4}} - {\left(125 \, B^{3} b^{3} c - 675 \, A B^{2} b^{2} c^{2} + 1215 \, A^{2} B b c^{3} - 729 \, A^{3} c^{4}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, {\left(5 \, B b c - 9 \, A c^{2}\right)} x^{4} + 4 \, A b^{2} + 4 \, {\left(5 \, B b^{2} - 9 \, A b c\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}"," ",0,"-1/40*(20*(b^3*c*x^5 + b^4*x^3)*(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13)^(1/4)*arctan((sqrt((15625*B^6*b^6*c^2 - 168750*A*B^5*b^5*c^3 + 759375*A^2*B^4*b^4*c^4 - 1822500*A^3*B^3*b^3*c^5 + 2460375*A^4*B^2*b^2*c^6 - 1771470*A^5*B*b*c^7 + 531441*A^6*c^8)*x - (625*B^4*b^11*c - 4500*A*B^3*b^10*c^2 + 12150*A^2*B^2*b^9*c^3 - 14580*A^3*B*b^8*c^4 + 6561*A^4*b^7*c^5)*sqrt(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13))*b^3*(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13)^(1/4) + (125*B^3*b^6*c - 675*A*B^2*b^5*c^2 + 1215*A^2*B*b^4*c^3 - 729*A^3*b^3*c^4)*sqrt(x)*(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13)^(1/4))/(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)) - 5*(b^3*c*x^5 + b^4*x^3)*(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13)^(1/4)*log(b^10*(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13)^(3/4) - (125*B^3*b^3*c - 675*A*B^2*b^2*c^2 + 1215*A^2*B*b*c^3 - 729*A^3*c^4)*sqrt(x)) + 5*(b^3*c*x^5 + b^4*x^3)*(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13)^(1/4)*log(-b^10*(-(625*B^4*b^4*c - 4500*A*B^3*b^3*c^2 + 12150*A^2*B^2*b^2*c^3 - 14580*A^3*B*b*c^4 + 6561*A^4*c^5)/b^13)^(3/4) - (125*B^3*b^3*c - 675*A*B^2*b^2*c^2 + 1215*A^2*B*b*c^3 - 729*A^3*c^4)*sqrt(x)) + 4*(5*(5*B*b*c - 9*A*c^2)*x^4 + 4*A*b^2 + 4*(5*B*b^2 - 9*A*b*c)*x^2)*sqrt(x))/(b^3*c*x^5 + b^4*x^3)","B",0
205,1,795,0,0.453360," ","integrate((B*x^2+A)/(c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""fricas"")","\frac{84 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{8} \sqrt{-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}} + {\left(49 \, B^{2} b^{2} c^{2} - 154 \, A B b c^{3} + 121 \, A^{2} c^{4}\right)} x} b^{11} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}\right)^{\frac{3}{4}} + {\left(7 \, B b^{12} c - 11 \, A b^{11} c^{2}\right)} \sqrt{x} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}\right)^{\frac{3}{4}}}{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}\right) + 21 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}\right)^{\frac{1}{4}} \log\left(b^{4} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}\right)^{\frac{1}{4}} - {\left(7 \, B b c - 11 \, A c^{2}\right)} \sqrt{x}\right) - 21 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}\right)^{\frac{1}{4}} \log\left(-b^{4} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 15092 \, A B^{3} b^{3} c^{4} + 35574 \, A^{2} B^{2} b^{2} c^{5} - 37268 \, A^{3} B b c^{6} + 14641 \, A^{4} c^{7}}{b^{15}}\right)^{\frac{1}{4}} - {\left(7 \, B b c - 11 \, A c^{2}\right)} \sqrt{x}\right) - 4 \, {\left(7 \, {\left(7 \, B b c - 11 \, A c^{2}\right)} x^{4} + 12 \, A b^{2} + 4 \, {\left(7 \, B b^{2} - 11 \, A b c\right)} x^{2}\right)} \sqrt{x}}{168 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)}}"," ",0,"1/168*(84*(b^3*c*x^6 + b^4*x^4)*(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15)^(1/4)*arctan((sqrt(b^8*sqrt(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15) + (49*B^2*b^2*c^2 - 154*A*B*b*c^3 + 121*A^2*c^4)*x)*b^11*(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15)^(3/4) + (7*B*b^12*c - 11*A*b^11*c^2)*sqrt(x)*(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15)^(3/4))/(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)) + 21*(b^3*c*x^6 + b^4*x^4)*(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15)^(1/4)*log(b^4*(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15)^(1/4) - (7*B*b*c - 11*A*c^2)*sqrt(x)) - 21*(b^3*c*x^6 + b^4*x^4)*(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15)^(1/4)*log(-b^4*(-(2401*B^4*b^4*c^3 - 15092*A*B^3*b^3*c^4 + 35574*A^2*B^2*b^2*c^5 - 37268*A^3*B*b*c^6 + 14641*A^4*c^7)/b^15)^(1/4) - (7*B*b*c - 11*A*c^2)*sqrt(x)) - 4*(7*(7*B*b*c - 11*A*c^2)*x^4 + 12*A*b^2 + 4*(7*B*b^2 - 11*A*b*c)*x^2)*sqrt(x))/(b^3*c*x^6 + b^4*x^4)","B",0
206,1,1024,0,0.475018," ","integrate((B*x^2+A)/x^(3/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{180 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(531441 \, B^{6} b^{6} c^{8} - 4605822 \, A B^{5} b^{5} c^{9} + 16632135 \, A^{2} B^{4} b^{4} c^{10} - 32032260 \, A^{3} B^{3} b^{3} c^{11} + 34701615 \, A^{4} B^{2} b^{2} c^{12} - 20049822 \, A^{5} B b c^{13} + 4826809 \, A^{6} c^{14}\right)} x - {\left(6561 \, B^{4} b^{13} c^{5} - 37908 \, A B^{3} b^{12} c^{6} + 82134 \, A^{2} B^{2} b^{11} c^{7} - 79092 \, A^{3} B b^{10} c^{8} + 28561 \, A^{4} b^{9} c^{9}\right)} \sqrt{-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}}} b^{4} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}\right)^{\frac{1}{4}} + {\left(729 \, B^{3} b^{7} c^{4} - 3159 \, A B^{2} b^{6} c^{5} + 4563 \, A^{2} B b^{5} c^{6} - 2197 \, A^{3} b^{4} c^{7}\right)} \sqrt{x} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}\right)^{\frac{1}{4}}}{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}\right) - 45 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}\right)^{\frac{1}{4}} \log\left(b^{13} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}\right)^{\frac{3}{4}} - {\left(729 \, B^{3} b^{3} c^{4} - 3159 \, A B^{2} b^{2} c^{5} + 4563 \, A^{2} B b c^{6} - 2197 \, A^{3} c^{7}\right)} \sqrt{x}\right) + 45 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}\right)^{\frac{1}{4}} \log\left(-b^{13} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 37908 \, A B^{3} b^{3} c^{6} + 82134 \, A^{2} B^{2} b^{2} c^{7} - 79092 \, A^{3} B b c^{8} + 28561 \, A^{4} c^{9}}{b^{17}}\right)^{\frac{3}{4}} - {\left(729 \, B^{3} b^{3} c^{4} - 3159 \, A B^{2} b^{2} c^{5} + 4563 \, A^{2} B b c^{6} - 2197 \, A^{3} c^{7}\right)} \sqrt{x}\right) + 4 \, {\left(45 \, {\left(9 \, B b c^{2} - 13 \, A c^{3}\right)} x^{6} + 36 \, {\left(9 \, B b^{2} c - 13 \, A b c^{2}\right)} x^{4} - 20 \, A b^{3} - 4 \, {\left(9 \, B b^{3} - 13 \, A b^{2} c\right)} x^{2}\right)} \sqrt{x}}{360 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}"," ",0,"1/360*(180*(b^4*c*x^7 + b^5*x^5)*(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17)^(1/4)*arctan((sqrt((531441*B^6*b^6*c^8 - 4605822*A*B^5*b^5*c^9 + 16632135*A^2*B^4*b^4*c^10 - 32032260*A^3*B^3*b^3*c^11 + 34701615*A^4*B^2*b^2*c^12 - 20049822*A^5*B*b*c^13 + 4826809*A^6*c^14)*x - (6561*B^4*b^13*c^5 - 37908*A*B^3*b^12*c^6 + 82134*A^2*B^2*b^11*c^7 - 79092*A^3*B*b^10*c^8 + 28561*A^4*b^9*c^9)*sqrt(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17))*b^4*(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17)^(1/4) + (729*B^3*b^7*c^4 - 3159*A*B^2*b^6*c^5 + 4563*A^2*B*b^5*c^6 - 2197*A^3*b^4*c^7)*sqrt(x)*(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17)^(1/4))/(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)) - 45*(b^4*c*x^7 + b^5*x^5)*(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17)^(1/4)*log(b^13*(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17)^(3/4) - (729*B^3*b^3*c^4 - 3159*A*B^2*b^2*c^5 + 4563*A^2*B*b*c^6 - 2197*A^3*c^7)*sqrt(x)) + 45*(b^4*c*x^7 + b^5*x^5)*(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17)^(1/4)*log(-b^13*(-(6561*B^4*b^4*c^5 - 37908*A*B^3*b^3*c^6 + 82134*A^2*B^2*b^2*c^7 - 79092*A^3*B*b*c^8 + 28561*A^4*c^9)/b^17)^(3/4) - (729*B^3*b^3*c^4 - 3159*A*B^2*b^2*c^5 + 4563*A^2*B*b*c^6 - 2197*A^3*c^7)*sqrt(x)) + 4*(45*(9*B*b*c^2 - 13*A*c^3)*x^6 + 36*(9*B*b^2*c - 13*A*b*c^2)*x^4 - 20*A*b^3 - 4*(9*B*b^3 - 13*A*b^2*c)*x^2)*sqrt(x))/(b^4*c*x^7 + b^5*x^5)","B",0
207,1,817,0,0.449003," ","integrate(x^(23/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{180 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)} \left(-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{8} \sqrt{-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}} + {\left(169 \, B^{2} b^{2} - 130 \, A B b c + 25 \, A^{2} c^{2}\right)} x} c^{13} \left(-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}\right)^{\frac{3}{4}} + {\left(13 \, B b c^{13} - 5 \, A c^{14}\right)} \sqrt{x} \left(-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}\right)^{\frac{3}{4}}}{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}\right) + 45 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)} \left(-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}\right)^{\frac{1}{4}} \log\left(9 \, c^{4} \left(-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}\right)^{\frac{1}{4}} - 9 \, {\left(13 \, B b - 5 \, A c\right)} \sqrt{x}\right) - 45 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)} \left(-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}\right)^{\frac{1}{4}} \log\left(-9 \, c^{4} \left(-\frac{28561 \, B^{4} b^{5} - 43940 \, A B^{3} b^{4} c + 25350 \, A^{2} B^{2} b^{3} c^{2} - 6500 \, A^{3} B b^{2} c^{3} + 625 \, A^{4} b c^{4}}{c^{17}}\right)^{\frac{1}{4}} - 9 \, {\left(13 \, B b - 5 \, A c\right)} \sqrt{x}\right) - 4 \, {\left(32 \, B c^{3} x^{6} - 32 \, {\left(13 \, B b c^{2} - 5 \, A c^{3}\right)} x^{4} - 585 \, B b^{3} + 225 \, A b^{2} c - 81 \, {\left(13 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2}\right)} \sqrt{x}}{320 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}}"," ",0,"-1/320*(180*(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)*(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17)^(1/4)*arctan((sqrt(c^8*sqrt(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17) + (169*B^2*b^2 - 130*A*B*b*c + 25*A^2*c^2)*x)*c^13*(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17)^(3/4) + (13*B*b*c^13 - 5*A*c^14)*sqrt(x)*(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17)^(3/4))/(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)) + 45*(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)*(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17)^(1/4)*log(9*c^4*(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17)^(1/4) - 9*(13*B*b - 5*A*c)*sqrt(x)) - 45*(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)*(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17)^(1/4)*log(-9*c^4*(-(28561*B^4*b^5 - 43940*A*B^3*b^4*c + 25350*A^2*B^2*b^3*c^2 - 6500*A^3*B*b^2*c^3 + 625*A^4*b*c^4)/c^17)^(1/4) - 9*(13*B*b - 5*A*c)*sqrt(x)) - 4*(32*B*c^3*x^6 - 32*(13*B*b*c^2 - 5*A*c^3)*x^4 - 585*B*b^3 + 225*A*b^2*c - 81*(13*B*b^2*c - 5*A*b*c^2)*x^2)*sqrt(x))/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)","B",0
208,1,993,0,0.465036," ","integrate(x^(21/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{84 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(1771561 \, B^{6} b^{6} - 2898918 \, A B^{5} b^{5} c + 1976535 \, A^{2} B^{4} b^{4} c^{2} - 718740 \, A^{3} B^{3} b^{3} c^{3} + 147015 \, A^{4} B^{2} b^{2} c^{4} - 16038 \, A^{5} B b c^{5} + 729 \, A^{6} c^{6}\right)} x - {\left(14641 \, B^{4} b^{5} c^{7} - 15972 \, A B^{3} b^{4} c^{8} + 6534 \, A^{2} B^{2} b^{3} c^{9} - 1188 \, A^{3} B b^{2} c^{10} + 81 \, A^{4} b c^{11}\right)} \sqrt{-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}}} c^{4} \left(-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}\right)^{\frac{1}{4}} + {\left(1331 \, B^{3} b^{3} c^{4} - 1089 \, A B^{2} b^{2} c^{5} + 297 \, A^{2} B b c^{6} - 27 \, A^{3} c^{7}\right)} \sqrt{x} \left(-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}\right)^{\frac{1}{4}}}{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}\right) - 21 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}\right)^{\frac{1}{4}} \log\left(343 \, b c^{11} \left(-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}\right)^{\frac{3}{4}} - 343 \, {\left(1331 \, B^{3} b^{3} - 1089 \, A B^{2} b^{2} c + 297 \, A^{2} B b c^{2} - 27 \, A^{3} c^{3}\right)} \sqrt{x}\right) + 21 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}\right)^{\frac{1}{4}} \log\left(-343 \, b c^{11} \left(-\frac{14641 \, B^{4} b^{4} - 15972 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 1188 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b c^{15}}\right)^{\frac{3}{4}} - 343 \, {\left(1331 \, B^{3} b^{3} - 1089 \, A B^{2} b^{2} c + 297 \, A^{2} B b c^{2} - 27 \, A^{3} c^{3}\right)} \sqrt{x}\right) - 4 \, {\left(32 \, B c^{2} x^{5} + 11 \, {\left(11 \, B b c - 3 \, A c^{2}\right)} x^{3} + 7 \, {\left(11 \, B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{x}}{192 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}}"," ",0,"-1/192*(84*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15))^(1/4)*arctan((sqrt((1771561*B^6*b^6 - 2898918*A*B^5*b^5*c + 1976535*A^2*B^4*b^4*c^2 - 718740*A^3*B^3*b^3*c^3 + 147015*A^4*B^2*b^2*c^4 - 16038*A^5*B*b*c^5 + 729*A^6*c^6)*x - (14641*B^4*b^5*c^7 - 15972*A*B^3*b^4*c^8 + 6534*A^2*B^2*b^3*c^9 - 1188*A^3*B*b^2*c^10 + 81*A^4*b*c^11)*sqrt(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15)))*c^4*(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15))^(1/4) + (1331*B^3*b^3*c^4 - 1089*A*B^2*b^2*c^5 + 297*A^2*B*b*c^6 - 27*A^3*c^7)*sqrt(x)*(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15))^(1/4))/(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)) - 21*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15))^(1/4)*log(343*b*c^11*(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15))^(3/4) - 343*(1331*B^3*b^3 - 1089*A*B^2*b^2*c + 297*A^2*B*b*c^2 - 27*A^3*c^3)*sqrt(x)) + 21*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15))^(1/4)*log(-343*b*c^11*(-(14641*B^4*b^4 - 15972*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 1188*A^3*B*b*c^3 + 81*A^4*c^4)/(b*c^15))^(3/4) - 343*(1331*B^3*b^3 - 1089*A*B^2*b^2*c + 297*A^2*B*b*c^2 - 27*A^3*c^3)*sqrt(x)) - 4*(32*B*c^2*x^5 + 11*(11*B*b*c - 3*A*c^2)*x^3 + 7*(11*B*b^2 - 3*A*b*c)*x)*sqrt(x))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)","B",0
209,1,793,0,0.444659," ","integrate(x^(19/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{20 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{2} c^{6} \sqrt{-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}} + {\left(81 \, B^{2} b^{2} - 18 \, A B b c + A^{2} c^{2}\right)} x} b^{2} c^{10} \left(-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}\right)^{\frac{3}{4}} + {\left(9 \, B b^{3} c^{10} - A b^{2} c^{11}\right)} \sqrt{x} \left(-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}\right)^{\frac{3}{4}}}{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) + 5 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}\right)^{\frac{1}{4}} \log\left(5 \, b c^{3} \left(-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}\right)^{\frac{1}{4}} - 5 \, {\left(9 \, B b - A c\right)} \sqrt{x}\right) - 5 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}\right)^{\frac{1}{4}} \log\left(-5 \, b c^{3} \left(-\frac{6561 \, B^{4} b^{4} - 2916 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 36 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{3} c^{13}}\right)^{\frac{1}{4}} - 5 \, {\left(9 \, B b - A c\right)} \sqrt{x}\right) + 4 \, {\left(32 \, B c^{2} x^{4} + 45 \, B b^{2} - 5 \, A b c + 9 \, {\left(9 \, B b c - A c^{2}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}}"," ",0,"1/64*(20*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13))^(1/4)*arctan((sqrt(b^2*c^6*sqrt(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13)) + (81*B^2*b^2 - 18*A*B*b*c + A^2*c^2)*x)*b^2*c^10*(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13))^(3/4) + (9*B*b^3*c^10 - A*b^2*c^11)*sqrt(x)*(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13))^(3/4))/(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)) + 5*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13))^(1/4)*log(5*b*c^3*(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13))^(1/4) - 5*(9*B*b - A*c)*sqrt(x)) - 5*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13))^(1/4)*log(-5*b*c^3*(-(6561*B^4*b^4 - 2916*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 36*A^3*B*b*c^3 + A^4*c^4)/(b^3*c^13))^(1/4) - 5*(9*B*b - A*c)*sqrt(x)) + 4*(32*B*c^2*x^4 + 45*B*b^2 - 5*A*b*c + 9*(9*B*b*c - A*c^2)*x^2)*sqrt(x))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)","B",0
210,1,990,0,0.460009," ","integrate(x^(17/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)} \left(-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(117649 \, B^{6} b^{6} + 100842 \, A B^{5} b^{5} c + 36015 \, A^{2} B^{4} b^{4} c^{2} + 6860 \, A^{3} B^{3} b^{3} c^{3} + 735 \, A^{4} B^{2} b^{2} c^{4} + 42 \, A^{5} B b c^{5} + A^{6} c^{6}\right)} x - {\left(2401 \, B^{4} b^{7} c^{5} + 1372 \, A B^{3} b^{6} c^{6} + 294 \, A^{2} B^{2} b^{5} c^{7} + 28 \, A^{3} B b^{4} c^{8} + A^{4} b^{3} c^{9}\right)} \sqrt{-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}}} b c^{3} \left(-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}\right)^{\frac{1}{4}} - {\left(343 \, B^{3} b^{4} c^{3} + 147 \, A B^{2} b^{3} c^{4} + 21 \, A^{2} B b^{2} c^{5} + A^{3} b c^{6}\right)} \sqrt{x} \left(-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}\right)^{\frac{1}{4}}}{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}\right) - 3 \, {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)} \left(-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}\right)^{\frac{1}{4}} \log\left(27 \, b^{4} c^{8} \left(-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}\right)^{\frac{3}{4}} + 27 \, {\left(343 \, B^{3} b^{3} + 147 \, A B^{2} b^{2} c + 21 \, A^{2} B b c^{2} + A^{3} c^{3}\right)} \sqrt{x}\right) + 3 \, {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)} \left(-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}\right)^{\frac{1}{4}} \log\left(-27 \, b^{4} c^{8} \left(-\frac{2401 \, B^{4} b^{4} + 1372 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 28 \, A^{3} B b c^{3} + A^{4} c^{4}}{b^{5} c^{11}}\right)^{\frac{3}{4}} + 27 \, {\left(343 \, B^{3} b^{3} + 147 \, A B^{2} b^{2} c + 21 \, A^{2} B b c^{2} + A^{3} c^{3}\right)} \sqrt{x}\right) + 4 \, {\left({\left(11 \, B b c - 3 \, A c^{2}\right)} x^{3} + {\left(7 \, B b^{2} + A b c\right)} x\right)} \sqrt{x}}{64 \, {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)}}"," ",0,"-1/64*(12*(b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)*(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11))^(1/4)*arctan((sqrt((117649*B^6*b^6 + 100842*A*B^5*b^5*c + 36015*A^2*B^4*b^4*c^2 + 6860*A^3*B^3*b^3*c^3 + 735*A^4*B^2*b^2*c^4 + 42*A^5*B*b*c^5 + A^6*c^6)*x - (2401*B^4*b^7*c^5 + 1372*A*B^3*b^6*c^6 + 294*A^2*B^2*b^5*c^7 + 28*A^3*B*b^4*c^8 + A^4*b^3*c^9)*sqrt(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11)))*b*c^3*(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11))^(1/4) - (343*B^3*b^4*c^3 + 147*A*B^2*b^3*c^4 + 21*A^2*B*b^2*c^5 + A^3*b*c^6)*sqrt(x)*(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11))^(1/4))/(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)) - 3*(b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)*(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11))^(1/4)*log(27*b^4*c^8*(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11))^(3/4) + 27*(343*B^3*b^3 + 147*A*B^2*b^2*c + 21*A^2*B*b*c^2 + A^3*c^3)*sqrt(x)) + 3*(b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)*(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11))^(1/4)*log(-27*b^4*c^8*(-(2401*B^4*b^4 + 1372*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 28*A^3*B*b*c^3 + A^4*c^4)/(b^5*c^11))^(3/4) + 27*(343*B^3*b^3 + 147*A*B^2*b^2*c + 21*A^2*B*b*c^2 + A^3*c^3)*sqrt(x)) + 4*((11*B*b*c - 3*A*c^2)*x^3 + (7*B*b^2 + A*b*c)*x)*sqrt(x))/(b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)","B",0
211,1,806,0,0.445462," ","integrate(x^(15/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)} \left(-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{4} c^{4} \sqrt{-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}} + {\left(25 \, B^{2} b^{2} + 30 \, A B b c + 9 \, A^{2} c^{2}\right)} x} b^{5} c^{7} \left(-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}\right)^{\frac{3}{4}} - {\left(5 \, B b^{6} c^{7} + 3 \, A b^{5} c^{8}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}\right)^{\frac{3}{4}}}{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}\right) + {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)} \left(-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}\right)^{\frac{1}{4}} \log\left(b^{2} c^{2} \left(-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}\right)^{\frac{1}{4}} + {\left(5 \, B b + 3 \, A c\right)} \sqrt{x}\right) - {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)} \left(-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}\right)^{\frac{1}{4}} \log\left(-b^{2} c^{2} \left(-\frac{625 \, B^{4} b^{4} + 1500 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 540 \, A^{3} B b c^{3} + 81 \, A^{4} c^{4}}{b^{7} c^{9}}\right)^{\frac{1}{4}} + {\left(5 \, B b + 3 \, A c\right)} \sqrt{x}\right) - 4 \, {\left(5 \, B b^{2} + 3 \, A b c + {\left(9 \, B b c - A c^{2}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(b c^{4} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{3} c^{2}\right)}}"," ",0,"1/64*(4*(b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)*(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9))^(1/4)*arctan((sqrt(b^4*c^4*sqrt(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9)) + (25*B^2*b^2 + 30*A*B*b*c + 9*A^2*c^2)*x)*b^5*c^7*(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9))^(3/4) - (5*B*b^6*c^7 + 3*A*b^5*c^8)*sqrt(x)*(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9))^(3/4))/(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)) + (b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)*(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9))^(1/4)*log(b^2*c^2*(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9))^(1/4) + (5*B*b + 3*A*c)*sqrt(x)) - (b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)*(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9))^(1/4)*log(-b^2*c^2*(-(625*B^4*b^4 + 1500*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 540*A^3*B*b*c^3 + 81*A^4*c^4)/(b^7*c^9))^(1/4) + (5*B*b + 3*A*c)*sqrt(x)) - 4*(5*B*b^2 + 3*A*b*c + (9*B*b*c - A*c^2)*x^2)*sqrt(x))/(b*c^4*x^4 + 2*b^2*c^3*x^2 + b^3*c^2)","B",0
212,1,1005,0,0.456787," ","integrate(x^(13/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)} \left(-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(729 \, B^{6} b^{6} + 7290 \, A B^{5} b^{5} c + 30375 \, A^{2} B^{4} b^{4} c^{2} + 67500 \, A^{3} B^{3} b^{3} c^{3} + 84375 \, A^{4} B^{2} b^{2} c^{4} + 56250 \, A^{5} B b c^{5} + 15625 \, A^{6} c^{6}\right)} x - {\left(81 \, B^{4} b^{9} c^{3} + 540 \, A B^{3} b^{8} c^{4} + 1350 \, A^{2} B^{2} b^{7} c^{5} + 1500 \, A^{3} B b^{6} c^{6} + 625 \, A^{4} b^{5} c^{7}\right)} \sqrt{-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}}} b^{2} c^{2} \left(-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}\right)^{\frac{1}{4}} - {\left(27 \, B^{3} b^{5} c^{2} + 135 \, A B^{2} b^{4} c^{3} + 225 \, A^{2} B b^{3} c^{4} + 125 \, A^{3} b^{2} c^{5}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}\right)^{\frac{1}{4}}}{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}\right) - {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)} \left(-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}\right)^{\frac{1}{4}} \log\left(b^{7} c^{5} \left(-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} b^{3} + 135 \, A B^{2} b^{2} c + 225 \, A^{2} B b c^{2} + 125 \, A^{3} c^{3}\right)} \sqrt{x}\right) + {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)} \left(-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}\right)^{\frac{1}{4}} \log\left(-b^{7} c^{5} \left(-\frac{81 \, B^{4} b^{4} + 540 \, A B^{3} b^{3} c + 1350 \, A^{2} B^{2} b^{2} c^{2} + 1500 \, A^{3} B b c^{3} + 625 \, A^{4} c^{4}}{b^{9} c^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} b^{3} + 135 \, A B^{2} b^{2} c + 225 \, A^{2} B b c^{2} + 125 \, A^{3} c^{3}\right)} \sqrt{x}\right) - 4 \, {\left({\left(3 \, B b c + 5 \, A c^{2}\right)} x^{3} - {\left(B b^{2} - 9 \, A b c\right)} x\right)} \sqrt{x}}{64 \, {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)}}"," ",0,"-1/64*(4*(b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)*(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7))^(1/4)*arctan((sqrt((729*B^6*b^6 + 7290*A*B^5*b^5*c + 30375*A^2*B^4*b^4*c^2 + 67500*A^3*B^3*b^3*c^3 + 84375*A^4*B^2*b^2*c^4 + 56250*A^5*B*b*c^5 + 15625*A^6*c^6)*x - (81*B^4*b^9*c^3 + 540*A*B^3*b^8*c^4 + 1350*A^2*B^2*b^7*c^5 + 1500*A^3*B*b^6*c^6 + 625*A^4*b^5*c^7)*sqrt(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7)))*b^2*c^2*(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7))^(1/4) - (27*B^3*b^5*c^2 + 135*A*B^2*b^4*c^3 + 225*A^2*B*b^3*c^4 + 125*A^3*b^2*c^5)*sqrt(x)*(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7))^(1/4))/(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)) - (b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)*(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7))^(1/4)*log(b^7*c^5*(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7))^(3/4) + (27*B^3*b^3 + 135*A*B^2*b^2*c + 225*A^2*B*b*c^2 + 125*A^3*c^3)*sqrt(x)) + (b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)*(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7))^(1/4)*log(-b^7*c^5*(-(81*B^4*b^4 + 540*A*B^3*b^3*c + 1350*A^2*B^2*b^2*c^2 + 1500*A^3*B*b*c^3 + 625*A^4*c^4)/(b^9*c^7))^(3/4) + (27*B^3*b^3 + 135*A*B^2*b^2*c + 225*A^2*B*b*c^2 + 125*A^3*c^3)*sqrt(x)) - 4*((3*B*b*c + 5*A*c^2)*x^3 - (B*b^2 - 9*A*b*c)*x)*sqrt(x))/(b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)","B",0
213,1,793,0,0.444491," ","integrate(x^(11/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{12 \, {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)} \left(-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{6} c^{2} \sqrt{-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}} + {\left(B^{2} b^{2} + 14 \, A B b c + 49 \, A^{2} c^{2}\right)} x} b^{8} c^{4} \left(-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}\right)^{\frac{3}{4}} - {\left(B b^{9} c^{4} + 7 \, A b^{8} c^{5}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}\right)^{\frac{3}{4}}}{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}\right) + 3 \, {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)} \left(-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}\right)^{\frac{1}{4}} \log\left(3 \, b^{3} c \left(-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}\right)^{\frac{1}{4}} + 3 \, {\left(B b + 7 \, A c\right)} \sqrt{x}\right) - 3 \, {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)} \left(-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}\right)^{\frac{1}{4}} \log\left(-3 \, b^{3} c \left(-\frac{B^{4} b^{4} + 28 \, A B^{3} b^{3} c + 294 \, A^{2} B^{2} b^{2} c^{2} + 1372 \, A^{3} B b c^{3} + 2401 \, A^{4} c^{4}}{b^{11} c^{5}}\right)^{\frac{1}{4}} + 3 \, {\left(B b + 7 \, A c\right)} \sqrt{x}\right) - 4 \, {\left(3 \, B b^{2} - 11 \, A b c - {\left(B b c + 7 \, A c^{2}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(b^{2} c^{3} x^{4} + 2 \, b^{3} c^{2} x^{2} + b^{4} c\right)}}"," ",0,"1/64*(12*(b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)*(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5))^(1/4)*arctan((sqrt(b^6*c^2*sqrt(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5)) + (B^2*b^2 + 14*A*B*b*c + 49*A^2*c^2)*x)*b^8*c^4*(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5))^(3/4) - (B*b^9*c^4 + 7*A*b^8*c^5)*sqrt(x)*(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5))^(3/4))/(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)) + 3*(b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)*(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5))^(1/4)*log(3*b^3*c*(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5))^(1/4) + 3*(B*b + 7*A*c)*sqrt(x)) - 3*(b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)*(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5))^(1/4)*log(-3*b^3*c*(-(B^4*b^4 + 28*A*B^3*b^3*c + 294*A^2*B^2*b^2*c^2 + 1372*A^3*B*b*c^3 + 2401*A^4*c^4)/(b^11*c^5))^(1/4) + 3*(B*b + 7*A*c)*sqrt(x)) - 4*(3*B*b^2 - 11*A*b*c - (B*b*c + 7*A*c^2)*x^2)*sqrt(x))/(b^2*c^3*x^4 + 2*b^3*c^2*x^2 + b^4*c)","B",0
214,1,988,0,0.469234," ","integrate(x^(9/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{20 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)} \left(-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} b^{6} - 54 \, A B^{5} b^{5} c + 1215 \, A^{2} B^{4} b^{4} c^{2} - 14580 \, A^{3} B^{3} b^{3} c^{3} + 98415 \, A^{4} B^{2} b^{2} c^{4} - 354294 \, A^{5} B b c^{5} + 531441 \, A^{6} c^{6}\right)} x - {\left(B^{4} b^{11} c - 36 \, A B^{3} b^{10} c^{2} + 486 \, A^{2} B^{2} b^{9} c^{3} - 2916 \, A^{3} B b^{8} c^{4} + 6561 \, A^{4} b^{7} c^{5}\right)} \sqrt{-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}}} b^{3} c \left(-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}\right)^{\frac{1}{4}} + {\left(B^{3} b^{6} c - 27 \, A B^{2} b^{5} c^{2} + 243 \, A^{2} B b^{4} c^{3} - 729 \, A^{3} b^{3} c^{4}\right)} \sqrt{x} \left(-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}\right)^{\frac{1}{4}}}{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}\right) - 5 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)} \left(-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}\right)^{\frac{1}{4}} \log\left(125 \, b^{10} c^{2} \left(-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}\right)^{\frac{3}{4}} - 125 \, {\left(B^{3} b^{3} - 27 \, A B^{2} b^{2} c + 243 \, A^{2} B b c^{2} - 729 \, A^{3} c^{3}\right)} \sqrt{x}\right) + 5 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)} \left(-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}\right)^{\frac{1}{4}} \log\left(-125 \, b^{10} c^{2} \left(-\frac{B^{4} b^{4} - 36 \, A B^{3} b^{3} c + 486 \, A^{2} B^{2} b^{2} c^{2} - 2916 \, A^{3} B b c^{3} + 6561 \, A^{4} c^{4}}{b^{13} c^{3}}\right)^{\frac{3}{4}} - 125 \, {\left(B^{3} b^{3} - 27 \, A B^{2} b^{2} c + 243 \, A^{2} B b c^{2} - 729 \, A^{3} c^{3}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, {\left(B b c - 9 \, A c^{2}\right)} x^{4} - 32 \, A b^{2} + 9 \, {\left(B b^{2} - 9 \, A b c\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)}}"," ",0,"1/64*(20*(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)*(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3))^(1/4)*arctan((sqrt((B^6*b^6 - 54*A*B^5*b^5*c + 1215*A^2*B^4*b^4*c^2 - 14580*A^3*B^3*b^3*c^3 + 98415*A^4*B^2*b^2*c^4 - 354294*A^5*B*b*c^5 + 531441*A^6*c^6)*x - (B^4*b^11*c - 36*A*B^3*b^10*c^2 + 486*A^2*B^2*b^9*c^3 - 2916*A^3*B*b^8*c^4 + 6561*A^4*b^7*c^5)*sqrt(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3)))*b^3*c*(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3))^(1/4) + (B^3*b^6*c - 27*A*B^2*b^5*c^2 + 243*A^2*B*b^4*c^3 - 729*A^3*b^3*c^4)*sqrt(x)*(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3))^(1/4))/(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)) - 5*(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)*(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3))^(1/4)*log(125*b^10*c^2*(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3))^(3/4) - 125*(B^3*b^3 - 27*A*B^2*b^2*c + 243*A^2*B*b*c^2 - 729*A^3*c^3)*sqrt(x)) + 5*(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)*(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3))^(1/4)*log(-125*b^10*c^2*(-(B^4*b^4 - 36*A*B^3*b^3*c + 486*A^2*B^2*b^2*c^2 - 2916*A^3*B*b*c^3 + 6561*A^4*c^4)/(b^13*c^3))^(3/4) - 125*(B^3*b^3 - 27*A*B^2*b^2*c + 243*A^2*B*b*c^2 - 729*A^3*c^3)*sqrt(x)) + 4*(5*(B*b*c - 9*A*c^2)*x^4 - 32*A*b^2 + 9*(B*b^2 - 9*A*b*c)*x^2)*sqrt(x))/(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)","B",0
215,1,809,0,0.460264," ","integrate(x^(7/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{84 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)} \left(-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{8} \sqrt{-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}} + {\left(9 \, B^{2} b^{2} - 66 \, A B b c + 121 \, A^{2} c^{2}\right)} x} b^{11} c \left(-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}\right)^{\frac{3}{4}} + {\left(3 \, B b^{12} c - 11 \, A b^{11} c^{2}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}\right)^{\frac{3}{4}}}{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}\right) + 21 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)} \left(-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}\right)^{\frac{1}{4}} \log\left(7 \, b^{4} \left(-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}\right)^{\frac{1}{4}} - 7 \, {\left(3 \, B b - 11 \, A c\right)} \sqrt{x}\right) - 21 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)} \left(-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}\right)^{\frac{1}{4}} \log\left(-7 \, b^{4} \left(-\frac{81 \, B^{4} b^{4} - 1188 \, A B^{3} b^{3} c + 6534 \, A^{2} B^{2} b^{2} c^{2} - 15972 \, A^{3} B b c^{3} + 14641 \, A^{4} c^{4}}{b^{15} c}\right)^{\frac{1}{4}} - 7 \, {\left(3 \, B b - 11 \, A c\right)} \sqrt{x}\right) - 4 \, {\left(7 \, {\left(3 \, B b c - 11 \, A c^{2}\right)} x^{4} - 32 \, A b^{2} + 11 \, {\left(3 \, B b^{2} - 11 \, A b c\right)} x^{2}\right)} \sqrt{x}}{192 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)}}"," ",0,"-1/192*(84*(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)*(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c))^(1/4)*arctan((sqrt(b^8*sqrt(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c)) + (9*B^2*b^2 - 66*A*B*b*c + 121*A^2*c^2)*x)*b^11*c*(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c))^(3/4) + (3*B*b^12*c - 11*A*b^11*c^2)*sqrt(x)*(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c))^(3/4))/(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)) + 21*(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)*(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c))^(1/4)*log(7*b^4*(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c))^(1/4) - 7*(3*B*b - 11*A*c)*sqrt(x)) - 21*(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)*(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c))^(1/4)*log(-7*b^4*(-(81*B^4*b^4 - 1188*A*B^3*b^3*c + 6534*A^2*B^2*b^2*c^2 - 15972*A^3*B*b*c^3 + 14641*A^4*c^4)/(b^15*c))^(1/4) - 7*(3*B*b - 11*A*c)*sqrt(x)) - 4*(7*(3*B*b*c - 11*A*c^2)*x^4 - 32*A*b^2 + 11*(3*B*b^2 - 11*A*b*c)*x^2)*sqrt(x))/(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)","B",0
216,1,1043,0,0.464820," ","integrate(x^(5/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{180 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)} \left(-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(15625 \, B^{6} b^{6} c^{2} - 243750 \, A B^{5} b^{5} c^{3} + 1584375 \, A^{2} B^{4} b^{4} c^{4} - 5492500 \, A^{3} B^{3} b^{3} c^{5} + 10710375 \, A^{4} B^{2} b^{2} c^{6} - 11138790 \, A^{5} B b c^{7} + 4826809 \, A^{6} c^{8}\right)} x - {\left(625 \, B^{4} b^{13} c - 6500 \, A B^{3} b^{12} c^{2} + 25350 \, A^{2} B^{2} b^{11} c^{3} - 43940 \, A^{3} B b^{10} c^{4} + 28561 \, A^{4} b^{9} c^{5}\right)} \sqrt{-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}}} b^{4} \left(-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}\right)^{\frac{1}{4}} + {\left(125 \, B^{3} b^{7} c - 975 \, A B^{2} b^{6} c^{2} + 2535 \, A^{2} B b^{5} c^{3} - 2197 \, A^{3} b^{4} c^{4}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}\right)^{\frac{1}{4}}}{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}\right) - 45 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)} \left(-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}\right)^{\frac{1}{4}} \log\left(729 \, b^{13} \left(-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}\right)^{\frac{3}{4}} - 729 \, {\left(125 \, B^{3} b^{3} c - 975 \, A B^{2} b^{2} c^{2} + 2535 \, A^{2} B b c^{3} - 2197 \, A^{3} c^{4}\right)} \sqrt{x}\right) + 45 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)} \left(-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}\right)^{\frac{1}{4}} \log\left(-729 \, b^{13} \left(-\frac{625 \, B^{4} b^{4} c - 6500 \, A B^{3} b^{3} c^{2} + 25350 \, A^{2} B^{2} b^{2} c^{3} - 43940 \, A^{3} B b c^{4} + 28561 \, A^{4} c^{5}}{b^{17}}\right)^{\frac{3}{4}} - 729 \, {\left(125 \, B^{3} b^{3} c - 975 \, A B^{2} b^{2} c^{2} + 2535 \, A^{2} B b c^{3} - 2197 \, A^{3} c^{4}\right)} \sqrt{x}\right) + 4 \, {\left(45 \, {\left(5 \, B b c^{2} - 13 \, A c^{3}\right)} x^{6} + 81 \, {\left(5 \, B b^{2} c - 13 \, A b c^{2}\right)} x^{4} + 32 \, A b^{3} + 32 \, {\left(5 \, B b^{3} - 13 \, A b^{2} c\right)} x^{2}\right)} \sqrt{x}}{320 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)}}"," ",0,"-1/320*(180*(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)*(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17)^(1/4)*arctan((sqrt((15625*B^6*b^6*c^2 - 243750*A*B^5*b^5*c^3 + 1584375*A^2*B^4*b^4*c^4 - 5492500*A^3*B^3*b^3*c^5 + 10710375*A^4*B^2*b^2*c^6 - 11138790*A^5*B*b*c^7 + 4826809*A^6*c^8)*x - (625*B^4*b^13*c - 6500*A*B^3*b^12*c^2 + 25350*A^2*B^2*b^11*c^3 - 43940*A^3*B*b^10*c^4 + 28561*A^4*b^9*c^5)*sqrt(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17))*b^4*(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17)^(1/4) + (125*B^3*b^7*c - 975*A*B^2*b^6*c^2 + 2535*A^2*B*b^5*c^3 - 2197*A^3*b^4*c^4)*sqrt(x)*(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17)^(1/4))/(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)) - 45*(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)*(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17)^(1/4)*log(729*b^13*(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17)^(3/4) - 729*(125*B^3*b^3*c - 975*A*B^2*b^2*c^2 + 2535*A^2*B*b*c^3 - 2197*A^3*c^4)*sqrt(x)) + 45*(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)*(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17)^(1/4)*log(-729*b^13*(-(625*B^4*b^4*c - 6500*A*B^3*b^3*c^2 + 25350*A^2*B^2*b^2*c^3 - 43940*A^3*B*b*c^4 + 28561*A^4*c^5)/b^17)^(3/4) - 729*(125*B^3*b^3*c - 975*A*B^2*b^2*c^2 + 2535*A^2*B*b*c^3 - 2197*A^3*c^4)*sqrt(x)) + 4*(45*(5*B*b*c^2 - 13*A*c^3)*x^6 + 81*(5*B*b^2*c - 13*A*b*c^2)*x^4 + 32*A*b^3 + 32*(5*B*b^3 - 13*A*b^2*c)*x^2)*sqrt(x))/(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)","B",0
217,1,864,0,0.462746," ","integrate(x^(3/2)*(B*x^2+A)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{924 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{10} \sqrt{-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}} + {\left(49 \, B^{2} b^{2} c^{2} - 210 \, A B b c^{3} + 225 \, A^{2} c^{4}\right)} x} b^{14} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}\right)^{\frac{3}{4}} + {\left(7 \, B b^{15} c - 15 \, A b^{14} c^{2}\right)} \sqrt{x} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}\right)^{\frac{3}{4}}}{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}\right) + 231 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}\right)^{\frac{1}{4}} \log\left(11 \, b^{5} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}\right)^{\frac{1}{4}} - 11 \, {\left(7 \, B b c - 15 \, A c^{2}\right)} \sqrt{x}\right) - 231 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}\right)^{\frac{1}{4}} \log\left(-11 \, b^{5} \left(-\frac{2401 \, B^{4} b^{4} c^{3} - 20580 \, A B^{3} b^{3} c^{4} + 66150 \, A^{2} B^{2} b^{2} c^{5} - 94500 \, A^{3} B b c^{6} + 50625 \, A^{4} c^{7}}{b^{19}}\right)^{\frac{1}{4}} - 11 \, {\left(7 \, B b c - 15 \, A c^{2}\right)} \sqrt{x}\right) - 4 \, {\left(77 \, {\left(7 \, B b c^{2} - 15 \, A c^{3}\right)} x^{6} + 121 \, {\left(7 \, B b^{2} c - 15 \, A b c^{2}\right)} x^{4} + 96 \, A b^{3} + 32 \, {\left(7 \, B b^{3} - 15 \, A b^{2} c\right)} x^{2}\right)} \sqrt{x}}{1344 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)}}"," ",0,"1/1344*(924*(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)*(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19)^(1/4)*arctan((sqrt(b^10*sqrt(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19) + (49*B^2*b^2*c^2 - 210*A*B*b*c^3 + 225*A^2*c^4)*x)*b^14*(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19)^(3/4) + (7*B*b^15*c - 15*A*b^14*c^2)*sqrt(x)*(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19)^(3/4))/(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)) + 231*(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)*(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19)^(1/4)*log(11*b^5*(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19)^(1/4) - 11*(7*B*b*c - 15*A*c^2)*sqrt(x)) - 231*(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)*(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19)^(1/4)*log(-11*b^5*(-(2401*B^4*b^4*c^3 - 20580*A*B^3*b^3*c^4 + 66150*A^2*B^2*b^2*c^5 - 94500*A^3*B*b*c^6 + 50625*A^4*c^7)/b^19)^(1/4) - 11*(7*B*b*c - 15*A*c^2)*sqrt(x)) - 4*(77*(7*B*b*c^2 - 15*A*c^3)*x^6 + 121*(7*B*b^2*c - 15*A*b*c^2)*x^4 + 96*A*b^3 + 32*(7*B*b^3 - 15*A*b^2*c)*x^2)*sqrt(x))/(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)","B",0
218,1,1093,0,0.455524," ","integrate((B*x^2+A)*x^(1/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2340 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(531441 \, B^{6} b^{6} c^{8} - 6022998 \, A B^{5} b^{5} c^{9} + 28441935 \, A^{2} B^{4} b^{4} c^{10} - 71631540 \, A^{3} B^{3} b^{3} c^{11} + 101478015 \, A^{4} B^{2} b^{2} c^{12} - 76672278 \, A^{5} B b c^{13} + 24137569 \, A^{6} c^{14}\right)} x - {\left(6561 \, B^{4} b^{15} c^{5} - 49572 \, A B^{3} b^{14} c^{6} + 140454 \, A^{2} B^{2} b^{13} c^{7} - 176868 \, A^{3} B b^{12} c^{8} + 83521 \, A^{4} b^{11} c^{9}\right)} \sqrt{-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}}} b^{5} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}\right)^{\frac{1}{4}} + {\left(729 \, B^{3} b^{8} c^{4} - 4131 \, A B^{2} b^{7} c^{5} + 7803 \, A^{2} B b^{6} c^{6} - 4913 \, A^{3} b^{5} c^{7}\right)} \sqrt{x} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}\right)^{\frac{1}{4}}}{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}\right) - 585 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}\right)^{\frac{1}{4}} \log\left(2197 \, b^{16} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}\right)^{\frac{3}{4}} - 2197 \, {\left(729 \, B^{3} b^{3} c^{4} - 4131 \, A B^{2} b^{2} c^{5} + 7803 \, A^{2} B b c^{6} - 4913 \, A^{3} c^{7}\right)} \sqrt{x}\right) + 585 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}\right)^{\frac{1}{4}} \log\left(-2197 \, b^{16} \left(-\frac{6561 \, B^{4} b^{4} c^{5} - 49572 \, A B^{3} b^{3} c^{6} + 140454 \, A^{2} B^{2} b^{2} c^{7} - 176868 \, A^{3} B b c^{8} + 83521 \, A^{4} c^{9}}{b^{21}}\right)^{\frac{3}{4}} - 2197 \, {\left(729 \, B^{3} b^{3} c^{4} - 4131 \, A B^{2} b^{2} c^{5} + 7803 \, A^{2} B b c^{6} - 4913 \, A^{3} c^{7}\right)} \sqrt{x}\right) + 4 \, {\left(585 \, {\left(9 \, B b c^{3} - 17 \, A c^{4}\right)} x^{8} + 1053 \, {\left(9 \, B b^{2} c^{2} - 17 \, A b c^{3}\right)} x^{6} - 160 \, A b^{4} + 416 \, {\left(9 \, B b^{3} c - 17 \, A b^{2} c^{2}\right)} x^{4} - 32 \, {\left(9 \, B b^{4} - 17 \, A b^{3} c\right)} x^{2}\right)} \sqrt{x}}{2880 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)}}"," ",0,"1/2880*(2340*(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)*(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21)^(1/4)*arctan((sqrt((531441*B^6*b^6*c^8 - 6022998*A*B^5*b^5*c^9 + 28441935*A^2*B^4*b^4*c^10 - 71631540*A^3*B^3*b^3*c^11 + 101478015*A^4*B^2*b^2*c^12 - 76672278*A^5*B*b*c^13 + 24137569*A^6*c^14)*x - (6561*B^4*b^15*c^5 - 49572*A*B^3*b^14*c^6 + 140454*A^2*B^2*b^13*c^7 - 176868*A^3*B*b^12*c^8 + 83521*A^4*b^11*c^9)*sqrt(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21))*b^5*(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21)^(1/4) + (729*B^3*b^8*c^4 - 4131*A*B^2*b^7*c^5 + 7803*A^2*B*b^6*c^6 - 4913*A^3*b^5*c^7)*sqrt(x)*(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21)^(1/4))/(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)) - 585*(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)*(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21)^(1/4)*log(2197*b^16*(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21)^(3/4) - 2197*(729*B^3*b^3*c^4 - 4131*A*B^2*b^2*c^5 + 7803*A^2*B*b*c^6 - 4913*A^3*c^7)*sqrt(x)) + 585*(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)*(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21)^(1/4)*log(-2197*b^16*(-(6561*B^4*b^4*c^5 - 49572*A*B^3*b^3*c^6 + 140454*A^2*B^2*b^2*c^7 - 176868*A^3*B*b*c^8 + 83521*A^4*c^9)/b^21)^(3/4) - 2197*(729*B^3*b^3*c^4 - 4131*A*B^2*b^2*c^5 + 7803*A^2*B*b*c^6 - 4913*A^3*c^7)*sqrt(x)) + 4*(585*(9*B*b*c^3 - 17*A*c^4)*x^8 + 1053*(9*B*b^2*c^2 - 17*A*b*c^3)*x^6 - 160*A*b^4 + 416*(9*B*b^3*c - 17*A*b^2*c^2)*x^4 - 32*(9*B*b^4 - 17*A*b^3*c)*x^2)*sqrt(x))/(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)","B",0
219,1,894,0,0.444561," ","integrate((B*x^2+A)/(c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""fricas"")","-\frac{4620 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)} \left(-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{12} \sqrt{-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}} + {\left(121 \, B^{2} b^{2} c^{4} - 418 \, A B b c^{5} + 361 \, A^{2} c^{6}\right)} x} b^{17} \left(-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}\right)^{\frac{3}{4}} + {\left(11 \, B b^{18} c^{2} - 19 \, A b^{17} c^{3}\right)} \sqrt{x} \left(-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}\right)^{\frac{3}{4}}}{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}\right) + 1155 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)} \left(-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}\right)^{\frac{1}{4}} \log\left(15 \, b^{6} \left(-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}\right)^{\frac{1}{4}} - 15 \, {\left(11 \, B b c^{2} - 19 \, A c^{3}\right)} \sqrt{x}\right) - 1155 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)} \left(-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}\right)^{\frac{1}{4}} \log\left(-15 \, b^{6} \left(-\frac{14641 \, B^{4} b^{4} c^{7} - 101156 \, A B^{3} b^{3} c^{8} + 262086 \, A^{2} B^{2} b^{2} c^{9} - 301796 \, A^{3} B b c^{10} + 130321 \, A^{4} c^{11}}{b^{23}}\right)^{\frac{1}{4}} - 15 \, {\left(11 \, B b c^{2} - 19 \, A c^{3}\right)} \sqrt{x}\right) - 4 \, {\left(385 \, {\left(11 \, B b c^{3} - 19 \, A c^{4}\right)} x^{8} + 605 \, {\left(11 \, B b^{2} c^{2} - 19 \, A b c^{3}\right)} x^{6} - 224 \, A b^{4} + 160 \, {\left(11 \, B b^{3} c - 19 \, A b^{2} c^{2}\right)} x^{4} - 32 \, {\left(11 \, B b^{4} - 19 \, A b^{3} c\right)} x^{2}\right)} \sqrt{x}}{4928 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)}}"," ",0,"-1/4928*(4620*(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)*(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23)^(1/4)*arctan((sqrt(b^12*sqrt(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23) + (121*B^2*b^2*c^4 - 418*A*B*b*c^5 + 361*A^2*c^6)*x)*b^17*(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23)^(3/4) + (11*B*b^18*c^2 - 19*A*b^17*c^3)*sqrt(x)*(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23)^(3/4))/(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)) + 1155*(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)*(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23)^(1/4)*log(15*b^6*(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23)^(1/4) - 15*(11*B*b*c^2 - 19*A*c^3)*sqrt(x)) - 1155*(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)*(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23)^(1/4)*log(-15*b^6*(-(14641*B^4*b^4*c^7 - 101156*A*B^3*b^3*c^8 + 262086*A^2*B^2*b^2*c^9 - 301796*A^3*B*b*c^10 + 130321*A^4*c^11)/b^23)^(1/4) - 15*(11*B*b*c^2 - 19*A*c^3)*sqrt(x)) - 4*(385*(11*B*b*c^3 - 19*A*c^4)*x^8 + 605*(11*B*b^2*c^2 - 19*A*b*c^3)*x^6 - 224*A*b^4 + 160*(11*B*b^3*c - 19*A*b^2*c^2)*x^4 - 32*(11*B*b^4 - 19*A*b^3*c)*x^2)*sqrt(x))/(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)","B",0
220,0,0,0,0.434757," ","integrate(x^(5/2)*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{4} + A x^{2}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((B*x^4 + A*x^2)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
221,0,0,0,0.437265," ","integrate(x^(3/2)*(B*x^2+A)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} {\left(B x^{3} + A x\right)} \sqrt{x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^3 + A*x)*sqrt(x), x)","F",0
222,0,0,0,0.424330," ","integrate((B*x^2+A)*x^(1/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x), x)","F",0
223,0,0,0,0.437831," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{\sqrt{x}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/sqrt(x), x)","F",0
224,0,0,0,0.427955," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/x^(3/2), x)","F",0
225,0,0,0,0.431113," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/x^(5/2), x)","F",0
226,0,0,0,0.430891," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/x^(7/2), x)","F",0
227,0,0,0,0.437192," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/x^(9/2), x)","F",0
228,0,0,0,0.425029," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/x^(11/2), x)","F",0
229,0,0,0,0.418860," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/x^(13/2), x)","F",0
230,0,0,0,0.418867," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(1/2)/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)}}{x^{\frac{15}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)/x^(15/2), x)","F",0
231,0,0,0,0.458800," ","integrate(x^(7/2)*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{9} + {\left(B b + A c\right)} x^{7} + A b x^{5}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((B*c*x^9 + (B*b + A*c)*x^7 + A*b*x^5)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
232,0,0,0,0.445639," ","integrate(x^(5/2)*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{8} + {\left(B b + A c\right)} x^{6} + A b x^{4}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((B*c*x^8 + (B*b + A*c)*x^6 + A*b*x^4)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
233,0,0,0,0.451041," ","integrate(x^(3/2)*(B*x^2+A)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{7} + {\left(B b + A c\right)} x^{5} + A b x^{3}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((B*c*x^7 + (B*b + A*c)*x^5 + A*b*x^3)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
234,0,0,0,0.450767," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{6} + {\left(B b + A c\right)} x^{4} + A b x^{2}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((B*c*x^6 + (B*b + A*c)*x^4 + A*b*x^2)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
235,0,0,0,0.443964," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{5} + {\left(B b + A c\right)} x^{3} + A b x\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((B*c*x^5 + (B*b + A*c)*x^3 + A*b*x)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
236,0,0,0,0.433920," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
237,0,0,0,0.427938," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}}}{\sqrt{x}}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)/sqrt(x), x)","F",0
238,0,0,0,0.433389," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}}}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)/x^(3/2), x)","F",0
239,0,0,0,0.444943," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}}}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)/x^(5/2), x)","F",0
240,0,0,0,0.440654," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}}}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)/x^(7/2), x)","F",0
241,0,0,0,0.433510," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)/x^(9/2), x)","F",0
242,0,0,0,0.449715," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)/x^(11/2), x)","F",0
243,0,0,0,0.456665," ","integrate((B*x^2+A)*(c*x^4+b*x^2)^(3/2)/x^(17/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{4} + {\left(B b + A c\right)} x^{2} + A b\right)} \sqrt{c x^{4} + b x^{2}}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral((B*c*x^4 + (B*b + A*c)*x^2 + A*b)*sqrt(c*x^4 + b*x^2)/x^(13/2), x)","F",0
244,0,0,0,0.442150," ","integrate(x^(13/2)*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{6} + A x^{4}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{2} + b}, x\right)"," ",0,"integral((B*x^6 + A*x^4)*sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^2 + b), x)","F",0
245,0,0,0,0.446385," ","integrate(x^(11/2)*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{5} + A x^{3}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{2} + b}, x\right)"," ",0,"integral((B*x^5 + A*x^3)*sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^2 + b), x)","F",0
246,0,0,0,0.427094," ","integrate(x^(9/2)*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{4} + A x^{2}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{2} + b}, x\right)"," ",0,"integral((B*x^4 + A*x^2)*sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^2 + b), x)","F",0
247,0,0,0,0.441857," ","integrate(x^(7/2)*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{3} + A x\right)} \sqrt{x}}{c x^{2} + b}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^3 + A*x)*sqrt(x)/(c*x^2 + b), x)","F",0
248,0,0,0,0.444453," ","integrate(x^(5/2)*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{2} + b}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^2 + b), x)","F",0
249,0,0,0,0.445328," ","integrate(x^(3/2)*(B*x^2+A)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{3} + b x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^3 + b*x), x)","F",0
250,0,0,0,0.432900," ","integrate((B*x^2+A)*x^(1/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{x}}{\sqrt{c x^{4} + b x^{2}}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(x)/sqrt(c*x^4 + b*x^2), x)","F",0
251,0,0,0,0.424013," ","integrate((B*x^2+A)/x^(1/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{5} + b x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^5 + b*x^3), x)","F",0
252,0,0,0,0.421062," ","integrate((B*x^2+A)/x^(3/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{6} + b x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^6 + b*x^4), x)","F",0
253,0,0,0,0.431924," ","integrate((B*x^2+A)/x^(5/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{7} + b x^{5}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^7 + b*x^5), x)","F",0
254,0,0,0,0.435379," ","integrate((B*x^2+A)/x^(7/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{8} + b x^{6}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^8 + b*x^6), x)","F",0
255,0,0,0,0.426407," ","integrate((B*x^2+A)/x^(9/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{9} + b x^{7}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^9 + b*x^7), x)","F",0
256,0,0,0,0.427197," ","integrate((B*x^2+A)/x^(11/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c x^{10} + b x^{8}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c*x^10 + b*x^8), x)","F",0
257,0,0,0,0.460044," ","integrate(x^(17/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{6} + A x^{4}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral((B*x^6 + A*x^4)*sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
258,0,0,0,0.459303," ","integrate(x^(15/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{5} + A x^{3}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral((B*x^5 + A*x^3)*sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
259,0,0,0,0.448640," ","integrate(x^(13/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{4} + A x^{2}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral((B*x^4 + A*x^2)*sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
260,0,0,0,0.452628," ","integrate(x^(11/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{3} + A x\right)} \sqrt{x}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^3 + A*x)*sqrt(x)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
261,0,0,0,0.435732," ","integrate(x^(9/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
262,0,0,0,0.421620," ","integrate(x^(7/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{5} + 2 \, b c x^{3} + b^{2} x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^5 + 2*b*c*x^3 + b^2*x), x)","F",0
263,0,0,0,0.423430," ","integrate(x^(5/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{6} + 2 \, b c x^{4} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^6 + 2*b*c*x^4 + b^2*x^2), x)","F",0
264,0,0,0,0.409782," ","integrate(x^(3/2)*(B*x^2+A)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{7} + 2 \, b c x^{5} + b^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^7 + 2*b*c*x^5 + b^2*x^3), x)","F",0
265,0,0,0,0.429019," ","integrate((B*x^2+A)*x^(1/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{8} + 2 \, b c x^{6} + b^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^8 + 2*b*c*x^6 + b^2*x^4), x)","F",0
266,0,0,0,0.415423," ","integrate((B*x^2+A)/(c*x^4+b*x^2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{9} + 2 \, b c x^{7} + b^{2} x^{5}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^9 + 2*b*c*x^7 + b^2*x^5), x)","F",0
267,0,0,0,0.418322," ","integrate((B*x^2+A)/x^(3/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{10} + 2 \, b c x^{8} + b^{2} x^{6}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^10 + 2*b*c*x^8 + b^2*x^6), x)","F",0
268,0,0,0,0.421423," ","integrate((B*x^2+A)/x^(5/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(B x^{2} + A\right)} \sqrt{x}}{c^{2} x^{11} + 2 \, b c x^{9} + b^{2} x^{7}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(B*x^2 + A)*sqrt(x)/(c^2*x^11 + 2*b*c*x^9 + b^2*x^7), x)","F",0
269,1,381,0,0.410969," ","integrate(x^m*(B*x^2+A)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{3} m^{4} + 40 \, B c^{3} m^{3} + 590 \, B c^{3} m^{2} + 3800 \, B c^{3} m + 9009 \, B c^{3}\right)} x^{15} + {\left({\left(3 \, B b c^{2} + A c^{3}\right)} m^{4} + 31185 \, B b c^{2} + 10395 \, A c^{3} + 42 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{3} + 644 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{2} + 4278 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m\right)} x^{13} + 3 \, {\left({\left(B b^{2} c + A b c^{2}\right)} m^{4} + 12285 \, B b^{2} c + 12285 \, A b c^{2} + 44 \, {\left(B b^{2} c + A b c^{2}\right)} m^{3} + 706 \, {\left(B b^{2} c + A b c^{2}\right)} m^{2} + 4884 \, {\left(B b^{2} c + A b c^{2}\right)} m\right)} x^{11} + {\left({\left(B b^{3} + 3 \, A b^{2} c\right)} m^{4} + 15015 \, B b^{3} + 45045 \, A b^{2} c + 46 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} m^{3} + 776 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} m^{2} + 5666 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} m\right)} x^{9} + {\left(A b^{3} m^{4} + 48 \, A b^{3} m^{3} + 854 \, A b^{3} m^{2} + 6672 \, A b^{3} m + 19305 \, A b^{3}\right)} x^{7}\right)} x^{m}}{m^{5} + 55 \, m^{4} + 1190 \, m^{3} + 12650 \, m^{2} + 66009 \, m + 135135}"," ",0,"((B*c^3*m^4 + 40*B*c^3*m^3 + 590*B*c^3*m^2 + 3800*B*c^3*m + 9009*B*c^3)*x^15 + ((3*B*b*c^2 + A*c^3)*m^4 + 31185*B*b*c^2 + 10395*A*c^3 + 42*(3*B*b*c^2 + A*c^3)*m^3 + 644*(3*B*b*c^2 + A*c^3)*m^2 + 4278*(3*B*b*c^2 + A*c^3)*m)*x^13 + 3*((B*b^2*c + A*b*c^2)*m^4 + 12285*B*b^2*c + 12285*A*b*c^2 + 44*(B*b^2*c + A*b*c^2)*m^3 + 706*(B*b^2*c + A*b*c^2)*m^2 + 4884*(B*b^2*c + A*b*c^2)*m)*x^11 + ((B*b^3 + 3*A*b^2*c)*m^4 + 15015*B*b^3 + 45045*A*b^2*c + 46*(B*b^3 + 3*A*b^2*c)*m^3 + 776*(B*b^3 + 3*A*b^2*c)*m^2 + 5666*(B*b^3 + 3*A*b^2*c)*m)*x^9 + (A*b^3*m^4 + 48*A*b^3*m^3 + 854*A*b^3*m^2 + 6672*A*b^3*m + 19305*A*b^3)*x^7)*x^m/(m^5 + 55*m^4 + 1190*m^3 + 12650*m^2 + 66009*m + 135135)","B",0
270,1,217,0,0.409747," ","integrate(x^m*(B*x^2+A)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{2} m^{3} + 21 \, B c^{2} m^{2} + 143 \, B c^{2} m + 315 \, B c^{2}\right)} x^{11} + {\left({\left(2 \, B b c + A c^{2}\right)} m^{3} + 770 \, B b c + 385 \, A c^{2} + 23 \, {\left(2 \, B b c + A c^{2}\right)} m^{2} + 167 \, {\left(2 \, B b c + A c^{2}\right)} m\right)} x^{9} + {\left({\left(B b^{2} + 2 \, A b c\right)} m^{3} + 495 \, B b^{2} + 990 \, A b c + 25 \, {\left(B b^{2} + 2 \, A b c\right)} m^{2} + 199 \, {\left(B b^{2} + 2 \, A b c\right)} m\right)} x^{7} + {\left(A b^{2} m^{3} + 27 \, A b^{2} m^{2} + 239 \, A b^{2} m + 693 \, A b^{2}\right)} x^{5}\right)} x^{m}}{m^{4} + 32 \, m^{3} + 374 \, m^{2} + 1888 \, m + 3465}"," ",0,"((B*c^2*m^3 + 21*B*c^2*m^2 + 143*B*c^2*m + 315*B*c^2)*x^11 + ((2*B*b*c + A*c^2)*m^3 + 770*B*b*c + 385*A*c^2 + 23*(2*B*b*c + A*c^2)*m^2 + 167*(2*B*b*c + A*c^2)*m)*x^9 + ((B*b^2 + 2*A*b*c)*m^3 + 495*B*b^2 + 990*A*b*c + 25*(B*b^2 + 2*A*b*c)*m^2 + 199*(B*b^2 + 2*A*b*c)*m)*x^7 + (A*b^2*m^3 + 27*A*b^2*m^2 + 239*A*b^2*m + 693*A*b^2)*x^5)*x^m/(m^4 + 32*m^3 + 374*m^2 + 1888*m + 3465)","B",0
271,1,94,0,0.419337," ","integrate(x^m*(B*x^2+A)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{{\left({\left(B c m^{2} + 8 \, B c m + 15 \, B c\right)} x^{7} + {\left({\left(B b + A c\right)} m^{2} + 21 \, B b + 21 \, A c + 10 \, {\left(B b + A c\right)} m\right)} x^{5} + {\left(A b m^{2} + 12 \, A b m + 35 \, A b\right)} x^{3}\right)} x^{m}}{m^{3} + 15 \, m^{2} + 71 \, m + 105}"," ",0,"((B*c*m^2 + 8*B*c*m + 15*B*c)*x^7 + ((B*b + A*c)*m^2 + 21*B*b + 21*A*c + 10*(B*b + A*c)*m)*x^5 + (A*b*m^2 + 12*A*b*m + 35*A*b)*x^3)*x^m/(m^3 + 15*m^2 + 71*m + 105)","B",0
272,0,0,0,0.398348," ","integrate(x^m*(B*x^2+A)/(c*x^4+b*x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} x^{m}}{c x^{4} + b x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*x^m/(c*x^4 + b*x^2), x)","F",0
273,0,0,0,0.424901," ","integrate(x^m*(B*x^2+A)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} x^{m}}{c^{2} x^{8} + 2 \, b c x^{6} + b^{2} x^{4}}, x\right)"," ",0,"integral((B*x^2 + A)*x^m/(c^2*x^8 + 2*b*c*x^6 + b^2*x^4), x)","F",0
274,0,0,0,0.435623," ","integrate(x^m*(B*x^2+A)*(c*x^4+b*x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{2} + A\right)} {\left(c x^{4} + b x^{2}\right)}^{p} x^{m}, x\right)"," ",0,"integral((B*x^2 + A)*(c*x^4 + b*x^2)^p*x^m, x)","F",0
275,1,140,0,0.433327," ","integrate(x^(-j*p+n-1)*(c+d*x^n)*(a*x^j+b*x^(j+n))^p,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} d p + b^{2} d\right)} x x^{-j p + n - 1} x^{2 \, n} + {\left(2 \, b^{2} c + {\left(b^{2} c + a b d\right)} p\right)} x x^{-j p + n - 1} x^{n} + {\left(a b c p + 2 \, a b c - a^{2} d\right)} x x^{-j p + n - 1}\right)} \left(\frac{{\left(b x^{n} + a\right)} x^{j + n}}{x^{n}}\right)^{p}}{{\left(b^{2} n p^{2} + 3 \, b^{2} n p + 2 \, b^{2} n\right)} x^{n}}"," ",0,"((b^2*d*p + b^2*d)*x*x^(-j*p + n - 1)*x^(2*n) + (2*b^2*c + (b^2*c + a*b*d)*p)*x*x^(-j*p + n - 1)*x^n + (a*b*c*p + 2*a*b*c - a^2*d)*x*x^(-j*p + n - 1))*((b*x^n + a)*x^(j + n)/x^n)^p/((b^2*n*p^2 + 3*b^2*n*p + 2*b^2*n)*x^n)","A",0
276,0,0,0,0.449517," ","integrate((e*x)^m*(c+d*x^n)^q*(a*x^j+b*x^(j+n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{j + n} + a x^{j}\right)}^{p} {\left(d x^{n} + c\right)}^{q} \left(e x\right)^{m}, x\right)"," ",0,"integral((b*x^(j + n) + a*x^j)^p*(d*x^n + c)^q*(e*x)^m, x)","F",0
277,0,0,0,0.445981," ","integrate((e*x)^(7/4)*(c+d*x^n)^q*(a*x^j+b*x^(j+n))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b e x x^{j + n} + a e x x^{j}\right)} {\left(b x^{j + n} + a x^{j}\right)}^{\frac{2}{3}} \left(e x\right)^{\frac{3}{4}} {\left(d x^{n} + c\right)}^{q}, x\right)"," ",0,"integral((b*e*x*x^(j + n) + a*e*x*x^j)*(b*x^(j + n) + a*x^j)^(2/3)*(e*x)^(3/4)*(d*x^n + c)^q, x)","F",0
278,1,15,0,0.387622," ","integrate((3*x^4+4)/(2*x^5+5*x),x, algorithm=""fricas"")","\frac{7}{40} \, \log\left(2 \, x^{4} + 5\right) + \frac{4}{5} \, \log\left(x\right)"," ",0,"7/40*log(2*x^4 + 5) + 4/5*log(x)","A",0
279,1,11,0,0.390434," ","integrate((x^6+1)/(-x^7+x),x, algorithm=""fricas"")","-\frac{1}{3} \, \log\left(x^{6} - 1\right) + \log\left(x\right)"," ",0,"-1/3*log(x^6 - 1) + log(x)","A",0
280,1,13,0,0.392111," ","integrate((5*x^10+8)/(-x^11+2*x),x, algorithm=""fricas"")","-\frac{9}{10} \, \log\left(x^{10} - 2\right) + 4 \, \log\left(x\right)"," ",0,"-9/10*log(x^10 - 2) + 4*log(x)","A",0
281,1,18,0,0.389367," ","integrate((-3+2*x)/(x^3-x^2),x, algorithm=""fricas"")","-\frac{x \log\left(x - 1\right) - x \log\left(x\right) + 3}{x}"," ",0,"-(x*log(x - 1) - x*log(x) + 3)/x","A",0
282,0,0,0,0.401808," ","integrate((a*x^m+b*x^n)/(c*x^m+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{m} + b x^{n}}{c x^{m} + d x^{n}}, x\right)"," ",0,"integral((a*x^m + b*x^n)/(c*x^m + d*x^n), x)","F",0
283,1,43,0,0.429925," ","integrate(x^m*(a+b*x^n)^p*(a*(1+m+q)*x^q+b*(1+m+n*(1+p)+q)*x^(n+q)),x, algorithm=""fricas"")","{\left(b x x^{m} x^{n + q} + a x x^{m} x^{q}\right)} \left(\frac{b x^{n + q} + a x^{q}}{x^{q}}\right)^{p}"," ",0,"(b*x*x^m*x^(n + q) + a*x*x^m*x^q)*((b*x^(n + q) + a*x^q)/x^q)^p","B",0
284,0,0,0,0.415193," ","integrate((a+b/x)^n*x^m/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \left(\frac{a x + b}{x}\right)^{n}}{d x + c}, x\right)"," ",0,"integral(x^m*((a*x + b)/x)^n/(d*x + c), x)","F",0
285,0,0,0,0.415319," ","integrate((a+b/x)^n*x^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \left(\frac{a x + b}{x}\right)^{n}}{d x + c}, x\right)"," ",0,"integral(x^2*((a*x + b)/x)^n/(d*x + c), x)","F",0
286,0,0,0,0.413326," ","integrate((a+b/x)^n*x/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \left(\frac{a x + b}{x}\right)^{n}}{d x + c}, x\right)"," ",0,"integral(x*((a*x + b)/x)^n/(d*x + c), x)","F",0
287,0,0,0,0.416273," ","integrate((a+b/x)^n/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d x + c}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d*x + c), x)","F",0
288,0,0,0,0.425301," ","integrate((a+b/x)^n/x/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d x^{2} + c x}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d*x^2 + c*x), x)","F",0
289,0,0,0,0.422805," ","integrate((a+b/x)^n/x^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d x^{3} + c x^{2}}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d*x^3 + c*x^2), x)","F",0
290,0,0,0,0.427897," ","integrate((a+b/x)^n/x^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d x^{4} + c x^{3}}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d*x^4 + c*x^3), x)","F",0
291,0,0,0,0.419507," ","integrate((a+b/x)^n/x^5/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d x^{6} + c x^{5}}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d*x^6 + c*x^5), x)","F",0
292,0,0,0,0.442669," ","integrate((a+b/x)^n*x^m/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \left(\frac{a x + b}{x}\right)^{n}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(x^m*((a*x + b)/x)^n/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
293,0,0,0,0.423750," ","integrate((a+b/x)^n*x^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \left(\frac{a x + b}{x}\right)^{n}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(x^2*((a*x + b)/x)^n/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
294,0,0,0,0.427593," ","integrate((a+b/x)^n*x/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \left(\frac{a x + b}{x}\right)^{n}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(x*((a*x + b)/x)^n/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
295,0,0,0,0.428199," ","integrate((a+b/x)^n/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
296,0,0,0,0.431312," ","integrate((a+b/x)^n/x/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d^{2} x^{3} + 2 \, c d x^{2} + c^{2} x}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d^2*x^3 + 2*c*d*x^2 + c^2*x), x)","F",0
297,0,0,0,0.413075," ","integrate((a+b/x)^n/x^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d^{2} x^{4} + 2 \, c d x^{3} + c^{2} x^{2}}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d^2*x^4 + 2*c*d*x^3 + c^2*x^2), x)","F",0
298,0,0,0,0.431070," ","integrate((a+b/x)^n/x^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{n}}{d^{2} x^{5} + 2 \, c d x^{4} + c^{2} x^{3}}, x\right)"," ",0,"integral(((a*x + b)/x)^n/(d^2*x^5 + 2*c*d*x^4 + c^2*x^3), x)","F",0
