1,1,97,0,0.932871," ","integrate((b*x^3+a)*(d*x^3+c)^4,x, algorithm=""fricas"")","\frac{1}{16} x^{16} d^{4} b + \frac{4}{13} x^{13} d^{3} c b + \frac{1}{13} x^{13} d^{4} a + \frac{3}{5} x^{10} d^{2} c^{2} b + \frac{2}{5} x^{10} d^{3} c a + \frac{4}{7} x^{7} d c^{3} b + \frac{6}{7} x^{7} d^{2} c^{2} a + \frac{1}{4} x^{4} c^{4} b + x^{4} d c^{3} a + x c^{4} a"," ",0,"1/16*x^16*d^4*b + 4/13*x^13*d^3*c*b + 1/13*x^13*d^4*a + 3/5*x^10*d^2*c^2*b + 2/5*x^10*d^3*c*a + 4/7*x^7*d*c^3*b + 6/7*x^7*d^2*c^2*a + 1/4*x^4*c^4*b + x^4*d*c^3*a + x*c^4*a","A",0
2,1,74,0,0.849397," ","integrate((b*x^3+a)*(d*x^3+c)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} d^{3} b + \frac{3}{10} x^{10} d^{2} c b + \frac{1}{10} x^{10} d^{3} a + \frac{3}{7} x^{7} d c^{2} b + \frac{3}{7} x^{7} d^{2} c a + \frac{1}{4} x^{4} c^{3} b + \frac{3}{4} x^{4} d c^{2} a + x c^{3} a"," ",0,"1/13*x^13*d^3*b + 3/10*x^10*d^2*c*b + 1/10*x^10*d^3*a + 3/7*x^7*d*c^2*b + 3/7*x^7*d^2*c*a + 1/4*x^4*c^3*b + 3/4*x^4*d*c^2*a + x*c^3*a","A",0
3,1,50,0,0.634887," ","integrate((b*x^3+a)*(d*x^3+c)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} d^{2} b + \frac{2}{7} x^{7} d c b + \frac{1}{7} x^{7} d^{2} a + \frac{1}{4} x^{4} c^{2} b + \frac{1}{2} x^{4} d c a + x c^{2} a"," ",0,"1/10*x^10*d^2*b + 2/7*x^7*d*c*b + 1/7*x^7*d^2*a + 1/4*x^4*c^2*b + 1/2*x^4*d*c*a + x*c^2*a","A",0
4,1,26,0,0.845926," ","integrate((b*x^3+a)*(d*x^3+c),x, algorithm=""fricas"")","\frac{1}{7} x^{7} d b + \frac{1}{4} x^{4} c b + \frac{1}{4} x^{4} d a + x c a"," ",0,"1/7*x^7*d*b + 1/4*x^4*c*b + 1/4*x^4*d*a + x*c*a","A",0
5,1,369,0,1.136820," ","integrate((b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{6 \, b c^{2} d x - 3 \, \sqrt{\frac{1}{3}} {\left(b c^{2} d - a c d^{2}\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(\frac{2 \, c d x^{3} - 3 \, \left(c^{2} d\right)^{\frac{1}{3}} c x - c^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d x^{2} + \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{d x^{3} + c}\right) + \left(c^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) - 2 \, \left(c^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right)}{6 \, c^{2} d^{2}}, \frac{6 \, b c^{2} d x - 6 \, \sqrt{\frac{1}{3}} {\left(b c^{2} d - a c d^{2}\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{c^{2}}\right) + \left(c^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) - 2 \, \left(c^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right)}{6 \, c^{2} d^{2}}\right]"," ",0,"[1/6*(6*b*c^2*d*x - 3*sqrt(1/3)*(b*c^2*d - a*c*d^2)*sqrt(-(c^2*d)^(1/3)/d)*log((2*c*d*x^3 - 3*(c^2*d)^(1/3)*c*x - c^2 + 3*sqrt(1/3)*(2*c*d*x^2 + (c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt(-(c^2*d)^(1/3)/d))/(d*x^3 + c)) + (c^2*d)^(2/3)*(b*c - a*d)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) - 2*(c^2*d)^(2/3)*(b*c - a*d)*log(c*d*x + (c^2*d)^(2/3)))/(c^2*d^2), 1/6*(6*b*c^2*d*x - 6*sqrt(1/3)*(b*c^2*d - a*c*d^2)*sqrt((c^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt((c^2*d)^(1/3)/d)/c^2) + (c^2*d)^(2/3)*(b*c - a*d)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) - 2*(c^2*d)^(2/3)*(b*c - a*d)*log(c*d*x + (c^2*d)^(2/3)))/(c^2*d^2)]","A",0
6,1,537,0,1.020752," ","integrate((b*x^3+a)/(d*x^3+c)^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(b c^{3} d + 2 \, a c^{2} d^{2} + {\left(b c^{2} d^{2} + 2 \, a c d^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(\frac{2 \, c d x^{3} - 3 \, \left(c^{2} d\right)^{\frac{1}{3}} c x - c^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d x^{2} + \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{d x^{3} + c}\right) - {\left({\left(b c d + 2 \, a d^{2}\right)} x^{3} + b c^{2} + 2 \, a c d\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) + 2 \, {\left({\left(b c d + 2 \, a d^{2}\right)} x^{3} + b c^{2} + 2 \, a c d\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) - 6 \, {\left(b c^{3} d - a c^{2} d^{2}\right)} x}{18 \, {\left(c^{3} d^{3} x^{3} + c^{4} d^{2}\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(b c^{3} d + 2 \, a c^{2} d^{2} + {\left(b c^{2} d^{2} + 2 \, a c d^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{c^{2}}\right) - {\left({\left(b c d + 2 \, a d^{2}\right)} x^{3} + b c^{2} + 2 \, a c d\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) + 2 \, {\left({\left(b c d + 2 \, a d^{2}\right)} x^{3} + b c^{2} + 2 \, a c d\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) - 6 \, {\left(b c^{3} d - a c^{2} d^{2}\right)} x}{18 \, {\left(c^{3} d^{3} x^{3} + c^{4} d^{2}\right)}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(b*c^3*d + 2*a*c^2*d^2 + (b*c^2*d^2 + 2*a*c*d^3)*x^3)*sqrt(-(c^2*d)^(1/3)/d)*log((2*c*d*x^3 - 3*(c^2*d)^(1/3)*c*x - c^2 + 3*sqrt(1/3)*(2*c*d*x^2 + (c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt(-(c^2*d)^(1/3)/d))/(d*x^3 + c)) - ((b*c*d + 2*a*d^2)*x^3 + b*c^2 + 2*a*c*d)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) + 2*((b*c*d + 2*a*d^2)*x^3 + b*c^2 + 2*a*c*d)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) - 6*(b*c^3*d - a*c^2*d^2)*x)/(c^3*d^3*x^3 + c^4*d^2), 1/18*(6*sqrt(1/3)*(b*c^3*d + 2*a*c^2*d^2 + (b*c^2*d^2 + 2*a*c*d^3)*x^3)*sqrt((c^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt((c^2*d)^(1/3)/d)/c^2) - ((b*c*d + 2*a*d^2)*x^3 + b*c^2 + 2*a*c*d)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) + 2*((b*c*d + 2*a*d^2)*x^3 + b*c^2 + 2*a*c*d)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) - 6*(b*c^3*d - a*c^2*d^2)*x)/(c^3*d^3*x^3 + c^4*d^2)]","A",0
7,1,743,0,1.175429," ","integrate((b*x^3+a)/(d*x^3+c)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c^{3} d^{2} + 5 \, a c^{2} d^{3}\right)} x^{4} + 3 \, \sqrt{\frac{1}{3}} {\left({\left(b c^{2} d^{3} + 5 \, a c d^{4}\right)} x^{6} + b c^{4} d + 5 \, a c^{3} d^{2} + 2 \, {\left(b c^{3} d^{2} + 5 \, a c^{2} d^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(\frac{2 \, c d x^{3} - 3 \, \left(c^{2} d\right)^{\frac{1}{3}} c x - c^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d x^{2} + \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{d x^{3} + c}\right) - {\left({\left(b c d^{2} + 5 \, a d^{3}\right)} x^{6} + b c^{3} + 5 \, a c^{2} d + 2 \, {\left(b c^{2} d + 5 \, a c d^{2}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) + 2 \, {\left({\left(b c d^{2} + 5 \, a d^{3}\right)} x^{6} + b c^{3} + 5 \, a c^{2} d + 2 \, {\left(b c^{2} d + 5 \, a c d^{2}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) - 6 \, {\left(b c^{4} d - 4 \, a c^{3} d^{2}\right)} x}{54 \, {\left(c^{4} d^{4} x^{6} + 2 \, c^{5} d^{3} x^{3} + c^{6} d^{2}\right)}}, \frac{3 \, {\left(b c^{3} d^{2} + 5 \, a c^{2} d^{3}\right)} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left({\left(b c^{2} d^{3} + 5 \, a c d^{4}\right)} x^{6} + b c^{4} d + 5 \, a c^{3} d^{2} + 2 \, {\left(b c^{3} d^{2} + 5 \, a c^{2} d^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{c^{2}}\right) - {\left({\left(b c d^{2} + 5 \, a d^{3}\right)} x^{6} + b c^{3} + 5 \, a c^{2} d + 2 \, {\left(b c^{2} d + 5 \, a c d^{2}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) + 2 \, {\left({\left(b c d^{2} + 5 \, a d^{3}\right)} x^{6} + b c^{3} + 5 \, a c^{2} d + 2 \, {\left(b c^{2} d + 5 \, a c d^{2}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) - 6 \, {\left(b c^{4} d - 4 \, a c^{3} d^{2}\right)} x}{54 \, {\left(c^{4} d^{4} x^{6} + 2 \, c^{5} d^{3} x^{3} + c^{6} d^{2}\right)}}\right]"," ",0,"[1/54*(3*(b*c^3*d^2 + 5*a*c^2*d^3)*x^4 + 3*sqrt(1/3)*((b*c^2*d^3 + 5*a*c*d^4)*x^6 + b*c^4*d + 5*a*c^3*d^2 + 2*(b*c^3*d^2 + 5*a*c^2*d^3)*x^3)*sqrt(-(c^2*d)^(1/3)/d)*log((2*c*d*x^3 - 3*(c^2*d)^(1/3)*c*x - c^2 + 3*sqrt(1/3)*(2*c*d*x^2 + (c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt(-(c^2*d)^(1/3)/d))/(d*x^3 + c)) - ((b*c*d^2 + 5*a*d^3)*x^6 + b*c^3 + 5*a*c^2*d + 2*(b*c^2*d + 5*a*c*d^2)*x^3)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) + 2*((b*c*d^2 + 5*a*d^3)*x^6 + b*c^3 + 5*a*c^2*d + 2*(b*c^2*d + 5*a*c*d^2)*x^3)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) - 6*(b*c^4*d - 4*a*c^3*d^2)*x)/(c^4*d^4*x^6 + 2*c^5*d^3*x^3 + c^6*d^2), 1/54*(3*(b*c^3*d^2 + 5*a*c^2*d^3)*x^4 + 6*sqrt(1/3)*((b*c^2*d^3 + 5*a*c*d^4)*x^6 + b*c^4*d + 5*a*c^3*d^2 + 2*(b*c^3*d^2 + 5*a*c^2*d^3)*x^3)*sqrt((c^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt((c^2*d)^(1/3)/d)/c^2) - ((b*c*d^2 + 5*a*d^3)*x^6 + b*c^3 + 5*a*c^2*d + 2*(b*c^2*d + 5*a*c*d^2)*x^3)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) + 2*((b*c*d^2 + 5*a*d^3)*x^6 + b*c^3 + 5*a*c^2*d + 2*(b*c^2*d + 5*a*c*d^2)*x^3)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) - 6*(b*c^4*d - 4*a*c^3*d^2)*x)/(c^4*d^4*x^6 + 2*c^5*d^3*x^3 + c^6*d^2)]","B",0
8,1,132,0,0.734025," ","integrate((b*x^3+a)^2*(d*x^3+c)^3,x, algorithm=""fricas"")","\frac{1}{16} x^{16} d^{3} b^{2} + \frac{3}{13} x^{13} d^{2} c b^{2} + \frac{2}{13} x^{13} d^{3} b a + \frac{3}{10} x^{10} d c^{2} b^{2} + \frac{3}{5} x^{10} d^{2} c b a + \frac{1}{10} x^{10} d^{3} a^{2} + \frac{1}{7} x^{7} c^{3} b^{2} + \frac{6}{7} x^{7} d c^{2} b a + \frac{3}{7} x^{7} d^{2} c a^{2} + \frac{1}{2} x^{4} c^{3} b a + \frac{3}{4} x^{4} d c^{2} a^{2} + x c^{3} a^{2}"," ",0,"1/16*x^16*d^3*b^2 + 3/13*x^13*d^2*c*b^2 + 2/13*x^13*d^3*b*a + 3/10*x^10*d*c^2*b^2 + 3/5*x^10*d^2*c*b*a + 1/10*x^10*d^3*a^2 + 1/7*x^7*c^3*b^2 + 6/7*x^7*d*c^2*b*a + 3/7*x^7*d^2*c*a^2 + 1/2*x^4*c^3*b*a + 3/4*x^4*d*c^2*a^2 + x*c^3*a^2","A",0
9,1,91,0,0.818416," ","integrate((b*x^3+a)^2*(d*x^3+c)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} d^{2} b^{2} + \frac{1}{5} x^{10} d c b^{2} + \frac{1}{5} x^{10} d^{2} b a + \frac{1}{7} x^{7} c^{2} b^{2} + \frac{4}{7} x^{7} d c b a + \frac{1}{7} x^{7} d^{2} a^{2} + \frac{1}{2} x^{4} c^{2} b a + \frac{1}{2} x^{4} d c a^{2} + x c^{2} a^{2}"," ",0,"1/13*x^13*d^2*b^2 + 1/5*x^10*d*c*b^2 + 1/5*x^10*d^2*b*a + 1/7*x^7*c^2*b^2 + 4/7*x^7*d*c*b*a + 1/7*x^7*d^2*a^2 + 1/2*x^4*c^2*b*a + 1/2*x^4*d*c*a^2 + x*c^2*a^2","A",0
10,1,50,0,0.509898," ","integrate((b*x^3+a)^2*(d*x^3+c),x, algorithm=""fricas"")","\frac{1}{10} x^{10} d b^{2} + \frac{1}{7} x^{7} c b^{2} + \frac{2}{7} x^{7} d b a + \frac{1}{2} x^{4} c b a + \frac{1}{4} x^{4} d a^{2} + x c a^{2}"," ",0,"1/10*x^10*d*b^2 + 1/7*x^7*c*b^2 + 2/7*x^7*d*b*a + 1/2*x^4*c*b*a + 1/4*x^4*d*a^2 + x*c*a^2","A",0
11,1,505,0,0.679720," ","integrate((b*x^3+a)^2/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} c^{2} d^{2} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(\frac{2 \, c d x^{3} - 3 \, \left(c^{2} d\right)^{\frac{1}{3}} c x - c^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d x^{2} + \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{d x^{3} + c}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) - 12 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2}\right)} x}{12 \, c^{2} d^{3}}, \frac{3 \, b^{2} c^{2} d^{2} x^{4} + 12 \, \sqrt{\frac{1}{3}} {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{c^{2}}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) - 12 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2}\right)} x}{12 \, c^{2} d^{3}}\right]"," ",0,"[1/12*(3*b^2*c^2*d^2*x^4 + 6*sqrt(1/3)*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*sqrt(-(c^2*d)^(1/3)/d)*log((2*c*d*x^3 - 3*(c^2*d)^(1/3)*c*x - c^2 + 3*sqrt(1/3)*(2*c*d*x^2 + (c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt(-(c^2*d)^(1/3)/d))/(d*x^3 + c)) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) + 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) - 12*(b^2*c^3*d - 2*a*b*c^2*d^2)*x)/(c^2*d^3), 1/12*(3*b^2*c^2*d^2*x^4 + 12*sqrt(1/3)*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*sqrt((c^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt((c^2*d)^(1/3)/d)/c^2) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) + 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) - 12*(b^2*c^3*d - 2*a*b*c^2*d^2)*x)/(c^2*d^3)]","A",0
12,1,771,0,1.006448," ","integrate((b*x^3+a)^2/(d*x^3+c)^2,x, algorithm=""fricas"")","\left[\frac{9 \, b^{2} c^{3} d^{2} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, b^{2} c^{4} d - a b c^{3} d^{2} - a^{2} c^{2} d^{3} + {\left(2 \, b^{2} c^{3} d^{2} - a b c^{2} d^{3} - a^{2} c d^{4}\right)} x^{3}\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(\frac{2 \, c d x^{3} - 3 \, \left(c^{2} d\right)^{\frac{1}{3}} c x - c^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d x^{2} + \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{d x^{3} + c}\right) + {\left(2 \, b^{2} c^{3} - a b c^{2} d - a^{2} c d^{2} + {\left(2 \, b^{2} c^{2} d - a b c d^{2} - a^{2} d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) - 2 \, {\left(2 \, b^{2} c^{3} - a b c^{2} d - a^{2} c d^{2} + {\left(2 \, b^{2} c^{2} d - a b c d^{2} - a^{2} d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) + 3 \, {\left(4 \, b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x}{9 \, {\left(c^{3} d^{4} x^{3} + c^{4} d^{3}\right)}}, \frac{9 \, b^{2} c^{3} d^{2} x^{4} - 6 \, \sqrt{\frac{1}{3}} {\left(2 \, b^{2} c^{4} d - a b c^{3} d^{2} - a^{2} c^{2} d^{3} + {\left(2 \, b^{2} c^{3} d^{2} - a b c^{2} d^{3} - a^{2} c d^{4}\right)} x^{3}\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{c^{2}}\right) + {\left(2 \, b^{2} c^{3} - a b c^{2} d - a^{2} c d^{2} + {\left(2 \, b^{2} c^{2} d - a b c d^{2} - a^{2} d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) - 2 \, {\left(2 \, b^{2} c^{3} - a b c^{2} d - a^{2} c d^{2} + {\left(2 \, b^{2} c^{2} d - a b c d^{2} - a^{2} d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) + 3 \, {\left(4 \, b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x}{9 \, {\left(c^{3} d^{4} x^{3} + c^{4} d^{3}\right)}}\right]"," ",0,"[1/9*(9*b^2*c^3*d^2*x^4 - 3*sqrt(1/3)*(2*b^2*c^4*d - a*b*c^3*d^2 - a^2*c^2*d^3 + (2*b^2*c^3*d^2 - a*b*c^2*d^3 - a^2*c*d^4)*x^3)*sqrt(-(c^2*d)^(1/3)/d)*log((2*c*d*x^3 - 3*(c^2*d)^(1/3)*c*x - c^2 + 3*sqrt(1/3)*(2*c*d*x^2 + (c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt(-(c^2*d)^(1/3)/d))/(d*x^3 + c)) + (2*b^2*c^3 - a*b*c^2*d - a^2*c*d^2 + (2*b^2*c^2*d - a*b*c*d^2 - a^2*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) - 2*(2*b^2*c^3 - a*b*c^2*d - a^2*c*d^2 + (2*b^2*c^2*d - a*b*c*d^2 - a^2*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) + 3*(4*b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x)/(c^3*d^4*x^3 + c^4*d^3), 1/9*(9*b^2*c^3*d^2*x^4 - 6*sqrt(1/3)*(2*b^2*c^4*d - a*b*c^3*d^2 - a^2*c^2*d^3 + (2*b^2*c^3*d^2 - a*b*c^2*d^3 - a^2*c*d^4)*x^3)*sqrt((c^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt((c^2*d)^(1/3)/d)/c^2) + (2*b^2*c^3 - a*b*c^2*d - a^2*c*d^2 + (2*b^2*c^2*d - a*b*c*d^2 - a^2*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) - 2*(2*b^2*c^3 - a*b*c^2*d - a^2*c*d^2 + (2*b^2*c^2*d - a*b*c*d^2 - a^2*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) + 3*(4*b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x)/(c^3*d^4*x^3 + c^4*d^3)]","B",0
13,1,1067,0,0.854431," ","integrate((b*x^3+a)^2/(d*x^3+c)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(7 \, b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} - 5 \, a^{2} c^{2} d^{4}\right)} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, b^{2} c^{5} d + 2 \, a b c^{4} d^{2} + 5 \, a^{2} c^{3} d^{3} + {\left(2 \, b^{2} c^{3} d^{3} + 2 \, a b c^{2} d^{4} + 5 \, a^{2} c d^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{2} c^{4} d^{2} + 2 \, a b c^{3} d^{3} + 5 \, a^{2} c^{2} d^{4}\right)} x^{3}\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(\frac{2 \, c d x^{3} - 3 \, \left(c^{2} d\right)^{\frac{1}{3}} c x - c^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d x^{2} + \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{-\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{d x^{3} + c}\right) + {\left({\left(2 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{6} + 2 \, b^{2} c^{4} + 2 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2} + 2 \, {\left(2 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) - 2 \, {\left({\left(2 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{6} + 2 \, b^{2} c^{4} + 2 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2} + 2 \, {\left(2 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) + 12 \, {\left(b^{2} c^{5} d + a b c^{4} d^{2} - 2 \, a^{2} c^{3} d^{3}\right)} x}{54 \, {\left(c^{4} d^{5} x^{6} + 2 \, c^{5} d^{4} x^{3} + c^{6} d^{3}\right)}}, -\frac{3 \, {\left(7 \, b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} - 5 \, a^{2} c^{2} d^{4}\right)} x^{4} - 6 \, \sqrt{\frac{1}{3}} {\left(2 \, b^{2} c^{5} d + 2 \, a b c^{4} d^{2} + 5 \, a^{2} c^{3} d^{3} + {\left(2 \, b^{2} c^{3} d^{3} + 2 \, a b c^{2} d^{4} + 5 \, a^{2} c d^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{2} c^{4} d^{2} + 2 \, a b c^{3} d^{3} + 5 \, a^{2} c^{2} d^{4}\right)} x^{3}\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(c^{2} d\right)^{\frac{2}{3}} x - \left(c^{2} d\right)^{\frac{1}{3}} c\right)} \sqrt{\frac{\left(c^{2} d\right)^{\frac{1}{3}}}{d}}}{c^{2}}\right) + {\left({\left(2 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{6} + 2 \, b^{2} c^{4} + 2 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2} + 2 \, {\left(2 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x^{2} - \left(c^{2} d\right)^{\frac{2}{3}} x + \left(c^{2} d\right)^{\frac{1}{3}} c\right) - 2 \, {\left({\left(2 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{6} + 2 \, b^{2} c^{4} + 2 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2} + 2 \, {\left(2 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{3}\right)} \left(c^{2} d\right)^{\frac{2}{3}} \log\left(c d x + \left(c^{2} d\right)^{\frac{2}{3}}\right) + 12 \, {\left(b^{2} c^{5} d + a b c^{4} d^{2} - 2 \, a^{2} c^{3} d^{3}\right)} x}{54 \, {\left(c^{4} d^{5} x^{6} + 2 \, c^{5} d^{4} x^{3} + c^{6} d^{3}\right)}}\right]"," ",0,"[-1/54*(3*(7*b^2*c^4*d^2 - 2*a*b*c^3*d^3 - 5*a^2*c^2*d^4)*x^4 - 3*sqrt(1/3)*(2*b^2*c^5*d + 2*a*b*c^4*d^2 + 5*a^2*c^3*d^3 + (2*b^2*c^3*d^3 + 2*a*b*c^2*d^4 + 5*a^2*c*d^5)*x^6 + 2*(2*b^2*c^4*d^2 + 2*a*b*c^3*d^3 + 5*a^2*c^2*d^4)*x^3)*sqrt(-(c^2*d)^(1/3)/d)*log((2*c*d*x^3 - 3*(c^2*d)^(1/3)*c*x - c^2 + 3*sqrt(1/3)*(2*c*d*x^2 + (c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt(-(c^2*d)^(1/3)/d))/(d*x^3 + c)) + ((2*b^2*c^2*d^2 + 2*a*b*c*d^3 + 5*a^2*d^4)*x^6 + 2*b^2*c^4 + 2*a*b*c^3*d + 5*a^2*c^2*d^2 + 2*(2*b^2*c^3*d + 2*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) - 2*((2*b^2*c^2*d^2 + 2*a*b*c*d^3 + 5*a^2*d^4)*x^6 + 2*b^2*c^4 + 2*a*b*c^3*d + 5*a^2*c^2*d^2 + 2*(2*b^2*c^3*d + 2*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) + 12*(b^2*c^5*d + a*b*c^4*d^2 - 2*a^2*c^3*d^3)*x)/(c^4*d^5*x^6 + 2*c^5*d^4*x^3 + c^6*d^3), -1/54*(3*(7*b^2*c^4*d^2 - 2*a*b*c^3*d^3 - 5*a^2*c^2*d^4)*x^4 - 6*sqrt(1/3)*(2*b^2*c^5*d + 2*a*b*c^4*d^2 + 5*a^2*c^3*d^3 + (2*b^2*c^3*d^3 + 2*a*b*c^2*d^4 + 5*a^2*c*d^5)*x^6 + 2*(2*b^2*c^4*d^2 + 2*a*b*c^3*d^3 + 5*a^2*c^2*d^4)*x^3)*sqrt((c^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(c^2*d)^(2/3)*x - (c^2*d)^(1/3)*c)*sqrt((c^2*d)^(1/3)/d)/c^2) + ((2*b^2*c^2*d^2 + 2*a*b*c*d^3 + 5*a^2*d^4)*x^6 + 2*b^2*c^4 + 2*a*b*c^3*d + 5*a^2*c^2*d^2 + 2*(2*b^2*c^3*d + 2*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x^2 - (c^2*d)^(2/3)*x + (c^2*d)^(1/3)*c) - 2*((2*b^2*c^2*d^2 + 2*a*b*c*d^3 + 5*a^2*d^4)*x^6 + 2*b^2*c^4 + 2*a*b*c^3*d + 5*a^2*c^2*d^2 + 2*(2*b^2*c^3*d + 2*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^3)*(c^2*d)^(2/3)*log(c*d*x + (c^2*d)^(2/3)) + 12*(b^2*c^5*d + a*b*c^4*d^2 - 2*a^2*c^3*d^3)*x)/(c^4*d^5*x^6 + 2*c^5*d^4*x^3 + c^6*d^3)]","B",0
14,1,873,0,1.225551," ","integrate((d*x^3+c)^4/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{42 \, a^{2} b^{4} d^{4} x^{10} + 60 \, {\left(4 \, a^{2} b^{4} c d^{3} - a^{3} b^{3} d^{4}\right)} x^{7} + 105 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{4} + 210 \, \sqrt{\frac{1}{3}} {\left(a b^{5} c^{4} - 4 \, a^{2} b^{4} c^{3} d + 6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 70 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 140 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 420 \, {\left(4 \, a^{2} b^{4} c^{3} d - 6 \, a^{3} b^{3} c^{2} d^{2} + 4 \, a^{4} b^{2} c d^{3} - a^{5} b d^{4}\right)} x}{420 \, a^{2} b^{5}}, \frac{42 \, a^{2} b^{4} d^{4} x^{10} + 60 \, {\left(4 \, a^{2} b^{4} c d^{3} - a^{3} b^{3} d^{4}\right)} x^{7} + 105 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{4} + 420 \, \sqrt{\frac{1}{3}} {\left(a b^{5} c^{4} - 4 \, a^{2} b^{4} c^{3} d + 6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 70 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 140 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 420 \, {\left(4 \, a^{2} b^{4} c^{3} d - 6 \, a^{3} b^{3} c^{2} d^{2} + 4 \, a^{4} b^{2} c d^{3} - a^{5} b d^{4}\right)} x}{420 \, a^{2} b^{5}}\right]"," ",0,"[1/420*(42*a^2*b^4*d^4*x^10 + 60*(4*a^2*b^4*c*d^3 - a^3*b^3*d^4)*x^7 + 105*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^4 + 210*sqrt(1/3)*(a*b^5*c^4 - 4*a^2*b^4*c^3*d + 6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 70*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 140*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 420*(4*a^2*b^4*c^3*d - 6*a^3*b^3*c^2*d^2 + 4*a^4*b^2*c*d^3 - a^5*b*d^4)*x)/(a^2*b^5), 1/420*(42*a^2*b^4*d^4*x^10 + 60*(4*a^2*b^4*c*d^3 - a^3*b^3*d^4)*x^7 + 105*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^4 + 420*sqrt(1/3)*(a*b^5*c^4 - 4*a^2*b^4*c^3*d + 6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 70*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 140*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 420*(4*a^2*b^4*c^3*d - 6*a^3*b^3*c^2*d^2 + 4*a^4*b^2*c*d^3 - a^5*b*d^4)*x)/(a^2*b^5)]","A",0
15,1,700,0,1.023601," ","integrate((d*x^3+c)^3/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{12 \, a^{2} b^{3} d^{3} x^{7} + 21 \, {\left(3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{4} - 42 \, \sqrt{\frac{1}{3}} {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x - a^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 14 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 28 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 84 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x}{84 \, a^{2} b^{4}}, \frac{12 \, a^{2} b^{3} d^{3} x^{7} + 21 \, {\left(3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{4} + 84 \, \sqrt{\frac{1}{3}} {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 14 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 28 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 84 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x}{84 \, a^{2} b^{4}}\right]"," ",0,"[1/84*(12*a^2*b^3*d^3*x^7 + 21*(3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^4 - 42*sqrt(1/3)*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x - a^2 - 3*sqrt(1/3)*(2*a*b*x^2 + (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 + a)) - 14*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 28*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)) + 84*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)/(a^2*b^4), 1/84*(12*a^2*b^3*d^3*x^7 + 21*(3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^4 + 84*sqrt(1/3)*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) - 14*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 28*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)) + 84*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)/(a^2*b^4)]","A",0
16,1,507,0,0.795195," ","integrate((d*x^3+c)^2/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{2} d^{2} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 12 \, {\left(2 \, a^{2} b^{2} c d - a^{3} b d^{2}\right)} x}{12 \, a^{2} b^{3}}, \frac{3 \, a^{2} b^{2} d^{2} x^{4} + 12 \, \sqrt{\frac{1}{3}} {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 12 \, {\left(2 \, a^{2} b^{2} c d - a^{3} b d^{2}\right)} x}{12 \, a^{2} b^{3}}\right]"," ",0,"[1/12*(3*a^2*b^2*d^2*x^4 + 6*sqrt(1/3)*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 12*(2*a^2*b^2*c*d - a^3*b*d^2)*x)/(a^2*b^3), 1/12*(3*a^2*b^2*d^2*x^4 + 12*sqrt(1/3)*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 12*(2*a^2*b^2*c*d - a^3*b*d^2)*x)/(a^2*b^3)]","A",0
17,1,390,0,0.955248," ","integrate((d*x^3+c)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{6 \, a^{2} b d x - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c - a^{2} b d\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x - a^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - \left(-a^{2} b\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b^{2}}, \frac{6 \, a^{2} b d x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c - a^{2} b d\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - \left(-a^{2} b\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b^{2}}\right]"," ",0,"[1/6*(6*a^2*b*d*x - 3*sqrt(1/3)*(a*b^2*c - a^2*b*d)*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x - a^2 - 3*sqrt(1/3)*(2*a*b*x^2 + (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 + a)) - (-a^2*b)^(2/3)*(b*c - a*d)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 2*(-a^2*b)^(2/3)*(b*c - a*d)*log(a*b*x + (-a^2*b)^(2/3)))/(a^2*b^2), 1/6*(6*a^2*b*d*x + 6*sqrt(1/3)*(a*b^2*c - a^2*b*d)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) - (-a^2*b)^(2/3)*(b*c - a*d)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 2*(-a^2*b)^(2/3)*(b*c - a*d)*log(a*b*x + (-a^2*b)^(2/3)))/(a^2*b^2)]","A",0
18,1,254,0,1.169814," ","integrate(1/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 2 \, \sqrt{3} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} c x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) - \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} - c d x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}}\right) + 2 \, \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d x + c \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}}\right)}{6 \, {\left(b c - a d\right)}}"," ",0,"-1/6*(2*sqrt(3)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 2*sqrt(3)*(d^2/c^2)^(1/3)*arctan(1/3*(2*sqrt(3)*c*x*(d^2/c^2)^(2/3) - sqrt(3)*d)/d) - (-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) - (d^2/c^2)^(1/3)*log(d^2*x^2 - c*d*x*(d^2/c^2)^(1/3) + c^2*(d^2/c^2)^(2/3)) + 2*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) + 2*(d^2/c^2)^(1/3)*log(d*x + c*(d^2/c^2)^(1/3)))/(b*c - a*d)","A",0
19,1,432,0,18.476253," ","integrate(1/(b*x^3+a)/(d*x^3+c)^2,x, algorithm=""fricas"")","\frac{6 \, \sqrt{3} {\left(b c d x^{3} + b c^{2}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 2 \, \sqrt{3} {\left({\left(5 \, b c d - 2 \, a d^{2}\right)} x^{3} + 5 \, b c^{2} - 2 \, a c d\right)} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} c x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) - 3 \, {\left(b c d x^{3} + b c^{2}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} - a b x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + {\left({\left(5 \, b c d - 2 \, a d^{2}\right)} x^{3} + 5 \, b c^{2} - 2 \, a c d\right)} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} - c d x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}}\right) + 6 \, {\left(b c d x^{3} + b c^{2}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 2 \, {\left({\left(5 \, b c d - 2 \, a d^{2}\right)} x^{3} + 5 \, b c^{2} - 2 \, a c d\right)} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d x + c \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}}\right) - 6 \, {\left(b c d - a d^{2}\right)} x}{18 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{3}\right)}}"," ",0,"1/18*(6*sqrt(3)*(b*c*d*x^3 + b*c^2)*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(2/3) - sqrt(3)*b)/b) - 2*sqrt(3)*((5*b*c*d - 2*a*d^2)*x^3 + 5*b*c^2 - 2*a*c*d)*(d^2/c^2)^(1/3)*arctan(1/3*(2*sqrt(3)*c*x*(d^2/c^2)^(2/3) - sqrt(3)*d)/d) - 3*(b*c*d*x^3 + b*c^2)*(b^2/a^2)^(1/3)*log(b^2*x^2 - a*b*x*(b^2/a^2)^(1/3) + a^2*(b^2/a^2)^(2/3)) + ((5*b*c*d - 2*a*d^2)*x^3 + 5*b*c^2 - 2*a*c*d)*(d^2/c^2)^(1/3)*log(d^2*x^2 - c*d*x*(d^2/c^2)^(1/3) + c^2*(d^2/c^2)^(2/3)) + 6*(b*c*d*x^3 + b*c^2)*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(1/3)) - 2*((5*b*c*d - 2*a*d^2)*x^3 + 5*b*c^2 - 2*a*c*d)*(d^2/c^2)^(1/3)*log(d*x + c*(d^2/c^2)^(1/3)) - 6*(b*c*d - a*d^2)*x)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^3)","A",0
20,1,1619,0,1.113109," ","integrate((d*x^3+c)^5/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{126 \, a^{3} b^{5} d^{5} x^{13} + 18 \, {\left(50 \, a^{3} b^{5} c d^{4} - 13 \, a^{4} b^{4} d^{5}\right)} x^{10} + 45 \, {\left(70 \, a^{3} b^{5} c^{2} d^{3} - 50 \, a^{4} b^{4} c d^{4} + 13 \, a^{5} b^{3} d^{5}\right)} x^{7} + 315 \, {\left(40 \, a^{3} b^{5} c^{3} d^{2} - 70 \, a^{4} b^{4} c^{2} d^{3} + 50 \, a^{5} b^{3} c d^{4} - 13 \, a^{6} b^{2} d^{5}\right)} x^{4} + 210 \, \sqrt{\frac{1}{3}} {\left(2 \, a^{2} b^{6} c^{5} + 5 \, a^{3} b^{5} c^{4} d - 40 \, a^{4} b^{4} c^{3} d^{2} + 70 \, a^{5} b^{3} c^{2} d^{3} - 50 \, a^{6} b^{2} c d^{4} + 13 \, a^{7} b d^{5} + {\left(2 \, a b^{7} c^{5} + 5 \, a^{2} b^{6} c^{4} d - 40 \, a^{3} b^{5} c^{3} d^{2} + 70 \, a^{4} b^{4} c^{2} d^{3} - 50 \, a^{5} b^{3} c d^{4} + 13 \, a^{6} b^{2} d^{5}\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 70 \, {\left(2 \, a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d - 40 \, a^{3} b^{3} c^{3} d^{2} + 70 \, a^{4} b^{2} c^{2} d^{3} - 50 \, a^{5} b c d^{4} + 13 \, a^{6} d^{5} + {\left(2 \, b^{6} c^{5} + 5 \, a b^{5} c^{4} d - 40 \, a^{2} b^{4} c^{3} d^{2} + 70 \, a^{3} b^{3} c^{2} d^{3} - 50 \, a^{4} b^{2} c d^{4} + 13 \, a^{5} b d^{5}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 140 \, {\left(2 \, a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d - 40 \, a^{3} b^{3} c^{3} d^{2} + 70 \, a^{4} b^{2} c^{2} d^{3} - 50 \, a^{5} b c d^{4} + 13 \, a^{6} d^{5} + {\left(2 \, b^{6} c^{5} + 5 \, a b^{5} c^{4} d - 40 \, a^{2} b^{4} c^{3} d^{2} + 70 \, a^{3} b^{3} c^{2} d^{3} - 50 \, a^{4} b^{2} c d^{4} + 13 \, a^{5} b d^{5}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 420 \, {\left(a^{2} b^{6} c^{5} - 5 \, a^{3} b^{5} c^{4} d + 40 \, a^{4} b^{4} c^{3} d^{2} - 70 \, a^{5} b^{3} c^{2} d^{3} + 50 \, a^{6} b^{2} c d^{4} - 13 \, a^{7} b d^{5}\right)} x}{1260 \, {\left(a^{3} b^{7} x^{3} + a^{4} b^{6}\right)}}, \frac{126 \, a^{3} b^{5} d^{5} x^{13} + 18 \, {\left(50 \, a^{3} b^{5} c d^{4} - 13 \, a^{4} b^{4} d^{5}\right)} x^{10} + 45 \, {\left(70 \, a^{3} b^{5} c^{2} d^{3} - 50 \, a^{4} b^{4} c d^{4} + 13 \, a^{5} b^{3} d^{5}\right)} x^{7} + 315 \, {\left(40 \, a^{3} b^{5} c^{3} d^{2} - 70 \, a^{4} b^{4} c^{2} d^{3} + 50 \, a^{5} b^{3} c d^{4} - 13 \, a^{6} b^{2} d^{5}\right)} x^{4} + 420 \, \sqrt{\frac{1}{3}} {\left(2 \, a^{2} b^{6} c^{5} + 5 \, a^{3} b^{5} c^{4} d - 40 \, a^{4} b^{4} c^{3} d^{2} + 70 \, a^{5} b^{3} c^{2} d^{3} - 50 \, a^{6} b^{2} c d^{4} + 13 \, a^{7} b d^{5} + {\left(2 \, a b^{7} c^{5} + 5 \, a^{2} b^{6} c^{4} d - 40 \, a^{3} b^{5} c^{3} d^{2} + 70 \, a^{4} b^{4} c^{2} d^{3} - 50 \, a^{5} b^{3} c d^{4} + 13 \, a^{6} b^{2} d^{5}\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 70 \, {\left(2 \, a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d - 40 \, a^{3} b^{3} c^{3} d^{2} + 70 \, a^{4} b^{2} c^{2} d^{3} - 50 \, a^{5} b c d^{4} + 13 \, a^{6} d^{5} + {\left(2 \, b^{6} c^{5} + 5 \, a b^{5} c^{4} d - 40 \, a^{2} b^{4} c^{3} d^{2} + 70 \, a^{3} b^{3} c^{2} d^{3} - 50 \, a^{4} b^{2} c d^{4} + 13 \, a^{5} b d^{5}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 140 \, {\left(2 \, a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d - 40 \, a^{3} b^{3} c^{3} d^{2} + 70 \, a^{4} b^{2} c^{2} d^{3} - 50 \, a^{5} b c d^{4} + 13 \, a^{6} d^{5} + {\left(2 \, b^{6} c^{5} + 5 \, a b^{5} c^{4} d - 40 \, a^{2} b^{4} c^{3} d^{2} + 70 \, a^{3} b^{3} c^{2} d^{3} - 50 \, a^{4} b^{2} c d^{4} + 13 \, a^{5} b d^{5}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 420 \, {\left(a^{2} b^{6} c^{5} - 5 \, a^{3} b^{5} c^{4} d + 40 \, a^{4} b^{4} c^{3} d^{2} - 70 \, a^{5} b^{3} c^{2} d^{3} + 50 \, a^{6} b^{2} c d^{4} - 13 \, a^{7} b d^{5}\right)} x}{1260 \, {\left(a^{3} b^{7} x^{3} + a^{4} b^{6}\right)}}\right]"," ",0,"[1/1260*(126*a^3*b^5*d^5*x^13 + 18*(50*a^3*b^5*c*d^4 - 13*a^4*b^4*d^5)*x^10 + 45*(70*a^3*b^5*c^2*d^3 - 50*a^4*b^4*c*d^4 + 13*a^5*b^3*d^5)*x^7 + 315*(40*a^3*b^5*c^3*d^2 - 70*a^4*b^4*c^2*d^3 + 50*a^5*b^3*c*d^4 - 13*a^6*b^2*d^5)*x^4 + 210*sqrt(1/3)*(2*a^2*b^6*c^5 + 5*a^3*b^5*c^4*d - 40*a^4*b^4*c^3*d^2 + 70*a^5*b^3*c^2*d^3 - 50*a^6*b^2*c*d^4 + 13*a^7*b*d^5 + (2*a*b^7*c^5 + 5*a^2*b^6*c^4*d - 40*a^3*b^5*c^3*d^2 + 70*a^4*b^4*c^2*d^3 - 50*a^5*b^3*c*d^4 + 13*a^6*b^2*d^5)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 70*(2*a*b^5*c^5 + 5*a^2*b^4*c^4*d - 40*a^3*b^3*c^3*d^2 + 70*a^4*b^2*c^2*d^3 - 50*a^5*b*c*d^4 + 13*a^6*d^5 + (2*b^6*c^5 + 5*a*b^5*c^4*d - 40*a^2*b^4*c^3*d^2 + 70*a^3*b^3*c^2*d^3 - 50*a^4*b^2*c*d^4 + 13*a^5*b*d^5)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 140*(2*a*b^5*c^5 + 5*a^2*b^4*c^4*d - 40*a^3*b^3*c^3*d^2 + 70*a^4*b^2*c^2*d^3 - 50*a^5*b*c*d^4 + 13*a^6*d^5 + (2*b^6*c^5 + 5*a*b^5*c^4*d - 40*a^2*b^4*c^3*d^2 + 70*a^3*b^3*c^2*d^3 - 50*a^4*b^2*c*d^4 + 13*a^5*b*d^5)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 420*(a^2*b^6*c^5 - 5*a^3*b^5*c^4*d + 40*a^4*b^4*c^3*d^2 - 70*a^5*b^3*c^2*d^3 + 50*a^6*b^2*c*d^4 - 13*a^7*b*d^5)*x)/(a^3*b^7*x^3 + a^4*b^6), 1/1260*(126*a^3*b^5*d^5*x^13 + 18*(50*a^3*b^5*c*d^4 - 13*a^4*b^4*d^5)*x^10 + 45*(70*a^3*b^5*c^2*d^3 - 50*a^4*b^4*c*d^4 + 13*a^5*b^3*d^5)*x^7 + 315*(40*a^3*b^5*c^3*d^2 - 70*a^4*b^4*c^2*d^3 + 50*a^5*b^3*c*d^4 - 13*a^6*b^2*d^5)*x^4 + 420*sqrt(1/3)*(2*a^2*b^6*c^5 + 5*a^3*b^5*c^4*d - 40*a^4*b^4*c^3*d^2 + 70*a^5*b^3*c^2*d^3 - 50*a^6*b^2*c*d^4 + 13*a^7*b*d^5 + (2*a*b^7*c^5 + 5*a^2*b^6*c^4*d - 40*a^3*b^5*c^3*d^2 + 70*a^4*b^4*c^2*d^3 - 50*a^5*b^3*c*d^4 + 13*a^6*b^2*d^5)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 70*(2*a*b^5*c^5 + 5*a^2*b^4*c^4*d - 40*a^3*b^3*c^3*d^2 + 70*a^4*b^2*c^2*d^3 - 50*a^5*b*c*d^4 + 13*a^6*d^5 + (2*b^6*c^5 + 5*a*b^5*c^4*d - 40*a^2*b^4*c^3*d^2 + 70*a^3*b^3*c^2*d^3 - 50*a^4*b^2*c*d^4 + 13*a^5*b*d^5)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 140*(2*a*b^5*c^5 + 5*a^2*b^4*c^4*d - 40*a^3*b^3*c^3*d^2 + 70*a^4*b^2*c^2*d^3 - 50*a^5*b*c*d^4 + 13*a^6*d^5 + (2*b^6*c^5 + 5*a*b^5*c^4*d - 40*a^2*b^4*c^3*d^2 + 70*a^3*b^3*c^2*d^3 - 50*a^4*b^2*c*d^4 + 13*a^5*b*d^5)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 420*(a^2*b^6*c^5 - 5*a^3*b^5*c^4*d + 40*a^4*b^4*c^3*d^2 - 70*a^5*b^3*c^2*d^3 + 50*a^6*b^2*c*d^4 - 13*a^7*b*d^5)*x)/(a^3*b^7*x^3 + a^4*b^6)]","B",0
21,1,1316,0,1.063123," ","integrate((d*x^3+c)^4/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{18 \, a^{3} b^{4} d^{4} x^{10} + 9 \, {\left(14 \, a^{3} b^{4} c d^{3} - 5 \, a^{4} b^{3} d^{4}\right)} x^{7} + 63 \, {\left(12 \, a^{3} b^{4} c^{2} d^{2} - 14 \, a^{4} b^{3} c d^{3} + 5 \, a^{5} b^{2} d^{4}\right)} x^{4} - 42 \, \sqrt{\frac{1}{3}} {\left(a^{2} b^{5} c^{4} + 2 \, a^{3} b^{4} c^{3} d - 12 \, a^{4} b^{3} c^{2} d^{2} + 14 \, a^{5} b^{2} c d^{3} - 5 \, a^{6} b d^{4} + {\left(a b^{6} c^{4} + 2 \, a^{2} b^{5} c^{3} d - 12 \, a^{3} b^{4} c^{2} d^{2} + 14 \, a^{4} b^{3} c d^{3} - 5 \, a^{5} b^{2} d^{4}\right)} x^{3}\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x - a^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 14 \, {\left(a b^{4} c^{4} + 2 \, a^{2} b^{3} c^{3} d - 12 \, a^{3} b^{2} c^{2} d^{2} + 14 \, a^{4} b c d^{3} - 5 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 2 \, a b^{4} c^{3} d - 12 \, a^{2} b^{3} c^{2} d^{2} + 14 \, a^{3} b^{2} c d^{3} - 5 \, a^{4} b d^{4}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 28 \, {\left(a b^{4} c^{4} + 2 \, a^{2} b^{3} c^{3} d - 12 \, a^{3} b^{2} c^{2} d^{2} + 14 \, a^{4} b c d^{3} - 5 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 2 \, a b^{4} c^{3} d - 12 \, a^{2} b^{3} c^{2} d^{2} + 14 \, a^{3} b^{2} c d^{3} - 5 \, a^{4} b d^{4}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 42 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 24 \, a^{4} b^{3} c^{2} d^{2} - 28 \, a^{5} b^{2} c d^{3} + 10 \, a^{6} b d^{4}\right)} x}{126 \, {\left(a^{3} b^{6} x^{3} + a^{4} b^{5}\right)}}, \frac{18 \, a^{3} b^{4} d^{4} x^{10} + 9 \, {\left(14 \, a^{3} b^{4} c d^{3} - 5 \, a^{4} b^{3} d^{4}\right)} x^{7} + 63 \, {\left(12 \, a^{3} b^{4} c^{2} d^{2} - 14 \, a^{4} b^{3} c d^{3} + 5 \, a^{5} b^{2} d^{4}\right)} x^{4} + 84 \, \sqrt{\frac{1}{3}} {\left(a^{2} b^{5} c^{4} + 2 \, a^{3} b^{4} c^{3} d - 12 \, a^{4} b^{3} c^{2} d^{2} + 14 \, a^{5} b^{2} c d^{3} - 5 \, a^{6} b d^{4} + {\left(a b^{6} c^{4} + 2 \, a^{2} b^{5} c^{3} d - 12 \, a^{3} b^{4} c^{2} d^{2} + 14 \, a^{4} b^{3} c d^{3} - 5 \, a^{5} b^{2} d^{4}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 14 \, {\left(a b^{4} c^{4} + 2 \, a^{2} b^{3} c^{3} d - 12 \, a^{3} b^{2} c^{2} d^{2} + 14 \, a^{4} b c d^{3} - 5 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 2 \, a b^{4} c^{3} d - 12 \, a^{2} b^{3} c^{2} d^{2} + 14 \, a^{3} b^{2} c d^{3} - 5 \, a^{4} b d^{4}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 28 \, {\left(a b^{4} c^{4} + 2 \, a^{2} b^{3} c^{3} d - 12 \, a^{3} b^{2} c^{2} d^{2} + 14 \, a^{4} b c d^{3} - 5 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 2 \, a b^{4} c^{3} d - 12 \, a^{2} b^{3} c^{2} d^{2} + 14 \, a^{3} b^{2} c d^{3} - 5 \, a^{4} b d^{4}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 42 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 24 \, a^{4} b^{3} c^{2} d^{2} - 28 \, a^{5} b^{2} c d^{3} + 10 \, a^{6} b d^{4}\right)} x}{126 \, {\left(a^{3} b^{6} x^{3} + a^{4} b^{5}\right)}}\right]"," ",0,"[1/126*(18*a^3*b^4*d^4*x^10 + 9*(14*a^3*b^4*c*d^3 - 5*a^4*b^3*d^4)*x^7 + 63*(12*a^3*b^4*c^2*d^2 - 14*a^4*b^3*c*d^3 + 5*a^5*b^2*d^4)*x^4 - 42*sqrt(1/3)*(a^2*b^5*c^4 + 2*a^3*b^4*c^3*d - 12*a^4*b^3*c^2*d^2 + 14*a^5*b^2*c*d^3 - 5*a^6*b*d^4 + (a*b^6*c^4 + 2*a^2*b^5*c^3*d - 12*a^3*b^4*c^2*d^2 + 14*a^4*b^3*c*d^3 - 5*a^5*b^2*d^4)*x^3)*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x - a^2 - 3*sqrt(1/3)*(2*a*b*x^2 + (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 + a)) - 14*(a*b^4*c^4 + 2*a^2*b^3*c^3*d - 12*a^3*b^2*c^2*d^2 + 14*a^4*b*c*d^3 - 5*a^5*d^4 + (b^5*c^4 + 2*a*b^4*c^3*d - 12*a^2*b^3*c^2*d^2 + 14*a^3*b^2*c*d^3 - 5*a^4*b*d^4)*x^3)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 28*(a*b^4*c^4 + 2*a^2*b^3*c^3*d - 12*a^3*b^2*c^2*d^2 + 14*a^4*b*c*d^3 - 5*a^5*d^4 + (b^5*c^4 + 2*a*b^4*c^3*d - 12*a^2*b^3*c^2*d^2 + 14*a^3*b^2*c*d^3 - 5*a^4*b*d^4)*x^3)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)) + 42*(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 24*a^4*b^3*c^2*d^2 - 28*a^5*b^2*c*d^3 + 10*a^6*b*d^4)*x)/(a^3*b^6*x^3 + a^4*b^5), 1/126*(18*a^3*b^4*d^4*x^10 + 9*(14*a^3*b^4*c*d^3 - 5*a^4*b^3*d^4)*x^7 + 63*(12*a^3*b^4*c^2*d^2 - 14*a^4*b^3*c*d^3 + 5*a^5*b^2*d^4)*x^4 + 84*sqrt(1/3)*(a^2*b^5*c^4 + 2*a^3*b^4*c^3*d - 12*a^4*b^3*c^2*d^2 + 14*a^5*b^2*c*d^3 - 5*a^6*b*d^4 + (a*b^6*c^4 + 2*a^2*b^5*c^3*d - 12*a^3*b^4*c^2*d^2 + 14*a^4*b^3*c*d^3 - 5*a^5*b^2*d^4)*x^3)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) - 14*(a*b^4*c^4 + 2*a^2*b^3*c^3*d - 12*a^3*b^2*c^2*d^2 + 14*a^4*b*c*d^3 - 5*a^5*d^4 + (b^5*c^4 + 2*a*b^4*c^3*d - 12*a^2*b^3*c^2*d^2 + 14*a^3*b^2*c*d^3 - 5*a^4*b*d^4)*x^3)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 28*(a*b^4*c^4 + 2*a^2*b^3*c^3*d - 12*a^3*b^2*c^2*d^2 + 14*a^4*b*c*d^3 - 5*a^5*d^4 + (b^5*c^4 + 2*a*b^4*c^3*d - 12*a^2*b^3*c^2*d^2 + 14*a^3*b^2*c*d^3 - 5*a^4*b*d^4)*x^3)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)) + 42*(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 24*a^4*b^3*c^2*d^2 - 28*a^5*b^2*c*d^3 + 10*a^6*b*d^4)*x)/(a^3*b^6*x^3 + a^4*b^5)]","B",0
22,1,1027,0,0.925263," ","integrate((d*x^3+c)^3/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{9 \, a^{3} b^{3} d^{3} x^{7} + 9 \, {\left(12 \, a^{3} b^{3} c d^{2} - 7 \, a^{4} b^{2} d^{3}\right)} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(2 \, a^{2} b^{4} c^{3} + 3 \, a^{3} b^{3} c^{2} d - 12 \, a^{4} b^{2} c d^{2} + 7 \, a^{5} b d^{3} + {\left(2 \, a b^{5} c^{3} + 3 \, a^{2} b^{4} c^{2} d - 12 \, a^{3} b^{3} c d^{2} + 7 \, a^{4} b^{2} d^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 2 \, {\left(2 \, a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 12 \, a^{3} b c d^{2} + 7 \, a^{4} d^{3} + {\left(2 \, b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 12 \, a^{2} b^{2} c d^{2} + 7 \, a^{3} b d^{3}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 4 \, {\left(2 \, a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 12 \, a^{3} b c d^{2} + 7 \, a^{4} d^{3} + {\left(2 \, b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 12 \, a^{2} b^{2} c d^{2} + 7 \, a^{3} b d^{3}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 12 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 12 \, a^{4} b^{2} c d^{2} - 7 \, a^{5} b d^{3}\right)} x}{36 \, {\left(a^{3} b^{5} x^{3} + a^{4} b^{4}\right)}}, \frac{9 \, a^{3} b^{3} d^{3} x^{7} + 9 \, {\left(12 \, a^{3} b^{3} c d^{2} - 7 \, a^{4} b^{2} d^{3}\right)} x^{4} + 12 \, \sqrt{\frac{1}{3}} {\left(2 \, a^{2} b^{4} c^{3} + 3 \, a^{3} b^{3} c^{2} d - 12 \, a^{4} b^{2} c d^{2} + 7 \, a^{5} b d^{3} + {\left(2 \, a b^{5} c^{3} + 3 \, a^{2} b^{4} c^{2} d - 12 \, a^{3} b^{3} c d^{2} + 7 \, a^{4} b^{2} d^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 2 \, {\left(2 \, a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 12 \, a^{3} b c d^{2} + 7 \, a^{4} d^{3} + {\left(2 \, b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 12 \, a^{2} b^{2} c d^{2} + 7 \, a^{3} b d^{3}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 4 \, {\left(2 \, a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 12 \, a^{3} b c d^{2} + 7 \, a^{4} d^{3} + {\left(2 \, b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 12 \, a^{2} b^{2} c d^{2} + 7 \, a^{3} b d^{3}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 12 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 12 \, a^{4} b^{2} c d^{2} - 7 \, a^{5} b d^{3}\right)} x}{36 \, {\left(a^{3} b^{5} x^{3} + a^{4} b^{4}\right)}}\right]"," ",0,"[1/36*(9*a^3*b^3*d^3*x^7 + 9*(12*a^3*b^3*c*d^2 - 7*a^4*b^2*d^3)*x^4 + 6*sqrt(1/3)*(2*a^2*b^4*c^3 + 3*a^3*b^3*c^2*d - 12*a^4*b^2*c*d^2 + 7*a^5*b*d^3 + (2*a*b^5*c^3 + 3*a^2*b^4*c^2*d - 12*a^3*b^3*c*d^2 + 7*a^4*b^2*d^3)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 2*(2*a*b^3*c^3 + 3*a^2*b^2*c^2*d - 12*a^3*b*c*d^2 + 7*a^4*d^3 + (2*b^4*c^3 + 3*a*b^3*c^2*d - 12*a^2*b^2*c*d^2 + 7*a^3*b*d^3)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 4*(2*a*b^3*c^3 + 3*a^2*b^2*c^2*d - 12*a^3*b*c*d^2 + 7*a^4*d^3 + (2*b^4*c^3 + 3*a*b^3*c^2*d - 12*a^2*b^2*c*d^2 + 7*a^3*b*d^3)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 12*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 12*a^4*b^2*c*d^2 - 7*a^5*b*d^3)*x)/(a^3*b^5*x^3 + a^4*b^4), 1/36*(9*a^3*b^3*d^3*x^7 + 9*(12*a^3*b^3*c*d^2 - 7*a^4*b^2*d^3)*x^4 + 12*sqrt(1/3)*(2*a^2*b^4*c^3 + 3*a^3*b^3*c^2*d - 12*a^4*b^2*c*d^2 + 7*a^5*b*d^3 + (2*a*b^5*c^3 + 3*a^2*b^4*c^2*d - 12*a^3*b^3*c*d^2 + 7*a^4*b^2*d^3)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 2*(2*a*b^3*c^3 + 3*a^2*b^2*c^2*d - 12*a^3*b*c*d^2 + 7*a^4*d^3 + (2*b^4*c^3 + 3*a*b^3*c^2*d - 12*a^2*b^2*c*d^2 + 7*a^3*b*d^3)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 4*(2*a*b^3*c^3 + 3*a^2*b^2*c^2*d - 12*a^3*b*c*d^2 + 7*a^4*d^3 + (2*b^4*c^3 + 3*a*b^3*c^2*d - 12*a^2*b^2*c*d^2 + 7*a^3*b*d^3)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 12*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 12*a^4*b^2*c*d^2 - 7*a^5*b*d^3)*x)/(a^3*b^5*x^3 + a^4*b^4)]","B",0
23,1,768,0,0.982795," ","integrate((d*x^3+c)^2/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{9 \, a^{3} b^{2} d^{2} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(a^{2} b^{3} c^{2} + a^{3} b^{2} c d - 2 \, a^{4} b d^{2} + {\left(a b^{4} c^{2} + a^{2} b^{3} c d - 2 \, a^{3} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x - a^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - {\left(a b^{2} c^{2} + a^{2} b c d - 2 \, a^{3} d^{2} + {\left(b^{3} c^{2} + a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(a b^{2} c^{2} + a^{2} b c d - 2 \, a^{3} d^{2} + {\left(b^{3} c^{2} + a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 3 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + 4 \, a^{4} b d^{2}\right)} x}{9 \, {\left(a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}, \frac{9 \, a^{3} b^{2} d^{2} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(a^{2} b^{3} c^{2} + a^{3} b^{2} c d - 2 \, a^{4} b d^{2} + {\left(a b^{4} c^{2} + a^{2} b^{3} c d - 2 \, a^{3} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(a b^{2} c^{2} + a^{2} b c d - 2 \, a^{3} d^{2} + {\left(b^{3} c^{2} + a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(a b^{2} c^{2} + a^{2} b c d - 2 \, a^{3} d^{2} + {\left(b^{3} c^{2} + a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 3 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + 4 \, a^{4} b d^{2}\right)} x}{9 \, {\left(a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}\right]"," ",0,"[1/9*(9*a^3*b^2*d^2*x^4 - 3*sqrt(1/3)*(a^2*b^3*c^2 + a^3*b^2*c*d - 2*a^4*b*d^2 + (a*b^4*c^2 + a^2*b^3*c*d - 2*a^3*b^2*d^2)*x^3)*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x - a^2 - 3*sqrt(1/3)*(2*a*b*x^2 + (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 + a)) - (a*b^2*c^2 + a^2*b*c*d - 2*a^3*d^2 + (b^3*c^2 + a*b^2*c*d - 2*a^2*b*d^2)*x^3)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 2*(a*b^2*c^2 + a^2*b*c*d - 2*a^3*d^2 + (b^3*c^2 + a*b^2*c*d - 2*a^2*b*d^2)*x^3)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)) + 3*(a^2*b^3*c^2 - 2*a^3*b^2*c*d + 4*a^4*b*d^2)*x)/(a^3*b^4*x^3 + a^4*b^3), 1/9*(9*a^3*b^2*d^2*x^4 + 6*sqrt(1/3)*(a^2*b^3*c^2 + a^3*b^2*c*d - 2*a^4*b*d^2 + (a*b^4*c^2 + a^2*b^3*c*d - 2*a^3*b^2*d^2)*x^3)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) - (a*b^2*c^2 + a^2*b*c*d - 2*a^3*d^2 + (b^3*c^2 + a*b^2*c*d - 2*a^2*b*d^2)*x^3)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 2*(a*b^2*c^2 + a^2*b*c*d - 2*a^3*d^2 + (b^3*c^2 + a*b^2*c*d - 2*a^2*b*d^2)*x^3)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)) + 3*(a^2*b^3*c^2 - 2*a^3*b^2*c*d + 4*a^4*b*d^2)*x)/(a^3*b^4*x^3 + a^4*b^3)]","B",0
24,1,537,0,0.949342," ","integrate((d*x^3+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(2 \, a^{2} b^{2} c + a^{3} b d + {\left(2 \, a b^{3} c + a^{2} b^{2} d\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - {\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 6 \, {\left(a^{2} b^{2} c - a^{3} b d\right)} x}{18 \, {\left(a^{3} b^{3} x^{3} + a^{4} b^{2}\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(2 \, a^{2} b^{2} c + a^{3} b d + {\left(2 \, a b^{3} c + a^{2} b^{2} d\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 6 \, {\left(a^{2} b^{2} c - a^{3} b d\right)} x}{18 \, {\left(a^{3} b^{3} x^{3} + a^{4} b^{2}\right)}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(2*a^2*b^2*c + a^3*b*d + (2*a*b^3*c + a^2*b^2*d)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - ((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 6*(a^2*b^2*c - a^3*b*d)*x)/(a^3*b^3*x^3 + a^4*b^2), 1/18*(6*sqrt(1/3)*(2*a^2*b^2*c + a^3*b*d + (2*a*b^3*c + a^2*b^2*d)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - ((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 6*(a^2*b^2*c - a^3*b*d)*x)/(a^3*b^3*x^3 + a^4*b^2)]","A",0
25,1,440,0,18.527727," ","integrate(1/(b*x^3+a)^2/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left({\left(2 \, b^{2} c - 5 \, a b d\right)} x^{3} + 2 \, a b c - 5 \, a^{2} d\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 6 \, \sqrt{3} {\left(a b d x^{3} + a^{2} d\right)} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} c x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) - {\left({\left(2 \, b^{2} c - 5 \, a b d\right)} x^{3} + 2 \, a b c - 5 \, a^{2} d\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 3 \, {\left(a b d x^{3} + a^{2} d\right)} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} - c d x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(2 \, b^{2} c - 5 \, a b d\right)} x^{3} + 2 \, a b c - 5 \, a^{2} d\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 6 \, {\left(a b d x^{3} + a^{2} d\right)} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d x + c \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}}\right) - 6 \, {\left(b^{2} c - a b d\right)} x}{18 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{3}\right)}}"," ",0,"-1/18*(2*sqrt(3)*((2*b^2*c - 5*a*b*d)*x^3 + 2*a*b*c - 5*a^2*d)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) - 6*sqrt(3)*(a*b*d*x^3 + a^2*d)*(d^2/c^2)^(1/3)*arctan(1/3*(2*sqrt(3)*c*x*(d^2/c^2)^(2/3) - sqrt(3)*d)/d) - ((2*b^2*c - 5*a*b*d)*x^3 + 2*a*b*c - 5*a^2*d)*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) + 3*(a*b*d*x^3 + a^2*d)*(d^2/c^2)^(1/3)*log(d^2*x^2 - c*d*x*(d^2/c^2)^(1/3) + c^2*(d^2/c^2)^(2/3)) + 2*((2*b^2*c - 5*a*b*d)*x^3 + 2*a*b*c - 5*a^2*d)*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) - 6*(a*b*d*x^3 + a^2*d)*(d^2/c^2)^(1/3)*log(d*x + c*(d^2/c^2)^(1/3)) - 6*(b^2*c - a*b*d)*x)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^3)","A",0
26,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^2/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,1,399,0,1.063682," ","integrate((-b*x^3+a)*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\left[\frac{21 \, \sqrt{\frac{1}{3}} a^{2} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 14 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 7 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(3 \, b^{2} x^{4} - 4 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b}, -\frac{42 \, \sqrt{\frac{1}{3}} a^{2} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 14 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 7 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(3 \, b^{2} x^{4} - 4 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b}\right]"," ",0,"[1/54*(21*sqrt(1/3)*a^2*b*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 14*a^2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + 7*a^2*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(3*b^2*x^4 - 4*a*b*x)*(b*x^3 + a)^(2/3))/b, -1/54*(42*sqrt(1/3)*a^2*b*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 14*a^2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - 7*a^2*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(3*b^2*x^4 - 4*a*b*x)*(b*x^3 + a)^(2/3))/b]","B",0
28,1,363,0,1.017423," ","integrate((-b*x^3+a)/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x - 4 \, a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 2 \, a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{9 \, b}, -\frac{12 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x + 4 \, a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 2 \, a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{9 \, b}\right]"," ",0,"[1/9*(6*sqrt(1/3)*a*b*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 3*(b*x^3 + a)^(2/3)*b*x - 4*a*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + 2*a*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b, -1/9*(12*sqrt(1/3)*a*b*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 3*(b*x^3 + a)^(2/3)*b*x + 4*a*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - 2*a*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b]","B",0
29,1,372,0,0.791892," ","integrate((-b*x^3+a)/(b*x^3+a)^(4/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(b^{2} x^{3} + a b\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 12 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x + 2 \, {\left(b x^{3} + a\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(b x^{3} + a\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, {\left(b^{2} x^{3} + a b\right)}}, \frac{12 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x + 2 \, {\left(b x^{3} + a\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(b x^{3} + a\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{6 \, \sqrt{\frac{1}{3}} {\left(b^{2} x^{3} + a b\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}}}{6 \, {\left(b^{2} x^{3} + a b\right)}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(b^2*x^3 + a*b)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 12*(b*x^3 + a)^(2/3)*b*x + 2*(b*x^3 + a)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (b*x^3 + a)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b^2*x^3 + a*b), 1/6*(12*(b*x^3 + a)^(2/3)*b*x + 2*(b*x^3 + a)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (b*x^3 + a)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 6*sqrt(1/3)*(b^2*x^3 + a*b)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3))/(b^2*x^3 + a*b)]","B",0
30,1,44,0,1.055728," ","integrate((-b*x^3+a)/(b*x^3+a)^(7/3),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + 2 \, a x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{2 \, {\left(a b^{2} x^{6} + 2 \, a^{2} b x^{3} + a^{3}\right)}}"," ",0,"1/2*(b*x^4 + 2*a*x)*(b*x^3 + a)^(2/3)/(a*b^2*x^6 + 2*a^2*b*x^3 + a^3)","A",0
31,1,69,0,0.669438," ","integrate((-b*x^3+a)/(b*x^3+a)^(10/3),x, algorithm=""fricas"")","\frac{{\left(15 \, b^{2} x^{7} + 35 \, a b x^{4} + 28 \, a^{2} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{28 \, {\left(a^{2} b^{3} x^{9} + 3 \, a^{3} b^{2} x^{6} + 3 \, a^{4} b x^{3} + a^{5}\right)}}"," ",0,"1/28*(15*b^2*x^7 + 35*a*b*x^4 + 28*a^2*x)*(b*x^3 + a)^(2/3)/(a^2*b^3*x^9 + 3*a^3*b^2*x^6 + 3*a^4*b*x^3 + a^5)","A",0
32,1,91,0,1.015428," ","integrate((-b*x^3+a)/(b*x^3+a)^(13/3),x, algorithm=""fricas"")","\frac{{\left(18 \, b^{3} x^{10} + 60 \, a b^{2} x^{7} + 70 \, a^{2} b x^{4} + 35 \, a^{3} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{35 \, {\left(a^{3} b^{4} x^{12} + 4 \, a^{4} b^{3} x^{9} + 6 \, a^{5} b^{2} x^{6} + 4 \, a^{6} b x^{3} + a^{7}\right)}}"," ",0,"1/35*(18*b^3*x^10 + 60*a*b^2*x^7 + 70*a^2*b*x^4 + 35*a^3*x)*(b*x^3 + a)^(2/3)/(a^3*b^4*x^12 + 4*a^4*b^3*x^9 + 6*a^5*b^2*x^6 + 4*a^6*b*x^3 + a^7)","A",0
33,1,113,0,0.969975," ","integrate((-b*x^3+a)/(b*x^3+a)^(16/3),x, algorithm=""fricas"")","\frac{{\left(891 \, b^{4} x^{13} + 3861 \, a b^{3} x^{10} + 6435 \, a^{2} b^{2} x^{7} + 5005 \, a^{3} b x^{4} + 1820 \, a^{4} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{1820 \, {\left(a^{4} b^{5} x^{15} + 5 \, a^{5} b^{4} x^{12} + 10 \, a^{6} b^{3} x^{9} + 10 \, a^{7} b^{2} x^{6} + 5 \, a^{8} b x^{3} + a^{9}\right)}}"," ",0,"1/1820*(891*b^4*x^13 + 3861*a*b^3*x^10 + 6435*a^2*b^2*x^7 + 5005*a^3*b*x^4 + 1820*a^4*x)*(b*x^3 + a)^(2/3)/(a^4*b^5*x^15 + 5*a^5*b^4*x^12 + 10*a^6*b^3*x^9 + 10*a^7*b^2*x^6 + 5*a^8*b*x^3 + a^9)","A",0
34,-1,0,0,0.000000," ","integrate((b*x^3+a)^(7/3)/(-b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,0,0,0,67.914263," ","integrate((b*x^3+a)^(4/3)/(-b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{b x^{3} - a}, x\right)"," ",0,"integral(-(b*x^3 + a)^(4/3)/(b*x^3 - a), x)","F",0
36,1,644,0,54.974626," ","integrate((b*x^3+a)^(1/3)/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{1}{18} \, \sqrt{3} 2^{\frac{1}{3}} \left(-\frac{1}{a b}\right)^{\frac{1}{3}} \arctan\left(\frac{6 \, \sqrt{3} 2^{\frac{2}{3}} {\left(a b^{6} x^{16} + 33 \, a^{2} b^{5} x^{13} + 110 \, a^{3} b^{4} x^{10} + 110 \, a^{4} b^{3} x^{7} + 33 \, a^{5} b^{2} x^{4} + a^{6} b x\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a b}\right)^{\frac{2}{3}} + 24 \, \sqrt{3} 2^{\frac{1}{3}} {\left(a b^{5} x^{14} + 2 \, a^{2} b^{4} x^{11} - 6 \, a^{3} b^{3} x^{8} + 2 \, a^{4} b^{2} x^{5} + a^{5} b x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-\frac{1}{a b}\right)^{\frac{1}{3}} - \sqrt{3} {\left(b^{6} x^{18} - 42 \, a b^{5} x^{15} - 417 \, a^{2} b^{4} x^{12} - 812 \, a^{3} b^{3} x^{9} - 417 \, a^{4} b^{2} x^{6} - 42 \, a^{5} b x^{3} + a^{6}\right)}}{3 \, {\left(b^{6} x^{18} + 102 \, a b^{5} x^{15} + 447 \, a^{2} b^{4} x^{12} + 628 \, a^{3} b^{3} x^{9} + 447 \, a^{4} b^{2} x^{6} + 102 \, a^{5} b x^{3} + a^{6}\right)}}\right) - \frac{1}{36} \cdot 2^{\frac{1}{3}} \left(-\frac{1}{a b}\right)^{\frac{1}{3}} \log\left(\frac{12 \cdot 2^{\frac{2}{3}} {\left(a b^{3} x^{8} + 4 \, a^{2} b^{2} x^{5} + a^{3} b x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-\frac{1}{a b}\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b^{4} x^{12} + 32 \, a b^{3} x^{9} + 78 \, a^{2} b^{2} x^{6} + 32 \, a^{3} b x^{3} + a^{4}\right)} \left(-\frac{1}{a b}\right)^{\frac{1}{3}} + 6 \, {\left(b^{3} x^{10} + 11 \, a b^{2} x^{7} + 11 \, a^{2} b x^{4} + a^{3} x\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{4} x^{12} - 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} - 4 \, a^{3} b x^{3} + a^{4}}\right) + \frac{1}{18} \cdot 2^{\frac{1}{3}} \left(-\frac{1}{a b}\right)^{\frac{1}{3}} \log\left(-\frac{12 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{2} + 2^{\frac{2}{3}} {\left(b^{2} x^{6} - 2 \, a b x^{3} + a^{2}\right)} \left(-\frac{1}{a b}\right)^{\frac{2}{3}} + 6 \cdot 2^{\frac{1}{3}} {\left(b x^{4} + a x\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a b}\right)^{\frac{1}{3}}}{b^{2} x^{6} - 2 \, a b x^{3} + a^{2}}\right)"," ",0,"-1/18*sqrt(3)*2^(1/3)*(-1/(a*b))^(1/3)*arctan(1/3*(6*sqrt(3)*2^(2/3)*(a*b^6*x^16 + 33*a^2*b^5*x^13 + 110*a^3*b^4*x^10 + 110*a^4*b^3*x^7 + 33*a^5*b^2*x^4 + a^6*b*x)*(b*x^3 + a)^(1/3)*(-1/(a*b))^(2/3) + 24*sqrt(3)*2^(1/3)*(a*b^5*x^14 + 2*a^2*b^4*x^11 - 6*a^3*b^3*x^8 + 2*a^4*b^2*x^5 + a^5*b*x^2)*(b*x^3 + a)^(2/3)*(-1/(a*b))^(1/3) - sqrt(3)*(b^6*x^18 - 42*a*b^5*x^15 - 417*a^2*b^4*x^12 - 812*a^3*b^3*x^9 - 417*a^4*b^2*x^6 - 42*a^5*b*x^3 + a^6))/(b^6*x^18 + 102*a*b^5*x^15 + 447*a^2*b^4*x^12 + 628*a^3*b^3*x^9 + 447*a^4*b^2*x^6 + 102*a^5*b*x^3 + a^6)) - 1/36*2^(1/3)*(-1/(a*b))^(1/3)*log((12*2^(2/3)*(a*b^3*x^8 + 4*a^2*b^2*x^5 + a^3*b*x^2)*(b*x^3 + a)^(2/3)*(-1/(a*b))^(2/3) - 2^(1/3)*(b^4*x^12 + 32*a*b^3*x^9 + 78*a^2*b^2*x^6 + 32*a^3*b*x^3 + a^4)*(-1/(a*b))^(1/3) + 6*(b^3*x^10 + 11*a*b^2*x^7 + 11*a^2*b*x^4 + a^3*x)*(b*x^3 + a)^(1/3))/(b^4*x^12 - 4*a*b^3*x^9 + 6*a^2*b^2*x^6 - 4*a^3*b*x^3 + a^4)) + 1/18*2^(1/3)*(-1/(a*b))^(1/3)*log(-(12*(b*x^3 + a)^(2/3)*x^2 + 2^(2/3)*(b^2*x^6 - 2*a*b*x^3 + a^2)*(-1/(a*b))^(2/3) + 6*2^(1/3)*(b*x^4 + a*x)*(b*x^3 + a)^(1/3)*(-1/(a*b))^(1/3))/(b^2*x^6 - 2*a*b*x^3 + a^2))","B",0
37,-1,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(8/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,1,421,0,1.253352," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\left[\frac{114 \, \sqrt{\frac{1}{3}} a^{3} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 76 \, a^{3} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 38 \, a^{3} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(9 \, b^{3} x^{7} - 24 \, a b^{2} x^{4} + 5 \, a^{2} b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{243 \, b}, -\frac{228 \, \sqrt{\frac{1}{3}} a^{3} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 76 \, a^{3} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 38 \, a^{3} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(9 \, b^{3} x^{7} - 24 \, a b^{2} x^{4} + 5 \, a^{2} b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{243 \, b}\right]"," ",0,"[1/243*(114*sqrt(1/3)*a^3*b*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 76*a^3*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + 38*a^3*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(9*b^3*x^7 - 24*a*b^2*x^4 + 5*a^2*b*x)*(b*x^3 + a)^(2/3))/b, -1/243*(228*sqrt(1/3)*a^3*b*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 76*a^3*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - 38*a^3*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(9*b^3*x^7 - 24*a*b^2*x^4 + 5*a^2*b*x)*(b*x^3 + a)^(2/3))/b]","A",0
41,1,399,0,1.655356," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{51 \, \sqrt{\frac{1}{3}} a^{2} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 34 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 17 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(3 \, b^{2} x^{4} - 16 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b}, -\frac{102 \, \sqrt{\frac{1}{3}} a^{2} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 34 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 17 \, a^{2} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(3 \, b^{2} x^{4} - 16 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b}\right]"," ",0,"[1/54*(51*sqrt(1/3)*a^2*b*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 34*a^2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + 17*a^2*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(3*b^2*x^4 - 16*a*b*x)*(b*x^3 + a)^(2/3))/b, -1/54*(102*sqrt(1/3)*a^2*b*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 34*a^2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - 17*a^2*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(3*b^2*x^4 - 16*a*b*x)*(b*x^3 + a)^(2/3))/b]","A",0
42,1,412,0,1.728831," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(4/3),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 10 \, {\left(a b x^{3} + a^{2}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 5 \, {\left(a b x^{3} + a^{2}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(b^{2} x^{4} + 13 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{9 \, {\left(b^{2} x^{3} + a b\right)}}, \frac{10 \, {\left(a b x^{3} + a^{2}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 5 \, {\left(a b x^{3} + a^{2}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{30 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}} + 3 \, {\left(b^{2} x^{4} + 13 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{9 \, {\left(b^{2} x^{3} + a b\right)}}\right]"," ",0,"[1/9*(15*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 10*(a*b*x^3 + a^2)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - 5*(a*b*x^3 + a^2)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(b^2*x^4 + 13*a*b*x)*(b*x^3 + a)^(2/3))/(b^2*x^3 + a*b), 1/9*(10*(a*b*x^3 + a^2)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - 5*(a*b*x^3 + a^2)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 30*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3) + 3*(b^2*x^4 + 13*a*b*x)*(b*x^3 + a)^(2/3))/(b^2*x^3 + a*b)]","B",0
43,1,521,0,1.164826," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(7/3),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{2} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}}, -\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{2} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}}\right]"," ",0,"[-1/6*(6*(b*x^3 + a)^(2/3)*b^2*x^4 - 3*sqrt(1/3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (b^2*x^6 + 2*a*b*x^3 + a^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b^3*x^6 + 2*a*b^2*x^3 + a^2*b), -1/6*(6*(b*x^3 + a)^(2/3)*b^2*x^4 + 6*sqrt(1/3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (b^2*x^6 + 2*a*b*x^3 + a^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)]","B",0
44,1,67,0,0.890015," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(10/3),x, algorithm=""fricas"")","\frac{{\left(4 \, b^{2} x^{7} + 7 \, a b x^{4} + 7 \, a^{2} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{7 \, {\left(a b^{3} x^{9} + 3 \, a^{2} b^{2} x^{6} + 3 \, a^{3} b x^{3} + a^{4}\right)}}"," ",0,"1/7*(4*b^2*x^7 + 7*a*b*x^4 + 7*a^2*x)*(b*x^3 + a)^(2/3)/(a*b^3*x^9 + 3*a^2*b^2*x^6 + 3*a^3*b*x^3 + a^4)","A",0
45,1,91,0,1.077592," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(13/3),x, algorithm=""fricas"")","\frac{{\left(69 \, b^{3} x^{10} + 230 \, a b^{2} x^{7} + 245 \, a^{2} b x^{4} + 140 \, a^{3} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{140 \, {\left(a^{2} b^{4} x^{12} + 4 \, a^{3} b^{3} x^{9} + 6 \, a^{4} b^{2} x^{6} + 4 \, a^{5} b x^{3} + a^{6}\right)}}"," ",0,"1/140*(69*b^3*x^10 + 230*a*b^2*x^7 + 245*a^2*b*x^4 + 140*a^3*x)*(b*x^3 + a)^(2/3)/(a^2*b^4*x^12 + 4*a^3*b^3*x^9 + 6*a^4*b^2*x^6 + 4*a^5*b*x^3 + a^6)","A",0
46,1,113,0,1.248945," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(16/3),x, algorithm=""fricas"")","\frac{{\left(423 \, b^{4} x^{13} + 1833 \, a b^{3} x^{10} + 3055 \, a^{2} b^{2} x^{7} + 2275 \, a^{3} b x^{4} + 910 \, a^{4} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{910 \, {\left(a^{3} b^{5} x^{15} + 5 \, a^{4} b^{4} x^{12} + 10 \, a^{5} b^{3} x^{9} + 10 \, a^{6} b^{2} x^{6} + 5 \, a^{7} b x^{3} + a^{8}\right)}}"," ",0,"1/910*(423*b^4*x^13 + 1833*a*b^3*x^10 + 3055*a^2*b^2*x^7 + 2275*a^3*b*x^4 + 910*a^4*x)*(b*x^3 + a)^(2/3)/(a^3*b^5*x^15 + 5*a^4*b^4*x^12 + 10*a^5*b^3*x^9 + 10*a^6*b^2*x^6 + 5*a^7*b*x^3 + a^8)","A",0
47,1,135,0,0.804322," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(19/3),x, algorithm=""fricas"")","\frac{{\left(162 \, b^{5} x^{16} + 864 \, a b^{4} x^{13} + 1872 \, a^{2} b^{3} x^{10} + 2080 \, a^{3} b^{2} x^{7} + 1183 \, a^{4} b x^{4} + 364 \, a^{5} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{364 \, {\left(a^{4} b^{6} x^{18} + 6 \, a^{5} b^{5} x^{15} + 15 \, a^{6} b^{4} x^{12} + 20 \, a^{7} b^{3} x^{9} + 15 \, a^{8} b^{2} x^{6} + 6 \, a^{9} b x^{3} + a^{10}\right)}}"," ",0,"1/364*(162*b^5*x^16 + 864*a*b^4*x^13 + 1872*a^2*b^3*x^10 + 2080*a^3*b^2*x^7 + 1183*a^4*b*x^4 + 364*a^5*x)*(b*x^3 + a)^(2/3)/(a^4*b^6*x^18 + 6*a^5*b^5*x^15 + 15*a^6*b^4*x^12 + 20*a^7*b^3*x^9 + 15*a^8*b^2*x^6 + 6*a^9*b*x^3 + a^10)","A",0
48,0,0,0,1.069793," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} x^{9} - a b^{2} x^{6} - a^{2} b x^{3} + a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b^3*x^9 - a*b^2*x^6 - a^2*b*x^3 + a^3)*(b*x^3 + a)^(1/3), x)","F",0
49,0,0,0,1.224223," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{6} - 2 \, a b x^{3} + a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b^2*x^6 - 2*a*b*x^3 + a^2)*(b*x^3 + a)^(1/3), x)","F",0
50,0,0,0,1.316873," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{6} - 2 \, a b x^{3} + a^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((b^2*x^6 - 2*a*b*x^3 + a^2)/(b*x^3 + a)^(2/3), x)","F",0
51,0,0,0,1.137104," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} - 2 \, a b x^{3} + a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((b^2*x^6 - 2*a*b*x^3 + a^2)*(b*x^3 + a)^(1/3)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
52,0,0,0,1.378668," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(8/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} - 2 \, a b x^{3} + a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((b^2*x^6 - 2*a*b*x^3 + a^2)*(b*x^3 + a)^(1/3)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
53,0,0,0,1.637748," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(11/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} - 2 \, a b x^{3} + a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}}, x\right)"," ",0,"integral((b^2*x^6 - 2*a*b*x^3 + a^2)*(b*x^3 + a)^(1/3)/(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4), x)","F",0
54,0,0,0,1.326993," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(14/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} - 2 \, a b x^{3} + a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{5} x^{15} + 5 \, a b^{4} x^{12} + 10 \, a^{2} b^{3} x^{9} + 10 \, a^{3} b^{2} x^{6} + 5 \, a^{4} b x^{3} + a^{5}}, x\right)"," ",0,"integral((b^2*x^6 - 2*a*b*x^3 + a^2)*(b*x^3 + a)^(1/3)/(b^5*x^15 + 5*a*b^4*x^12 + 10*a^2*b^3*x^9 + 10*a^3*b^2*x^6 + 5*a^4*b*x^3 + a^5), x)","F",0
55,0,0,0,1.299447," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(17/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} - 2 \, a b x^{3} + a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{6} x^{18} + 6 \, a b^{5} x^{15} + 15 \, a^{2} b^{4} x^{12} + 20 \, a^{3} b^{3} x^{9} + 15 \, a^{4} b^{2} x^{6} + 6 \, a^{5} b x^{3} + a^{6}}, x\right)"," ",0,"integral((b^2*x^6 - 2*a*b*x^3 + a^2)*(b*x^3 + a)^(1/3)/(b^6*x^18 + 6*a*b^5*x^15 + 15*a^2*b^4*x^12 + 20*a^3*b^3*x^9 + 15*a^4*b^2*x^6 + 6*a^5*b*x^3 + a^6), x)","F",0
56,1,482,0,1.210499," ","integrate((b*x^3+a)^(5/3)*(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{\frac{1}{3}} {\left(9 \, a^{2} b^{2} c - a^{3} b d\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 10 \, {\left(9 \, a^{2} b c - a^{3} d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 5 \, {\left(9 \, a^{2} b c - a^{3} d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(18 \, b^{3} d x^{7} + 3 \, {\left(9 \, b^{3} c + 11 \, a b^{2} d\right)} x^{4} + 2 \, {\left(36 \, a b^{2} c + 5 \, a^{2} b d\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{486 \, b^{2}}, -\frac{10 \, {\left(9 \, a^{2} b c - a^{3} d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 5 \, {\left(9 \, a^{2} b c - a^{3} d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{30 \, \sqrt{\frac{1}{3}} {\left(9 \, a^{2} b^{2} c - a^{3} b d\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}} - 3 \, {\left(18 \, b^{3} d x^{7} + 3 \, {\left(9 \, b^{3} c + 11 \, a b^{2} d\right)} x^{4} + 2 \, {\left(36 \, a b^{2} c + 5 \, a^{2} b d\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{486 \, b^{2}}\right]"," ",0,"[-1/486*(15*sqrt(1/3)*(9*a^2*b^2*c - a^3*b*d)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 10*(9*a^2*b*c - a^3*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - 5*(9*a^2*b*c - a^3*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(18*b^3*d*x^7 + 3*(9*b^3*c + 11*a*b^2*d)*x^4 + 2*(36*a*b^2*c + 5*a^2*b*d)*x)*(b*x^3 + a)^(2/3))/b^2, -1/486*(10*(9*a^2*b*c - a^3*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - 5*(9*a^2*b*c - a^3*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 30*sqrt(1/3)*(9*a^2*b^2*c - a^3*b*d)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3) - 3*(18*b^3*d*x^7 + 3*(9*b^3*c + 11*a*b^2*d)*x^4 + 2*(36*a*b^2*c + 5*a^2*b*d)*x)*(b*x^3 + a)^(2/3))/b^2]","A",0
57,1,424,0,1.095206," ","integrate((b*x^3+a)^(2/3)*(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(6 \, a b^{2} c - a^{2} b d\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 2 \, {\left(6 \, a b c - a^{2} d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(6 \, a b c - a^{2} d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(3 \, b^{2} d x^{4} + 2 \, {\left(3 \, b^{2} c + a b d\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{2}}, -\frac{2 \, {\left(6 \, a b c - a^{2} d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(6 \, a b c - a^{2} d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{6 \, \sqrt{\frac{1}{3}} {\left(6 \, a b^{2} c - a^{2} b d\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}} - 3 \, {\left(3 \, b^{2} d x^{4} + 2 \, {\left(3 \, b^{2} c + a b d\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{2}}\right]"," ",0,"[-1/54*(3*sqrt(1/3)*(6*a*b^2*c - a^2*b*d)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 2*(6*a*b*c - a^2*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (6*a*b*c - a^2*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(3*b^2*d*x^4 + 2*(3*b^2*c + a*b*d)*x)*(b*x^3 + a)^(2/3))/b^2, -1/54*(2*(6*a*b*c - a^2*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (6*a*b*c - a^2*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 6*sqrt(1/3)*(6*a*b^2*c - a^2*b*d)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3) - 3*(3*b^2*d*x^4 + 2*(3*b^2*c + a*b*d)*x)*(b*x^3 + a)^(2/3))/b^2]","A",0
58,1,362,0,1.308378," ","integrate((d*x^3+c)/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b d x - 3 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} c - a b d\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) - 2 \, {\left(3 \, b c - a d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(3 \, b c - a d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{18 \, b^{2}}, \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b d x - 2 \, {\left(3 \, b c - a d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(3 \, b c - a d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - \frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} c - a b d\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}}}{18 \, b^{2}}\right]"," ",0,"[1/18*(6*(b*x^3 + a)^(2/3)*b*d*x - 3*sqrt(1/3)*(3*b^2*c - a*b*d)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) - 2*(3*b*c - a*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + (3*b*c - a*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b^2, 1/18*(6*(b*x^3 + a)^(2/3)*b*d*x - 2*(3*b*c - a*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + (3*b*c - a*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 6*sqrt(1/3)*(3*b^2*c - a*b*d)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3))/b^2]","A",0
59,1,488,0,1.058728," ","integrate((d*x^3+c)/(b*x^3+a)^(4/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d x^{3} + a^{2} b d\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b^{2} c - a b d\right)} x - 2 \, {\left(a b d x^{3} + a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(a b d x^{3} + a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, {\left(a b^{3} x^{3} + a^{2} b^{2}\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d x^{3} + a^{2} b d\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b^{2} c - a b d\right)} x + 2 \, {\left(a b d x^{3} + a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(a b d x^{3} + a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, {\left(a b^{3} x^{3} + a^{2} b^{2}\right)}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(a*b^2*d*x^3 + a^2*b*d)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) + 6*(b*x^3 + a)^(2/3)*(b^2*c - a*b*d)*x - 2*(a*b*d*x^3 + a^2*d)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + (a*b*d*x^3 + a^2*d)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(a*b^3*x^3 + a^2*b^2), -1/6*(6*sqrt(1/3)*(a*b^2*d*x^3 + a^2*b*d)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) - 6*(b*x^3 + a)^(2/3)*(b^2*c - a*b*d)*x + 2*(a*b*d*x^3 + a^2*d)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (a*b*d*x^3 + a^2*d)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(a*b^3*x^3 + a^2*b^2)]","B",0
60,1,54,0,1.231194," ","integrate((d*x^3+c)/(b*x^3+a)^(7/3),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, b c + a d\right)} x^{4} + 4 \, a c x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{4 \, {\left(a^{2} b^{2} x^{6} + 2 \, a^{3} b x^{3} + a^{4}\right)}}"," ",0,"1/4*((3*b*c + a*d)*x^4 + 4*a*c*x)*(b*x^3 + a)^(2/3)/(a^2*b^2*x^6 + 2*a^3*b*x^3 + a^4)","A",0
61,1,87,0,0.718899," ","integrate((d*x^3+c)/(b*x^3+a)^(10/3),x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(6 \, b^{2} c + a b d\right)} x^{7} + 7 \, {\left(6 \, a b c + a^{2} d\right)} x^{4} + 28 \, a^{2} c x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{28 \, {\left(a^{3} b^{3} x^{9} + 3 \, a^{4} b^{2} x^{6} + 3 \, a^{5} b x^{3} + a^{6}\right)}}"," ",0,"1/28*(3*(6*b^2*c + a*b*d)*x^7 + 7*(6*a*b*c + a^2*d)*x^4 + 28*a^2*c*x)*(b*x^3 + a)^(2/3)/(a^3*b^3*x^9 + 3*a^4*b^2*x^6 + 3*a^5*b*x^3 + a^6)","A",0
62,1,121,0,0.914663," ","integrate((d*x^3+c)/(b*x^3+a)^(13/3),x, algorithm=""fricas"")","\frac{{\left(9 \, {\left(9 \, b^{3} c + a b^{2} d\right)} x^{10} + 30 \, {\left(9 \, a b^{2} c + a^{2} b d\right)} x^{7} + 140 \, a^{3} c x + 35 \, {\left(9 \, a^{2} b c + a^{3} d\right)} x^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{140 \, {\left(a^{4} b^{4} x^{12} + 4 \, a^{5} b^{3} x^{9} + 6 \, a^{6} b^{2} x^{6} + 4 \, a^{7} b x^{3} + a^{8}\right)}}"," ",0,"1/140*(9*(9*b^3*c + a*b^2*d)*x^10 + 30*(9*a*b^2*c + a^2*b*d)*x^7 + 140*a^3*c*x + 35*(9*a^2*b*c + a^3*d)*x^4)*(b*x^3 + a)^(2/3)/(a^4*b^4*x^12 + 4*a^5*b^3*x^9 + 6*a^6*b^2*x^6 + 4*a^7*b*x^3 + a^8)","A",0
63,1,155,0,1.297588," ","integrate((d*x^3+c)/(b*x^3+a)^(16/3),x, algorithm=""fricas"")","\frac{{\left(81 \, {\left(12 \, b^{4} c + a b^{3} d\right)} x^{13} + 351 \, {\left(12 \, a b^{3} c + a^{2} b^{2} d\right)} x^{10} + 585 \, {\left(12 \, a^{2} b^{2} c + a^{3} b d\right)} x^{7} + 1820 \, a^{4} c x + 455 \, {\left(12 \, a^{3} b c + a^{4} d\right)} x^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{1820 \, {\left(a^{5} b^{5} x^{15} + 5 \, a^{6} b^{4} x^{12} + 10 \, a^{7} b^{3} x^{9} + 10 \, a^{8} b^{2} x^{6} + 5 \, a^{9} b x^{3} + a^{10}\right)}}"," ",0,"1/1820*(81*(12*b^4*c + a*b^3*d)*x^13 + 351*(12*a*b^3*c + a^2*b^2*d)*x^10 + 585*(12*a^2*b^2*c + a^3*b*d)*x^7 + 1820*a^4*c*x + 455*(12*a^3*b*c + a^4*d)*x^4)*(b*x^3 + a)^(2/3)/(a^5*b^5*x^15 + 5*a^6*b^4*x^12 + 10*a^7*b^3*x^9 + 10*a^8*b^2*x^6 + 5*a^9*b*x^3 + a^10)","A",0
64,0,0,0,1.152265," ","integrate((b*x^3+a)^(7/3)*(d*x^3+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d x^{9} + {\left(b^{2} c + 2 \, a b d\right)} x^{6} + {\left(2 \, a b c + a^{2} d\right)} x^{3} + a^{2} c\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b^2*d*x^9 + (b^2*c + 2*a*b*d)*x^6 + (2*a*b*c + a^2*d)*x^3 + a^2*c)*(b*x^3 + a)^(1/3), x)","F",0
65,0,0,0,1.232205," ","integrate((b*x^3+a)^(4/3)*(d*x^3+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d x^{6} + {\left(b c + a d\right)} x^{3} + a c\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b*d*x^6 + (b*c + a*d)*x^3 + a*c)*(b*x^3 + a)^(1/3), x)","F",0
66,0,0,0,1.748831," ","integrate((b*x^3+a)^(1/3)*(d*x^3+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)*(d*x^3 + c), x)","F",0
67,0,0,0,1.070686," ","integrate((d*x^3+c)/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((d*x^3 + c)/(b*x^3 + a)^(2/3), x)","F",0
68,0,0,0,0.644878," ","integrate((d*x^3+c)/(b*x^3+a)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)*(d*x^3 + c)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
69,0,0,0,1.221089," ","integrate((d*x^3+c)/(b*x^3+a)^(8/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)*(d*x^3 + c)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
70,1,717,0,1.224411," ","integrate((b*x^3+a)^(5/3)*(d*x^3+c)^2,x, algorithm=""fricas"")","\left[\frac{30 \, \sqrt{\frac{1}{3}} {\left(27 \, a^{2} b^{3} c^{2} - 6 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 20 \, {\left(27 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 10 \, {\left(27 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(81 \, b^{4} d^{2} x^{10} + 18 \, {\left(12 \, b^{4} c d + 7 \, a b^{3} d^{2}\right)} x^{7} + 3 \, {\left(54 \, b^{4} c^{2} + 132 \, a b^{3} c d + 5 \, a^{2} b^{2} d^{2}\right)} x^{4} + 4 \, {\left(108 \, a b^{3} c^{2} + 30 \, a^{2} b^{2} c d - 5 \, a^{3} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{2916 \, b^{3}}, -\frac{60 \, \sqrt{\frac{1}{3}} {\left(27 \, a^{2} b^{3} c^{2} - 6 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 20 \, {\left(27 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 10 \, {\left(27 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(81 \, b^{4} d^{2} x^{10} + 18 \, {\left(12 \, b^{4} c d + 7 \, a b^{3} d^{2}\right)} x^{7} + 3 \, {\left(54 \, b^{4} c^{2} + 132 \, a b^{3} c d + 5 \, a^{2} b^{2} d^{2}\right)} x^{4} + 4 \, {\left(108 \, a b^{3} c^{2} + 30 \, a^{2} b^{2} c d - 5 \, a^{3} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{2916 \, b^{3}}\right]"," ",0,"[1/2916*(30*sqrt(1/3)*(27*a^2*b^3*c^2 - 6*a^3*b^2*c*d + a^4*b*d^2)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 20*(27*a^2*b^2*c^2 - 6*a^3*b*c*d + a^4*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + 10*(27*a^2*b^2*c^2 - 6*a^3*b*c*d + a^4*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(81*b^4*d^2*x^10 + 18*(12*b^4*c*d + 7*a*b^3*d^2)*x^7 + 3*(54*b^4*c^2 + 132*a*b^3*c*d + 5*a^2*b^2*d^2)*x^4 + 4*(108*a*b^3*c^2 + 30*a^2*b^2*c*d - 5*a^3*b*d^2)*x)*(b*x^3 + a)^(2/3))/b^3, -1/2916*(60*sqrt(1/3)*(27*a^2*b^3*c^2 - 6*a^3*b^2*c*d + a^4*b*d^2)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 20*(27*a^2*b^2*c^2 - 6*a^3*b*c*d + a^4*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - 10*(27*a^2*b^2*c^2 - 6*a^3*b*c*d + a^4*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(81*b^4*d^2*x^10 + 18*(12*b^4*c*d + 7*a*b^3*d^2)*x^7 + 3*(54*b^4*c^2 + 132*a*b^3*c*d + 5*a^2*b^2*d^2)*x^4 + 4*(108*a*b^3*c^2 + 30*a^2*b^2*c*d - 5*a^3*b*d^2)*x)*(b*x^3 + a)^(2/3))/b^3]","A",0
71,1,634,0,1.245126," ","integrate((b*x^3+a)^(2/3)*(d*x^3+c)^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(27 \, a b^{3} c^{2} - 9 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 2 \, {\left(27 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 2 \, a^{3} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(27 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 2 \, a^{3} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(9 \, b^{3} d^{2} x^{7} + 3 \, {\left(9 \, b^{3} c d + a b^{2} d^{2}\right)} x^{4} + {\left(27 \, b^{3} c^{2} + 18 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{243 \, b^{3}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(27 \, a b^{3} c^{2} - 9 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 2 \, {\left(27 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 2 \, a^{3} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(27 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 2 \, a^{3} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(9 \, b^{3} d^{2} x^{7} + 3 \, {\left(9 \, b^{3} c d + a b^{2} d^{2}\right)} x^{4} + {\left(27 \, b^{3} c^{2} + 18 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{243 \, b^{3}}\right]"," ",0,"[1/243*(3*sqrt(1/3)*(27*a*b^3*c^2 - 9*a^2*b^2*c*d + 2*a^3*b*d^2)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 2*(27*a*b^2*c^2 - 9*a^2*b*c*d + 2*a^3*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + (27*a*b^2*c^2 - 9*a^2*b*c*d + 2*a^3*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(9*b^3*d^2*x^7 + 3*(9*b^3*c*d + a*b^2*d^2)*x^4 + (27*b^3*c^2 + 18*a*b^2*c*d - 4*a^2*b*d^2)*x)*(b*x^3 + a)^(2/3))/b^3, -1/243*(6*sqrt(1/3)*(27*a*b^3*c^2 - 9*a^2*b^2*c*d + 2*a^3*b*d^2)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 2*(27*a*b^2*c^2 - 9*a^2*b*c*d + 2*a^3*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (27*a*b^2*c^2 - 9*a^2*b*c*d + 2*a^3*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(9*b^3*d^2*x^7 + 3*(9*b^3*c*d + a*b^2*d^2)*x^4 + (27*b^3*c^2 + 18*a*b^2*c*d - 4*a^2*b*d^2)*x)*(b*x^3 + a)^(2/3))/b^3]","A",0
72,1,554,0,1.257808," ","integrate((d*x^3+c)^2/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} c^{2} - 6 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 2 \, {\left(9 \, b^{2} c^{2} - 6 \, a b c d + 2 \, a^{2} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(9 \, b^{2} c^{2} - 6 \, a b c d + 2 \, a^{2} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(3 \, b^{2} d^{2} x^{4} + 4 \, {\left(3 \, b^{2} c d - a b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{3}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} c^{2} - 6 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 2 \, {\left(9 \, b^{2} c^{2} - 6 \, a b c d + 2 \, a^{2} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(9 \, b^{2} c^{2} - 6 \, a b c d + 2 \, a^{2} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(3 \, b^{2} d^{2} x^{4} + 4 \, {\left(3 \, b^{2} c d - a b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{3}}\right]"," ",0,"[1/54*(3*sqrt(1/3)*(9*b^3*c^2 - 6*a*b^2*c*d + 2*a^2*b*d^2)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 2*(9*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + (9*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(3*b^2*d^2*x^4 + 4*(3*b^2*c*d - a*b*d^2)*x)*(b*x^3 + a)^(2/3))/b^3, -1/54*(6*sqrt(1/3)*(9*b^3*c^2 - 6*a*b^2*c*d + 2*a^2*b*d^2)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 2*(9*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (9*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(3*b^2*d^2*x^4 + 4*(3*b^2*c*d - a*b*d^2)*x)*(b*x^3 + a)^(2/3))/b^3]","A",0
73,1,652,0,1.169768," ","integrate((d*x^3+c)^2/(b*x^3+a)^(4/3),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(3 \, a^{2} b^{2} c d - 2 \, a^{3} b d^{2} + {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 2 \, {\left(3 \, a^{2} b c d - 2 \, a^{3} d^{2} + {\left(3 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(3 \, a^{2} b c d - 2 \, a^{3} d^{2} + {\left(3 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(a b^{2} d^{2} x^{4} + {\left(3 \, b^{3} c^{2} - 6 \, a b^{2} c d + 4 \, a^{2} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{9 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}}, -\frac{2 \, {\left(3 \, a^{2} b c d - 2 \, a^{3} d^{2} + {\left(3 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(3 \, a^{2} b c d - 2 \, a^{3} d^{2} + {\left(3 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, a^{2} b^{2} c d - 2 \, a^{3} b d^{2} + {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{3}\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}} - 3 \, {\left(a b^{2} d^{2} x^{4} + {\left(3 \, b^{3} c^{2} - 6 \, a b^{2} c d + 4 \, a^{2} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{9 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}}\right]"," ",0,"[-1/9*(3*sqrt(1/3)*(3*a^2*b^2*c*d - 2*a^3*b*d^2 + (3*a*b^3*c*d - 2*a^2*b^2*d^2)*x^3)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 2*(3*a^2*b*c*d - 2*a^3*d^2 + (3*a*b^2*c*d - 2*a^2*b*d^2)*x^3)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (3*a^2*b*c*d - 2*a^3*d^2 + (3*a*b^2*c*d - 2*a^2*b*d^2)*x^3)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(a*b^2*d^2*x^4 + (3*b^3*c^2 - 6*a*b^2*c*d + 4*a^2*b*d^2)*x)*(b*x^3 + a)^(2/3))/(a*b^4*x^3 + a^2*b^3), -1/9*(2*(3*a^2*b*c*d - 2*a^3*d^2 + (3*a*b^2*c*d - 2*a^2*b*d^2)*x^3)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (3*a^2*b*c*d - 2*a^3*d^2 + (3*a*b^2*c*d - 2*a^2*b*d^2)*x^3)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 6*sqrt(1/3)*(3*a^2*b^2*c*d - 2*a^3*b*d^2 + (3*a*b^3*c*d - 2*a^2*b^2*d^2)*x^3)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3) - 3*(a*b^2*d^2*x^4 + (3*b^3*c^2 - 6*a*b^2*c*d + 4*a^2*b*d^2)*x)*(b*x^3 + a)^(2/3))/(a*b^4*x^3 + a^2*b^3)]","B",0
74,1,719,0,1.299241," ","integrate((d*x^3+c)^2/(b*x^3+a)^(7/3),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{\frac{1}{3}} {\left(a^{2} b^{3} d^{2} x^{6} + 2 \, a^{3} b^{2} d^{2} x^{3} + a^{4} b d^{2}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 4 \, {\left(a^{2} b^{2} d^{2} x^{6} + 2 \, a^{3} b d^{2} x^{3} + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 2 \, {\left(a^{2} b^{2} d^{2} x^{6} + 2 \, a^{3} b d^{2} x^{3} + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left({\left(3 \, b^{4} c^{2} + 2 \, a b^{3} c d - 5 \, a^{2} b^{2} d^{2}\right)} x^{4} + 4 \, {\left(a b^{3} c^{2} - a^{3} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{12 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}, -\frac{12 \, \sqrt{\frac{1}{3}} {\left(a^{2} b^{3} d^{2} x^{6} + 2 \, a^{3} b^{2} d^{2} x^{3} + a^{4} b d^{2}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 4 \, {\left(a^{2} b^{2} d^{2} x^{6} + 2 \, a^{3} b d^{2} x^{3} + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 2 \, {\left(a^{2} b^{2} d^{2} x^{6} + 2 \, a^{3} b d^{2} x^{3} + a^{4} d^{2}\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left({\left(3 \, b^{4} c^{2} + 2 \, a b^{3} c d - 5 \, a^{2} b^{2} d^{2}\right)} x^{4} + 4 \, {\left(a b^{3} c^{2} - a^{3} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{12 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}\right]"," ",0,"[1/12*(6*sqrt(1/3)*(a^2*b^3*d^2*x^6 + 2*a^3*b^2*d^2*x^3 + a^4*b*d^2)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 4*(a^2*b^2*d^2*x^6 + 2*a^3*b*d^2*x^3 + a^4*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + 2*(a^2*b^2*d^2*x^6 + 2*a^3*b*d^2*x^3 + a^4*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*((3*b^4*c^2 + 2*a*b^3*c*d - 5*a^2*b^2*d^2)*x^4 + 4*(a*b^3*c^2 - a^3*b*d^2)*x)*(b*x^3 + a)^(2/3))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3), -1/12*(12*sqrt(1/3)*(a^2*b^3*d^2*x^6 + 2*a^3*b^2*d^2*x^3 + a^4*b*d^2)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 4*(a^2*b^2*d^2*x^6 + 2*a^3*b*d^2*x^3 + a^4*d^2)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - 2*(a^2*b^2*d^2*x^6 + 2*a^3*b*d^2*x^3 + a^4*d^2)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*((3*b^4*c^2 + 2*a*b^3*c*d - 5*a^2*b^2*d^2)*x^4 + 4*(a*b^3*c^2 - a^3*b*d^2)*x)*(b*x^3 + a)^(2/3))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3)]","B",0
75,1,103,0,1.191319," ","integrate((d*x^3+c)^2/(b*x^3+a)^(10/3),x, algorithm=""fricas"")","\frac{{\left({\left(9 \, b^{2} c^{2} + 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{7} + 14 \, a^{2} c^{2} x + 7 \, {\left(3 \, a b c^{2} + a^{2} c d\right)} x^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{14 \, {\left(a^{3} b^{3} x^{9} + 3 \, a^{4} b^{2} x^{6} + 3 \, a^{5} b x^{3} + a^{6}\right)}}"," ",0,"1/14*((9*b^2*c^2 + 3*a*b*c*d + 2*a^2*d^2)*x^7 + 14*a^2*c^2*x + 7*(3*a*b*c^2 + a^2*c*d)*x^4)*(b*x^3 + a)^(2/3)/(a^3*b^3*x^9 + 3*a^4*b^2*x^6 + 3*a^5*b*x^3 + a^6)","A",0
76,1,152,0,0.994885," ","integrate((d*x^3+c)^2/(b*x^3+a)^(13/3),x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(27 \, b^{3} c^{2} + 6 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x^{10} + 10 \, {\left(27 \, a b^{2} c^{2} + 6 \, a^{2} b c d + 2 \, a^{3} d^{2}\right)} x^{7} + 140 \, a^{3} c^{2} x + 35 \, {\left(9 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} x^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{140 \, {\left(a^{4} b^{4} x^{12} + 4 \, a^{5} b^{3} x^{9} + 6 \, a^{6} b^{2} x^{6} + 4 \, a^{7} b x^{3} + a^{8}\right)}}"," ",0,"1/140*(3*(27*b^3*c^2 + 6*a*b^2*c*d + 2*a^2*b*d^2)*x^10 + 10*(27*a*b^2*c^2 + 6*a^2*b*c*d + 2*a^3*d^2)*x^7 + 140*a^3*c^2*x + 35*(9*a^2*b*c^2 + 2*a^3*c*d)*x^4)*(b*x^3 + a)^(2/3)/(a^4*b^4*x^12 + 4*a^5*b^3*x^9 + 6*a^6*b^2*x^6 + 4*a^7*b*x^3 + a^8)","A",0
77,1,200,0,1.065322," ","integrate((d*x^3+c)^2/(b*x^3+a)^(16/3),x, algorithm=""fricas"")","\frac{{\left(9 \, {\left(54 \, b^{4} c^{2} + 9 \, a b^{3} c d + 2 \, a^{2} b^{2} d^{2}\right)} x^{13} + 39 \, {\left(54 \, a b^{3} c^{2} + 9 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{10} + 65 \, {\left(54 \, a^{2} b^{2} c^{2} + 9 \, a^{3} b c d + 2 \, a^{4} d^{2}\right)} x^{7} + 910 \, a^{4} c^{2} x + 455 \, {\left(6 \, a^{3} b c^{2} + a^{4} c d\right)} x^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{910 \, {\left(a^{5} b^{5} x^{15} + 5 \, a^{6} b^{4} x^{12} + 10 \, a^{7} b^{3} x^{9} + 10 \, a^{8} b^{2} x^{6} + 5 \, a^{9} b x^{3} + a^{10}\right)}}"," ",0,"1/910*(9*(54*b^4*c^2 + 9*a*b^3*c*d + 2*a^2*b^2*d^2)*x^13 + 39*(54*a*b^3*c^2 + 9*a^2*b^2*c*d + 2*a^3*b*d^2)*x^10 + 65*(54*a^2*b^2*c^2 + 9*a^3*b*c*d + 2*a^4*d^2)*x^7 + 910*a^4*c^2*x + 455*(6*a^3*b*c^2 + a^4*c*d)*x^4)*(b*x^3 + a)^(2/3)/(a^5*b^5*x^15 + 5*a^6*b^4*x^12 + 10*a^7*b^3*x^9 + 10*a^8*b^2*x^6 + 5*a^9*b*x^3 + a^10)","A",0
78,1,246,0,1.406803," ","integrate((d*x^3+c)^2/(b*x^3+a)^(19/3),x, algorithm=""fricas"")","\frac{{\left(81 \, {\left(45 \, b^{5} c^{2} + 6 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{16} + 432 \, {\left(45 \, a b^{4} c^{2} + 6 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x^{13} + 936 \, {\left(45 \, a^{2} b^{3} c^{2} + 6 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{10} + 7280 \, a^{5} c^{2} x + 1040 \, {\left(45 \, a^{3} b^{2} c^{2} + 6 \, a^{4} b c d + a^{5} d^{2}\right)} x^{7} + 1820 \, {\left(15 \, a^{4} b c^{2} + 2 \, a^{5} c d\right)} x^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{7280 \, {\left(a^{6} b^{6} x^{18} + 6 \, a^{7} b^{5} x^{15} + 15 \, a^{8} b^{4} x^{12} + 20 \, a^{9} b^{3} x^{9} + 15 \, a^{10} b^{2} x^{6} + 6 \, a^{11} b x^{3} + a^{12}\right)}}"," ",0,"1/7280*(81*(45*b^5*c^2 + 6*a*b^4*c*d + a^2*b^3*d^2)*x^16 + 432*(45*a*b^4*c^2 + 6*a^2*b^3*c*d + a^3*b^2*d^2)*x^13 + 936*(45*a^2*b^3*c^2 + 6*a^3*b^2*c*d + a^4*b*d^2)*x^10 + 7280*a^5*c^2*x + 1040*(45*a^3*b^2*c^2 + 6*a^4*b*c*d + a^5*d^2)*x^7 + 1820*(15*a^4*b*c^2 + 2*a^5*c*d)*x^4)*(b*x^3 + a)^(2/3)/(a^6*b^6*x^18 + 6*a^7*b^5*x^15 + 15*a^8*b^4*x^12 + 20*a^9*b^3*x^9 + 15*a^10*b^2*x^6 + 6*a^11*b*x^3 + a^12)","A",0
79,0,0,0,1.213079," ","integrate((b*x^3+a)^(7/3)*(d*x^3+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d^{2} x^{12} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x^{9} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{6} + a^{2} c^{2} + 2 \, {\left(a b c^{2} + a^{2} c d\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b^2*d^2*x^12 + 2*(b^2*c*d + a*b*d^2)*x^9 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^6 + a^2*c^2 + 2*(a*b*c^2 + a^2*c*d)*x^3)*(b*x^3 + a)^(1/3), x)","F",0
80,0,0,0,1.126127," ","integrate((b*x^3+a)^(4/3)*(d*x^3+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b d^{2} x^{9} + {\left(2 \, b c d + a d^{2}\right)} x^{6} + {\left(b c^{2} + 2 \, a c d\right)} x^{3} + a c^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b*d^2*x^9 + (2*b*c*d + a*d^2)*x^6 + (b*c^2 + 2*a*c*d)*x^3 + a*c^2)*(b*x^3 + a)^(1/3), x)","F",0
81,0,0,0,1.308010," ","integrate((b*x^3+a)^(1/3)*(d*x^3+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} x^{6} + 2 \, c d x^{3} + c^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^3 + c^2)*(b*x^3 + a)^(1/3), x)","F",0
82,0,0,0,1.275036," ","integrate((d*x^3+c)^2/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{2} x^{6} + 2 \, c d x^{3} + c^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^3 + c^2)/(b*x^3 + a)^(2/3), x)","F",0
83,0,0,0,1.278003," ","integrate((d*x^3+c)^2/(b*x^3+a)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{6} + 2 \, c d x^{3} + c^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^3 + c^2)*(b*x^3 + a)^(1/3)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
84,0,0,0,1.222087," ","integrate((d*x^3+c)^2/(b*x^3+a)^(8/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{6} + 2 \, c d x^{3} + c^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^3 + c^2)*(b*x^3 + a)^(1/3)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
85,1,166,0,0.894570," ","integrate((b*x^3+a)^3/(d*x^3+c)^(13/3),x, algorithm=""fricas"")","\frac{{\left({\left(14 \, b^{3} c^{3} + 18 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} + 81 \, a^{3} d^{3}\right)} x^{10} + 30 \, {\left(2 \, a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + 9 \, a^{3} c d^{2}\right)} x^{7} + 140 \, a^{3} c^{3} x + 105 \, {\left(a^{2} b c^{3} + 3 \, a^{3} c^{2} d\right)} x^{4}\right)} {\left(d x^{3} + c\right)}^{\frac{2}{3}}}{140 \, {\left(c^{4} d^{4} x^{12} + 4 \, c^{5} d^{3} x^{9} + 6 \, c^{6} d^{2} x^{6} + 4 \, c^{7} d x^{3} + c^{8}\right)}}"," ",0,"1/140*((14*b^3*c^3 + 18*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 81*a^3*d^3)*x^10 + 30*(2*a*b^2*c^3 + 3*a^2*b*c^2*d + 9*a^3*c*d^2)*x^7 + 140*a^3*c^3*x + 105*(a^2*b*c^3 + 3*a^3*c^2*d)*x^4)*(d*x^3 + c)^(2/3)/(c^4*d^4*x^12 + 4*c^5*d^3*x^9 + 6*c^6*d^2*x^6 + 4*c^7*d*x^3 + c^8)","A",0
86,1,643,0,36.577303," ","integrate((b*x^3+a)^(8/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{18 \, \sqrt{3} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, \sqrt{3} {\left(9 \, b^{2} c^{2} - 24 \, a b c d + 20 \, a^{2} d^{2}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) - 18 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 2 \, {\left(9 \, b^{2} c^{2} - 24 \, a b c d + 20 \, a^{2} d^{2}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + {\left(9 \, b^{2} c^{2} - 24 \, a b c d + 20 \, a^{2} d^{2}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + 9 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right) - 3 \, {\left(3 \, b^{2} d^{2} x^{4} - 2 \, {\left(3 \, b^{2} c d - 7 \, a b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, d^{3}}"," ",0,"-1/54*(18*sqrt(3)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 2*sqrt(3)*(9*b^2*c^2 - 24*a*b*c*d + 20*a^2*d^2)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) - 18*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 2*(9*b^2*c^2 - 24*a*b*c*d + 20*a^2*d^2)*(-b^2)^(1/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (9*b^2*c^2 - 24*a*b*c*d + 20*a^2*d^2)*(-b^2)^(1/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + 9*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2) - 3*(3*b^2*d^2*x^4 - 2*(3*b^2*c*d - 7*a*b*d^2)*x)*(b*x^3 + a)^(2/3))/d^3","B",0
87,1,535,0,3.506933," ","integrate((b*x^3+a)^(5/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b d x + 6 \, \sqrt{3} {\left(b c - a d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} {\left(3 \, b c - 5 \, a d\right)} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) - 6 \, {\left(b c - a d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 2 \, \left(-b^{2}\right)^{\frac{1}{3}} {\left(3 \, b c - 5 \, a d\right)} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + \left(-b^{2}\right)^{\frac{1}{3}} {\left(3 \, b c - 5 \, a d\right)} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + 3 \, {\left(b c - a d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right)}{18 \, d^{2}}"," ",0,"1/18*(6*(b*x^3 + a)^(2/3)*b*d*x + 6*sqrt(3)*(b*c - a*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 2*sqrt(3)*(-b^2)^(1/3)*(3*b*c - 5*a*d)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) - 6*(b*c - a*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 2*(-b^2)^(1/3)*(3*b*c - 5*a*d)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (-b^2)^(1/3)*(3*b*c - 5*a*d)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + 3*(b*c - a*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2))/d^2","B",0
88,1,469,0,1.579166," ","integrate((b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) - 2 \, \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 2 \, \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right)}{6 \, d}"," ",0,"-1/6*(2*sqrt(3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 2*sqrt(3)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) - 2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 2*(-b^2)^(1/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (-b^2)^(1/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + ((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2))/d","B",0
89,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(10/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(8/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,1,819,0,19.124251," ","integrate((b*x^3+a)^(8/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, \sqrt{3} {\left(3 \, b^{2} c^{3} - 4 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x^{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) - 2 \, {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 2 \, {\left(3 \, b^{2} c^{3} - 4 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x^{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + {\left(3 \, b^{2} c^{3} - 4 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x^{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right) + 3 \, {\left(b^{2} c d^{2} x^{4} + {\left(2 \, b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{9 \, {\left(c d^{4} x^{3} + c^{2} d^{3}\right)}}"," ",0,"1/9*(2*sqrt(3)*(3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2 + (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 2*sqrt(3)*(3*b^2*c^3 - 4*a*b*c^2*d + (3*b^2*c^2*d - 4*a*b*c*d^2)*x^3)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) - 2*(3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2 + (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 2*(3*b^2*c^3 - 4*a*b*c^2*d + (3*b^2*c^2*d - 4*a*b*c*d^2)*x^3)*(-b^2)^(1/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (3*b^2*c^3 - 4*a*b*c^2*d + (3*b^2*c^2*d - 4*a*b*c*d^2)*x^3)*(-b^2)^(1/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + (3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2 + (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2) + 3*(b^2*c*d^2*x^4 + (2*b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*(b*x^3 + a)^(2/3))/(c*d^4*x^3 + c^2*d^3)","B",0
99,1,631,0,2.322723," ","integrate((b*x^3+a)^(5/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left({\left(3 \, b c d + 2 \, a d^{2}\right)} x^{3} + 3 \, b c^{2} + 2 \, a c d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 6 \, \sqrt{3} {\left(b c d x^{3} + b c^{2}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} x - 2 \, {\left({\left(3 \, b c d + 2 \, a d^{2}\right)} x^{3} + 3 \, b c^{2} + 2 \, a c d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 6 \, {\left(b c d x^{3} + b c^{2}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + 3 \, {\left(b c d x^{3} + b c^{2}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + {\left({\left(3 \, b c d + 2 \, a d^{2}\right)} x^{3} + 3 \, b c^{2} + 2 \, a c d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right)}{18 \, {\left(c d^{3} x^{3} + c^{2} d^{2}\right)}}"," ",0,"-1/18*(2*sqrt(3)*((3*b*c*d + 2*a*d^2)*x^3 + 3*b*c^2 + 2*a*c*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 6*sqrt(3)*(b*c*d*x^3 + b*c^2)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) + 6*(b*x^3 + a)^(2/3)*(b*c*d - a*d^2)*x - 2*((3*b*c*d + 2*a*d^2)*x^3 + 3*b*c^2 + 2*a*c*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 6*(b*c*d*x^3 + b*c^2)*(-b^2)^(1/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + 3*(b*c*d*x^3 + b*c^2)*(-b^2)^(1/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + ((3*b*c*d + 2*a*d^2)*x^3 + 3*b*c^2 + 2*a*c*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2))/(c*d^3*x^3 + c^2*d^2)","B",0
100,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(4/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(8/3)/(d*x^3+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((b*x^3+a)^(14/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,1,1246,0,114.550237," ","integrate((b*x^3+a)^(11/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} {\left(27 \, b^{3} c^{5} - 15 \, a b^{2} c^{4} d - 7 \, a^{2} b c^{3} d^{2} - 5 \, a^{3} c^{2} d^{3} + {\left(27 \, b^{3} c^{3} d^{2} - 15 \, a b^{2} c^{2} d^{3} - 7 \, a^{2} b c d^{4} - 5 \, a^{3} d^{5}\right)} x^{6} + 2 \, {\left(27 \, b^{3} c^{4} d - 15 \, a b^{2} c^{3} d^{2} - 7 \, a^{2} b c^{2} d^{3} - 5 \, a^{3} c d^{4}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 6 \, \sqrt{3} {\left(9 \, b^{3} c^{5} - 11 \, a b^{2} c^{4} d + {\left(9 \, b^{3} c^{3} d^{2} - 11 \, a b^{2} c^{2} d^{3}\right)} x^{6} + 2 \, {\left(9 \, b^{3} c^{4} d - 11 \, a b^{2} c^{3} d^{2}\right)} x^{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) - 2 \, {\left(27 \, b^{3} c^{5} - 15 \, a b^{2} c^{4} d - 7 \, a^{2} b c^{3} d^{2} - 5 \, a^{3} c^{2} d^{3} + {\left(27 \, b^{3} c^{3} d^{2} - 15 \, a b^{2} c^{2} d^{3} - 7 \, a^{2} b c d^{4} - 5 \, a^{3} d^{5}\right)} x^{6} + 2 \, {\left(27 \, b^{3} c^{4} d - 15 \, a b^{2} c^{3} d^{2} - 7 \, a^{2} b c^{2} d^{3} - 5 \, a^{3} c d^{4}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 6 \, {\left(9 \, b^{3} c^{5} - 11 \, a b^{2} c^{4} d + {\left(9 \, b^{3} c^{3} d^{2} - 11 \, a b^{2} c^{2} d^{3}\right)} x^{6} + 2 \, {\left(9 \, b^{3} c^{4} d - 11 \, a b^{2} c^{3} d^{2}\right)} x^{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + 3 \, {\left(9 \, b^{3} c^{5} - 11 \, a b^{2} c^{4} d + {\left(9 \, b^{3} c^{3} d^{2} - 11 \, a b^{2} c^{2} d^{3}\right)} x^{6} + 2 \, {\left(9 \, b^{3} c^{4} d - 11 \, a b^{2} c^{3} d^{2}\right)} x^{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + {\left(27 \, b^{3} c^{5} - 15 \, a b^{2} c^{4} d - 7 \, a^{2} b c^{3} d^{2} - 5 \, a^{3} c^{2} d^{3} + {\left(27 \, b^{3} c^{3} d^{2} - 15 \, a b^{2} c^{2} d^{3} - 7 \, a^{2} b c d^{4} - 5 \, a^{3} d^{5}\right)} x^{6} + 2 \, {\left(27 \, b^{3} c^{4} d - 15 \, a b^{2} c^{3} d^{2} - 7 \, a^{2} b c^{2} d^{3} - 5 \, a^{3} c d^{4}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right) + 3 \, {\left(6 \, b^{3} c^{2} d^{3} x^{7} + {\left(27 \, b^{3} c^{3} d^{2} - 25 \, a b^{2} c^{2} d^{3} + 5 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{4} + 2 \, {\left(9 \, b^{3} c^{4} d - 8 \, a b^{2} c^{3} d^{2} - 2 \, a^{2} b c^{2} d^{3} + 4 \, a^{3} c d^{4}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, {\left(c^{2} d^{6} x^{6} + 2 \, c^{3} d^{5} x^{3} + c^{4} d^{4}\right)}}"," ",0,"1/54*(2*sqrt(3)*(27*b^3*c^5 - 15*a*b^2*c^4*d - 7*a^2*b*c^3*d^2 - 5*a^3*c^2*d^3 + (27*b^3*c^3*d^2 - 15*a*b^2*c^2*d^3 - 7*a^2*b*c*d^4 - 5*a^3*d^5)*x^6 + 2*(27*b^3*c^4*d - 15*a*b^2*c^3*d^2 - 7*a^2*b*c^2*d^3 - 5*a^3*c*d^4)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 6*sqrt(3)*(9*b^3*c^5 - 11*a*b^2*c^4*d + (9*b^3*c^3*d^2 - 11*a*b^2*c^2*d^3)*x^6 + 2*(9*b^3*c^4*d - 11*a*b^2*c^3*d^2)*x^3)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) - 2*(27*b^3*c^5 - 15*a*b^2*c^4*d - 7*a^2*b*c^3*d^2 - 5*a^3*c^2*d^3 + (27*b^3*c^3*d^2 - 15*a*b^2*c^2*d^3 - 7*a^2*b*c*d^4 - 5*a^3*d^5)*x^6 + 2*(27*b^3*c^4*d - 15*a*b^2*c^3*d^2 - 7*a^2*b*c^2*d^3 - 5*a^3*c*d^4)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 6*(9*b^3*c^5 - 11*a*b^2*c^4*d + (9*b^3*c^3*d^2 - 11*a*b^2*c^2*d^3)*x^6 + 2*(9*b^3*c^4*d - 11*a*b^2*c^3*d^2)*x^3)*(-b^2)^(1/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + 3*(9*b^3*c^5 - 11*a*b^2*c^4*d + (9*b^3*c^3*d^2 - 11*a*b^2*c^2*d^3)*x^6 + 2*(9*b^3*c^4*d - 11*a*b^2*c^3*d^2)*x^3)*(-b^2)^(1/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + (27*b^3*c^5 - 15*a*b^2*c^4*d - 7*a^2*b*c^3*d^2 - 5*a^3*c^2*d^3 + (27*b^3*c^3*d^2 - 15*a*b^2*c^2*d^3 - 7*a^2*b*c*d^4 - 5*a^3*d^5)*x^6 + 2*(27*b^3*c^4*d - 15*a*b^2*c^3*d^2 - 7*a^2*b*c^2*d^3 - 5*a^3*c*d^4)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2) + 3*(6*b^3*c^2*d^3*x^7 + (27*b^3*c^3*d^2 - 25*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 + 5*a^3*d^5)*x^4 + 2*(9*b^3*c^4*d - 8*a*b^2*c^3*d^2 - 2*a^2*b*c^2*d^3 + 4*a^3*c*d^4)*x)*(b*x^3 + a)^(2/3))/(c^2*d^6*x^6 + 2*c^3*d^5*x^3 + c^4*d^4)","B",0
111,1,954,0,12.613835," ","integrate((b*x^3+a)^(8/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left({\left(9 \, b^{2} c^{2} d^{2} + 6 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{6} + 9 \, b^{2} c^{4} + 6 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2} + 2 \, {\left(9 \, b^{2} c^{3} d + 6 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 18 \, \sqrt{3} {\left(b^{2} c^{2} d^{2} x^{6} + 2 \, b^{2} c^{3} d x^{3} + b^{2} c^{4}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) - 2 \, {\left({\left(9 \, b^{2} c^{2} d^{2} + 6 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{6} + 9 \, b^{2} c^{4} + 6 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2} + 2 \, {\left(9 \, b^{2} c^{3} d + 6 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 18 \, {\left(b^{2} c^{2} d^{2} x^{6} + 2 \, b^{2} c^{3} d x^{3} + b^{2} c^{4}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + 9 \, {\left(b^{2} c^{2} d^{2} x^{6} + 2 \, b^{2} c^{3} d x^{3} + b^{2} c^{4}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + {\left({\left(9 \, b^{2} c^{2} d^{2} + 6 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{6} + 9 \, b^{2} c^{4} + 6 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2} + 2 \, {\left(9 \, b^{2} c^{3} d + 6 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{3}\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right) + 3 \, {\left({\left(9 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} - 5 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + a b c^{2} d^{2} - 4 \, a^{2} c d^{3}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, {\left(c^{2} d^{5} x^{6} + 2 \, c^{3} d^{4} x^{3} + c^{4} d^{3}\right)}}"," ",0,"-1/54*(2*sqrt(3)*((9*b^2*c^2*d^2 + 6*a*b*c*d^3 + 5*a^2*d^4)*x^6 + 9*b^2*c^4 + 6*a*b*c^3*d + 5*a^2*c^2*d^2 + 2*(9*b^2*c^3*d + 6*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 18*sqrt(3)*(b^2*c^2*d^2*x^6 + 2*b^2*c^3*d*x^3 + b^2*c^4)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) - 2*((9*b^2*c^2*d^2 + 6*a*b*c*d^3 + 5*a^2*d^4)*x^6 + 9*b^2*c^4 + 6*a*b*c^3*d + 5*a^2*c^2*d^2 + 2*(9*b^2*c^3*d + 6*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 18*(b^2*c^2*d^2*x^6 + 2*b^2*c^3*d*x^3 + b^2*c^4)*(-b^2)^(1/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + 9*(b^2*c^2*d^2*x^6 + 2*b^2*c^3*d*x^3 + b^2*c^4)*(-b^2)^(1/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + ((9*b^2*c^2*d^2 + 6*a*b*c*d^3 + 5*a^2*d^4)*x^6 + 9*b^2*c^4 + 6*a*b*c^3*d + 5*a^2*c^2*d^2 + 2*(9*b^2*c^3*d + 6*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2) + 3*((9*b^2*c^2*d^2 - 4*a*b*c*d^3 - 5*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + a*b*c^2*d^2 - 4*a^2*c*d^3)*x)*(b*x^3 + a)^(2/3))/(c^2*d^5*x^6 + 2*c^3*d^4*x^3 + c^4*d^3)","B",0
112,-1,0,0,0.000000," ","integrate((b*x^3+a)^(5/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(4/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(8/3)/(d*x^3+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,0,0,0,80.474975," ","integrate((b*x^3+a)^(7/4)/(d*x^3+c)^(37/12),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{7}{4}} {\left(d x^{3} + c\right)}^{\frac{11}{12}}}{d^{4} x^{12} + 4 \, c d^{3} x^{9} + 6 \, c^{2} d^{2} x^{6} + 4 \, c^{3} d x^{3} + c^{4}}, x\right)"," ",0,"integral((b*x^3 + a)^(7/4)*(d*x^3 + c)^(11/12)/(d^4*x^12 + 4*c*d^3*x^9 + 6*c^2*d^2*x^6 + 4*c^3*d*x^3 + c^4), x)","F",0
123,0,0,0,3.342811," ","integrate((b*x^3+a)^(5/4)/(d*x^3+c)^(31/12),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{5}{4}} {\left(d x^{3} + c\right)}^{\frac{5}{12}}}{d^{3} x^{9} + 3 \, c d^{2} x^{6} + 3 \, c^{2} d x^{3} + c^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(5/4)*(d*x^3 + c)^(5/12)/(d^3*x^9 + 3*c*d^2*x^6 + 3*c^2*d*x^3 + c^3), x)","F",0
124,0,0,0,65.235330," ","integrate((b*x^3+a)^(3/4)/(d*x^3+c)^(25/12),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{4}} {\left(d x^{3} + c\right)}^{\frac{11}{12}}}{d^{3} x^{9} + 3 \, c d^{2} x^{6} + 3 \, c^{2} d x^{3} + c^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/4)*(d*x^3 + c)^(11/12)/(d^3*x^9 + 3*c*d^2*x^6 + 3*c^2*d*x^3 + c^3), x)","F",0
125,0,0,0,3.061296," ","integrate((b*x^3+a)^(1/4)/(d*x^3+c)^(19/12),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{4}} {\left(d x^{3} + c\right)}^{\frac{5}{12}}}{d^{2} x^{6} + 2 \, c d x^{3} + c^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/4)*(d*x^3 + c)^(5/12)/(d^2*x^6 + 2*c*d*x^3 + c^2), x)","F",0
126,0,0,0,65.017911," ","integrate(1/(b*x^3+a)^(1/4)/(d*x^3+c)^(13/12),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{4}} {\left(d x^{3} + c\right)}^{\frac{11}{12}}}{b d^{2} x^{9} + {\left(2 \, b c d + a d^{2}\right)} x^{6} + {\left(b c^{2} + 2 \, a c d\right)} x^{3} + a c^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/4)*(d*x^3 + c)^(11/12)/(b*d^2*x^9 + (2*b*c*d + a*d^2)*x^6 + (b*c^2 + 2*a*c*d)*x^3 + a*c^2), x)","F",0
127,0,0,0,3.263359," ","integrate(1/(b*x^3+a)^(3/4)/(d*x^3+c)^(7/12),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{4}} {\left(d x^{3} + c\right)}^{\frac{5}{12}}}{b d x^{6} + {\left(b c + a d\right)} x^{3} + a c}, x\right)"," ",0,"integral((b*x^3 + a)^(1/4)*(d*x^3 + c)^(5/12)/(b*d*x^6 + (b*c + a*d)*x^3 + a*c), x)","F",0
128,0,0,0,65.807217," ","integrate(1/(b*x^3+a)^(5/4)/(d*x^3+c)^(1/12),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{4}} {\left(d x^{3} + c\right)}^{\frac{11}{12}}}{b^{2} d x^{9} + {\left(b^{2} c + 2 \, a b d\right)} x^{6} + {\left(2 \, a b c + a^{2} d\right)} x^{3} + a^{2} c}, x\right)"," ",0,"integral((b*x^3 + a)^(3/4)*(d*x^3 + c)^(11/12)/(b^2*d*x^9 + (b^2*c + 2*a*b*d)*x^6 + (2*a*b*c + a^2*d)*x^3 + a^2*c), x)","F",0
129,0,0,0,3.109791," ","integrate((d*x^3+c)^(5/12)/(b*x^3+a)^(7/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{4}} {\left(d x^{3} + c\right)}^{\frac{5}{12}}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/4)*(d*x^3 + c)^(5/12)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
130,0,0,0,66.014019," ","integrate((d*x^3+c)^(11/12)/(b*x^3+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{4}} {\left(d x^{3} + c\right)}^{\frac{11}{12}}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/4)*(d*x^3 + c)^(11/12)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
131,0,0,0,3.207238," ","integrate((d*x^3+c)^(17/12)/(b*x^3+a)^(11/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{4}} {\left(d x^{3} + c\right)}^{\frac{17}{12}}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/4)*(d*x^3 + c)^(17/12)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
132,0,0,0,68.170136," ","integrate((d*x^3+c)^(23/12)/(b*x^3+a)^(13/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{4}} {\left(d x^{3} + c\right)}^{\frac{23}{12}}}{b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/4)*(d*x^3 + c)^(23/12)/(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4), x)","F",0
133,0,0,0,1.583533," ","integrate((b*x^3+a)^m*(d*x^3+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{m} {\left(d x^{3} + c\right)}^{p}, x\right)"," ",0,"integral((b*x^3 + a)^m*(d*x^3 + c)^p, x)","F",0
134,0,0,0,1.263489," ","integrate((b*x^3+a)^2*(d*x^3+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} {\left(d x^{3} + c\right)}^{q}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)*(d*x^3 + c)^q, x)","F",0
135,0,0,0,1.176872," ","integrate((b*x^3+a)*(d*x^3+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)} {\left(d x^{3} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^3 + a)*(d*x^3 + c)^q, x)","F",0
136,0,0,0,1.322931," ","integrate((d*x^3+c)^q/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{3} + c\right)}^{q}}{b x^{3} + a}, x\right)"," ",0,"integral((d*x^3 + c)^q/(b*x^3 + a), x)","F",0
137,0,0,0,1.199736," ","integrate((d*x^3+c)^q/(b*x^3+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{3} + c\right)}^{q}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((d*x^3 + c)^q/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
138,0,0,0,1.140883," ","integrate((b*x^3+a)^m*(d*x^3+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{3} x^{9} + 3 \, c d^{2} x^{6} + 3 \, c^{2} d x^{3} + c^{3}\right)} {\left(b x^{3} + a\right)}^{m}, x\right)"," ",0,"integral((d^3*x^9 + 3*c*d^2*x^6 + 3*c^2*d*x^3 + c^3)*(b*x^3 + a)^m, x)","F",0
139,0,0,0,1.167797," ","integrate((b*x^3+a)^m*(d*x^3+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} x^{6} + 2 \, c d x^{3} + c^{2}\right)} {\left(b x^{3} + a\right)}^{m}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^3 + c^2)*(b*x^3 + a)^m, x)","F",0
140,0,0,0,1.302091," ","integrate((b*x^3+a)^m*(d*x^3+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x^{3} + c\right)} {\left(b x^{3} + a\right)}^{m}, x\right)"," ",0,"integral((d*x^3 + c)*(b*x^3 + a)^m, x)","F",0
141,0,0,0,1.237844," ","integrate((b*x^3+a)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{m}, x\right)"," ",0,"integral((b*x^3 + a)^m, x)","F",0
142,0,0,0,1.311961," ","integrate((b*x^3+a)^m/(d*x^3+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{m}}{d x^{3} + c}, x\right)"," ",0,"integral((b*x^3 + a)^m/(d*x^3 + c), x)","F",0
143,0,0,0,1.161947," ","integrate((b*x^3+a)^m/(d*x^3+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{m}}{d^{2} x^{6} + 2 \, c d x^{3} + c^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^m/(d^2*x^6 + 2*c*d*x^3 + c^2), x)","F",0
144,0,0,0,0.952398," ","integrate((b*x^3+a)^m/(d*x^3+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{m}}{d^{3} x^{9} + 3 \, c d^{2} x^{6} + 3 \, c^{2} d x^{3} + c^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^m/(d^3*x^9 + 3*c*d^2*x^6 + 3*c^2*d*x^3 + c^3), x)","F",0
145,1,91,0,1.348431," ","integrate((b*x^3+a)^(-1-b*c/(-3*a*d+3*b*c))*(d*x^3+c)^(-1+a*d/(-3*a*d+3*b*c)),x, algorithm=""fricas"")","\frac{b d x^{7} + {\left(b c + a d\right)} x^{4} + a c x}{{\left(b x^{3} + a\right)}^{\frac{4 \, b c - 3 \, a d}{3 \, {\left(b c - a d\right)}}} {\left(d x^{3} + c\right)}^{\frac{3 \, b c - 4 \, a d}{3 \, {\left(b c - a d\right)}}} a c}"," ",0,"(b*d*x^7 + (b*c + a*d)*x^4 + a*c*x)/((b*x^3 + a)^(1/3*(4*b*c - 3*a*d)/(b*c - a*d))*(d*x^3 + c)^(1/3*(3*b*c - 4*a*d)/(b*c - a*d))*a*c)","A",0
146,1,98,0,0.977154," ","integrate((b*x^4+a)*(d*x^4+c)^4,x, algorithm=""fricas"")","\frac{1}{21} x^{21} d^{4} b + \frac{4}{17} x^{17} d^{3} c b + \frac{1}{17} x^{17} d^{4} a + \frac{6}{13} x^{13} d^{2} c^{2} b + \frac{4}{13} x^{13} d^{3} c a + \frac{4}{9} x^{9} d c^{3} b + \frac{2}{3} x^{9} d^{2} c^{2} a + \frac{1}{5} x^{5} c^{4} b + \frac{4}{5} x^{5} d c^{3} a + x c^{4} a"," ",0,"1/21*x^21*d^4*b + 4/17*x^17*d^3*c*b + 1/17*x^17*d^4*a + 6/13*x^13*d^2*c^2*b + 4/13*x^13*d^3*c*a + 4/9*x^9*d*c^3*b + 2/3*x^9*d^2*c^2*a + 1/5*x^5*c^4*b + 4/5*x^5*d*c^3*a + x*c^4*a","A",0
147,1,74,0,0.897099," ","integrate((b*x^4+a)*(d*x^4+c)^3,x, algorithm=""fricas"")","\frac{1}{17} x^{17} d^{3} b + \frac{3}{13} x^{13} d^{2} c b + \frac{1}{13} x^{13} d^{3} a + \frac{1}{3} x^{9} d c^{2} b + \frac{1}{3} x^{9} d^{2} c a + \frac{1}{5} x^{5} c^{3} b + \frac{3}{5} x^{5} d c^{2} a + x c^{3} a"," ",0,"1/17*x^17*d^3*b + 3/13*x^13*d^2*c*b + 1/13*x^13*d^3*a + 1/3*x^9*d*c^2*b + 1/3*x^9*d^2*c*a + 1/5*x^5*c^3*b + 3/5*x^5*d*c^2*a + x*c^3*a","A",0
148,1,50,0,0.864587," ","integrate((b*x^4+a)*(d*x^4+c)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} d^{2} b + \frac{2}{9} x^{9} d c b + \frac{1}{9} x^{9} d^{2} a + \frac{1}{5} x^{5} c^{2} b + \frac{2}{5} x^{5} d c a + x c^{2} a"," ",0,"1/13*x^13*d^2*b + 2/9*x^9*d*c*b + 1/9*x^9*d^2*a + 1/5*x^5*c^2*b + 2/5*x^5*d*c*a + x*c^2*a","A",0
149,1,26,0,0.759373," ","integrate((b*x^4+a)*(d*x^4+c),x, algorithm=""fricas"")","\frac{1}{9} x^{9} d b + \frac{1}{5} x^{5} c b + \frac{1}{5} x^{5} d a + x c a"," ",0,"1/9*x^9*d*b + 1/5*x^5*c*b + 1/5*x^5*d*a + x*c*a","A",0
150,1,639,0,1.288337," ","integrate((b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\frac{4 \, d \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{c^{2} d^{4} x \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}\right)^{\frac{3}{4}} - c^{2} d^{4} \sqrt{\frac{c^{2} d^{2} \sqrt{-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}} \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}\right)^{\frac{3}{4}}}{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}\right) + d \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}\right)^{\frac{1}{4}} \log\left(c d \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}\right)^{\frac{1}{4}} - {\left(b c - a d\right)} x\right) - d \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}\right)^{\frac{1}{4}} \log\left(-c d \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{c^{3} d^{5}}\right)^{\frac{1}{4}} - {\left(b c - a d\right)} x\right) + 4 \, b x}{4 \, d}"," ",0,"1/4*(4*d*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5))^(1/4)*arctan((c^2*d^4*x*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5))^(3/4) - c^2*d^4*sqrt((c^2*d^2*sqrt(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5)) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5))^(3/4))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)) + d*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5))^(1/4)*log(c*d*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5))^(1/4) - (b*c - a*d)*x) - d*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5))^(1/4)*log(-c*d*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(c^3*d^5))^(1/4) - (b*c - a*d)*x) + 4*b*x)/d","B",0
151,1,711,0,1.417207," ","integrate((b*x^4+a)/(d*x^4+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(c d^{2} x^{4} + c^{2} d\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c^{5} d^{4} x \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}\right)^{\frac{3}{4}} - c^{5} d^{4} \sqrt{\frac{c^{4} d^{2} \sqrt{-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}} + {\left(b^{2} c^{2} + 6 \, a b c d + 9 \, a^{2} d^{2}\right)} x^{2}}{b^{2} c^{2} + 6 \, a b c d + 9 \, a^{2} d^{2}}} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}\right)^{\frac{3}{4}}}{b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} + 27 \, a^{3} d^{3}}\right) + {\left(c d^{2} x^{4} + c^{2} d\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}\right)^{\frac{1}{4}} \log\left(c^{2} d \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}\right)^{\frac{1}{4}} + {\left(b c + 3 \, a d\right)} x\right) - {\left(c d^{2} x^{4} + c^{2} d\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}\right)^{\frac{1}{4}} \log\left(-c^{2} d \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{c^{7} d^{5}}\right)^{\frac{1}{4}} + {\left(b c + 3 \, a d\right)} x\right) - 4 \, {\left(b c - a d\right)} x}{16 \, {\left(c d^{2} x^{4} + c^{2} d\right)}}"," ",0,"1/16*(4*(c*d^2*x^4 + c^2*d)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5))^(1/4)*arctan(-(c^5*d^4*x*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5))^(3/4) - c^5*d^4*sqrt((c^4*d^2*sqrt(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5)) + (b^2*c^2 + 6*a*b*c*d + 9*a^2*d^2)*x^2)/(b^2*c^2 + 6*a*b*c*d + 9*a^2*d^2))*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5))^(3/4))/(b^3*c^3 + 9*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 27*a^3*d^3)) + (c*d^2*x^4 + c^2*d)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5))^(1/4)*log(c^2*d*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5))^(1/4) + (b*c + 3*a*d)*x) - (c*d^2*x^4 + c^2*d)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5))^(1/4)*log(-c^2*d*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(c^7*d^5))^(1/4) + (b*c + 3*a*d)*x) - 4*(b*c - a*d)*x)/(c*d^2*x^4 + c^2*d)","B",0
152,1,787,0,1.320604," ","integrate((b*x^4+a)/(d*x^4+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(b c d + 7 \, a d^{2}\right)} x^{5} + 12 \, {\left(c^{2} d^{3} x^{8} + 2 \, c^{3} d^{2} x^{4} + c^{4} d\right)} \left(-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c^{8} d^{4} x \left(-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}\right)^{\frac{3}{4}} - c^{8} d^{4} \sqrt{\frac{c^{6} d^{2} \sqrt{-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}} + {\left(b^{2} c^{2} + 14 \, a b c d + 49 \, a^{2} d^{2}\right)} x^{2}}{b^{2} c^{2} + 14 \, a b c d + 49 \, a^{2} d^{2}}} \left(-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}\right)^{\frac{3}{4}}}{b^{3} c^{3} + 21 \, a b^{2} c^{2} d + 147 \, a^{2} b c d^{2} + 343 \, a^{3} d^{3}}\right) + 3 \, {\left(c^{2} d^{3} x^{8} + 2 \, c^{3} d^{2} x^{4} + c^{4} d\right)} \left(-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}\right)^{\frac{1}{4}} \log\left(3 \, c^{3} d \left(-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}\right)^{\frac{1}{4}} + 3 \, {\left(b c + 7 \, a d\right)} x\right) - 3 \, {\left(c^{2} d^{3} x^{8} + 2 \, c^{3} d^{2} x^{4} + c^{4} d\right)} \left(-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}\right)^{\frac{1}{4}} \log\left(-3 \, c^{3} d \left(-\frac{b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 294 \, a^{2} b^{2} c^{2} d^{2} + 1372 \, a^{3} b c d^{3} + 2401 \, a^{4} d^{4}}{c^{11} d^{5}}\right)^{\frac{1}{4}} + 3 \, {\left(b c + 7 \, a d\right)} x\right) - 4 \, {\left(3 \, b c^{2} - 11 \, a c d\right)} x}{128 \, {\left(c^{2} d^{3} x^{8} + 2 \, c^{3} d^{2} x^{4} + c^{4} d\right)}}"," ",0,"1/128*(4*(b*c*d + 7*a*d^2)*x^5 + 12*(c^2*d^3*x^8 + 2*c^3*d^2*x^4 + c^4*d)*(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5))^(1/4)*arctan(-(c^8*d^4*x*(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5))^(3/4) - c^8*d^4*sqrt((c^6*d^2*sqrt(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5)) + (b^2*c^2 + 14*a*b*c*d + 49*a^2*d^2)*x^2)/(b^2*c^2 + 14*a*b*c*d + 49*a^2*d^2))*(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5))^(3/4))/(b^3*c^3 + 21*a*b^2*c^2*d + 147*a^2*b*c*d^2 + 343*a^3*d^3)) + 3*(c^2*d^3*x^8 + 2*c^3*d^2*x^4 + c^4*d)*(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5))^(1/4)*log(3*c^3*d*(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5))^(1/4) + 3*(b*c + 7*a*d)*x) - 3*(c^2*d^3*x^8 + 2*c^3*d^2*x^4 + c^4*d)*(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5))^(1/4)*log(-3*c^3*d*(-(b^4*c^4 + 28*a*b^3*c^3*d + 294*a^2*b^2*c^2*d^2 + 1372*a^3*b*c*d^3 + 2401*a^4*d^4)/(c^11*d^5))^(1/4) + 3*(b*c + 7*a*d)*x) - 4*(3*b*c^2 - 11*a*c*d)*x)/(c^2*d^3*x^8 + 2*c^3*d^2*x^4 + c^4*d)","B",0
153,1,173,0,1.050261," ","integrate((b*x^4+a)^2*(d*x^4+c)^4,x, algorithm=""fricas"")","\frac{1}{25} x^{25} d^{4} b^{2} + \frac{4}{21} x^{21} d^{3} c b^{2} + \frac{2}{21} x^{21} d^{4} b a + \frac{6}{17} x^{17} d^{2} c^{2} b^{2} + \frac{8}{17} x^{17} d^{3} c b a + \frac{1}{17} x^{17} d^{4} a^{2} + \frac{4}{13} x^{13} d c^{3} b^{2} + \frac{12}{13} x^{13} d^{2} c^{2} b a + \frac{4}{13} x^{13} d^{3} c a^{2} + \frac{1}{9} x^{9} c^{4} b^{2} + \frac{8}{9} x^{9} d c^{3} b a + \frac{2}{3} x^{9} d^{2} c^{2} a^{2} + \frac{2}{5} x^{5} c^{4} b a + \frac{4}{5} x^{5} d c^{3} a^{2} + x c^{4} a^{2}"," ",0,"1/25*x^25*d^4*b^2 + 4/21*x^21*d^3*c*b^2 + 2/21*x^21*d^4*b*a + 6/17*x^17*d^2*c^2*b^2 + 8/17*x^17*d^3*c*b*a + 1/17*x^17*d^4*a^2 + 4/13*x^13*d*c^3*b^2 + 12/13*x^13*d^2*c^2*b*a + 4/13*x^13*d^3*c*a^2 + 1/9*x^9*c^4*b^2 + 8/9*x^9*d*c^3*b*a + 2/3*x^9*d^2*c^2*a^2 + 2/5*x^5*c^4*b*a + 4/5*x^5*d*c^3*a^2 + x*c^4*a^2","A",0
154,1,132,0,1.076803," ","integrate((b*x^4+a)^2*(d*x^4+c)^3,x, algorithm=""fricas"")","\frac{1}{21} x^{21} d^{3} b^{2} + \frac{3}{17} x^{17} d^{2} c b^{2} + \frac{2}{17} x^{17} d^{3} b a + \frac{3}{13} x^{13} d c^{2} b^{2} + \frac{6}{13} x^{13} d^{2} c b a + \frac{1}{13} x^{13} d^{3} a^{2} + \frac{1}{9} x^{9} c^{3} b^{2} + \frac{2}{3} x^{9} d c^{2} b a + \frac{1}{3} x^{9} d^{2} c a^{2} + \frac{2}{5} x^{5} c^{3} b a + \frac{3}{5} x^{5} d c^{2} a^{2} + x c^{3} a^{2}"," ",0,"1/21*x^21*d^3*b^2 + 3/17*x^17*d^2*c*b^2 + 2/17*x^17*d^3*b*a + 3/13*x^13*d*c^2*b^2 + 6/13*x^13*d^2*c*b*a + 1/13*x^13*d^3*a^2 + 1/9*x^9*c^3*b^2 + 2/3*x^9*d*c^2*b*a + 1/3*x^9*d^2*c*a^2 + 2/5*x^5*c^3*b*a + 3/5*x^5*d*c^2*a^2 + x*c^3*a^2","A",0
155,1,91,0,0.558839," ","integrate((b*x^4+a)^2*(d*x^4+c)^2,x, algorithm=""fricas"")","\frac{1}{17} x^{17} d^{2} b^{2} + \frac{2}{13} x^{13} d c b^{2} + \frac{2}{13} x^{13} d^{2} b a + \frac{1}{9} x^{9} c^{2} b^{2} + \frac{4}{9} x^{9} d c b a + \frac{1}{9} x^{9} d^{2} a^{2} + \frac{2}{5} x^{5} c^{2} b a + \frac{2}{5} x^{5} d c a^{2} + x c^{2} a^{2}"," ",0,"1/17*x^17*d^2*b^2 + 2/13*x^13*d*c*b^2 + 2/13*x^13*d^2*b*a + 1/9*x^9*c^2*b^2 + 4/9*x^9*d*c*b*a + 1/9*x^9*d^2*a^2 + 2/5*x^5*c^2*b*a + 2/5*x^5*d*c*a^2 + x*c^2*a^2","A",0
156,1,50,0,0.533712," ","integrate((b*x^4+a)^2*(d*x^4+c),x, algorithm=""fricas"")","\frac{1}{13} x^{13} d b^{2} + \frac{1}{9} x^{9} c b^{2} + \frac{2}{9} x^{9} d b a + \frac{2}{5} x^{5} c b a + \frac{1}{5} x^{5} d a^{2} + x c a^{2}"," ",0,"1/13*x^13*d*b^2 + 1/9*x^9*c*b^2 + 2/9*x^9*d*b*a + 2/5*x^5*c*b*a + 1/5*x^5*d*a^2 + x*c*a^2","A",0
157,1,1239,0,1.182454," ","integrate((b*x^4+a)^2/(d*x^4+c),x, algorithm=""fricas"")","\frac{4 \, b^{2} d x^{5} + 20 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c^{2} d^{7} x \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{3}{4}} - c^{2} d^{7} \sqrt{\frac{c^{2} d^{4} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x^{2}}{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{3}{4}}}{b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}}\right) + 5 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} \log\left(c d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x\right) - 5 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} \log\left(-c d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x\right) - 20 \, {\left(b^{2} c - 2 \, a b d\right)} x}{20 \, d^{2}}"," ",0,"1/20*(4*b^2*d*x^5 + 20*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4)*arctan(-(c^2*d^7*x*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(3/4) - c^2*d^7*sqrt((c^2*d^4*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9)) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x^2)/(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4))*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(3/4))/(b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)) + 5*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4)*log(c*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x) - 5*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4)*log(-c*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x) - 20*(b^2*c - 2*a*b*d)*x)/d^2","B",0
158,1,1335,0,0.932249," ","integrate((b*x^4+a)^2/(d*x^4+c)^2,x, algorithm=""fricas"")","\frac{16 \, b^{2} c d x^{5} + 4 \, {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{c^{5} d^{7} x \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{3}{4}} - c^{5} d^{7} \sqrt{\frac{c^{4} d^{4} \sqrt{-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}} + {\left(25 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 26 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4}\right)} x^{2}}{25 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 26 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4}}} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{3}{4}}}{125 \, b^{6} c^{6} - 150 \, a b^{5} c^{5} d - 165 \, a^{2} b^{4} c^{4} d^{2} + 172 \, a^{3} b^{3} c^{3} d^{3} + 99 \, a^{4} b^{2} c^{2} d^{4} - 54 \, a^{5} b c d^{5} - 27 \, a^{6} d^{6}}\right) + {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} \log\left(c^{2} d^{2} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} - {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} x\right) - {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} \log\left(-c^{2} d^{2} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} - {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} x\right) + 4 \, {\left(5 \, b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{16 \, {\left(c d^{3} x^{4} + c^{2} d^{2}\right)}}"," ",0,"1/16*(16*b^2*c*d*x^5 + 4*(c*d^3*x^4 + c^2*d^2)*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4)*arctan((c^5*d^7*x*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(3/4) - c^5*d^7*sqrt((c^4*d^4*sqrt(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9)) + (25*b^4*c^4 - 20*a*b^3*c^3*d - 26*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + 9*a^4*d^4)*x^2)/(25*b^4*c^4 - 20*a*b^3*c^3*d - 26*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + 9*a^4*d^4))*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(3/4))/(125*b^6*c^6 - 150*a*b^5*c^5*d - 165*a^2*b^4*c^4*d^2 + 172*a^3*b^3*c^3*d^3 + 99*a^4*b^2*c^2*d^4 - 54*a^5*b*c*d^5 - 27*a^6*d^6)) + (c*d^3*x^4 + c^2*d^2)*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4)*log(c^2*d^2*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4) - (5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*x) - (c*d^3*x^4 + c^2*d^2)*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4)*log(-c^2*d^2*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4) - (5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*x) + 4*(5*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/(c*d^3*x^4 + c^2*d^2)","B",0
159,1,1411,0,1.201918," ","integrate((b*x^4+a)^2/(d*x^4+c)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(9 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 7 \, a^{2} d^{3}\right)} x^{5} - 4 \, {\left(c^{2} d^{4} x^{8} + 2 \, c^{3} d^{3} x^{4} + c^{4} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c^{8} d^{7} x \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{3}{4}} - c^{8} d^{7} \sqrt{\frac{c^{6} d^{4} \sqrt{-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}} + {\left(25 \, b^{4} c^{4} + 60 \, a b^{3} c^{3} d + 246 \, a^{2} b^{2} c^{2} d^{2} + 252 \, a^{3} b c d^{3} + 441 \, a^{4} d^{4}\right)} x^{2}}{25 \, b^{4} c^{4} + 60 \, a b^{3} c^{3} d + 246 \, a^{2} b^{2} c^{2} d^{2} + 252 \, a^{3} b c d^{3} + 441 \, a^{4} d^{4}}} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{3}{4}}}{125 \, b^{6} c^{6} + 450 \, a b^{5} c^{5} d + 2115 \, a^{2} b^{4} c^{4} d^{2} + 3996 \, a^{3} b^{3} c^{3} d^{3} + 8883 \, a^{4} b^{2} c^{2} d^{4} + 7938 \, a^{5} b c d^{5} + 9261 \, a^{6} d^{6}}\right) - {\left(c^{2} d^{4} x^{8} + 2 \, c^{3} d^{3} x^{4} + c^{4} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} \log\left(c^{3} d^{2} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} + {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} x\right) + {\left(c^{2} d^{4} x^{8} + 2 \, c^{3} d^{3} x^{4} + c^{4} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} \log\left(-c^{3} d^{2} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} + {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} x\right) + 4 \, {\left(5 \, b^{2} c^{3} + 6 \, a b c^{2} d - 11 \, a^{2} c d^{2}\right)} x}{128 \, {\left(c^{2} d^{4} x^{8} + 2 \, c^{3} d^{3} x^{4} + c^{4} d^{2}\right)}}"," ",0,"-1/128*(4*(9*b^2*c^2*d - 2*a*b*c*d^2 - 7*a^2*d^3)*x^5 - 4*(c^2*d^4*x^8 + 2*c^3*d^3*x^4 + c^4*d^2)*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4)*arctan(-(c^8*d^7*x*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(3/4) - c^8*d^7*sqrt((c^6*d^4*sqrt(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9)) + (25*b^4*c^4 + 60*a*b^3*c^3*d + 246*a^2*b^2*c^2*d^2 + 252*a^3*b*c*d^3 + 441*a^4*d^4)*x^2)/(25*b^4*c^4 + 60*a*b^3*c^3*d + 246*a^2*b^2*c^2*d^2 + 252*a^3*b*c*d^3 + 441*a^4*d^4))*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(3/4))/(125*b^6*c^6 + 450*a*b^5*c^5*d + 2115*a^2*b^4*c^4*d^2 + 3996*a^3*b^3*c^3*d^3 + 8883*a^4*b^2*c^2*d^4 + 7938*a^5*b*c*d^5 + 9261*a^6*d^6)) - (c^2*d^4*x^8 + 2*c^3*d^3*x^4 + c^4*d^2)*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4)*log(c^3*d^2*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4) + (5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*x) + (c^2*d^4*x^8 + 2*c^3*d^3*x^4 + c^4*d^2)*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4)*log(-c^3*d^2*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4) + (5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*x) + 4*(5*b^2*c^3 + 6*a*b*c^2*d - 11*a^2*c*d^2)*x)/(c^2*d^4*x^8 + 2*c^3*d^3*x^4 + c^4*d^2)","B",0
160,1,2477,0,1.220104," ","integrate((d*x^4+c)^4/(b*x^4+a),x, algorithm=""fricas"")","\frac{180 \, b^{3} d^{4} x^{13} + 260 \, {\left(4 \, b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{9} + 468 \, {\left(6 \, b^{3} c^{2} d^{2} - 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{5} + 2340 \, b^{4} \left(-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{2} b^{13} x \left(-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}\right)^{\frac{3}{4}} - a^{2} b^{13} \sqrt{\frac{a^{2} b^{8} \sqrt{-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}} + {\left(b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}\right)} x^{2}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}} \left(-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}\right)^{\frac{3}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) + 585 \, b^{4} \left(-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \log\left(a b^{4} \left(-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}\right)^{\frac{1}{4}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x\right) - 585 \, b^{4} \left(-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \log\left(-a b^{4} \left(-\frac{b^{16} c^{16} - 16 \, a b^{15} c^{15} d + 120 \, a^{2} b^{14} c^{14} d^{2} - 560 \, a^{3} b^{13} c^{13} d^{3} + 1820 \, a^{4} b^{12} c^{12} d^{4} - 4368 \, a^{5} b^{11} c^{11} d^{5} + 8008 \, a^{6} b^{10} c^{10} d^{6} - 11440 \, a^{7} b^{9} c^{9} d^{7} + 12870 \, a^{8} b^{8} c^{8} d^{8} - 11440 \, a^{9} b^{7} c^{7} d^{9} + 8008 \, a^{10} b^{6} c^{6} d^{10} - 4368 \, a^{11} b^{5} c^{5} d^{11} + 1820 \, a^{12} b^{4} c^{4} d^{12} - 560 \, a^{13} b^{3} c^{3} d^{13} + 120 \, a^{14} b^{2} c^{2} d^{14} - 16 \, a^{15} b c d^{15} + a^{16} d^{16}}{a^{3} b^{17}}\right)^{\frac{1}{4}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x\right) + 2340 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x}{2340 \, b^{4}}"," ",0,"1/2340*(180*b^3*d^4*x^13 + 260*(4*b^3*c*d^3 - a*b^2*d^4)*x^9 + 468*(6*b^3*c^2*d^2 - 4*a*b^2*c*d^3 + a^2*b*d^4)*x^5 + 2340*b^4*(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17))^(1/4)*arctan(-(a^2*b^13*x*(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17))^(3/4) - a^2*b^13*sqrt((a^2*b^8*sqrt(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17)) + (b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)*x^2)/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))*(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17))^(3/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) + 585*b^4*(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17))^(1/4)*log(a*b^4*(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17))^(1/4) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x) - 585*b^4*(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17))^(1/4)*log(-a*b^4*(-(b^16*c^16 - 16*a*b^15*c^15*d + 120*a^2*b^14*c^14*d^2 - 560*a^3*b^13*c^13*d^3 + 1820*a^4*b^12*c^12*d^4 - 4368*a^5*b^11*c^11*d^5 + 8008*a^6*b^10*c^10*d^6 - 11440*a^7*b^9*c^9*d^7 + 12870*a^8*b^8*c^8*d^8 - 11440*a^9*b^7*c^7*d^9 + 8008*a^10*b^6*c^6*d^10 - 4368*a^11*b^5*c^5*d^11 + 1820*a^12*b^4*c^4*d^12 - 560*a^13*b^3*c^3*d^13 + 120*a^14*b^2*c^2*d^14 - 16*a^15*b*c*d^15 + a^16*d^16)/(a^3*b^17))^(1/4) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x) + 2340*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*x)/b^4","B",0
161,1,1855,0,1.478719," ","integrate((d*x^4+c)^3/(b*x^4+a),x, algorithm=""fricas"")","\frac{20 \, b^{2} d^{3} x^{9} + 36 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{5} - 180 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{a^{2} b^{10} x \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{3}{4}} - a^{2} b^{10} \sqrt{\frac{a^{2} b^{6} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x^{2}}{b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}}} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{3}{4}}}{b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}}\right) - 45 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(a b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x\right) + 45 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(-a b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x\right) + 180 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} x}{180 \, b^{3}}"," ",0,"1/180*(20*b^2*d^3*x^9 + 36*(3*b^2*c*d^2 - a*b*d^3)*x^5 - 180*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4)*arctan((a^2*b^10*x*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(3/4) - a^2*b^10*sqrt((a^2*b^6*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13)) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*x^2)/(b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6))*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(3/4))/(b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)) - 45*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4)*log(a*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x) + 45*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4)*log(-a*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x) + 180*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*x)/b^3","B",0
162,1,1240,0,1.430969," ","integrate((d*x^4+c)^2/(b*x^4+a),x, algorithm=""fricas"")","\frac{4 \, b d^{2} x^{5} + 20 \, b^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{2} b^{7} x \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}\right)^{\frac{3}{4}} - a^{2} b^{7} \sqrt{\frac{a^{2} b^{4} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x^{2}}{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}\right)^{\frac{3}{4}}}{b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}}\right) + 5 \, b^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \log\left(a b^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x\right) - 5 \, b^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \log\left(-a b^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{a^{3} b^{9}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x\right) + 20 \, {\left(2 \, b c d - a d^{2}\right)} x}{20 \, b^{2}}"," ",0,"1/20*(4*b*d^2*x^5 + 20*b^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9))^(1/4)*arctan(-(a^2*b^7*x*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9))^(3/4) - a^2*b^7*sqrt((a^2*b^4*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9)) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x^2)/(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4))*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9))^(3/4))/(b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)) + 5*b^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9))^(1/4)*log(a*b^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x) - 5*b^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9))^(1/4)*log(-a*b^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(a^3*b^9))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x) + 20*(2*b*c*d - a*d^2)*x)/b^2","B",0
163,1,639,0,0.744220," ","integrate((d*x^4+c)/(b*x^4+a),x, algorithm=""fricas"")","-\frac{4 \, b \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{a^{2} b^{4} x \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}\right)^{\frac{3}{4}} - a^{2} b^{4} \sqrt{\frac{a^{2} b^{2} \sqrt{-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}} \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}\right)^{\frac{3}{4}}}{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}\right) + b \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \log\left(a b \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} - {\left(b c - a d\right)} x\right) - b \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \log\left(-a b \left(-\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} - {\left(b c - a d\right)} x\right) - 4 \, d x}{4 \, b}"," ",0,"-1/4*(4*b*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5))^(1/4)*arctan((a^2*b^4*x*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5))^(3/4) - a^2*b^4*sqrt((a^2*b^2*sqrt(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5)) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5))^(3/4))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)) + b*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5))^(1/4)*log(a*b*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5))^(1/4) - (b*c - a*d)*x) - b*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5))^(1/4)*log(-a*b*(-(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*b^5))^(1/4) - (b*c - a*d)*x) - 4*d*x)/b","B",0
164,1,1356,0,1.742304," ","integrate(1/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","-\left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{3}{4}} x - {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{b^{2} x^{2} + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}}}{b^{2}}}}{b^{2}}\right) + \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{3}{4}} x - {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{d^{2} x^{2} + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \sqrt{-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}}}{d^{2}}}}{d^{2}}\right) + \frac{1}{4} \, \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \log\left(b x + {\left(a b c - a^{2} d\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}}\right) - \frac{1}{4} \, \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \log\left(b x - {\left(a b c - a^{2} d\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}}\right) - \frac{1}{4} \, \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(d x + {\left(b c^{2} - a c d\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}}\right) + \frac{1}{4} \, \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(d x - {\left(b c^{2} - a c d\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}}\right)"," ",0,"-(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*arctan(((a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(3/4)*x - (a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(3/4)*sqrt((b^2*x^2 + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)))/b^2))/b^2) + (-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*arctan(((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(3/4)*x - (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(3/4)*sqrt((d^2*x^2 + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*sqrt(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4)))/d^2))/d^2) + 1/4*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*log(b*x + (a*b*c - a^2*d)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)) - 1/4*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*log(b*x - (a*b*c - a^2*d)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)) - 1/4*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*log(d*x + (b*c^2 - a*c*d)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)) + 1/4*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*log(d*x - (b*c^2 - a*c*d)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4))","B",0
165,1,3299,0,58.700432," ","integrate(1/(b*x^4+a)/(d*x^4+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{6} c^{11} - 6 \, a b^{5} c^{10} d + 15 \, a^{2} b^{4} c^{9} d^{2} - 20 \, a^{3} b^{3} c^{8} d^{3} + 15 \, a^{4} b^{2} c^{7} d^{4} - 6 \, a^{5} b c^{6} d^{5} + a^{6} c^{5} d^{6}\right)} x \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{3}{4}} - {\left(b^{6} c^{11} - 6 \, a b^{5} c^{10} d + 15 \, a^{2} b^{4} c^{9} d^{2} - 20 \, a^{3} b^{3} c^{8} d^{3} + 15 \, a^{4} b^{2} c^{7} d^{4} - 6 \, a^{5} b c^{6} d^{5} + a^{6} c^{5} d^{6}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(49 \, b^{2} c^{2} d^{2} - 42 \, a b c d^{3} + 9 \, a^{2} d^{4}\right)} x^{2} + {\left(b^{4} c^{8} - 4 \, a b^{3} c^{7} d + 6 \, a^{2} b^{2} c^{6} d^{2} - 4 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} \sqrt{-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}}}{49 \, b^{2} c^{2} d^{2} - 42 \, a b c d^{3} + 9 \, a^{2} d^{4}}}}{343 \, b^{3} c^{3} d^{2} - 441 \, a b^{2} c^{2} d^{3} + 189 \, a^{2} b c d^{4} - 27 \, a^{3} d^{5}}\right) + 16 \, \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)} \arctan\left(-\frac{{\left(a^{2} b^{6} c^{6} - 6 \, a^{3} b^{5} c^{5} d + 15 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 15 \, a^{6} b^{2} c^{2} d^{4} - 6 \, a^{7} b c d^{5} + a^{8} d^{6}\right)} \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{3}{4}} x - {\left(a^{2} b^{6} c^{6} - 6 \, a^{3} b^{5} c^{5} d + 15 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 15 \, a^{6} b^{2} c^{2} d^{4} - 6 \, a^{7} b c d^{5} + a^{8} d^{6}\right)} \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{3}{4}} \sqrt{\frac{b^{4} x^{2} + {\left(a^{2} b^{4} c^{4} - 4 \, a^{3} b^{3} c^{3} d + 6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4}\right)} \sqrt{-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}}}{b^{4}}}}{b^{5}}\right) + 4 \, \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)} \log\left(b^{2} x + \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}\right) - 4 \, \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)} \log\left(b^{2} x - \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}\right) + {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(7 \, b c d - 3 \, a d^{2}\right)} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}}\right) - {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(7 \, b c d - 3 \, a d^{2}\right)} x - {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}}\right) - 4 \, d x}{16 \, {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)}}"," ",0,"1/16*(4*((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)*arctan(((b^6*c^11 - 6*a*b^5*c^10*d + 15*a^2*b^4*c^9*d^2 - 20*a^3*b^3*c^8*d^3 + 15*a^4*b^2*c^7*d^4 - 6*a^5*b*c^6*d^5 + a^6*c^5*d^6)*x*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(3/4) - (b^6*c^11 - 6*a*b^5*c^10*d + 15*a^2*b^4*c^9*d^2 - 20*a^3*b^3*c^8*d^3 + 15*a^4*b^2*c^7*d^4 - 6*a^5*b*c^6*d^5 + a^6*c^5*d^6)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(3/4)*sqrt(((49*b^2*c^2*d^2 - 42*a*b*c*d^3 + 9*a^2*d^4)*x^2 + (b^4*c^8 - 4*a*b^3*c^7*d + 6*a^2*b^2*c^6*d^2 - 4*a^3*b*c^5*d^3 + a^4*c^4*d^4)*sqrt(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8)))/(49*b^2*c^2*d^2 - 42*a*b*c*d^3 + 9*a^2*d^4)))/(343*b^3*c^3*d^2 - 441*a*b^2*c^2*d^3 + 189*a^2*b*c*d^4 - 27*a^3*d^5)) + 16*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d)*arctan(-((a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5 + a^8*d^6)*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(3/4)*x - (a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5 + a^8*d^6)*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(3/4)*sqrt((b^4*x^2 + (a^2*b^4*c^4 - 4*a^3*b^3*c^3*d + 6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4)*sqrt(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8)))/b^4))/b^5) + 4*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d)*log(b^2*x + (-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)) - 4*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d)*log(b^2*x - (-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)) + ((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)*log(-(7*b*c*d - 3*a*d^2)*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)) - ((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)*log(-(7*b*c*d - 3*a*d^2)*x - (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)) - 4*d*x)/((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d)","B",0
166,1,3222,0,1.488933," ","integrate((d*x^4+c)^5/(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{720 \, a b^{4} d^{5} x^{17} + 80 \, {\left(65 \, a b^{4} c d^{4} - 17 \, a^{2} b^{3} d^{5}\right)} x^{13} + 208 \, {\left(90 \, a b^{4} c^{2} d^{3} - 65 \, a^{2} b^{3} c d^{4} + 17 \, a^{3} b^{2} d^{5}\right)} x^{9} + 1872 \, {\left(50 \, a b^{4} c^{3} d^{2} - 90 \, a^{2} b^{3} c^{2} d^{3} + 65 \, a^{3} b^{2} c d^{4} - 17 \, a^{4} b d^{5}\right)} x^{5} + 2340 \, {\left(a b^{6} x^{4} + a^{2} b^{5}\right)} \left(-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{5} b^{16} x \left(-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}\right)^{\frac{3}{4}} - a^{5} b^{16} \sqrt{\frac{a^{4} b^{10} \sqrt{-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}} + {\left(9 \, b^{10} c^{10} + 30 \, a b^{9} c^{9} d - 275 \, a^{2} b^{8} c^{8} d^{2} + 40 \, a^{3} b^{7} c^{7} d^{3} + 3010 \, a^{4} b^{6} c^{6} d^{4} - 9548 \, a^{5} b^{5} c^{5} d^{5} + 14770 \, a^{6} b^{4} c^{4} d^{6} - 13400 \, a^{7} b^{3} c^{3} d^{7} + 7285 \, a^{8} b^{2} c^{2} d^{8} - 2210 \, a^{9} b c d^{9} + 289 \, a^{10} d^{10}\right)} x^{2}}{9 \, b^{10} c^{10} + 30 \, a b^{9} c^{9} d - 275 \, a^{2} b^{8} c^{8} d^{2} + 40 \, a^{3} b^{7} c^{7} d^{3} + 3010 \, a^{4} b^{6} c^{6} d^{4} - 9548 \, a^{5} b^{5} c^{5} d^{5} + 14770 \, a^{6} b^{4} c^{4} d^{6} - 13400 \, a^{7} b^{3} c^{3} d^{7} + 7285 \, a^{8} b^{2} c^{2} d^{8} - 2210 \, a^{9} b c d^{9} + 289 \, a^{10} d^{10}}} \left(-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}\right)^{\frac{3}{4}}}{27 \, b^{15} c^{15} + 135 \, a b^{14} c^{14} d - 1125 \, a^{2} b^{13} c^{13} d^{2} - 1945 \, a^{3} b^{12} c^{12} d^{3} + 25095 \, a^{4} b^{11} c^{11} d^{4} - 42141 \, a^{5} b^{10} c^{10} d^{5} - 131945 \, a^{6} b^{9} c^{9} d^{6} + 774675 \, a^{7} b^{8} c^{8} d^{7} - 1837935 \, a^{8} b^{7} c^{7} d^{8} + 2700885 \, a^{9} b^{6} c^{6} d^{9} - 2702799 \, a^{10} b^{5} c^{5} d^{10} + 1889685 \, a^{11} b^{4} c^{4} d^{11} - 914675 \, a^{12} b^{3} c^{3} d^{12} + 293505 \, a^{13} b^{2} c^{2} d^{13} - 56355 \, a^{14} b c d^{14} + 4913 \, a^{15} d^{15}}\right) + 585 \, {\left(a b^{6} x^{4} + a^{2} b^{5}\right)} \left(-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}\right)^{\frac{1}{4}} \log\left(a^{2} b^{5} \left(-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}\right)^{\frac{1}{4}} + {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 50 \, a^{2} b^{3} c^{3} d^{2} + 90 \, a^{3} b^{2} c^{2} d^{3} - 65 \, a^{4} b c d^{4} + 17 \, a^{5} d^{5}\right)} x\right) - 585 \, {\left(a b^{6} x^{4} + a^{2} b^{5}\right)} \left(-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}\right)^{\frac{1}{4}} \log\left(-a^{2} b^{5} \left(-\frac{81 \, b^{20} c^{20} + 540 \, a b^{19} c^{19} d - 4050 \, a^{2} b^{18} c^{18} d^{2} - 15780 \, a^{3} b^{17} c^{17} d^{3} + 132205 \, a^{4} b^{16} c^{16} d^{4} - 13264 \, a^{5} b^{15} c^{15} d^{5} - 1960920 \, a^{6} b^{14} c^{14} d^{6} + 6137200 \, a^{7} b^{13} c^{13} d^{7} - 500110 \, a^{8} b^{12} c^{12} d^{8} - 48530040 \, a^{9} b^{11} c^{11} d^{9} + 174873556 \, a^{10} b^{10} c^{10} d^{10} - 360900280 \, a^{11} b^{9} c^{9} d^{11} + 517559250 \, a^{12} b^{8} c^{8} d^{12} - 548231440 \, a^{13} b^{7} c^{7} d^{13} + 438700840 \, a^{14} b^{6} c^{6} d^{14} - 266040144 \, a^{15} b^{5} c^{5} d^{15} + 120836285 \, a^{16} b^{4} c^{4} d^{16} - 39944900 \, a^{17} b^{3} c^{3} d^{17} + 9094830 \, a^{18} b^{2} c^{2} d^{18} - 1277380 \, a^{19} b c d^{19} + 83521 \, a^{20} d^{20}}{a^{7} b^{21}}\right)^{\frac{1}{4}} + {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 50 \, a^{2} b^{3} c^{3} d^{2} + 90 \, a^{3} b^{2} c^{2} d^{3} - 65 \, a^{4} b c d^{4} + 17 \, a^{5} d^{5}\right)} x\right) + 2340 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 50 \, a^{2} b^{3} c^{3} d^{2} - 90 \, a^{3} b^{2} c^{2} d^{3} + 65 \, a^{4} b c d^{4} - 17 \, a^{5} d^{5}\right)} x}{9360 \, {\left(a b^{6} x^{4} + a^{2} b^{5}\right)}}"," ",0,"1/9360*(720*a*b^4*d^5*x^17 + 80*(65*a*b^4*c*d^4 - 17*a^2*b^3*d^5)*x^13 + 208*(90*a*b^4*c^2*d^3 - 65*a^2*b^3*c*d^4 + 17*a^3*b^2*d^5)*x^9 + 1872*(50*a*b^4*c^3*d^2 - 90*a^2*b^3*c^2*d^3 + 65*a^3*b^2*c*d^4 - 17*a^4*b*d^5)*x^5 + 2340*(a*b^6*x^4 + a^2*b^5)*(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21))^(1/4)*arctan(-(a^5*b^16*x*(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21))^(3/4) - a^5*b^16*sqrt((a^4*b^10*sqrt(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21)) + (9*b^10*c^10 + 30*a*b^9*c^9*d - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 - 2210*a^9*b*c*d^9 + 289*a^10*d^10)*x^2)/(9*b^10*c^10 + 30*a*b^9*c^9*d - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 - 2210*a^9*b*c*d^9 + 289*a^10*d^10))*(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21))^(3/4))/(27*b^15*c^15 + 135*a*b^14*c^14*d - 1125*a^2*b^13*c^13*d^2 - 1945*a^3*b^12*c^12*d^3 + 25095*a^4*b^11*c^11*d^4 - 42141*a^5*b^10*c^10*d^5 - 131945*a^6*b^9*c^9*d^6 + 774675*a^7*b^8*c^8*d^7 - 1837935*a^8*b^7*c^7*d^8 + 2700885*a^9*b^6*c^6*d^9 - 2702799*a^10*b^5*c^5*d^10 + 1889685*a^11*b^4*c^4*d^11 - 914675*a^12*b^3*c^3*d^12 + 293505*a^13*b^2*c^2*d^13 - 56355*a^14*b*c*d^14 + 4913*a^15*d^15)) + 585*(a*b^6*x^4 + a^2*b^5)*(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21))^(1/4)*log(a^2*b^5*(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21))^(1/4) + (3*b^5*c^5 + 5*a*b^4*c^4*d - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 65*a^4*b*c*d^4 + 17*a^5*d^5)*x) - 585*(a*b^6*x^4 + a^2*b^5)*(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21))^(1/4)*log(-a^2*b^5*(-(81*b^20*c^20 + 540*a*b^19*c^19*d - 4050*a^2*b^18*c^18*d^2 - 15780*a^3*b^17*c^17*d^3 + 132205*a^4*b^16*c^16*d^4 - 13264*a^5*b^15*c^15*d^5 - 1960920*a^6*b^14*c^14*d^6 + 6137200*a^7*b^13*c^13*d^7 - 500110*a^8*b^12*c^12*d^8 - 48530040*a^9*b^11*c^11*d^9 + 174873556*a^10*b^10*c^10*d^10 - 360900280*a^11*b^9*c^9*d^11 + 517559250*a^12*b^8*c^8*d^12 - 548231440*a^13*b^7*c^7*d^13 + 438700840*a^14*b^6*c^6*d^14 - 266040144*a^15*b^5*c^5*d^15 + 120836285*a^16*b^4*c^4*d^16 - 39944900*a^17*b^3*c^3*d^17 + 9094830*a^18*b^2*c^2*d^18 - 1277380*a^19*b*c*d^19 + 83521*a^20*d^20)/(a^7*b^21))^(1/4) + (3*b^5*c^5 + 5*a*b^4*c^4*d - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 65*a^4*b*c*d^4 + 17*a^5*d^5)*x) + 2340*(b^5*c^5 - 5*a*b^4*c^4*d + 50*a^2*b^3*c^3*d^2 - 90*a^3*b^2*c^2*d^3 + 65*a^4*b*c*d^4 - 17*a^5*d^5)*x)/(a*b^6*x^4 + a^2*b^5)","B",0
167,1,2580,0,1.370076," ","integrate((d*x^4+c)^4/(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{80 \, a b^{3} d^{4} x^{13} + 16 \, {\left(36 \, a b^{3} c d^{3} - 13 \, a^{2} b^{2} d^{4}\right)} x^{9} + 144 \, {\left(30 \, a b^{3} c^{2} d^{2} - 36 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} x^{5} - 180 \, {\left(a b^{5} x^{4} + a^{2} b^{4}\right)} \left(-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{a^{5} b^{13} x \left(-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}\right)^{\frac{3}{4}} - a^{5} b^{13} \sqrt{\frac{a^{4} b^{8} \sqrt{-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}} + {\left(9 \, b^{8} c^{8} + 24 \, a b^{7} c^{7} d - 164 \, a^{2} b^{6} c^{6} d^{2} - 24 \, a^{3} b^{5} c^{5} d^{3} + 1110 \, a^{4} b^{4} c^{4} d^{4} - 2264 \, a^{5} b^{3} c^{3} d^{5} + 2076 \, a^{6} b^{2} c^{2} d^{6} - 936 \, a^{7} b c d^{7} + 169 \, a^{8} d^{8}\right)} x^{2}}{9 \, b^{8} c^{8} + 24 \, a b^{7} c^{7} d - 164 \, a^{2} b^{6} c^{6} d^{2} - 24 \, a^{3} b^{5} c^{5} d^{3} + 1110 \, a^{4} b^{4} c^{4} d^{4} - 2264 \, a^{5} b^{3} c^{3} d^{5} + 2076 \, a^{6} b^{2} c^{2} d^{6} - 936 \, a^{7} b c d^{7} + 169 \, a^{8} d^{8}}} \left(-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}\right)^{\frac{3}{4}}}{27 \, b^{12} c^{12} + 108 \, a b^{11} c^{11} d - 666 \, a^{2} b^{10} c^{10} d^{2} - 1124 \, a^{3} b^{9} c^{9} d^{3} + 8901 \, a^{4} b^{8} c^{8} d^{4} - 7848 \, a^{5} b^{7} c^{7} d^{5} - 34860 \, a^{6} b^{6} c^{6} d^{6} + 113688 \, a^{7} b^{5} c^{5} d^{7} - 161451 \, a^{8} b^{4} c^{4} d^{8} + 132924 \, a^{9} b^{3} c^{3} d^{9} - 65754 \, a^{10} b^{2} c^{2} d^{10} + 18252 \, a^{11} b c d^{11} - 2197 \, a^{12} d^{12}}\right) - 45 \, {\left(a b^{5} x^{4} + a^{2} b^{4}\right)} \left(-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}\right)^{\frac{1}{4}} \log\left(a^{2} b^{4} \left(-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}\right)^{\frac{1}{4}} - {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 13 \, a^{4} d^{4}\right)} x\right) + 45 \, {\left(a b^{5} x^{4} + a^{2} b^{4}\right)} \left(-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}\right)^{\frac{1}{4}} \log\left(-a^{2} b^{4} \left(-\frac{81 \, b^{16} c^{16} + 432 \, a b^{15} c^{15} d - 2376 \, a^{2} b^{14} c^{14} d^{2} - 8304 \, a^{3} b^{13} c^{13} d^{3} + 45724 \, a^{4} b^{12} c^{12} d^{4} + 20400 \, a^{5} b^{11} c^{11} d^{5} - 434808 \, a^{6} b^{10} c^{10} d^{6} + 772112 \, a^{7} b^{9} c^{9} d^{7} + 617958 \, a^{8} b^{8} c^{8} d^{8} - 4810608 \, a^{9} b^{7} c^{7} d^{9} + 9723912 \, a^{10} b^{6} c^{6} d^{10} - 11486160 \, a^{11} b^{5} c^{5} d^{11} + 8923164 \, a^{12} b^{4} c^{4} d^{12} - 4651504 \, a^{13} b^{3} c^{3} d^{13} + 1577784 \, a^{14} b^{2} c^{2} d^{14} - 316368 \, a^{15} b c d^{15} + 28561 \, a^{16} d^{16}}{a^{7} b^{17}}\right)^{\frac{1}{4}} - {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 13 \, a^{4} d^{4}\right)} x\right) + 180 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} - 36 \, a^{3} b c d^{3} + 13 \, a^{4} d^{4}\right)} x}{720 \, {\left(a b^{5} x^{4} + a^{2} b^{4}\right)}}"," ",0,"1/720*(80*a*b^3*d^4*x^13 + 16*(36*a*b^3*c*d^3 - 13*a^2*b^2*d^4)*x^9 + 144*(30*a*b^3*c^2*d^2 - 36*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*x^5 - 180*(a*b^5*x^4 + a^2*b^4)*(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17))^(1/4)*arctan((a^5*b^13*x*(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17))^(3/4) - a^5*b^13*sqrt((a^4*b^8*sqrt(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17)) + (9*b^8*c^8 + 24*a*b^7*c^7*d - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 - 936*a^7*b*c*d^7 + 169*a^8*d^8)*x^2)/(9*b^8*c^8 + 24*a*b^7*c^7*d - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 - 936*a^7*b*c*d^7 + 169*a^8*d^8))*(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17))^(3/4))/(27*b^12*c^12 + 108*a*b^11*c^11*d - 666*a^2*b^10*c^10*d^2 - 1124*a^3*b^9*c^9*d^3 + 8901*a^4*b^8*c^8*d^4 - 7848*a^5*b^7*c^7*d^5 - 34860*a^6*b^6*c^6*d^6 + 113688*a^7*b^5*c^5*d^7 - 161451*a^8*b^4*c^4*d^8 + 132924*a^9*b^3*c^3*d^9 - 65754*a^10*b^2*c^2*d^10 + 18252*a^11*b*c*d^11 - 2197*a^12*d^12)) - 45*(a*b^5*x^4 + a^2*b^4)*(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17))^(1/4)*log(a^2*b^4*(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17))^(1/4) - (3*b^4*c^4 + 4*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 13*a^4*d^4)*x) + 45*(a*b^5*x^4 + a^2*b^4)*(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17))^(1/4)*log(-a^2*b^4*(-(81*b^16*c^16 + 432*a*b^15*c^15*d - 2376*a^2*b^14*c^14*d^2 - 8304*a^3*b^13*c^13*d^3 + 45724*a^4*b^12*c^12*d^4 + 20400*a^5*b^11*c^11*d^5 - 434808*a^6*b^10*c^10*d^6 + 772112*a^7*b^9*c^9*d^7 + 617958*a^8*b^8*c^8*d^8 - 4810608*a^9*b^7*c^7*d^9 + 9723912*a^10*b^6*c^6*d^10 - 11486160*a^11*b^5*c^5*d^11 + 8923164*a^12*b^4*c^4*d^12 - 4651504*a^13*b^3*c^3*d^13 + 1577784*a^14*b^2*c^2*d^14 - 316368*a^15*b*c*d^15 + 28561*a^16*d^16)/(a^7*b^17))^(1/4) - (3*b^4*c^4 + 4*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 13*a^4*d^4)*x) + 180*(b^4*c^4 - 4*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 - 36*a^3*b*c*d^3 + 13*a^4*d^4)*x)/(a*b^5*x^4 + a^2*b^4)","B",0
168,1,1938,0,1.107819," ","integrate((d*x^4+c)^3/(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{16 \, a b^{2} d^{3} x^{9} + 48 \, {\left(5 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x^{5} + 60 \, {\left(a b^{4} x^{4} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{5} b^{10} x \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{3}{4}} - a^{5} b^{10} \sqrt{\frac{a^{4} b^{6} \sqrt{-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}} + {\left(b^{6} c^{6} + 2 \, a b^{5} c^{5} d - 9 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{3} b^{3} c^{3} d^{3} + 31 \, a^{4} b^{2} c^{2} d^{4} - 30 \, a^{5} b c d^{5} + 9 \, a^{6} d^{6}\right)} x^{2}}{b^{6} c^{6} + 2 \, a b^{5} c^{5} d - 9 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{3} b^{3} c^{3} d^{3} + 31 \, a^{4} b^{2} c^{2} d^{4} - 30 \, a^{5} b c d^{5} + 9 \, a^{6} d^{6}}} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{3}{4}}}{b^{9} c^{9} + 3 \, a b^{8} c^{8} d - 12 \, a^{2} b^{7} c^{7} d^{2} - 20 \, a^{3} b^{6} c^{6} d^{3} + 78 \, a^{4} b^{5} c^{5} d^{4} - 6 \, a^{5} b^{4} c^{4} d^{5} - 188 \, a^{6} b^{3} c^{3} d^{6} + 252 \, a^{7} b^{2} c^{2} d^{7} - 135 \, a^{8} b c d^{8} + 27 \, a^{9} d^{9}}\right) + 15 \, {\left(a b^{4} x^{4} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \log\left(3 \, a^{2} b^{3} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} + 3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} x\right) - 15 \, {\left(a b^{4} x^{4} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \log\left(-3 \, a^{2} b^{3} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} + 3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} x\right) + 20 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 9 \, a^{3} d^{3}\right)} x}{80 \, {\left(a b^{4} x^{4} + a^{2} b^{3}\right)}}"," ",0,"1/80*(16*a*b^2*d^3*x^9 + 48*(5*a*b^2*c*d^2 - 3*a^2*b*d^3)*x^5 + 60*(a*b^4*x^4 + a^2*b^3)*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4)*arctan(-(a^5*b^10*x*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(3/4) - a^5*b^10*sqrt((a^4*b^6*sqrt(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13)) + (b^6*c^6 + 2*a*b^5*c^5*d - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 - 30*a^5*b*c*d^5 + 9*a^6*d^6)*x^2)/(b^6*c^6 + 2*a*b^5*c^5*d - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 - 30*a^5*b*c*d^5 + 9*a^6*d^6))*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(3/4))/(b^9*c^9 + 3*a*b^8*c^8*d - 12*a^2*b^7*c^7*d^2 - 20*a^3*b^6*c^6*d^3 + 78*a^4*b^5*c^5*d^4 - 6*a^5*b^4*c^4*d^5 - 188*a^6*b^3*c^3*d^6 + 252*a^7*b^2*c^2*d^7 - 135*a^8*b*c*d^8 + 27*a^9*d^9)) + 15*(a*b^4*x^4 + a^2*b^3)*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4)*log(3*a^2*b^3*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4) + 3*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*x) - 15*(a*b^4*x^4 + a^2*b^3)*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4)*log(-3*a^2*b^3*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4) + 3*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*x) + 20*(b^3*c^3 - 3*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 9*a^3*d^3)*x)/(a*b^4*x^4 + a^2*b^3)","B",0
169,1,1335,0,1.379718," ","integrate((d*x^4+c)^2/(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{16 \, a b d^{2} x^{5} - 4 \, {\left(a b^{3} x^{4} + a^{2} b^{2}\right)} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{a^{5} b^{7} x \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}\right)^{\frac{3}{4}} - a^{5} b^{7} \sqrt{\frac{a^{4} b^{4} \sqrt{-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}} + {\left(9 \, b^{4} c^{4} + 12 \, a b^{3} c^{3} d - 26 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + 25 \, a^{4} d^{4}\right)} x^{2}}{9 \, b^{4} c^{4} + 12 \, a b^{3} c^{3} d - 26 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + 25 \, a^{4} d^{4}}} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}\right)^{\frac{3}{4}}}{27 \, b^{6} c^{6} + 54 \, a b^{5} c^{5} d - 99 \, a^{2} b^{4} c^{4} d^{2} - 172 \, a^{3} b^{3} c^{3} d^{3} + 165 \, a^{4} b^{2} c^{2} d^{4} + 150 \, a^{5} b c d^{5} - 125 \, a^{6} d^{6}}\right) - {\left(a b^{3} x^{4} + a^{2} b^{2}\right)} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(a^{2} b^{2} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}\right)^{\frac{1}{4}} - {\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} x\right) + {\left(a b^{3} x^{4} + a^{2} b^{2}\right)} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(-a^{2} b^{2} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} b^{9}}\right)^{\frac{1}{4}} - {\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} x\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + 5 \, a^{2} d^{2}\right)} x}{16 \, {\left(a b^{3} x^{4} + a^{2} b^{2}\right)}}"," ",0,"1/16*(16*a*b*d^2*x^5 - 4*(a*b^3*x^4 + a^2*b^2)*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9))^(1/4)*arctan((a^5*b^7*x*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9))^(3/4) - a^5*b^7*sqrt((a^4*b^4*sqrt(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9)) + (9*b^4*c^4 + 12*a*b^3*c^3*d - 26*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + 25*a^4*d^4)*x^2)/(9*b^4*c^4 + 12*a*b^3*c^3*d - 26*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + 25*a^4*d^4))*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9))^(3/4))/(27*b^6*c^6 + 54*a*b^5*c^5*d - 99*a^2*b^4*c^4*d^2 - 172*a^3*b^3*c^3*d^3 + 165*a^4*b^2*c^2*d^4 + 150*a^5*b*c*d^5 - 125*a^6*d^6)) - (a*b^3*x^4 + a^2*b^2)*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9))^(1/4)*log(a^2*b^2*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9))^(1/4) - (3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*x) + (a*b^3*x^4 + a^2*b^2)*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9))^(1/4)*log(-a^2*b^2*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*b^9))^(1/4) - (3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*x) + 4*(b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*x)/(a*b^3*x^4 + a^2*b^2)","B",0
170,1,711,0,0.829850," ","integrate((d*x^4+c)/(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a b^{2} x^{4} + a^{2} b\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{5} b^{4} x \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}\right)^{\frac{3}{4}} - a^{5} b^{4} \sqrt{\frac{a^{4} b^{2} \sqrt{-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}} + {\left(9 \, b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2}}{9 \, b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}}} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}\right)^{\frac{3}{4}}}{27 \, b^{3} c^{3} + 27 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}}\right) + {\left(a b^{2} x^{4} + a^{2} b\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \log\left(a^{2} b \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} + {\left(3 \, b c + a d\right)} x\right) - {\left(a b^{2} x^{4} + a^{2} b\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \log\left(-a^{2} b \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} + {\left(3 \, b c + a d\right)} x\right) + 4 \, {\left(b c - a d\right)} x}{16 \, {\left(a b^{2} x^{4} + a^{2} b\right)}}"," ",0,"1/16*(4*(a*b^2*x^4 + a^2*b)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5))^(1/4)*arctan(-(a^5*b^4*x*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5))^(3/4) - a^5*b^4*sqrt((a^4*b^2*sqrt(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5)) + (9*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2)/(9*b^2*c^2 + 6*a*b*c*d + a^2*d^2))*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5))^(3/4))/(27*b^3*c^3 + 27*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)) + (a*b^2*x^4 + a^2*b)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5))^(1/4)*log(a^2*b*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5))^(1/4) + (3*b*c + a*d)*x) - (a*b^2*x^4 + a^2*b)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5))^(1/4)*log(-a^2*b*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*b^5))^(1/4) + (3*b*c + a*d)*x) + 4*(b*c - a*d)*x)/(a*b^2*x^4 + a^2*b)","B",0
171,1,3299,0,59.891660," ","integrate(1/(b*x^4+a)^2/(d*x^4+c),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)} \left(-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(a^{5} b^{6} c^{6} - 6 \, a^{6} b^{5} c^{5} d + 15 \, a^{7} b^{4} c^{4} d^{2} - 20 \, a^{8} b^{3} c^{3} d^{3} + 15 \, a^{9} b^{2} c^{2} d^{4} - 6 \, a^{10} b c d^{5} + a^{11} d^{6}\right)} x \left(-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}\right)^{\frac{3}{4}} - {\left(a^{5} b^{6} c^{6} - 6 \, a^{6} b^{5} c^{5} d + 15 \, a^{7} b^{4} c^{4} d^{2} - 20 \, a^{8} b^{3} c^{3} d^{3} + 15 \, a^{9} b^{2} c^{2} d^{4} - 6 \, a^{10} b c d^{5} + a^{11} d^{6}\right)} \left(-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(9 \, b^{4} c^{2} - 42 \, a b^{3} c d + 49 \, a^{2} b^{2} d^{2}\right)} x^{2} + {\left(a^{4} b^{4} c^{4} - 4 \, a^{5} b^{3} c^{3} d + 6 \, a^{6} b^{2} c^{2} d^{2} - 4 \, a^{7} b c d^{3} + a^{8} d^{4}\right)} \sqrt{-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}}}{9 \, b^{4} c^{2} - 42 \, a b^{3} c d + 49 \, a^{2} b^{2} d^{2}}}}{27 \, b^{5} c^{3} - 189 \, a b^{4} c^{2} d + 441 \, a^{2} b^{3} c d^{2} - 343 \, a^{3} b^{2} d^{3}}\right) - 16 \, \left(-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right)^{\frac{1}{4}} {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)} \arctan\left(-\frac{{\left(b^{6} c^{8} - 6 \, a b^{5} c^{7} d + 15 \, a^{2} b^{4} c^{6} d^{2} - 20 \, a^{3} b^{3} c^{5} d^{3} + 15 \, a^{4} b^{2} c^{4} d^{4} - 6 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} \left(-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right)^{\frac{3}{4}} x - {\left(b^{6} c^{8} - 6 \, a b^{5} c^{7} d + 15 \, a^{2} b^{4} c^{6} d^{2} - 20 \, a^{3} b^{3} c^{5} d^{3} + 15 \, a^{4} b^{2} c^{4} d^{4} - 6 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} \left(-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right)^{\frac{3}{4}} \sqrt{\frac{d^{4} x^{2} + {\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right)} \sqrt{-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}}}{d^{4}}}}{d^{5}}\right) - 4 \, \left(-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right)^{\frac{1}{4}} {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)} \log\left(d^{2} x + \left(-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}\right) + 4 \, \left(-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right)^{\frac{1}{4}} {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)} \log\left(d^{2} x - \left(-\frac{d^{7}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}\right) + {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)} \left(-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(3 \, b^{2} c - 7 \, a b d\right)} x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \left(-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}\right)^{\frac{1}{4}}\right) - {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)} \left(-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(3 \, b^{2} c - 7 \, a b d\right)} x - {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \left(-\frac{81 \, b^{7} c^{4} - 756 \, a b^{6} c^{3} d + 2646 \, a^{2} b^{5} c^{2} d^{2} - 4116 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{7} b^{8} c^{8} - 8 \, a^{8} b^{7} c^{7} d + 28 \, a^{9} b^{6} c^{6} d^{2} - 56 \, a^{10} b^{5} c^{5} d^{3} + 70 \, a^{11} b^{4} c^{4} d^{4} - 56 \, a^{12} b^{3} c^{3} d^{5} + 28 \, a^{13} b^{2} c^{2} d^{6} - 8 \, a^{14} b c d^{7} + a^{15} d^{8}}\right)^{\frac{1}{4}}\right) - 4 \, b x}{16 \, {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)}}"," ",0,"-1/16*(4*((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d)*(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8))^(1/4)*arctan(((a^5*b^6*c^6 - 6*a^6*b^5*c^5*d + 15*a^7*b^4*c^4*d^2 - 20*a^8*b^3*c^3*d^3 + 15*a^9*b^2*c^2*d^4 - 6*a^10*b*c*d^5 + a^11*d^6)*x*(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8))^(3/4) - (a^5*b^6*c^6 - 6*a^6*b^5*c^5*d + 15*a^7*b^4*c^4*d^2 - 20*a^8*b^3*c^3*d^3 + 15*a^9*b^2*c^2*d^4 - 6*a^10*b*c*d^5 + a^11*d^6)*(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8))^(3/4)*sqrt(((9*b^4*c^2 - 42*a*b^3*c*d + 49*a^2*b^2*d^2)*x^2 + (a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3 + a^8*d^4)*sqrt(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8)))/(9*b^4*c^2 - 42*a*b^3*c*d + 49*a^2*b^2*d^2)))/(27*b^5*c^3 - 189*a*b^4*c^2*d + 441*a^2*b^3*c*d^2 - 343*a^3*b^2*d^3)) - 16*(-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8))^(1/4)*((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d)*arctan(-((b^6*c^8 - 6*a*b^5*c^7*d + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a^5*b*c^3*d^5 + a^6*c^2*d^6)*(-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8))^(3/4)*x - (b^6*c^8 - 6*a*b^5*c^7*d + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a^5*b*c^3*d^5 + a^6*c^2*d^6)*(-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8))^(3/4)*sqrt((d^4*x^2 + (b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 + a^4*c^2*d^4)*sqrt(-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)))/d^4))/d^5) - 4*(-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8))^(1/4)*((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d)*log(d^2*x + (-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8))^(1/4)*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)) + 4*(-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8))^(1/4)*((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d)*log(d^2*x - (-d^7/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8))^(1/4)*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)) + ((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d)*(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8))^(1/4)*log(-(3*b^2*c - 7*a*b*d)*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8))^(1/4)) - ((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d)*(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8))^(1/4)*log(-(3*b^2*c - 7*a*b*d)*x - (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*(-(81*b^7*c^4 - 756*a*b^6*c^3*d + 2646*a^2*b^5*c^2*d^2 - 4116*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^7*b^8*c^8 - 8*a^8*b^7*c^7*d + 28*a^9*b^6*c^6*d^2 - 56*a^10*b^5*c^5*d^3 + 70*a^11*b^4*c^4*d^4 - 56*a^12*b^3*c^3*d^5 + 28*a^13*b^2*c^2*d^6 - 8*a^14*b*c*d^7 + a^15*d^8))^(1/4)) - 4*b*x)/((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d)","B",0
172,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^2/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(5/2)/(-d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(3/2)/(-d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(-d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/2)/(-d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(3/2)/(-d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(5/2)/(-d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate((b*x^4+a)^(3/2)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate((b*x^4+a)^(1/2)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/2)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/2)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/2)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(7/2)/(-d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,1,315,0,3.923872," ","integrate((b*x^4+a)^(1/2)/(-b*c*x^4+a*c),x, algorithm=""fricas"")","-\left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} \sqrt{b x^{4} + a} c \left(\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} - \frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a b c^{3} \left(\frac{1}{a b c^{4}}\right)^{\frac{3}{4}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} b c x^{2} \left(\frac{1}{a b c^{4}}\right)^{\frac{1}{4}}}{\sqrt{b}}}{x}\right) + \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} \log\left(\frac{4 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a b c^{3} x^{3} \left(\frac{1}{a b c^{4}}\right)^{\frac{3}{4}} + 2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} a c x \left(\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} {\left(a c^{2} \sqrt{\frac{1}{a b c^{4}}} + x^{2}\right)}}{b x^{4} - a}\right) - \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{4 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a b c^{3} x^{3} \left(\frac{1}{a b c^{4}}\right)^{\frac{3}{4}} + 2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} a c x \left(\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} - \sqrt{b x^{4} + a} {\left(a c^{2} \sqrt{\frac{1}{a b c^{4}}} + x^{2}\right)}}{b x^{4} - a}\right)"," ",0,"-(1/4)^(1/4)*(1/(a*b*c^4))^(1/4)*arctan(((1/4)^(1/4)*sqrt(b*x^4 + a)*c*(1/(a*b*c^4))^(1/4) - (2*(1/4)^(3/4)*a*b*c^3*(1/(a*b*c^4))^(3/4) + (1/4)^(1/4)*b*c*x^2*(1/(a*b*c^4))^(1/4))/sqrt(b))/x) + 1/4*(1/4)^(1/4)*(1/(a*b*c^4))^(1/4)*log((4*(1/4)^(3/4)*a*b*c^3*x^3*(1/(a*b*c^4))^(3/4) + 2*(1/4)^(1/4)*a*c*x*(1/(a*b*c^4))^(1/4) + sqrt(b*x^4 + a)*(a*c^2*sqrt(1/(a*b*c^4)) + x^2))/(b*x^4 - a)) - 1/4*(1/4)^(1/4)*(1/(a*b*c^4))^(1/4)*log(-(4*(1/4)^(3/4)*a*b*c^3*x^3*(1/(a*b*c^4))^(3/4) + 2*(1/4)^(1/4)*a*c*x*(1/(a*b*c^4))^(1/4) - sqrt(b*x^4 + a)*(a*c^2*sqrt(1/(a*b*c^4)) + x^2))/(b*x^4 - a))","B",0
192,1,339,0,3.543516," ","integrate((-b*x^4+a)^(1/2)/(b*c*x^4+a*c),x, algorithm=""fricas"")","-\left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a b c^{3} \sqrt{-\frac{1}{b}} \left(-\frac{1}{a b c^{4}}\right)^{\frac{3}{4}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} {\left(b c x^{2} \sqrt{-\frac{1}{b}} + \sqrt{-b x^{4} + a} c\right)} \left(-\frac{1}{a b c^{4}}\right)^{\frac{1}{4}}}{x}\right) - \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{4 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a b c^{3} x^{3} \left(-\frac{1}{a b c^{4}}\right)^{\frac{3}{4}} + \sqrt{-b x^{4} + a} a c^{2} \sqrt{-\frac{1}{a b c^{4}}} - 2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} a c x \left(-\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} x^{2}}{b x^{4} + a}\right) + \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} \log\left(\frac{4 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a b c^{3} x^{3} \left(-\frac{1}{a b c^{4}}\right)^{\frac{3}{4}} - \sqrt{-b x^{4} + a} a c^{2} \sqrt{-\frac{1}{a b c^{4}}} - 2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} a c x \left(-\frac{1}{a b c^{4}}\right)^{\frac{1}{4}} - \sqrt{-b x^{4} + a} x^{2}}{b x^{4} + a}\right)"," ",0,"-(1/4)^(1/4)*(-1/(a*b*c^4))^(1/4)*arctan((2*(1/4)^(3/4)*a*b*c^3*sqrt(-1/b)*(-1/(a*b*c^4))^(3/4) + (1/4)^(1/4)*(b*c*x^2*sqrt(-1/b) + sqrt(-b*x^4 + a)*c)*(-1/(a*b*c^4))^(1/4))/x) - 1/4*(1/4)^(1/4)*(-1/(a*b*c^4))^(1/4)*log(-(4*(1/4)^(3/4)*a*b*c^3*x^3*(-1/(a*b*c^4))^(3/4) + sqrt(-b*x^4 + a)*a*c^2*sqrt(-1/(a*b*c^4)) - 2*(1/4)^(1/4)*a*c*x*(-1/(a*b*c^4))^(1/4) + sqrt(-b*x^4 + a)*x^2)/(b*x^4 + a)) + 1/4*(1/4)^(1/4)*(-1/(a*b*c^4))^(1/4)*log((4*(1/4)^(3/4)*a*b*c^3*x^3*(-1/(a*b*c^4))^(3/4) - sqrt(-b*x^4 + a)*a*c^2*sqrt(-1/(a*b*c^4)) - 2*(1/4)^(1/4)*a*c*x*(-1/(a*b*c^4))^(1/4) - sqrt(-b*x^4 + a)*x^2)/(b*x^4 + a))","B",0
193,1,2381,0,10.959179," ","integrate((b*x^4+a)^(7/4)/(d*x^4+c),x, algorithm=""fricas"")","\frac{4 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} b x + 16 \, d \left(\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c d^{2} x \sqrt{\frac{{\left(b^{7} c^{8} d^{4} - 7 \, a b^{6} c^{7} d^{5} + 21 \, a^{2} b^{5} c^{6} d^{6} - 35 \, a^{3} b^{4} c^{5} d^{7} + 35 \, a^{4} b^{3} c^{4} d^{8} - 21 \, a^{5} b^{2} c^{3} d^{9} + 7 \, a^{6} b c^{2} d^{10} - a^{7} c d^{11}\right)} x^{2} \sqrt{\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}} + {\left(b^{10} c^{10} - 10 \, a b^{9} c^{9} d + 45 \, a^{2} b^{8} c^{8} d^{2} - 120 \, a^{3} b^{7} c^{7} d^{3} + 210 \, a^{4} b^{6} c^{6} d^{4} - 252 \, a^{5} b^{5} c^{5} d^{5} + 210 \, a^{6} b^{4} c^{4} d^{6} - 120 \, a^{7} b^{3} c^{3} d^{7} + 45 \, a^{8} b^{2} c^{2} d^{8} - 10 \, a^{9} b c d^{9} + a^{10} d^{10}\right)} \sqrt{b x^{4} + a}}{x^{2}}} \left(\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}\right)^{\frac{1}{4}} + {\left(b^{5} c^{6} d^{2} - 5 \, a b^{4} c^{5} d^{3} + 10 \, a^{2} b^{3} c^{4} d^{4} - 10 \, a^{3} b^{2} c^{3} d^{5} + 5 \, a^{4} b c^{2} d^{6} - a^{5} c d^{7}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}\right)^{\frac{1}{4}}}{{\left(b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}\right)} x}\right) + 4 \, d \left(\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}\right)^{\frac{1}{4}} \arctan\left(\frac{d^{2} x \sqrt{\frac{{\left(256 \, b^{7} c^{4} d^{4} - 1792 \, a b^{6} c^{3} d^{5} + 4704 \, a^{2} b^{5} c^{2} d^{6} - 5488 \, a^{3} b^{4} c d^{7} + 2401 \, a^{4} b^{3} d^{8}\right)} x^{2} \sqrt{\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}} + {\left(4096 \, b^{10} c^{6} - 43008 \, a b^{9} c^{5} d + 188160 \, a^{2} b^{8} c^{4} d^{2} - 439040 \, a^{3} b^{7} c^{3} d^{3} + 576240 \, a^{4} b^{6} c^{2} d^{4} - 403368 \, a^{5} b^{5} c d^{5} + 117649 \, a^{6} b^{4} d^{6}\right)} \sqrt{b x^{4} + a}}{x^{2}}} \left(\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}\right)^{\frac{1}{4}} + {\left(64 \, b^{5} c^{3} d^{2} - 336 \, a b^{4} c^{2} d^{3} + 588 \, a^{2} b^{3} c d^{4} - 343 \, a^{3} b^{2} d^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}\right)^{\frac{1}{4}}}{{\left(256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}\right)} x}\right) + 4 \, d \left(\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}\right)^{\frac{1}{4}} \log\left(-\frac{c^{2} d^{6} x \left(\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}\right)^{\frac{3}{4}} + {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - 4 \, d \left(\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}\right)^{\frac{1}{4}} \log\left(\frac{c^{2} d^{6} x \left(\frac{b^{7} c^{7} - 7 \, a b^{6} c^{6} d + 21 \, a^{2} b^{5} c^{5} d^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 21 \, a^{5} b^{2} c^{2} d^{5} + 7 \, a^{6} b c d^{6} - a^{7} d^{7}}{c^{3} d^{8}}\right)^{\frac{3}{4}} - {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - d \left(\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}\right)^{\frac{1}{4}} \log\left(-\frac{d^{6} x \left(\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}\right)^{\frac{3}{4}} + {\left(64 \, b^{5} c^{3} - 336 \, a b^{4} c^{2} d + 588 \, a^{2} b^{3} c d^{2} - 343 \, a^{3} b^{2} d^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) + d \left(\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}\right)^{\frac{1}{4}} \log\left(\frac{d^{6} x \left(\frac{256 \, b^{7} c^{4} - 1792 \, a b^{6} c^{3} d + 4704 \, a^{2} b^{5} c^{2} d^{2} - 5488 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{d^{8}}\right)^{\frac{3}{4}} - {\left(64 \, b^{5} c^{3} - 336 \, a b^{4} c^{2} d + 588 \, a^{2} b^{3} c d^{2} - 343 \, a^{3} b^{2} d^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right)}{16 \, d}"," ",0,"1/16*(4*(b*x^4 + a)^(3/4)*b*x + 16*d*((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8))^(1/4)*arctan(-(c*d^2*x*sqrt(((b^7*c^8*d^4 - 7*a*b^6*c^7*d^5 + 21*a^2*b^5*c^6*d^6 - 35*a^3*b^4*c^5*d^7 + 35*a^4*b^3*c^4*d^8 - 21*a^5*b^2*c^3*d^9 + 7*a^6*b*c^2*d^10 - a^7*c*d^11)*x^2*sqrt((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8)) + (b^10*c^10 - 10*a*b^9*c^9*d + 45*a^2*b^8*c^8*d^2 - 120*a^3*b^7*c^7*d^3 + 210*a^4*b^6*c^6*d^4 - 252*a^5*b^5*c^5*d^5 + 210*a^6*b^4*c^4*d^6 - 120*a^7*b^3*c^3*d^7 + 45*a^8*b^2*c^2*d^8 - 10*a^9*b*c*d^9 + a^10*d^10)*sqrt(b*x^4 + a))/x^2)*((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8))^(1/4) + (b^5*c^6*d^2 - 5*a*b^4*c^5*d^3 + 10*a^2*b^3*c^4*d^4 - 10*a^3*b^2*c^3*d^5 + 5*a^4*b*c^2*d^6 - a^5*c*d^7)*(b*x^4 + a)^(1/4)*((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8))^(1/4))/((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)*x)) + 4*d*((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8)^(1/4)*arctan((d^2*x*sqrt(((256*b^7*c^4*d^4 - 1792*a*b^6*c^3*d^5 + 4704*a^2*b^5*c^2*d^6 - 5488*a^3*b^4*c*d^7 + 2401*a^4*b^3*d^8)*x^2*sqrt((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8) + (4096*b^10*c^6 - 43008*a*b^9*c^5*d + 188160*a^2*b^8*c^4*d^2 - 439040*a^3*b^7*c^3*d^3 + 576240*a^4*b^6*c^2*d^4 - 403368*a^5*b^5*c*d^5 + 117649*a^6*b^4*d^6)*sqrt(b*x^4 + a))/x^2)*((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8)^(1/4) + (64*b^5*c^3*d^2 - 336*a*b^4*c^2*d^3 + 588*a^2*b^3*c*d^4 - 343*a^3*b^2*d^5)*(b*x^4 + a)^(1/4)*((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8)^(1/4))/((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)*x)) + 4*d*((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8))^(1/4)*log(-(c^2*d^6*x*((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8))^(3/4) + (b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*(b*x^4 + a)^(1/4))/x) - 4*d*((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8))^(1/4)*log((c^2*d^6*x*((b^7*c^7 - 7*a*b^6*c^6*d + 21*a^2*b^5*c^5*d^2 - 35*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 21*a^5*b^2*c^2*d^5 + 7*a^6*b*c*d^6 - a^7*d^7)/(c^3*d^8))^(3/4) - (b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*(b*x^4 + a)^(1/4))/x) - d*((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8)^(1/4)*log(-(d^6*x*((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8)^(3/4) + (64*b^5*c^3 - 336*a*b^4*c^2*d + 588*a^2*b^3*c*d^2 - 343*a^3*b^2*d^3)*(b*x^4 + a)^(1/4))/x) + d*((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8)^(1/4)*log((d^6*x*((256*b^7*c^4 - 1792*a*b^6*c^3*d + 4704*a^2*b^5*c^2*d^2 - 5488*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/d^8)^(3/4) - (64*b^5*c^3 - 336*a*b^4*c^2*d + 588*a^2*b^3*c*d^2 - 343*a^3*b^2*d^3)*(b*x^4 + a)^(1/4))/x))/d","B",0
194,1,844,0,1.830723," ","integrate((b*x^4+a)^(3/4)/(d*x^4+c),x, algorithm=""fricas"")","\left(\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c d x \sqrt{\frac{{\left(b^{3} c^{4} d^{2} - 3 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b c^{2} d^{4} - a^{3} c d^{5}\right)} x^{2} \sqrt{\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{b x^{4} + a}}{x^{2}}} \left(\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}\right)^{\frac{1}{4}} - {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}\right)^{\frac{1}{4}}}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}\right) + \left(\frac{b^{3}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2} d \left(\frac{b^{3}}{d^{4}}\right)^{\frac{1}{4}} - d x \left(\frac{b^{3}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{b^{3} d^{2} x^{2} \sqrt{\frac{b^{3}}{d^{4}}} + \sqrt{b x^{4} + a} b^{4}}{x^{2}}}}{b^{3} x}\right) - \frac{1}{4} \, \left(\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{c^{2} d^{3} x \left(\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}{x}\right) + \frac{1}{4} \, \left(\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{c^{2} d^{3} x \left(\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{c^{3} d^{4}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}{x}\right) + \frac{1}{4} \, \left(\frac{b^{3}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{d^{3} x \left(\frac{b^{3}}{d^{4}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2}}{x}\right) - \frac{1}{4} \, \left(\frac{b^{3}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{d^{3} x \left(\frac{b^{3}}{d^{4}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2}}{x}\right)"," ",0,"((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4))^(1/4)*arctan(-(c*d*x*sqrt(((b^3*c^4*d^2 - 3*a*b^2*c^3*d^3 + 3*a^2*b*c^2*d^4 - a^3*c*d^5)*x^2*sqrt((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4)) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(b*x^4 + a))/x^2)*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4))^(1/4) - (b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*(b*x^4 + a)^(1/4)*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4))^(1/4))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x)) + (b^3/d^4)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*b^2*d*(b^3/d^4)^(1/4) - d*x*(b^3/d^4)^(1/4)*sqrt((b^3*d^2*x^2*sqrt(b^3/d^4) + sqrt(b*x^4 + a)*b^4)/x^2))/(b^3*x)) - 1/4*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4))^(1/4)*log((c^2*d^3*x*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4))^(3/4) + (b*x^4 + a)^(1/4)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))/x) + 1/4*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4))^(1/4)*log(-(c^2*d^3*x*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^4))^(3/4) - (b*x^4 + a)^(1/4)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))/x) + 1/4*(b^3/d^4)^(1/4)*log((d^3*x*(b^3/d^4)^(3/4) + (b*x^4 + a)^(1/4)*b^2)/x) - 1/4*(b^3/d^4)^(1/4)*log(-(d^3*x*(b^3/d^4)^(3/4) - (b*x^4 + a)^(1/4)*b^2)/x)","B",0
195,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(9/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(13/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate((b*x^4+a)^(9/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(7/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(11/4)/(d*x^4+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,1,3308,0,47.324049," ","integrate((b*x^4+a)^(11/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c^{2} d^{3} x \sqrt{\frac{{\left(4096 \, b^{11} c^{14} d^{6} - 22528 \, a b^{10} c^{13} d^{7} + 46464 \, a^{2} b^{9} c^{12} d^{8} - 37664 \, a^{3} b^{8} c^{11} d^{9} - 5071 \, a^{4} b^{7} c^{10} d^{10} + 25641 \, a^{5} b^{6} c^{9} d^{11} - 7931 \, a^{6} b^{5} c^{8} d^{12} - 6259 \, a^{7} b^{4} c^{7} d^{13} + 2739 \, a^{8} b^{3} c^{6} d^{14} + 891 \, a^{9} b^{2} c^{5} d^{15} - 297 \, a^{10} b c^{4} d^{16} - 81 \, a^{11} c^{3} d^{17}\right)} x^{2} \sqrt{\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}} + {\left(262144 \, b^{16} c^{16} - 2031616 \, a b^{15} c^{15} d + 6451200 \, a^{2} b^{14} c^{14} d^{2} - 10168320 \, a^{3} b^{13} c^{13} d^{3} + 6467520 \, a^{4} b^{12} c^{12} d^{4} + 3123216 \, a^{5} b^{11} c^{11} d^{5} - 7258119 \, a^{6} b^{10} c^{10} d^{6} + 2307030 \, a^{7} b^{9} c^{9} d^{7} + 2428965 \, a^{8} b^{8} c^{8} d^{8} - 1607320 \, a^{9} b^{7} c^{7} d^{9} - 387134 \, a^{10} b^{6} c^{6} d^{10} + 436356 \, a^{11} b^{5} c^{5} d^{11} + 40770 \, a^{12} b^{4} c^{4} d^{12} - 63720 \, a^{13} b^{3} c^{3} d^{13} - 6075 \, a^{14} b^{2} c^{2} d^{14} + 4374 \, a^{15} b c d^{15} + 729 \, a^{16} d^{16}\right)} \sqrt{b x^{4} + a}}{x^{2}}} \left(\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}\right)^{\frac{1}{4}} + {\left(512 \, b^{8} c^{10} d^{3} - 1984 \, a b^{7} c^{9} d^{4} + 2456 \, a^{2} b^{6} c^{8} d^{5} - 413 \, a^{3} b^{5} c^{7} d^{6} - 1175 \, a^{4} b^{4} c^{6} d^{7} + 478 \, a^{5} b^{3} c^{5} d^{8} + 234 \, a^{6} b^{2} c^{4} d^{9} - 81 \, a^{7} b c^{3} d^{10} - 27 \, a^{8} c^{2} d^{11}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}\right)^{\frac{1}{4}}}{{\left(4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}\right)} x}\right) + 4 \, {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}\right)^{\frac{1}{4}} \arctan\left(\frac{d^{3} x \sqrt{\frac{{\left(4096 \, b^{11} c^{4} d^{6} - 22528 \, a b^{10} c^{3} d^{7} + 46464 \, a^{2} b^{9} c^{2} d^{8} - 42592 \, a^{3} b^{8} c d^{9} + 14641 \, a^{4} b^{7} d^{10}\right)} x^{2} \sqrt{\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}} + {\left(262144 \, b^{16} c^{6} - 2162688 \, a b^{15} c^{5} d + 7434240 \, a^{2} b^{14} c^{4} d^{2} - 13629440 \, a^{3} b^{13} c^{3} d^{3} + 14055360 \, a^{4} b^{12} c^{2} d^{4} - 7730448 \, a^{5} b^{11} c d^{5} + 1771561 \, a^{6} b^{10} d^{6}\right)} \sqrt{b x^{4} + a}}{x^{2}}} \left(\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}\right)^{\frac{1}{4}} + {\left(512 \, b^{8} c^{3} d^{3} - 2112 \, a b^{7} c^{2} d^{4} + 2904 \, a^{2} b^{6} c d^{5} - 1331 \, a^{3} b^{5} d^{6}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}\right)^{\frac{1}{4}}}{{\left(4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}\right)} x}\right) + {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}\right)^{\frac{1}{4}} \log\left(-\frac{c^{5} d^{9} x \left(\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}\right)^{\frac{3}{4}} + {\left(512 \, b^{8} c^{8} - 1984 \, a b^{7} c^{7} d + 2456 \, a^{2} b^{6} c^{6} d^{2} - 413 \, a^{3} b^{5} c^{5} d^{3} - 1175 \, a^{4} b^{4} c^{4} d^{4} + 478 \, a^{5} b^{3} c^{3} d^{5} + 234 \, a^{6} b^{2} c^{2} d^{6} - 81 \, a^{7} b c d^{7} - 27 \, a^{8} d^{8}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}\right)^{\frac{1}{4}} \log\left(\frac{c^{5} d^{9} x \left(\frac{4096 \, b^{11} c^{11} - 22528 \, a b^{10} c^{10} d + 46464 \, a^{2} b^{9} c^{9} d^{2} - 37664 \, a^{3} b^{8} c^{8} d^{3} - 5071 \, a^{4} b^{7} c^{7} d^{4} + 25641 \, a^{5} b^{6} c^{6} d^{5} - 7931 \, a^{6} b^{5} c^{5} d^{6} - 6259 \, a^{7} b^{4} c^{4} d^{7} + 2739 \, a^{8} b^{3} c^{3} d^{8} + 891 \, a^{9} b^{2} c^{2} d^{9} - 297 \, a^{10} b c d^{10} - 81 \, a^{11} d^{11}}{c^{7} d^{12}}\right)^{\frac{3}{4}} - {\left(512 \, b^{8} c^{8} - 1984 \, a b^{7} c^{7} d + 2456 \, a^{2} b^{6} c^{6} d^{2} - 413 \, a^{3} b^{5} c^{5} d^{3} - 1175 \, a^{4} b^{4} c^{4} d^{4} + 478 \, a^{5} b^{3} c^{3} d^{5} + 234 \, a^{6} b^{2} c^{2} d^{6} - 81 \, a^{7} b c d^{7} - 27 \, a^{8} d^{8}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}\right)^{\frac{1}{4}} \log\left(-\frac{d^{9} x \left(\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}\right)^{\frac{3}{4}} + {\left(512 \, b^{8} c^{3} - 2112 \, a b^{7} c^{2} d + 2904 \, a^{2} b^{6} c d^{2} - 1331 \, a^{3} b^{5} d^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) + {\left(c d^{3} x^{4} + c^{2} d^{2}\right)} \left(\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}\right)^{\frac{1}{4}} \log\left(\frac{d^{9} x \left(\frac{4096 \, b^{11} c^{4} - 22528 \, a b^{10} c^{3} d + 46464 \, a^{2} b^{9} c^{2} d^{2} - 42592 \, a^{3} b^{8} c d^{3} + 14641 \, a^{4} b^{7} d^{4}}{d^{12}}\right)^{\frac{3}{4}} - {\left(512 \, b^{8} c^{3} - 2112 \, a b^{7} c^{2} d + 2904 \, a^{2} b^{6} c d^{2} - 1331 \, a^{3} b^{5} d^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) + 4 \, {\left(b^{2} c d x^{5} + {\left(2 \, b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{16 \, {\left(c d^{3} x^{4} + c^{2} d^{2}\right)}}"," ",0,"1/16*(4*(c*d^3*x^4 + c^2*d^2)*((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12))^(1/4)*arctan(-(c^2*d^3*x*sqrt(((4096*b^11*c^14*d^6 - 22528*a*b^10*c^13*d^7 + 46464*a^2*b^9*c^12*d^8 - 37664*a^3*b^8*c^11*d^9 - 5071*a^4*b^7*c^10*d^10 + 25641*a^5*b^6*c^9*d^11 - 7931*a^6*b^5*c^8*d^12 - 6259*a^7*b^4*c^7*d^13 + 2739*a^8*b^3*c^6*d^14 + 891*a^9*b^2*c^5*d^15 - 297*a^10*b*c^4*d^16 - 81*a^11*c^3*d^17)*x^2*sqrt((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12)) + (262144*b^16*c^16 - 2031616*a*b^15*c^15*d + 6451200*a^2*b^14*c^14*d^2 - 10168320*a^3*b^13*c^13*d^3 + 6467520*a^4*b^12*c^12*d^4 + 3123216*a^5*b^11*c^11*d^5 - 7258119*a^6*b^10*c^10*d^6 + 2307030*a^7*b^9*c^9*d^7 + 2428965*a^8*b^8*c^8*d^8 - 1607320*a^9*b^7*c^7*d^9 - 387134*a^10*b^6*c^6*d^10 + 436356*a^11*b^5*c^5*d^11 + 40770*a^12*b^4*c^4*d^12 - 63720*a^13*b^3*c^3*d^13 - 6075*a^14*b^2*c^2*d^14 + 4374*a^15*b*c*d^15 + 729*a^16*d^16)*sqrt(b*x^4 + a))/x^2)*((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12))^(1/4) + (512*b^8*c^10*d^3 - 1984*a*b^7*c^9*d^4 + 2456*a^2*b^6*c^8*d^5 - 413*a^3*b^5*c^7*d^6 - 1175*a^4*b^4*c^6*d^7 + 478*a^5*b^3*c^5*d^8 + 234*a^6*b^2*c^4*d^9 - 81*a^7*b*c^3*d^10 - 27*a^8*c^2*d^11)*(b*x^4 + a)^(1/4)*((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12))^(1/4))/((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)*x)) + 4*(c*d^3*x^4 + c^2*d^2)*((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12)^(1/4)*arctan((d^3*x*sqrt(((4096*b^11*c^4*d^6 - 22528*a*b^10*c^3*d^7 + 46464*a^2*b^9*c^2*d^8 - 42592*a^3*b^8*c*d^9 + 14641*a^4*b^7*d^10)*x^2*sqrt((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12) + (262144*b^16*c^6 - 2162688*a*b^15*c^5*d + 7434240*a^2*b^14*c^4*d^2 - 13629440*a^3*b^13*c^3*d^3 + 14055360*a^4*b^12*c^2*d^4 - 7730448*a^5*b^11*c*d^5 + 1771561*a^6*b^10*d^6)*sqrt(b*x^4 + a))/x^2)*((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12)^(1/4) + (512*b^8*c^3*d^3 - 2112*a*b^7*c^2*d^4 + 2904*a^2*b^6*c*d^5 - 1331*a^3*b^5*d^6)*(b*x^4 + a)^(1/4)*((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12)^(1/4))/((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)*x)) + (c*d^3*x^4 + c^2*d^2)*((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12))^(1/4)*log(-(c^5*d^9*x*((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12))^(3/4) + (512*b^8*c^8 - 1984*a*b^7*c^7*d + 2456*a^2*b^6*c^6*d^2 - 413*a^3*b^5*c^5*d^3 - 1175*a^4*b^4*c^4*d^4 + 478*a^5*b^3*c^3*d^5 + 234*a^6*b^2*c^2*d^6 - 81*a^7*b*c*d^7 - 27*a^8*d^8)*(b*x^4 + a)^(1/4))/x) - (c*d^3*x^4 + c^2*d^2)*((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12))^(1/4)*log((c^5*d^9*x*((4096*b^11*c^11 - 22528*a*b^10*c^10*d + 46464*a^2*b^9*c^9*d^2 - 37664*a^3*b^8*c^8*d^3 - 5071*a^4*b^7*c^7*d^4 + 25641*a^5*b^6*c^6*d^5 - 7931*a^6*b^5*c^5*d^6 - 6259*a^7*b^4*c^4*d^7 + 2739*a^8*b^3*c^3*d^8 + 891*a^9*b^2*c^2*d^9 - 297*a^10*b*c*d^10 - 81*a^11*d^11)/(c^7*d^12))^(3/4) - (512*b^8*c^8 - 1984*a*b^7*c^7*d + 2456*a^2*b^6*c^6*d^2 - 413*a^3*b^5*c^5*d^3 - 1175*a^4*b^4*c^4*d^4 + 478*a^5*b^3*c^3*d^5 + 234*a^6*b^2*c^2*d^6 - 81*a^7*b*c*d^7 - 27*a^8*d^8)*(b*x^4 + a)^(1/4))/x) - (c*d^3*x^4 + c^2*d^2)*((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12)^(1/4)*log(-(d^9*x*((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12)^(3/4) + (512*b^8*c^3 - 2112*a*b^7*c^2*d + 2904*a^2*b^6*c*d^2 - 1331*a^3*b^5*d^3)*(b*x^4 + a)^(1/4))/x) + (c*d^3*x^4 + c^2*d^2)*((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12)^(1/4)*log((d^9*x*((4096*b^11*c^4 - 22528*a*b^10*c^3*d + 46464*a^2*b^9*c^2*d^2 - 42592*a^3*b^8*c*d^3 + 14641*a^4*b^7*d^4)/d^12)^(3/4) - (512*b^8*c^3 - 2112*a*b^7*c^2*d + 2904*a^2*b^6*c*d^2 - 1331*a^3*b^5*d^3)*(b*x^4 + a)^(1/4))/x) + 4*(b^2*c*d*x^5 + (2*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)*(b*x^4 + a)^(3/4))/(c*d^3*x^4 + c^2*d^2)","B",0
206,1,1667,0,3.507224," ","integrate((b*x^4+a)^(7/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} {\left(b c - a d\right)} x - 4 \, {\left(c d^{2} x^{4} + c^{2} d\right)} \left(\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c^{2} d^{2} x \sqrt{\frac{{\left(256 \, b^{7} c^{10} d^{4} - 672 \, a^{2} b^{5} c^{8} d^{6} - 112 \, a^{3} b^{4} c^{7} d^{7} + 609 \, a^{4} b^{3} c^{6} d^{8} + 189 \, a^{5} b^{2} c^{5} d^{9} - 189 \, a^{6} b c^{4} d^{10} - 81 \, a^{7} c^{3} d^{11}\right)} x^{2} \sqrt{\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}} + {\left(4096 \, b^{10} c^{10} + 2048 \, a b^{9} c^{9} d - 14592 \, a^{2} b^{8} c^{8} d^{2} - 9472 \, a^{3} b^{7} c^{7} d^{3} + 18928 \, a^{4} b^{6} c^{6} d^{4} + 15624 \, a^{5} b^{5} c^{5} d^{5} - 9639 \, a^{6} b^{4} c^{4} d^{6} - 11124 \, a^{7} b^{3} c^{3} d^{7} + 486 \, a^{8} b^{2} c^{2} d^{8} + 2916 \, a^{9} b c d^{9} + 729 \, a^{10} d^{10}\right)} \sqrt{b x^{4} + a}}{x^{2}}} \left(\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}\right)^{\frac{1}{4}} - {\left(64 \, b^{5} c^{7} d^{2} + 16 \, a b^{4} c^{6} d^{3} - 116 \, a^{2} b^{3} c^{5} d^{4} - 45 \, a^{3} b^{2} c^{4} d^{5} + 54 \, a^{4} b c^{3} d^{6} + 27 \, a^{5} c^{2} d^{7}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}\right)^{\frac{1}{4}}}{{\left(256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}\right)} x}\right) - 16 \, {\left(c d^{2} x^{4} + c^{2} d\right)} \left(\frac{b^{7}}{d^{8}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{5} d^{2} \left(\frac{b^{7}}{d^{8}}\right)^{\frac{1}{4}} - d^{2} x \left(\frac{b^{7}}{d^{8}}\right)^{\frac{1}{4}} \sqrt{\frac{b^{7} d^{4} x^{2} \sqrt{\frac{b^{7}}{d^{8}}} + \sqrt{b x^{4} + a} b^{10}}{x^{2}}}}{b^{7} x}\right) + {\left(c d^{2} x^{4} + c^{2} d\right)} \left(\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}\right)^{\frac{1}{4}} \log\left(\frac{c^{5} d^{6} x \left(\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}\right)^{\frac{3}{4}} + {\left(64 \, b^{5} c^{5} + 16 \, a b^{4} c^{4} d - 116 \, a^{2} b^{3} c^{3} d^{2} - 45 \, a^{3} b^{2} c^{2} d^{3} + 54 \, a^{4} b c d^{4} + 27 \, a^{5} d^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - {\left(c d^{2} x^{4} + c^{2} d\right)} \left(\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}\right)^{\frac{1}{4}} \log\left(-\frac{c^{5} d^{6} x \left(\frac{256 \, b^{7} c^{7} - 672 \, a^{2} b^{5} c^{5} d^{2} - 112 \, a^{3} b^{4} c^{4} d^{3} + 609 \, a^{4} b^{3} c^{3} d^{4} + 189 \, a^{5} b^{2} c^{2} d^{5} - 189 \, a^{6} b c d^{6} - 81 \, a^{7} d^{7}}{c^{7} d^{8}}\right)^{\frac{3}{4}} - {\left(64 \, b^{5} c^{5} + 16 \, a b^{4} c^{4} d - 116 \, a^{2} b^{3} c^{3} d^{2} - 45 \, a^{3} b^{2} c^{2} d^{3} + 54 \, a^{4} b c d^{4} + 27 \, a^{5} d^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - 4 \, {\left(c d^{2} x^{4} + c^{2} d\right)} \left(\frac{b^{7}}{d^{8}}\right)^{\frac{1}{4}} \log\left(\frac{d^{6} x \left(\frac{b^{7}}{d^{8}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{5}}{x}\right) + 4 \, {\left(c d^{2} x^{4} + c^{2} d\right)} \left(\frac{b^{7}}{d^{8}}\right)^{\frac{1}{4}} \log\left(-\frac{d^{6} x \left(\frac{b^{7}}{d^{8}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{5}}{x}\right)}{16 \, {\left(c d^{2} x^{4} + c^{2} d\right)}}"," ",0,"-1/16*(4*(b*x^4 + a)^(3/4)*(b*c - a*d)*x - 4*(c*d^2*x^4 + c^2*d)*((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8))^(1/4)*arctan(-(c^2*d^2*x*sqrt(((256*b^7*c^10*d^4 - 672*a^2*b^5*c^8*d^6 - 112*a^3*b^4*c^7*d^7 + 609*a^4*b^3*c^6*d^8 + 189*a^5*b^2*c^5*d^9 - 189*a^6*b*c^4*d^10 - 81*a^7*c^3*d^11)*x^2*sqrt((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8)) + (4096*b^10*c^10 + 2048*a*b^9*c^9*d - 14592*a^2*b^8*c^8*d^2 - 9472*a^3*b^7*c^7*d^3 + 18928*a^4*b^6*c^6*d^4 + 15624*a^5*b^5*c^5*d^5 - 9639*a^6*b^4*c^4*d^6 - 11124*a^7*b^3*c^3*d^7 + 486*a^8*b^2*c^2*d^8 + 2916*a^9*b*c*d^9 + 729*a^10*d^10)*sqrt(b*x^4 + a))/x^2)*((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8))^(1/4) - (64*b^5*c^7*d^2 + 16*a*b^4*c^6*d^3 - 116*a^2*b^3*c^5*d^4 - 45*a^3*b^2*c^4*d^5 + 54*a^4*b*c^3*d^6 + 27*a^5*c^2*d^7)*(b*x^4 + a)^(1/4)*((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8))^(1/4))/((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)*x)) - 16*(c*d^2*x^4 + c^2*d)*(b^7/d^8)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*b^5*d^2*(b^7/d^8)^(1/4) - d^2*x*(b^7/d^8)^(1/4)*sqrt((b^7*d^4*x^2*sqrt(b^7/d^8) + sqrt(b*x^4 + a)*b^10)/x^2))/(b^7*x)) + (c*d^2*x^4 + c^2*d)*((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8))^(1/4)*log((c^5*d^6*x*((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8))^(3/4) + (64*b^5*c^5 + 16*a*b^4*c^4*d - 116*a^2*b^3*c^3*d^2 - 45*a^3*b^2*c^2*d^3 + 54*a^4*b*c*d^4 + 27*a^5*d^5)*(b*x^4 + a)^(1/4))/x) - (c*d^2*x^4 + c^2*d)*((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8))^(1/4)*log(-(c^5*d^6*x*((256*b^7*c^7 - 672*a^2*b^5*c^5*d^2 - 112*a^3*b^4*c^4*d^3 + 609*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 - 189*a^6*b*c*d^6 - 81*a^7*d^7)/(c^7*d^8))^(3/4) - (64*b^5*c^5 + 16*a*b^4*c^4*d - 116*a^2*b^3*c^3*d^2 - 45*a^3*b^2*c^2*d^3 + 54*a^4*b*c*d^4 + 27*a^5*d^5)*(b*x^4 + a)^(1/4))/x) - 4*(c*d^2*x^4 + c^2*d)*(b^7/d^8)^(1/4)*log((d^6*x*(b^7/d^8)^(3/4) + (b*x^4 + a)^(1/4)*b^5)/x) + 4*(c*d^2*x^4 + c^2*d)*(b^7/d^8)^(1/4)*log(-(d^6*x*(b^7/d^8)^(3/4) - (b*x^4 + a)^(1/4)*b^5)/x))/(c*d^2*x^4 + c^2*d)","B",0
207,-1,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(9/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((b*x^4+a)^(9/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^(7/4)/(d*x^4+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,1,208,0,16.480268," ","integrate(1/(x^4+1)^(1/4)/(x^4+2),x, algorithm=""fricas"")","-\frac{1}{16} \cdot 8^{\frac{3}{4}} \arctan\left(-\frac{8^{\frac{3}{4}} {\left(x^{4} + 1\right)}^{\frac{1}{4}} x^{3} + 4 \cdot 8^{\frac{1}{4}} {\left(x^{4} + 1\right)}^{\frac{3}{4}} x - 2^{\frac{1}{4}} {\left(8^{\frac{3}{4}} \sqrt{x^{4} + 1} x^{2} + 8^{\frac{1}{4}} {\left(3 \, x^{4} + 2\right)}\right)}}{2 \, {\left(x^{4} + 2\right)}}\right) + \frac{1}{64} \cdot 8^{\frac{3}{4}} \log\left(\frac{8 \, \sqrt{2} {\left(x^{4} + 1\right)}^{\frac{1}{4}} x^{3} + 8 \cdot 8^{\frac{1}{4}} \sqrt{x^{4} + 1} x^{2} + 8^{\frac{3}{4}} {\left(3 \, x^{4} + 2\right)} + 16 \, {\left(x^{4} + 1\right)}^{\frac{3}{4}} x}{x^{4} + 2}\right) - \frac{1}{64} \cdot 8^{\frac{3}{4}} \log\left(\frac{8 \, \sqrt{2} {\left(x^{4} + 1\right)}^{\frac{1}{4}} x^{3} - 8 \cdot 8^{\frac{1}{4}} \sqrt{x^{4} + 1} x^{2} - 8^{\frac{3}{4}} {\left(3 \, x^{4} + 2\right)} + 16 \, {\left(x^{4} + 1\right)}^{\frac{3}{4}} x}{x^{4} + 2}\right)"," ",0,"-1/16*8^(3/4)*arctan(-1/2*(8^(3/4)*(x^4 + 1)^(1/4)*x^3 + 4*8^(1/4)*(x^4 + 1)^(3/4)*x - 2^(1/4)*(8^(3/4)*sqrt(x^4 + 1)*x^2 + 8^(1/4)*(3*x^4 + 2)))/(x^4 + 2)) + 1/64*8^(3/4)*log((8*sqrt(2)*(x^4 + 1)^(1/4)*x^3 + 8*8^(1/4)*sqrt(x^4 + 1)*x^2 + 8^(3/4)*(3*x^4 + 2) + 16*(x^4 + 1)^(3/4)*x)/(x^4 + 2)) - 1/64*8^(3/4)*log((8*sqrt(2)*(x^4 + 1)^(1/4)*x^3 - 8*8^(1/4)*sqrt(x^4 + 1)*x^2 - 8^(3/4)*(3*x^4 + 2) + 16*(x^4 + 1)^(3/4)*x)/(x^4 + 2))","B",0
217,-1,0,0,0.000000," ","integrate(1/(a-(a-b)*x^4)/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,0,0,0,1.491421," ","integrate((b*x^4+a)^p*(d*x^4+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{p} {\left(d x^{4} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^4 + a)^p*(d*x^4 + c)^q, x)","F",0
219,0,0,0,0.966679," ","integrate((b*x^4+a)^2*(d*x^4+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right)} {\left(d x^{4} + c\right)}^{q}, x\right)"," ",0,"integral((b^2*x^8 + 2*a*b*x^4 + a^2)*(d*x^4 + c)^q, x)","F",0
220,0,0,0,0.766165," ","integrate((b*x^4+a)*(d*x^4+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)} {\left(d x^{4} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^4 + a)*(d*x^4 + c)^q, x)","F",0
221,0,0,0,0.838713," ","integrate((d*x^4+c)^q/(b*x^4+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{4} + c\right)}^{q}}{b x^{4} + a}, x\right)"," ",0,"integral((d*x^4 + c)^q/(b*x^4 + a), x)","F",0
222,0,0,0,0.905428," ","integrate((d*x^4+c)^q/(b*x^4+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{4} + c\right)}^{q}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((d*x^4 + c)^q/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
223,-2,0,0,0.000000," ","integrate(1/(b*x^5+a)^(1/5)/(d*x^5+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (trace 0)","F(-2)",0
224,1,306,0,0.863230," ","integrate((c+d/x)^3*(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} c^{3} + 6 \, a b^{2} c^{2} d\right)} \sqrt{a} x^{2} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(15 \, a b^{2} c^{3} x^{3} - 6 \, a b^{2} d^{3} - 2 \, {\left(45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x^{2} - 2 \, {\left(15 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{30 \, a b^{2} x^{2}}, -\frac{15 \, {\left(b^{3} c^{3} + 6 \, a b^{2} c^{2} d\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(15 \, a b^{2} c^{3} x^{3} - 6 \, a b^{2} d^{3} - 2 \, {\left(45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x^{2} - 2 \, {\left(15 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{15 \, a b^{2} x^{2}}\right]"," ",0,"[1/30*(15*(b^3*c^3 + 6*a*b^2*c^2*d)*sqrt(a)*x^2*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(15*a*b^2*c^3*x^3 - 6*a*b^2*d^3 - 2*(45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 2*a^3*d^3)*x^2 - 2*(15*a*b^2*c*d^2 + a^2*b*d^3)*x)*sqrt((a*x + b)/x))/(a*b^2*x^2), -1/15*(15*(b^3*c^3 + 6*a*b^2*c^2*d)*sqrt(-a)*x^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (15*a*b^2*c^3*x^3 - 6*a*b^2*d^3 - 2*(45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 2*a^3*d^3)*x^2 - 2*(15*a*b^2*c*d^2 + a^2*b*d^3)*x)*sqrt((a*x + b)/x))/(a*b^2*x^2)]","A",0
225,1,208,0,0.755481," ","integrate((c+d/x)^2*(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{a} x \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(3 \, a b c^{2} x^{2} - 2 \, a b d^{2} - 2 \, {\left(6 \, a b c d + a^{2} d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, a b x}, -\frac{3 \, {\left(b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(3 \, a b c^{2} x^{2} - 2 \, a b d^{2} - 2 \, {\left(6 \, a b c d + a^{2} d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, a b x}\right]"," ",0,"[1/6*(3*(b^2*c^2 + 4*a*b*c*d)*sqrt(a)*x*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(3*a*b*c^2*x^2 - 2*a*b*d^2 - 2*(6*a*b*c*d + a^2*d^2)*x)*sqrt((a*x + b)/x))/(a*b*x), -1/3*(3*(b^2*c^2 + 4*a*b*c*d)*sqrt(-a)*x*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (3*a*b*c^2*x^2 - 2*a*b*d^2 - 2*(6*a*b*c*d + a^2*d^2)*x)*sqrt((a*x + b)/x))/(a*b*x)]","A",0
226,1,128,0,0.853999," ","integrate((c+d/x)*(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c + 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(a c x - 2 \, a d\right)} \sqrt{\frac{a x + b}{x}}}{2 \, a}, -\frac{{\left(b c + 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(a c x - 2 \, a d\right)} \sqrt{\frac{a x + b}{x}}}{a}\right]"," ",0,"[1/2*((b*c + 2*a*d)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(a*c*x - 2*a*d)*sqrt((a*x + b)/x))/a, -((b*c + 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (a*c*x - 2*a*d)*sqrt((a*x + b)/x))/a]","A",0
227,1,99,0,0.747709," ","integrate((a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a x + b}{x}} + \sqrt{a} b \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a}, \frac{a x \sqrt{\frac{a x + b}{x}} - \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*x + b)/x) + sqrt(a)*b*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/a, (a*x*sqrt((a*x + b)/x) - sqrt(-a)*b*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/a]","A",0
228,1,482,0,0.937091," ","integrate((a+b/x)^(1/2)/(c+d/x),x, algorithm=""fricas"")","\left[\frac{2 \, a c x \sqrt{\frac{a x + b}{x}} - {\left(b c - 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, \sqrt{-b c d + a d^{2}} a \log\left(\frac{b d - {\left(b c - 2 \, a d\right)} x + 2 \, \sqrt{-b c d + a d^{2}} x \sqrt{\frac{a x + b}{x}}}{c x + d}\right)}{2 \, a c^{2}}, \frac{2 \, a c x \sqrt{\frac{a x + b}{x}} - 4 \, \sqrt{b c d - a d^{2}} a \arctan\left(\frac{\sqrt{b c d - a d^{2}} x \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - {\left(b c - 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a c^{2}}, \frac{a c x \sqrt{\frac{a x + b}{x}} - {\left(b c - 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + \sqrt{-b c d + a d^{2}} a \log\left(\frac{b d - {\left(b c - 2 \, a d\right)} x + 2 \, \sqrt{-b c d + a d^{2}} x \sqrt{\frac{a x + b}{x}}}{c x + d}\right)}{a c^{2}}, \frac{a c x \sqrt{\frac{a x + b}{x}} - 2 \, \sqrt{b c d - a d^{2}} a \arctan\left(\frac{\sqrt{b c d - a d^{2}} x \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - {\left(b c - 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a c^{2}}\right]"," ",0,"[1/2*(2*a*c*x*sqrt((a*x + b)/x) - (b*c - 2*a*d)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*sqrt(-b*c*d + a*d^2)*a*log((b*d - (b*c - 2*a*d)*x + 2*sqrt(-b*c*d + a*d^2)*x*sqrt((a*x + b)/x))/(c*x + d)))/(a*c^2), 1/2*(2*a*c*x*sqrt((a*x + b)/x) - 4*sqrt(b*c*d - a*d^2)*a*arctan(sqrt(b*c*d - a*d^2)*x*sqrt((a*x + b)/x)/(a*d*x + b*d)) - (b*c - 2*a*d)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/(a*c^2), (a*c*x*sqrt((a*x + b)/x) - (b*c - 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + sqrt(-b*c*d + a*d^2)*a*log((b*d - (b*c - 2*a*d)*x + 2*sqrt(-b*c*d + a*d^2)*x*sqrt((a*x + b)/x))/(c*x + d)))/(a*c^2), (a*c*x*sqrt((a*x + b)/x) - 2*sqrt(b*c*d - a*d^2)*a*arctan(sqrt(b*c*d - a*d^2)*x*sqrt((a*x + b)/x)/(a*d*x + b*d)) - (b*c - 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/(a*c^2)]","A",0
229,1,801,0,0.906786," ","integrate((a+b/x)^(1/2)/(c+d/x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(a c^{2} x^{2} + 2 \, a c d x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a c^{4} x + a c^{3} d\right)}}, -\frac{2 \, {\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(a c^{2} x^{2} + 2 \, a c d x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a c^{4} x + a c^{3} d\right)}}, \frac{2 \, {\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - {\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(a c^{2} x^{2} + 2 \, a c d x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a c^{4} x + a c^{3} d\right)}}, \frac{{\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - {\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a c^{2} x^{2} + 2 \, a c d x\right)} \sqrt{\frac{a x + b}{x}}}{a c^{4} x + a c^{3} d}\right]"," ",0,"[-1/2*((b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (3*a*b*c*d - 4*a^2*d^2 + (3*a*b*c^2 - 4*a^2*c*d)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) - 2*(a*c^2*x^2 + 2*a*c*d*x)*sqrt((a*x + b)/x))/(a*c^4*x + a*c^3*d), -1/2*(2*(b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (3*a*b*c*d - 4*a^2*d^2 + (3*a*b*c^2 - 4*a^2*c*d)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) - 2*(a*c^2*x^2 + 2*a*c*d*x)*sqrt((a*x + b)/x))/(a*c^4*x + a*c^3*d), 1/2*(2*(3*a*b*c*d - 4*a^2*d^2 + (3*a*b*c^2 - 4*a^2*c*d)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - (b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(a*c^2*x^2 + 2*a*c*d*x)*sqrt((a*x + b)/x))/(a*c^4*x + a*c^3*d), ((3*a*b*c*d - 4*a^2*d^2 + (3*a*b*c^2 - 4*a^2*c*d)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - (b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a*c^2*x^2 + 2*a*c*d*x)*sqrt((a*x + b)/x))/(a*c^4*x + a*c^3*d)]","A",0
230,1,1749,0,1.076193," ","integrate((a+b/x)^(1/2)/(c+d/x)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(b^{2} c^{2} d^{2} - 7 \, a b c d^{3} + 6 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 7 \, a b c^{3} d + 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 7 \, a b c^{2} d^{2} + 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(15 \, a b^{2} c^{2} d^{2} - 40 \, a^{2} b c d^{3} + 24 \, a^{3} d^{4} + {\left(15 \, a b^{2} c^{4} - 40 \, a^{2} b c^{3} d + 24 \, a^{3} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(15 \, a b^{2} c^{3} d - 40 \, a^{2} b c^{2} d^{2} + 24 \, a^{3} c d^{3}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(4 \, {\left(a b c^{4} - a^{2} c^{3} d\right)} x^{3} + {\left(17 \, a b c^{3} d - 18 \, a^{2} c^{2} d^{2}\right)} x^{2} + {\left(11 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a b c^{5} d^{2} - a^{2} c^{4} d^{3} + {\left(a b c^{7} - a^{2} c^{6} d\right)} x^{2} + 2 \, {\left(a b c^{6} d - a^{2} c^{5} d^{2}\right)} x\right)}}, \frac{{\left(15 \, a b^{2} c^{2} d^{2} - 40 \, a^{2} b c d^{3} + 24 \, a^{3} d^{4} + {\left(15 \, a b^{2} c^{4} - 40 \, a^{2} b c^{3} d + 24 \, a^{3} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(15 \, a b^{2} c^{3} d - 40 \, a^{2} b c^{2} d^{2} + 24 \, a^{3} c d^{3}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 2 \, {\left(b^{2} c^{2} d^{2} - 7 \, a b c d^{3} + 6 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 7 \, a b c^{3} d + 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 7 \, a b c^{2} d^{2} + 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(4 \, {\left(a b c^{4} - a^{2} c^{3} d\right)} x^{3} + {\left(17 \, a b c^{3} d - 18 \, a^{2} c^{2} d^{2}\right)} x^{2} + {\left(11 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a b c^{5} d^{2} - a^{2} c^{4} d^{3} + {\left(a b c^{7} - a^{2} c^{6} d\right)} x^{2} + 2 \, {\left(a b c^{6} d - a^{2} c^{5} d^{2}\right)} x\right)}}, -\frac{8 \, {\left(b^{2} c^{2} d^{2} - 7 \, a b c d^{3} + 6 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 7 \, a b c^{3} d + 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 7 \, a b c^{2} d^{2} + 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(15 \, a b^{2} c^{2} d^{2} - 40 \, a^{2} b c d^{3} + 24 \, a^{3} d^{4} + {\left(15 \, a b^{2} c^{4} - 40 \, a^{2} b c^{3} d + 24 \, a^{3} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(15 \, a b^{2} c^{3} d - 40 \, a^{2} b c^{2} d^{2} + 24 \, a^{3} c d^{3}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(4 \, {\left(a b c^{4} - a^{2} c^{3} d\right)} x^{3} + {\left(17 \, a b c^{3} d - 18 \, a^{2} c^{2} d^{2}\right)} x^{2} + {\left(11 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a b c^{5} d^{2} - a^{2} c^{4} d^{3} + {\left(a b c^{7} - a^{2} c^{6} d\right)} x^{2} + 2 \, {\left(a b c^{6} d - a^{2} c^{5} d^{2}\right)} x\right)}}, \frac{{\left(15 \, a b^{2} c^{2} d^{2} - 40 \, a^{2} b c d^{3} + 24 \, a^{3} d^{4} + {\left(15 \, a b^{2} c^{4} - 40 \, a^{2} b c^{3} d + 24 \, a^{3} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(15 \, a b^{2} c^{3} d - 40 \, a^{2} b c^{2} d^{2} + 24 \, a^{3} c d^{3}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 4 \, {\left(b^{2} c^{2} d^{2} - 7 \, a b c d^{3} + 6 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 7 \, a b c^{3} d + 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 7 \, a b c^{2} d^{2} + 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(4 \, {\left(a b c^{4} - a^{2} c^{3} d\right)} x^{3} + {\left(17 \, a b c^{3} d - 18 \, a^{2} c^{2} d^{2}\right)} x^{2} + {\left(11 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a b c^{5} d^{2} - a^{2} c^{4} d^{3} + {\left(a b c^{7} - a^{2} c^{6} d\right)} x^{2} + 2 \, {\left(a b c^{6} d - a^{2} c^{5} d^{2}\right)} x\right)}}\right]"," ",0,"[-1/8*(4*(b^2*c^2*d^2 - 7*a*b*c*d^3 + 6*a^2*d^4 + (b^2*c^4 - 7*a*b*c^3*d + 6*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 7*a*b*c^2*d^2 + 6*a^2*c*d^3)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (15*a*b^2*c^2*d^2 - 40*a^2*b*c*d^3 + 24*a^3*d^4 + (15*a*b^2*c^4 - 40*a^2*b*c^3*d + 24*a^3*c^2*d^2)*x^2 + 2*(15*a*b^2*c^3*d - 40*a^2*b*c^2*d^2 + 24*a^3*c*d^3)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) - 2*(4*(a*b*c^4 - a^2*c^3*d)*x^3 + (17*a*b*c^3*d - 18*a^2*c^2*d^2)*x^2 + (11*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(a*b*c^5*d^2 - a^2*c^4*d^3 + (a*b*c^7 - a^2*c^6*d)*x^2 + 2*(a*b*c^6*d - a^2*c^5*d^2)*x), 1/4*((15*a*b^2*c^2*d^2 - 40*a^2*b*c*d^3 + 24*a^3*d^4 + (15*a*b^2*c^4 - 40*a^2*b*c^3*d + 24*a^3*c^2*d^2)*x^2 + 2*(15*a*b^2*c^3*d - 40*a^2*b*c^2*d^2 + 24*a^3*c*d^3)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 2*(b^2*c^2*d^2 - 7*a*b*c*d^3 + 6*a^2*d^4 + (b^2*c^4 - 7*a*b*c^3*d + 6*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 7*a*b*c^2*d^2 + 6*a^2*c*d^3)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (4*(a*b*c^4 - a^2*c^3*d)*x^3 + (17*a*b*c^3*d - 18*a^2*c^2*d^2)*x^2 + (11*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(a*b*c^5*d^2 - a^2*c^4*d^3 + (a*b*c^7 - a^2*c^6*d)*x^2 + 2*(a*b*c^6*d - a^2*c^5*d^2)*x), -1/8*(8*(b^2*c^2*d^2 - 7*a*b*c*d^3 + 6*a^2*d^4 + (b^2*c^4 - 7*a*b*c^3*d + 6*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 7*a*b*c^2*d^2 + 6*a^2*c*d^3)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (15*a*b^2*c^2*d^2 - 40*a^2*b*c*d^3 + 24*a^3*d^4 + (15*a*b^2*c^4 - 40*a^2*b*c^3*d + 24*a^3*c^2*d^2)*x^2 + 2*(15*a*b^2*c^3*d - 40*a^2*b*c^2*d^2 + 24*a^3*c*d^3)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) - 2*(4*(a*b*c^4 - a^2*c^3*d)*x^3 + (17*a*b*c^3*d - 18*a^2*c^2*d^2)*x^2 + (11*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(a*b*c^5*d^2 - a^2*c^4*d^3 + (a*b*c^7 - a^2*c^6*d)*x^2 + 2*(a*b*c^6*d - a^2*c^5*d^2)*x), 1/4*((15*a*b^2*c^2*d^2 - 40*a^2*b*c*d^3 + 24*a^3*d^4 + (15*a*b^2*c^4 - 40*a^2*b*c^3*d + 24*a^3*c^2*d^2)*x^2 + 2*(15*a*b^2*c^3*d - 40*a^2*b*c^2*d^2 + 24*a^3*c*d^3)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 4*(b^2*c^2*d^2 - 7*a*b*c*d^3 + 6*a^2*d^4 + (b^2*c^4 - 7*a*b*c^3*d + 6*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 7*a*b*c^2*d^2 + 6*a^2*c*d^3)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (4*(a*b*c^4 - a^2*c^3*d)*x^3 + (17*a*b*c^3*d - 18*a^2*c^2*d^2)*x^2 + (11*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(a*b*c^5*d^2 - a^2*c^4*d^3 + (a*b*c^7 - a^2*c^6*d)*x^2 + 2*(a*b*c^6*d - a^2*c^5*d^2)*x)]","B",0
231,1,380,0,0.762630," ","integrate((a+b/x)^(3/2)*(c+d/x)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} c^{3} + 2 \, a b^{2} c^{2} d\right)} \sqrt{a} x^{3} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(35 \, a b^{2} c^{3} x^{4} - 10 \, b^{3} d^{3} - 2 \, {\left(35 \, b^{3} c^{3} + 140 \, a b^{2} c^{2} d + 21 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x^{3} - 2 \, {\left(35 \, b^{3} c^{2} d + 42 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} - 2 \, {\left(21 \, b^{3} c d^{2} + 8 \, a b^{2} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{70 \, b^{2} x^{3}}, -\frac{105 \, {\left(b^{3} c^{3} + 2 \, a b^{2} c^{2} d\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(35 \, a b^{2} c^{3} x^{4} - 10 \, b^{3} d^{3} - 2 \, {\left(35 \, b^{3} c^{3} + 140 \, a b^{2} c^{2} d + 21 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x^{3} - 2 \, {\left(35 \, b^{3} c^{2} d + 42 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} - 2 \, {\left(21 \, b^{3} c d^{2} + 8 \, a b^{2} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{35 \, b^{2} x^{3}}\right]"," ",0,"[1/70*(105*(b^3*c^3 + 2*a*b^2*c^2*d)*sqrt(a)*x^3*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(35*a*b^2*c^3*x^4 - 10*b^3*d^3 - 2*(35*b^3*c^3 + 140*a*b^2*c^2*d + 21*a^2*b*c*d^2 - 2*a^3*d^3)*x^3 - 2*(35*b^3*c^2*d + 42*a*b^2*c*d^2 + a^2*b*d^3)*x^2 - 2*(21*b^3*c*d^2 + 8*a*b^2*d^3)*x)*sqrt((a*x + b)/x))/(b^2*x^3), -1/35*(105*(b^3*c^3 + 2*a*b^2*c^2*d)*sqrt(-a)*x^3*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (35*a*b^2*c^3*x^4 - 10*b^3*d^3 - 2*(35*b^3*c^3 + 140*a*b^2*c^2*d + 21*a^2*b*c*d^2 - 2*a^3*d^3)*x^3 - 2*(35*b^3*c^2*d + 42*a*b^2*c*d^2 + a^2*b*d^3)*x^2 - 2*(21*b^3*c*d^2 + 8*a*b^2*d^3)*x)*sqrt((a*x + b)/x))/(b^2*x^3)]","A",0
232,1,268,0,0.606483," ","integrate((a+b/x)^(3/2)*(c+d/x)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{a} x^{2} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(15 \, a b c^{2} x^{3} - 6 \, b^{2} d^{2} - 2 \, {\left(15 \, b^{2} c^{2} + 40 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(5 \, b^{2} c d + 3 \, a b d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{30 \, b x^{2}}, -\frac{15 \, {\left(3 \, b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(15 \, a b c^{2} x^{3} - 6 \, b^{2} d^{2} - 2 \, {\left(15 \, b^{2} c^{2} + 40 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(5 \, b^{2} c d + 3 \, a b d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{15 \, b x^{2}}\right]"," ",0,"[1/30*(15*(3*b^2*c^2 + 4*a*b*c*d)*sqrt(a)*x^2*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(15*a*b*c^2*x^3 - 6*b^2*d^2 - 2*(15*b^2*c^2 + 40*a*b*c*d + 3*a^2*d^2)*x^2 - 4*(5*b^2*c*d + 3*a*b*d^2)*x)*sqrt((a*x + b)/x))/(b*x^2), -1/15*(15*(3*b^2*c^2 + 4*a*b*c*d)*sqrt(-a)*x^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (15*a*b*c^2*x^3 - 6*b^2*d^2 - 2*(15*b^2*c^2 + 40*a*b*c*d + 3*a^2*d^2)*x^2 - 4*(5*b^2*c*d + 3*a*b*d^2)*x)*sqrt((a*x + b)/x))/(b*x^2)]","A",0
233,1,164,0,0.868139," ","integrate((a+b/x)^(3/2)*(c+d/x),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, b c + 2 \, a d\right)} \sqrt{a} x \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(3 \, a c x^{2} - 2 \, b d - 2 \, {\left(3 \, b c + 4 \, a d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, x}, -\frac{3 \, {\left(3 \, b c + 2 \, a d\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(3 \, a c x^{2} - 2 \, b d - 2 \, {\left(3 \, b c + 4 \, a d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, x}\right]"," ",0,"[1/6*(3*(3*b*c + 2*a*d)*sqrt(a)*x*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(3*a*c*x^2 - 2*b*d - 2*(3*b*c + 4*a*d)*x)*sqrt((a*x + b)/x))/x, -1/3*(3*(3*b*c + 2*a*d)*sqrt(-a)*x*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (3*a*c*x^2 - 2*b*d - 2*(3*b*c + 4*a*d)*x)*sqrt((a*x + b)/x))/x]","A",0
234,1,100,0,0.801538," ","integrate((a+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3}{2} \, \sqrt{a} b \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(a x - 2 \, b\right)} \sqrt{\frac{a x + b}{x}}, -3 \, \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a x - 2 \, b\right)} \sqrt{\frac{a x + b}{x}}\right]"," ",0,"[3/2*sqrt(a)*b*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (a*x - 2*b)*sqrt((a*x + b)/x), -3*sqrt(-a)*b*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a*x - 2*b)*sqrt((a*x + b)/x)]","A",0
235,1,519,0,0.903984," ","integrate((a+b/x)^(3/2)/(c+d/x),x, algorithm=""fricas"")","\left[\frac{2 \, a c x \sqrt{\frac{a x + b}{x}} - {\left(3 \, b c - 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right)}{2 \, c^{2}}, \frac{a c x \sqrt{\frac{a x + b}{x}} - {\left(3 \, b c - 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right)}{c^{2}}, \frac{2 \, a c x \sqrt{\frac{a x + b}{x}} + 4 \, {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - {\left(3 \, b c - 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, c^{2}}, \frac{a c x \sqrt{\frac{a x + b}{x}} + 2 \, {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - {\left(3 \, b c - 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{c^{2}}\right]"," ",0,"[1/2*(2*a*c*x*sqrt((a*x + b)/x) - (3*b*c - 2*a*d)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(b*c - a*d)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)))/c^2, (a*c*x*sqrt((a*x + b)/x) - (3*b*c - 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (b*c - a*d)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)))/c^2, 1/2*(2*a*c*x*sqrt((a*x + b)/x) + 4*(b*c - a*d)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - (3*b*c - 2*a*d)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/c^2, (a*c*x*sqrt((a*x + b)/x) + 2*(b*c - a*d)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - (3*b*c - 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/c^2]","A",0
236,1,769,0,0.928644," ","integrate((a+b/x)^(3/2)/(c+d/x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b c d - 4 \, a d^{2} + {\left(3 \, b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(a c^{2} x^{2} - {\left(b c^{2} - 2 \, a c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(c^{4} x + c^{3} d\right)}}, \frac{2 \, {\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - {\left(3 \, b c d - 4 \, a d^{2} + {\left(3 \, b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(a c^{2} x^{2} - {\left(b c^{2} - 2 \, a c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(c^{4} x + c^{3} d\right)}}, -\frac{2 \, {\left(3 \, b c d - 4 \, a d^{2} + {\left(3 \, b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(a c^{2} x^{2} - {\left(b c^{2} - 2 \, a c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(c^{4} x + c^{3} d\right)}}, \frac{{\left(b c d - 4 \, a d^{2} + {\left(b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - {\left(3 \, b c d - 4 \, a d^{2} + {\left(3 \, b c^{2} - 4 \, a c d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a c^{2} x^{2} - {\left(b c^{2} - 2 \, a c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{c^{4} x + c^{3} d}\right]"," ",0,"[-1/2*((3*b*c*d - 4*a*d^2 + (3*b*c^2 - 4*a*c*d)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - 2*(a*c^2*x^2 - (b*c^2 - 2*a*c*d)*x)*sqrt((a*x + b)/x))/(c^4*x + c^3*d), 1/2*(2*(b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - (3*b*c*d - 4*a*d^2 + (3*b*c^2 - 4*a*c*d)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(a*c^2*x^2 - (b*c^2 - 2*a*c*d)*x)*sqrt((a*x + b)/x))/(c^4*x + c^3*d), -1/2*(2*(3*b*c*d - 4*a*d^2 + (3*b*c^2 - 4*a*c*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - 2*(a*c^2*x^2 - (b*c^2 - 2*a*c*d)*x)*sqrt((a*x + b)/x))/(c^4*x + c^3*d), ((b*c*d - 4*a*d^2 + (b*c^2 - 4*a*c*d)*x)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - (3*b*c*d - 4*a*d^2 + (3*b*c^2 - 4*a*c*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a*c^2*x^2 - (b*c^2 - 2*a*c*d)*x)*sqrt((a*x + b)/x))/(c^4*x + c^3*d)]","A",0
237,1,1765,0,1.060227," ","integrate((a+b/x)^(3/2)/(c+d/x)^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(b^{2} c^{2} d^{3} - 3 \, a b c d^{4} + 2 \, a^{2} d^{5} + {\left(b^{2} c^{4} d - 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 3 \, a b c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 3 \, {\left(b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 8 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 8 \, a b c^{3} d + 8 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 8 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-b c d + a d^{2}} \log\left(\frac{b d - {\left(b c - 2 \, a d\right)} x + 2 \, \sqrt{-b c d + a d^{2}} x \sqrt{\frac{a x + b}{x}}}{c x + d}\right) - 2 \, {\left(4 \, {\left(a b c^{4} d - a^{2} c^{3} d^{2}\right)} x^{3} - {\left(5 \, b^{2} c^{4} d - 23 \, a b c^{3} d^{2} + 18 \, a^{2} c^{2} d^{3}\right)} x^{2} - 3 \, {\left(b^{2} c^{3} d^{2} - 5 \, a b c^{2} d^{3} + 4 \, a^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(b c^{5} d^{3} - a c^{4} d^{4} + {\left(b c^{7} d - a c^{6} d^{2}\right)} x^{2} + 2 \, {\left(b c^{6} d^{2} - a c^{5} d^{3}\right)} x\right)}}, -\frac{24 \, {\left(b^{2} c^{2} d^{3} - 3 \, a b c d^{4} + 2 \, a^{2} d^{5} + {\left(b^{2} c^{4} d - 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 3 \, a b c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + 3 \, {\left(b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 8 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 8 \, a b c^{3} d + 8 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 8 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-b c d + a d^{2}} \log\left(\frac{b d - {\left(b c - 2 \, a d\right)} x + 2 \, \sqrt{-b c d + a d^{2}} x \sqrt{\frac{a x + b}{x}}}{c x + d}\right) - 2 \, {\left(4 \, {\left(a b c^{4} d - a^{2} c^{3} d^{2}\right)} x^{3} - {\left(5 \, b^{2} c^{4} d - 23 \, a b c^{3} d^{2} + 18 \, a^{2} c^{2} d^{3}\right)} x^{2} - 3 \, {\left(b^{2} c^{3} d^{2} - 5 \, a b c^{2} d^{3} + 4 \, a^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(b c^{5} d^{3} - a c^{4} d^{4} + {\left(b c^{7} d - a c^{6} d^{2}\right)} x^{2} + 2 \, {\left(b c^{6} d^{2} - a c^{5} d^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 8 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 8 \, a b c^{3} d + 8 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 8 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b c d - a d^{2}} \arctan\left(\frac{\sqrt{b c d - a d^{2}} x \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 6 \, {\left(b^{2} c^{2} d^{3} - 3 \, a b c d^{4} + 2 \, a^{2} d^{5} + {\left(b^{2} c^{4} d - 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 3 \, a b c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(4 \, {\left(a b c^{4} d - a^{2} c^{3} d^{2}\right)} x^{3} - {\left(5 \, b^{2} c^{4} d - 23 \, a b c^{3} d^{2} + 18 \, a^{2} c^{2} d^{3}\right)} x^{2} - 3 \, {\left(b^{2} c^{3} d^{2} - 5 \, a b c^{2} d^{3} + 4 \, a^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(b c^{5} d^{3} - a c^{4} d^{4} + {\left(b c^{7} d - a c^{6} d^{2}\right)} x^{2} + 2 \, {\left(b c^{6} d^{2} - a c^{5} d^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 8 \, a^{2} d^{4} + {\left(b^{2} c^{4} - 8 \, a b c^{3} d + 8 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 8 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b c d - a d^{2}} \arctan\left(\frac{\sqrt{b c d - a d^{2}} x \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 12 \, {\left(b^{2} c^{2} d^{3} - 3 \, a b c d^{4} + 2 \, a^{2} d^{5} + {\left(b^{2} c^{4} d - 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 3 \, a b c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(4 \, {\left(a b c^{4} d - a^{2} c^{3} d^{2}\right)} x^{3} - {\left(5 \, b^{2} c^{4} d - 23 \, a b c^{3} d^{2} + 18 \, a^{2} c^{2} d^{3}\right)} x^{2} - 3 \, {\left(b^{2} c^{3} d^{2} - 5 \, a b c^{2} d^{3} + 4 \, a^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(b c^{5} d^{3} - a c^{4} d^{4} + {\left(b c^{7} d - a c^{6} d^{2}\right)} x^{2} + 2 \, {\left(b c^{6} d^{2} - a c^{5} d^{3}\right)} x\right)}}\right]"," ",0,"[-1/8*(12*(b^2*c^2*d^3 - 3*a*b*c*d^4 + 2*a^2*d^5 + (b^2*c^4*d - 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2 + 2*(b^2*c^3*d^2 - 3*a*b*c^2*d^3 + 2*a^2*c*d^4)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 3*(b^2*c^2*d^2 - 8*a*b*c*d^3 + 8*a^2*d^4 + (b^2*c^4 - 8*a*b*c^3*d + 8*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 8*a*b*c^2*d^2 + 8*a^2*c*d^3)*x)*sqrt(-b*c*d + a*d^2)*log((b*d - (b*c - 2*a*d)*x + 2*sqrt(-b*c*d + a*d^2)*x*sqrt((a*x + b)/x))/(c*x + d)) - 2*(4*(a*b*c^4*d - a^2*c^3*d^2)*x^3 - (5*b^2*c^4*d - 23*a*b*c^3*d^2 + 18*a^2*c^2*d^3)*x^2 - 3*(b^2*c^3*d^2 - 5*a*b*c^2*d^3 + 4*a^2*c*d^4)*x)*sqrt((a*x + b)/x))/(b*c^5*d^3 - a*c^4*d^4 + (b*c^7*d - a*c^6*d^2)*x^2 + 2*(b*c^6*d^2 - a*c^5*d^3)*x), -1/8*(24*(b^2*c^2*d^3 - 3*a*b*c*d^4 + 2*a^2*d^5 + (b^2*c^4*d - 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2 + 2*(b^2*c^3*d^2 - 3*a*b*c^2*d^3 + 2*a^2*c*d^4)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + 3*(b^2*c^2*d^2 - 8*a*b*c*d^3 + 8*a^2*d^4 + (b^2*c^4 - 8*a*b*c^3*d + 8*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 8*a*b*c^2*d^2 + 8*a^2*c*d^3)*x)*sqrt(-b*c*d + a*d^2)*log((b*d - (b*c - 2*a*d)*x + 2*sqrt(-b*c*d + a*d^2)*x*sqrt((a*x + b)/x))/(c*x + d)) - 2*(4*(a*b*c^4*d - a^2*c^3*d^2)*x^3 - (5*b^2*c^4*d - 23*a*b*c^3*d^2 + 18*a^2*c^2*d^3)*x^2 - 3*(b^2*c^3*d^2 - 5*a*b*c^2*d^3 + 4*a^2*c*d^4)*x)*sqrt((a*x + b)/x))/(b*c^5*d^3 - a*c^4*d^4 + (b*c^7*d - a*c^6*d^2)*x^2 + 2*(b*c^6*d^2 - a*c^5*d^3)*x), 1/4*(3*(b^2*c^2*d^2 - 8*a*b*c*d^3 + 8*a^2*d^4 + (b^2*c^4 - 8*a*b*c^3*d + 8*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 8*a*b*c^2*d^2 + 8*a^2*c*d^3)*x)*sqrt(b*c*d - a*d^2)*arctan(sqrt(b*c*d - a*d^2)*x*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 6*(b^2*c^2*d^3 - 3*a*b*c*d^4 + 2*a^2*d^5 + (b^2*c^4*d - 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2 + 2*(b^2*c^3*d^2 - 3*a*b*c^2*d^3 + 2*a^2*c*d^4)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (4*(a*b*c^4*d - a^2*c^3*d^2)*x^3 - (5*b^2*c^4*d - 23*a*b*c^3*d^2 + 18*a^2*c^2*d^3)*x^2 - 3*(b^2*c^3*d^2 - 5*a*b*c^2*d^3 + 4*a^2*c*d^4)*x)*sqrt((a*x + b)/x))/(b*c^5*d^3 - a*c^4*d^4 + (b*c^7*d - a*c^6*d^2)*x^2 + 2*(b*c^6*d^2 - a*c^5*d^3)*x), 1/4*(3*(b^2*c^2*d^2 - 8*a*b*c*d^3 + 8*a^2*d^4 + (b^2*c^4 - 8*a*b*c^3*d + 8*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d - 8*a*b*c^2*d^2 + 8*a^2*c*d^3)*x)*sqrt(b*c*d - a*d^2)*arctan(sqrt(b*c*d - a*d^2)*x*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 12*(b^2*c^2*d^3 - 3*a*b*c*d^4 + 2*a^2*d^5 + (b^2*c^4*d - 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2 + 2*(b^2*c^3*d^2 - 3*a*b*c^2*d^3 + 2*a^2*c*d^4)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (4*(a*b*c^4*d - a^2*c^3*d^2)*x^3 - (5*b^2*c^4*d - 23*a*b*c^3*d^2 + 18*a^2*c^2*d^3)*x^2 - 3*(b^2*c^3*d^2 - 5*a*b*c^2*d^3 + 4*a^2*c*d^4)*x)*sqrt((a*x + b)/x))/(b*c^5*d^3 - a*c^4*d^4 + (b*c^7*d - a*c^6*d^2)*x^2 + 2*(b*c^6*d^2 - a*c^5*d^3)*x)]","B",0
238,1,494,0,0.857835," ","integrate((a+b/x)^(5/2)*(c+d/x)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(5 \, a b^{3} c^{3} + 6 \, a^{2} b^{2} c^{2} d\right)} \sqrt{a} x^{4} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(315 \, a^{2} b^{2} c^{3} x^{5} - 70 \, b^{4} d^{3} - 2 \, {\left(735 \, a b^{3} c^{3} + 1449 \, a^{2} b^{2} c^{2} d + 135 \, a^{3} b c d^{2} - 10 \, a^{4} d^{3}\right)} x^{4} - 2 \, {\left(105 \, b^{4} c^{3} + 693 \, a b^{3} c^{2} d + 405 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{3} - 6 \, {\left(63 \, b^{4} c^{2} d + 135 \, a b^{3} c d^{2} + 25 \, a^{2} b^{2} d^{3}\right)} x^{2} - 10 \, {\left(27 \, b^{4} c d^{2} + 19 \, a b^{3} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{630 \, b^{2} x^{4}}, -\frac{315 \, {\left(5 \, a b^{3} c^{3} + 6 \, a^{2} b^{2} c^{2} d\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(315 \, a^{2} b^{2} c^{3} x^{5} - 70 \, b^{4} d^{3} - 2 \, {\left(735 \, a b^{3} c^{3} + 1449 \, a^{2} b^{2} c^{2} d + 135 \, a^{3} b c d^{2} - 10 \, a^{4} d^{3}\right)} x^{4} - 2 \, {\left(105 \, b^{4} c^{3} + 693 \, a b^{3} c^{2} d + 405 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{3} - 6 \, {\left(63 \, b^{4} c^{2} d + 135 \, a b^{3} c d^{2} + 25 \, a^{2} b^{2} d^{3}\right)} x^{2} - 10 \, {\left(27 \, b^{4} c d^{2} + 19 \, a b^{3} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{315 \, b^{2} x^{4}}\right]"," ",0,"[1/630*(315*(5*a*b^3*c^3 + 6*a^2*b^2*c^2*d)*sqrt(a)*x^4*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(315*a^2*b^2*c^3*x^5 - 70*b^4*d^3 - 2*(735*a*b^3*c^3 + 1449*a^2*b^2*c^2*d + 135*a^3*b*c*d^2 - 10*a^4*d^3)*x^4 - 2*(105*b^4*c^3 + 693*a*b^3*c^2*d + 405*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^3 - 6*(63*b^4*c^2*d + 135*a*b^3*c*d^2 + 25*a^2*b^2*d^3)*x^2 - 10*(27*b^4*c*d^2 + 19*a*b^3*d^3)*x)*sqrt((a*x + b)/x))/(b^2*x^4), -1/315*(315*(5*a*b^3*c^3 + 6*a^2*b^2*c^2*d)*sqrt(-a)*x^4*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (315*a^2*b^2*c^3*x^5 - 70*b^4*d^3 - 2*(735*a*b^3*c^3 + 1449*a^2*b^2*c^2*d + 135*a^3*b*c*d^2 - 10*a^4*d^3)*x^4 - 2*(105*b^4*c^3 + 693*a*b^3*c^2*d + 405*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^3 - 6*(63*b^4*c^2*d + 135*a*b^3*c*d^2 + 25*a^2*b^2*d^3)*x^2 - 10*(27*b^4*c*d^2 + 19*a*b^3*d^3)*x)*sqrt((a*x + b)/x))/(b^2*x^4)]","A",0
239,1,350,0,0.816172," ","integrate((a+b/x)^(5/2)*(c+d/x)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(5 \, a b^{2} c^{2} + 4 \, a^{2} b c d\right)} \sqrt{a} x^{3} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(105 \, a^{2} b c^{2} x^{4} - 30 \, b^{3} d^{2} - 2 \, {\left(245 \, a b^{2} c^{2} + 322 \, a^{2} b c d + 15 \, a^{3} d^{2}\right)} x^{3} - 2 \, {\left(35 \, b^{3} c^{2} + 154 \, a b^{2} c d + 45 \, a^{2} b d^{2}\right)} x^{2} - 6 \, {\left(14 \, b^{3} c d + 15 \, a b^{2} d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{210 \, b x^{3}}, -\frac{105 \, {\left(5 \, a b^{2} c^{2} + 4 \, a^{2} b c d\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(105 \, a^{2} b c^{2} x^{4} - 30 \, b^{3} d^{2} - 2 \, {\left(245 \, a b^{2} c^{2} + 322 \, a^{2} b c d + 15 \, a^{3} d^{2}\right)} x^{3} - 2 \, {\left(35 \, b^{3} c^{2} + 154 \, a b^{2} c d + 45 \, a^{2} b d^{2}\right)} x^{2} - 6 \, {\left(14 \, b^{3} c d + 15 \, a b^{2} d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{105 \, b x^{3}}\right]"," ",0,"[1/210*(105*(5*a*b^2*c^2 + 4*a^2*b*c*d)*sqrt(a)*x^3*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(105*a^2*b*c^2*x^4 - 30*b^3*d^2 - 2*(245*a*b^2*c^2 + 322*a^2*b*c*d + 15*a^3*d^2)*x^3 - 2*(35*b^3*c^2 + 154*a*b^2*c*d + 45*a^2*b*d^2)*x^2 - 6*(14*b^3*c*d + 15*a*b^2*d^2)*x)*sqrt((a*x + b)/x))/(b*x^3), -1/105*(105*(5*a*b^2*c^2 + 4*a^2*b*c*d)*sqrt(-a)*x^3*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (105*a^2*b*c^2*x^4 - 30*b^3*d^2 - 2*(245*a*b^2*c^2 + 322*a^2*b*c*d + 15*a^3*d^2)*x^3 - 2*(35*b^3*c^2 + 154*a*b^2*c*d + 45*a^2*b*d^2)*x^2 - 6*(14*b^3*c*d + 15*a*b^2*d^2)*x)*sqrt((a*x + b)/x))/(b*x^3)]","A",0
240,1,222,0,0.662983," ","integrate((a+b/x)^(5/2)*(c+d/x),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, a b c + 2 \, a^{2} d\right)} \sqrt{a} x^{2} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(15 \, a^{2} c x^{3} - 6 \, b^{2} d - 2 \, {\left(35 \, a b c + 23 \, a^{2} d\right)} x^{2} - 2 \, {\left(5 \, b^{2} c + 11 \, a b d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{30 \, x^{2}}, -\frac{15 \, {\left(5 \, a b c + 2 \, a^{2} d\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(15 \, a^{2} c x^{3} - 6 \, b^{2} d - 2 \, {\left(35 \, a b c + 23 \, a^{2} d\right)} x^{2} - 2 \, {\left(5 \, b^{2} c + 11 \, a b d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{15 \, x^{2}}\right]"," ",0,"[1/30*(15*(5*a*b*c + 2*a^2*d)*sqrt(a)*x^2*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(15*a^2*c*x^3 - 6*b^2*d - 2*(35*a*b*c + 23*a^2*d)*x^2 - 2*(5*b^2*c + 11*a*b*d)*x)*sqrt((a*x + b)/x))/x^2, -1/15*(15*(5*a*b*c + 2*a^2*d)*sqrt(-a)*x^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (15*a^2*c*x^3 - 6*b^2*d - 2*(35*a*b*c + 23*a^2*d)*x^2 - 2*(5*b^2*c + 11*a*b*d)*x)*sqrt((a*x + b)/x))/x^2]","A",0
241,1,139,0,0.884878," ","integrate((a+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{3}{2}} b x \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(3 \, a^{2} x^{2} - 14 \, a b x - 2 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{6 \, x}, -\frac{15 \, \sqrt{-a} a b x \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(3 \, a^{2} x^{2} - 14 \, a b x - 2 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{3 \, x}\right]"," ",0,"[1/6*(15*a^(3/2)*b*x*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(3*a^2*x^2 - 14*a*b*x - 2*b^2)*sqrt((a*x + b)/x))/x, -1/3*(15*sqrt(-a)*a*b*x*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (3*a^2*x^2 - 14*a*b*x - 2*b^2)*sqrt((a*x + b)/x))/x]","A",0
242,1,659,0,1.148925," ","integrate((a+b/x)^(5/2)/(c+d/x),x, algorithm=""fricas"")","\left[-\frac{{\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(a^{2} c d x - 2 \, b^{2} c^{2}\right)} \sqrt{\frac{a x + b}{x}}}{2 \, c^{2} d}, -\frac{{\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - {\left(a^{2} c d x - 2 \, b^{2} c^{2}\right)} \sqrt{\frac{a x + b}{x}}}{c^{2} d}, -\frac{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) + {\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(a^{2} c d x - 2 \, b^{2} c^{2}\right)} \sqrt{\frac{a x + b}{x}}}{2 \, c^{2} d}, -\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) + {\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(a^{2} c d x - 2 \, b^{2} c^{2}\right)} \sqrt{\frac{a x + b}{x}}}{c^{2} d}\right]"," ",0,"[-1/2*((5*a*b*c*d - 2*a^2*d^2)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - 2*(a^2*c*d*x - 2*b^2*c^2)*sqrt((a*x + b)/x))/(c^2*d), -((5*a*b*c*d - 2*a^2*d^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - (a^2*c*d*x - 2*b^2*c^2)*sqrt((a*x + b)/x))/(c^2*d), -1/2*(4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) + (5*a*b*c*d - 2*a^2*d^2)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(a^2*c*d*x - 2*b^2*c^2)*sqrt((a*x + b)/x))/(c^2*d), -(2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) + (5*a*b*c*d - 2*a^2*d^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (a^2*c*d*x - 2*b^2*c^2)*sqrt((a*x + b)/x))/(c^2*d)]","A",0
243,1,1001,0,1.152773," ","integrate((a+b/x)^(5/2)/(c+d/x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(5 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(5 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(a^{2} c^{2} d x^{2} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(c^{4} d x + c^{3} d^{2}\right)}}, -\frac{2 \, {\left(5 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(5 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(a^{2} c^{2} d x^{2} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(c^{4} d x + c^{3} d^{2}\right)}}, \frac{2 \, {\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - {\left(5 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(5 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(a^{2} c^{2} d x^{2} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(c^{4} d x + c^{3} d^{2}\right)}}, \frac{{\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - {\left(5 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(5 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a^{2} c^{2} d x^{2} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{c^{4} d x + c^{3} d^{2}}\right]"," ",0,"[-1/2*((5*a*b*c*d^2 - 4*a^2*d^3 + (5*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - 2*(a^2*c^2*d*x^2 + (b^2*c^3 - 2*a*b*c^2*d + 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(c^4*d*x + c^3*d^2), -1/2*(2*(5*a*b*c*d^2 - 4*a^2*d^3 + (5*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - 2*(a^2*c^2*d*x^2 + (b^2*c^3 - 2*a*b*c^2*d + 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(c^4*d*x + c^3*d^2), 1/2*(2*(b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - (5*a*b*c*d^2 - 4*a^2*d^3 + (5*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(a^2*c^2*d*x^2 + (b^2*c^3 - 2*a*b*c^2*d + 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(c^4*d*x + c^3*d^2), ((b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - (5*a*b*c*d^2 - 4*a^2*d^3 + (5*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a^2*c^2*d*x^2 + (b^2*c^3 - 2*a*b*c^2*d + 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(c^4*d*x + c^3*d^2)]","A",0
244,1,1445,0,0.963535," ","integrate((a+b/x)^(5/2)/(c+d/x)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(5 \, a b c d^{3} - 6 \, a^{2} d^{4} + {\left(5 \, a b c^{3} d - 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(5 \, a b c^{2} d^{2} - 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(b^{2} c^{2} d^{2} + 8 \, a b c d^{3} - 24 \, a^{2} d^{4} + {\left(b^{2} c^{4} + 8 \, a b c^{3} d - 24 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d + 8 \, a b c^{2} d^{2} - 24 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(4 \, a^{2} c^{3} d x^{3} + {\left(b^{2} c^{4} - 11 \, a b c^{3} d + 18 \, a^{2} c^{2} d^{2}\right)} x^{2} - {\left(b^{2} c^{3} d + 7 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(c^{6} d x^{2} + 2 \, c^{5} d^{2} x + c^{4} d^{3}\right)}}, \frac{{\left(b^{2} c^{2} d^{2} + 8 \, a b c d^{3} - 24 \, a^{2} d^{4} + {\left(b^{2} c^{4} + 8 \, a b c^{3} d - 24 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d + 8 \, a b c^{2} d^{2} - 24 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - 2 \, {\left(5 \, a b c d^{3} - 6 \, a^{2} d^{4} + {\left(5 \, a b c^{3} d - 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(5 \, a b c^{2} d^{2} - 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(4 \, a^{2} c^{3} d x^{3} + {\left(b^{2} c^{4} - 11 \, a b c^{3} d + 18 \, a^{2} c^{2} d^{2}\right)} x^{2} - {\left(b^{2} c^{3} d + 7 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(c^{6} d x^{2} + 2 \, c^{5} d^{2} x + c^{4} d^{3}\right)}}, -\frac{8 \, {\left(5 \, a b c d^{3} - 6 \, a^{2} d^{4} + {\left(5 \, a b c^{3} d - 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(5 \, a b c^{2} d^{2} - 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(b^{2} c^{2} d^{2} + 8 \, a b c d^{3} - 24 \, a^{2} d^{4} + {\left(b^{2} c^{4} + 8 \, a b c^{3} d - 24 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d + 8 \, a b c^{2} d^{2} - 24 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{2 \, d x \sqrt{-\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}} + b d - {\left(b c - 2 \, a d\right)} x}{c x + d}\right) - 2 \, {\left(4 \, a^{2} c^{3} d x^{3} + {\left(b^{2} c^{4} - 11 \, a b c^{3} d + 18 \, a^{2} c^{2} d^{2}\right)} x^{2} - {\left(b^{2} c^{3} d + 7 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(c^{6} d x^{2} + 2 \, c^{5} d^{2} x + c^{4} d^{3}\right)}}, \frac{{\left(b^{2} c^{2} d^{2} + 8 \, a b c d^{3} - 24 \, a^{2} d^{4} + {\left(b^{2} c^{4} + 8 \, a b c^{3} d - 24 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d + 8 \, a b c^{2} d^{2} - 24 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{d \sqrt{\frac{b c - a d}{d}} \sqrt{\frac{a x + b}{x}}}{b c - a d}\right) - 4 \, {\left(5 \, a b c d^{3} - 6 \, a^{2} d^{4} + {\left(5 \, a b c^{3} d - 6 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(5 \, a b c^{2} d^{2} - 6 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(4 \, a^{2} c^{3} d x^{3} + {\left(b^{2} c^{4} - 11 \, a b c^{3} d + 18 \, a^{2} c^{2} d^{2}\right)} x^{2} - {\left(b^{2} c^{3} d + 7 \, a b c^{2} d^{2} - 12 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(c^{6} d x^{2} + 2 \, c^{5} d^{2} x + c^{4} d^{3}\right)}}\right]"," ",0,"[-1/8*(4*(5*a*b*c*d^3 - 6*a^2*d^4 + (5*a*b*c^3*d - 6*a^2*c^2*d^2)*x^2 + 2*(5*a*b*c^2*d^2 - 6*a^2*c*d^3)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (b^2*c^2*d^2 + 8*a*b*c*d^3 - 24*a^2*d^4 + (b^2*c^4 + 8*a*b*c^3*d - 24*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d + 8*a*b*c^2*d^2 - 24*a^2*c*d^3)*x)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - 2*(4*a^2*c^3*d*x^3 + (b^2*c^4 - 11*a*b*c^3*d + 18*a^2*c^2*d^2)*x^2 - (b^2*c^3*d + 7*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(c^6*d*x^2 + 2*c^5*d^2*x + c^4*d^3), 1/4*((b^2*c^2*d^2 + 8*a*b*c*d^3 - 24*a^2*d^4 + (b^2*c^4 + 8*a*b*c^3*d - 24*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d + 8*a*b*c^2*d^2 - 24*a^2*c*d^3)*x)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - 2*(5*a*b*c*d^3 - 6*a^2*d^4 + (5*a*b*c^3*d - 6*a^2*c^2*d^2)*x^2 + 2*(5*a*b*c^2*d^2 - 6*a^2*c*d^3)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (4*a^2*c^3*d*x^3 + (b^2*c^4 - 11*a*b*c^3*d + 18*a^2*c^2*d^2)*x^2 - (b^2*c^3*d + 7*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(c^6*d*x^2 + 2*c^5*d^2*x + c^4*d^3), -1/8*(8*(5*a*b*c*d^3 - 6*a^2*d^4 + (5*a*b*c^3*d - 6*a^2*c^2*d^2)*x^2 + 2*(5*a*b*c^2*d^2 - 6*a^2*c*d^3)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (b^2*c^2*d^2 + 8*a*b*c*d^3 - 24*a^2*d^4 + (b^2*c^4 + 8*a*b*c^3*d - 24*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d + 8*a*b*c^2*d^2 - 24*a^2*c*d^3)*x)*sqrt(-(b*c - a*d)/d)*log((2*d*x*sqrt(-(b*c - a*d)/d)*sqrt((a*x + b)/x) + b*d - (b*c - 2*a*d)*x)/(c*x + d)) - 2*(4*a^2*c^3*d*x^3 + (b^2*c^4 - 11*a*b*c^3*d + 18*a^2*c^2*d^2)*x^2 - (b^2*c^3*d + 7*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(c^6*d*x^2 + 2*c^5*d^2*x + c^4*d^3), 1/4*((b^2*c^2*d^2 + 8*a*b*c*d^3 - 24*a^2*d^4 + (b^2*c^4 + 8*a*b*c^3*d - 24*a^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d + 8*a*b*c^2*d^2 - 24*a^2*c*d^3)*x)*sqrt((b*c - a*d)/d)*arctan(-d*sqrt((b*c - a*d)/d)*sqrt((a*x + b)/x)/(b*c - a*d)) - 4*(5*a*b*c*d^3 - 6*a^2*d^4 + (5*a*b*c^3*d - 6*a^2*c^2*d^2)*x^2 + 2*(5*a*b*c^2*d^2 - 6*a^2*c*d^3)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (4*a^2*c^3*d*x^3 + (b^2*c^4 - 11*a*b*c^3*d + 18*a^2*c^2*d^2)*x^2 - (b^2*c^3*d + 7*a*b*c^2*d^2 - 12*a^2*c*d^3)*x)*sqrt((a*x + b)/x))/(c^6*d*x^2 + 2*c^5*d^2*x + c^4*d^3)]","A",0
245,1,233,0,0.556347," ","integrate((c+d/x)^3/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} - 6 \, a b^{2} c^{2} d\right)} \sqrt{a} x \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(3 \, a b^{2} c^{3} x^{2} - 2 \, a^{2} b d^{3} - 2 \, {\left(9 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, a^{2} b^{2} x}, \frac{3 \, {\left(b^{3} c^{3} - 6 \, a b^{2} c^{2} d\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(3 \, a b^{2} c^{3} x^{2} - 2 \, a^{2} b d^{3} - 2 \, {\left(9 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, a^{2} b^{2} x}\right]"," ",0,"[-1/6*(3*(b^3*c^3 - 6*a*b^2*c^2*d)*sqrt(a)*x*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(3*a*b^2*c^3*x^2 - 2*a^2*b*d^3 - 2*(9*a^2*b*c*d^2 - 2*a^3*d^3)*x)*sqrt((a*x + b)/x))/(a^2*b^2*x), 1/3*(3*(b^3*c^3 - 6*a*b^2*c^2*d)*sqrt(-a)*x*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (3*a*b^2*c^3*x^2 - 2*a^2*b*d^3 - 2*(9*a^2*b*c*d^2 - 2*a^3*d^3)*x)*sqrt((a*x + b)/x))/(a^2*b^2*x)]","A",0
246,1,158,0,0.612521," ","integrate((c+d/x)^2/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} - 4 \, a b c d\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(a b c^{2} x - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a x + b}{x}}}{2 \, a^{2} b}, \frac{{\left(b^{2} c^{2} - 4 \, a b c d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a b c^{2} x - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a x + b}{x}}}{a^{2} b}\right]"," ",0,"[-1/2*((b^2*c^2 - 4*a*b*c*d)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(a*b*c^2*x - 2*a^2*d^2)*sqrt((a*x + b)/x))/(a^2*b), ((b^2*c^2 - 4*a*b*c*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a*b*c^2*x - 2*a^2*d^2)*sqrt((a*x + b)/x))/(a^2*b)]","A",0
247,1,115,0,0.847126," ","integrate((c+d/x)/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a c x \sqrt{\frac{a x + b}{x}} - {\left(b c - 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a^{2}}, \frac{a c x \sqrt{\frac{a x + b}{x}} + {\left(b c - 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a^{2}}\right]"," ",0,"[1/2*(2*a*c*x*sqrt((a*x + b)/x) - (b*c - 2*a*d)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/a^2, (a*c*x*sqrt((a*x + b)/x) + (b*c - 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/a^2]","A",0
248,1,98,0,0.782208," ","integrate(1/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a x + b}{x}} + \sqrt{a} b \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a^{2}}, \frac{a x \sqrt{\frac{a x + b}{x}} + \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a^{2}}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*x + b)/x) + sqrt(a)*b*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/a^2, (a*x*sqrt((a*x + b)/x) + sqrt(-a)*b*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/a^2]","A",0
249,1,542,0,0.770528," ","integrate(1/(c+d/x)/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} d \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, a c x \sqrt{\frac{a x + b}{x}} + {\left(b c + 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a^{2} c^{2}}, \frac{a^{2} d \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + a c x \sqrt{\frac{a x + b}{x}} + {\left(b c + 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a^{2} c^{2}}, -\frac{4 \, a^{2} d \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 2 \, a c x \sqrt{\frac{a x + b}{x}} - {\left(b c + 2 \, a d\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a^{2} c^{2}}, -\frac{2 \, a^{2} d \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - a c x \sqrt{\frac{a x + b}{x}} - {\left(b c + 2 \, a d\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a^{2} c^{2}}\right]"," ",0,"[1/2*(2*a^2*d*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*a*c*x*sqrt((a*x + b)/x) + (b*c + 2*a*d)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/(a^2*c^2), (a^2*d*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + a*c*x*sqrt((a*x + b)/x) + (b*c + 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/(a^2*c^2), -1/2*(4*a^2*d*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 2*a*c*x*sqrt((a*x + b)/x) - (b*c + 2*a*d)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/(a^2*c^2), -(2*a^2*d*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - a*c*x*sqrt((a*x + b)/x) - (b*c + 2*a*d)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/(a^2*c^2)]","A",0
250,1,1163,0,1.057389," ","integrate(1/(c+d/x)^2/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a^{2} b c^{2} d - 4 \, a^{3} c d^{2}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left({\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2} + {\left(a b c^{2} d - 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x\right)}}, -\frac{2 \, {\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a^{2} b c^{2} d - 4 \, a^{3} c d^{2}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - {\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left({\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2} + {\left(a b c^{2} d - 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x\right)}}, \frac{2 \, {\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a^{2} b c^{2} d - 4 \, a^{3} c d^{2}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left({\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2} + {\left(a b c^{2} d - 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x\right)}}, -\frac{{\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a^{2} b c^{2} d - 4 \, a^{3} c d^{2}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - {\left(b^{2} c^{2} d + 3 \, a b c d^{2} - 4 \, a^{2} d^{3} + {\left(b^{2} c^{3} + 3 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left({\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2} + {\left(a b c^{2} d - 2 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{a^{2} b c^{4} d - a^{3} c^{3} d^{2} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x}\right]"," ",0,"[1/2*((b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a^2*b*c^2*d - 4*a^3*c*d^2)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*((a*b*c^3 - a^2*c^2*d)*x^2 + (a*b*c^2*d - 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^2*b*c^4*d - a^3*c^3*d^2 + (a^2*b*c^5 - a^3*c^4*d)*x), -1/2*(2*(5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a^2*b*c^2*d - 4*a^3*c*d^2)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - (b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*((a*b*c^3 - a^2*c^2*d)*x^2 + (a*b*c^2*d - 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^2*b*c^4*d - a^3*c^3*d^2 + (a^2*b*c^5 - a^3*c^4*d)*x), 1/2*(2*(b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a^2*b*c^2*d - 4*a^3*c*d^2)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*((a*b*c^3 - a^2*c^2*d)*x^2 + (a*b*c^2*d - 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^2*b*c^4*d - a^3*c^3*d^2 + (a^2*b*c^5 - a^3*c^4*d)*x), -((5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a^2*b*c^2*d - 4*a^3*c*d^2)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - (b^2*c^2*d + 3*a*b*c*d^2 - 4*a^2*d^3 + (b^2*c^3 + 3*a*b*c^2*d - 4*a^2*c*d^2)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - ((a*b*c^3 - a^2*c^2*d)*x^2 + (a*b*c^2*d - 2*a^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^2*b*c^4*d - a^3*c^3*d^2 + (a^2*b*c^5 - a^3*c^4*d)*x)]","A",0
251,1,2307,0,2.222590," ","integrate(1/(c+d/x)^3/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{3} c^{3} d^{2} + 4 \, a b^{2} c^{2} d^{3} - 11 \, a^{2} b c d^{4} + 6 \, a^{3} d^{5} + {\left(b^{3} c^{5} + 4 \, a b^{2} c^{4} d - 11 \, a^{2} b c^{3} d^{2} + 6 \, a^{3} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d + 4 \, a b^{2} c^{3} d^{2} - 11 \, a^{2} b c^{2} d^{3} + 6 \, a^{3} c d^{4}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(35 \, a^{2} b^{2} c^{2} d^{3} - 56 \, a^{3} b c d^{4} + 24 \, a^{4} d^{5} + {\left(35 \, a^{2} b^{2} c^{4} d - 56 \, a^{3} b c^{3} d^{2} + 24 \, a^{4} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(35 \, a^{2} b^{2} c^{3} d^{2} - 56 \, a^{3} b c^{2} d^{3} + 24 \, a^{4} c d^{4}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(4 \, {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x^{3} + {\left(8 \, a b^{2} c^{4} d - 29 \, a^{2} b c^{3} d^{2} + 18 \, a^{3} c^{2} d^{3}\right)} x^{2} + {\left(4 \, a b^{2} c^{3} d^{2} - 19 \, a^{2} b c^{2} d^{3} + 12 \, a^{3} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x\right)}}, \frac{8 \, {\left(b^{3} c^{3} d^{2} + 4 \, a b^{2} c^{2} d^{3} - 11 \, a^{2} b c d^{4} + 6 \, a^{3} d^{5} + {\left(b^{3} c^{5} + 4 \, a b^{2} c^{4} d - 11 \, a^{2} b c^{3} d^{2} + 6 \, a^{3} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d + 4 \, a b^{2} c^{3} d^{2} - 11 \, a^{2} b c^{2} d^{3} + 6 \, a^{3} c d^{4}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(35 \, a^{2} b^{2} c^{2} d^{3} - 56 \, a^{3} b c d^{4} + 24 \, a^{4} d^{5} + {\left(35 \, a^{2} b^{2} c^{4} d - 56 \, a^{3} b c^{3} d^{2} + 24 \, a^{4} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(35 \, a^{2} b^{2} c^{3} d^{2} - 56 \, a^{3} b c^{2} d^{3} + 24 \, a^{4} c d^{4}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(4 \, {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x^{3} + {\left(8 \, a b^{2} c^{4} d - 29 \, a^{2} b c^{3} d^{2} + 18 \, a^{3} c^{2} d^{3}\right)} x^{2} + {\left(4 \, a b^{2} c^{3} d^{2} - 19 \, a^{2} b c^{2} d^{3} + 12 \, a^{3} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x\right)}}, -\frac{{\left(35 \, a^{2} b^{2} c^{2} d^{3} - 56 \, a^{3} b c d^{4} + 24 \, a^{4} d^{5} + {\left(35 \, a^{2} b^{2} c^{4} d - 56 \, a^{3} b c^{3} d^{2} + 24 \, a^{4} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(35 \, a^{2} b^{2} c^{3} d^{2} - 56 \, a^{3} b c^{2} d^{3} + 24 \, a^{4} c d^{4}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 2 \, {\left(b^{3} c^{3} d^{2} + 4 \, a b^{2} c^{2} d^{3} - 11 \, a^{2} b c d^{4} + 6 \, a^{3} d^{5} + {\left(b^{3} c^{5} + 4 \, a b^{2} c^{4} d - 11 \, a^{2} b c^{3} d^{2} + 6 \, a^{3} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d + 4 \, a b^{2} c^{3} d^{2} - 11 \, a^{2} b c^{2} d^{3} + 6 \, a^{3} c d^{4}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - {\left(4 \, {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x^{3} + {\left(8 \, a b^{2} c^{4} d - 29 \, a^{2} b c^{3} d^{2} + 18 \, a^{3} c^{2} d^{3}\right)} x^{2} + {\left(4 \, a b^{2} c^{3} d^{2} - 19 \, a^{2} b c^{2} d^{3} + 12 \, a^{3} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x\right)}}, -\frac{{\left(35 \, a^{2} b^{2} c^{2} d^{3} - 56 \, a^{3} b c d^{4} + 24 \, a^{4} d^{5} + {\left(35 \, a^{2} b^{2} c^{4} d - 56 \, a^{3} b c^{3} d^{2} + 24 \, a^{4} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(35 \, a^{2} b^{2} c^{3} d^{2} - 56 \, a^{3} b c^{2} d^{3} + 24 \, a^{4} c d^{4}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 4 \, {\left(b^{3} c^{3} d^{2} + 4 \, a b^{2} c^{2} d^{3} - 11 \, a^{2} b c d^{4} + 6 \, a^{3} d^{5} + {\left(b^{3} c^{5} + 4 \, a b^{2} c^{4} d - 11 \, a^{2} b c^{3} d^{2} + 6 \, a^{3} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d + 4 \, a b^{2} c^{3} d^{2} - 11 \, a^{2} b c^{2} d^{3} + 6 \, a^{3} c d^{4}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(4 \, {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x^{3} + {\left(8 \, a b^{2} c^{4} d - 29 \, a^{2} b c^{3} d^{2} + 18 \, a^{3} c^{2} d^{3}\right)} x^{2} + {\left(4 \, a b^{2} c^{3} d^{2} - 19 \, a^{2} b c^{2} d^{3} + 12 \, a^{3} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x\right)}}\right]"," ",0,"[1/8*(4*(b^3*c^3*d^2 + 4*a*b^2*c^2*d^3 - 11*a^2*b*c*d^4 + 6*a^3*d^5 + (b^3*c^5 + 4*a*b^2*c^4*d - 11*a^2*b*c^3*d^2 + 6*a^3*c^2*d^3)*x^2 + 2*(b^3*c^4*d + 4*a*b^2*c^3*d^2 - 11*a^2*b*c^2*d^3 + 6*a^3*c*d^4)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (35*a^2*b^2*c^2*d^3 - 56*a^3*b*c*d^4 + 24*a^4*d^5 + (35*a^2*b^2*c^4*d - 56*a^3*b*c^3*d^2 + 24*a^4*c^2*d^3)*x^2 + 2*(35*a^2*b^2*c^3*d^2 - 56*a^3*b*c^2*d^3 + 24*a^4*c*d^4)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(4*(a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x^3 + (8*a*b^2*c^4*d - 29*a^2*b*c^3*d^2 + 18*a^3*c^2*d^3)*x^2 + (4*a*b^2*c^3*d^2 - 19*a^2*b*c^2*d^3 + 12*a^3*c*d^4)*x)*sqrt((a*x + b)/x))/(a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x), 1/8*(8*(b^3*c^3*d^2 + 4*a*b^2*c^2*d^3 - 11*a^2*b*c*d^4 + 6*a^3*d^5 + (b^3*c^5 + 4*a*b^2*c^4*d - 11*a^2*b*c^3*d^2 + 6*a^3*c^2*d^3)*x^2 + 2*(b^3*c^4*d + 4*a*b^2*c^3*d^2 - 11*a^2*b*c^2*d^3 + 6*a^3*c*d^4)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (35*a^2*b^2*c^2*d^3 - 56*a^3*b*c*d^4 + 24*a^4*d^5 + (35*a^2*b^2*c^4*d - 56*a^3*b*c^3*d^2 + 24*a^4*c^2*d^3)*x^2 + 2*(35*a^2*b^2*c^3*d^2 - 56*a^3*b*c^2*d^3 + 24*a^4*c*d^4)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(4*(a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x^3 + (8*a*b^2*c^4*d - 29*a^2*b*c^3*d^2 + 18*a^3*c^2*d^3)*x^2 + (4*a*b^2*c^3*d^2 - 19*a^2*b*c^2*d^3 + 12*a^3*c*d^4)*x)*sqrt((a*x + b)/x))/(a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x), -1/4*((35*a^2*b^2*c^2*d^3 - 56*a^3*b*c*d^4 + 24*a^4*d^5 + (35*a^2*b^2*c^4*d - 56*a^3*b*c^3*d^2 + 24*a^4*c^2*d^3)*x^2 + 2*(35*a^2*b^2*c^3*d^2 - 56*a^3*b*c^2*d^3 + 24*a^4*c*d^4)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 2*(b^3*c^3*d^2 + 4*a*b^2*c^2*d^3 - 11*a^2*b*c*d^4 + 6*a^3*d^5 + (b^3*c^5 + 4*a*b^2*c^4*d - 11*a^2*b*c^3*d^2 + 6*a^3*c^2*d^3)*x^2 + 2*(b^3*c^4*d + 4*a*b^2*c^3*d^2 - 11*a^2*b*c^2*d^3 + 6*a^3*c*d^4)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - (4*(a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x^3 + (8*a*b^2*c^4*d - 29*a^2*b*c^3*d^2 + 18*a^3*c^2*d^3)*x^2 + (4*a*b^2*c^3*d^2 - 19*a^2*b*c^2*d^3 + 12*a^3*c*d^4)*x)*sqrt((a*x + b)/x))/(a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x), -1/4*((35*a^2*b^2*c^2*d^3 - 56*a^3*b*c*d^4 + 24*a^4*d^5 + (35*a^2*b^2*c^4*d - 56*a^3*b*c^3*d^2 + 24*a^4*c^2*d^3)*x^2 + 2*(35*a^2*b^2*c^3*d^2 - 56*a^3*b*c^2*d^3 + 24*a^4*c*d^4)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 4*(b^3*c^3*d^2 + 4*a*b^2*c^2*d^3 - 11*a^2*b*c*d^4 + 6*a^3*d^5 + (b^3*c^5 + 4*a*b^2*c^4*d - 11*a^2*b*c^3*d^2 + 6*a^3*c^2*d^3)*x^2 + 2*(b^3*c^4*d + 4*a*b^2*c^3*d^2 - 11*a^2*b*c^2*d^3 + 6*a^3*c*d^4)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (4*(a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x^3 + (8*a*b^2*c^4*d - 29*a^2*b*c^3*d^2 + 18*a^3*c^2*d^3)*x^2 + (4*a*b^2*c^3*d^2 - 19*a^2*b*c^2*d^3 + 12*a^3*c*d^4)*x)*sqrt((a*x + b)/x))/(a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x)]","B",0
252,1,336,0,1.541861," ","integrate((c+d/x)^3/(a+b/x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{4} c^{3} - 2 \, a b^{3} c^{2} d + {\left(a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d\right)} x\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(a^{2} b^{2} c^{3} x^{2} - 2 \, a^{3} b d^{3} + {\left(3 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2} - 4 \, a^{4} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{4} b^{2} x + a^{3} b^{3}\right)}}, \frac{3 \, {\left(b^{4} c^{3} - 2 \, a b^{3} c^{2} d + {\left(a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a^{2} b^{2} c^{3} x^{2} - 2 \, a^{3} b d^{3} + {\left(3 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2} - 4 \, a^{4} d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{a^{4} b^{2} x + a^{3} b^{3}}\right]"," ",0,"[-1/2*(3*(b^4*c^3 - 2*a*b^3*c^2*d + (a*b^3*c^3 - 2*a^2*b^2*c^2*d)*x)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(a^2*b^2*c^3*x^2 - 2*a^3*b*d^3 + (3*a*b^3*c^3 - 6*a^2*b^2*c^2*d + 6*a^3*b*c*d^2 - 4*a^4*d^3)*x)*sqrt((a*x + b)/x))/(a^4*b^2*x + a^3*b^3), (3*(b^4*c^3 - 2*a*b^3*c^2*d + (a*b^3*c^3 - 2*a^2*b^2*c^2*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a^2*b^2*c^3*x^2 - 2*a^3*b*d^3 + (3*a*b^3*c^3 - 6*a^2*b^2*c^2*d + 6*a^3*b*c*d^2 - 4*a^4*d^3)*x)*sqrt((a*x + b)/x))/(a^4*b^2*x + a^3*b^3)]","A",0
253,1,272,0,0.615909," ","integrate((c+d/x)^2/(a+b/x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(a^{2} b c^{2} x^{2} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d + 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{4} b x + a^{3} b^{2}\right)}}, \frac{{\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a^{2} b c^{2} x^{2} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d + 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{a^{4} b x + a^{3} b^{2}}\right]"," ",0,"[-1/2*((3*b^3*c^2 - 4*a*b^2*c*d + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(a^2*b*c^2*x^2 + (3*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2)*x)*sqrt((a*x + b)/x))/(a^4*b*x + a^3*b^2), ((3*b^3*c^2 - 4*a*b^2*c*d + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a^2*b*c^2*x^2 + (3*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2)*x)*sqrt((a*x + b)/x))/(a^4*b*x + a^3*b^2)]","A",0
254,1,210,0,0.891773," ","integrate((c+d/x)/(a+b/x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c - 2 \, a b d + {\left(3 \, a b c - 2 \, a^{2} d\right)} x\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(a^{2} c x^{2} + {\left(3 \, a b c - 2 \, a^{2} d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{4} x + a^{3} b\right)}}, \frac{{\left(3 \, b^{2} c - 2 \, a b d + {\left(3 \, a b c - 2 \, a^{2} d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a^{2} c x^{2} + {\left(3 \, a b c - 2 \, a^{2} d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{a^{4} x + a^{3} b}\right]"," ",0,"[-1/2*((3*b^2*c - 2*a*b*d + (3*a*b*c - 2*a^2*d)*x)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(a^2*c*x^2 + (3*a*b*c - 2*a^2*d)*x)*sqrt((a*x + b)/x))/(a^4*x + a^3*b), ((3*b^2*c - 2*a*b*d + (3*a*b*c - 2*a^2*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a^2*c*x^2 + (3*a*b*c - 2*a^2*d)*x)*sqrt((a*x + b)/x))/(a^4*x + a^3*b)]","A",0
255,1,156,0,0.834419," ","integrate(1/(a+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b x + b^{2}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(a^{2} x^{2} + 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{4} x + a^{3} b\right)}}, \frac{3 \, {\left(a b x + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a^{2} x^{2} + 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{a^{4} x + a^{3} b}\right]"," ",0,"[1/2*(3*(a*b*x + b^2)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(a^2*x^2 + 3*a*b*x)*sqrt((a*x + b)/x))/(a^4*x + a^3*b), (3*(a*b*x + b^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a^2*x^2 + 3*a*b*x)*sqrt((a*x + b)/x))/(a^4*x + a^3*b)]","A",0
256,1,1075,0,1.321587," ","integrate(1/(a+b/x)^(3/2)/(c+d/x),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(a^{4} d^{2} x + a^{3} b d^{2}\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left({\left(a^{2} b c^{2} - a^{3} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x\right)}}, \frac{{\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(a^{4} d^{2} x + a^{3} b d^{2}\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + {\left({\left(a^{2} b c^{2} - a^{3} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{a^{3} b^{2} c^{3} - a^{4} b c^{2} d + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x}, \frac{4 \, {\left(a^{4} d^{2} x + a^{3} b d^{2}\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) + {\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left({\left(a^{2} b c^{2} - a^{3} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x\right)}}, \frac{2 \, {\left(a^{4} d^{2} x + a^{3} b d^{2}\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) + {\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left({\left(a^{2} b c^{2} - a^{3} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{a^{3} b^{2} c^{3} - a^{4} b c^{2} d + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x}\right]"," ",0,"[1/2*((3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(a^4*d^2*x + a^3*b*d^2)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*((a^2*b*c^2 - a^3*c*d)*x^2 + (3*a*b^2*c^2 - a^2*b*c*d)*x)*sqrt((a*x + b)/x))/(a^3*b^2*c^3 - a^4*b*c^2*d + (a^4*b*c^3 - a^5*c^2*d)*x), ((3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (a^4*d^2*x + a^3*b*d^2)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + ((a^2*b*c^2 - a^3*c*d)*x^2 + (3*a*b^2*c^2 - a^2*b*c*d)*x)*sqrt((a*x + b)/x))/(a^3*b^2*c^3 - a^4*b*c^2*d + (a^4*b*c^3 - a^5*c^2*d)*x), 1/2*(4*(a^4*d^2*x + a^3*b*d^2)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) + (3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*((a^2*b*c^2 - a^3*c*d)*x^2 + (3*a*b^2*c^2 - a^2*b*c*d)*x)*sqrt((a*x + b)/x))/(a^3*b^2*c^3 - a^4*b*c^2*d + (a^4*b*c^3 - a^5*c^2*d)*x), (2*(a^4*d^2*x + a^3*b*d^2)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) + (3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + ((a^2*b*c^2 - a^3*c*d)*x^2 + (3*a*b^2*c^2 - a^2*b*c*d)*x)*sqrt((a*x + b)/x))/(a^3*b^2*c^3 - a^4*b*c^2*d + (a^4*b*c^3 - a^5*c^2*d)*x)]","B",0
257,1,2321,0,2.360395," ","integrate(1/(a+b/x)^(3/2)/(c+d/x)^2,x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{4} c^{3} d - 2 \, a b^{3} c^{2} d^{2} - 5 \, a^{2} b^{2} c d^{3} + 4 \, a^{3} b d^{4} + {\left(3 \, a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d - 5 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, b^{4} c^{4} + a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} - a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - {\left(7 \, a^{3} b^{2} c d^{3} - 4 \, a^{4} b d^{4} + {\left(7 \, a^{4} b c^{2} d^{2} - 4 \, a^{5} c d^{3}\right)} x^{2} + {\left(7 \, a^{3} b^{2} c^{2} d^{2} + 3 \, a^{4} b c d^{3} - 4 \, a^{5} d^{4}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left({\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 2 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 2 \, a^{3} b c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x\right)}}, \frac{2 \, {\left(7 \, a^{3} b^{2} c d^{3} - 4 \, a^{4} b d^{4} + {\left(7 \, a^{4} b c^{2} d^{2} - 4 \, a^{5} c d^{3}\right)} x^{2} + {\left(7 \, a^{3} b^{2} c^{2} d^{2} + 3 \, a^{4} b c d^{3} - 4 \, a^{5} d^{4}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) + {\left(3 \, b^{4} c^{3} d - 2 \, a b^{3} c^{2} d^{2} - 5 \, a^{2} b^{2} c d^{3} + 4 \, a^{3} b d^{4} + {\left(3 \, a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d - 5 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, b^{4} c^{4} + a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} - a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left({\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 2 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 2 \, a^{3} b c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x\right)}}, \frac{2 \, {\left(3 \, b^{4} c^{3} d - 2 \, a b^{3} c^{2} d^{2} - 5 \, a^{2} b^{2} c d^{3} + 4 \, a^{3} b d^{4} + {\left(3 \, a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d - 5 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, b^{4} c^{4} + a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} - a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(7 \, a^{3} b^{2} c d^{3} - 4 \, a^{4} b d^{4} + {\left(7 \, a^{4} b c^{2} d^{2} - 4 \, a^{5} c d^{3}\right)} x^{2} + {\left(7 \, a^{3} b^{2} c^{2} d^{2} + 3 \, a^{4} b c d^{3} - 4 \, a^{5} d^{4}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left({\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 2 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 2 \, a^{3} b c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x\right)}}, \frac{{\left(7 \, a^{3} b^{2} c d^{3} - 4 \, a^{4} b d^{4} + {\left(7 \, a^{4} b c^{2} d^{2} - 4 \, a^{5} c d^{3}\right)} x^{2} + {\left(7 \, a^{3} b^{2} c^{2} d^{2} + 3 \, a^{4} b c d^{3} - 4 \, a^{5} d^{4}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) + {\left(3 \, b^{4} c^{3} d - 2 \, a b^{3} c^{2} d^{2} - 5 \, a^{2} b^{2} c d^{3} + 4 \, a^{3} b d^{4} + {\left(3 \, a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d - 5 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, b^{4} c^{4} + a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} - a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left({\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 2 \, a^{4} c d^{3}\right)} x^{2} + {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 2 \, a^{3} b c d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x}\right]"," ",0,"[1/2*((3*b^4*c^3*d - 2*a*b^3*c^2*d^2 - 5*a^2*b^2*c*d^3 + 4*a^3*b*d^4 + (3*a*b^3*c^4 - 2*a^2*b^2*c^3*d - 5*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*x^2 + (3*b^4*c^4 + a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 - a^3*b*c*d^3 + 4*a^4*d^4)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - (7*a^3*b^2*c*d^3 - 4*a^4*b*d^4 + (7*a^4*b*c^2*d^2 - 4*a^5*c*d^3)*x^2 + (7*a^3*b^2*c^2*d^2 + 3*a^4*b*c*d^3 - 4*a^5*d^4)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*x^3 + (3*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 2*a^4*c*d^3)*x^2 + (3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 2*a^3*b*c*d^3)*x)*sqrt((a*x + b)/x))/(a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x), 1/2*(2*(7*a^3*b^2*c*d^3 - 4*a^4*b*d^4 + (7*a^4*b*c^2*d^2 - 4*a^5*c*d^3)*x^2 + (7*a^3*b^2*c^2*d^2 + 3*a^4*b*c*d^3 - 4*a^5*d^4)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) + (3*b^4*c^3*d - 2*a*b^3*c^2*d^2 - 5*a^2*b^2*c*d^3 + 4*a^3*b*d^4 + (3*a*b^3*c^4 - 2*a^2*b^2*c^3*d - 5*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*x^2 + (3*b^4*c^4 + a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 - a^3*b*c*d^3 + 4*a^4*d^4)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*x^3 + (3*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 2*a^4*c*d^3)*x^2 + (3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 2*a^3*b*c*d^3)*x)*sqrt((a*x + b)/x))/(a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x), 1/2*(2*(3*b^4*c^3*d - 2*a*b^3*c^2*d^2 - 5*a^2*b^2*c*d^3 + 4*a^3*b*d^4 + (3*a*b^3*c^4 - 2*a^2*b^2*c^3*d - 5*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*x^2 + (3*b^4*c^4 + a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 - a^3*b*c*d^3 + 4*a^4*d^4)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (7*a^3*b^2*c*d^3 - 4*a^4*b*d^4 + (7*a^4*b*c^2*d^2 - 4*a^5*c*d^3)*x^2 + (7*a^3*b^2*c^2*d^2 + 3*a^4*b*c*d^3 - 4*a^5*d^4)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*x^3 + (3*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 2*a^4*c*d^3)*x^2 + (3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 2*a^3*b*c*d^3)*x)*sqrt((a*x + b)/x))/(a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x), ((7*a^3*b^2*c*d^3 - 4*a^4*b*d^4 + (7*a^4*b*c^2*d^2 - 4*a^5*c*d^3)*x^2 + (7*a^3*b^2*c^2*d^2 + 3*a^4*b*c*d^3 - 4*a^5*d^4)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) + (3*b^4*c^3*d - 2*a*b^3*c^2*d^2 - 5*a^2*b^2*c*d^3 + 4*a^3*b*d^4 + (3*a*b^3*c^4 - 2*a^2*b^2*c^3*d - 5*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*x^2 + (3*b^4*c^4 + a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 - a^3*b*c*d^3 + 4*a^4*d^4)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + ((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*x^3 + (3*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 2*a^4*c*d^3)*x^2 + (3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 2*a^3*b*c*d^3)*x)*sqrt((a*x + b)/x))/(a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x)]","B",0
258,1,4093,0,4.782235," ","integrate(1/(a+b/x)^(3/2)/(c+d/x)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(b^{5} c^{4} d^{2} - a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 5 \, a^{3} b^{2} c d^{5} - 2 \, a^{4} b d^{6} + {\left(a b^{4} c^{6} - a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 5 \, a^{4} b c^{3} d^{3} - 2 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(b^{5} c^{6} + a b^{4} c^{5} d - 5 \, a^{2} b^{3} c^{4} d^{2} - a^{3} b^{2} c^{3} d^{3} + 8 \, a^{4} b c^{2} d^{4} - 4 \, a^{5} c d^{5}\right)} x^{2} + {\left(2 \, b^{5} c^{5} d - a b^{4} c^{4} d^{2} - 7 \, a^{2} b^{3} c^{3} d^{3} + 7 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 2 \, a^{5} d^{6}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 3 \, {\left(21 \, a^{3} b^{3} c^{2} d^{4} - 24 \, a^{4} b^{2} c d^{5} + 8 \, a^{5} b d^{6} + {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 24 \, a^{5} b c^{3} d^{3} + 8 \, a^{6} c^{2} d^{4}\right)} x^{3} + {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 18 \, a^{4} b^{2} c^{3} d^{3} - 40 \, a^{5} b c^{2} d^{4} + 16 \, a^{6} c d^{5}\right)} x^{2} + {\left(42 \, a^{3} b^{3} c^{3} d^{3} - 27 \, a^{4} b^{2} c^{2} d^{4} - 8 \, a^{5} b c d^{5} + 8 \, a^{6} d^{6}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(4 \, {\left(a^{2} b^{3} c^{6} - 3 \, a^{3} b^{2} c^{5} d + 3 \, a^{4} b c^{4} d^{2} - a^{5} c^{3} d^{3}\right)} x^{4} + {\left(12 \, a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d - 12 \, a^{3} b^{2} c^{4} d^{2} + 37 \, a^{4} b c^{3} d^{3} - 18 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(24 \, a b^{4} c^{5} d - 20 \, a^{2} b^{3} c^{4} d^{2} + 29 \, a^{3} b^{2} c^{3} d^{3} + 9 \, a^{4} b c^{2} d^{4} - 12 \, a^{5} c d^{5}\right)} x^{2} + 3 \, {\left(4 \, a b^{4} c^{4} d^{2} - 4 \, a^{2} b^{3} c^{3} d^{3} + 9 \, a^{3} b^{2} c^{2} d^{4} - 4 \, a^{4} b c d^{5}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x\right)}}, \frac{24 \, {\left(b^{5} c^{4} d^{2} - a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 5 \, a^{3} b^{2} c d^{5} - 2 \, a^{4} b d^{6} + {\left(a b^{4} c^{6} - a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 5 \, a^{4} b c^{3} d^{3} - 2 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(b^{5} c^{6} + a b^{4} c^{5} d - 5 \, a^{2} b^{3} c^{4} d^{2} - a^{3} b^{2} c^{3} d^{3} + 8 \, a^{4} b c^{2} d^{4} - 4 \, a^{5} c d^{5}\right)} x^{2} + {\left(2 \, b^{5} c^{5} d - a b^{4} c^{4} d^{2} - 7 \, a^{2} b^{3} c^{3} d^{3} + 7 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 2 \, a^{5} d^{6}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - 3 \, {\left(21 \, a^{3} b^{3} c^{2} d^{4} - 24 \, a^{4} b^{2} c d^{5} + 8 \, a^{5} b d^{6} + {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 24 \, a^{5} b c^{3} d^{3} + 8 \, a^{6} c^{2} d^{4}\right)} x^{3} + {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 18 \, a^{4} b^{2} c^{3} d^{3} - 40 \, a^{5} b c^{2} d^{4} + 16 \, a^{6} c d^{5}\right)} x^{2} + {\left(42 \, a^{3} b^{3} c^{3} d^{3} - 27 \, a^{4} b^{2} c^{2} d^{4} - 8 \, a^{5} b c d^{5} + 8 \, a^{6} d^{6}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(4 \, {\left(a^{2} b^{3} c^{6} - 3 \, a^{3} b^{2} c^{5} d + 3 \, a^{4} b c^{4} d^{2} - a^{5} c^{3} d^{3}\right)} x^{4} + {\left(12 \, a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d - 12 \, a^{3} b^{2} c^{4} d^{2} + 37 \, a^{4} b c^{3} d^{3} - 18 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(24 \, a b^{4} c^{5} d - 20 \, a^{2} b^{3} c^{4} d^{2} + 29 \, a^{3} b^{2} c^{3} d^{3} + 9 \, a^{4} b c^{2} d^{4} - 12 \, a^{5} c d^{5}\right)} x^{2} + 3 \, {\left(4 \, a b^{4} c^{4} d^{2} - 4 \, a^{2} b^{3} c^{3} d^{3} + 9 \, a^{3} b^{2} c^{2} d^{4} - 4 \, a^{4} b c d^{5}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x\right)}}, \frac{3 \, {\left(21 \, a^{3} b^{3} c^{2} d^{4} - 24 \, a^{4} b^{2} c d^{5} + 8 \, a^{5} b d^{6} + {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 24 \, a^{5} b c^{3} d^{3} + 8 \, a^{6} c^{2} d^{4}\right)} x^{3} + {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 18 \, a^{4} b^{2} c^{3} d^{3} - 40 \, a^{5} b c^{2} d^{4} + 16 \, a^{6} c d^{5}\right)} x^{2} + {\left(42 \, a^{3} b^{3} c^{3} d^{3} - 27 \, a^{4} b^{2} c^{2} d^{4} - 8 \, a^{5} b c d^{5} + 8 \, a^{6} d^{6}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) + 6 \, {\left(b^{5} c^{4} d^{2} - a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 5 \, a^{3} b^{2} c d^{5} - 2 \, a^{4} b d^{6} + {\left(a b^{4} c^{6} - a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 5 \, a^{4} b c^{3} d^{3} - 2 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(b^{5} c^{6} + a b^{4} c^{5} d - 5 \, a^{2} b^{3} c^{4} d^{2} - a^{3} b^{2} c^{3} d^{3} + 8 \, a^{4} b c^{2} d^{4} - 4 \, a^{5} c d^{5}\right)} x^{2} + {\left(2 \, b^{5} c^{5} d - a b^{4} c^{4} d^{2} - 7 \, a^{2} b^{3} c^{3} d^{3} + 7 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 2 \, a^{5} d^{6}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(4 \, {\left(a^{2} b^{3} c^{6} - 3 \, a^{3} b^{2} c^{5} d + 3 \, a^{4} b c^{4} d^{2} - a^{5} c^{3} d^{3}\right)} x^{4} + {\left(12 \, a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d - 12 \, a^{3} b^{2} c^{4} d^{2} + 37 \, a^{4} b c^{3} d^{3} - 18 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(24 \, a b^{4} c^{5} d - 20 \, a^{2} b^{3} c^{4} d^{2} + 29 \, a^{3} b^{2} c^{3} d^{3} + 9 \, a^{4} b c^{2} d^{4} - 12 \, a^{5} c d^{5}\right)} x^{2} + 3 \, {\left(4 \, a b^{4} c^{4} d^{2} - 4 \, a^{2} b^{3} c^{3} d^{3} + 9 \, a^{3} b^{2} c^{2} d^{4} - 4 \, a^{4} b c d^{5}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x\right)}}, \frac{3 \, {\left(21 \, a^{3} b^{3} c^{2} d^{4} - 24 \, a^{4} b^{2} c d^{5} + 8 \, a^{5} b d^{6} + {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 24 \, a^{5} b c^{3} d^{3} + 8 \, a^{6} c^{2} d^{4}\right)} x^{3} + {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 18 \, a^{4} b^{2} c^{3} d^{3} - 40 \, a^{5} b c^{2} d^{4} + 16 \, a^{6} c d^{5}\right)} x^{2} + {\left(42 \, a^{3} b^{3} c^{3} d^{3} - 27 \, a^{4} b^{2} c^{2} d^{4} - 8 \, a^{5} b c d^{5} + 8 \, a^{6} d^{6}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) + 12 \, {\left(b^{5} c^{4} d^{2} - a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 5 \, a^{3} b^{2} c d^{5} - 2 \, a^{4} b d^{6} + {\left(a b^{4} c^{6} - a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 5 \, a^{4} b c^{3} d^{3} - 2 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(b^{5} c^{6} + a b^{4} c^{5} d - 5 \, a^{2} b^{3} c^{4} d^{2} - a^{3} b^{2} c^{3} d^{3} + 8 \, a^{4} b c^{2} d^{4} - 4 \, a^{5} c d^{5}\right)} x^{2} + {\left(2 \, b^{5} c^{5} d - a b^{4} c^{4} d^{2} - 7 \, a^{2} b^{3} c^{3} d^{3} + 7 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 2 \, a^{5} d^{6}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(4 \, {\left(a^{2} b^{3} c^{6} - 3 \, a^{3} b^{2} c^{5} d + 3 \, a^{4} b c^{4} d^{2} - a^{5} c^{3} d^{3}\right)} x^{4} + {\left(12 \, a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d - 12 \, a^{3} b^{2} c^{4} d^{2} + 37 \, a^{4} b c^{3} d^{3} - 18 \, a^{5} c^{2} d^{4}\right)} x^{3} + {\left(24 \, a b^{4} c^{5} d - 20 \, a^{2} b^{3} c^{4} d^{2} + 29 \, a^{3} b^{2} c^{3} d^{3} + 9 \, a^{4} b c^{2} d^{4} - 12 \, a^{5} c d^{5}\right)} x^{2} + 3 \, {\left(4 \, a b^{4} c^{4} d^{2} - 4 \, a^{2} b^{3} c^{3} d^{3} + 9 \, a^{3} b^{2} c^{2} d^{4} - 4 \, a^{4} b c d^{5}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x\right)}}\right]"," ",0,"[1/8*(12*(b^5*c^4*d^2 - a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 5*a^3*b^2*c*d^5 - 2*a^4*b*d^6 + (a*b^4*c^6 - a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 5*a^4*b*c^3*d^3 - 2*a^5*c^2*d^4)*x^3 + (b^5*c^6 + a*b^4*c^5*d - 5*a^2*b^3*c^4*d^2 - a^3*b^2*c^3*d^3 + 8*a^4*b*c^2*d^4 - 4*a^5*c*d^5)*x^2 + (2*b^5*c^5*d - a*b^4*c^4*d^2 - 7*a^2*b^3*c^3*d^3 + 7*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 2*a^5*d^6)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 3*(21*a^3*b^3*c^2*d^4 - 24*a^4*b^2*c*d^5 + 8*a^5*b*d^6 + (21*a^4*b^2*c^4*d^2 - 24*a^5*b*c^3*d^3 + 8*a^6*c^2*d^4)*x^3 + (21*a^3*b^3*c^4*d^2 + 18*a^4*b^2*c^3*d^3 - 40*a^5*b*c^2*d^4 + 16*a^6*c*d^5)*x^2 + (42*a^3*b^3*c^3*d^3 - 27*a^4*b^2*c^2*d^4 - 8*a^5*b*c*d^5 + 8*a^6*d^6)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(4*(a^2*b^3*c^6 - 3*a^3*b^2*c^5*d + 3*a^4*b*c^4*d^2 - a^5*c^3*d^3)*x^4 + (12*a*b^4*c^6 - 4*a^2*b^3*c^5*d - 12*a^3*b^2*c^4*d^2 + 37*a^4*b*c^3*d^3 - 18*a^5*c^2*d^4)*x^3 + (24*a*b^4*c^5*d - 20*a^2*b^3*c^4*d^2 + 29*a^3*b^2*c^3*d^3 + 9*a^4*b*c^2*d^4 - 12*a^5*c*d^5)*x^2 + 3*(4*a*b^4*c^4*d^2 - 4*a^2*b^3*c^3*d^3 + 9*a^3*b^2*c^2*d^4 - 4*a^4*b*c*d^5)*x)*sqrt((a*x + b)/x))/(a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x), 1/8*(24*(b^5*c^4*d^2 - a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 5*a^3*b^2*c*d^5 - 2*a^4*b*d^6 + (a*b^4*c^6 - a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 5*a^4*b*c^3*d^3 - 2*a^5*c^2*d^4)*x^3 + (b^5*c^6 + a*b^4*c^5*d - 5*a^2*b^3*c^4*d^2 - a^3*b^2*c^3*d^3 + 8*a^4*b*c^2*d^4 - 4*a^5*c*d^5)*x^2 + (2*b^5*c^5*d - a*b^4*c^4*d^2 - 7*a^2*b^3*c^3*d^3 + 7*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 2*a^5*d^6)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - 3*(21*a^3*b^3*c^2*d^4 - 24*a^4*b^2*c*d^5 + 8*a^5*b*d^6 + (21*a^4*b^2*c^4*d^2 - 24*a^5*b*c^3*d^3 + 8*a^6*c^2*d^4)*x^3 + (21*a^3*b^3*c^4*d^2 + 18*a^4*b^2*c^3*d^3 - 40*a^5*b*c^2*d^4 + 16*a^6*c*d^5)*x^2 + (42*a^3*b^3*c^3*d^3 - 27*a^4*b^2*c^2*d^4 - 8*a^5*b*c*d^5 + 8*a^6*d^6)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(4*(a^2*b^3*c^6 - 3*a^3*b^2*c^5*d + 3*a^4*b*c^4*d^2 - a^5*c^3*d^3)*x^4 + (12*a*b^4*c^6 - 4*a^2*b^3*c^5*d - 12*a^3*b^2*c^4*d^2 + 37*a^4*b*c^3*d^3 - 18*a^5*c^2*d^4)*x^3 + (24*a*b^4*c^5*d - 20*a^2*b^3*c^4*d^2 + 29*a^3*b^2*c^3*d^3 + 9*a^4*b*c^2*d^4 - 12*a^5*c*d^5)*x^2 + 3*(4*a*b^4*c^4*d^2 - 4*a^2*b^3*c^3*d^3 + 9*a^3*b^2*c^2*d^4 - 4*a^4*b*c*d^5)*x)*sqrt((a*x + b)/x))/(a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x), 1/4*(3*(21*a^3*b^3*c^2*d^4 - 24*a^4*b^2*c*d^5 + 8*a^5*b*d^6 + (21*a^4*b^2*c^4*d^2 - 24*a^5*b*c^3*d^3 + 8*a^6*c^2*d^4)*x^3 + (21*a^3*b^3*c^4*d^2 + 18*a^4*b^2*c^3*d^3 - 40*a^5*b*c^2*d^4 + 16*a^6*c*d^5)*x^2 + (42*a^3*b^3*c^3*d^3 - 27*a^4*b^2*c^2*d^4 - 8*a^5*b*c*d^5 + 8*a^6*d^6)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) + 6*(b^5*c^4*d^2 - a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 5*a^3*b^2*c*d^5 - 2*a^4*b*d^6 + (a*b^4*c^6 - a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 5*a^4*b*c^3*d^3 - 2*a^5*c^2*d^4)*x^3 + (b^5*c^6 + a*b^4*c^5*d - 5*a^2*b^3*c^4*d^2 - a^3*b^2*c^3*d^3 + 8*a^4*b*c^2*d^4 - 4*a^5*c*d^5)*x^2 + (2*b^5*c^5*d - a*b^4*c^4*d^2 - 7*a^2*b^3*c^3*d^3 + 7*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 2*a^5*d^6)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (4*(a^2*b^3*c^6 - 3*a^3*b^2*c^5*d + 3*a^4*b*c^4*d^2 - a^5*c^3*d^3)*x^4 + (12*a*b^4*c^6 - 4*a^2*b^3*c^5*d - 12*a^3*b^2*c^4*d^2 + 37*a^4*b*c^3*d^3 - 18*a^5*c^2*d^4)*x^3 + (24*a*b^4*c^5*d - 20*a^2*b^3*c^4*d^2 + 29*a^3*b^2*c^3*d^3 + 9*a^4*b*c^2*d^4 - 12*a^5*c*d^5)*x^2 + 3*(4*a*b^4*c^4*d^2 - 4*a^2*b^3*c^3*d^3 + 9*a^3*b^2*c^2*d^4 - 4*a^4*b*c*d^5)*x)*sqrt((a*x + b)/x))/(a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x), 1/4*(3*(21*a^3*b^3*c^2*d^4 - 24*a^4*b^2*c*d^5 + 8*a^5*b*d^6 + (21*a^4*b^2*c^4*d^2 - 24*a^5*b*c^3*d^3 + 8*a^6*c^2*d^4)*x^3 + (21*a^3*b^3*c^4*d^2 + 18*a^4*b^2*c^3*d^3 - 40*a^5*b*c^2*d^4 + 16*a^6*c*d^5)*x^2 + (42*a^3*b^3*c^3*d^3 - 27*a^4*b^2*c^2*d^4 - 8*a^5*b*c*d^5 + 8*a^6*d^6)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) + 12*(b^5*c^4*d^2 - a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 5*a^3*b^2*c*d^5 - 2*a^4*b*d^6 + (a*b^4*c^6 - a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 5*a^4*b*c^3*d^3 - 2*a^5*c^2*d^4)*x^3 + (b^5*c^6 + a*b^4*c^5*d - 5*a^2*b^3*c^4*d^2 - a^3*b^2*c^3*d^3 + 8*a^4*b*c^2*d^4 - 4*a^5*c*d^5)*x^2 + (2*b^5*c^5*d - a*b^4*c^4*d^2 - 7*a^2*b^3*c^3*d^3 + 7*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 2*a^5*d^6)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (4*(a^2*b^3*c^6 - 3*a^3*b^2*c^5*d + 3*a^4*b*c^4*d^2 - a^5*c^3*d^3)*x^4 + (12*a*b^4*c^6 - 4*a^2*b^3*c^5*d - 12*a^3*b^2*c^4*d^2 + 37*a^4*b*c^3*d^3 - 18*a^5*c^2*d^4)*x^3 + (24*a*b^4*c^5*d - 20*a^2*b^3*c^4*d^2 + 29*a^3*b^2*c^3*d^3 + 9*a^4*b*c^2*d^4 - 12*a^5*c*d^5)*x^2 + 3*(4*a*b^4*c^4*d^2 - 4*a^2*b^3*c^3*d^3 + 9*a^3*b^2*c^2*d^4 - 4*a^4*b*c*d^5)*x)*sqrt((a*x + b)/x))/(a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x)]","B",0
259,1,483,0,0.818879," ","integrate((c+d/x)^3/(a+b/x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{5} c^{3} - 6 \, a b^{4} c^{2} d + {\left(5 \, a^{2} b^{3} c^{3} - 6 \, a^{3} b^{2} c^{2} d\right)} x^{2} + 2 \, {\left(5 \, a b^{4} c^{3} - 6 \, a^{2} b^{3} c^{2} d\right)} x\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(3 \, a^{3} b^{2} c^{3} x^{3} + 2 \, {\left(10 \, a^{2} b^{3} c^{3} - 12 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2} + 3 \, {\left(5 \, a b^{4} c^{3} - 6 \, a^{2} b^{3} c^{2} d + 2 \, a^{4} b d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{6} b^{2} x^{2} + 2 \, a^{5} b^{3} x + a^{4} b^{4}\right)}}, \frac{3 \, {\left(5 \, b^{5} c^{3} - 6 \, a b^{4} c^{2} d + {\left(5 \, a^{2} b^{3} c^{3} - 6 \, a^{3} b^{2} c^{2} d\right)} x^{2} + 2 \, {\left(5 \, a b^{4} c^{3} - 6 \, a^{2} b^{3} c^{2} d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(3 \, a^{3} b^{2} c^{3} x^{3} + 2 \, {\left(10 \, a^{2} b^{3} c^{3} - 12 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2} + 3 \, {\left(5 \, a b^{4} c^{3} - 6 \, a^{2} b^{3} c^{2} d + 2 \, a^{4} b d^{3}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{6} b^{2} x^{2} + 2 \, a^{5} b^{3} x + a^{4} b^{4}\right)}}\right]"," ",0,"[-1/6*(3*(5*b^5*c^3 - 6*a*b^4*c^2*d + (5*a^2*b^3*c^3 - 6*a^3*b^2*c^2*d)*x^2 + 2*(5*a*b^4*c^3 - 6*a^2*b^3*c^2*d)*x)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(3*a^3*b^2*c^3*x^3 + 2*(10*a^2*b^3*c^3 - 12*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 + 2*a^5*d^3)*x^2 + 3*(5*a*b^4*c^3 - 6*a^2*b^3*c^2*d + 2*a^4*b*d^3)*x)*sqrt((a*x + b)/x))/(a^6*b^2*x^2 + 2*a^5*b^3*x + a^4*b^4), 1/3*(3*(5*b^5*c^3 - 6*a*b^4*c^2*d + (5*a^2*b^3*c^3 - 6*a^3*b^2*c^2*d)*x^2 + 2*(5*a*b^4*c^3 - 6*a^2*b^3*c^2*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (3*a^3*b^2*c^3*x^3 + 2*(10*a^2*b^3*c^3 - 12*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 + 2*a^5*d^3)*x^2 + 3*(5*a*b^4*c^3 - 6*a^2*b^3*c^2*d + 2*a^4*b*d^3)*x)*sqrt((a*x + b)/x))/(a^6*b^2*x^2 + 2*a^5*b^3*x + a^4*b^4)]","A",0
260,1,407,0,0.985178," ","integrate((c+d/x)^2/(a+b/x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{4} c^{2} - 4 \, a b^{3} c d + {\left(5 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d\right)} x^{2} + 2 \, {\left(5 \, a b^{3} c^{2} - 4 \, a^{2} b^{2} c d\right)} x\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(3 \, a^{3} b c^{2} x^{3} + 2 \, {\left(10 \, a^{2} b^{2} c^{2} - 8 \, a^{3} b c d + a^{4} d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b^{3} c^{2} - 4 \, a^{2} b^{2} c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{6} b x^{2} + 2 \, a^{5} b^{2} x + a^{4} b^{3}\right)}}, \frac{3 \, {\left(5 \, b^{4} c^{2} - 4 \, a b^{3} c d + {\left(5 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d\right)} x^{2} + 2 \, {\left(5 \, a b^{3} c^{2} - 4 \, a^{2} b^{2} c d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(3 \, a^{3} b c^{2} x^{3} + 2 \, {\left(10 \, a^{2} b^{2} c^{2} - 8 \, a^{3} b c d + a^{4} d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b^{3} c^{2} - 4 \, a^{2} b^{2} c d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{6} b x^{2} + 2 \, a^{5} b^{2} x + a^{4} b^{3}\right)}}\right]"," ",0,"[-1/6*(3*(5*b^4*c^2 - 4*a*b^3*c*d + (5*a^2*b^2*c^2 - 4*a^3*b*c*d)*x^2 + 2*(5*a*b^3*c^2 - 4*a^2*b^2*c*d)*x)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(3*a^3*b*c^2*x^3 + 2*(10*a^2*b^2*c^2 - 8*a^3*b*c*d + a^4*d^2)*x^2 + 3*(5*a*b^3*c^2 - 4*a^2*b^2*c*d)*x)*sqrt((a*x + b)/x))/(a^6*b*x^2 + 2*a^5*b^2*x + a^4*b^3), 1/3*(3*(5*b^4*c^2 - 4*a*b^3*c*d + (5*a^2*b^2*c^2 - 4*a^3*b*c*d)*x^2 + 2*(5*a*b^3*c^2 - 4*a^2*b^2*c*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (3*a^3*b*c^2*x^3 + 2*(10*a^2*b^2*c^2 - 8*a^3*b*c*d + a^4*d^2)*x^2 + 3*(5*a*b^3*c^2 - 4*a^2*b^2*c*d)*x)*sqrt((a*x + b)/x))/(a^6*b*x^2 + 2*a^5*b^2*x + a^4*b^3)]","A",0
261,1,331,0,0.628402," ","integrate((c+d/x)/(a+b/x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c - 2 \, a b^{2} d + {\left(5 \, a^{2} b c - 2 \, a^{3} d\right)} x^{2} + 2 \, {\left(5 \, a b^{2} c - 2 \, a^{2} b d\right)} x\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(3 \, a^{3} c x^{3} + 4 \, {\left(5 \, a^{2} b c - 2 \, a^{3} d\right)} x^{2} + 3 \, {\left(5 \, a b^{2} c - 2 \, a^{2} b d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}, \frac{3 \, {\left(5 \, b^{3} c - 2 \, a b^{2} d + {\left(5 \, a^{2} b c - 2 \, a^{3} d\right)} x^{2} + 2 \, {\left(5 \, a b^{2} c - 2 \, a^{2} b d\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(3 \, a^{3} c x^{3} + 4 \, {\left(5 \, a^{2} b c - 2 \, a^{3} d\right)} x^{2} + 3 \, {\left(5 \, a b^{2} c - 2 \, a^{2} b d\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}\right]"," ",0,"[-1/6*(3*(5*b^3*c - 2*a*b^2*d + (5*a^2*b*c - 2*a^3*d)*x^2 + 2*(5*a*b^2*c - 2*a^2*b*d)*x)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(3*a^3*c*x^3 + 4*(5*a^2*b*c - 2*a^3*d)*x^2 + 3*(5*a*b^2*c - 2*a^2*b*d)*x)*sqrt((a*x + b)/x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2), 1/3*(3*(5*b^3*c - 2*a*b^2*d + (5*a^2*b*c - 2*a^3*d)*x^2 + 2*(5*a*b^2*c - 2*a^2*b*d)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (3*a^3*c*x^3 + 4*(5*a^2*b*c - 2*a^3*d)*x^2 + 3*(5*a*b^2*c - 2*a^2*b*d)*x)*sqrt((a*x + b)/x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2)]","A",0
262,1,225,0,0.828631," ","integrate(1/(a+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(3 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}, \frac{15 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(3 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}\right]"," ",0,"[1/6*(15*(a^2*b*x^2 + 2*a*b^2*x + b^3)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(3*a^3*x^3 + 20*a^2*b*x^2 + 15*a*b^2*x)*sqrt((a*x + b)/x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2), 1/3*(15*(a^2*b*x^2 + 2*a*b^2*x + b^3)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (3*a^3*x^3 + 20*a^2*b*x^2 + 15*a*b^2*x)*sqrt((a*x + b)/x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2)]","A",0
263,1,1990,0,4.965137," ","integrate(1/(a+b/x)^(5/2)/(c+d/x),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{5} c^{3} - 8 \, a b^{4} c^{2} d + a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3} + {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2} + 2 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 6 \, {\left(a^{6} d^{3} x^{2} + 2 \, a^{5} b d^{3} x + a^{4} b^{2} d^{3}\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(3 \, {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x^{3} + 2 \, {\left(10 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{4} b^{4} c^{4} - 2 \, a^{5} b^{3} c^{3} d + a^{6} b^{2} c^{2} d^{2} + {\left(a^{6} b^{2} c^{4} - 2 \, a^{7} b c^{3} d + a^{8} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(a^{5} b^{3} c^{4} - 2 \, a^{6} b^{2} c^{3} d + a^{7} b c^{2} d^{2}\right)} x\right)}}, \frac{3 \, {\left(5 \, b^{5} c^{3} - 8 \, a b^{4} c^{2} d + a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3} + {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2} + 2 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + 3 \, {\left(a^{6} d^{3} x^{2} + 2 \, a^{5} b d^{3} x + a^{4} b^{2} d^{3}\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + {\left(3 \, {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x^{3} + 2 \, {\left(10 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{4} b^{4} c^{4} - 2 \, a^{5} b^{3} c^{3} d + a^{6} b^{2} c^{2} d^{2} + {\left(a^{6} b^{2} c^{4} - 2 \, a^{7} b c^{3} d + a^{8} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(a^{5} b^{3} c^{4} - 2 \, a^{6} b^{2} c^{3} d + a^{7} b c^{2} d^{2}\right)} x\right)}}, -\frac{12 \, {\left(a^{6} d^{3} x^{2} + 2 \, a^{5} b d^{3} x + a^{4} b^{2} d^{3}\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 3 \, {\left(5 \, b^{5} c^{3} - 8 \, a b^{4} c^{2} d + a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3} + {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2} + 2 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(3 \, {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x^{3} + 2 \, {\left(10 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{4} b^{4} c^{4} - 2 \, a^{5} b^{3} c^{3} d + a^{6} b^{2} c^{2} d^{2} + {\left(a^{6} b^{2} c^{4} - 2 \, a^{7} b c^{3} d + a^{8} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(a^{5} b^{3} c^{4} - 2 \, a^{6} b^{2} c^{3} d + a^{7} b c^{2} d^{2}\right)} x\right)}}, -\frac{6 \, {\left(a^{6} d^{3} x^{2} + 2 \, a^{5} b d^{3} x + a^{4} b^{2} d^{3}\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 3 \, {\left(5 \, b^{5} c^{3} - 8 \, a b^{4} c^{2} d + a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3} + {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2} + 2 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(3 \, {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x^{3} + 2 \, {\left(10 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b^{4} c^{3} - 8 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{4} b^{4} c^{4} - 2 \, a^{5} b^{3} c^{3} d + a^{6} b^{2} c^{2} d^{2} + {\left(a^{6} b^{2} c^{4} - 2 \, a^{7} b c^{3} d + a^{8} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(a^{5} b^{3} c^{4} - 2 \, a^{6} b^{2} c^{3} d + a^{7} b c^{2} d^{2}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(5*b^5*c^3 - 8*a*b^4*c^2*d + a^2*b^3*c*d^2 + 2*a^3*b^2*d^3 + (5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^2 + 2*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 6*(a^6*d^3*x^2 + 2*a^5*b*d^3*x + a^4*b^2*d^3)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(3*(a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x^3 + 2*(10*a^2*b^3*c^3 - 16*a^3*b^2*c^2*d + 3*a^4*b*c*d^2)*x^2 + 3*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^4*b^4*c^4 - 2*a^5*b^3*c^3*d + a^6*b^2*c^2*d^2 + (a^6*b^2*c^4 - 2*a^7*b*c^3*d + a^8*c^2*d^2)*x^2 + 2*(a^5*b^3*c^4 - 2*a^6*b^2*c^3*d + a^7*b*c^2*d^2)*x), 1/3*(3*(5*b^5*c^3 - 8*a*b^4*c^2*d + a^2*b^3*c*d^2 + 2*a^3*b^2*d^3 + (5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^2 + 2*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + 3*(a^6*d^3*x^2 + 2*a^5*b*d^3*x + a^4*b^2*d^3)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + (3*(a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x^3 + 2*(10*a^2*b^3*c^3 - 16*a^3*b^2*c^2*d + 3*a^4*b*c*d^2)*x^2 + 3*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^4*b^4*c^4 - 2*a^5*b^3*c^3*d + a^6*b^2*c^2*d^2 + (a^6*b^2*c^4 - 2*a^7*b*c^3*d + a^8*c^2*d^2)*x^2 + 2*(a^5*b^3*c^4 - 2*a^6*b^2*c^3*d + a^7*b*c^2*d^2)*x), -1/6*(12*(a^6*d^3*x^2 + 2*a^5*b*d^3*x + a^4*b^2*d^3)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 3*(5*b^5*c^3 - 8*a*b^4*c^2*d + a^2*b^3*c*d^2 + 2*a^3*b^2*d^3 + (5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^2 + 2*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(3*(a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x^3 + 2*(10*a^2*b^3*c^3 - 16*a^3*b^2*c^2*d + 3*a^4*b*c*d^2)*x^2 + 3*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^4*b^4*c^4 - 2*a^5*b^3*c^3*d + a^6*b^2*c^2*d^2 + (a^6*b^2*c^4 - 2*a^7*b*c^3*d + a^8*c^2*d^2)*x^2 + 2*(a^5*b^3*c^4 - 2*a^6*b^2*c^3*d + a^7*b*c^2*d^2)*x), -1/3*(6*(a^6*d^3*x^2 + 2*a^5*b*d^3*x + a^4*b^2*d^3)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 3*(5*b^5*c^3 - 8*a*b^4*c^2*d + a^2*b^3*c*d^2 + 2*a^3*b^2*d^3 + (5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^2 + 2*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (3*(a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x^3 + 2*(10*a^2*b^3*c^3 - 16*a^3*b^2*c^2*d + 3*a^4*b*c*d^2)*x^2 + 3*(5*a*b^4*c^3 - 8*a^2*b^3*c^2*d + a^3*b^2*c*d^2)*x)*sqrt((a*x + b)/x))/(a^4*b^4*c^4 - 2*a^5*b^3*c^3*d + a^6*b^2*c^2*d^2 + (a^6*b^2*c^4 - 2*a^7*b*c^3*d + a^8*c^2*d^2)*x^2 + 2*(a^5*b^3*c^4 - 2*a^6*b^2*c^3*d + a^7*b*c^2*d^2)*x)]","B",0
264,1,3887,0,5.151265," ","integrate(1/(a+b/x)^(5/2)/(c+d/x)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{6} c^{4} d - 11 \, a b^{5} c^{3} d^{2} + 3 \, a^{2} b^{4} c^{2} d^{3} + 7 \, a^{3} b^{3} c d^{4} - 4 \, a^{4} b^{2} d^{5} + {\left(5 \, a^{2} b^{4} c^{5} - 11 \, a^{3} b^{3} c^{4} d + 3 \, a^{4} b^{2} c^{3} d^{2} + 7 \, a^{5} b c^{2} d^{3} - 4 \, a^{6} c d^{4}\right)} x^{3} + {\left(10 \, a b^{5} c^{5} - 17 \, a^{2} b^{4} c^{4} d - 5 \, a^{3} b^{3} c^{3} d^{2} + 17 \, a^{4} b^{2} c^{2} d^{3} - a^{5} b c d^{4} - 4 \, a^{6} d^{5}\right)} x^{2} + {\left(5 \, b^{6} c^{5} - a b^{5} c^{4} d - 19 \, a^{2} b^{4} c^{3} d^{2} + 13 \, a^{3} b^{3} c^{2} d^{3} + 10 \, a^{4} b^{2} c d^{4} - 8 \, a^{5} b d^{5}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 3 \, {\left(9 \, a^{4} b^{3} c d^{4} - 4 \, a^{5} b^{2} d^{5} + {\left(9 \, a^{6} b c^{2} d^{3} - 4 \, a^{7} c d^{4}\right)} x^{3} + {\left(18 \, a^{5} b^{2} c^{2} d^{3} + a^{6} b c d^{4} - 4 \, a^{7} d^{5}\right)} x^{2} + {\left(9 \, a^{4} b^{3} c^{2} d^{3} + 14 \, a^{5} b^{2} c d^{4} - 8 \, a^{6} b d^{5}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(3 \, {\left(a^{3} b^{3} c^{5} - 3 \, a^{4} b^{2} c^{4} d + 3 \, a^{5} b c^{3} d^{2} - a^{6} c^{2} d^{3}\right)} x^{4} + {\left(20 \, a^{2} b^{4} c^{5} - 41 \, a^{3} b^{3} c^{4} d + 9 \, a^{4} b^{2} c^{3} d^{2} + 3 \, a^{5} b c^{2} d^{3} - 6 \, a^{6} c d^{4}\right)} x^{3} + {\left(15 \, a b^{5} c^{5} - 13 \, a^{2} b^{4} c^{4} d - 35 \, a^{3} b^{3} c^{3} d^{2} + 15 \, a^{4} b^{2} c^{2} d^{3} - 12 \, a^{5} b c d^{4}\right)} x^{2} + 3 \, {\left(5 \, a b^{5} c^{4} d - 11 \, a^{2} b^{4} c^{3} d^{2} + 3 \, a^{3} b^{3} c^{2} d^{3} - 2 \, a^{4} b^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{4} b^{5} c^{6} d - 3 \, a^{5} b^{4} c^{5} d^{2} + 3 \, a^{6} b^{3} c^{4} d^{3} - a^{7} b^{2} c^{3} d^{4} + {\left(a^{6} b^{3} c^{7} - 3 \, a^{7} b^{2} c^{6} d + 3 \, a^{8} b c^{5} d^{2} - a^{9} c^{4} d^{3}\right)} x^{3} + {\left(2 \, a^{5} b^{4} c^{7} - 5 \, a^{6} b^{3} c^{6} d + 3 \, a^{7} b^{2} c^{5} d^{2} + a^{8} b c^{4} d^{3} - a^{9} c^{3} d^{4}\right)} x^{2} + {\left(a^{4} b^{5} c^{7} - a^{5} b^{4} c^{6} d - 3 \, a^{6} b^{3} c^{5} d^{2} + 5 \, a^{7} b^{2} c^{4} d^{3} - 2 \, a^{8} b c^{3} d^{4}\right)} x\right)}}, -\frac{6 \, {\left(9 \, a^{4} b^{3} c d^{4} - 4 \, a^{5} b^{2} d^{5} + {\left(9 \, a^{6} b c^{2} d^{3} - 4 \, a^{7} c d^{4}\right)} x^{3} + {\left(18 \, a^{5} b^{2} c^{2} d^{3} + a^{6} b c d^{4} - 4 \, a^{7} d^{5}\right)} x^{2} + {\left(9 \, a^{4} b^{3} c^{2} d^{3} + 14 \, a^{5} b^{2} c d^{4} - 8 \, a^{6} b d^{5}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 3 \, {\left(5 \, b^{6} c^{4} d - 11 \, a b^{5} c^{3} d^{2} + 3 \, a^{2} b^{4} c^{2} d^{3} + 7 \, a^{3} b^{3} c d^{4} - 4 \, a^{4} b^{2} d^{5} + {\left(5 \, a^{2} b^{4} c^{5} - 11 \, a^{3} b^{3} c^{4} d + 3 \, a^{4} b^{2} c^{3} d^{2} + 7 \, a^{5} b c^{2} d^{3} - 4 \, a^{6} c d^{4}\right)} x^{3} + {\left(10 \, a b^{5} c^{5} - 17 \, a^{2} b^{4} c^{4} d - 5 \, a^{3} b^{3} c^{3} d^{2} + 17 \, a^{4} b^{2} c^{2} d^{3} - a^{5} b c d^{4} - 4 \, a^{6} d^{5}\right)} x^{2} + {\left(5 \, b^{6} c^{5} - a b^{5} c^{4} d - 19 \, a^{2} b^{4} c^{3} d^{2} + 13 \, a^{3} b^{3} c^{2} d^{3} + 10 \, a^{4} b^{2} c d^{4} - 8 \, a^{5} b d^{5}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(3 \, {\left(a^{3} b^{3} c^{5} - 3 \, a^{4} b^{2} c^{4} d + 3 \, a^{5} b c^{3} d^{2} - a^{6} c^{2} d^{3}\right)} x^{4} + {\left(20 \, a^{2} b^{4} c^{5} - 41 \, a^{3} b^{3} c^{4} d + 9 \, a^{4} b^{2} c^{3} d^{2} + 3 \, a^{5} b c^{2} d^{3} - 6 \, a^{6} c d^{4}\right)} x^{3} + {\left(15 \, a b^{5} c^{5} - 13 \, a^{2} b^{4} c^{4} d - 35 \, a^{3} b^{3} c^{3} d^{2} + 15 \, a^{4} b^{2} c^{2} d^{3} - 12 \, a^{5} b c d^{4}\right)} x^{2} + 3 \, {\left(5 \, a b^{5} c^{4} d - 11 \, a^{2} b^{4} c^{3} d^{2} + 3 \, a^{3} b^{3} c^{2} d^{3} - 2 \, a^{4} b^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{4} b^{5} c^{6} d - 3 \, a^{5} b^{4} c^{5} d^{2} + 3 \, a^{6} b^{3} c^{4} d^{3} - a^{7} b^{2} c^{3} d^{4} + {\left(a^{6} b^{3} c^{7} - 3 \, a^{7} b^{2} c^{6} d + 3 \, a^{8} b c^{5} d^{2} - a^{9} c^{4} d^{3}\right)} x^{3} + {\left(2 \, a^{5} b^{4} c^{7} - 5 \, a^{6} b^{3} c^{6} d + 3 \, a^{7} b^{2} c^{5} d^{2} + a^{8} b c^{4} d^{3} - a^{9} c^{3} d^{4}\right)} x^{2} + {\left(a^{4} b^{5} c^{7} - a^{5} b^{4} c^{6} d - 3 \, a^{6} b^{3} c^{5} d^{2} + 5 \, a^{7} b^{2} c^{4} d^{3} - 2 \, a^{8} b c^{3} d^{4}\right)} x\right)}}, \frac{6 \, {\left(5 \, b^{6} c^{4} d - 11 \, a b^{5} c^{3} d^{2} + 3 \, a^{2} b^{4} c^{2} d^{3} + 7 \, a^{3} b^{3} c d^{4} - 4 \, a^{4} b^{2} d^{5} + {\left(5 \, a^{2} b^{4} c^{5} - 11 \, a^{3} b^{3} c^{4} d + 3 \, a^{4} b^{2} c^{3} d^{2} + 7 \, a^{5} b c^{2} d^{3} - 4 \, a^{6} c d^{4}\right)} x^{3} + {\left(10 \, a b^{5} c^{5} - 17 \, a^{2} b^{4} c^{4} d - 5 \, a^{3} b^{3} c^{3} d^{2} + 17 \, a^{4} b^{2} c^{2} d^{3} - a^{5} b c d^{4} - 4 \, a^{6} d^{5}\right)} x^{2} + {\left(5 \, b^{6} c^{5} - a b^{5} c^{4} d - 19 \, a^{2} b^{4} c^{3} d^{2} + 13 \, a^{3} b^{3} c^{2} d^{3} + 10 \, a^{4} b^{2} c d^{4} - 8 \, a^{5} b d^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + 3 \, {\left(9 \, a^{4} b^{3} c d^{4} - 4 \, a^{5} b^{2} d^{5} + {\left(9 \, a^{6} b c^{2} d^{3} - 4 \, a^{7} c d^{4}\right)} x^{3} + {\left(18 \, a^{5} b^{2} c^{2} d^{3} + a^{6} b c d^{4} - 4 \, a^{7} d^{5}\right)} x^{2} + {\left(9 \, a^{4} b^{3} c^{2} d^{3} + 14 \, a^{5} b^{2} c d^{4} - 8 \, a^{6} b d^{5}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(3 \, {\left(a^{3} b^{3} c^{5} - 3 \, a^{4} b^{2} c^{4} d + 3 \, a^{5} b c^{3} d^{2} - a^{6} c^{2} d^{3}\right)} x^{4} + {\left(20 \, a^{2} b^{4} c^{5} - 41 \, a^{3} b^{3} c^{4} d + 9 \, a^{4} b^{2} c^{3} d^{2} + 3 \, a^{5} b c^{2} d^{3} - 6 \, a^{6} c d^{4}\right)} x^{3} + {\left(15 \, a b^{5} c^{5} - 13 \, a^{2} b^{4} c^{4} d - 35 \, a^{3} b^{3} c^{3} d^{2} + 15 \, a^{4} b^{2} c^{2} d^{3} - 12 \, a^{5} b c d^{4}\right)} x^{2} + 3 \, {\left(5 \, a b^{5} c^{4} d - 11 \, a^{2} b^{4} c^{3} d^{2} + 3 \, a^{3} b^{3} c^{2} d^{3} - 2 \, a^{4} b^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{4} b^{5} c^{6} d - 3 \, a^{5} b^{4} c^{5} d^{2} + 3 \, a^{6} b^{3} c^{4} d^{3} - a^{7} b^{2} c^{3} d^{4} + {\left(a^{6} b^{3} c^{7} - 3 \, a^{7} b^{2} c^{6} d + 3 \, a^{8} b c^{5} d^{2} - a^{9} c^{4} d^{3}\right)} x^{3} + {\left(2 \, a^{5} b^{4} c^{7} - 5 \, a^{6} b^{3} c^{6} d + 3 \, a^{7} b^{2} c^{5} d^{2} + a^{8} b c^{4} d^{3} - a^{9} c^{3} d^{4}\right)} x^{2} + {\left(a^{4} b^{5} c^{7} - a^{5} b^{4} c^{6} d - 3 \, a^{6} b^{3} c^{5} d^{2} + 5 \, a^{7} b^{2} c^{4} d^{3} - 2 \, a^{8} b c^{3} d^{4}\right)} x\right)}}, -\frac{3 \, {\left(9 \, a^{4} b^{3} c d^{4} - 4 \, a^{5} b^{2} d^{5} + {\left(9 \, a^{6} b c^{2} d^{3} - 4 \, a^{7} c d^{4}\right)} x^{3} + {\left(18 \, a^{5} b^{2} c^{2} d^{3} + a^{6} b c d^{4} - 4 \, a^{7} d^{5}\right)} x^{2} + {\left(9 \, a^{4} b^{3} c^{2} d^{3} + 14 \, a^{5} b^{2} c d^{4} - 8 \, a^{6} b d^{5}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 3 \, {\left(5 \, b^{6} c^{4} d - 11 \, a b^{5} c^{3} d^{2} + 3 \, a^{2} b^{4} c^{2} d^{3} + 7 \, a^{3} b^{3} c d^{4} - 4 \, a^{4} b^{2} d^{5} + {\left(5 \, a^{2} b^{4} c^{5} - 11 \, a^{3} b^{3} c^{4} d + 3 \, a^{4} b^{2} c^{3} d^{2} + 7 \, a^{5} b c^{2} d^{3} - 4 \, a^{6} c d^{4}\right)} x^{3} + {\left(10 \, a b^{5} c^{5} - 17 \, a^{2} b^{4} c^{4} d - 5 \, a^{3} b^{3} c^{3} d^{2} + 17 \, a^{4} b^{2} c^{2} d^{3} - a^{5} b c d^{4} - 4 \, a^{6} d^{5}\right)} x^{2} + {\left(5 \, b^{6} c^{5} - a b^{5} c^{4} d - 19 \, a^{2} b^{4} c^{3} d^{2} + 13 \, a^{3} b^{3} c^{2} d^{3} + 10 \, a^{4} b^{2} c d^{4} - 8 \, a^{5} b d^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(3 \, {\left(a^{3} b^{3} c^{5} - 3 \, a^{4} b^{2} c^{4} d + 3 \, a^{5} b c^{3} d^{2} - a^{6} c^{2} d^{3}\right)} x^{4} + {\left(20 \, a^{2} b^{4} c^{5} - 41 \, a^{3} b^{3} c^{4} d + 9 \, a^{4} b^{2} c^{3} d^{2} + 3 \, a^{5} b c^{2} d^{3} - 6 \, a^{6} c d^{4}\right)} x^{3} + {\left(15 \, a b^{5} c^{5} - 13 \, a^{2} b^{4} c^{4} d - 35 \, a^{3} b^{3} c^{3} d^{2} + 15 \, a^{4} b^{2} c^{2} d^{3} - 12 \, a^{5} b c d^{4}\right)} x^{2} + 3 \, {\left(5 \, a b^{5} c^{4} d - 11 \, a^{2} b^{4} c^{3} d^{2} + 3 \, a^{3} b^{3} c^{2} d^{3} - 2 \, a^{4} b^{2} c d^{4}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{4} b^{5} c^{6} d - 3 \, a^{5} b^{4} c^{5} d^{2} + 3 \, a^{6} b^{3} c^{4} d^{3} - a^{7} b^{2} c^{3} d^{4} + {\left(a^{6} b^{3} c^{7} - 3 \, a^{7} b^{2} c^{6} d + 3 \, a^{8} b c^{5} d^{2} - a^{9} c^{4} d^{3}\right)} x^{3} + {\left(2 \, a^{5} b^{4} c^{7} - 5 \, a^{6} b^{3} c^{6} d + 3 \, a^{7} b^{2} c^{5} d^{2} + a^{8} b c^{4} d^{3} - a^{9} c^{3} d^{4}\right)} x^{2} + {\left(a^{4} b^{5} c^{7} - a^{5} b^{4} c^{6} d - 3 \, a^{6} b^{3} c^{5} d^{2} + 5 \, a^{7} b^{2} c^{4} d^{3} - 2 \, a^{8} b c^{3} d^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(5*b^6*c^4*d - 11*a*b^5*c^3*d^2 + 3*a^2*b^4*c^2*d^3 + 7*a^3*b^3*c*d^4 - 4*a^4*b^2*d^5 + (5*a^2*b^4*c^5 - 11*a^3*b^3*c^4*d + 3*a^4*b^2*c^3*d^2 + 7*a^5*b*c^2*d^3 - 4*a^6*c*d^4)*x^3 + (10*a*b^5*c^5 - 17*a^2*b^4*c^4*d - 5*a^3*b^3*c^3*d^2 + 17*a^4*b^2*c^2*d^3 - a^5*b*c*d^4 - 4*a^6*d^5)*x^2 + (5*b^6*c^5 - a*b^5*c^4*d - 19*a^2*b^4*c^3*d^2 + 13*a^3*b^3*c^2*d^3 + 10*a^4*b^2*c*d^4 - 8*a^5*b*d^5)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 3*(9*a^4*b^3*c*d^4 - 4*a^5*b^2*d^5 + (9*a^6*b*c^2*d^3 - 4*a^7*c*d^4)*x^3 + (18*a^5*b^2*c^2*d^3 + a^6*b*c*d^4 - 4*a^7*d^5)*x^2 + (9*a^4*b^3*c^2*d^3 + 14*a^5*b^2*c*d^4 - 8*a^6*b*d^5)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(3*(a^3*b^3*c^5 - 3*a^4*b^2*c^4*d + 3*a^5*b*c^3*d^2 - a^6*c^2*d^3)*x^4 + (20*a^2*b^4*c^5 - 41*a^3*b^3*c^4*d + 9*a^4*b^2*c^3*d^2 + 3*a^5*b*c^2*d^3 - 6*a^6*c*d^4)*x^3 + (15*a*b^5*c^5 - 13*a^2*b^4*c^4*d - 35*a^3*b^3*c^3*d^2 + 15*a^4*b^2*c^2*d^3 - 12*a^5*b*c*d^4)*x^2 + 3*(5*a*b^5*c^4*d - 11*a^2*b^4*c^3*d^2 + 3*a^3*b^3*c^2*d^3 - 2*a^4*b^2*c*d^4)*x)*sqrt((a*x + b)/x))/(a^4*b^5*c^6*d - 3*a^5*b^4*c^5*d^2 + 3*a^6*b^3*c^4*d^3 - a^7*b^2*c^3*d^4 + (a^6*b^3*c^7 - 3*a^7*b^2*c^6*d + 3*a^8*b*c^5*d^2 - a^9*c^4*d^3)*x^3 + (2*a^5*b^4*c^7 - 5*a^6*b^3*c^6*d + 3*a^7*b^2*c^5*d^2 + a^8*b*c^4*d^3 - a^9*c^3*d^4)*x^2 + (a^4*b^5*c^7 - a^5*b^4*c^6*d - 3*a^6*b^3*c^5*d^2 + 5*a^7*b^2*c^4*d^3 - 2*a^8*b*c^3*d^4)*x), -1/6*(6*(9*a^4*b^3*c*d^4 - 4*a^5*b^2*d^5 + (9*a^6*b*c^2*d^3 - 4*a^7*c*d^4)*x^3 + (18*a^5*b^2*c^2*d^3 + a^6*b*c*d^4 - 4*a^7*d^5)*x^2 + (9*a^4*b^3*c^2*d^3 + 14*a^5*b^2*c*d^4 - 8*a^6*b*d^5)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 3*(5*b^6*c^4*d - 11*a*b^5*c^3*d^2 + 3*a^2*b^4*c^2*d^3 + 7*a^3*b^3*c*d^4 - 4*a^4*b^2*d^5 + (5*a^2*b^4*c^5 - 11*a^3*b^3*c^4*d + 3*a^4*b^2*c^3*d^2 + 7*a^5*b*c^2*d^3 - 4*a^6*c*d^4)*x^3 + (10*a*b^5*c^5 - 17*a^2*b^4*c^4*d - 5*a^3*b^3*c^3*d^2 + 17*a^4*b^2*c^2*d^3 - a^5*b*c*d^4 - 4*a^6*d^5)*x^2 + (5*b^6*c^5 - a*b^5*c^4*d - 19*a^2*b^4*c^3*d^2 + 13*a^3*b^3*c^2*d^3 + 10*a^4*b^2*c*d^4 - 8*a^5*b*d^5)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(3*(a^3*b^3*c^5 - 3*a^4*b^2*c^4*d + 3*a^5*b*c^3*d^2 - a^6*c^2*d^3)*x^4 + (20*a^2*b^4*c^5 - 41*a^3*b^3*c^4*d + 9*a^4*b^2*c^3*d^2 + 3*a^5*b*c^2*d^3 - 6*a^6*c*d^4)*x^3 + (15*a*b^5*c^5 - 13*a^2*b^4*c^4*d - 35*a^3*b^3*c^3*d^2 + 15*a^4*b^2*c^2*d^3 - 12*a^5*b*c*d^4)*x^2 + 3*(5*a*b^5*c^4*d - 11*a^2*b^4*c^3*d^2 + 3*a^3*b^3*c^2*d^3 - 2*a^4*b^2*c*d^4)*x)*sqrt((a*x + b)/x))/(a^4*b^5*c^6*d - 3*a^5*b^4*c^5*d^2 + 3*a^6*b^3*c^4*d^3 - a^7*b^2*c^3*d^4 + (a^6*b^3*c^7 - 3*a^7*b^2*c^6*d + 3*a^8*b*c^5*d^2 - a^9*c^4*d^3)*x^3 + (2*a^5*b^4*c^7 - 5*a^6*b^3*c^6*d + 3*a^7*b^2*c^5*d^2 + a^8*b*c^4*d^3 - a^9*c^3*d^4)*x^2 + (a^4*b^5*c^7 - a^5*b^4*c^6*d - 3*a^6*b^3*c^5*d^2 + 5*a^7*b^2*c^4*d^3 - 2*a^8*b*c^3*d^4)*x), 1/6*(6*(5*b^6*c^4*d - 11*a*b^5*c^3*d^2 + 3*a^2*b^4*c^2*d^3 + 7*a^3*b^3*c*d^4 - 4*a^4*b^2*d^5 + (5*a^2*b^4*c^5 - 11*a^3*b^3*c^4*d + 3*a^4*b^2*c^3*d^2 + 7*a^5*b*c^2*d^3 - 4*a^6*c*d^4)*x^3 + (10*a*b^5*c^5 - 17*a^2*b^4*c^4*d - 5*a^3*b^3*c^3*d^2 + 17*a^4*b^2*c^2*d^3 - a^5*b*c*d^4 - 4*a^6*d^5)*x^2 + (5*b^6*c^5 - a*b^5*c^4*d - 19*a^2*b^4*c^3*d^2 + 13*a^3*b^3*c^2*d^3 + 10*a^4*b^2*c*d^4 - 8*a^5*b*d^5)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + 3*(9*a^4*b^3*c*d^4 - 4*a^5*b^2*d^5 + (9*a^6*b*c^2*d^3 - 4*a^7*c*d^4)*x^3 + (18*a^5*b^2*c^2*d^3 + a^6*b*c*d^4 - 4*a^7*d^5)*x^2 + (9*a^4*b^3*c^2*d^3 + 14*a^5*b^2*c*d^4 - 8*a^6*b*d^5)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(3*(a^3*b^3*c^5 - 3*a^4*b^2*c^4*d + 3*a^5*b*c^3*d^2 - a^6*c^2*d^3)*x^4 + (20*a^2*b^4*c^5 - 41*a^3*b^3*c^4*d + 9*a^4*b^2*c^3*d^2 + 3*a^5*b*c^2*d^3 - 6*a^6*c*d^4)*x^3 + (15*a*b^5*c^5 - 13*a^2*b^4*c^4*d - 35*a^3*b^3*c^3*d^2 + 15*a^4*b^2*c^2*d^3 - 12*a^5*b*c*d^4)*x^2 + 3*(5*a*b^5*c^4*d - 11*a^2*b^4*c^3*d^2 + 3*a^3*b^3*c^2*d^3 - 2*a^4*b^2*c*d^4)*x)*sqrt((a*x + b)/x))/(a^4*b^5*c^6*d - 3*a^5*b^4*c^5*d^2 + 3*a^6*b^3*c^4*d^3 - a^7*b^2*c^3*d^4 + (a^6*b^3*c^7 - 3*a^7*b^2*c^6*d + 3*a^8*b*c^5*d^2 - a^9*c^4*d^3)*x^3 + (2*a^5*b^4*c^7 - 5*a^6*b^3*c^6*d + 3*a^7*b^2*c^5*d^2 + a^8*b*c^4*d^3 - a^9*c^3*d^4)*x^2 + (a^4*b^5*c^7 - a^5*b^4*c^6*d - 3*a^6*b^3*c^5*d^2 + 5*a^7*b^2*c^4*d^3 - 2*a^8*b*c^3*d^4)*x), -1/3*(3*(9*a^4*b^3*c*d^4 - 4*a^5*b^2*d^5 + (9*a^6*b*c^2*d^3 - 4*a^7*c*d^4)*x^3 + (18*a^5*b^2*c^2*d^3 + a^6*b*c*d^4 - 4*a^7*d^5)*x^2 + (9*a^4*b^3*c^2*d^3 + 14*a^5*b^2*c*d^4 - 8*a^6*b*d^5)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 3*(5*b^6*c^4*d - 11*a*b^5*c^3*d^2 + 3*a^2*b^4*c^2*d^3 + 7*a^3*b^3*c*d^4 - 4*a^4*b^2*d^5 + (5*a^2*b^4*c^5 - 11*a^3*b^3*c^4*d + 3*a^4*b^2*c^3*d^2 + 7*a^5*b*c^2*d^3 - 4*a^6*c*d^4)*x^3 + (10*a*b^5*c^5 - 17*a^2*b^4*c^4*d - 5*a^3*b^3*c^3*d^2 + 17*a^4*b^2*c^2*d^3 - a^5*b*c*d^4 - 4*a^6*d^5)*x^2 + (5*b^6*c^5 - a*b^5*c^4*d - 19*a^2*b^4*c^3*d^2 + 13*a^3*b^3*c^2*d^3 + 10*a^4*b^2*c*d^4 - 8*a^5*b*d^5)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (3*(a^3*b^3*c^5 - 3*a^4*b^2*c^4*d + 3*a^5*b*c^3*d^2 - a^6*c^2*d^3)*x^4 + (20*a^2*b^4*c^5 - 41*a^3*b^3*c^4*d + 9*a^4*b^2*c^3*d^2 + 3*a^5*b*c^2*d^3 - 6*a^6*c*d^4)*x^3 + (15*a*b^5*c^5 - 13*a^2*b^4*c^4*d - 35*a^3*b^3*c^3*d^2 + 15*a^4*b^2*c^2*d^3 - 12*a^5*b*c*d^4)*x^2 + 3*(5*a*b^5*c^4*d - 11*a^2*b^4*c^3*d^2 + 3*a^3*b^3*c^2*d^3 - 2*a^4*b^2*c*d^4)*x)*sqrt((a*x + b)/x))/(a^4*b^5*c^6*d - 3*a^5*b^4*c^5*d^2 + 3*a^6*b^3*c^4*d^3 - a^7*b^2*c^3*d^4 + (a^6*b^3*c^7 - 3*a^7*b^2*c^6*d + 3*a^8*b*c^5*d^2 - a^9*c^4*d^3)*x^3 + (2*a^5*b^4*c^7 - 5*a^6*b^3*c^6*d + 3*a^7*b^2*c^5*d^2 + a^8*b*c^4*d^3 - a^9*c^3*d^4)*x^2 + (a^4*b^5*c^7 - a^5*b^4*c^6*d - 3*a^6*b^3*c^5*d^2 + 5*a^7*b^2*c^4*d^3 - 2*a^8*b*c^3*d^4)*x)]","B",0
265,1,6171,0,16.664052," ","integrate(1/(a+b/x)^(5/2)/(c+d/x)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(5 \, b^{7} c^{5} d^{2} - 14 \, a b^{6} c^{4} d^{3} + 6 \, a^{2} b^{5} c^{3} d^{4} + 16 \, a^{3} b^{4} c^{2} d^{5} - 19 \, a^{4} b^{3} c d^{6} + 6 \, a^{5} b^{2} d^{7} + {\left(5 \, a^{2} b^{5} c^{7} - 14 \, a^{3} b^{4} c^{6} d + 6 \, a^{4} b^{3} c^{5} d^{2} + 16 \, a^{5} b^{2} c^{4} d^{3} - 19 \, a^{6} b c^{3} d^{4} + 6 \, a^{7} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(5 \, a b^{6} c^{7} - 9 \, a^{2} b^{5} c^{6} d - 8 \, a^{3} b^{4} c^{5} d^{2} + 22 \, a^{4} b^{3} c^{4} d^{3} - 3 \, a^{5} b^{2} c^{3} d^{4} - 13 \, a^{6} b c^{2} d^{5} + 6 \, a^{7} c d^{6}\right)} x^{3} + {\left(5 \, b^{7} c^{7} + 6 \, a b^{6} c^{6} d - 45 \, a^{2} b^{5} c^{5} d^{2} + 26 \, a^{3} b^{4} c^{4} d^{3} + 51 \, a^{4} b^{3} c^{3} d^{4} - 54 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6} + 6 \, a^{7} d^{7}\right)} x^{2} + 2 \, {\left(5 \, b^{7} c^{6} d - 9 \, a b^{6} c^{5} d^{2} - 8 \, a^{2} b^{5} c^{4} d^{3} + 22 \, a^{3} b^{4} c^{3} d^{4} - 3 \, a^{4} b^{3} c^{2} d^{5} - 13 \, a^{5} b^{2} c d^{6} + 6 \, a^{6} b d^{7}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 3 \, {\left(99 \, a^{4} b^{4} c^{2} d^{5} - 88 \, a^{5} b^{3} c d^{6} + 24 \, a^{6} b^{2} d^{7} + {\left(99 \, a^{6} b^{2} c^{4} d^{3} - 88 \, a^{7} b c^{3} d^{4} + 24 \, a^{8} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(99 \, a^{5} b^{3} c^{4} d^{3} + 11 \, a^{6} b^{2} c^{3} d^{4} - 64 \, a^{7} b c^{2} d^{5} + 24 \, a^{8} c d^{6}\right)} x^{3} + {\left(99 \, a^{4} b^{4} c^{4} d^{3} + 308 \, a^{5} b^{3} c^{3} d^{4} - 229 \, a^{6} b^{2} c^{2} d^{5} + 8 \, a^{7} b c d^{6} + 24 \, a^{8} d^{7}\right)} x^{2} + 2 \, {\left(99 \, a^{4} b^{4} c^{3} d^{4} + 11 \, a^{5} b^{3} c^{2} d^{5} - 64 \, a^{6} b^{2} c d^{6} + 24 \, a^{7} b d^{7}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(12 \, {\left(a^{3} b^{4} c^{7} - 4 \, a^{4} b^{3} c^{6} d + 6 \, a^{5} b^{2} c^{5} d^{2} - 4 \, a^{6} b c^{4} d^{3} + a^{7} c^{3} d^{4}\right)} x^{5} + {\left(80 \, a^{2} b^{5} c^{7} - 200 \, a^{3} b^{4} c^{6} d + 48 \, a^{4} b^{3} c^{5} d^{2} + 48 \, a^{5} b^{2} c^{4} d^{3} - 135 \, a^{6} b c^{3} d^{4} + 54 \, a^{7} c^{2} d^{5}\right)} x^{4} + {\left(60 \, a b^{6} c^{7} - 8 \, a^{2} b^{5} c^{6} d - 364 \, a^{3} b^{4} c^{5} d^{2} + 192 \, a^{4} b^{3} c^{4} d^{3} - 234 \, a^{5} b^{2} c^{3} d^{4} + 3 \, a^{6} b c^{2} d^{5} + 36 \, a^{7} c d^{6}\right)} x^{3} + {\left(120 \, a b^{6} c^{6} d - 256 \, a^{2} b^{5} c^{5} d^{2} - 80 \, a^{3} b^{4} c^{4} d^{3} - 15 \, a^{4} b^{3} c^{3} d^{4} - 156 \, a^{5} b^{2} c^{2} d^{5} + 72 \, a^{6} b c d^{6}\right)} x^{2} + 3 \, {\left(20 \, a b^{6} c^{5} d^{2} - 56 \, a^{2} b^{5} c^{4} d^{3} + 24 \, a^{3} b^{4} c^{3} d^{4} - 35 \, a^{4} b^{3} c^{2} d^{5} + 12 \, a^{5} b^{2} c d^{6}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, {\left(a^{4} b^{6} c^{8} d^{2} - 4 \, a^{5} b^{5} c^{7} d^{3} + 6 \, a^{6} b^{4} c^{6} d^{4} - 4 \, a^{7} b^{3} c^{5} d^{5} + a^{8} b^{2} c^{4} d^{6} + {\left(a^{6} b^{4} c^{10} - 4 \, a^{7} b^{3} c^{9} d + 6 \, a^{8} b^{2} c^{8} d^{2} - 4 \, a^{9} b c^{7} d^{3} + a^{10} c^{6} d^{4}\right)} x^{4} + 2 \, {\left(a^{5} b^{5} c^{10} - 3 \, a^{6} b^{4} c^{9} d + 2 \, a^{7} b^{3} c^{8} d^{2} + 2 \, a^{8} b^{2} c^{7} d^{3} - 3 \, a^{9} b c^{6} d^{4} + a^{10} c^{5} d^{5}\right)} x^{3} + {\left(a^{4} b^{6} c^{10} - 9 \, a^{6} b^{4} c^{8} d^{2} + 16 \, a^{7} b^{3} c^{7} d^{3} - 9 \, a^{8} b^{2} c^{6} d^{4} + a^{10} c^{4} d^{6}\right)} x^{2} + 2 \, {\left(a^{4} b^{6} c^{9} d - 3 \, a^{5} b^{5} c^{8} d^{2} + 2 \, a^{6} b^{4} c^{7} d^{3} + 2 \, a^{7} b^{3} c^{6} d^{4} - 3 \, a^{8} b^{2} c^{5} d^{5} + a^{9} b c^{4} d^{6}\right)} x\right)}}, \frac{24 \, {\left(5 \, b^{7} c^{5} d^{2} - 14 \, a b^{6} c^{4} d^{3} + 6 \, a^{2} b^{5} c^{3} d^{4} + 16 \, a^{3} b^{4} c^{2} d^{5} - 19 \, a^{4} b^{3} c d^{6} + 6 \, a^{5} b^{2} d^{7} + {\left(5 \, a^{2} b^{5} c^{7} - 14 \, a^{3} b^{4} c^{6} d + 6 \, a^{4} b^{3} c^{5} d^{2} + 16 \, a^{5} b^{2} c^{4} d^{3} - 19 \, a^{6} b c^{3} d^{4} + 6 \, a^{7} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(5 \, a b^{6} c^{7} - 9 \, a^{2} b^{5} c^{6} d - 8 \, a^{3} b^{4} c^{5} d^{2} + 22 \, a^{4} b^{3} c^{4} d^{3} - 3 \, a^{5} b^{2} c^{3} d^{4} - 13 \, a^{6} b c^{2} d^{5} + 6 \, a^{7} c d^{6}\right)} x^{3} + {\left(5 \, b^{7} c^{7} + 6 \, a b^{6} c^{6} d - 45 \, a^{2} b^{5} c^{5} d^{2} + 26 \, a^{3} b^{4} c^{4} d^{3} + 51 \, a^{4} b^{3} c^{3} d^{4} - 54 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6} + 6 \, a^{7} d^{7}\right)} x^{2} + 2 \, {\left(5 \, b^{7} c^{6} d - 9 \, a b^{6} c^{5} d^{2} - 8 \, a^{2} b^{5} c^{4} d^{3} + 22 \, a^{3} b^{4} c^{3} d^{4} - 3 \, a^{4} b^{3} c^{2} d^{5} - 13 \, a^{5} b^{2} c d^{6} + 6 \, a^{6} b d^{7}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + 3 \, {\left(99 \, a^{4} b^{4} c^{2} d^{5} - 88 \, a^{5} b^{3} c d^{6} + 24 \, a^{6} b^{2} d^{7} + {\left(99 \, a^{6} b^{2} c^{4} d^{3} - 88 \, a^{7} b c^{3} d^{4} + 24 \, a^{8} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(99 \, a^{5} b^{3} c^{4} d^{3} + 11 \, a^{6} b^{2} c^{3} d^{4} - 64 \, a^{7} b c^{2} d^{5} + 24 \, a^{8} c d^{6}\right)} x^{3} + {\left(99 \, a^{4} b^{4} c^{4} d^{3} + 308 \, a^{5} b^{3} c^{3} d^{4} - 229 \, a^{6} b^{2} c^{2} d^{5} + 8 \, a^{7} b c d^{6} + 24 \, a^{8} d^{7}\right)} x^{2} + 2 \, {\left(99 \, a^{4} b^{4} c^{3} d^{4} + 11 \, a^{5} b^{3} c^{2} d^{5} - 64 \, a^{6} b^{2} c d^{6} + 24 \, a^{7} b d^{7}\right)} x\right)} \sqrt{-\frac{d}{b c - a d}} \log\left(-\frac{2 \, {\left(b c - a d\right)} x \sqrt{-\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}} - b d + {\left(b c - 2 \, a d\right)} x}{c x + d}\right) + 2 \, {\left(12 \, {\left(a^{3} b^{4} c^{7} - 4 \, a^{4} b^{3} c^{6} d + 6 \, a^{5} b^{2} c^{5} d^{2} - 4 \, a^{6} b c^{4} d^{3} + a^{7} c^{3} d^{4}\right)} x^{5} + {\left(80 \, a^{2} b^{5} c^{7} - 200 \, a^{3} b^{4} c^{6} d + 48 \, a^{4} b^{3} c^{5} d^{2} + 48 \, a^{5} b^{2} c^{4} d^{3} - 135 \, a^{6} b c^{3} d^{4} + 54 \, a^{7} c^{2} d^{5}\right)} x^{4} + {\left(60 \, a b^{6} c^{7} - 8 \, a^{2} b^{5} c^{6} d - 364 \, a^{3} b^{4} c^{5} d^{2} + 192 \, a^{4} b^{3} c^{4} d^{3} - 234 \, a^{5} b^{2} c^{3} d^{4} + 3 \, a^{6} b c^{2} d^{5} + 36 \, a^{7} c d^{6}\right)} x^{3} + {\left(120 \, a b^{6} c^{6} d - 256 \, a^{2} b^{5} c^{5} d^{2} - 80 \, a^{3} b^{4} c^{4} d^{3} - 15 \, a^{4} b^{3} c^{3} d^{4} - 156 \, a^{5} b^{2} c^{2} d^{5} + 72 \, a^{6} b c d^{6}\right)} x^{2} + 3 \, {\left(20 \, a b^{6} c^{5} d^{2} - 56 \, a^{2} b^{5} c^{4} d^{3} + 24 \, a^{3} b^{4} c^{3} d^{4} - 35 \, a^{4} b^{3} c^{2} d^{5} + 12 \, a^{5} b^{2} c d^{6}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, {\left(a^{4} b^{6} c^{8} d^{2} - 4 \, a^{5} b^{5} c^{7} d^{3} + 6 \, a^{6} b^{4} c^{6} d^{4} - 4 \, a^{7} b^{3} c^{5} d^{5} + a^{8} b^{2} c^{4} d^{6} + {\left(a^{6} b^{4} c^{10} - 4 \, a^{7} b^{3} c^{9} d + 6 \, a^{8} b^{2} c^{8} d^{2} - 4 \, a^{9} b c^{7} d^{3} + a^{10} c^{6} d^{4}\right)} x^{4} + 2 \, {\left(a^{5} b^{5} c^{10} - 3 \, a^{6} b^{4} c^{9} d + 2 \, a^{7} b^{3} c^{8} d^{2} + 2 \, a^{8} b^{2} c^{7} d^{3} - 3 \, a^{9} b c^{6} d^{4} + a^{10} c^{5} d^{5}\right)} x^{3} + {\left(a^{4} b^{6} c^{10} - 9 \, a^{6} b^{4} c^{8} d^{2} + 16 \, a^{7} b^{3} c^{7} d^{3} - 9 \, a^{8} b^{2} c^{6} d^{4} + a^{10} c^{4} d^{6}\right)} x^{2} + 2 \, {\left(a^{4} b^{6} c^{9} d - 3 \, a^{5} b^{5} c^{8} d^{2} + 2 \, a^{6} b^{4} c^{7} d^{3} + 2 \, a^{7} b^{3} c^{6} d^{4} - 3 \, a^{8} b^{2} c^{5} d^{5} + a^{9} b c^{4} d^{6}\right)} x\right)}}, -\frac{3 \, {\left(99 \, a^{4} b^{4} c^{2} d^{5} - 88 \, a^{5} b^{3} c d^{6} + 24 \, a^{6} b^{2} d^{7} + {\left(99 \, a^{6} b^{2} c^{4} d^{3} - 88 \, a^{7} b c^{3} d^{4} + 24 \, a^{8} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(99 \, a^{5} b^{3} c^{4} d^{3} + 11 \, a^{6} b^{2} c^{3} d^{4} - 64 \, a^{7} b c^{2} d^{5} + 24 \, a^{8} c d^{6}\right)} x^{3} + {\left(99 \, a^{4} b^{4} c^{4} d^{3} + 308 \, a^{5} b^{3} c^{3} d^{4} - 229 \, a^{6} b^{2} c^{2} d^{5} + 8 \, a^{7} b c d^{6} + 24 \, a^{8} d^{7}\right)} x^{2} + 2 \, {\left(99 \, a^{4} b^{4} c^{3} d^{4} + 11 \, a^{5} b^{3} c^{2} d^{5} - 64 \, a^{6} b^{2} c d^{6} + 24 \, a^{7} b d^{7}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 6 \, {\left(5 \, b^{7} c^{5} d^{2} - 14 \, a b^{6} c^{4} d^{3} + 6 \, a^{2} b^{5} c^{3} d^{4} + 16 \, a^{3} b^{4} c^{2} d^{5} - 19 \, a^{4} b^{3} c d^{6} + 6 \, a^{5} b^{2} d^{7} + {\left(5 \, a^{2} b^{5} c^{7} - 14 \, a^{3} b^{4} c^{6} d + 6 \, a^{4} b^{3} c^{5} d^{2} + 16 \, a^{5} b^{2} c^{4} d^{3} - 19 \, a^{6} b c^{3} d^{4} + 6 \, a^{7} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(5 \, a b^{6} c^{7} - 9 \, a^{2} b^{5} c^{6} d - 8 \, a^{3} b^{4} c^{5} d^{2} + 22 \, a^{4} b^{3} c^{4} d^{3} - 3 \, a^{5} b^{2} c^{3} d^{4} - 13 \, a^{6} b c^{2} d^{5} + 6 \, a^{7} c d^{6}\right)} x^{3} + {\left(5 \, b^{7} c^{7} + 6 \, a b^{6} c^{6} d - 45 \, a^{2} b^{5} c^{5} d^{2} + 26 \, a^{3} b^{4} c^{4} d^{3} + 51 \, a^{4} b^{3} c^{3} d^{4} - 54 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6} + 6 \, a^{7} d^{7}\right)} x^{2} + 2 \, {\left(5 \, b^{7} c^{6} d - 9 \, a b^{6} c^{5} d^{2} - 8 \, a^{2} b^{5} c^{4} d^{3} + 22 \, a^{3} b^{4} c^{3} d^{4} - 3 \, a^{4} b^{3} c^{2} d^{5} - 13 \, a^{5} b^{2} c d^{6} + 6 \, a^{6} b d^{7}\right)} x\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - {\left(12 \, {\left(a^{3} b^{4} c^{7} - 4 \, a^{4} b^{3} c^{6} d + 6 \, a^{5} b^{2} c^{5} d^{2} - 4 \, a^{6} b c^{4} d^{3} + a^{7} c^{3} d^{4}\right)} x^{5} + {\left(80 \, a^{2} b^{5} c^{7} - 200 \, a^{3} b^{4} c^{6} d + 48 \, a^{4} b^{3} c^{5} d^{2} + 48 \, a^{5} b^{2} c^{4} d^{3} - 135 \, a^{6} b c^{3} d^{4} + 54 \, a^{7} c^{2} d^{5}\right)} x^{4} + {\left(60 \, a b^{6} c^{7} - 8 \, a^{2} b^{5} c^{6} d - 364 \, a^{3} b^{4} c^{5} d^{2} + 192 \, a^{4} b^{3} c^{4} d^{3} - 234 \, a^{5} b^{2} c^{3} d^{4} + 3 \, a^{6} b c^{2} d^{5} + 36 \, a^{7} c d^{6}\right)} x^{3} + {\left(120 \, a b^{6} c^{6} d - 256 \, a^{2} b^{5} c^{5} d^{2} - 80 \, a^{3} b^{4} c^{4} d^{3} - 15 \, a^{4} b^{3} c^{3} d^{4} - 156 \, a^{5} b^{2} c^{2} d^{5} + 72 \, a^{6} b c d^{6}\right)} x^{2} + 3 \, {\left(20 \, a b^{6} c^{5} d^{2} - 56 \, a^{2} b^{5} c^{4} d^{3} + 24 \, a^{3} b^{4} c^{3} d^{4} - 35 \, a^{4} b^{3} c^{2} d^{5} + 12 \, a^{5} b^{2} c d^{6}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{12 \, {\left(a^{4} b^{6} c^{8} d^{2} - 4 \, a^{5} b^{5} c^{7} d^{3} + 6 \, a^{6} b^{4} c^{6} d^{4} - 4 \, a^{7} b^{3} c^{5} d^{5} + a^{8} b^{2} c^{4} d^{6} + {\left(a^{6} b^{4} c^{10} - 4 \, a^{7} b^{3} c^{9} d + 6 \, a^{8} b^{2} c^{8} d^{2} - 4 \, a^{9} b c^{7} d^{3} + a^{10} c^{6} d^{4}\right)} x^{4} + 2 \, {\left(a^{5} b^{5} c^{10} - 3 \, a^{6} b^{4} c^{9} d + 2 \, a^{7} b^{3} c^{8} d^{2} + 2 \, a^{8} b^{2} c^{7} d^{3} - 3 \, a^{9} b c^{6} d^{4} + a^{10} c^{5} d^{5}\right)} x^{3} + {\left(a^{4} b^{6} c^{10} - 9 \, a^{6} b^{4} c^{8} d^{2} + 16 \, a^{7} b^{3} c^{7} d^{3} - 9 \, a^{8} b^{2} c^{6} d^{4} + a^{10} c^{4} d^{6}\right)} x^{2} + 2 \, {\left(a^{4} b^{6} c^{9} d - 3 \, a^{5} b^{5} c^{8} d^{2} + 2 \, a^{6} b^{4} c^{7} d^{3} + 2 \, a^{7} b^{3} c^{6} d^{4} - 3 \, a^{8} b^{2} c^{5} d^{5} + a^{9} b c^{4} d^{6}\right)} x\right)}}, -\frac{3 \, {\left(99 \, a^{4} b^{4} c^{2} d^{5} - 88 \, a^{5} b^{3} c d^{6} + 24 \, a^{6} b^{2} d^{7} + {\left(99 \, a^{6} b^{2} c^{4} d^{3} - 88 \, a^{7} b c^{3} d^{4} + 24 \, a^{8} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(99 \, a^{5} b^{3} c^{4} d^{3} + 11 \, a^{6} b^{2} c^{3} d^{4} - 64 \, a^{7} b c^{2} d^{5} + 24 \, a^{8} c d^{6}\right)} x^{3} + {\left(99 \, a^{4} b^{4} c^{4} d^{3} + 308 \, a^{5} b^{3} c^{3} d^{4} - 229 \, a^{6} b^{2} c^{2} d^{5} + 8 \, a^{7} b c d^{6} + 24 \, a^{8} d^{7}\right)} x^{2} + 2 \, {\left(99 \, a^{4} b^{4} c^{3} d^{4} + 11 \, a^{5} b^{3} c^{2} d^{5} - 64 \, a^{6} b^{2} c d^{6} + 24 \, a^{7} b d^{7}\right)} x\right)} \sqrt{\frac{d}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} x \sqrt{\frac{d}{b c - a d}} \sqrt{\frac{a x + b}{x}}}{a d x + b d}\right) - 12 \, {\left(5 \, b^{7} c^{5} d^{2} - 14 \, a b^{6} c^{4} d^{3} + 6 \, a^{2} b^{5} c^{3} d^{4} + 16 \, a^{3} b^{4} c^{2} d^{5} - 19 \, a^{4} b^{3} c d^{6} + 6 \, a^{5} b^{2} d^{7} + {\left(5 \, a^{2} b^{5} c^{7} - 14 \, a^{3} b^{4} c^{6} d + 6 \, a^{4} b^{3} c^{5} d^{2} + 16 \, a^{5} b^{2} c^{4} d^{3} - 19 \, a^{6} b c^{3} d^{4} + 6 \, a^{7} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(5 \, a b^{6} c^{7} - 9 \, a^{2} b^{5} c^{6} d - 8 \, a^{3} b^{4} c^{5} d^{2} + 22 \, a^{4} b^{3} c^{4} d^{3} - 3 \, a^{5} b^{2} c^{3} d^{4} - 13 \, a^{6} b c^{2} d^{5} + 6 \, a^{7} c d^{6}\right)} x^{3} + {\left(5 \, b^{7} c^{7} + 6 \, a b^{6} c^{6} d - 45 \, a^{2} b^{5} c^{5} d^{2} + 26 \, a^{3} b^{4} c^{4} d^{3} + 51 \, a^{4} b^{3} c^{3} d^{4} - 54 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6} + 6 \, a^{7} d^{7}\right)} x^{2} + 2 \, {\left(5 \, b^{7} c^{6} d - 9 \, a b^{6} c^{5} d^{2} - 8 \, a^{2} b^{5} c^{4} d^{3} + 22 \, a^{3} b^{4} c^{3} d^{4} - 3 \, a^{4} b^{3} c^{2} d^{5} - 13 \, a^{5} b^{2} c d^{6} + 6 \, a^{6} b d^{7}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(12 \, {\left(a^{3} b^{4} c^{7} - 4 \, a^{4} b^{3} c^{6} d + 6 \, a^{5} b^{2} c^{5} d^{2} - 4 \, a^{6} b c^{4} d^{3} + a^{7} c^{3} d^{4}\right)} x^{5} + {\left(80 \, a^{2} b^{5} c^{7} - 200 \, a^{3} b^{4} c^{6} d + 48 \, a^{4} b^{3} c^{5} d^{2} + 48 \, a^{5} b^{2} c^{4} d^{3} - 135 \, a^{6} b c^{3} d^{4} + 54 \, a^{7} c^{2} d^{5}\right)} x^{4} + {\left(60 \, a b^{6} c^{7} - 8 \, a^{2} b^{5} c^{6} d - 364 \, a^{3} b^{4} c^{5} d^{2} + 192 \, a^{4} b^{3} c^{4} d^{3} - 234 \, a^{5} b^{2} c^{3} d^{4} + 3 \, a^{6} b c^{2} d^{5} + 36 \, a^{7} c d^{6}\right)} x^{3} + {\left(120 \, a b^{6} c^{6} d - 256 \, a^{2} b^{5} c^{5} d^{2} - 80 \, a^{3} b^{4} c^{4} d^{3} - 15 \, a^{4} b^{3} c^{3} d^{4} - 156 \, a^{5} b^{2} c^{2} d^{5} + 72 \, a^{6} b c d^{6}\right)} x^{2} + 3 \, {\left(20 \, a b^{6} c^{5} d^{2} - 56 \, a^{2} b^{5} c^{4} d^{3} + 24 \, a^{3} b^{4} c^{3} d^{4} - 35 \, a^{4} b^{3} c^{2} d^{5} + 12 \, a^{5} b^{2} c d^{6}\right)} x\right)} \sqrt{\frac{a x + b}{x}}}{12 \, {\left(a^{4} b^{6} c^{8} d^{2} - 4 \, a^{5} b^{5} c^{7} d^{3} + 6 \, a^{6} b^{4} c^{6} d^{4} - 4 \, a^{7} b^{3} c^{5} d^{5} + a^{8} b^{2} c^{4} d^{6} + {\left(a^{6} b^{4} c^{10} - 4 \, a^{7} b^{3} c^{9} d + 6 \, a^{8} b^{2} c^{8} d^{2} - 4 \, a^{9} b c^{7} d^{3} + a^{10} c^{6} d^{4}\right)} x^{4} + 2 \, {\left(a^{5} b^{5} c^{10} - 3 \, a^{6} b^{4} c^{9} d + 2 \, a^{7} b^{3} c^{8} d^{2} + 2 \, a^{8} b^{2} c^{7} d^{3} - 3 \, a^{9} b c^{6} d^{4} + a^{10} c^{5} d^{5}\right)} x^{3} + {\left(a^{4} b^{6} c^{10} - 9 \, a^{6} b^{4} c^{8} d^{2} + 16 \, a^{7} b^{3} c^{7} d^{3} - 9 \, a^{8} b^{2} c^{6} d^{4} + a^{10} c^{4} d^{6}\right)} x^{2} + 2 \, {\left(a^{4} b^{6} c^{9} d - 3 \, a^{5} b^{5} c^{8} d^{2} + 2 \, a^{6} b^{4} c^{7} d^{3} + 2 \, a^{7} b^{3} c^{6} d^{4} - 3 \, a^{8} b^{2} c^{5} d^{5} + a^{9} b c^{4} d^{6}\right)} x\right)}}\right]"," ",0,"[1/24*(12*(5*b^7*c^5*d^2 - 14*a*b^6*c^4*d^3 + 6*a^2*b^5*c^3*d^4 + 16*a^3*b^4*c^2*d^5 - 19*a^4*b^3*c*d^6 + 6*a^5*b^2*d^7 + (5*a^2*b^5*c^7 - 14*a^3*b^4*c^6*d + 6*a^4*b^3*c^5*d^2 + 16*a^5*b^2*c^4*d^3 - 19*a^6*b*c^3*d^4 + 6*a^7*c^2*d^5)*x^4 + 2*(5*a*b^6*c^7 - 9*a^2*b^5*c^6*d - 8*a^3*b^4*c^5*d^2 + 22*a^4*b^3*c^4*d^3 - 3*a^5*b^2*c^3*d^4 - 13*a^6*b*c^2*d^5 + 6*a^7*c*d^6)*x^3 + (5*b^7*c^7 + 6*a*b^6*c^6*d - 45*a^2*b^5*c^5*d^2 + 26*a^3*b^4*c^4*d^3 + 51*a^4*b^3*c^3*d^4 - 54*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6 + 6*a^7*d^7)*x^2 + 2*(5*b^7*c^6*d - 9*a*b^6*c^5*d^2 - 8*a^2*b^5*c^4*d^3 + 22*a^3*b^4*c^3*d^4 - 3*a^4*b^3*c^2*d^5 - 13*a^5*b^2*c*d^6 + 6*a^6*b*d^7)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 3*(99*a^4*b^4*c^2*d^5 - 88*a^5*b^3*c*d^6 + 24*a^6*b^2*d^7 + (99*a^6*b^2*c^4*d^3 - 88*a^7*b*c^3*d^4 + 24*a^8*c^2*d^5)*x^4 + 2*(99*a^5*b^3*c^4*d^3 + 11*a^6*b^2*c^3*d^4 - 64*a^7*b*c^2*d^5 + 24*a^8*c*d^6)*x^3 + (99*a^4*b^4*c^4*d^3 + 308*a^5*b^3*c^3*d^4 - 229*a^6*b^2*c^2*d^5 + 8*a^7*b*c*d^6 + 24*a^8*d^7)*x^2 + 2*(99*a^4*b^4*c^3*d^4 + 11*a^5*b^3*c^2*d^5 - 64*a^6*b^2*c*d^6 + 24*a^7*b*d^7)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(12*(a^3*b^4*c^7 - 4*a^4*b^3*c^6*d + 6*a^5*b^2*c^5*d^2 - 4*a^6*b*c^4*d^3 + a^7*c^3*d^4)*x^5 + (80*a^2*b^5*c^7 - 200*a^3*b^4*c^6*d + 48*a^4*b^3*c^5*d^2 + 48*a^5*b^2*c^4*d^3 - 135*a^6*b*c^3*d^4 + 54*a^7*c^2*d^5)*x^4 + (60*a*b^6*c^7 - 8*a^2*b^5*c^6*d - 364*a^3*b^4*c^5*d^2 + 192*a^4*b^3*c^4*d^3 - 234*a^5*b^2*c^3*d^4 + 3*a^6*b*c^2*d^5 + 36*a^7*c*d^6)*x^3 + (120*a*b^6*c^6*d - 256*a^2*b^5*c^5*d^2 - 80*a^3*b^4*c^4*d^3 - 15*a^4*b^3*c^3*d^4 - 156*a^5*b^2*c^2*d^5 + 72*a^6*b*c*d^6)*x^2 + 3*(20*a*b^6*c^5*d^2 - 56*a^2*b^5*c^4*d^3 + 24*a^3*b^4*c^3*d^4 - 35*a^4*b^3*c^2*d^5 + 12*a^5*b^2*c*d^6)*x)*sqrt((a*x + b)/x))/(a^4*b^6*c^8*d^2 - 4*a^5*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*x^4 + 2*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*x^3 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*x^2 + 2*(a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*x), 1/24*(24*(5*b^7*c^5*d^2 - 14*a*b^6*c^4*d^3 + 6*a^2*b^5*c^3*d^4 + 16*a^3*b^4*c^2*d^5 - 19*a^4*b^3*c*d^6 + 6*a^5*b^2*d^7 + (5*a^2*b^5*c^7 - 14*a^3*b^4*c^6*d + 6*a^4*b^3*c^5*d^2 + 16*a^5*b^2*c^4*d^3 - 19*a^6*b*c^3*d^4 + 6*a^7*c^2*d^5)*x^4 + 2*(5*a*b^6*c^7 - 9*a^2*b^5*c^6*d - 8*a^3*b^4*c^5*d^2 + 22*a^4*b^3*c^4*d^3 - 3*a^5*b^2*c^3*d^4 - 13*a^6*b*c^2*d^5 + 6*a^7*c*d^6)*x^3 + (5*b^7*c^7 + 6*a*b^6*c^6*d - 45*a^2*b^5*c^5*d^2 + 26*a^3*b^4*c^4*d^3 + 51*a^4*b^3*c^3*d^4 - 54*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6 + 6*a^7*d^7)*x^2 + 2*(5*b^7*c^6*d - 9*a*b^6*c^5*d^2 - 8*a^2*b^5*c^4*d^3 + 22*a^3*b^4*c^3*d^4 - 3*a^4*b^3*c^2*d^5 - 13*a^5*b^2*c*d^6 + 6*a^6*b*d^7)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + 3*(99*a^4*b^4*c^2*d^5 - 88*a^5*b^3*c*d^6 + 24*a^6*b^2*d^7 + (99*a^6*b^2*c^4*d^3 - 88*a^7*b*c^3*d^4 + 24*a^8*c^2*d^5)*x^4 + 2*(99*a^5*b^3*c^4*d^3 + 11*a^6*b^2*c^3*d^4 - 64*a^7*b*c^2*d^5 + 24*a^8*c*d^6)*x^3 + (99*a^4*b^4*c^4*d^3 + 308*a^5*b^3*c^3*d^4 - 229*a^6*b^2*c^2*d^5 + 8*a^7*b*c*d^6 + 24*a^8*d^7)*x^2 + 2*(99*a^4*b^4*c^3*d^4 + 11*a^5*b^3*c^2*d^5 - 64*a^6*b^2*c*d^6 + 24*a^7*b*d^7)*x)*sqrt(-d/(b*c - a*d))*log(-(2*(b*c - a*d)*x*sqrt(-d/(b*c - a*d))*sqrt((a*x + b)/x) - b*d + (b*c - 2*a*d)*x)/(c*x + d)) + 2*(12*(a^3*b^4*c^7 - 4*a^4*b^3*c^6*d + 6*a^5*b^2*c^5*d^2 - 4*a^6*b*c^4*d^3 + a^7*c^3*d^4)*x^5 + (80*a^2*b^5*c^7 - 200*a^3*b^4*c^6*d + 48*a^4*b^3*c^5*d^2 + 48*a^5*b^2*c^4*d^3 - 135*a^6*b*c^3*d^4 + 54*a^7*c^2*d^5)*x^4 + (60*a*b^6*c^7 - 8*a^2*b^5*c^6*d - 364*a^3*b^4*c^5*d^2 + 192*a^4*b^3*c^4*d^3 - 234*a^5*b^2*c^3*d^4 + 3*a^6*b*c^2*d^5 + 36*a^7*c*d^6)*x^3 + (120*a*b^6*c^6*d - 256*a^2*b^5*c^5*d^2 - 80*a^3*b^4*c^4*d^3 - 15*a^4*b^3*c^3*d^4 - 156*a^5*b^2*c^2*d^5 + 72*a^6*b*c*d^6)*x^2 + 3*(20*a*b^6*c^5*d^2 - 56*a^2*b^5*c^4*d^3 + 24*a^3*b^4*c^3*d^4 - 35*a^4*b^3*c^2*d^5 + 12*a^5*b^2*c*d^6)*x)*sqrt((a*x + b)/x))/(a^4*b^6*c^8*d^2 - 4*a^5*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*x^4 + 2*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*x^3 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*x^2 + 2*(a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*x), -1/12*(3*(99*a^4*b^4*c^2*d^5 - 88*a^5*b^3*c*d^6 + 24*a^6*b^2*d^7 + (99*a^6*b^2*c^4*d^3 - 88*a^7*b*c^3*d^4 + 24*a^8*c^2*d^5)*x^4 + 2*(99*a^5*b^3*c^4*d^3 + 11*a^6*b^2*c^3*d^4 - 64*a^7*b*c^2*d^5 + 24*a^8*c*d^6)*x^3 + (99*a^4*b^4*c^4*d^3 + 308*a^5*b^3*c^3*d^4 - 229*a^6*b^2*c^2*d^5 + 8*a^7*b*c*d^6 + 24*a^8*d^7)*x^2 + 2*(99*a^4*b^4*c^3*d^4 + 11*a^5*b^3*c^2*d^5 - 64*a^6*b^2*c*d^6 + 24*a^7*b*d^7)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 6*(5*b^7*c^5*d^2 - 14*a*b^6*c^4*d^3 + 6*a^2*b^5*c^3*d^4 + 16*a^3*b^4*c^2*d^5 - 19*a^4*b^3*c*d^6 + 6*a^5*b^2*d^7 + (5*a^2*b^5*c^7 - 14*a^3*b^4*c^6*d + 6*a^4*b^3*c^5*d^2 + 16*a^5*b^2*c^4*d^3 - 19*a^6*b*c^3*d^4 + 6*a^7*c^2*d^5)*x^4 + 2*(5*a*b^6*c^7 - 9*a^2*b^5*c^6*d - 8*a^3*b^4*c^5*d^2 + 22*a^4*b^3*c^4*d^3 - 3*a^5*b^2*c^3*d^4 - 13*a^6*b*c^2*d^5 + 6*a^7*c*d^6)*x^3 + (5*b^7*c^7 + 6*a*b^6*c^6*d - 45*a^2*b^5*c^5*d^2 + 26*a^3*b^4*c^4*d^3 + 51*a^4*b^3*c^3*d^4 - 54*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6 + 6*a^7*d^7)*x^2 + 2*(5*b^7*c^6*d - 9*a*b^6*c^5*d^2 - 8*a^2*b^5*c^4*d^3 + 22*a^3*b^4*c^3*d^4 - 3*a^4*b^3*c^2*d^5 - 13*a^5*b^2*c*d^6 + 6*a^6*b*d^7)*x)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - (12*(a^3*b^4*c^7 - 4*a^4*b^3*c^6*d + 6*a^5*b^2*c^5*d^2 - 4*a^6*b*c^4*d^3 + a^7*c^3*d^4)*x^5 + (80*a^2*b^5*c^7 - 200*a^3*b^4*c^6*d + 48*a^4*b^3*c^5*d^2 + 48*a^5*b^2*c^4*d^3 - 135*a^6*b*c^3*d^4 + 54*a^7*c^2*d^5)*x^4 + (60*a*b^6*c^7 - 8*a^2*b^5*c^6*d - 364*a^3*b^4*c^5*d^2 + 192*a^4*b^3*c^4*d^3 - 234*a^5*b^2*c^3*d^4 + 3*a^6*b*c^2*d^5 + 36*a^7*c*d^6)*x^3 + (120*a*b^6*c^6*d - 256*a^2*b^5*c^5*d^2 - 80*a^3*b^4*c^4*d^3 - 15*a^4*b^3*c^3*d^4 - 156*a^5*b^2*c^2*d^5 + 72*a^6*b*c*d^6)*x^2 + 3*(20*a*b^6*c^5*d^2 - 56*a^2*b^5*c^4*d^3 + 24*a^3*b^4*c^3*d^4 - 35*a^4*b^3*c^2*d^5 + 12*a^5*b^2*c*d^6)*x)*sqrt((a*x + b)/x))/(a^4*b^6*c^8*d^2 - 4*a^5*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*x^4 + 2*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*x^3 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*x^2 + 2*(a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*x), -1/12*(3*(99*a^4*b^4*c^2*d^5 - 88*a^5*b^3*c*d^6 + 24*a^6*b^2*d^7 + (99*a^6*b^2*c^4*d^3 - 88*a^7*b*c^3*d^4 + 24*a^8*c^2*d^5)*x^4 + 2*(99*a^5*b^3*c^4*d^3 + 11*a^6*b^2*c^3*d^4 - 64*a^7*b*c^2*d^5 + 24*a^8*c*d^6)*x^3 + (99*a^4*b^4*c^4*d^3 + 308*a^5*b^3*c^3*d^4 - 229*a^6*b^2*c^2*d^5 + 8*a^7*b*c*d^6 + 24*a^8*d^7)*x^2 + 2*(99*a^4*b^4*c^3*d^4 + 11*a^5*b^3*c^2*d^5 - 64*a^6*b^2*c*d^6 + 24*a^7*b*d^7)*x)*sqrt(d/(b*c - a*d))*arctan(-(b*c - a*d)*x*sqrt(d/(b*c - a*d))*sqrt((a*x + b)/x)/(a*d*x + b*d)) - 12*(5*b^7*c^5*d^2 - 14*a*b^6*c^4*d^3 + 6*a^2*b^5*c^3*d^4 + 16*a^3*b^4*c^2*d^5 - 19*a^4*b^3*c*d^6 + 6*a^5*b^2*d^7 + (5*a^2*b^5*c^7 - 14*a^3*b^4*c^6*d + 6*a^4*b^3*c^5*d^2 + 16*a^5*b^2*c^4*d^3 - 19*a^6*b*c^3*d^4 + 6*a^7*c^2*d^5)*x^4 + 2*(5*a*b^6*c^7 - 9*a^2*b^5*c^6*d - 8*a^3*b^4*c^5*d^2 + 22*a^4*b^3*c^4*d^3 - 3*a^5*b^2*c^3*d^4 - 13*a^6*b*c^2*d^5 + 6*a^7*c*d^6)*x^3 + (5*b^7*c^7 + 6*a*b^6*c^6*d - 45*a^2*b^5*c^5*d^2 + 26*a^3*b^4*c^4*d^3 + 51*a^4*b^3*c^3*d^4 - 54*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6 + 6*a^7*d^7)*x^2 + 2*(5*b^7*c^6*d - 9*a*b^6*c^5*d^2 - 8*a^2*b^5*c^4*d^3 + 22*a^3*b^4*c^3*d^4 - 3*a^4*b^3*c^2*d^5 - 13*a^5*b^2*c*d^6 + 6*a^6*b*d^7)*x)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (12*(a^3*b^4*c^7 - 4*a^4*b^3*c^6*d + 6*a^5*b^2*c^5*d^2 - 4*a^6*b*c^4*d^3 + a^7*c^3*d^4)*x^5 + (80*a^2*b^5*c^7 - 200*a^3*b^4*c^6*d + 48*a^4*b^3*c^5*d^2 + 48*a^5*b^2*c^4*d^3 - 135*a^6*b*c^3*d^4 + 54*a^7*c^2*d^5)*x^4 + (60*a*b^6*c^7 - 8*a^2*b^5*c^6*d - 364*a^3*b^4*c^5*d^2 + 192*a^4*b^3*c^4*d^3 - 234*a^5*b^2*c^3*d^4 + 3*a^6*b*c^2*d^5 + 36*a^7*c*d^6)*x^3 + (120*a*b^6*c^6*d - 256*a^2*b^5*c^5*d^2 - 80*a^3*b^4*c^4*d^3 - 15*a^4*b^3*c^3*d^4 - 156*a^5*b^2*c^2*d^5 + 72*a^6*b*c*d^6)*x^2 + 3*(20*a*b^6*c^5*d^2 - 56*a^2*b^5*c^4*d^3 + 24*a^3*b^4*c^3*d^4 - 35*a^4*b^3*c^2*d^5 + 12*a^5*b^2*c*d^6)*x)*sqrt((a*x + b)/x))/(a^4*b^6*c^8*d^2 - 4*a^5*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*x^4 + 2*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*x^3 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*x^2 + 2*(a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*x)]","B",0
266,1,890,0,1.776013," ","integrate((c+d/x)^(1/2)*(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a c x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + 2 \, \sqrt{b d} a c \log\left(-\frac{8 \, b^{2} d^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x + {\left(b c + a d\right)} x^{2}\right)} \sqrt{b d} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x}{x^{2}}\right) + \sqrt{a c} {\left(b c + a d\right)} \log\left(-8 \, a^{2} c^{2} x^{2} - b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2} - 4 \, {\left(2 \, a c x^{2} + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)}{4 \, a c}, \frac{4 \, a c x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + 4 \, \sqrt{-b d} a c \arctan\left(\frac{{\left(2 \, b d x + {\left(b c + a d\right)} x^{2}\right)} \sqrt{-b d} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, {\left(a b c d x^{2} + b^{2} d^{2} + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + \sqrt{a c} {\left(b c + a d\right)} \log\left(-8 \, a^{2} c^{2} x^{2} - b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2} - 4 \, {\left(2 \, a c x^{2} + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)}{4 \, a c}, \frac{2 \, a c x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + \sqrt{b d} a c \log\left(-\frac{8 \, b^{2} d^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x + {\left(b c + a d\right)} x^{2}\right)} \sqrt{b d} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x}{x^{2}}\right) - \sqrt{-a c} {\left(b c + a d\right)} \arctan\left(\frac{2 \, \sqrt{-a c} x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, a c x + b c + a d}\right)}{2 \, a c}, \frac{2 \, a c x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + 2 \, \sqrt{-b d} a c \arctan\left(\frac{{\left(2 \, b d x + {\left(b c + a d\right)} x^{2}\right)} \sqrt{-b d} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, {\left(a b c d x^{2} + b^{2} d^{2} + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - \sqrt{-a c} {\left(b c + a d\right)} \arctan\left(\frac{2 \, \sqrt{-a c} x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, a c x + b c + a d}\right)}{2 \, a c}\right]"," ",0,"[1/4*(4*a*c*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + 2*sqrt(b*d)*a*c*log(-(8*b^2*d^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*b*d*x + (b*c + a*d)*x^2)*sqrt(b*d)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + 8*(b^2*c*d + a*b*d^2)*x)/x^2) + sqrt(a*c)*(b*c + a*d)*log(-8*a^2*c^2*x^2 - b^2*c^2 - 6*a*b*c*d - a^2*d^2 - 4*(2*a*c*x^2 + (b*c + a*d)*x)*sqrt(a*c)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - 8*(a*b*c^2 + a^2*c*d)*x))/(a*c), 1/4*(4*a*c*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + 4*sqrt(-b*d)*a*c*arctan(1/2*(2*b*d*x + (b*c + a*d)*x^2)*sqrt(-b*d)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(a*b*c*d*x^2 + b^2*d^2 + (b^2*c*d + a*b*d^2)*x)) + sqrt(a*c)*(b*c + a*d)*log(-8*a^2*c^2*x^2 - b^2*c^2 - 6*a*b*c*d - a^2*d^2 - 4*(2*a*c*x^2 + (b*c + a*d)*x)*sqrt(a*c)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - 8*(a*b*c^2 + a^2*c*d)*x))/(a*c), 1/2*(2*a*c*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + sqrt(b*d)*a*c*log(-(8*b^2*d^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*b*d*x + (b*c + a*d)*x^2)*sqrt(b*d)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + 8*(b^2*c*d + a*b*d^2)*x)/x^2) - sqrt(-a*c)*(b*c + a*d)*arctan(2*sqrt(-a*c)*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(2*a*c*x + b*c + a*d)))/(a*c), 1/2*(2*a*c*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + 2*sqrt(-b*d)*a*c*arctan(1/2*(2*b*d*x + (b*c + a*d)*x^2)*sqrt(-b*d)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(a*b*c*d*x^2 + b^2*d^2 + (b^2*c*d + a*b*d^2)*x)) - sqrt(-a*c)*(b*c + a*d)*arctan(2*sqrt(-a*c)*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(2*a*c*x + b*c + a*d)))/(a*c)]","A",0
267,1,247,0,1.185779," ","integrate((a+b/x)^(1/2)/(c+d/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a c x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - \sqrt{a c} {\left(b c - a d\right)} \log\left(-8 \, a^{2} c^{2} x^{2} - b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2} + 4 \, {\left(2 \, a c x^{2} + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)}{4 \, a c^{2}}, \frac{2 \, a c x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - \sqrt{-a c} {\left(b c - a d\right)} \arctan\left(\frac{2 \, \sqrt{-a c} x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, a c x + b c + a d}\right)}{2 \, a c^{2}}\right]"," ",0,"[1/4*(4*a*c*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - sqrt(a*c)*(b*c - a*d)*log(-8*a^2*c^2*x^2 - b^2*c^2 - 6*a*b*c*d - a^2*d^2 + 4*(2*a*c*x^2 + (b*c + a*d)*x)*sqrt(a*c)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - 8*(a*b*c^2 + a^2*c*d)*x))/(a*c^2), 1/2*(2*a*c*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - sqrt(-a*c)*(b*c - a*d)*arctan(2*sqrt(-a*c)*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(2*a*c*x + b*c + a*d)))/(a*c^2)]","A",0
268,1,319,0,1.198836," ","integrate((a+b/x)^(1/2)/(c+d/x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c d - 3 \, a d^{2} + {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{a c} \log\left(-8 \, a^{2} c^{2} x^{2} - b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2} + 4 \, {\left(2 \, a c x^{2} + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} x\right) - 4 \, {\left(a c^{2} x^{2} + 3 \, a c d x\right)} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{4 \, {\left(a c^{4} x + a c^{3} d\right)}}, -\frac{{\left(b c d - 3 \, a d^{2} + {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{2 \, \sqrt{-a c} x \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, a c x + b c + a d}\right) - 2 \, {\left(a c^{2} x^{2} + 3 \, a c d x\right)} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, {\left(a c^{4} x + a c^{3} d\right)}}\right]"," ",0,"[-1/4*((b*c*d - 3*a*d^2 + (b*c^2 - 3*a*c*d)*x)*sqrt(a*c)*log(-8*a^2*c^2*x^2 - b^2*c^2 - 6*a*b*c*d - a^2*d^2 + 4*(2*a*c*x^2 + (b*c + a*d)*x)*sqrt(a*c)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - 8*(a*b*c^2 + a^2*c*d)*x) - 4*(a*c^2*x^2 + 3*a*c*d*x)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x))/(a*c^4*x + a*c^3*d), -1/2*((b*c*d - 3*a*d^2 + (b*c^2 - 3*a*c*d)*x)*sqrt(-a*c)*arctan(2*sqrt(-a*c)*x*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(2*a*c*x + b*c + a*d)) - 2*(a*c^2*x^2 + 3*a*c*d*x)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x))/(a*c^4*x + a*c^3*d)]","A",0
269,0,0,0,0.750505," ","integrate((a+b/x)^p*(c+d/x)^q,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x + b}{x}\right)^{p} \left(\frac{c x + d}{x}\right)^{q}, x\right)"," ",0,"integral(((a*x + b)/x)^p*((c*x + d)/x)^q, x)","F",0
270,1,98,0,0.739211," ","integrate((a+b/x^2)/(c+d/x^2),x, algorithm=""fricas"")","\left[\frac{2 \, a c d x + {\left(b c - a d\right)} \sqrt{-c d} \log\left(\frac{c x^{2} + 2 \, \sqrt{-c d} x - d}{c x^{2} + d}\right)}{2 \, c^{2} d}, \frac{a c d x + {\left(b c - a d\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{d}\right)}{c^{2} d}\right]"," ",0,"[1/2*(2*a*c*d*x + (b*c - a*d)*sqrt(-c*d)*log((c*x^2 + 2*sqrt(-c*d)*x - d)/(c*x^2 + d)))/(c^2*d), (a*c*d*x + (b*c - a*d)*sqrt(c*d)*arctan(sqrt(c*d)*x/d))/(c^2*d)]","A",0
271,0,0,0,1.283764," ","integrate((c+d/x^2)^(1/2)*(a+b/x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\frac{a x^{2} + b}{x^{2}}} \sqrt{\frac{c x^{2} + d}{x^{2}}}, x\right)"," ",0,"integral(sqrt((a*x^2 + b)/x^2)*sqrt((c*x^2 + d)/x^2), x)","F",0
272,0,0,0,1.175096," ","integrate((a+b/x^2)^(1/2)/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}, x\right)"," ",0,"integral(x^2*sqrt((a*x^2 + b)/x^2)*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d), x)","F",0
273,0,0,0,0.772283," ","integrate((a+b/x^2)^(1/2)/(c+d/x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \sqrt{\frac{a x^{2} + b}{x^{2}}} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c^{2} x^{4} + 2 \, c d x^{2} + d^{2}}, x\right)"," ",0,"integral(x^4*sqrt((a*x^2 + b)/x^2)*sqrt((c*x^2 + d)/x^2)/(c^2*x^4 + 2*c*d*x^2 + d^2), x)","F",0
274,0,0,0,1.041928," ","integrate((a+b/x^2)^p*(c+d/x^2)^q,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
275,1,390,0,0.924822," ","integrate((a+b/x^3)/(c+d/x^3),x, algorithm=""fricas"")","\left[\frac{6 \, a c d^{2} x - 3 \, \sqrt{\frac{1}{3}} {\left(b c^{2} d - a c d^{2}\right)} \sqrt{\frac{\left(-c d^{2}\right)^{\frac{1}{3}}}{c}} \log\left(\frac{2 \, c d x^{3} + 3 \, \left(-c d^{2}\right)^{\frac{1}{3}} d x - d^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d x^{2} + \left(-c d^{2}\right)^{\frac{2}{3}} x + \left(-c d^{2}\right)^{\frac{1}{3}} d\right)} \sqrt{\frac{\left(-c d^{2}\right)^{\frac{1}{3}}}{c}}}{c x^{3} + d}\right) - \left(-c d^{2}\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x^{2} - \left(-c d^{2}\right)^{\frac{2}{3}} x - \left(-c d^{2}\right)^{\frac{1}{3}} d\right) + 2 \, \left(-c d^{2}\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x + \left(-c d^{2}\right)^{\frac{2}{3}}\right)}{6 \, c^{2} d^{2}}, \frac{6 \, a c d^{2} x + 6 \, \sqrt{\frac{1}{3}} {\left(b c^{2} d - a c d^{2}\right)} \sqrt{-\frac{\left(-c d^{2}\right)^{\frac{1}{3}}}{c}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-c d^{2}\right)^{\frac{2}{3}} x + \left(-c d^{2}\right)^{\frac{1}{3}} d\right)} \sqrt{-\frac{\left(-c d^{2}\right)^{\frac{1}{3}}}{c}}}{d^{2}}\right) - \left(-c d^{2}\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x^{2} - \left(-c d^{2}\right)^{\frac{2}{3}} x - \left(-c d^{2}\right)^{\frac{1}{3}} d\right) + 2 \, \left(-c d^{2}\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(c d x + \left(-c d^{2}\right)^{\frac{2}{3}}\right)}{6 \, c^{2} d^{2}}\right]"," ",0,"[1/6*(6*a*c*d^2*x - 3*sqrt(1/3)*(b*c^2*d - a*c*d^2)*sqrt((-c*d^2)^(1/3)/c)*log((2*c*d*x^3 + 3*(-c*d^2)^(1/3)*d*x - d^2 - 3*sqrt(1/3)*(2*c*d*x^2 + (-c*d^2)^(2/3)*x + (-c*d^2)^(1/3)*d)*sqrt((-c*d^2)^(1/3)/c))/(c*x^3 + d)) - (-c*d^2)^(2/3)*(b*c - a*d)*log(c*d*x^2 - (-c*d^2)^(2/3)*x - (-c*d^2)^(1/3)*d) + 2*(-c*d^2)^(2/3)*(b*c - a*d)*log(c*d*x + (-c*d^2)^(2/3)))/(c^2*d^2), 1/6*(6*a*c*d^2*x + 6*sqrt(1/3)*(b*c^2*d - a*c*d^2)*sqrt(-(-c*d^2)^(1/3)/c)*arctan(sqrt(1/3)*(2*(-c*d^2)^(2/3)*x + (-c*d^2)^(1/3)*d)*sqrt(-(-c*d^2)^(1/3)/c)/d^2) - (-c*d^2)^(2/3)*(b*c - a*d)*log(c*d*x^2 - (-c*d^2)^(2/3)*x - (-c*d^2)^(1/3)*d) + 2*(-c*d^2)^(2/3)*(b*c - a*d)*log(c*d*x + (-c*d^2)^(2/3)))/(c^2*d^2)]","A",0
276,1,48,0,0.815659," ","integrate((a+b*x^(1/2))/(c+d*x^(1/2)),x, algorithm=""fricas"")","\frac{b d^{2} x + 2 \, {\left(b c^{2} - a c d\right)} \log\left(d \sqrt{x} + c\right) - 2 \, {\left(b c d - a d^{2}\right)} \sqrt{x}}{d^{3}}"," ",0,"(b*d^2*x + 2*(b*c^2 - a*c*d)*log(d*sqrt(x) + c) - 2*(b*c*d - a*d^2)*sqrt(x))/d^3","A",0
277,1,20,0,0.805377," ","integrate((-1+x^(1/3))/(1+x^(1/3)),x, algorithm=""fricas"")","x - 3 \, x^{\frac{2}{3}} + 6 \, x^{\frac{1}{3}} - 6 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"x - 3*x^(2/3) + 6*x^(1/3) - 6*log(x^(1/3) + 1)","A",0
278,1,23,0,0.620293," ","integrate((1+x^(2/3))/(-1+x^(2/3)),x, algorithm=""fricas"")","x + 6 \, x^{\frac{1}{3}} - 3 \, \log\left(x^{\frac{1}{3}} + 1\right) + 3 \, \log\left(x^{\frac{1}{3}} - 1\right)"," ",0,"x + 6*x^(1/3) - 3*log(x^(1/3) + 1) + 3*log(x^(1/3) - 1)","A",0
279,1,71,0,0.823634," ","integrate((-16+x^(3/4))/(16+x^(3/4)),x, algorithm=""fricas"")","\frac{256}{3} \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} x^{\frac{1}{4}} - \frac{1}{3} \, \sqrt{3}\right) - \frac{128}{3} \cdot 2^{\frac{1}{3}} \log\left(4 \cdot 2^{\frac{2}{3}} - 2 \cdot 2^{\frac{1}{3}} x^{\frac{1}{4}} + \sqrt{x}\right) + \frac{256}{3} \cdot 2^{\frac{1}{3}} \log\left(2 \cdot 2^{\frac{1}{3}} + x^{\frac{1}{4}}\right) + x - 128 \, x^{\frac{1}{4}}"," ",0,"256/3*sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*x^(1/4) - 1/3*sqrt(3)) - 128/3*2^(1/3)*log(4*2^(2/3) - 2*2^(1/3)*x^(1/4) + sqrt(x)) + 256/3*2^(1/3)*log(2*2^(1/3) + x^(1/4)) + x - 128*x^(1/4)","A",0
280,1,22,0,0.559344," ","integrate((1+1/x^(1/3))/(-1+1/x^(1/3)),x, algorithm=""fricas"")","-x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log\left(x^{\frac{1}{3}} - 1\right)"," ",0,"-x - 3*x^(2/3) - 6*x^(1/3) - 6*log(x^(1/3) - 1)","A",0
281,-2,0,0,0.000000," ","integrate((a-b*x^n)^(3/2)*(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
282,-2,0,0,0.000000," ","integrate((a-b*x^n)^(1/2)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
283,0,0,0,0.892897," ","integrate((a-b*x^n)^p*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
284,1,527,0,0.860329," ","integrate((a+b*x^n)*(c+d*x^n)^4,x, algorithm=""fricas"")","\frac{{\left(24 \, b d^{4} n^{4} + 50 \, b d^{4} n^{3} + 35 \, b d^{4} n^{2} + 10 \, b d^{4} n + b d^{4}\right)} x x^{5 \, n} + {\left(4 \, b c d^{3} + a d^{4} + 30 \, {\left(4 \, b c d^{3} + a d^{4}\right)} n^{4} + 61 \, {\left(4 \, b c d^{3} + a d^{4}\right)} n^{3} + 41 \, {\left(4 \, b c d^{3} + a d^{4}\right)} n^{2} + 11 \, {\left(4 \, b c d^{3} + a d^{4}\right)} n\right)} x x^{4 \, n} + 2 \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3} + 40 \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} n^{4} + 78 \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} n^{3} + 49 \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} n^{2} + 12 \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} n\right)} x x^{3 \, n} + 2 \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2} + 60 \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} n^{4} + 107 \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} n^{3} + 59 \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} n^{2} + 13 \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} n\right)} x x^{2 \, n} + {\left(b c^{4} + 4 \, a c^{3} d + 120 \, {\left(b c^{4} + 4 \, a c^{3} d\right)} n^{4} + 154 \, {\left(b c^{4} + 4 \, a c^{3} d\right)} n^{3} + 71 \, {\left(b c^{4} + 4 \, a c^{3} d\right)} n^{2} + 14 \, {\left(b c^{4} + 4 \, a c^{3} d\right)} n\right)} x x^{n} + {\left(120 \, a c^{4} n^{5} + 274 \, a c^{4} n^{4} + 225 \, a c^{4} n^{3} + 85 \, a c^{4} n^{2} + 15 \, a c^{4} n + a c^{4}\right)} x}{120 \, n^{5} + 274 \, n^{4} + 225 \, n^{3} + 85 \, n^{2} + 15 \, n + 1}"," ",0,"((24*b*d^4*n^4 + 50*b*d^4*n^3 + 35*b*d^4*n^2 + 10*b*d^4*n + b*d^4)*x*x^(5*n) + (4*b*c*d^3 + a*d^4 + 30*(4*b*c*d^3 + a*d^4)*n^4 + 61*(4*b*c*d^3 + a*d^4)*n^3 + 41*(4*b*c*d^3 + a*d^4)*n^2 + 11*(4*b*c*d^3 + a*d^4)*n)*x*x^(4*n) + 2*(3*b*c^2*d^2 + 2*a*c*d^3 + 40*(3*b*c^2*d^2 + 2*a*c*d^3)*n^4 + 78*(3*b*c^2*d^2 + 2*a*c*d^3)*n^3 + 49*(3*b*c^2*d^2 + 2*a*c*d^3)*n^2 + 12*(3*b*c^2*d^2 + 2*a*c*d^3)*n)*x*x^(3*n) + 2*(2*b*c^3*d + 3*a*c^2*d^2 + 60*(2*b*c^3*d + 3*a*c^2*d^2)*n^4 + 107*(2*b*c^3*d + 3*a*c^2*d^2)*n^3 + 59*(2*b*c^3*d + 3*a*c^2*d^2)*n^2 + 13*(2*b*c^3*d + 3*a*c^2*d^2)*n)*x*x^(2*n) + (b*c^4 + 4*a*c^3*d + 120*(b*c^4 + 4*a*c^3*d)*n^4 + 154*(b*c^4 + 4*a*c^3*d)*n^3 + 71*(b*c^4 + 4*a*c^3*d)*n^2 + 14*(b*c^4 + 4*a*c^3*d)*n)*x*x^n + (120*a*c^4*n^5 + 274*a*c^4*n^4 + 225*a*c^4*n^3 + 85*a*c^4*n^2 + 15*a*c^4*n + a*c^4)*x)/(120*n^5 + 274*n^4 + 225*n^3 + 85*n^2 + 15*n + 1)","B",0
285,1,319,0,0.740281," ","integrate((a+b*x^n)*(c+d*x^n)^3,x, algorithm=""fricas"")","\frac{{\left(6 \, b d^{3} n^{3} + 11 \, b d^{3} n^{2} + 6 \, b d^{3} n + b d^{3}\right)} x x^{4 \, n} + {\left(3 \, b c d^{2} + a d^{3} + 8 \, {\left(3 \, b c d^{2} + a d^{3}\right)} n^{3} + 14 \, {\left(3 \, b c d^{2} + a d^{3}\right)} n^{2} + 7 \, {\left(3 \, b c d^{2} + a d^{3}\right)} n\right)} x x^{3 \, n} + 3 \, {\left(b c^{2} d + a c d^{2} + 12 \, {\left(b c^{2} d + a c d^{2}\right)} n^{3} + 19 \, {\left(b c^{2} d + a c d^{2}\right)} n^{2} + 8 \, {\left(b c^{2} d + a c d^{2}\right)} n\right)} x x^{2 \, n} + {\left(b c^{3} + 3 \, a c^{2} d + 24 \, {\left(b c^{3} + 3 \, a c^{2} d\right)} n^{3} + 26 \, {\left(b c^{3} + 3 \, a c^{2} d\right)} n^{2} + 9 \, {\left(b c^{3} + 3 \, a c^{2} d\right)} n\right)} x x^{n} + {\left(24 \, a c^{3} n^{4} + 50 \, a c^{3} n^{3} + 35 \, a c^{3} n^{2} + 10 \, a c^{3} n + a c^{3}\right)} x}{24 \, n^{4} + 50 \, n^{3} + 35 \, n^{2} + 10 \, n + 1}"," ",0,"((6*b*d^3*n^3 + 11*b*d^3*n^2 + 6*b*d^3*n + b*d^3)*x*x^(4*n) + (3*b*c*d^2 + a*d^3 + 8*(3*b*c*d^2 + a*d^3)*n^3 + 14*(3*b*c*d^2 + a*d^3)*n^2 + 7*(3*b*c*d^2 + a*d^3)*n)*x*x^(3*n) + 3*(b*c^2*d + a*c*d^2 + 12*(b*c^2*d + a*c*d^2)*n^3 + 19*(b*c^2*d + a*c*d^2)*n^2 + 8*(b*c^2*d + a*c*d^2)*n)*x*x^(2*n) + (b*c^3 + 3*a*c^2*d + 24*(b*c^3 + 3*a*c^2*d)*n^3 + 26*(b*c^3 + 3*a*c^2*d)*n^2 + 9*(b*c^3 + 3*a*c^2*d)*n)*x*x^n + (24*a*c^3*n^4 + 50*a*c^3*n^3 + 35*a*c^3*n^2 + 10*a*c^3*n + a*c^3)*x)/(24*n^4 + 50*n^3 + 35*n^2 + 10*n + 1)","B",0
286,1,175,0,0.912600," ","integrate((a+b*x^n)*(c+d*x^n)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, b d^{2} n^{2} + 3 \, b d^{2} n + b d^{2}\right)} x x^{3 \, n} + {\left(2 \, b c d + a d^{2} + 3 \, {\left(2 \, b c d + a d^{2}\right)} n^{2} + 4 \, {\left(2 \, b c d + a d^{2}\right)} n\right)} x x^{2 \, n} + {\left(b c^{2} + 2 \, a c d + 6 \, {\left(b c^{2} + 2 \, a c d\right)} n^{2} + 5 \, {\left(b c^{2} + 2 \, a c d\right)} n\right)} x x^{n} + {\left(6 \, a c^{2} n^{3} + 11 \, a c^{2} n^{2} + 6 \, a c^{2} n + a c^{2}\right)} x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"((2*b*d^2*n^2 + 3*b*d^2*n + b*d^2)*x*x^(3*n) + (2*b*c*d + a*d^2 + 3*(2*b*c*d + a*d^2)*n^2 + 4*(2*b*c*d + a*d^2)*n)*x*x^(2*n) + (b*c^2 + 2*a*c*d + 6*(b*c^2 + 2*a*c*d)*n^2 + 5*(b*c^2 + 2*a*c*d)*n)*x*x^n + (6*a*c^2*n^3 + 11*a*c^2*n^2 + 6*a*c^2*n + a*c^2)*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
287,1,69,0,0.941516," ","integrate((a+b*x^n)*(c+d*x^n),x, algorithm=""fricas"")","\frac{{\left(b d n + b d\right)} x x^{2 \, n} + {\left(b c + a d + 2 \, {\left(b c + a d\right)} n\right)} x x^{n} + {\left(2 \, a c n^{2} + 3 \, a c n + a c\right)} x}{2 \, n^{2} + 3 \, n + 1}"," ",0,"((b*d*n + b*d)*x*x^(2*n) + (b*c + a*d + 2*(b*c + a*d)*n)*x*x^n + (2*a*c*n^2 + 3*a*c*n + a*c)*x)/(2*n^2 + 3*n + 1)","A",0
288,0,0,0,1.060869," ","integrate((a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{n} + a}{d x^{n} + c}, x\right)"," ",0,"integral((b*x^n + a)/(d*x^n + c), x)","F",0
289,0,0,0,0.872177," ","integrate((a+b*x^n)/(c+d*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{n} + a}{d^{2} x^{2 \, n} + 2 \, c d x^{n} + c^{2}}, x\right)"," ",0,"integral((b*x^n + a)/(d^2*x^(2*n) + 2*c*d*x^n + c^2), x)","F",0
290,0,0,0,0.848470," ","integrate((a+b*x^n)/(c+d*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{n} + a}{d^{3} x^{3 \, n} + 3 \, c d^{2} x^{2 \, n} + 3 \, c^{2} d x^{n} + c^{3}}, x\right)"," ",0,"integral((b*x^n + a)/(d^3*x^(3*n) + 3*c*d^2*x^(2*n) + 3*c^2*d*x^n + c^3), x)","F",0
291,0,0,0,0.785916," ","integrate((a+b*x^n)/(c+d*x^n)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{n} + a}{d^{4} x^{4 \, n} + 4 \, c d^{3} x^{3 \, n} + 6 \, c^{2} d^{2} x^{2 \, n} + 4 \, c^{3} d x^{n} + c^{4}}, x\right)"," ",0,"integral((b*x^n + a)/(d^4*x^(4*n) + 4*c*d^3*x^(3*n) + 6*c^2*d^2*x^(2*n) + 4*c^3*d*x^n + c^4), x)","F",0
292,1,667,0,0.876273," ","integrate((a+b*x^n)^2*(d+e*x^n)^3,x, algorithm=""fricas"")","\frac{{\left(24 \, b^{2} e^{3} n^{4} + 50 \, b^{2} e^{3} n^{3} + 35 \, b^{2} e^{3} n^{2} + 10 \, b^{2} e^{3} n + b^{2} e^{3}\right)} x x^{5 \, n} + {\left(3 \, b^{2} d e^{2} + 2 \, a b e^{3} + 30 \, {\left(3 \, b^{2} d e^{2} + 2 \, a b e^{3}\right)} n^{4} + 61 \, {\left(3 \, b^{2} d e^{2} + 2 \, a b e^{3}\right)} n^{3} + 41 \, {\left(3 \, b^{2} d e^{2} + 2 \, a b e^{3}\right)} n^{2} + 11 \, {\left(3 \, b^{2} d e^{2} + 2 \, a b e^{3}\right)} n\right)} x x^{4 \, n} + {\left(3 \, b^{2} d^{2} e + 6 \, a b d e^{2} + a^{2} e^{3} + 40 \, {\left(3 \, b^{2} d^{2} e + 6 \, a b d e^{2} + a^{2} e^{3}\right)} n^{4} + 78 \, {\left(3 \, b^{2} d^{2} e + 6 \, a b d e^{2} + a^{2} e^{3}\right)} n^{3} + 49 \, {\left(3 \, b^{2} d^{2} e + 6 \, a b d e^{2} + a^{2} e^{3}\right)} n^{2} + 12 \, {\left(3 \, b^{2} d^{2} e + 6 \, a b d e^{2} + a^{2} e^{3}\right)} n\right)} x x^{3 \, n} + {\left(b^{2} d^{3} + 6 \, a b d^{2} e + 3 \, a^{2} d e^{2} + 60 \, {\left(b^{2} d^{3} + 6 \, a b d^{2} e + 3 \, a^{2} d e^{2}\right)} n^{4} + 107 \, {\left(b^{2} d^{3} + 6 \, a b d^{2} e + 3 \, a^{2} d e^{2}\right)} n^{3} + 59 \, {\left(b^{2} d^{3} + 6 \, a b d^{2} e + 3 \, a^{2} d e^{2}\right)} n^{2} + 13 \, {\left(b^{2} d^{3} + 6 \, a b d^{2} e + 3 \, a^{2} d e^{2}\right)} n\right)} x x^{2 \, n} + {\left(2 \, a b d^{3} + 3 \, a^{2} d^{2} e + 120 \, {\left(2 \, a b d^{3} + 3 \, a^{2} d^{2} e\right)} n^{4} + 154 \, {\left(2 \, a b d^{3} + 3 \, a^{2} d^{2} e\right)} n^{3} + 71 \, {\left(2 \, a b d^{3} + 3 \, a^{2} d^{2} e\right)} n^{2} + 14 \, {\left(2 \, a b d^{3} + 3 \, a^{2} d^{2} e\right)} n\right)} x x^{n} + {\left(120 \, a^{2} d^{3} n^{5} + 274 \, a^{2} d^{3} n^{4} + 225 \, a^{2} d^{3} n^{3} + 85 \, a^{2} d^{3} n^{2} + 15 \, a^{2} d^{3} n + a^{2} d^{3}\right)} x}{120 \, n^{5} + 274 \, n^{4} + 225 \, n^{3} + 85 \, n^{2} + 15 \, n + 1}"," ",0,"((24*b^2*e^3*n^4 + 50*b^2*e^3*n^3 + 35*b^2*e^3*n^2 + 10*b^2*e^3*n + b^2*e^3)*x*x^(5*n) + (3*b^2*d*e^2 + 2*a*b*e^3 + 30*(3*b^2*d*e^2 + 2*a*b*e^3)*n^4 + 61*(3*b^2*d*e^2 + 2*a*b*e^3)*n^3 + 41*(3*b^2*d*e^2 + 2*a*b*e^3)*n^2 + 11*(3*b^2*d*e^2 + 2*a*b*e^3)*n)*x*x^(4*n) + (3*b^2*d^2*e + 6*a*b*d*e^2 + a^2*e^3 + 40*(3*b^2*d^2*e + 6*a*b*d*e^2 + a^2*e^3)*n^4 + 78*(3*b^2*d^2*e + 6*a*b*d*e^2 + a^2*e^3)*n^3 + 49*(3*b^2*d^2*e + 6*a*b*d*e^2 + a^2*e^3)*n^2 + 12*(3*b^2*d^2*e + 6*a*b*d*e^2 + a^2*e^3)*n)*x*x^(3*n) + (b^2*d^3 + 6*a*b*d^2*e + 3*a^2*d*e^2 + 60*(b^2*d^3 + 6*a*b*d^2*e + 3*a^2*d*e^2)*n^4 + 107*(b^2*d^3 + 6*a*b*d^2*e + 3*a^2*d*e^2)*n^3 + 59*(b^2*d^3 + 6*a*b*d^2*e + 3*a^2*d*e^2)*n^2 + 13*(b^2*d^3 + 6*a*b*d^2*e + 3*a^2*d*e^2)*n)*x*x^(2*n) + (2*a*b*d^3 + 3*a^2*d^2*e + 120*(2*a*b*d^3 + 3*a^2*d^2*e)*n^4 + 154*(2*a*b*d^3 + 3*a^2*d^2*e)*n^3 + 71*(2*a*b*d^3 + 3*a^2*d^2*e)*n^2 + 14*(2*a*b*d^3 + 3*a^2*d^2*e)*n)*x*x^n + (120*a^2*d^3*n^5 + 274*a^2*d^3*n^4 + 225*a^2*d^3*n^3 + 85*a^2*d^3*n^2 + 15*a^2*d^3*n + a^2*d^3)*x)/(120*n^5 + 274*n^4 + 225*n^3 + 85*n^2 + 15*n + 1)","B",0
293,1,370,0,0.837293," ","integrate((a+b*x^n)^2*(d+e*x^n)^2,x, algorithm=""fricas"")","\frac{{\left(6 \, b^{2} e^{2} n^{3} + 11 \, b^{2} e^{2} n^{2} + 6 \, b^{2} e^{2} n + b^{2} e^{2}\right)} x x^{4 \, n} + 2 \, {\left(b^{2} d e + a b e^{2} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} n^{3} + 14 \, {\left(b^{2} d e + a b e^{2}\right)} n^{2} + 7 \, {\left(b^{2} d e + a b e^{2}\right)} n\right)} x x^{3 \, n} + {\left(b^{2} d^{2} + 4 \, a b d e + a^{2} e^{2} + 12 \, {\left(b^{2} d^{2} + 4 \, a b d e + a^{2} e^{2}\right)} n^{3} + 19 \, {\left(b^{2} d^{2} + 4 \, a b d e + a^{2} e^{2}\right)} n^{2} + 8 \, {\left(b^{2} d^{2} + 4 \, a b d e + a^{2} e^{2}\right)} n\right)} x x^{2 \, n} + 2 \, {\left(a b d^{2} + a^{2} d e + 24 \, {\left(a b d^{2} + a^{2} d e\right)} n^{3} + 26 \, {\left(a b d^{2} + a^{2} d e\right)} n^{2} + 9 \, {\left(a b d^{2} + a^{2} d e\right)} n\right)} x x^{n} + {\left(24 \, a^{2} d^{2} n^{4} + 50 \, a^{2} d^{2} n^{3} + 35 \, a^{2} d^{2} n^{2} + 10 \, a^{2} d^{2} n + a^{2} d^{2}\right)} x}{24 \, n^{4} + 50 \, n^{3} + 35 \, n^{2} + 10 \, n + 1}"," ",0,"((6*b^2*e^2*n^3 + 11*b^2*e^2*n^2 + 6*b^2*e^2*n + b^2*e^2)*x*x^(4*n) + 2*(b^2*d*e + a*b*e^2 + 8*(b^2*d*e + a*b*e^2)*n^3 + 14*(b^2*d*e + a*b*e^2)*n^2 + 7*(b^2*d*e + a*b*e^2)*n)*x*x^(3*n) + (b^2*d^2 + 4*a*b*d*e + a^2*e^2 + 12*(b^2*d^2 + 4*a*b*d*e + a^2*e^2)*n^3 + 19*(b^2*d^2 + 4*a*b*d*e + a^2*e^2)*n^2 + 8*(b^2*d^2 + 4*a*b*d*e + a^2*e^2)*n)*x*x^(2*n) + 2*(a*b*d^2 + a^2*d*e + 24*(a*b*d^2 + a^2*d*e)*n^3 + 26*(a*b*d^2 + a^2*d*e)*n^2 + 9*(a*b*d^2 + a^2*d*e)*n)*x*x^n + (24*a^2*d^2*n^4 + 50*a^2*d^2*n^3 + 35*a^2*d^2*n^2 + 10*a^2*d^2*n + a^2*d^2)*x)/(24*n^4 + 50*n^3 + 35*n^2 + 10*n + 1)","B",0
294,1,175,0,0.796752," ","integrate((a+b*x^n)^2*(c+d*x^n),x, algorithm=""fricas"")","\frac{{\left(2 \, b^{2} d n^{2} + 3 \, b^{2} d n + b^{2} d\right)} x x^{3 \, n} + {\left(b^{2} c + 2 \, a b d + 3 \, {\left(b^{2} c + 2 \, a b d\right)} n^{2} + 4 \, {\left(b^{2} c + 2 \, a b d\right)} n\right)} x x^{2 \, n} + {\left(2 \, a b c + a^{2} d + 6 \, {\left(2 \, a b c + a^{2} d\right)} n^{2} + 5 \, {\left(2 \, a b c + a^{2} d\right)} n\right)} x x^{n} + {\left(6 \, a^{2} c n^{3} + 11 \, a^{2} c n^{2} + 6 \, a^{2} c n + a^{2} c\right)} x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"((2*b^2*d*n^2 + 3*b^2*d*n + b^2*d)*x*x^(3*n) + (b^2*c + 2*a*b*d + 3*(b^2*c + 2*a*b*d)*n^2 + 4*(b^2*c + 2*a*b*d)*n)*x*x^(2*n) + (2*a*b*c + a^2*d + 6*(2*a*b*c + a^2*d)*n^2 + 5*(2*a*b*c + a^2*d)*n)*x*x^n + (6*a^2*c*n^3 + 11*a^2*c*n^2 + 6*a^2*c*n + a^2*c)*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
295,0,0,0,0.521504," ","integrate((a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}{d x^{n} + c}, x\right)"," ",0,"integral((b^2*x^(2*n) + 2*a*b*x^n + a^2)/(d*x^n + c), x)","F",0
296,0,0,0,0.806036," ","integrate((a+b*x^n)^2/(c+d*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}{d^{2} x^{2 \, n} + 2 \, c d x^{n} + c^{2}}, x\right)"," ",0,"integral((b^2*x^(2*n) + 2*a*b*x^n + a^2)/(d^2*x^(2*n) + 2*c*d*x^n + c^2), x)","F",0
297,0,0,0,0.730575," ","integrate((a+b*x^n)^2/(c+d*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}{d^{3} x^{3 \, n} + 3 \, c d^{2} x^{2 \, n} + 3 \, c^{2} d x^{n} + c^{3}}, x\right)"," ",0,"integral((b^2*x^(2*n) + 2*a*b*x^n + a^2)/(d^3*x^(3*n) + 3*c*d^2*x^(2*n) + 3*c^2*d*x^n + c^3), x)","F",0
298,0,0,0,0.911522," ","integrate((c+d*x^n)^4/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{4} x^{4 \, n} + 4 \, c d^{3} x^{3 \, n} + 6 \, c^{2} d^{2} x^{2 \, n} + 4 \, c^{3} d x^{n} + c^{4}}{b x^{n} + a}, x\right)"," ",0,"integral((d^4*x^(4*n) + 4*c*d^3*x^(3*n) + 6*c^2*d^2*x^(2*n) + 4*c^3*d*x^n + c^4)/(b*x^n + a), x)","F",0
299,0,0,0,0.875149," ","integrate((c+d*x^n)^3/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{3} x^{3 \, n} + 3 \, c d^{2} x^{2 \, n} + 3 \, c^{2} d x^{n} + c^{3}}{b x^{n} + a}, x\right)"," ",0,"integral((d^3*x^(3*n) + 3*c*d^2*x^(2*n) + 3*c^2*d*x^n + c^3)/(b*x^n + a), x)","F",0
300,0,0,0,0.893255," ","integrate((c+d*x^n)^2/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{2} x^{2 \, n} + 2 \, c d x^{n} + c^{2}}{b x^{n} + a}, x\right)"," ",0,"integral((d^2*x^(2*n) + 2*c*d*x^n + c^2)/(b*x^n + a), x)","F",0
301,0,0,0,0.778488," ","integrate((c+d*x^n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d x^{n} + c}{b x^{n} + a}, x\right)"," ",0,"integral((d*x^n + c)/(b*x^n + a), x)","F",0
302,0,0,0,0.831804," ","integrate(1/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b d x^{2 \, n} + a c + {\left(b c + a d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b*d*x^(2*n) + a*c + (b*c + a*d)*x^n), x)","F",0
303,0,0,0,0.891181," ","integrate(1/(a+b*x^n)/(c+d*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b d^{2} x^{3 \, n} + a c^{2} + {\left(2 \, b c d + a d^{2}\right)} x^{2 \, n} + {\left(b c^{2} + 2 \, a c d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b*d^2*x^(3*n) + a*c^2 + (2*b*c*d + a*d^2)*x^(2*n) + (b*c^2 + 2*a*c*d)*x^n), x)","F",0
304,0,0,0,0.657612," ","integrate(1/(a+b*x^n)/(c+d*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b d^{3} x^{4 \, n} + a c^{3} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{3 \, n} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} x^{2 \, n} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b*d^3*x^(4*n) + a*c^3 + (3*b*c*d^2 + a*d^3)*x^(3*n) + 3*(b*c^2*d + a*c*d^2)*x^(2*n) + (b*c^3 + 3*a*c^2*d)*x^n), x)","F",0
305,0,0,0,0.824455," ","integrate((c+d*x^n)^4/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{4} x^{4 \, n} + 4 \, c d^{3} x^{3 \, n} + 6 \, c^{2} d^{2} x^{2 \, n} + 4 \, c^{3} d x^{n} + c^{4}}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral((d^4*x^(4*n) + 4*c*d^3*x^(3*n) + 6*c^2*d^2*x^(2*n) + 4*c^3*d*x^n + c^4)/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
306,0,0,0,0.832555," ","integrate((c+d*x^n)^3/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{3} x^{3 \, n} + 3 \, c d^{2} x^{2 \, n} + 3 \, c^{2} d x^{n} + c^{3}}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral((d^3*x^(3*n) + 3*c*d^2*x^(2*n) + 3*c^2*d*x^n + c^3)/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
307,0,0,0,0.936637," ","integrate((c+d*x^n)^2/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{2} x^{2 \, n} + 2 \, c d x^{n} + c^{2}}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral((d^2*x^(2*n) + 2*c*d*x^n + c^2)/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
308,0,0,0,0.601151," ","integrate((c+d*x^n)/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{d x^{n} + c}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral((d*x^n + c)/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
309,0,0,0,0.676222," ","integrate(1/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} d x^{3 \, n} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} x^{2 \, n} + {\left(2 \, a b c + a^{2} d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^2*d*x^(3*n) + a^2*c + (b^2*c + 2*a*b*d)*x^(2*n) + (2*a*b*c + a^2*d)*x^n), x)","F",0
310,0,0,0,0.960538," ","integrate(1/(a+b*x^n)^2/(c+d*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} d^{2} x^{4 \, n} + a^{2} c^{2} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x^{3 \, n} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2 \, n} + 2 \, {\left(a b c^{2} + a^{2} c d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^2*d^2*x^(4*n) + a^2*c^2 + 2*(b^2*c*d + a*b*d^2)*x^(3*n) + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(2*n) + 2*(a*b*c^2 + a^2*c*d)*x^n), x)","F",0
311,0,0,0,0.998802," ","integrate(1/(a+b*x^n)^2/(c+d*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} d^{3} x^{5 \, n} + a^{2} c^{3} + {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{4 \, n} + {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3 \, n} + {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{2 \, n} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^2*d^3*x^(5*n) + a^2*c^3 + (3*b^2*c*d^2 + 2*a*b*d^3)*x^(4*n) + (3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(3*n) + (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(2*n) + (2*a*b*c^3 + 3*a^2*c^2*d)*x^n), x)","F",0
312,0,0,0,0.538023," ","integrate((a+b*x^n)^p*(c+d*x^n)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^n + a)^p*(d*x^n + c)^q, x)","F",0
313,0,0,0,0.796789," ","integrate((a+b*x^n)^p*(c+d*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{3} x^{3 \, n} + 3 \, c d^{2} x^{2 \, n} + 3 \, c^{2} d x^{n} + c^{3}\right)} {\left(b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((d^3*x^(3*n) + 3*c*d^2*x^(2*n) + 3*c^2*d*x^n + c^3)*(b*x^n + a)^p, x)","F",0
314,0,0,0,0.833810," ","integrate((a+b*x^n)^p*(c+d*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} x^{2 \, n} + 2 \, c d x^{n} + c^{2}\right)} {\left(b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((d^2*x^(2*n) + 2*c*d*x^n + c^2)*(b*x^n + a)^p, x)","F",0
315,0,0,0,0.843485," ","integrate((a+b*x^n)^p*(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x^{n} + c\right)} {\left(b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((d*x^n + c)*(b*x^n + a)^p, x)","F",0
316,0,0,0,0.829842," ","integrate((a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((b*x^n + a)^p, x)","F",0
317,0,0,0,0.865594," ","integrate((a+b*x^n)^p/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{d x^{n} + c}, x\right)"," ",0,"integral((b*x^n + a)^p/(d*x^n + c), x)","F",0
318,0,0,0,0.857012," ","integrate((a+b*x^n)^p/(c+d*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{d^{2} x^{2 \, n} + 2 \, c d x^{n} + c^{2}}, x\right)"," ",0,"integral((b*x^n + a)^p/(d^2*x^(2*n) + 2*c*d*x^n + c^2), x)","F",0
319,0,0,0,0.963524," ","integrate((a+b*x^n)^p/(c+d*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{d^{3} x^{3 \, n} + 3 \, c d^{2} x^{2 \, n} + 3 \, c^{2} d x^{n} + c^{3}}, x\right)"," ",0,"integral((b*x^n + a)^p/(d^3*x^(3*n) + 3*c*d^2*x^(2*n) + 3*c^2*d*x^n + c^3), x)","F",0
320,0,0,0,0.933833," ","integrate((a+b*x^n)^p*(c+d*x^n)^(-1-1/n-p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{{\left(d x^{n} + c\right)}^{\frac{n p + n + 1}{n}}}, x\right)"," ",0,"integral((b*x^n + a)^p/(d*x^n + c)^((n*p + n + 1)/n), x)","F",0
321,1,478,0,0.910319," ","integrate((a+b*x^n)^3*(c+d*x^n)^(-4-1/n),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{3} d^{4} n^{3} + b^{3} c^{3} d + {\left(2 \, b^{3} c^{3} d + 3 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3}\right)} n^{2} + 3 \, {\left(b^{3} c^{3} d + a b^{2} c^{2} d^{2}\right)} n\right)} x x^{4 \, n} + {\left(24 \, a^{3} c d^{3} n^{3} + b^{3} c^{4} + 3 \, a b^{2} c^{3} d + 2 \, {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d + 12 \, a^{2} b c^{2} d^{2} + 3 \, a^{3} c d^{3}\right)} n^{2} + 3 \, {\left(b^{3} c^{4} + 5 \, a b^{2} c^{3} d + 2 \, a^{2} b c^{2} d^{2}\right)} n\right)} x x^{3 \, n} + 3 \, {\left(12 \, a^{3} c^{2} d^{2} n^{3} + a b^{2} c^{4} + a^{2} b c^{3} d + {\left(3 \, a b^{2} c^{4} + 12 \, a^{2} b c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} n^{2} + {\left(4 \, a b^{2} c^{4} + 7 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2}\right)} n\right)} x x^{2 \, n} + {\left(24 \, a^{3} c^{3} d n^{3} + 3 \, a^{2} b c^{4} + a^{3} c^{3} d + 2 \, {\left(9 \, a^{2} b c^{4} + 13 \, a^{3} c^{3} d\right)} n^{2} + 3 \, {\left(5 \, a^{2} b c^{4} + 3 \, a^{3} c^{3} d\right)} n\right)} x x^{n} + {\left(6 \, a^{3} c^{4} n^{3} + 11 \, a^{3} c^{4} n^{2} + 6 \, a^{3} c^{4} n + a^{3} c^{4}\right)} x}{{\left(6 \, c^{4} n^{3} + 11 \, c^{4} n^{2} + 6 \, c^{4} n + c^{4}\right)} {\left(d x^{n} + c\right)}^{\frac{4 \, n + 1}{n}}}"," ",0,"((6*a^3*d^4*n^3 + b^3*c^3*d + (2*b^3*c^3*d + 3*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3)*n^2 + 3*(b^3*c^3*d + a*b^2*c^2*d^2)*n)*x*x^(4*n) + (24*a^3*c*d^3*n^3 + b^3*c^4 + 3*a*b^2*c^3*d + 2*(b^3*c^4 + 6*a*b^2*c^3*d + 12*a^2*b*c^2*d^2 + 3*a^3*c*d^3)*n^2 + 3*(b^3*c^4 + 5*a*b^2*c^3*d + 2*a^2*b*c^2*d^2)*n)*x*x^(3*n) + 3*(12*a^3*c^2*d^2*n^3 + a*b^2*c^4 + a^2*b*c^3*d + (3*a*b^2*c^4 + 12*a^2*b*c^3*d + 7*a^3*c^2*d^2)*n^2 + (4*a*b^2*c^4 + 7*a^2*b*c^3*d + a^3*c^2*d^2)*n)*x*x^(2*n) + (24*a^3*c^3*d*n^3 + 3*a^2*b*c^4 + a^3*c^3*d + 2*(9*a^2*b*c^4 + 13*a^3*c^3*d)*n^2 + 3*(5*a^2*b*c^4 + 3*a^3*c^3*d)*n)*x*x^n + (6*a^3*c^4*n^3 + 11*a^3*c^4*n^2 + 6*a^3*c^4*n + a^3*c^4)*x)/((6*c^4*n^3 + 11*c^4*n^2 + 6*c^4*n + c^4)*(d*x^n + c)^((4*n + 1)/n))","B",0
322,1,231,0,0.635423," ","integrate((a+b*x^n)^2*(c+d*x^n)^(-3-1/n),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} d^{3} n^{2} + b^{2} c^{2} d + {\left(b^{2} c^{2} d + 2 \, a b c d^{2}\right)} n\right)} x x^{3 \, n} + {\left(6 \, a^{2} c d^{2} n^{2} + b^{2} c^{3} + 2 \, a b c^{2} d + {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 2 \, a^{2} c d^{2}\right)} n\right)} x x^{2 \, n} + {\left(6 \, a^{2} c^{2} d n^{2} + 2 \, a b c^{3} + a^{2} c^{2} d + {\left(4 \, a b c^{3} + 5 \, a^{2} c^{2} d\right)} n\right)} x x^{n} + {\left(2 \, a^{2} c^{3} n^{2} + 3 \, a^{2} c^{3} n + a^{2} c^{3}\right)} x}{{\left(2 \, c^{3} n^{2} + 3 \, c^{3} n + c^{3}\right)} {\left(d x^{n} + c\right)}^{\frac{3 \, n + 1}{n}}}"," ",0,"((2*a^2*d^3*n^2 + b^2*c^2*d + (b^2*c^2*d + 2*a*b*c*d^2)*n)*x*x^(3*n) + (6*a^2*c*d^2*n^2 + b^2*c^3 + 2*a*b*c^2*d + (b^2*c^3 + 6*a*b*c^2*d + 2*a^2*c*d^2)*n)*x*x^(2*n) + (6*a^2*c^2*d*n^2 + 2*a*b*c^3 + a^2*c^2*d + (4*a*b*c^3 + 5*a^2*c^2*d)*n)*x*x^n + (2*a^2*c^3*n^2 + 3*a^2*c^3*n + a^2*c^3)*x)/((2*c^3*n^2 + 3*c^3*n + c^3)*(d*x^n + c)^((3*n + 1)/n))","A",0
323,1,85,0,0.912890," ","integrate((a+b*x^n)*(c+d*x^n)^(-2-1/n),x, algorithm=""fricas"")","\frac{{\left(a d^{2} n + b c d\right)} x x^{2 \, n} + {\left(2 \, a c d n + b c^{2} + a c d\right)} x x^{n} + {\left(a c^{2} n + a c^{2}\right)} x}{{\left(c^{2} n + c^{2}\right)} {\left(d x^{n} + c\right)}^{\frac{2 \, n + 1}{n}}}"," ",0,"((a*d^2*n + b*c*d)*x*x^(2*n) + (2*a*c*d*n + b*c^2 + a*c*d)*x*x^n + (a*c^2*n + a*c^2)*x)/((c^2*n + c^2)*(d*x^n + c)^((2*n + 1)/n))","A",0
324,1,31,0,0.725192," ","integrate((c+d*x^n)^(-1-1/n),x, algorithm=""fricas"")","\frac{d x x^{n} + c x}{{\left(d x^{n} + c\right)}^{\frac{n + 1}{n}} c}"," ",0,"(d*x*x^n + c*x)/((d*x^n + c)^((n + 1)/n)*c)","A",0
325,0,0,0,0.946284," ","integrate(1/(a+b*x^n)/((c+d*x^n)^(1/n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{\left(\frac{1}{n}\right)}}, x\right)"," ",0,"integral(1/((b*x^n + a)*(d*x^n + c)^(1/n)), x)","F",0
326,0,0,0,0.795497," ","integrate((c+d*x^n)^(1-1/n)/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{n} + c\right)}^{\frac{n - 1}{n}}}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral((d*x^n + c)^((n - 1)/n)/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
327,0,0,0,0.963257," ","integrate((c+d*x^n)^(2-1/n)/(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{n} + c\right)}^{\frac{2 \, n - 1}{n}}}{b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} + 3 \, a^{2} b x^{n} + a^{3}}, x\right)"," ",0,"integral((d*x^n + c)^((2*n - 1)/n)/(b^3*x^(3*n) + 3*a*b^2*x^(2*n) + 3*a^2*b*x^n + a^3), x)","F",0
328,0,0,0,0.878804," ","integrate((a+b*x^n)^p*(c+d*x^n)^(-2-1/n-p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{{\left(d x^{n} + c\right)}^{\frac{n p + 2 \, n + 1}{n}}}, x\right)"," ",0,"integral((b*x^n + a)^p/(d*x^n + c)^((n*p + 2*n + 1)/n), x)","F",0
329,1,108,0,0.851954," ","integrate((a+b*x^n)^((a*d*n-b*c*(1+n))/(-a*d+b*c)/n)*(c+d*x^n)^((a*d*n-b*c*n+a*d)/(-a*d*n+b*c*n)),x, algorithm=""fricas"")","\frac{{\left(b d x x^{2 \, n} + a c x + {\left(b c + a d\right)} x x^{n}\right)} {\left(d x^{n} + c\right)}^{\frac{a d - {\left(b c - a d\right)} n}{{\left(b c - a d\right)} n}}}{{\left(b x^{n} + a\right)}^{\frac{b c + {\left(b c - a d\right)} n}{{\left(b c - a d\right)} n}} a c}"," ",0,"(b*d*x*x^(2*n) + a*c*x + (b*c + a*d)*x*x^n)*(d*x^n + c)^((a*d - (b*c - a*d)*n)/((b*c - a*d)*n))/((b*x^n + a)^((b*c + (b*c - a*d)*n)/((b*c - a*d)*n))*a*c)","A",0
330,1,400,0,0.873675," ","integrate((a+b*x^n)^2*(c+d*x^n)^(-4-1/n),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{2} d^{4} n^{3} + b^{2} c^{2} d^{2} n + {\left(b^{2} c^{2} d^{2} + 4 \, a b c d^{3}\right)} n^{2}\right)} x x^{4 \, n} + {\left(24 \, a^{2} c d^{3} n^{3} + b^{2} c^{3} d + 2 \, {\left(2 \, b^{2} c^{3} d + 8 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} n^{2} + {\left(5 \, b^{2} c^{3} d + 4 \, a b c^{2} d^{2}\right)} n\right)} x x^{3 \, n} + {\left(36 \, a^{2} c^{2} d^{2} n^{3} + b^{2} c^{4} + 2 \, a b c^{3} d + 3 \, {\left(b^{2} c^{4} + 8 \, a b c^{3} d + 7 \, a^{2} c^{2} d^{2}\right)} n^{2} + {\left(4 \, b^{2} c^{4} + 14 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2}\right)} n\right)} x x^{2 \, n} + {\left(24 \, a^{2} c^{3} d n^{3} + 2 \, a b c^{4} + a^{2} c^{3} d + 2 \, {\left(6 \, a b c^{4} + 13 \, a^{2} c^{3} d\right)} n^{2} + {\left(10 \, a b c^{4} + 9 \, a^{2} c^{3} d\right)} n\right)} x x^{n} + {\left(6 \, a^{2} c^{4} n^{3} + 11 \, a^{2} c^{4} n^{2} + 6 \, a^{2} c^{4} n + a^{2} c^{4}\right)} x}{{\left(6 \, c^{4} n^{3} + 11 \, c^{4} n^{2} + 6 \, c^{4} n + c^{4}\right)} {\left(d x^{n} + c\right)}^{\frac{4 \, n + 1}{n}}}"," ",0,"((6*a^2*d^4*n^3 + b^2*c^2*d^2*n + (b^2*c^2*d^2 + 4*a*b*c*d^3)*n^2)*x*x^(4*n) + (24*a^2*c*d^3*n^3 + b^2*c^3*d + 2*(2*b^2*c^3*d + 8*a*b*c^2*d^2 + 3*a^2*c*d^3)*n^2 + (5*b^2*c^3*d + 4*a*b*c^2*d^2)*n)*x*x^(3*n) + (36*a^2*c^2*d^2*n^3 + b^2*c^4 + 2*a*b*c^3*d + 3*(b^2*c^4 + 8*a*b*c^3*d + 7*a^2*c^2*d^2)*n^2 + (4*b^2*c^4 + 14*a*b*c^3*d + 3*a^2*c^2*d^2)*n)*x*x^(2*n) + (24*a^2*c^3*d*n^3 + 2*a*b*c^4 + a^2*c^3*d + 2*(6*a*b*c^4 + 13*a^2*c^3*d)*n^2 + (10*a*b*c^4 + 9*a^2*c^3*d)*n)*x*x^n + (6*a^2*c^4*n^3 + 11*a^2*c^4*n^2 + 6*a^2*c^4*n + a^2*c^4)*x)/((6*c^4*n^3 + 11*c^4*n^2 + 6*c^4*n + c^4)*(d*x^n + c)^((4*n + 1)/n))","A",0
331,1,173,0,0.851218," ","integrate((a+b*x^n)*(c+d*x^n)^(-3-1/n),x, algorithm=""fricas"")","\frac{{\left(2 \, a d^{3} n^{2} + b c d^{2} n\right)} x x^{3 \, n} + {\left(6 \, a c d^{2} n^{2} + b c^{2} d + {\left(3 \, b c^{2} d + 2 \, a c d^{2}\right)} n\right)} x x^{2 \, n} + {\left(6 \, a c^{2} d n^{2} + b c^{3} + a c^{2} d + {\left(2 \, b c^{3} + 5 \, a c^{2} d\right)} n\right)} x x^{n} + {\left(2 \, a c^{3} n^{2} + 3 \, a c^{3} n + a c^{3}\right)} x}{{\left(2 \, c^{3} n^{2} + 3 \, c^{3} n + c^{3}\right)} {\left(d x^{n} + c\right)}^{\frac{3 \, n + 1}{n}}}"," ",0,"((2*a*d^3*n^2 + b*c*d^2*n)*x*x^(3*n) + (6*a*c*d^2*n^2 + b*c^2*d + (3*b*c^2*d + 2*a*c*d^2)*n)*x*x^(2*n) + (6*a*c^2*d*n^2 + b*c^3 + a*c^2*d + (2*b*c^3 + 5*a*c^2*d)*n)*x*x^n + (2*a*c^3*n^2 + 3*a*c^3*n + a*c^3)*x)/((2*c^3*n^2 + 3*c^3*n + c^3)*(d*x^n + c)^((3*n + 1)/n))","A",0
332,1,68,0,0.903403," ","integrate((c+d*x^n)^(-2-1/n),x, algorithm=""fricas"")","\frac{d^{2} n x x^{2 \, n} + {\left(2 \, c d n + c d\right)} x x^{n} + {\left(c^{2} n + c^{2}\right)} x}{{\left(c^{2} n + c^{2}\right)} {\left(d x^{n} + c\right)}^{\frac{2 \, n + 1}{n}}}"," ",0,"(d^2*n*x*x^(2*n) + (2*c*d*n + c*d)*x*x^n + (c^2*n + c^2)*x)/((c^2*n + c^2)*(d*x^n + c)^((2*n + 1)/n))","A",0
333,0,0,0,0.855603," ","integrate((c+d*x^n)^(-1-1/n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{\frac{n + 1}{n}}}, x\right)"," ",0,"integral(1/((b*x^n + a)*(d*x^n + c)^((n + 1)/n)), x)","F",0
334,0,0,0,0.832145," ","integrate(1/(a+b*x^n)^2/((c+d*x^n)^(1/n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)} {\left(d x^{n} + c\right)}^{\left(\frac{1}{n}\right)}}, x\right)"," ",0,"integral(1/((b^2*x^(2*n) + 2*a*b*x^n + a^2)*(d*x^n + c)^(1/n)), x)","F",0
335,0,0,0,0.749801," ","integrate((c+d*x^n)^(1-1/n)/(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{n} + c\right)}^{\frac{n - 1}{n}}}{b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} + 3 \, a^{2} b x^{n} + a^{3}}, x\right)"," ",0,"integral((d*x^n + c)^((n - 1)/n)/(b^3*x^(3*n) + 3*a*b^2*x^(2*n) + 3*a^2*b*x^n + a^3), x)","F",0
336,0,0,0,0.928016," ","integrate((c+d*x^n)^(2-1/n)/(a+b*x^n)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{n} + c\right)}^{\frac{2 \, n - 1}{n}}}{b^{4} x^{4 \, n} + 4 \, a b^{3} x^{3 \, n} + 6 \, a^{2} b^{2} x^{2 \, n} + 4 \, a^{3} b x^{n} + a^{4}}, x\right)"," ",0,"integral((d*x^n + c)^((2*n - 1)/n)/(b^4*x^(4*n) + 4*a*b^3*x^(3*n) + 6*a^2*b^2*x^(2*n) + 4*a^3*b*x^n + a^4), x)","F",0
337,1,114,0,0.957199," ","integrate(x^5*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(35 \, b d^{8} x^{8} - 16 \, b c^{8} - 24 \, a c^{6} d^{2} - 5 \, {\left(b c^{2} d^{6} - 9 \, a d^{8}\right)} x^{6} - 3 \, {\left(2 \, b c^{4} d^{4} + 3 \, a c^{2} d^{6}\right)} x^{4} - 4 \, {\left(2 \, b c^{6} d^{2} + 3 \, a c^{4} d^{4}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{315 \, d^{8}}"," ",0,"1/315*(35*b*d^8*x^8 - 16*b*c^8 - 24*a*c^6*d^2 - 5*(b*c^2*d^6 - 9*a*d^8)*x^6 - 3*(2*b*c^4*d^4 + 3*a*c^2*d^6)*x^4 - 4*(2*b*c^6*d^2 + 3*a*c^4*d^4)*x^2)*sqrt(d*x + c)*sqrt(d*x - c)/d^8","A",0
338,1,90,0,0.822907," ","integrate(x^3*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, b d^{6} x^{6} - 8 \, b c^{6} - 14 \, a c^{4} d^{2} - 3 \, {\left(b c^{2} d^{4} - 7 \, a d^{6}\right)} x^{4} - {\left(4 \, b c^{4} d^{2} + 7 \, a c^{2} d^{4}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{105 \, d^{6}}"," ",0,"1/105*(15*b*d^6*x^6 - 8*b*c^6 - 14*a*c^4*d^2 - 3*(b*c^2*d^4 - 7*a*d^6)*x^4 - (4*b*c^4*d^2 + 7*a*c^2*d^4)*x^2)*sqrt(d*x + c)*sqrt(d*x - c)/d^6","A",0
339,1,66,0,0.633683," ","integrate(x*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b d^{4} x^{4} - 2 \, b c^{4} - 5 \, a c^{2} d^{2} - {\left(b c^{2} d^{2} - 5 \, a d^{4}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{15 \, d^{4}}"," ",0,"1/15*(3*b*d^4*x^4 - 2*b*c^4 - 5*a*c^2*d^2 - (b*c^2*d^2 - 5*a*d^4)*x^2)*sqrt(d*x + c)*sqrt(d*x - c)/d^4","A",0
340,1,80,0,0.703577," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","-\frac{6 \, a c d^{2} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right) - {\left(b d^{2} x^{2} - b c^{2} + 3 \, a d^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{3 \, d^{2}}"," ",0,"-1/3*(6*a*c*d^2*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c) - (b*d^2*x^2 - b*c^2 + 3*a*d^2)*sqrt(d*x + c)*sqrt(d*x - c))/d^2","A",0
341,1,85,0,0.909881," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b c^{2} - a d^{2}\right)} x^{2} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right) - {\left(2 \, b c x^{2} - a c\right)} \sqrt{d x + c} \sqrt{d x - c}}{2 \, c x^{2}}"," ",0,"-1/2*(2*(2*b*c^2 - a*d^2)*x^2*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c) - (2*b*c*x^2 - a*c)*sqrt(d*x + c)*sqrt(d*x - c))/(c*x^2)","A",0
342,1,100,0,0.803192," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, b c^{2} d^{2} + a d^{4}\right)} x^{4} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right) - {\left(2 \, a c^{3} + {\left(4 \, b c^{3} - a c d^{2}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{8 \, c^{3} x^{4}}"," ",0,"1/8*(2*(4*b*c^2*d^2 + a*d^4)*x^4*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c) - (2*a*c^3 + (4*b*c^3 - a*c*d^2)*x^2)*sqrt(d*x + c)*sqrt(d*x - c))/(c^3*x^4)","A",0
343,1,138,0,1.415834," ","integrate(x^4*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(48 \, b d^{7} x^{7} - 8 \, {\left(b c^{2} d^{5} - 8 \, a d^{7}\right)} x^{5} - 2 \, {\left(5 \, b c^{4} d^{3} + 8 \, a c^{2} d^{5}\right)} x^{3} - 3 \, {\left(5 \, b c^{6} d + 8 \, a c^{4} d^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{d x - c} + 3 \, {\left(5 \, b c^{8} + 8 \, a c^{6} d^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{384 \, d^{7}}"," ",0,"1/384*((48*b*d^7*x^7 - 8*(b*c^2*d^5 - 8*a*d^7)*x^5 - 2*(5*b*c^4*d^3 + 8*a*c^2*d^5)*x^3 - 3*(5*b*c^6*d + 8*a*c^4*d^3)*x)*sqrt(d*x + c)*sqrt(d*x - c) + 3*(5*b*c^8 + 8*a*c^6*d^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/d^7","A",0
344,1,112,0,0.818236," ","integrate(x^2*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, b d^{5} x^{5} - 2 \, {\left(b c^{2} d^{3} - 6 \, a d^{5}\right)} x^{3} - 3 \, {\left(b c^{4} d + 2 \, a c^{2} d^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{d x - c} + 3 \, {\left(b c^{6} + 2 \, a c^{4} d^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{48 \, d^{5}}"," ",0,"1/48*((8*b*d^5*x^5 - 2*(b*c^2*d^3 - 6*a*d^5)*x^3 - 3*(b*c^4*d + 2*a*c^2*d^3)*x)*sqrt(d*x + c)*sqrt(d*x - c) + 3*(b*c^6 + 2*a*c^4*d^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/d^5","A",0
345,1,88,0,0.870699," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b d^{3} x^{3} - {\left(b c^{2} d - 4 \, a d^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{d x - c} + {\left(b c^{4} + 4 \, a c^{2} d^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{8 \, d^{3}}"," ",0,"1/8*((2*b*d^3*x^3 - (b*c^2*d - 4*a*d^3)*x)*sqrt(d*x + c)*sqrt(d*x - c) + (b*c^4 + 4*a*c^2*d^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/d^3","A",0
346,1,83,0,0.740462," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a d^{2} x - {\left(b c^{2} - 2 \, a d^{2}\right)} x \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right) - {\left(b d x^{2} - 2 \, a d\right)} \sqrt{d x + c} \sqrt{d x - c}}{2 \, d x}"," ",0,"-1/2*(2*a*d^2*x - (b*c^2 - 2*a*d^2)*x*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)) - (b*d*x^2 - 2*a*d)*sqrt(d*x + c)*sqrt(d*x - c))/(d*x)","A",0
347,1,100,0,0.794833," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{3 \, b c^{2} d x^{3} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right) + {\left(3 \, b c^{2} d - a d^{3}\right)} x^{3} + {\left(a c^{2} + {\left(3 \, b c^{2} - a d^{2}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{3 \, c^{2} x^{3}}"," ",0,"-1/3*(3*b*c^2*d*x^3*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)) + (3*b*c^2*d - a*d^3)*x^3 + (a*c^2 + (3*b*c^2 - a*d^2)*x^2)*sqrt(d*x + c)*sqrt(d*x - c))/(c^2*x^3)","A",0
348,1,96,0,0.884369," ","integrate(x^4*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, b c^{5} x^{5} + 2 \, {\left(6 \, a c^{5} + 5 \, b c^{3}\right)} x^{3} + 3 \, {\left(6 \, a c^{3} + 5 \, b c\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 3 \, {\left(6 \, a c^{2} + 5 \, b\right)} \log\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{48 \, c^{7}}"," ",0,"1/48*((8*b*c^5*x^5 + 2*(6*a*c^5 + 5*b*c^3)*x^3 + 3*(6*a*c^3 + 5*b*c)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - 3*(6*a*c^2 + 5*b)*log(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/c^7","A",0
349,1,55,0,1.046083," ","integrate(x^3*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b c^{4} x^{4} + 10 \, a c^{2} + {\left(5 \, a c^{4} + 4 \, b c^{2}\right)} x^{2} + 8 \, b\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{15 \, c^{6}}"," ",0,"1/15*(3*b*c^4*x^4 + 10*a*c^2 + (5*a*c^4 + 4*b*c^2)*x^2 + 8*b)*sqrt(c*x + 1)*sqrt(c*x - 1)/c^6","A",0
350,1,77,0,0.825880," ","integrate(x^2*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b c^{3} x^{3} + {\left(4 \, a c^{3} + 3 \, b c\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - {\left(4 \, a c^{2} + 3 \, b\right)} \log\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{8 \, c^{5}}"," ",0,"1/8*((2*b*c^3*x^3 + (4*a*c^3 + 3*b*c)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - (4*a*c^2 + 3*b)*log(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/c^5","A",0
351,1,37,0,0.775583," ","integrate(x*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(b c^{2} x^{2} + 3 \, a c^{2} + 2 \, b\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{3 \, c^{4}}"," ",0,"1/3*(b*c^2*x^2 + 3*a*c^2 + 2*b)*sqrt(c*x + 1)*sqrt(c*x - 1)/c^4","A",0
352,1,55,0,0.875220," ","integrate((b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x + 1} \sqrt{c x - 1} b c x - {\left(2 \, a c^{2} + b\right)} \log\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{2 \, c^{3}}"," ",0,"1/2*(sqrt(c*x + 1)*sqrt(c*x - 1)*b*c*x - (2*a*c^2 + b)*log(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/c^3","A",0
353,1,48,0,0.830376," ","integrate((b*x^2+a)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a c^{2} \arctan\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \sqrt{c x + 1} \sqrt{c x - 1} b}{c^{2}}"," ",0,"(2*a*c^2*arctan(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + sqrt(c*x + 1)*sqrt(c*x - 1)*b)/c^2","A",0
354,1,56,0,0.869467," ","integrate((b*x^2+a)/x^2/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{a c^{2} x + \sqrt{c x + 1} \sqrt{c x - 1} a c - b x \log\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c x}"," ",0,"(a*c^2*x + sqrt(c*x + 1)*sqrt(c*x - 1)*a*c - b*x*log(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c*x)","A",0
355,1,57,0,0.838755," ","integrate((b*x^2+a)/x^3/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a c^{2} + 2 \, b\right)} x^{2} \arctan\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \sqrt{c x + 1} \sqrt{c x - 1} a}{2 \, x^{2}}"," ",0,"1/2*(2*(a*c^2 + 2*b)*x^2*arctan(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + sqrt(c*x + 1)*sqrt(c*x - 1)*a)/x^2","A",0
356,1,52,0,0.849493," ","integrate((b*x^2+a)/x^4/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a c^{3} + 3 \, b c\right)} x^{3} + {\left({\left(2 \, a c^{2} + 3 \, b\right)} x^{2} + a\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{3 \, x^{3}}"," ",0,"1/3*((2*a*c^3 + 3*b*c)*x^3 + ((2*a*c^2 + 3*b)*x^2 + a)*sqrt(c*x + 1)*sqrt(c*x - 1))/x^3","A",0
357,1,78,0,0.591394," ","integrate((b*x^2+a)/x^5/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a c^{4} + 4 \, b c^{2}\right)} x^{4} \arctan\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(3 \, a c^{2} + 4 \, b\right)} x^{2} + 2 \, a\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{8 \, x^{4}}"," ",0,"1/8*(2*(3*a*c^4 + 4*b*c^2)*x^4*arctan(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((3*a*c^2 + 4*b)*x^2 + 2*a)*sqrt(c*x + 1)*sqrt(c*x - 1))/x^4","A",0
358,1,115,0,0.777897," ","integrate(x^4*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, b d^{5} x^{5} + 2 \, {\left(5 \, b c^{2} d^{3} + 6 \, a d^{5}\right)} x^{3} + 3 \, {\left(5 \, b c^{4} d + 6 \, a c^{2} d^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{d x - c} - 3 \, {\left(5 \, b c^{6} + 6 \, a c^{4} d^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{48 \, d^{7}}"," ",0,"1/48*((8*b*d^5*x^5 + 2*(5*b*c^2*d^3 + 6*a*d^5)*x^3 + 3*(5*b*c^4*d + 6*a*c^2*d^3)*x)*sqrt(d*x + c)*sqrt(d*x - c) - 3*(5*b*c^6 + 6*a*c^4*d^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/d^7","A",0
359,1,66,0,0.781829," ","integrate(x^3*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b d^{4} x^{4} + 8 \, b c^{4} + 10 \, a c^{2} d^{2} + {\left(4 \, b c^{2} d^{2} + 5 \, a d^{4}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{15 \, d^{6}}"," ",0,"1/15*(3*b*d^4*x^4 + 8*b*c^4 + 10*a*c^2*d^2 + (4*b*c^2*d^2 + 5*a*d^4)*x^2)*sqrt(d*x + c)*sqrt(d*x - c)/d^6","A",0
360,1,90,0,1.204964," ","integrate(x^2*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b d^{3} x^{3} + {\left(3 \, b c^{2} d + 4 \, a d^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{d x - c} - {\left(3 \, b c^{4} + 4 \, a c^{2} d^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{8 \, d^{5}}"," ",0,"1/8*((2*b*d^3*x^3 + (3*b*c^2*d + 4*a*d^3)*x)*sqrt(d*x + c)*sqrt(d*x - c) - (3*b*c^4 + 4*a*c^2*d^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/d^5","A",0
361,1,42,0,0.763878," ","integrate(x*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(b d^{2} x^{2} + 2 \, b c^{2} + 3 \, a d^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{3 \, d^{4}}"," ",0,"1/3*(b*d^2*x^2 + 2*b*c^2 + 3*a*d^2)*sqrt(d*x + c)*sqrt(d*x - c)/d^4","A",0
362,1,63,0,0.863341," ","integrate((b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{d x + c} \sqrt{d x - c} b d x - {\left(b c^{2} + 2 \, a d^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{2 \, d^{3}}"," ",0,"1/2*(sqrt(d*x + c)*sqrt(d*x - c)*b*d*x - (b*c^2 + 2*a*d^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/d^3","A",0
363,1,61,0,0.846560," ","integrate((b*x^2+a)/x/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a d^{2} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right) + \sqrt{d x + c} \sqrt{d x - c} b c}{c d^{2}}"," ",0,"(2*a*d^2*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c) + sqrt(d*x + c)*sqrt(d*x - c)*b*c)/(c*d^2)","A",0
364,1,68,0,1.085011," ","integrate((b*x^2+a)/x^2/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{b c^{2} x \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right) - a d^{2} x - \sqrt{d x + c} \sqrt{d x - c} a d}{c^{2} d x}"," ",0,"-(b*c^2*x*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)) - a*d^2*x - sqrt(d*x + c)*sqrt(d*x - c)*a*d)/(c^2*d*x)","A",0
365,1,73,0,0.812844," ","integrate((b*x^2+a)/x^3/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b c^{2} + a d^{2}\right)} x^{2} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right) + \sqrt{d x + c} \sqrt{d x - c} a c}{2 \, c^{3} x^{2}}"," ",0,"1/2*(2*(2*b*c^2 + a*d^2)*x^2*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c) + sqrt(d*x + c)*sqrt(d*x - c)*a*c)/(c^3*x^2)","A",0
366,1,67,0,0.744465," ","integrate((b*x^2+a)/x^4/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b c^{2} d + 2 \, a d^{3}\right)} x^{3} + {\left(a c^{2} + {\left(3 \, b c^{2} + 2 \, a d^{2}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{3 \, c^{4} x^{3}}"," ",0,"1/3*((3*b*c^2*d + 2*a*d^3)*x^3 + (a*c^2 + (3*b*c^2 + 2*a*d^2)*x^2)*sqrt(d*x + c)*sqrt(d*x - c))/(c^4*x^3)","A",0
367,1,100,0,0.857338," ","integrate((b*x^2+a)/x^5/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, b c^{2} d^{2} + 3 \, a d^{4}\right)} x^{4} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right) + {\left(2 \, a c^{3} + {\left(4 \, b c^{3} + 3 \, a c d^{2}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{8 \, c^{5} x^{4}}"," ",0,"1/8*(2*(4*b*c^2*d^2 + 3*a*d^4)*x^4*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c) + (2*a*c^3 + (4*b*c^3 + 3*a*c*d^2)*x^2)*sqrt(d*x + c)*sqrt(d*x - c))/(c^5*x^4)","A",0
368,1,190,0,0.862733," ","integrate(x^4*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{8 \, b c^{6} + 8 \, a c^{4} d^{2} - 8 \, {\left(b c^{4} d^{2} + a c^{2} d^{4}\right)} x^{2} + {\left(2 \, b d^{5} x^{5} + {\left(5 \, b c^{2} d^{3} + 4 \, a d^{5}\right)} x^{3} - 3 \, {\left(5 \, b c^{4} d + 4 \, a c^{2} d^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{d x - c} + 3 \, {\left(5 \, b c^{6} + 4 \, a c^{4} d^{2} - {\left(5 \, b c^{4} d^{2} + 4 \, a c^{2} d^{4}\right)} x^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{8 \, {\left(d^{9} x^{2} - c^{2} d^{7}\right)}}"," ",0,"1/8*(8*b*c^6 + 8*a*c^4*d^2 - 8*(b*c^4*d^2 + a*c^2*d^4)*x^2 + (2*b*d^5*x^5 + (5*b*c^2*d^3 + 4*a*d^5)*x^3 - 3*(5*b*c^4*d + 4*a*c^2*d^3)*x)*sqrt(d*x + c)*sqrt(d*x - c) + 3*(5*b*c^6 + 4*a*c^4*d^2 - (5*b*c^4*d^2 + 4*a*c^2*d^4)*x^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/(d^9*x^2 - c^2*d^7)","A",0
369,1,80,0,0.663167," ","integrate(x^3*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b d^{4} x^{4} - 8 \, b c^{4} - 6 \, a c^{2} d^{2} + {\left(4 \, b c^{2} d^{2} + 3 \, a d^{4}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{3 \, {\left(d^{8} x^{2} - c^{2} d^{6}\right)}}"," ",0,"1/3*(b*d^4*x^4 - 8*b*c^4 - 6*a*c^2*d^2 + (4*b*c^2*d^2 + 3*a*d^4)*x^2)*sqrt(d*x + c)*sqrt(d*x - c)/(d^8*x^2 - c^2*d^6)","A",0
370,1,159,0,0.665955," ","integrate(x^2*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, b c^{4} + 2 \, a c^{2} d^{2} - 2 \, {\left(b c^{2} d^{2} + a d^{4}\right)} x^{2} + {\left(b d^{3} x^{3} - {\left(3 \, b c^{2} d + 2 \, a d^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{d x - c} + {\left(3 \, b c^{4} + 2 \, a c^{2} d^{2} - {\left(3 \, b c^{2} d^{2} + 2 \, a d^{4}\right)} x^{2}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{2 \, {\left(d^{7} x^{2} - c^{2} d^{5}\right)}}"," ",0,"1/2*(2*b*c^4 + 2*a*c^2*d^2 - 2*(b*c^2*d^2 + a*d^4)*x^2 + (b*d^3*x^3 - (3*b*c^2*d + 2*a*d^3)*x)*sqrt(d*x + c)*sqrt(d*x - c) + (3*b*c^4 + 2*a*c^2*d^2 - (3*b*c^2*d^2 + 2*a*d^4)*x^2)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/(d^7*x^2 - c^2*d^5)","A",0
371,1,56,0,0.770467," ","integrate(x*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b d^{2} x^{2} - 2 \, b c^{2} - a d^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{d^{6} x^{2} - c^{2} d^{4}}"," ",0,"(b*d^2*x^2 - 2*b*c^2 - a*d^2)*sqrt(d*x + c)*sqrt(d*x - c)/(d^6*x^2 - c^2*d^4)","A",0
372,1,129,0,0.837497," ","integrate((b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{b c^{4} + a c^{2} d^{2} - {\left(b c^{2} d + a d^{3}\right)} \sqrt{d x + c} \sqrt{d x - c} x - {\left(b c^{2} d^{2} + a d^{4}\right)} x^{2} - {\left(b c^{2} d^{2} x^{2} - b c^{4}\right)} \log\left(-d x + \sqrt{d x + c} \sqrt{d x - c}\right)}{c^{2} d^{5} x^{2} - c^{4} d^{3}}"," ",0,"(b*c^4 + a*c^2*d^2 - (b*c^2*d + a*d^3)*sqrt(d*x + c)*sqrt(d*x - c)*x - (b*c^2*d^2 + a*d^4)*x^2 - (b*c^2*d^2*x^2 - b*c^4)*log(-d*x + sqrt(d*x + c)*sqrt(d*x - c)))/(c^2*d^5*x^2 - c^4*d^3)","B",0
373,1,101,0,0.813219," ","integrate((b*x^2+a)/x/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(b c^{3} + a c d^{2}\right)} \sqrt{d x + c} \sqrt{d x - c} + 2 \, {\left(a d^{4} x^{2} - a c^{2} d^{2}\right)} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right)}{c^{3} d^{4} x^{2} - c^{5} d^{2}}"," ",0,"-((b*c^3 + a*c*d^2)*sqrt(d*x + c)*sqrt(d*x - c) + 2*(a*d^4*x^2 - a*c^2*d^2)*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c))/(c^3*d^4*x^2 - c^5*d^2)","A",0
374,1,103,0,0.780565," ","integrate((b*x^2+a)/x^2/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(b c^{2} d^{2} + 2 \, a d^{4}\right)} x^{3} - {\left(a c^{2} d - {\left(b c^{2} d + 2 \, a d^{3}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c} - {\left(b c^{4} + 2 \, a c^{2} d^{2}\right)} x}{c^{4} d^{3} x^{3} - c^{6} d x}"," ",0,"-((b*c^2*d^2 + 2*a*d^4)*x^3 - (a*c^2*d - (b*c^2*d + 2*a*d^3)*x^2)*sqrt(d*x + c)*sqrt(d*x - c) - (b*c^4 + 2*a*c^2*d^2)*x)/(c^4*d^3*x^3 - c^6*d*x)","A",0
375,1,138,0,0.716252," ","integrate((b*x^2+a)/x^3/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a c^{3} - {\left(2 \, b c^{3} + 3 \, a c d^{2}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c} - 2 \, {\left({\left(2 \, b c^{2} d^{2} + 3 \, a d^{4}\right)} x^{4} - {\left(2 \, b c^{4} + 3 \, a c^{2} d^{2}\right)} x^{2}\right)} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right)}{2 \, {\left(c^{5} d^{2} x^{4} - c^{7} x^{2}\right)}}"," ",0,"1/2*((a*c^3 - (2*b*c^3 + 3*a*c*d^2)*x^2)*sqrt(d*x + c)*sqrt(d*x - c) - 2*((2*b*c^2*d^2 + 3*a*d^4)*x^4 - (2*b*c^4 + 3*a*c^2*d^2)*x^2)*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c))/(c^5*d^2*x^4 - c^7*x^2)","A",0
376,1,132,0,0.803831," ","integrate((b*x^2+a)/x^4/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b c^{2} d^{3} + 4 \, a d^{5}\right)} x^{5} - 2 \, {\left(3 \, b c^{4} d + 4 \, a c^{2} d^{3}\right)} x^{3} - {\left(a c^{4} - 2 \, {\left(3 \, b c^{2} d^{2} + 4 \, a d^{4}\right)} x^{4} + {\left(3 \, b c^{4} + 4 \, a c^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c}}{3 \, {\left(c^{6} d^{2} x^{5} - c^{8} x^{3}\right)}}"," ",0,"-1/3*(2*(3*b*c^2*d^3 + 4*a*d^5)*x^5 - 2*(3*b*c^4*d + 4*a*c^2*d^3)*x^3 - (a*c^4 - 2*(3*b*c^2*d^2 + 4*a*d^4)*x^4 + (3*b*c^4 + 4*a*c^2*d^2)*x^2)*sqrt(d*x + c)*sqrt(d*x - c))/(c^6*d^2*x^5 - c^8*x^3)","A",0
377,1,165,0,0.884100," ","integrate((b*x^2+a)/x^5/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a c^{5} - 3 \, {\left(4 \, b c^{3} d^{2} + 5 \, a c d^{4}\right)} x^{4} + {\left(4 \, b c^{5} + 5 \, a c^{3} d^{2}\right)} x^{2}\right)} \sqrt{d x + c} \sqrt{d x - c} - 6 \, {\left({\left(4 \, b c^{2} d^{4} + 5 \, a d^{6}\right)} x^{6} - {\left(4 \, b c^{4} d^{2} + 5 \, a c^{2} d^{4}\right)} x^{4}\right)} \arctan\left(-\frac{d x - \sqrt{d x + c} \sqrt{d x - c}}{c}\right)}{8 \, {\left(c^{7} d^{2} x^{6} - c^{9} x^{4}\right)}}"," ",0,"1/8*((2*a*c^5 - 3*(4*b*c^3*d^2 + 5*a*c*d^4)*x^4 + (4*b*c^5 + 5*a*c^3*d^2)*x^2)*sqrt(d*x + c)*sqrt(d*x - c) - 6*((4*b*c^2*d^4 + 5*a*d^6)*x^6 - (4*b*c^4*d^2 + 5*a*c^2*d^4)*x^4)*arctan(-(d*x - sqrt(d*x + c)*sqrt(d*x - c))/c))/(c^7*d^2*x^6 - c^9*x^4)","A",0
378,1,39,0,0.885409," ","integrate((c^2*x^2+1)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","\sqrt{c x + 1} \sqrt{c x - 1} + 2 \, \arctan\left(-c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)"," ",0,"sqrt(c*x + 1)*sqrt(c*x - 1) + 2*arctan(-c*x + sqrt(c*x + 1)*sqrt(c*x - 1))","A",0
379,1,65,0,0.857649," ","integrate((d*x^2+c)/(x^((a^2*d+2*b^2*c)/(a^2*d+b^2*c)))/(b*x-a)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(b^{2} c + a^{2} d\right)} \sqrt{b x + a} \sqrt{b x - a} x}{a^{2} b^{2} x^{\frac{2 \, b^{2} c + a^{2} d}{b^{2} c + a^{2} d}}}"," ",0,"(b^2*c + a^2*d)*sqrt(b*x + a)*sqrt(b*x - a)*x/(a^2*b^2*x^((2*b^2*c + a^2*d)/(b^2*c + a^2*d)))","A",0
380,1,69,0,0.871195," ","integrate(1/(1+x)^(1/2)/(-1-x^(1/2))^(1/2)/(-1+x^(1/2))^(1/2),x, algorithm=""fricas"")","-i \, \log\left(\frac{\sqrt{x + 1} \sqrt{\sqrt{x} - 1} \sqrt{-\sqrt{x} - 1} + i \, x - 1}{x}\right) + i \, \log\left(\frac{\sqrt{x + 1} \sqrt{\sqrt{x} - 1} \sqrt{-\sqrt{x} - 1} - i \, x - 1}{x}\right)"," ",0,"-I*log((sqrt(x + 1)*sqrt(sqrt(x) - 1)*sqrt(-sqrt(x) - 1) + I*x - 1)/x) + I*log((sqrt(x + 1)*sqrt(sqrt(x) - 1)*sqrt(-sqrt(x) - 1) - I*x - 1)/x)","C",0
381,1,50,0,0.724882," ","integrate(1/(b^2*x+a^2)^(1/2)/(a-b*x^(1/2))^(1/2)/(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(-\frac{a^{2} - \sqrt{b^{2} x + a^{2}} \sqrt{b \sqrt{x} + a} \sqrt{-b \sqrt{x} + a}}{b^{2} x}\right)}{b^{2}}"," ",0,"-2*arctan(-(a^2 - sqrt(b^2*x + a^2)*sqrt(b*sqrt(x) + a)*sqrt(-b*sqrt(x) + a))/(b^2*x))/b^2","A",0
382,0,0,0,0.998828," ","integrate((a-b*x^n)^p*(a+b*x^n)^p*(c+d*x^(2*n))^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x^{2 \, n} + c\right)}^{q} {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((d*x^(2*n) + c)^q*(b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
383,0,0,0,0.986074," ","integrate((a-b*x^n)^p*(a+b*x^n)^p*(a^2+b^2*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{2 \, n} + a^{2}\right)}^{p} {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((b^2*x^(2*n) + a^2)^p*(b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
384,0,0,0,0.988839," ","integrate((c+d*x^(2*n))^p/(a-b*x^n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x^{2 \, n} + c\right)}^{p}}{b^{2} x^{2 \, n} - a^{2}}, x\right)"," ",0,"integral(-(d*x^(2*n) + c)^p/(b^2*x^(2*n) - a^2), x)","F",0
385,1,180,0,0.846151," ","integrate((a-b*x^(1/2*n))^p*(a+b*x^(1/2*n))^p*(a^2*d*(1+p)/b^2/(1+(-n*p-2*n-1)/n)+d*x^n)^((-n*p-2*n-1)/n),x, algorithm=""fricas"")","\frac{{\left({\left(b^{4} n p + b^{4} n + b^{4}\right)} x x^{2 \, n} - {\left(2 \, a^{2} b^{2} n p + 2 \, a^{2} b^{2} n + a^{2} b^{2}\right)} x x^{n} + {\left(a^{4} n p + a^{4} n\right)} x\right)} {\left(b x^{\frac{1}{2} \, n} + a\right)}^{p} {\left(-b x^{\frac{1}{2} \, n} + a\right)}^{p}}{{\left(a^{4} n p + a^{4} n\right)} \left(-\frac{a^{2} d n p + a^{2} d n - {\left(b^{2} d n p + b^{2} d n + b^{2} d\right)} x^{n}}{b^{2} n p + b^{2} n + b^{2}}\right)^{\frac{n p + 2 \, n + 1}{n}}}"," ",0,"((b^4*n*p + b^4*n + b^4)*x*x^(2*n) - (2*a^2*b^2*n*p + 2*a^2*b^2*n + a^2*b^2)*x*x^n + (a^4*n*p + a^4*n)*x)*(b*x^(1/2*n) + a)^p*(-b*x^(1/2*n) + a)^p/((a^4*n*p + a^4*n)*(-(a^2*d*n*p + a^2*d*n - (b^2*d*n*p + b^2*d*n + b^2*d)*x^n)/(b^2*n*p + b^2*n + b^2))^((n*p + 2*n + 1)/n))","A",0
