1,1,98,0,0.486029," ","integrate((b*x^2+a)*(d*x^2+c)^4,x, algorithm=""fricas"")","\frac{1}{11} x^{11} d^{4} b + \frac{4}{9} x^{9} d^{3} c b + \frac{1}{9} x^{9} d^{4} a + \frac{6}{7} x^{7} d^{2} c^{2} b + \frac{4}{7} x^{7} d^{3} c a + \frac{4}{5} x^{5} d c^{3} b + \frac{6}{5} x^{5} d^{2} c^{2} a + \frac{1}{3} x^{3} c^{4} b + \frac{4}{3} x^{3} d c^{3} a + x c^{4} a"," ",0,"1/11*x^11*d^4*b + 4/9*x^9*d^3*c*b + 1/9*x^9*d^4*a + 6/7*x^7*d^2*c^2*b + 4/7*x^7*d^3*c*a + 4/5*x^5*d*c^3*b + 6/5*x^5*d^2*c^2*a + 1/3*x^3*c^4*b + 4/3*x^3*d*c^3*a + x*c^4*a","A",0
2,1,73,0,0.802654," ","integrate((b*x^2+a)*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} d^{3} b + \frac{3}{7} x^{7} d^{2} c b + \frac{1}{7} x^{7} d^{3} a + \frac{3}{5} x^{5} d c^{2} b + \frac{3}{5} x^{5} d^{2} c a + \frac{1}{3} x^{3} c^{3} b + x^{3} d c^{2} a + x c^{3} a"," ",0,"1/9*x^9*d^3*b + 3/7*x^7*d^2*c*b + 1/7*x^7*d^3*a + 3/5*x^5*d*c^2*b + 3/5*x^5*d^2*c*a + 1/3*x^3*c^3*b + x^3*d*c^2*a + x*c^3*a","A",0
3,1,50,0,0.403289," ","integrate((b*x^2+a)*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} d^{2} b + \frac{2}{5} x^{5} d c b + \frac{1}{5} x^{5} d^{2} a + \frac{1}{3} x^{3} c^{2} b + \frac{2}{3} x^{3} d c a + x c^{2} a"," ",0,"1/7*x^7*d^2*b + 2/5*x^5*d*c*b + 1/5*x^5*d^2*a + 1/3*x^3*c^2*b + 2/3*x^3*d*c*a + x*c^2*a","A",0
4,1,26,0,0.767133," ","integrate((b*x^2+a)*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{5} x^{5} d b + \frac{1}{3} x^{3} c b + \frac{1}{3} x^{3} d a + x c a"," ",0,"1/5*x^5*d*b + 1/3*x^3*c*b + 1/3*x^3*d*a + x*c*a","A",0
5,1,99,0,0.799304," ","integrate((b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{2 \, b c d x + {\left(b c - a d\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right)}{2 \, c d^{2}}, \frac{b c d x - {\left(b c - a d\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right)}{c d^{2}}\right]"," ",0,"[1/2*(2*b*c*d*x + (b*c - a*d)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)))/(c*d^2), (b*c*d*x - (b*c - a*d)*sqrt(c*d)*arctan(sqrt(c*d)*x/c))/(c*d^2)]","A",0
6,1,182,0,0.821729," ","integrate((b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b c^{2} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(b c^{2} d - a c d^{2}\right)} x}{4 \, {\left(c^{2} d^{3} x^{2} + c^{3} d^{2}\right)}}, \frac{{\left(b c^{2} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - {\left(b c^{2} d - a c d^{2}\right)} x}{2 \, {\left(c^{2} d^{3} x^{2} + c^{3} d^{2}\right)}}\right]"," ",0,"[-1/4*((b*c^2 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(b*c^2*d - a*c*d^2)*x)/(c^2*d^3*x^2 + c^3*d^2), 1/2*((b*c^2 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - (b*c^2*d - a*c*d^2)*x)/(c^2*d^3*x^2 + c^3*d^2)]","A",0
7,1,300,0,0.819256," ","integrate((b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{3} - {\left({\left(b c d^{2} + 3 \, a d^{3}\right)} x^{4} + b c^{3} + 3 \, a c^{2} d + 2 \, {\left(b c^{2} d + 3 \, a c d^{2}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 2 \, {\left(b c^{3} d - 5 \, a c^{2} d^{2}\right)} x}{16 \, {\left(c^{3} d^{4} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{5} d^{2}\right)}}, \frac{{\left(b c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{3} + {\left({\left(b c d^{2} + 3 \, a d^{3}\right)} x^{4} + b c^{3} + 3 \, a c^{2} d + 2 \, {\left(b c^{2} d + 3 \, a c d^{2}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - {\left(b c^{3} d - 5 \, a c^{2} d^{2}\right)} x}{8 \, {\left(c^{3} d^{4} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{5} d^{2}\right)}}\right]"," ",0,"[1/16*(2*(b*c^2*d^2 + 3*a*c*d^3)*x^3 - ((b*c*d^2 + 3*a*d^3)*x^4 + b*c^3 + 3*a*c^2*d + 2*(b*c^2*d + 3*a*c*d^2)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 2*(b*c^3*d - 5*a*c^2*d^2)*x)/(c^3*d^4*x^4 + 2*c^4*d^3*x^2 + c^5*d^2), 1/8*((b*c^2*d^2 + 3*a*c*d^3)*x^3 + ((b*c*d^2 + 3*a*d^3)*x^4 + b*c^3 + 3*a*c^2*d + 2*(b*c^2*d + 3*a*c*d^2)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - (b*c^3*d - 5*a*c^2*d^2)*x)/(c^3*d^4*x^4 + 2*c^4*d^3*x^2 + c^5*d^2)]","A",0
8,1,131,0,0.741893," ","integrate((b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} d^{3} b^{2} + \frac{1}{3} x^{9} d^{2} c b^{2} + \frac{2}{9} x^{9} d^{3} b a + \frac{3}{7} x^{7} d c^{2} b^{2} + \frac{6}{7} x^{7} d^{2} c b a + \frac{1}{7} x^{7} d^{3} a^{2} + \frac{1}{5} x^{5} c^{3} b^{2} + \frac{6}{5} x^{5} d c^{2} b a + \frac{3}{5} x^{5} d^{2} c a^{2} + \frac{2}{3} x^{3} c^{3} b a + x^{3} d c^{2} a^{2} + x c^{3} a^{2}"," ",0,"1/11*x^11*d^3*b^2 + 1/3*x^9*d^2*c*b^2 + 2/9*x^9*d^3*b*a + 3/7*x^7*d*c^2*b^2 + 6/7*x^7*d^2*c*b*a + 1/7*x^7*d^3*a^2 + 1/5*x^5*c^3*b^2 + 6/5*x^5*d*c^2*b*a + 3/5*x^5*d^2*c*a^2 + 2/3*x^3*c^3*b*a + x^3*d*c^2*a^2 + x*c^3*a^2","A",0
9,1,91,0,0.656518," ","integrate((b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} d^{2} b^{2} + \frac{2}{7} x^{7} d c b^{2} + \frac{2}{7} x^{7} d^{2} b a + \frac{1}{5} x^{5} c^{2} b^{2} + \frac{4}{5} x^{5} d c b a + \frac{1}{5} x^{5} d^{2} a^{2} + \frac{2}{3} x^{3} c^{2} b a + \frac{2}{3} x^{3} d c a^{2} + x c^{2} a^{2}"," ",0,"1/9*x^9*d^2*b^2 + 2/7*x^7*d*c*b^2 + 2/7*x^7*d^2*b*a + 1/5*x^5*c^2*b^2 + 4/5*x^5*d*c*b*a + 1/5*x^5*d^2*a^2 + 2/3*x^3*c^2*b*a + 2/3*x^3*d*c*a^2 + x*c^2*a^2","A",0
10,1,50,0,0.476408," ","integrate((b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{7} x^{7} d b^{2} + \frac{1}{5} x^{5} c b^{2} + \frac{2}{5} x^{5} d b a + \frac{2}{3} x^{3} c b a + \frac{1}{3} x^{3} d a^{2} + x c a^{2}"," ",0,"1/7*x^7*d*b^2 + 1/5*x^5*c*b^2 + 2/5*x^5*d*b*a + 2/3*x^3*c*b*a + 1/3*x^3*d*a^2 + x*c*a^2","A",0
11,1,179,0,0.866787," ","integrate((b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{2 \, b^{2} c d^{2} x^{3} - 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x}{6 \, c d^{3}}, \frac{b^{2} c d^{2} x^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x}{3 \, c d^{3}}\right]"," ",0,"[1/6*(2*b^2*c*d^2*x^3 - 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 6*(b^2*c^2*d - 2*a*b*c*d^2)*x)/(c*d^3), 1/3*(b^2*c*d^2*x^3 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - 3*(b^2*c^2*d - 2*a*b*c*d^2)*x)/(c*d^3)]","A",0
12,1,302,0,0.870190," ","integrate((b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{4 \, b^{2} c^{2} d^{2} x^{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^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(3 \, b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x}{4 \, {\left(c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}}, \frac{2 \, b^{2} c^{2} d^{2} x^{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^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(3 \, b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x}{2 \, {\left(c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}}\right]"," ",0,"[1/4*(4*b^2*c^2*d^2*x^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^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(3*b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)/(c^2*d^4*x^2 + c^3*d^3), 1/2*(2*b^2*c^2*d^2*x^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^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (3*b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)/(c^2*d^4*x^2 + c^3*d^3)]","B",0
13,1,449,0,0.753059," ","integrate((b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - 3 \, a^{2} c d^{4}\right)} x^{3} + {\left(3 \, b^{2} c^{4} + 2 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(3 \, b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 5 \, a^{2} c^{2} d^{3}\right)} x}{16 \, {\left(c^{3} d^{5} x^{4} + 2 \, c^{4} d^{4} x^{2} + c^{5} d^{3}\right)}}, -\frac{{\left(5 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - 3 \, a^{2} c d^{4}\right)} x^{3} - {\left(3 \, b^{2} c^{4} + 2 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(3 \, b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 5 \, a^{2} c^{2} d^{3}\right)} x}{8 \, {\left(c^{3} d^{5} x^{4} + 2 \, c^{4} d^{4} x^{2} + c^{5} d^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - 3*a^2*c*d^4)*x^3 + (3*b^2*c^4 + 2*a*b*c^3*d + 3*a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 2*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 2*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(3*b^2*c^4*d + 2*a*b*c^3*d^2 - 5*a^2*c^2*d^3)*x)/(c^3*d^5*x^4 + 2*c^4*d^4*x^2 + c^5*d^3), -1/8*((5*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - 3*a^2*c*d^4)*x^3 - (3*b^2*c^4 + 2*a*b*c^3*d + 3*a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 2*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 2*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (3*b^2*c^4*d + 2*a*b*c^3*d^2 - 5*a^2*c^2*d^3)*x)/(c^3*d^5*x^4 + 2*c^4*d^4*x^2 + c^5*d^3)]","B",0
14,1,187,0,0.663019," ","integrate((b*x^2+a)^3*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} d^{3} b^{3} + \frac{3}{11} x^{11} d^{2} c b^{3} + \frac{3}{11} x^{11} d^{3} b^{2} a + \frac{1}{3} x^{9} d c^{2} b^{3} + x^{9} d^{2} c b^{2} a + \frac{1}{3} x^{9} d^{3} b a^{2} + \frac{1}{7} x^{7} c^{3} b^{3} + \frac{9}{7} x^{7} d c^{2} b^{2} a + \frac{9}{7} x^{7} d^{2} c b a^{2} + \frac{1}{7} x^{7} d^{3} a^{3} + \frac{3}{5} x^{5} c^{3} b^{2} a + \frac{9}{5} x^{5} d c^{2} b a^{2} + \frac{3}{5} x^{5} d^{2} c a^{3} + x^{3} c^{3} b a^{2} + x^{3} d c^{2} a^{3} + x c^{3} a^{3}"," ",0,"1/13*x^13*d^3*b^3 + 3/11*x^11*d^2*c*b^3 + 3/11*x^11*d^3*b^2*a + 1/3*x^9*d*c^2*b^3 + x^9*d^2*c*b^2*a + 1/3*x^9*d^3*b*a^2 + 1/7*x^7*c^3*b^3 + 9/7*x^7*d*c^2*b^2*a + 9/7*x^7*d^2*c*b*a^2 + 1/7*x^7*d^3*a^3 + 3/5*x^5*c^3*b^2*a + 9/5*x^5*d*c^2*b*a^2 + 3/5*x^5*d^2*c*a^3 + x^3*c^3*b*a^2 + x^3*d*c^2*a^3 + x*c^3*a^3","A",0
15,1,131,0,0.738294," ","integrate((b*x^2+a)^3*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} d^{2} b^{3} + \frac{2}{9} x^{9} d c b^{3} + \frac{1}{3} x^{9} d^{2} b^{2} a + \frac{1}{7} x^{7} c^{2} b^{3} + \frac{6}{7} x^{7} d c b^{2} a + \frac{3}{7} x^{7} d^{2} b a^{2} + \frac{3}{5} x^{5} c^{2} b^{2} a + \frac{6}{5} x^{5} d c b a^{2} + \frac{1}{5} x^{5} d^{2} a^{3} + x^{3} c^{2} b a^{2} + \frac{2}{3} x^{3} d c a^{3} + x c^{2} a^{3}"," ",0,"1/11*x^11*d^2*b^3 + 2/9*x^9*d*c*b^3 + 1/3*x^9*d^2*b^2*a + 1/7*x^7*c^2*b^3 + 6/7*x^7*d*c*b^2*a + 3/7*x^7*d^2*b*a^2 + 3/5*x^5*c^2*b^2*a + 6/5*x^5*d*c*b*a^2 + 1/5*x^5*d^2*a^3 + x^3*c^2*b*a^2 + 2/3*x^3*d*c*a^3 + x*c^2*a^3","A",0
16,1,73,0,0.490386," ","integrate((b*x^2+a)^3*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{9} x^{9} d b^{3} + \frac{1}{7} x^{7} c b^{3} + \frac{3}{7} x^{7} d b^{2} a + \frac{3}{5} x^{5} c b^{2} a + \frac{3}{5} x^{5} d b a^{2} + x^{3} c b a^{2} + \frac{1}{3} x^{3} d a^{3} + x c a^{3}"," ",0,"1/9*x^9*d*b^3 + 1/7*x^7*c*b^3 + 3/7*x^7*d*b^2*a + 3/5*x^5*c*b^2*a + 3/5*x^5*d*b*a^2 + x^3*c*b*a^2 + 1/3*x^3*d*a^3 + x*c*a^3","A",0
17,1,290,0,0.567418," ","integrate((b*x^2+a)^3/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{6 \, b^{3} c d^{3} x^{5} - 10 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3}\right)} x^{3} + 15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 30 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3}\right)} x}{30 \, c d^{4}}, \frac{3 \, b^{3} c d^{3} x^{5} - 5 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3}\right)} x^{3} - 15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + 15 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3}\right)} x}{15 \, c d^{4}}\right]"," ",0,"[1/30*(6*b^3*c*d^3*x^5 - 10*(b^3*c^2*d^2 - 3*a*b^2*c*d^3)*x^3 + 15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 30*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3)*x)/(c*d^4), 1/15*(3*b^3*c*d^3*x^5 - 5*(b^3*c^2*d^2 - 3*a*b^2*c*d^3)*x^3 - 15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + 15*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3)*x)/(c*d^4)]","A",0
18,1,444,0,0.819187," ","integrate((b*x^2+a)^3/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{4 \, b^{3} c^{2} d^{3} x^{5} - 4 \, {\left(5 \, b^{3} c^{3} d^{2} - 9 \, a b^{2} c^{2} d^{3}\right)} x^{3} - 3 \, {\left(5 \, b^{3} c^{4} - 9 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3} + {\left(5 \, b^{3} c^{3} d - 9 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 6 \, {\left(5 \, b^{3} c^{4} d - 9 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x}{12 \, {\left(c^{2} d^{5} x^{2} + c^{3} d^{4}\right)}}, \frac{2 \, b^{3} c^{2} d^{3} x^{5} - 2 \, {\left(5 \, b^{3} c^{3} d^{2} - 9 \, a b^{2} c^{2} d^{3}\right)} x^{3} + 3 \, {\left(5 \, b^{3} c^{4} - 9 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3} + {\left(5 \, b^{3} c^{3} d - 9 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - 3 \, {\left(5 \, b^{3} c^{4} d - 9 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x}{6 \, {\left(c^{2} d^{5} x^{2} + c^{3} d^{4}\right)}}\right]"," ",0,"[1/12*(4*b^3*c^2*d^3*x^5 - 4*(5*b^3*c^3*d^2 - 9*a*b^2*c^2*d^3)*x^3 - 3*(5*b^3*c^4 - 9*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 + a^3*c*d^3 + (5*b^3*c^3*d - 9*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 + a^3*d^4)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 6*(5*b^3*c^4*d - 9*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x)/(c^2*d^5*x^2 + c^3*d^4), 1/6*(2*b^3*c^2*d^3*x^5 - 2*(5*b^3*c^3*d^2 - 9*a*b^2*c^2*d^3)*x^3 + 3*(5*b^3*c^4 - 9*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 + a^3*c*d^3 + (5*b^3*c^3*d - 9*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 + a^3*d^4)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - 3*(5*b^3*c^4*d - 9*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x)/(c^2*d^5*x^2 + c^3*d^4)]","B",0
19,1,618,0,0.788588," ","integrate((b*x^2+a)^3/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{16 \, b^{3} c^{3} d^{3} x^{5} + 2 \, {\left(25 \, b^{3} c^{4} d^{2} - 15 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b c^{2} d^{4} + 3 \, a^{3} c d^{5}\right)} x^{3} + 3 \, {\left(5 \, b^{3} c^{5} - 3 \, a b^{2} c^{4} d - a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\left(5 \, b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} - a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{4} + 2 \, {\left(5 \, b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} - a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(15 \, b^{3} c^{5} d - 9 \, a b^{2} c^{4} d^{2} - 3 \, a^{2} b c^{3} d^{3} + 5 \, a^{3} c^{2} d^{4}\right)} x}{16 \, {\left(c^{3} d^{6} x^{4} + 2 \, c^{4} d^{5} x^{2} + c^{5} d^{4}\right)}}, \frac{8 \, b^{3} c^{3} d^{3} x^{5} + {\left(25 \, b^{3} c^{4} d^{2} - 15 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b c^{2} d^{4} + 3 \, a^{3} c d^{5}\right)} x^{3} - 3 \, {\left(5 \, b^{3} c^{5} - 3 \, a b^{2} c^{4} d - a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\left(5 \, b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} - a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{4} + 2 \, {\left(5 \, b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} - a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(15 \, b^{3} c^{5} d - 9 \, a b^{2} c^{4} d^{2} - 3 \, a^{2} b c^{3} d^{3} + 5 \, a^{3} c^{2} d^{4}\right)} x}{8 \, {\left(c^{3} d^{6} x^{4} + 2 \, c^{4} d^{5} x^{2} + c^{5} d^{4}\right)}}\right]"," ",0,"[1/16*(16*b^3*c^3*d^3*x^5 + 2*(25*b^3*c^4*d^2 - 15*a*b^2*c^3*d^3 + 3*a^2*b*c^2*d^4 + 3*a^3*c*d^5)*x^3 + 3*(5*b^3*c^5 - 3*a*b^2*c^4*d - a^2*b*c^3*d^2 - a^3*c^2*d^3 + (5*b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 - a^2*b*c*d^4 - a^3*d^5)*x^4 + 2*(5*b^3*c^4*d - 3*a*b^2*c^3*d^2 - a^2*b*c^2*d^3 - a^3*c*d^4)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(15*b^3*c^5*d - 9*a*b^2*c^4*d^2 - 3*a^2*b*c^3*d^3 + 5*a^3*c^2*d^4)*x)/(c^3*d^6*x^4 + 2*c^4*d^5*x^2 + c^5*d^4), 1/8*(8*b^3*c^3*d^3*x^5 + (25*b^3*c^4*d^2 - 15*a*b^2*c^3*d^3 + 3*a^2*b*c^2*d^4 + 3*a^3*c*d^5)*x^3 - 3*(5*b^3*c^5 - 3*a*b^2*c^4*d - a^2*b*c^3*d^2 - a^3*c^2*d^3 + (5*b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 - a^2*b*c*d^4 - a^3*d^5)*x^4 + 2*(5*b^3*c^4*d - 3*a*b^2*c^3*d^2 - a^2*b*c^2*d^3 - a^3*c*d^4)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (15*b^3*c^5*d - 9*a*b^2*c^4*d^2 - 3*a^2*b*c^3*d^3 + 5*a^3*c^2*d^4)*x)/(c^3*d^6*x^4 + 2*c^4*d^5*x^2 + c^5*d^4)]","B",0
20,1,428,0,0.633409," ","integrate((d*x^2+c)^4/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{30 \, a b^{4} d^{4} x^{7} + 42 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{5} + 70 \, {\left(6 \, a b^{4} c^{2} d^{2} - 4 \, a^{2} b^{3} c d^{3} + a^{3} b^{2} d^{4}\right)} x^{3} - 105 \, {\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{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 210 \, {\left(4 \, a b^{4} c^{3} d - 6 \, a^{2} b^{3} c^{2} d^{2} + 4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x}{210 \, a b^{5}}, \frac{15 \, a b^{4} d^{4} x^{7} + 21 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{5} + 35 \, {\left(6 \, a b^{4} c^{2} d^{2} - 4 \, a^{2} b^{3} c d^{3} + a^{3} b^{2} d^{4}\right)} x^{3} + 105 \, {\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{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 105 \, {\left(4 \, a b^{4} c^{3} d - 6 \, a^{2} b^{3} c^{2} d^{2} + 4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x}{105 \, a b^{5}}\right]"," ",0,"[1/210*(30*a*b^4*d^4*x^7 + 42*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^5 + 70*(6*a*b^4*c^2*d^2 - 4*a^2*b^3*c*d^3 + a^3*b^2*d^4)*x^3 - 105*(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(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 210*(4*a*b^4*c^3*d - 6*a^2*b^3*c^2*d^2 + 4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)/(a*b^5), 1/105*(15*a*b^4*d^4*x^7 + 21*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^5 + 35*(6*a*b^4*c^2*d^2 - 4*a^2*b^3*c*d^3 + a^3*b^2*d^4)*x^3 + 105*(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(a*b)*arctan(sqrt(a*b)*x/a) + 105*(4*a*b^4*c^3*d - 6*a^2*b^3*c^2*d^2 + 4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)/(a*b^5)]","A",0
21,1,292,0,0.804445," ","integrate((d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} d^{3} x^{5} + 10 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 30 \, {\left(3 \, a b^{3} c^{2} d - 3 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x}{30 \, a b^{4}}, \frac{3 \, a b^{3} d^{3} x^{5} + 5 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 15 \, {\left(3 \, a b^{3} c^{2} d - 3 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x}{15 \, a b^{4}}\right]"," ",0,"[1/30*(6*a*b^3*d^3*x^5 + 10*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^3 + 15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 30*(3*a*b^3*c^2*d - 3*a^2*b^2*c*d^2 + a^3*b*d^3)*x)/(a*b^4), 1/15*(3*a*b^3*d^3*x^5 + 5*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^3 + 15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 15*(3*a*b^3*c^2*d - 3*a^2*b^2*c*d^2 + a^3*b*d^3)*x)/(a*b^4)]","A",0
22,1,181,0,0.913340," ","integrate((d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a b^{2} d^{2} x^{3} - 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x}{6 \, a b^{3}}, \frac{a b^{2} d^{2} x^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x}{3 \, a b^{3}}\right]"," ",0,"[1/6*(2*a*b^2*d^2*x^3 - 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(2*a*b^2*c*d - a^2*b*d^2)*x)/(a*b^3), 1/3*(a*b^2*d^2*x^3 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(2*a*b^2*c*d - a^2*b*d^2)*x)/(a*b^3)]","A",0
23,1,98,0,1.053390," ","integrate((d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a b d x + \sqrt{-a b} {\left(b c - a d\right)} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2 \, a b^{2}}, \frac{a b d x + \sqrt{a b} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{a b^{2}}\right]"," ",0,"[1/2*(2*a*b*d*x + sqrt(-a*b)*(b*c - a*d)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^2), (a*b*d*x + sqrt(a*b)*(b*c - a*d)*arctan(sqrt(a*b)*x/a))/(a*b^2)]","A",0
24,1,292,0,0.922787," ","integrate(1/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{2 \, {\left(b c - a d\right)}}, -\frac{2 \, \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{2 \, {\left(b c - a d\right)}}, \frac{2 \, \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{2 \, {\left(b c - a d\right)}}, \frac{\sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{b c - a d}\right]"," ",0,"[-1/2*(sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/(b*c - a*d), -1/2*(2*sqrt(d/c)*arctan(x*sqrt(d/c)) + sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(b*c - a*d), 1/2*(2*sqrt(b/a)*arctan(x*sqrt(b/a)) - sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/(b*c - a*d), (sqrt(b/a)*arctan(x*sqrt(b/a)) - sqrt(d/c)*arctan(x*sqrt(d/c)))/(b*c - a*d)]","A",0
25,1,711,0,1.036323," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - {\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 2 \, {\left(b c d - a d^{2}\right)} x}{4 \, {\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^{2}\right)}}, -\frac{{\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(b c d - a d^{2}\right)} x}{2 \, {\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^{2}\right)}}, \frac{4 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 2 \, {\left(b c d - a d^{2}\right)} x}{4 \, {\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^{2}\right)}}, \frac{2 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(b c d - a d^{2}\right)} x}{2 \, {\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^{2}\right)}}\right]"," ",0,"[1/4*(2*(b*c*d*x^2 + b*c^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - (3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 2*(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^2), -1/2*((3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (b*c*d*x^2 + b*c^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (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^2), 1/4*(4*(b*c*d*x^2 + b*c^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - (3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 2*(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^2), 1/2*(2*(b*c*d*x^2 + b*c^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - (3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (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^2)]","A",0
26,1,1585,0,2.417321," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} + 8 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{16 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}, -\frac{{\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 4 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{8 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}, -\frac{2 \, {\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} - 16 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{16 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}, -\frac{{\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} - 8 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{8 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(2*(7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 + 8*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2), -1/8*((7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 4*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2), -1/16*(2*(7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 - 16*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2), -1/8*((7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 - 8*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2)]","B",0
27,1,810,0,0.680025," ","integrate((d*x^2+c)^5/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{60 \, a^{2} b^{5} d^{5} x^{9} + 12 \, {\left(35 \, a^{2} b^{5} c d^{4} - 9 \, a^{3} b^{4} d^{5}\right)} x^{7} + 28 \, {\left(50 \, a^{2} b^{5} c^{2} d^{3} - 35 \, a^{3} b^{4} c d^{4} + 9 \, a^{4} b^{3} d^{5}\right)} x^{5} + 140 \, {\left(30 \, a^{2} b^{5} c^{3} d^{2} - 50 \, a^{3} b^{4} c^{2} d^{3} + 35 \, a^{4} b^{3} c d^{4} - 9 \, a^{5} b^{2} d^{5}\right)} x^{3} - 105 \, {\left(a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d - 30 \, a^{3} b^{3} c^{3} d^{2} + 50 \, a^{4} b^{2} c^{2} d^{3} - 35 \, a^{5} b c d^{4} + 9 \, a^{6} d^{5} + {\left(b^{6} c^{5} + 5 \, a b^{5} c^{4} d - 30 \, a^{2} b^{4} c^{3} d^{2} + 50 \, a^{3} b^{3} c^{2} d^{3} - 35 \, a^{4} b^{2} c d^{4} + 9 \, a^{5} b d^{5}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 210 \, {\left(a b^{6} c^{5} - 5 \, a^{2} b^{5} c^{4} d + 30 \, a^{3} b^{4} c^{3} d^{2} - 50 \, a^{4} b^{3} c^{2} d^{3} + 35 \, a^{5} b^{2} c d^{4} - 9 \, a^{6} b d^{5}\right)} x}{420 \, {\left(a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}}, \frac{30 \, a^{2} b^{5} d^{5} x^{9} + 6 \, {\left(35 \, a^{2} b^{5} c d^{4} - 9 \, a^{3} b^{4} d^{5}\right)} x^{7} + 14 \, {\left(50 \, a^{2} b^{5} c^{2} d^{3} - 35 \, a^{3} b^{4} c d^{4} + 9 \, a^{4} b^{3} d^{5}\right)} x^{5} + 70 \, {\left(30 \, a^{2} b^{5} c^{3} d^{2} - 50 \, a^{3} b^{4} c^{2} d^{3} + 35 \, a^{4} b^{3} c d^{4} - 9 \, a^{5} b^{2} d^{5}\right)} x^{3} + 105 \, {\left(a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d - 30 \, a^{3} b^{3} c^{3} d^{2} + 50 \, a^{4} b^{2} c^{2} d^{3} - 35 \, a^{5} b c d^{4} + 9 \, a^{6} d^{5} + {\left(b^{6} c^{5} + 5 \, a b^{5} c^{4} d - 30 \, a^{2} b^{4} c^{3} d^{2} + 50 \, a^{3} b^{3} c^{2} d^{3} - 35 \, a^{4} b^{2} c d^{4} + 9 \, a^{5} b d^{5}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 105 \, {\left(a b^{6} c^{5} - 5 \, a^{2} b^{5} c^{4} d + 30 \, a^{3} b^{4} c^{3} d^{2} - 50 \, a^{4} b^{3} c^{2} d^{3} + 35 \, a^{5} b^{2} c d^{4} - 9 \, a^{6} b d^{5}\right)} x}{210 \, {\left(a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}}\right]"," ",0,"[1/420*(60*a^2*b^5*d^5*x^9 + 12*(35*a^2*b^5*c*d^4 - 9*a^3*b^4*d^5)*x^7 + 28*(50*a^2*b^5*c^2*d^3 - 35*a^3*b^4*c*d^4 + 9*a^4*b^3*d^5)*x^5 + 140*(30*a^2*b^5*c^3*d^2 - 50*a^3*b^4*c^2*d^3 + 35*a^4*b^3*c*d^4 - 9*a^5*b^2*d^5)*x^3 - 105*(a*b^5*c^5 + 5*a^2*b^4*c^4*d - 30*a^3*b^3*c^3*d^2 + 50*a^4*b^2*c^2*d^3 - 35*a^5*b*c*d^4 + 9*a^6*d^5 + (b^6*c^5 + 5*a*b^5*c^4*d - 30*a^2*b^4*c^3*d^2 + 50*a^3*b^3*c^2*d^3 - 35*a^4*b^2*c*d^4 + 9*a^5*b*d^5)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 210*(a*b^6*c^5 - 5*a^2*b^5*c^4*d + 30*a^3*b^4*c^3*d^2 - 50*a^4*b^3*c^2*d^3 + 35*a^5*b^2*c*d^4 - 9*a^6*b*d^5)*x)/(a^2*b^7*x^2 + a^3*b^6), 1/210*(30*a^2*b^5*d^5*x^9 + 6*(35*a^2*b^5*c*d^4 - 9*a^3*b^4*d^5)*x^7 + 14*(50*a^2*b^5*c^2*d^3 - 35*a^3*b^4*c*d^4 + 9*a^4*b^3*d^5)*x^5 + 70*(30*a^2*b^5*c^3*d^2 - 50*a^3*b^4*c^2*d^3 + 35*a^4*b^3*c*d^4 - 9*a^5*b^2*d^5)*x^3 + 105*(a*b^5*c^5 + 5*a^2*b^4*c^4*d - 30*a^3*b^3*c^3*d^2 + 50*a^4*b^2*c^2*d^3 - 35*a^5*b*c*d^4 + 9*a^6*d^5 + (b^6*c^5 + 5*a*b^5*c^4*d - 30*a^2*b^4*c^3*d^2 + 50*a^3*b^3*c^2*d^3 - 35*a^4*b^2*c*d^4 + 9*a^5*b*d^5)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 105*(a*b^6*c^5 - 5*a^2*b^5*c^4*d + 30*a^3*b^4*c^3*d^2 - 50*a^4*b^3*c^2*d^3 + 35*a^5*b^2*c*d^4 - 9*a^6*b*d^5)*x)/(a^2*b^7*x^2 + a^3*b^6)]","B",0
28,1,612,0,0.858880," ","integrate((d*x^2+c)^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{12 \, a^{2} b^{4} d^{4} x^{7} + 4 \, {\left(20 \, a^{2} b^{4} c d^{3} - 7 \, a^{3} b^{3} d^{4}\right)} x^{5} + 20 \, {\left(18 \, a^{2} b^{4} c^{2} d^{2} - 20 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{3} + 15 \, {\left(a b^{4} c^{4} + 4 \, a^{2} b^{3} c^{3} d - 18 \, a^{3} b^{2} c^{2} d^{2} + 20 \, a^{4} b c d^{3} - 7 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 4 \, a b^{4} c^{3} d - 18 \, a^{2} b^{3} c^{2} d^{2} + 20 \, a^{3} b^{2} c d^{3} - 7 \, a^{4} b d^{4}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 30 \, {\left(a b^{5} c^{4} - 4 \, a^{2} b^{4} c^{3} d + 18 \, a^{3} b^{3} c^{2} d^{2} - 20 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x}{60 \, {\left(a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}}, \frac{6 \, a^{2} b^{4} d^{4} x^{7} + 2 \, {\left(20 \, a^{2} b^{4} c d^{3} - 7 \, a^{3} b^{3} d^{4}\right)} x^{5} + 10 \, {\left(18 \, a^{2} b^{4} c^{2} d^{2} - 20 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{3} + 15 \, {\left(a b^{4} c^{4} + 4 \, a^{2} b^{3} c^{3} d - 18 \, a^{3} b^{2} c^{2} d^{2} + 20 \, a^{4} b c d^{3} - 7 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 4 \, a b^{4} c^{3} d - 18 \, a^{2} b^{3} c^{2} d^{2} + 20 \, a^{3} b^{2} c d^{3} - 7 \, a^{4} b d^{4}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 15 \, {\left(a b^{5} c^{4} - 4 \, a^{2} b^{4} c^{3} d + 18 \, a^{3} b^{3} c^{2} d^{2} - 20 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x}{30 \, {\left(a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}}\right]"," ",0,"[1/60*(12*a^2*b^4*d^4*x^7 + 4*(20*a^2*b^4*c*d^3 - 7*a^3*b^3*d^4)*x^5 + 20*(18*a^2*b^4*c^2*d^2 - 20*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^3 + 15*(a*b^4*c^4 + 4*a^2*b^3*c^3*d - 18*a^3*b^2*c^2*d^2 + 20*a^4*b*c*d^3 - 7*a^5*d^4 + (b^5*c^4 + 4*a*b^4*c^3*d - 18*a^2*b^3*c^2*d^2 + 20*a^3*b^2*c*d^3 - 7*a^4*b*d^4)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 30*(a*b^5*c^4 - 4*a^2*b^4*c^3*d + 18*a^3*b^3*c^2*d^2 - 20*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x)/(a^2*b^6*x^2 + a^3*b^5), 1/30*(6*a^2*b^4*d^4*x^7 + 2*(20*a^2*b^4*c*d^3 - 7*a^3*b^3*d^4)*x^5 + 10*(18*a^2*b^4*c^2*d^2 - 20*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^3 + 15*(a*b^4*c^4 + 4*a^2*b^3*c^3*d - 18*a^3*b^2*c^2*d^2 + 20*a^4*b*c*d^3 - 7*a^5*d^4 + (b^5*c^4 + 4*a*b^4*c^3*d - 18*a^2*b^3*c^2*d^2 + 20*a^3*b^2*c*d^3 - 7*a^4*b*d^4)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 15*(a*b^5*c^4 - 4*a^2*b^4*c^3*d + 18*a^3*b^3*c^2*d^2 - 20*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x)/(a^2*b^6*x^2 + a^3*b^5)]","B",0
29,1,442,0,0.848029," ","integrate((d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b^{3} d^{3} x^{5} + 4 \, {\left(9 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{3} - 3 \, {\left(a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 9 \, a^{3} b c d^{2} + 5 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 9 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x}{12 \, {\left(a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}, \frac{2 \, a^{2} b^{3} d^{3} x^{5} + 2 \, {\left(9 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 9 \, a^{3} b c d^{2} + 5 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 9 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x}{6 \, {\left(a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}\right]"," ",0,"[1/12*(4*a^2*b^3*d^3*x^5 + 4*(9*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^3 - 3*(a*b^3*c^3 + 3*a^2*b^2*c^2*d - 9*a^3*b*c*d^2 + 5*a^4*d^3 + (b^4*c^3 + 3*a*b^3*c^2*d - 9*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x)/(a^2*b^5*x^2 + a^3*b^4), 1/6*(2*a^2*b^3*d^3*x^5 + 2*(9*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^3 + 3*(a*b^3*c^3 + 3*a^2*b^2*c^2*d - 9*a^3*b*c*d^2 + 5*a^4*d^3 + (b^4*c^3 + 3*a*b^3*c^2*d - 9*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x)/(a^2*b^5*x^2 + a^3*b^4)]","B",0
30,1,297,0,0.953557," ","integrate((d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b^{2} d^{2} x^{3} + {\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x}{4 \, {\left(a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}, \frac{2 \, a^{2} b^{2} d^{2} x^{3} + {\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x}{2 \, {\left(a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}\right]"," ",0,"[1/4*(4*a^2*b^2*d^2*x^3 + (a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2 + (b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + 3*a^3*b*d^2)*x)/(a^2*b^4*x^2 + a^3*b^3), 1/2*(2*a^2*b^2*d^2*x^3 + (a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2 + (b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (a*b^3*c^2 - 2*a^2*b^2*c*d + 3*a^3*b*d^2)*x)/(a^2*b^4*x^2 + a^3*b^3)]","A",0
31,1,181,0,0.581829," ","integrate((d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(a b^{2} c - a^{2} b d\right)} x}{4 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, \frac{{\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(a b^{2} c - a^{2} b d\right)} x}{2 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/4*((a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(a*b^2*c - a^2*b*d)*x)/(a^2*b^3*x^2 + a^3*b^2), 1/2*((a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (a*b^2*c - a^2*b*d)*x)/(a^2*b^3*x^2 + a^3*b^2)]","A",0
32,1,699,0,1.118866," ","integrate(1/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{{\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 2 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 2 \, {\left(b^{2} c - a b d\right)} x}{4 \, {\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^{2}\right)}}, \frac{4 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(b^{2} c - a b d\right)} x}{4 \, {\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^{2}\right)}}, \frac{{\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + {\left(b^{2} c - a b d\right)} x}{2 \, {\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^{2}\right)}}, \frac{{\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 2 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(b^{2} c - a b d\right)} x}{2 \, {\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^{2}\right)}}\right]"," ",0,"[-1/4*((a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 2*(a*b*d*x^2 + a^2*d)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 2*(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^2), 1/4*(4*(a*b*d*x^2 + a^2*d)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(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^2), 1/2*((a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (a*b*d*x^2 + a^2*d)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + (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^2), 1/2*((a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 2*(a*b*d*x^2 + a^2*d)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (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^2)]","A",0
33,1,1681,0,2.413805," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{4 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + 2 \, {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{4 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + 2 \, {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{4 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}, \frac{{\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{2 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(b^3*c^2*d - a^2*b*d^3)*x^3 + (a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2), 1/4*(2*(b^3*c^2*d - a^2*b*d^3)*x^3 + 2*(5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2), 1/4*(2*(b^3*c^2*d - a^2*b*d^3)*x^3 + 2*(a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2), 1/2*((b^3*c^2*d - a^2*b*d^3)*x^3 + (a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2)]","B",0
34,1,3239,0,8.316467," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + 2 \, {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} - 4 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{16 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{{\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - 2 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{8 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{2 \, {\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + 2 \, {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} + 8 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{16 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{{\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} + 4 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{8 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(2*(4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + 2*(8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 - 4*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2), 1/8*((4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + (8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - 2*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2), 1/16*(2*(4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + 2*(8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 + 8*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2), 1/8*((4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + (8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 + 4*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2)]","B",0
35,1,1044,0,0.919291," ","integrate((d*x^2+c)^5/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{48 \, a^{3} b^{5} d^{5} x^{9} + 16 \, {\left(25 \, a^{3} b^{5} c d^{4} - 9 \, a^{4} b^{4} d^{5}\right)} x^{7} + 16 \, {\left(150 \, a^{3} b^{5} c^{2} d^{3} - 175 \, a^{4} b^{4} c d^{4} + 63 \, a^{5} b^{3} d^{5}\right)} x^{5} + 10 \, {\left(9 \, a b^{7} c^{5} + 15 \, a^{2} b^{6} c^{4} d - 150 \, a^{3} b^{5} c^{3} d^{2} + 750 \, a^{4} b^{4} c^{2} d^{3} - 875 \, a^{5} b^{3} c d^{4} + 315 \, a^{6} b^{2} d^{5}\right)} x^{3} + 15 \, {\left(3 \, a^{2} b^{5} c^{5} + 5 \, a^{3} b^{4} c^{4} d + 30 \, a^{4} b^{3} c^{3} d^{2} - 150 \, a^{5} b^{2} c^{2} d^{3} + 175 \, a^{6} b c d^{4} - 63 \, a^{7} d^{5} + {\left(3 \, b^{7} c^{5} + 5 \, a b^{6} c^{4} d + 30 \, a^{2} b^{5} c^{3} d^{2} - 150 \, a^{3} b^{4} c^{2} d^{3} + 175 \, a^{4} b^{3} c d^{4} - 63 \, a^{5} b^{2} d^{5}\right)} x^{4} + 2 \, {\left(3 \, a b^{6} c^{5} + 5 \, a^{2} b^{5} c^{4} d + 30 \, a^{3} b^{4} c^{3} d^{2} - 150 \, a^{4} b^{3} c^{2} d^{3} + 175 \, a^{5} b^{2} c d^{4} - 63 \, a^{6} b d^{5}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 30 \, {\left(5 \, a^{2} b^{6} c^{5} - 5 \, a^{3} b^{5} c^{4} d - 30 \, a^{4} b^{4} c^{3} d^{2} + 150 \, a^{5} b^{3} c^{2} d^{3} - 175 \, a^{6} b^{2} c d^{4} + 63 \, a^{7} b d^{5}\right)} x}{240 \, {\left(a^{3} b^{8} x^{4} + 2 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}}, \frac{24 \, a^{3} b^{5} d^{5} x^{9} + 8 \, {\left(25 \, a^{3} b^{5} c d^{4} - 9 \, a^{4} b^{4} d^{5}\right)} x^{7} + 8 \, {\left(150 \, a^{3} b^{5} c^{2} d^{3} - 175 \, a^{4} b^{4} c d^{4} + 63 \, a^{5} b^{3} d^{5}\right)} x^{5} + 5 \, {\left(9 \, a b^{7} c^{5} + 15 \, a^{2} b^{6} c^{4} d - 150 \, a^{3} b^{5} c^{3} d^{2} + 750 \, a^{4} b^{4} c^{2} d^{3} - 875 \, a^{5} b^{3} c d^{4} + 315 \, a^{6} b^{2} d^{5}\right)} x^{3} + 15 \, {\left(3 \, a^{2} b^{5} c^{5} + 5 \, a^{3} b^{4} c^{4} d + 30 \, a^{4} b^{3} c^{3} d^{2} - 150 \, a^{5} b^{2} c^{2} d^{3} + 175 \, a^{6} b c d^{4} - 63 \, a^{7} d^{5} + {\left(3 \, b^{7} c^{5} + 5 \, a b^{6} c^{4} d + 30 \, a^{2} b^{5} c^{3} d^{2} - 150 \, a^{3} b^{4} c^{2} d^{3} + 175 \, a^{4} b^{3} c d^{4} - 63 \, a^{5} b^{2} d^{5}\right)} x^{4} + 2 \, {\left(3 \, a b^{6} c^{5} + 5 \, a^{2} b^{5} c^{4} d + 30 \, a^{3} b^{4} c^{3} d^{2} - 150 \, a^{4} b^{3} c^{2} d^{3} + 175 \, a^{5} b^{2} c d^{4} - 63 \, a^{6} b d^{5}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 15 \, {\left(5 \, a^{2} b^{6} c^{5} - 5 \, a^{3} b^{5} c^{4} d - 30 \, a^{4} b^{4} c^{3} d^{2} + 150 \, a^{5} b^{3} c^{2} d^{3} - 175 \, a^{6} b^{2} c d^{4} + 63 \, a^{7} b d^{5}\right)} x}{120 \, {\left(a^{3} b^{8} x^{4} + 2 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}}\right]"," ",0,"[1/240*(48*a^3*b^5*d^5*x^9 + 16*(25*a^3*b^5*c*d^4 - 9*a^4*b^4*d^5)*x^7 + 16*(150*a^3*b^5*c^2*d^3 - 175*a^4*b^4*c*d^4 + 63*a^5*b^3*d^5)*x^5 + 10*(9*a*b^7*c^5 + 15*a^2*b^6*c^4*d - 150*a^3*b^5*c^3*d^2 + 750*a^4*b^4*c^2*d^3 - 875*a^5*b^3*c*d^4 + 315*a^6*b^2*d^5)*x^3 + 15*(3*a^2*b^5*c^5 + 5*a^3*b^4*c^4*d + 30*a^4*b^3*c^3*d^2 - 150*a^5*b^2*c^2*d^3 + 175*a^6*b*c*d^4 - 63*a^7*d^5 + (3*b^7*c^5 + 5*a*b^6*c^4*d + 30*a^2*b^5*c^3*d^2 - 150*a^3*b^4*c^2*d^3 + 175*a^4*b^3*c*d^4 - 63*a^5*b^2*d^5)*x^4 + 2*(3*a*b^6*c^5 + 5*a^2*b^5*c^4*d + 30*a^3*b^4*c^3*d^2 - 150*a^4*b^3*c^2*d^3 + 175*a^5*b^2*c*d^4 - 63*a^6*b*d^5)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 30*(5*a^2*b^6*c^5 - 5*a^3*b^5*c^4*d - 30*a^4*b^4*c^3*d^2 + 150*a^5*b^3*c^2*d^3 - 175*a^6*b^2*c*d^4 + 63*a^7*b*d^5)*x)/(a^3*b^8*x^4 + 2*a^4*b^7*x^2 + a^5*b^6), 1/120*(24*a^3*b^5*d^5*x^9 + 8*(25*a^3*b^5*c*d^4 - 9*a^4*b^4*d^5)*x^7 + 8*(150*a^3*b^5*c^2*d^3 - 175*a^4*b^4*c*d^4 + 63*a^5*b^3*d^5)*x^5 + 5*(9*a*b^7*c^5 + 15*a^2*b^6*c^4*d - 150*a^3*b^5*c^3*d^2 + 750*a^4*b^4*c^2*d^3 - 875*a^5*b^3*c*d^4 + 315*a^6*b^2*d^5)*x^3 + 15*(3*a^2*b^5*c^5 + 5*a^3*b^4*c^4*d + 30*a^4*b^3*c^3*d^2 - 150*a^5*b^2*c^2*d^3 + 175*a^6*b*c*d^4 - 63*a^7*d^5 + (3*b^7*c^5 + 5*a*b^6*c^4*d + 30*a^2*b^5*c^3*d^2 - 150*a^3*b^4*c^2*d^3 + 175*a^4*b^3*c*d^4 - 63*a^5*b^2*d^5)*x^4 + 2*(3*a*b^6*c^5 + 5*a^2*b^5*c^4*d + 30*a^3*b^4*c^3*d^2 - 150*a^4*b^3*c^2*d^3 + 175*a^5*b^2*c*d^4 - 63*a^6*b*d^5)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 15*(5*a^2*b^6*c^5 - 5*a^3*b^5*c^4*d - 30*a^4*b^4*c^3*d^2 + 150*a^5*b^3*c^2*d^3 - 175*a^6*b^2*c*d^4 + 63*a^7*b*d^5)*x)/(a^3*b^8*x^4 + 2*a^4*b^7*x^2 + a^5*b^6)]","B",0
36,1,817,0,0.867484," ","integrate((d*x^2+c)^4/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{3} b^{4} d^{4} x^{7} + 16 \, {\left(12 \, a^{3} b^{4} c d^{3} - 7 \, a^{4} b^{3} d^{4}\right)} x^{5} + 2 \, {\left(9 \, a b^{6} c^{4} + 12 \, a^{2} b^{5} c^{3} d - 90 \, a^{3} b^{4} c^{2} d^{2} + 300 \, a^{4} b^{3} c d^{3} - 175 \, a^{5} b^{2} d^{4}\right)} x^{3} - 3 \, {\left(3 \, a^{2} b^{4} c^{4} + 4 \, a^{3} b^{3} c^{3} d + 18 \, a^{4} b^{2} c^{2} d^{2} - 60 \, a^{5} b c d^{3} + 35 \, a^{6} d^{4} + {\left(3 \, b^{6} c^{4} + 4 \, a b^{5} c^{3} d + 18 \, a^{2} b^{4} c^{2} d^{2} - 60 \, a^{3} b^{3} c d^{3} + 35 \, a^{4} b^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{5} c^{4} + 4 \, a^{2} b^{4} c^{3} d + 18 \, a^{3} b^{3} c^{2} d^{2} - 60 \, a^{4} b^{2} c d^{3} + 35 \, a^{5} b d^{4}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(5 \, a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d - 18 \, a^{4} b^{3} c^{2} d^{2} + 60 \, a^{5} b^{2} c d^{3} - 35 \, a^{6} b d^{4}\right)} x}{48 \, {\left(a^{3} b^{7} x^{4} + 2 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}, \frac{8 \, a^{3} b^{4} d^{4} x^{7} + 8 \, {\left(12 \, a^{3} b^{4} c d^{3} - 7 \, a^{4} b^{3} d^{4}\right)} x^{5} + {\left(9 \, a b^{6} c^{4} + 12 \, a^{2} b^{5} c^{3} d - 90 \, a^{3} b^{4} c^{2} d^{2} + 300 \, a^{4} b^{3} c d^{3} - 175 \, a^{5} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(3 \, a^{2} b^{4} c^{4} + 4 \, a^{3} b^{3} c^{3} d + 18 \, a^{4} b^{2} c^{2} d^{2} - 60 \, a^{5} b c d^{3} + 35 \, a^{6} d^{4} + {\left(3 \, b^{6} c^{4} + 4 \, a b^{5} c^{3} d + 18 \, a^{2} b^{4} c^{2} d^{2} - 60 \, a^{3} b^{3} c d^{3} + 35 \, a^{4} b^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{5} c^{4} + 4 \, a^{2} b^{4} c^{3} d + 18 \, a^{3} b^{3} c^{2} d^{2} - 60 \, a^{4} b^{2} c d^{3} + 35 \, a^{5} b d^{4}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(5 \, a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d - 18 \, a^{4} b^{3} c^{2} d^{2} + 60 \, a^{5} b^{2} c d^{3} - 35 \, a^{6} b d^{4}\right)} x}{24 \, {\left(a^{3} b^{7} x^{4} + 2 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}\right]"," ",0,"[1/48*(16*a^3*b^4*d^4*x^7 + 16*(12*a^3*b^4*c*d^3 - 7*a^4*b^3*d^4)*x^5 + 2*(9*a*b^6*c^4 + 12*a^2*b^5*c^3*d - 90*a^3*b^4*c^2*d^2 + 300*a^4*b^3*c*d^3 - 175*a^5*b^2*d^4)*x^3 - 3*(3*a^2*b^4*c^4 + 4*a^3*b^3*c^3*d + 18*a^4*b^2*c^2*d^2 - 60*a^5*b*c*d^3 + 35*a^6*d^4 + (3*b^6*c^4 + 4*a*b^5*c^3*d + 18*a^2*b^4*c^2*d^2 - 60*a^3*b^3*c*d^3 + 35*a^4*b^2*d^4)*x^4 + 2*(3*a*b^5*c^4 + 4*a^2*b^4*c^3*d + 18*a^3*b^3*c^2*d^2 - 60*a^4*b^2*c*d^3 + 35*a^5*b*d^4)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(5*a^2*b^5*c^4 - 4*a^3*b^4*c^3*d - 18*a^4*b^3*c^2*d^2 + 60*a^5*b^2*c*d^3 - 35*a^6*b*d^4)*x)/(a^3*b^7*x^4 + 2*a^4*b^6*x^2 + a^5*b^5), 1/24*(8*a^3*b^4*d^4*x^7 + 8*(12*a^3*b^4*c*d^3 - 7*a^4*b^3*d^4)*x^5 + (9*a*b^6*c^4 + 12*a^2*b^5*c^3*d - 90*a^3*b^4*c^2*d^2 + 300*a^4*b^3*c*d^3 - 175*a^5*b^2*d^4)*x^3 + 3*(3*a^2*b^4*c^4 + 4*a^3*b^3*c^3*d + 18*a^4*b^2*c^2*d^2 - 60*a^5*b*c*d^3 + 35*a^6*d^4 + (3*b^6*c^4 + 4*a*b^5*c^3*d + 18*a^2*b^4*c^2*d^2 - 60*a^3*b^3*c*d^3 + 35*a^4*b^2*d^4)*x^4 + 2*(3*a*b^5*c^4 + 4*a^2*b^4*c^3*d + 18*a^3*b^3*c^2*d^2 - 60*a^4*b^2*c*d^3 + 35*a^5*b*d^4)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(5*a^2*b^5*c^4 - 4*a^3*b^4*c^3*d - 18*a^4*b^3*c^2*d^2 + 60*a^5*b^2*c*d^3 - 35*a^6*b*d^4)*x)/(a^3*b^7*x^4 + 2*a^4*b^6*x^2 + a^5*b^5)]","B",0
37,1,606,0,0.642229," ","integrate((d*x^2+c)^3/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{3} b^{3} d^{3} x^{5} + 2 \, {\left(3 \, a b^{5} c^{3} + 3 \, a^{2} b^{4} c^{2} d - 15 \, a^{3} b^{3} c d^{2} + 25 \, a^{4} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(a^{2} b^{3} c^{3} + a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - 5 \, a^{5} d^{3} + {\left(b^{5} c^{3} + a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(a b^{4} c^{3} + a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d - 9 \, a^{4} b^{2} c d^{2} + 15 \, a^{5} b d^{3}\right)} x}{16 \, {\left(a^{3} b^{6} x^{4} + 2 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)}}, \frac{8 \, a^{3} b^{3} d^{3} x^{5} + {\left(3 \, a b^{5} c^{3} + 3 \, a^{2} b^{4} c^{2} d - 15 \, a^{3} b^{3} c d^{2} + 25 \, a^{4} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(a^{2} b^{3} c^{3} + a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - 5 \, a^{5} d^{3} + {\left(b^{5} c^{3} + a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(a b^{4} c^{3} + a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(5 \, a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d - 9 \, a^{4} b^{2} c d^{2} + 15 \, a^{5} b d^{3}\right)} x}{8 \, {\left(a^{3} b^{6} x^{4} + 2 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)}}\right]"," ",0,"[1/16*(16*a^3*b^3*d^3*x^5 + 2*(3*a*b^5*c^3 + 3*a^2*b^4*c^2*d - 15*a^3*b^3*c*d^2 + 25*a^4*b^2*d^3)*x^3 + 3*(a^2*b^3*c^3 + a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - 5*a^5*d^3 + (b^5*c^3 + a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^4 + 2*(a*b^4*c^3 + a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(5*a^2*b^4*c^3 - 3*a^3*b^3*c^2*d - 9*a^4*b^2*c*d^2 + 15*a^5*b*d^3)*x)/(a^3*b^6*x^4 + 2*a^4*b^5*x^2 + a^5*b^4), 1/8*(8*a^3*b^3*d^3*x^5 + (3*a*b^5*c^3 + 3*a^2*b^4*c^2*d - 15*a^3*b^3*c*d^2 + 25*a^4*b^2*d^3)*x^3 + 3*(a^2*b^3*c^3 + a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - 5*a^5*d^3 + (b^5*c^3 + a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^4 + 2*(a*b^4*c^3 + a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (5*a^2*b^4*c^3 - 3*a^3*b^3*c^2*d - 9*a^4*b^2*c*d^2 + 15*a^5*b*d^3)*x)/(a^3*b^6*x^4 + 2*a^4*b^5*x^2 + a^5*b^4)]","B",0
38,1,449,0,0.811492," ","integrate((d*x^2+c)^2/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, a b^{4} c^{2} + 2 \, a^{2} b^{3} c d - 5 \, a^{3} b^{2} d^{2}\right)} x^{3} - {\left(3 \, a^{2} b^{2} c^{2} + 2 \, a^{3} b c d + 3 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} + 2 \, a b^{3} c d + 3 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{2} + 2 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d - 3 \, a^{4} b d^{2}\right)} x}{16 \, {\left(a^{3} b^{5} x^{4} + 2 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}, \frac{{\left(3 \, a b^{4} c^{2} + 2 \, a^{2} b^{3} c d - 5 \, a^{3} b^{2} d^{2}\right)} x^{3} + {\left(3 \, a^{2} b^{2} c^{2} + 2 \, a^{3} b c d + 3 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} + 2 \, a b^{3} c d + 3 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{2} + 2 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(5 \, a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d - 3 \, a^{4} b d^{2}\right)} x}{8 \, {\left(a^{3} b^{5} x^{4} + 2 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}\right]"," ",0,"[1/16*(2*(3*a*b^4*c^2 + 2*a^2*b^3*c*d - 5*a^3*b^2*d^2)*x^3 - (3*a^2*b^2*c^2 + 2*a^3*b*c*d + 3*a^4*d^2 + (3*b^4*c^2 + 2*a*b^3*c*d + 3*a^2*b^2*d^2)*x^4 + 2*(3*a*b^3*c^2 + 2*a^2*b^2*c*d + 3*a^3*b*d^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(5*a^2*b^3*c^2 - 2*a^3*b^2*c*d - 3*a^4*b*d^2)*x)/(a^3*b^5*x^4 + 2*a^4*b^4*x^2 + a^5*b^3), 1/8*((3*a*b^4*c^2 + 2*a^2*b^3*c*d - 5*a^3*b^2*d^2)*x^3 + (3*a^2*b^2*c^2 + 2*a^3*b*c*d + 3*a^4*d^2 + (3*b^4*c^2 + 2*a*b^3*c*d + 3*a^2*b^2*d^2)*x^4 + 2*(3*a*b^3*c^2 + 2*a^2*b^2*c*d + 3*a^3*b*d^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (5*a^2*b^3*c^2 - 2*a^3*b^2*c*d - 3*a^4*b*d^2)*x)/(a^3*b^5*x^4 + 2*a^4*b^4*x^2 + a^5*b^3)]","B",0
39,1,301,0,0.792796," ","integrate((d*x^2+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, a b^{3} c + a^{2} b^{2} d\right)} x^{3} - {\left({\left(3 \, b^{3} c + a b^{2} d\right)} x^{4} + 3 \, a^{2} b c + a^{3} d + 2 \, {\left(3 \, a b^{2} c + a^{2} b d\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a^{2} b^{2} c - a^{3} b d\right)} x}{16 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}, \frac{{\left(3 \, a b^{3} c + a^{2} b^{2} d\right)} x^{3} + {\left({\left(3 \, b^{3} c + a b^{2} d\right)} x^{4} + 3 \, a^{2} b c + a^{3} d + 2 \, {\left(3 \, a b^{2} c + a^{2} b d\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(5 \, a^{2} b^{2} c - a^{3} b d\right)} x}{8 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/16*(2*(3*a*b^3*c + a^2*b^2*d)*x^3 - ((3*b^3*c + a*b^2*d)*x^4 + 3*a^2*b*c + a^3*d + 2*(3*a*b^2*c + a^2*b*d)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(5*a^2*b^2*c - a^3*b*d)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2), 1/8*((3*a*b^3*c + a^2*b^2*d)*x^3 + ((3*b^3*c + a*b^2*d)*x^4 + 3*a^2*b*c + a^3*d + 2*(3*a*b^2*c + a^2*b*d)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (5*a^2*b^2*c - a^3*b*d)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2)]","A",0
40,1,1587,0,2.483771," ","integrate(1/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 7 \, a^{2} b^{2} d^{2}\right)} x^{3} - {\left(3 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 15 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 15 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 15 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 8 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(5 \, a b^{3} c^{2} - 14 \, a^{2} b^{2} c d + 9 \, a^{3} b d^{2}\right)} x}{16 \, {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3} + {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3}\right)} x^{2}\right)}}, \frac{2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 7 \, a^{2} b^{2} d^{2}\right)} x^{3} - 16 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(3 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 15 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 15 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 15 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a b^{3} c^{2} - 14 \, a^{2} b^{2} c d + 9 \, a^{3} b d^{2}\right)} x}{16 \, {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3} + {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3}\right)} x^{2}\right)}}, \frac{{\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 7 \, a^{2} b^{2} d^{2}\right)} x^{3} + {\left(3 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 15 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 15 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 15 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 4 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + {\left(5 \, a b^{3} c^{2} - 14 \, a^{2} b^{2} c d + 9 \, a^{3} b d^{2}\right)} x}{8 \, {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3} + {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3}\right)} x^{2}\right)}}, \frac{{\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 7 \, a^{2} b^{2} d^{2}\right)} x^{3} + {\left(3 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 15 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 15 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 15 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 8 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(5 \, a b^{3} c^{2} - 14 \, a^{2} b^{2} c d + 9 \, a^{3} b d^{2}\right)} x}{8 \, {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3} + {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(2*(3*b^4*c^2 - 10*a*b^3*c*d + 7*a^2*b^2*d^2)*x^3 - (3*a^2*b^2*c^2 - 10*a^3*b*c*d + 15*a^4*d^2 + (3*b^4*c^2 - 10*a*b^3*c*d + 15*a^2*b^2*d^2)*x^4 + 2*(3*a*b^3*c^2 - 10*a^2*b^2*c*d + 15*a^3*b*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 8*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(5*a*b^3*c^2 - 14*a^2*b^2*c*d + 9*a^3*b*d^2)*x)/(a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3 + (a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x^4 + 2*(a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3)*x^2), 1/16*(2*(3*b^4*c^2 - 10*a*b^3*c*d + 7*a^2*b^2*d^2)*x^3 - 16*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (3*a^2*b^2*c^2 - 10*a^3*b*c*d + 15*a^4*d^2 + (3*b^4*c^2 - 10*a*b^3*c*d + 15*a^2*b^2*d^2)*x^4 + 2*(3*a*b^3*c^2 - 10*a^2*b^2*c*d + 15*a^3*b*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(5*a*b^3*c^2 - 14*a^2*b^2*c*d + 9*a^3*b*d^2)*x)/(a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3 + (a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x^4 + 2*(a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3)*x^2), 1/8*((3*b^4*c^2 - 10*a*b^3*c*d + 7*a^2*b^2*d^2)*x^3 + (3*a^2*b^2*c^2 - 10*a^3*b*c*d + 15*a^4*d^2 + (3*b^4*c^2 - 10*a*b^3*c*d + 15*a^2*b^2*d^2)*x^4 + 2*(3*a*b^3*c^2 - 10*a^2*b^2*c*d + 15*a^3*b*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 4*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + (5*a*b^3*c^2 - 14*a^2*b^2*c*d + 9*a^3*b*d^2)*x)/(a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3 + (a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x^4 + 2*(a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3)*x^2), 1/8*((3*b^4*c^2 - 10*a*b^3*c*d + 7*a^2*b^2*d^2)*x^3 + (3*a^2*b^2*c^2 - 10*a^3*b*c*d + 15*a^4*d^2 + (3*b^4*c^2 - 10*a*b^3*c*d + 15*a^2*b^2*d^2)*x^4 + 2*(3*a*b^3*c^2 - 10*a^2*b^2*c*d + 15*a^3*b*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 8*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (5*a*b^3*c^2 - 14*a^2*b^2*c*d + 9*a^3*b*d^2)*x)/(a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3 + (a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x^4 + 2*(a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3)*x^2)]","B",0
41,1,3251,0,8.542270," ","integrate(1/(b*x^2+a)^3/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 7 \, a^{2} b^{3} c d^{3} + 4 \, a^{3} b^{2} d^{4}\right)} x^{5} + 2 \, {\left(3 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d - 7 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} + 8 \, a^{4} b d^{4}\right)} x^{3} + {\left(3 \, a^{2} b^{3} c^{4} - 14 \, a^{3} b^{2} c^{3} d + 35 \, a^{4} b c^{2} d^{2} + {\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 35 \, a^{2} b^{3} c d^{3}\right)} x^{6} + {\left(3 \, b^{5} c^{4} - 8 \, a b^{4} c^{3} d + 7 \, a^{2} b^{3} c^{2} d^{2} + 70 \, a^{3} b^{2} c d^{3}\right)} x^{4} + {\left(6 \, a b^{4} c^{4} - 25 \, a^{2} b^{3} c^{3} d + 56 \, a^{3} b^{2} c^{2} d^{2} + 35 \, a^{4} b c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 4 \, {\left(7 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(7 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(7 \, a^{2} b^{3} c^{2} d^{2} + 13 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} x^{4} + {\left(14 \, a^{3} b^{2} c^{2} d^{2} + 5 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(5 \, a b^{4} c^{4} - 18 \, a^{2} b^{3} c^{3} d + 13 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + 4 \, a^{5} d^{4}\right)} x}{16 \, {\left(a^{4} b^{4} c^{6} - 4 \, a^{5} b^{3} c^{5} d + 6 \, a^{6} b^{2} c^{4} d^{2} - 4 \, a^{7} b c^{3} d^{3} + a^{8} c^{2} d^{4} + {\left(a^{2} b^{6} c^{5} d - 4 \, a^{3} b^{5} c^{4} d^{2} + 6 \, a^{4} b^{4} c^{3} d^{3} - 4 \, a^{5} b^{3} c^{2} d^{4} + a^{6} b^{2} c d^{5}\right)} x^{6} + {\left(a^{2} b^{6} c^{6} - 2 \, a^{3} b^{5} c^{5} d - 2 \, a^{4} b^{4} c^{4} d^{2} + 8 \, a^{5} b^{3} c^{3} d^{3} - 7 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{5} c^{6} - 7 \, a^{4} b^{4} c^{5} d + 8 \, a^{5} b^{3} c^{4} d^{2} - 2 \, a^{6} b^{2} c^{3} d^{3} - 2 \, a^{7} b c^{2} d^{4} + a^{8} c d^{5}\right)} x^{2}\right)}}, \frac{2 \, {\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 7 \, a^{2} b^{3} c d^{3} + 4 \, a^{3} b^{2} d^{4}\right)} x^{5} + 2 \, {\left(3 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d - 7 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} + 8 \, a^{4} b d^{4}\right)} x^{3} - 8 \, {\left(7 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(7 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(7 \, a^{2} b^{3} c^{2} d^{2} + 13 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} x^{4} + {\left(14 \, a^{3} b^{2} c^{2} d^{2} + 5 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(3 \, a^{2} b^{3} c^{4} - 14 \, a^{3} b^{2} c^{3} d + 35 \, a^{4} b c^{2} d^{2} + {\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 35 \, a^{2} b^{3} c d^{3}\right)} x^{6} + {\left(3 \, b^{5} c^{4} - 8 \, a b^{4} c^{3} d + 7 \, a^{2} b^{3} c^{2} d^{2} + 70 \, a^{3} b^{2} c d^{3}\right)} x^{4} + {\left(6 \, a b^{4} c^{4} - 25 \, a^{2} b^{3} c^{3} d + 56 \, a^{3} b^{2} c^{2} d^{2} + 35 \, a^{4} b c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a b^{4} c^{4} - 18 \, a^{2} b^{3} c^{3} d + 13 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + 4 \, a^{5} d^{4}\right)} x}{16 \, {\left(a^{4} b^{4} c^{6} - 4 \, a^{5} b^{3} c^{5} d + 6 \, a^{6} b^{2} c^{4} d^{2} - 4 \, a^{7} b c^{3} d^{3} + a^{8} c^{2} d^{4} + {\left(a^{2} b^{6} c^{5} d - 4 \, a^{3} b^{5} c^{4} d^{2} + 6 \, a^{4} b^{4} c^{3} d^{3} - 4 \, a^{5} b^{3} c^{2} d^{4} + a^{6} b^{2} c d^{5}\right)} x^{6} + {\left(a^{2} b^{6} c^{6} - 2 \, a^{3} b^{5} c^{5} d - 2 \, a^{4} b^{4} c^{4} d^{2} + 8 \, a^{5} b^{3} c^{3} d^{3} - 7 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{5} c^{6} - 7 \, a^{4} b^{4} c^{5} d + 8 \, a^{5} b^{3} c^{4} d^{2} - 2 \, a^{6} b^{2} c^{3} d^{3} - 2 \, a^{7} b c^{2} d^{4} + a^{8} c d^{5}\right)} x^{2}\right)}}, \frac{{\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 7 \, a^{2} b^{3} c d^{3} + 4 \, a^{3} b^{2} d^{4}\right)} x^{5} + {\left(3 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d - 7 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} + 8 \, a^{4} b d^{4}\right)} x^{3} + {\left(3 \, a^{2} b^{3} c^{4} - 14 \, a^{3} b^{2} c^{3} d + 35 \, a^{4} b c^{2} d^{2} + {\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 35 \, a^{2} b^{3} c d^{3}\right)} x^{6} + {\left(3 \, b^{5} c^{4} - 8 \, a b^{4} c^{3} d + 7 \, a^{2} b^{3} c^{2} d^{2} + 70 \, a^{3} b^{2} c d^{3}\right)} x^{4} + {\left(6 \, a b^{4} c^{4} - 25 \, a^{2} b^{3} c^{3} d + 56 \, a^{3} b^{2} c^{2} d^{2} + 35 \, a^{4} b c d^{3}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 2 \, {\left(7 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(7 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(7 \, a^{2} b^{3} c^{2} d^{2} + 13 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} x^{4} + {\left(14 \, a^{3} b^{2} c^{2} d^{2} + 5 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + {\left(5 \, a b^{4} c^{4} - 18 \, a^{2} b^{3} c^{3} d + 13 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + 4 \, a^{5} d^{4}\right)} x}{8 \, {\left(a^{4} b^{4} c^{6} - 4 \, a^{5} b^{3} c^{5} d + 6 \, a^{6} b^{2} c^{4} d^{2} - 4 \, a^{7} b c^{3} d^{3} + a^{8} c^{2} d^{4} + {\left(a^{2} b^{6} c^{5} d - 4 \, a^{3} b^{5} c^{4} d^{2} + 6 \, a^{4} b^{4} c^{3} d^{3} - 4 \, a^{5} b^{3} c^{2} d^{4} + a^{6} b^{2} c d^{5}\right)} x^{6} + {\left(a^{2} b^{6} c^{6} - 2 \, a^{3} b^{5} c^{5} d - 2 \, a^{4} b^{4} c^{4} d^{2} + 8 \, a^{5} b^{3} c^{3} d^{3} - 7 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{5} c^{6} - 7 \, a^{4} b^{4} c^{5} d + 8 \, a^{5} b^{3} c^{4} d^{2} - 2 \, a^{6} b^{2} c^{3} d^{3} - 2 \, a^{7} b c^{2} d^{4} + a^{8} c d^{5}\right)} x^{2}\right)}}, \frac{{\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 7 \, a^{2} b^{3} c d^{3} + 4 \, a^{3} b^{2} d^{4}\right)} x^{5} + {\left(3 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d - 7 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} + 8 \, a^{4} b d^{4}\right)} x^{3} + {\left(3 \, a^{2} b^{3} c^{4} - 14 \, a^{3} b^{2} c^{3} d + 35 \, a^{4} b c^{2} d^{2} + {\left(3 \, b^{5} c^{3} d - 14 \, a b^{4} c^{2} d^{2} + 35 \, a^{2} b^{3} c d^{3}\right)} x^{6} + {\left(3 \, b^{5} c^{4} - 8 \, a b^{4} c^{3} d + 7 \, a^{2} b^{3} c^{2} d^{2} + 70 \, a^{3} b^{2} c d^{3}\right)} x^{4} + {\left(6 \, a b^{4} c^{4} - 25 \, a^{2} b^{3} c^{3} d + 56 \, a^{3} b^{2} c^{2} d^{2} + 35 \, a^{4} b c d^{3}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 4 \, {\left(7 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(7 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(7 \, a^{2} b^{3} c^{2} d^{2} + 13 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} x^{4} + {\left(14 \, a^{3} b^{2} c^{2} d^{2} + 5 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(5 \, a b^{4} c^{4} - 18 \, a^{2} b^{3} c^{3} d + 13 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + 4 \, a^{5} d^{4}\right)} x}{8 \, {\left(a^{4} b^{4} c^{6} - 4 \, a^{5} b^{3} c^{5} d + 6 \, a^{6} b^{2} c^{4} d^{2} - 4 \, a^{7} b c^{3} d^{3} + a^{8} c^{2} d^{4} + {\left(a^{2} b^{6} c^{5} d - 4 \, a^{3} b^{5} c^{4} d^{2} + 6 \, a^{4} b^{4} c^{3} d^{3} - 4 \, a^{5} b^{3} c^{2} d^{4} + a^{6} b^{2} c d^{5}\right)} x^{6} + {\left(a^{2} b^{6} c^{6} - 2 \, a^{3} b^{5} c^{5} d - 2 \, a^{4} b^{4} c^{4} d^{2} + 8 \, a^{5} b^{3} c^{3} d^{3} - 7 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{5} c^{6} - 7 \, a^{4} b^{4} c^{5} d + 8 \, a^{5} b^{3} c^{4} d^{2} - 2 \, a^{6} b^{2} c^{3} d^{3} - 2 \, a^{7} b c^{2} d^{4} + a^{8} c d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(2*(3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 7*a^2*b^3*c*d^3 + 4*a^3*b^2*d^4)*x^5 + 2*(3*b^5*c^4 - 9*a*b^4*c^3*d - 7*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 + 8*a^4*b*d^4)*x^3 + (3*a^2*b^3*c^4 - 14*a^3*b^2*c^3*d + 35*a^4*b*c^2*d^2 + (3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 35*a^2*b^3*c*d^3)*x^6 + (3*b^5*c^4 - 8*a*b^4*c^3*d + 7*a^2*b^3*c^2*d^2 + 70*a^3*b^2*c*d^3)*x^4 + (6*a*b^4*c^4 - 25*a^2*b^3*c^3*d + 56*a^3*b^2*c^2*d^2 + 35*a^4*b*c*d^3)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 4*(7*a^4*b*c^2*d^2 - a^5*c*d^3 + (7*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (7*a^2*b^3*c^2*d^2 + 13*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*x^4 + (14*a^3*b^2*c^2*d^2 + 5*a^4*b*c*d^3 - a^5*d^4)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(5*a*b^4*c^4 - 18*a^2*b^3*c^3*d + 13*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + 4*a^5*d^4)*x)/(a^4*b^4*c^6 - 4*a^5*b^3*c^5*d + 6*a^6*b^2*c^4*d^2 - 4*a^7*b*c^3*d^3 + a^8*c^2*d^4 + (a^2*b^6*c^5*d - 4*a^3*b^5*c^4*d^2 + 6*a^4*b^4*c^3*d^3 - 4*a^5*b^3*c^2*d^4 + a^6*b^2*c*d^5)*x^6 + (a^2*b^6*c^6 - 2*a^3*b^5*c^5*d - 2*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 7*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5)*x^4 + (2*a^3*b^5*c^6 - 7*a^4*b^4*c^5*d + 8*a^5*b^3*c^4*d^2 - 2*a^6*b^2*c^3*d^3 - 2*a^7*b*c^2*d^4 + a^8*c*d^5)*x^2), 1/16*(2*(3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 7*a^2*b^3*c*d^3 + 4*a^3*b^2*d^4)*x^5 + 2*(3*b^5*c^4 - 9*a*b^4*c^3*d - 7*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 + 8*a^4*b*d^4)*x^3 - 8*(7*a^4*b*c^2*d^2 - a^5*c*d^3 + (7*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (7*a^2*b^3*c^2*d^2 + 13*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*x^4 + (14*a^3*b^2*c^2*d^2 + 5*a^4*b*c*d^3 - a^5*d^4)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (3*a^2*b^3*c^4 - 14*a^3*b^2*c^3*d + 35*a^4*b*c^2*d^2 + (3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 35*a^2*b^3*c*d^3)*x^6 + (3*b^5*c^4 - 8*a*b^4*c^3*d + 7*a^2*b^3*c^2*d^2 + 70*a^3*b^2*c*d^3)*x^4 + (6*a*b^4*c^4 - 25*a^2*b^3*c^3*d + 56*a^3*b^2*c^2*d^2 + 35*a^4*b*c*d^3)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(5*a*b^4*c^4 - 18*a^2*b^3*c^3*d + 13*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + 4*a^5*d^4)*x)/(a^4*b^4*c^6 - 4*a^5*b^3*c^5*d + 6*a^6*b^2*c^4*d^2 - 4*a^7*b*c^3*d^3 + a^8*c^2*d^4 + (a^2*b^6*c^5*d - 4*a^3*b^5*c^4*d^2 + 6*a^4*b^4*c^3*d^3 - 4*a^5*b^3*c^2*d^4 + a^6*b^2*c*d^5)*x^6 + (a^2*b^6*c^6 - 2*a^3*b^5*c^5*d - 2*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 7*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5)*x^4 + (2*a^3*b^5*c^6 - 7*a^4*b^4*c^5*d + 8*a^5*b^3*c^4*d^2 - 2*a^6*b^2*c^3*d^3 - 2*a^7*b*c^2*d^4 + a^8*c*d^5)*x^2), 1/8*((3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 7*a^2*b^3*c*d^3 + 4*a^3*b^2*d^4)*x^5 + (3*b^5*c^4 - 9*a*b^4*c^3*d - 7*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 + 8*a^4*b*d^4)*x^3 + (3*a^2*b^3*c^4 - 14*a^3*b^2*c^3*d + 35*a^4*b*c^2*d^2 + (3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 35*a^2*b^3*c*d^3)*x^6 + (3*b^5*c^4 - 8*a*b^4*c^3*d + 7*a^2*b^3*c^2*d^2 + 70*a^3*b^2*c*d^3)*x^4 + (6*a*b^4*c^4 - 25*a^2*b^3*c^3*d + 56*a^3*b^2*c^2*d^2 + 35*a^4*b*c*d^3)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 2*(7*a^4*b*c^2*d^2 - a^5*c*d^3 + (7*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (7*a^2*b^3*c^2*d^2 + 13*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*x^4 + (14*a^3*b^2*c^2*d^2 + 5*a^4*b*c*d^3 - a^5*d^4)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + (5*a*b^4*c^4 - 18*a^2*b^3*c^3*d + 13*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + 4*a^5*d^4)*x)/(a^4*b^4*c^6 - 4*a^5*b^3*c^5*d + 6*a^6*b^2*c^4*d^2 - 4*a^7*b*c^3*d^3 + a^8*c^2*d^4 + (a^2*b^6*c^5*d - 4*a^3*b^5*c^4*d^2 + 6*a^4*b^4*c^3*d^3 - 4*a^5*b^3*c^2*d^4 + a^6*b^2*c*d^5)*x^6 + (a^2*b^6*c^6 - 2*a^3*b^5*c^5*d - 2*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 7*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5)*x^4 + (2*a^3*b^5*c^6 - 7*a^4*b^4*c^5*d + 8*a^5*b^3*c^4*d^2 - 2*a^6*b^2*c^3*d^3 - 2*a^7*b*c^2*d^4 + a^8*c*d^5)*x^2), 1/8*((3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 7*a^2*b^3*c*d^3 + 4*a^3*b^2*d^4)*x^5 + (3*b^5*c^4 - 9*a*b^4*c^3*d - 7*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 + 8*a^4*b*d^4)*x^3 + (3*a^2*b^3*c^4 - 14*a^3*b^2*c^3*d + 35*a^4*b*c^2*d^2 + (3*b^5*c^3*d - 14*a*b^4*c^2*d^2 + 35*a^2*b^3*c*d^3)*x^6 + (3*b^5*c^4 - 8*a*b^4*c^3*d + 7*a^2*b^3*c^2*d^2 + 70*a^3*b^2*c*d^3)*x^4 + (6*a*b^4*c^4 - 25*a^2*b^3*c^3*d + 56*a^3*b^2*c^2*d^2 + 35*a^4*b*c*d^3)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 4*(7*a^4*b*c^2*d^2 - a^5*c*d^3 + (7*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (7*a^2*b^3*c^2*d^2 + 13*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*x^4 + (14*a^3*b^2*c^2*d^2 + 5*a^4*b*c*d^3 - a^5*d^4)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (5*a*b^4*c^4 - 18*a^2*b^3*c^3*d + 13*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + 4*a^5*d^4)*x)/(a^4*b^4*c^6 - 4*a^5*b^3*c^5*d + 6*a^6*b^2*c^4*d^2 - 4*a^7*b*c^3*d^3 + a^8*c^2*d^4 + (a^2*b^6*c^5*d - 4*a^3*b^5*c^4*d^2 + 6*a^4*b^4*c^3*d^3 - 4*a^5*b^3*c^2*d^4 + a^6*b^2*c*d^5)*x^6 + (a^2*b^6*c^6 - 2*a^3*b^5*c^5*d - 2*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 7*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5)*x^4 + (2*a^3*b^5*c^6 - 7*a^4*b^4*c^5*d + 8*a^5*b^3*c^4*d^2 - 2*a^6*b^2*c^3*d^3 - 2*a^7*b*c^2*d^4 + a^8*c*d^5)*x^2)]","B",0
42,1,5070,0,32.350894," ","integrate(1/(b*x^2+a)^3/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 6 \, a^{3} b^{3} c d^{5} - a^{4} b^{2} d^{6}\right)} x^{7} + 2 \, {\left(6 \, b^{6} c^{5} d - 31 \, a b^{5} c^{4} d^{2} - 9 \, a^{2} b^{4} c^{3} d^{3} + 9 \, a^{3} b^{3} c^{2} d^{4} + 31 \, a^{4} b^{2} c d^{5} - 6 \, a^{5} b d^{6}\right)} x^{5} + 2 \, {\left(3 \, b^{6} c^{6} - 8 \, a b^{5} c^{5} d - 29 \, a^{2} b^{4} c^{4} d^{2} + 29 \, a^{4} b^{2} c^{2} d^{4} + 8 \, a^{5} b c d^{5} - 3 \, a^{6} d^{6}\right)} x^{3} - 3 \, {\left(a^{2} b^{4} c^{6} - 6 \, a^{3} b^{3} c^{5} d + 21 \, a^{4} b^{2} c^{4} d^{2} + {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 21 \, a^{2} b^{4} c^{2} d^{4}\right)} x^{8} + 2 \, {\left(b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2} + 15 \, a^{2} b^{4} c^{3} d^{3} + 21 \, a^{3} b^{3} c^{2} d^{4}\right)} x^{6} + {\left(b^{6} c^{6} - 2 \, a b^{5} c^{5} d - 2 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} + 21 \, a^{4} b^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d + 15 \, a^{3} b^{3} c^{4} d^{2} + 21 \, a^{4} b^{2} c^{3} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 3 \, {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 6 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(21 \, a^{2} b^{4} c^{2} d^{4} - 6 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{8} + 2 \, {\left(21 \, a^{2} b^{4} c^{3} d^{3} + 15 \, a^{3} b^{3} c^{2} d^{4} - 5 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{6} + {\left(21 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} - 2 \, a^{4} b^{2} c^{2} d^{4} - 2 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x^{4} + 2 \, {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 15 \, a^{4} b^{2} c^{3} d^{3} - 5 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(5 \, a b^{5} c^{6} - 22 \, a^{2} b^{4} c^{5} d + 17 \, a^{3} b^{3} c^{4} d^{2} - 17 \, a^{4} b^{2} c^{3} d^{3} + 22 \, a^{5} b c^{2} d^{4} - 5 \, a^{6} c d^{5}\right)} x}{16 \, {\left(a^{4} b^{5} c^{9} - 5 \, a^{5} b^{4} c^{8} d + 10 \, a^{6} b^{3} c^{7} d^{2} - 10 \, a^{7} b^{2} c^{6} d^{3} + 5 \, a^{8} b c^{5} d^{4} - a^{9} c^{4} d^{5} + {\left(a^{2} b^{7} c^{7} d^{2} - 5 \, a^{3} b^{6} c^{6} d^{3} + 10 \, a^{4} b^{5} c^{5} d^{4} - 10 \, a^{5} b^{4} c^{4} d^{5} + 5 \, a^{6} b^{3} c^{3} d^{6} - a^{7} b^{2} c^{2} d^{7}\right)} x^{8} + 2 \, {\left(a^{2} b^{7} c^{8} d - 4 \, a^{3} b^{6} c^{7} d^{2} + 5 \, a^{4} b^{5} c^{6} d^{3} - 5 \, a^{6} b^{3} c^{4} d^{5} + 4 \, a^{7} b^{2} c^{3} d^{6} - a^{8} b c^{2} d^{7}\right)} x^{6} + {\left(a^{2} b^{7} c^{9} - a^{3} b^{6} c^{8} d - 9 \, a^{4} b^{5} c^{7} d^{2} + 25 \, a^{5} b^{4} c^{6} d^{3} - 25 \, a^{6} b^{3} c^{5} d^{4} + 9 \, a^{7} b^{2} c^{4} d^{5} + a^{8} b c^{3} d^{6} - a^{9} c^{2} d^{7}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{9} - 4 \, a^{4} b^{5} c^{8} d + 5 \, a^{5} b^{4} c^{7} d^{2} - 5 \, a^{7} b^{2} c^{5} d^{4} + 4 \, a^{8} b c^{4} d^{5} - a^{9} c^{3} d^{6}\right)} x^{2}\right)}}, \frac{6 \, {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 6 \, a^{3} b^{3} c d^{5} - a^{4} b^{2} d^{6}\right)} x^{7} + 2 \, {\left(6 \, b^{6} c^{5} d - 31 \, a b^{5} c^{4} d^{2} - 9 \, a^{2} b^{4} c^{3} d^{3} + 9 \, a^{3} b^{3} c^{2} d^{4} + 31 \, a^{4} b^{2} c d^{5} - 6 \, a^{5} b d^{6}\right)} x^{5} + 2 \, {\left(3 \, b^{6} c^{6} - 8 \, a b^{5} c^{5} d - 29 \, a^{2} b^{4} c^{4} d^{2} + 29 \, a^{4} b^{2} c^{2} d^{4} + 8 \, a^{5} b c d^{5} - 3 \, a^{6} d^{6}\right)} x^{3} - 6 \, {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 6 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(21 \, a^{2} b^{4} c^{2} d^{4} - 6 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{8} + 2 \, {\left(21 \, a^{2} b^{4} c^{3} d^{3} + 15 \, a^{3} b^{3} c^{2} d^{4} - 5 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{6} + {\left(21 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} - 2 \, a^{4} b^{2} c^{2} d^{4} - 2 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x^{4} + 2 \, {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 15 \, a^{4} b^{2} c^{3} d^{3} - 5 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - 3 \, {\left(a^{2} b^{4} c^{6} - 6 \, a^{3} b^{3} c^{5} d + 21 \, a^{4} b^{2} c^{4} d^{2} + {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 21 \, a^{2} b^{4} c^{2} d^{4}\right)} x^{8} + 2 \, {\left(b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2} + 15 \, a^{2} b^{4} c^{3} d^{3} + 21 \, a^{3} b^{3} c^{2} d^{4}\right)} x^{6} + {\left(b^{6} c^{6} - 2 \, a b^{5} c^{5} d - 2 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} + 21 \, a^{4} b^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d + 15 \, a^{3} b^{3} c^{4} d^{2} + 21 \, a^{4} b^{2} c^{3} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a b^{5} c^{6} - 22 \, a^{2} b^{4} c^{5} d + 17 \, a^{3} b^{3} c^{4} d^{2} - 17 \, a^{4} b^{2} c^{3} d^{3} + 22 \, a^{5} b c^{2} d^{4} - 5 \, a^{6} c d^{5}\right)} x}{16 \, {\left(a^{4} b^{5} c^{9} - 5 \, a^{5} b^{4} c^{8} d + 10 \, a^{6} b^{3} c^{7} d^{2} - 10 \, a^{7} b^{2} c^{6} d^{3} + 5 \, a^{8} b c^{5} d^{4} - a^{9} c^{4} d^{5} + {\left(a^{2} b^{7} c^{7} d^{2} - 5 \, a^{3} b^{6} c^{6} d^{3} + 10 \, a^{4} b^{5} c^{5} d^{4} - 10 \, a^{5} b^{4} c^{4} d^{5} + 5 \, a^{6} b^{3} c^{3} d^{6} - a^{7} b^{2} c^{2} d^{7}\right)} x^{8} + 2 \, {\left(a^{2} b^{7} c^{8} d - 4 \, a^{3} b^{6} c^{7} d^{2} + 5 \, a^{4} b^{5} c^{6} d^{3} - 5 \, a^{6} b^{3} c^{4} d^{5} + 4 \, a^{7} b^{2} c^{3} d^{6} - a^{8} b c^{2} d^{7}\right)} x^{6} + {\left(a^{2} b^{7} c^{9} - a^{3} b^{6} c^{8} d - 9 \, a^{4} b^{5} c^{7} d^{2} + 25 \, a^{5} b^{4} c^{6} d^{3} - 25 \, a^{6} b^{3} c^{5} d^{4} + 9 \, a^{7} b^{2} c^{4} d^{5} + a^{8} b c^{3} d^{6} - a^{9} c^{2} d^{7}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{9} - 4 \, a^{4} b^{5} c^{8} d + 5 \, a^{5} b^{4} c^{7} d^{2} - 5 \, a^{7} b^{2} c^{5} d^{4} + 4 \, a^{8} b c^{4} d^{5} - a^{9} c^{3} d^{6}\right)} x^{2}\right)}}, \frac{6 \, {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 6 \, a^{3} b^{3} c d^{5} - a^{4} b^{2} d^{6}\right)} x^{7} + 2 \, {\left(6 \, b^{6} c^{5} d - 31 \, a b^{5} c^{4} d^{2} - 9 \, a^{2} b^{4} c^{3} d^{3} + 9 \, a^{3} b^{3} c^{2} d^{4} + 31 \, a^{4} b^{2} c d^{5} - 6 \, a^{5} b d^{6}\right)} x^{5} + 2 \, {\left(3 \, b^{6} c^{6} - 8 \, a b^{5} c^{5} d - 29 \, a^{2} b^{4} c^{4} d^{2} + 29 \, a^{4} b^{2} c^{2} d^{4} + 8 \, a^{5} b c d^{5} - 3 \, a^{6} d^{6}\right)} x^{3} + 6 \, {\left(a^{2} b^{4} c^{6} - 6 \, a^{3} b^{3} c^{5} d + 21 \, a^{4} b^{2} c^{4} d^{2} + {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 21 \, a^{2} b^{4} c^{2} d^{4}\right)} x^{8} + 2 \, {\left(b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2} + 15 \, a^{2} b^{4} c^{3} d^{3} + 21 \, a^{3} b^{3} c^{2} d^{4}\right)} x^{6} + {\left(b^{6} c^{6} - 2 \, a b^{5} c^{5} d - 2 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} + 21 \, a^{4} b^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d + 15 \, a^{3} b^{3} c^{4} d^{2} + 21 \, a^{4} b^{2} c^{3} d^{3}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 6 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(21 \, a^{2} b^{4} c^{2} d^{4} - 6 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{8} + 2 \, {\left(21 \, a^{2} b^{4} c^{3} d^{3} + 15 \, a^{3} b^{3} c^{2} d^{4} - 5 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{6} + {\left(21 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} - 2 \, a^{4} b^{2} c^{2} d^{4} - 2 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x^{4} + 2 \, {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 15 \, a^{4} b^{2} c^{3} d^{3} - 5 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(5 \, a b^{5} c^{6} - 22 \, a^{2} b^{4} c^{5} d + 17 \, a^{3} b^{3} c^{4} d^{2} - 17 \, a^{4} b^{2} c^{3} d^{3} + 22 \, a^{5} b c^{2} d^{4} - 5 \, a^{6} c d^{5}\right)} x}{16 \, {\left(a^{4} b^{5} c^{9} - 5 \, a^{5} b^{4} c^{8} d + 10 \, a^{6} b^{3} c^{7} d^{2} - 10 \, a^{7} b^{2} c^{6} d^{3} + 5 \, a^{8} b c^{5} d^{4} - a^{9} c^{4} d^{5} + {\left(a^{2} b^{7} c^{7} d^{2} - 5 \, a^{3} b^{6} c^{6} d^{3} + 10 \, a^{4} b^{5} c^{5} d^{4} - 10 \, a^{5} b^{4} c^{4} d^{5} + 5 \, a^{6} b^{3} c^{3} d^{6} - a^{7} b^{2} c^{2} d^{7}\right)} x^{8} + 2 \, {\left(a^{2} b^{7} c^{8} d - 4 \, a^{3} b^{6} c^{7} d^{2} + 5 \, a^{4} b^{5} c^{6} d^{3} - 5 \, a^{6} b^{3} c^{4} d^{5} + 4 \, a^{7} b^{2} c^{3} d^{6} - a^{8} b c^{2} d^{7}\right)} x^{6} + {\left(a^{2} b^{7} c^{9} - a^{3} b^{6} c^{8} d - 9 \, a^{4} b^{5} c^{7} d^{2} + 25 \, a^{5} b^{4} c^{6} d^{3} - 25 \, a^{6} b^{3} c^{5} d^{4} + 9 \, a^{7} b^{2} c^{4} d^{5} + a^{8} b c^{3} d^{6} - a^{9} c^{2} d^{7}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{9} - 4 \, a^{4} b^{5} c^{8} d + 5 \, a^{5} b^{4} c^{7} d^{2} - 5 \, a^{7} b^{2} c^{5} d^{4} + 4 \, a^{8} b c^{4} d^{5} - a^{9} c^{3} d^{6}\right)} x^{2}\right)}}, \frac{3 \, {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 6 \, a^{3} b^{3} c d^{5} - a^{4} b^{2} d^{6}\right)} x^{7} + {\left(6 \, b^{6} c^{5} d - 31 \, a b^{5} c^{4} d^{2} - 9 \, a^{2} b^{4} c^{3} d^{3} + 9 \, a^{3} b^{3} c^{2} d^{4} + 31 \, a^{4} b^{2} c d^{5} - 6 \, a^{5} b d^{6}\right)} x^{5} + {\left(3 \, b^{6} c^{6} - 8 \, a b^{5} c^{5} d - 29 \, a^{2} b^{4} c^{4} d^{2} + 29 \, a^{4} b^{2} c^{2} d^{4} + 8 \, a^{5} b c d^{5} - 3 \, a^{6} d^{6}\right)} x^{3} + 3 \, {\left(a^{2} b^{4} c^{6} - 6 \, a^{3} b^{3} c^{5} d + 21 \, a^{4} b^{2} c^{4} d^{2} + {\left(b^{6} c^{4} d^{2} - 6 \, a b^{5} c^{3} d^{3} + 21 \, a^{2} b^{4} c^{2} d^{4}\right)} x^{8} + 2 \, {\left(b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2} + 15 \, a^{2} b^{4} c^{3} d^{3} + 21 \, a^{3} b^{3} c^{2} d^{4}\right)} x^{6} + {\left(b^{6} c^{6} - 2 \, a b^{5} c^{5} d - 2 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} + 21 \, a^{4} b^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d + 15 \, a^{3} b^{3} c^{4} d^{2} + 21 \, a^{4} b^{2} c^{3} d^{3}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left(21 \, a^{4} b^{2} c^{4} d^{2} - 6 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(21 \, a^{2} b^{4} c^{2} d^{4} - 6 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{8} + 2 \, {\left(21 \, a^{2} b^{4} c^{3} d^{3} + 15 \, a^{3} b^{3} c^{2} d^{4} - 5 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{6} + {\left(21 \, a^{2} b^{4} c^{4} d^{2} + 78 \, a^{3} b^{3} c^{3} d^{3} - 2 \, a^{4} b^{2} c^{2} d^{4} - 2 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x^{4} + 2 \, {\left(21 \, a^{3} b^{3} c^{4} d^{2} + 15 \, a^{4} b^{2} c^{3} d^{3} - 5 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(5 \, a b^{5} c^{6} - 22 \, a^{2} b^{4} c^{5} d + 17 \, a^{3} b^{3} c^{4} d^{2} - 17 \, a^{4} b^{2} c^{3} d^{3} + 22 \, a^{5} b c^{2} d^{4} - 5 \, a^{6} c d^{5}\right)} x}{8 \, {\left(a^{4} b^{5} c^{9} - 5 \, a^{5} b^{4} c^{8} d + 10 \, a^{6} b^{3} c^{7} d^{2} - 10 \, a^{7} b^{2} c^{6} d^{3} + 5 \, a^{8} b c^{5} d^{4} - a^{9} c^{4} d^{5} + {\left(a^{2} b^{7} c^{7} d^{2} - 5 \, a^{3} b^{6} c^{6} d^{3} + 10 \, a^{4} b^{5} c^{5} d^{4} - 10 \, a^{5} b^{4} c^{4} d^{5} + 5 \, a^{6} b^{3} c^{3} d^{6} - a^{7} b^{2} c^{2} d^{7}\right)} x^{8} + 2 \, {\left(a^{2} b^{7} c^{8} d - 4 \, a^{3} b^{6} c^{7} d^{2} + 5 \, a^{4} b^{5} c^{6} d^{3} - 5 \, a^{6} b^{3} c^{4} d^{5} + 4 \, a^{7} b^{2} c^{3} d^{6} - a^{8} b c^{2} d^{7}\right)} x^{6} + {\left(a^{2} b^{7} c^{9} - a^{3} b^{6} c^{8} d - 9 \, a^{4} b^{5} c^{7} d^{2} + 25 \, a^{5} b^{4} c^{6} d^{3} - 25 \, a^{6} b^{3} c^{5} d^{4} + 9 \, a^{7} b^{2} c^{4} d^{5} + a^{8} b c^{3} d^{6} - a^{9} c^{2} d^{7}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{9} - 4 \, a^{4} b^{5} c^{8} d + 5 \, a^{5} b^{4} c^{7} d^{2} - 5 \, a^{7} b^{2} c^{5} d^{4} + 4 \, a^{8} b c^{4} d^{5} - a^{9} c^{3} d^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(6*(b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 6*a^3*b^3*c*d^5 - a^4*b^2*d^6)*x^7 + 2*(6*b^6*c^5*d - 31*a*b^5*c^4*d^2 - 9*a^2*b^4*c^3*d^3 + 9*a^3*b^3*c^2*d^4 + 31*a^4*b^2*c*d^5 - 6*a^5*b*d^6)*x^5 + 2*(3*b^6*c^6 - 8*a*b^5*c^5*d - 29*a^2*b^4*c^4*d^2 + 29*a^4*b^2*c^2*d^4 + 8*a^5*b*c*d^5 - 3*a^6*d^6)*x^3 - 3*(a^2*b^4*c^6 - 6*a^3*b^3*c^5*d + 21*a^4*b^2*c^4*d^2 + (b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 21*a^2*b^4*c^2*d^4)*x^8 + 2*(b^6*c^5*d - 5*a*b^5*c^4*d^2 + 15*a^2*b^4*c^3*d^3 + 21*a^3*b^3*c^2*d^4)*x^6 + (b^6*c^6 - 2*a*b^5*c^5*d - 2*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 + 21*a^4*b^2*c^2*d^4)*x^4 + 2*(a*b^5*c^6 - 5*a^2*b^4*c^5*d + 15*a^3*b^3*c^4*d^2 + 21*a^4*b^2*c^3*d^3)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 3*(21*a^4*b^2*c^4*d^2 - 6*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (21*a^2*b^4*c^2*d^4 - 6*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^8 + 2*(21*a^2*b^4*c^3*d^3 + 15*a^3*b^3*c^2*d^4 - 5*a^4*b^2*c*d^5 + a^5*b*d^6)*x^6 + (21*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 - 2*a^4*b^2*c^2*d^4 - 2*a^5*b*c*d^5 + a^6*d^6)*x^4 + 2*(21*a^3*b^3*c^4*d^2 + 15*a^4*b^2*c^3*d^3 - 5*a^5*b*c^2*d^4 + a^6*c*d^5)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(5*a*b^5*c^6 - 22*a^2*b^4*c^5*d + 17*a^3*b^3*c^4*d^2 - 17*a^4*b^2*c^3*d^3 + 22*a^5*b*c^2*d^4 - 5*a^6*c*d^5)*x)/(a^4*b^5*c^9 - 5*a^5*b^4*c^8*d + 10*a^6*b^3*c^7*d^2 - 10*a^7*b^2*c^6*d^3 + 5*a^8*b*c^5*d^4 - a^9*c^4*d^5 + (a^2*b^7*c^7*d^2 - 5*a^3*b^6*c^6*d^3 + 10*a^4*b^5*c^5*d^4 - 10*a^5*b^4*c^4*d^5 + 5*a^6*b^3*c^3*d^6 - a^7*b^2*c^2*d^7)*x^8 + 2*(a^2*b^7*c^8*d - 4*a^3*b^6*c^7*d^2 + 5*a^4*b^5*c^6*d^3 - 5*a^6*b^3*c^4*d^5 + 4*a^7*b^2*c^3*d^6 - a^8*b*c^2*d^7)*x^6 + (a^2*b^7*c^9 - a^3*b^6*c^8*d - 9*a^4*b^5*c^7*d^2 + 25*a^5*b^4*c^6*d^3 - 25*a^6*b^3*c^5*d^4 + 9*a^7*b^2*c^4*d^5 + a^8*b*c^3*d^6 - a^9*c^2*d^7)*x^4 + 2*(a^3*b^6*c^9 - 4*a^4*b^5*c^8*d + 5*a^5*b^4*c^7*d^2 - 5*a^7*b^2*c^5*d^4 + 4*a^8*b*c^4*d^5 - a^9*c^3*d^6)*x^2), 1/16*(6*(b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 6*a^3*b^3*c*d^5 - a^4*b^2*d^6)*x^7 + 2*(6*b^6*c^5*d - 31*a*b^5*c^4*d^2 - 9*a^2*b^4*c^3*d^3 + 9*a^3*b^3*c^2*d^4 + 31*a^4*b^2*c*d^5 - 6*a^5*b*d^6)*x^5 + 2*(3*b^6*c^6 - 8*a*b^5*c^5*d - 29*a^2*b^4*c^4*d^2 + 29*a^4*b^2*c^2*d^4 + 8*a^5*b*c*d^5 - 3*a^6*d^6)*x^3 - 6*(21*a^4*b^2*c^4*d^2 - 6*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (21*a^2*b^4*c^2*d^4 - 6*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^8 + 2*(21*a^2*b^4*c^3*d^3 + 15*a^3*b^3*c^2*d^4 - 5*a^4*b^2*c*d^5 + a^5*b*d^6)*x^6 + (21*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 - 2*a^4*b^2*c^2*d^4 - 2*a^5*b*c*d^5 + a^6*d^6)*x^4 + 2*(21*a^3*b^3*c^4*d^2 + 15*a^4*b^2*c^3*d^3 - 5*a^5*b*c^2*d^4 + a^6*c*d^5)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - 3*(a^2*b^4*c^6 - 6*a^3*b^3*c^5*d + 21*a^4*b^2*c^4*d^2 + (b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 21*a^2*b^4*c^2*d^4)*x^8 + 2*(b^6*c^5*d - 5*a*b^5*c^4*d^2 + 15*a^2*b^4*c^3*d^3 + 21*a^3*b^3*c^2*d^4)*x^6 + (b^6*c^6 - 2*a*b^5*c^5*d - 2*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 + 21*a^4*b^2*c^2*d^4)*x^4 + 2*(a*b^5*c^6 - 5*a^2*b^4*c^5*d + 15*a^3*b^3*c^4*d^2 + 21*a^4*b^2*c^3*d^3)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(5*a*b^5*c^6 - 22*a^2*b^4*c^5*d + 17*a^3*b^3*c^4*d^2 - 17*a^4*b^2*c^3*d^3 + 22*a^5*b*c^2*d^4 - 5*a^6*c*d^5)*x)/(a^4*b^5*c^9 - 5*a^5*b^4*c^8*d + 10*a^6*b^3*c^7*d^2 - 10*a^7*b^2*c^6*d^3 + 5*a^8*b*c^5*d^4 - a^9*c^4*d^5 + (a^2*b^7*c^7*d^2 - 5*a^3*b^6*c^6*d^3 + 10*a^4*b^5*c^5*d^4 - 10*a^5*b^4*c^4*d^5 + 5*a^6*b^3*c^3*d^6 - a^7*b^2*c^2*d^7)*x^8 + 2*(a^2*b^7*c^8*d - 4*a^3*b^6*c^7*d^2 + 5*a^4*b^5*c^6*d^3 - 5*a^6*b^3*c^4*d^5 + 4*a^7*b^2*c^3*d^6 - a^8*b*c^2*d^7)*x^6 + (a^2*b^7*c^9 - a^3*b^6*c^8*d - 9*a^4*b^5*c^7*d^2 + 25*a^5*b^4*c^6*d^3 - 25*a^6*b^3*c^5*d^4 + 9*a^7*b^2*c^4*d^5 + a^8*b*c^3*d^6 - a^9*c^2*d^7)*x^4 + 2*(a^3*b^6*c^9 - 4*a^4*b^5*c^8*d + 5*a^5*b^4*c^7*d^2 - 5*a^7*b^2*c^5*d^4 + 4*a^8*b*c^4*d^5 - a^9*c^3*d^6)*x^2), 1/16*(6*(b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 6*a^3*b^3*c*d^5 - a^4*b^2*d^6)*x^7 + 2*(6*b^6*c^5*d - 31*a*b^5*c^4*d^2 - 9*a^2*b^4*c^3*d^3 + 9*a^3*b^3*c^2*d^4 + 31*a^4*b^2*c*d^5 - 6*a^5*b*d^6)*x^5 + 2*(3*b^6*c^6 - 8*a*b^5*c^5*d - 29*a^2*b^4*c^4*d^2 + 29*a^4*b^2*c^2*d^4 + 8*a^5*b*c*d^5 - 3*a^6*d^6)*x^3 + 6*(a^2*b^4*c^6 - 6*a^3*b^3*c^5*d + 21*a^4*b^2*c^4*d^2 + (b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 21*a^2*b^4*c^2*d^4)*x^8 + 2*(b^6*c^5*d - 5*a*b^5*c^4*d^2 + 15*a^2*b^4*c^3*d^3 + 21*a^3*b^3*c^2*d^4)*x^6 + (b^6*c^6 - 2*a*b^5*c^5*d - 2*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 + 21*a^4*b^2*c^2*d^4)*x^4 + 2*(a*b^5*c^6 - 5*a^2*b^4*c^5*d + 15*a^3*b^3*c^4*d^2 + 21*a^4*b^2*c^3*d^3)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*(21*a^4*b^2*c^4*d^2 - 6*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (21*a^2*b^4*c^2*d^4 - 6*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^8 + 2*(21*a^2*b^4*c^3*d^3 + 15*a^3*b^3*c^2*d^4 - 5*a^4*b^2*c*d^5 + a^5*b*d^6)*x^6 + (21*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 - 2*a^4*b^2*c^2*d^4 - 2*a^5*b*c*d^5 + a^6*d^6)*x^4 + 2*(21*a^3*b^3*c^4*d^2 + 15*a^4*b^2*c^3*d^3 - 5*a^5*b*c^2*d^4 + a^6*c*d^5)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(5*a*b^5*c^6 - 22*a^2*b^4*c^5*d + 17*a^3*b^3*c^4*d^2 - 17*a^4*b^2*c^3*d^3 + 22*a^5*b*c^2*d^4 - 5*a^6*c*d^5)*x)/(a^4*b^5*c^9 - 5*a^5*b^4*c^8*d + 10*a^6*b^3*c^7*d^2 - 10*a^7*b^2*c^6*d^3 + 5*a^8*b*c^5*d^4 - a^9*c^4*d^5 + (a^2*b^7*c^7*d^2 - 5*a^3*b^6*c^6*d^3 + 10*a^4*b^5*c^5*d^4 - 10*a^5*b^4*c^4*d^5 + 5*a^6*b^3*c^3*d^6 - a^7*b^2*c^2*d^7)*x^8 + 2*(a^2*b^7*c^8*d - 4*a^3*b^6*c^7*d^2 + 5*a^4*b^5*c^6*d^3 - 5*a^6*b^3*c^4*d^5 + 4*a^7*b^2*c^3*d^6 - a^8*b*c^2*d^7)*x^6 + (a^2*b^7*c^9 - a^3*b^6*c^8*d - 9*a^4*b^5*c^7*d^2 + 25*a^5*b^4*c^6*d^3 - 25*a^6*b^3*c^5*d^4 + 9*a^7*b^2*c^4*d^5 + a^8*b*c^3*d^6 - a^9*c^2*d^7)*x^4 + 2*(a^3*b^6*c^9 - 4*a^4*b^5*c^8*d + 5*a^5*b^4*c^7*d^2 - 5*a^7*b^2*c^5*d^4 + 4*a^8*b*c^4*d^5 - a^9*c^3*d^6)*x^2), 1/8*(3*(b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 6*a^3*b^3*c*d^5 - a^4*b^2*d^6)*x^7 + (6*b^6*c^5*d - 31*a*b^5*c^4*d^2 - 9*a^2*b^4*c^3*d^3 + 9*a^3*b^3*c^2*d^4 + 31*a^4*b^2*c*d^5 - 6*a^5*b*d^6)*x^5 + (3*b^6*c^6 - 8*a*b^5*c^5*d - 29*a^2*b^4*c^4*d^2 + 29*a^4*b^2*c^2*d^4 + 8*a^5*b*c*d^5 - 3*a^6*d^6)*x^3 + 3*(a^2*b^4*c^6 - 6*a^3*b^3*c^5*d + 21*a^4*b^2*c^4*d^2 + (b^6*c^4*d^2 - 6*a*b^5*c^3*d^3 + 21*a^2*b^4*c^2*d^4)*x^8 + 2*(b^6*c^5*d - 5*a*b^5*c^4*d^2 + 15*a^2*b^4*c^3*d^3 + 21*a^3*b^3*c^2*d^4)*x^6 + (b^6*c^6 - 2*a*b^5*c^5*d - 2*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 + 21*a^4*b^2*c^2*d^4)*x^4 + 2*(a*b^5*c^6 - 5*a^2*b^4*c^5*d + 15*a^3*b^3*c^4*d^2 + 21*a^4*b^2*c^3*d^3)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*(21*a^4*b^2*c^4*d^2 - 6*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (21*a^2*b^4*c^2*d^4 - 6*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^8 + 2*(21*a^2*b^4*c^3*d^3 + 15*a^3*b^3*c^2*d^4 - 5*a^4*b^2*c*d^5 + a^5*b*d^6)*x^6 + (21*a^2*b^4*c^4*d^2 + 78*a^3*b^3*c^3*d^3 - 2*a^4*b^2*c^2*d^4 - 2*a^5*b*c*d^5 + a^6*d^6)*x^4 + 2*(21*a^3*b^3*c^4*d^2 + 15*a^4*b^2*c^3*d^3 - 5*a^5*b*c^2*d^4 + a^6*c*d^5)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (5*a*b^5*c^6 - 22*a^2*b^4*c^5*d + 17*a^3*b^3*c^4*d^2 - 17*a^4*b^2*c^3*d^3 + 22*a^5*b*c^2*d^4 - 5*a^6*c*d^5)*x)/(a^4*b^5*c^9 - 5*a^5*b^4*c^8*d + 10*a^6*b^3*c^7*d^2 - 10*a^7*b^2*c^6*d^3 + 5*a^8*b*c^5*d^4 - a^9*c^4*d^5 + (a^2*b^7*c^7*d^2 - 5*a^3*b^6*c^6*d^3 + 10*a^4*b^5*c^5*d^4 - 10*a^5*b^4*c^4*d^5 + 5*a^6*b^3*c^3*d^6 - a^7*b^2*c^2*d^7)*x^8 + 2*(a^2*b^7*c^8*d - 4*a^3*b^6*c^7*d^2 + 5*a^4*b^5*c^6*d^3 - 5*a^6*b^3*c^4*d^5 + 4*a^7*b^2*c^3*d^6 - a^8*b*c^2*d^7)*x^6 + (a^2*b^7*c^9 - a^3*b^6*c^8*d - 9*a^4*b^5*c^7*d^2 + 25*a^5*b^4*c^6*d^3 - 25*a^6*b^3*c^5*d^4 + 9*a^7*b^2*c^4*d^5 + a^8*b*c^3*d^6 - a^9*c^2*d^7)*x^4 + 2*(a^3*b^6*c^9 - 4*a^4*b^5*c^8*d + 5*a^5*b^4*c^7*d^2 - 5*a^7*b^2*c^5*d^4 + 4*a^8*b*c^4*d^5 - a^9*c^3*d^6)*x^2)]","B",0
43,1,33,0,1.039836," ","integrate((x^2-1)^3/(x^2+1)^4,x, algorithm=""fricas"")","-\frac{3 \, x^{5} + 2 \, x^{3} + 3 \, x}{3 \, {\left(x^{6} + 3 \, x^{4} + 3 \, x^{2} + 1\right)}}"," ",0,"-1/3*(3*x^5 + 2*x^3 + 3*x)/(x^6 + 3*x^4 + 3*x^2 + 1)","A",0
44,1,67,0,1.018955," ","integrate((x^2-1)^4/(x^2+1)^5,x, algorithm=""fricas"")","-\frac{5 \, x^{7} - 3 \, x^{5} + 3 \, x^{3} - 3 \, {\left(x^{8} + 4 \, x^{6} + 6 \, x^{4} + 4 \, x^{2} + 1\right)} \arctan\left(x\right) - 5 \, x}{8 \, {\left(x^{8} + 4 \, x^{6} + 6 \, x^{4} + 4 \, x^{2} + 1\right)}}"," ",0,"-1/8*(5*x^7 - 3*x^5 + 3*x^3 - 3*(x^8 + 4*x^6 + 6*x^4 + 4*x^2 + 1)*arctan(x) - 5*x)/(x^8 + 4*x^6 + 6*x^4 + 4*x^2 + 1)","A",0
45,1,398,0,0.848106," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, a b^{3} c^{3} - 48 \, a^{2} b^{2} c^{2} d + 24 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(48 \, b^{4} d^{3} x^{7} + 8 \, {\left(24 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} x^{5} + 2 \, {\left(144 \, b^{4} c^{2} d + 24 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(64 \, b^{4} c^{3} + 48 \, a b^{3} c^{2} d - 24 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, b^{4}}, -\frac{3 \, {\left(64 \, a b^{3} c^{3} - 48 \, a^{2} b^{2} c^{2} d + 24 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(48 \, b^{4} d^{3} x^{7} + 8 \, {\left(24 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} x^{5} + 2 \, {\left(144 \, b^{4} c^{2} d + 24 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(64 \, b^{4} c^{3} + 48 \, a b^{3} c^{2} d - 24 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{384 \, b^{4}}\right]"," ",0,"[-1/768*(3*(64*a*b^3*c^3 - 48*a^2*b^2*c^2*d + 24*a^3*b*c*d^2 - 5*a^4*d^3)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(48*b^4*d^3*x^7 + 8*(24*b^4*c*d^2 + a*b^3*d^3)*x^5 + 2*(144*b^4*c^2*d + 24*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^3 + 3*(64*b^4*c^3 + 48*a*b^3*c^2*d - 24*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x)*sqrt(b*x^2 + a))/b^4, -1/384*(3*(64*a*b^3*c^3 - 48*a^2*b^2*c^2*d + 24*a^3*b*c*d^2 - 5*a^4*d^3)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (48*b^4*d^3*x^7 + 8*(24*b^4*c*d^2 + a*b^3*d^3)*x^5 + 2*(144*b^4*c^2*d + 24*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^3 + 3*(64*b^4*c^3 + 48*a*b^3*c^2*d - 24*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x)*sqrt(b*x^2 + a))/b^4]","A",0
46,1,264,0,0.976042," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a b^{2} c^{2} - 4 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(8 \, b^{3} d^{2} x^{5} + 2 \, {\left(12 \, b^{3} c d + a b^{2} d^{2}\right)} x^{3} + 3 \, {\left(8 \, b^{3} c^{2} + 4 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, b^{3}}, -\frac{3 \, {\left(8 \, a b^{2} c^{2} - 4 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, b^{3} d^{2} x^{5} + 2 \, {\left(12 \, b^{3} c d + a b^{2} d^{2}\right)} x^{3} + 3 \, {\left(8 \, b^{3} c^{2} + 4 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, b^{3}}\right]"," ",0,"[1/96*(3*(8*a*b^2*c^2 - 4*a^2*b*c*d + a^3*d^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(8*b^3*d^2*x^5 + 2*(12*b^3*c*d + a*b^2*d^2)*x^3 + 3*(8*b^3*c^2 + 4*a*b^2*c*d - a^2*b*d^2)*x)*sqrt(b*x^2 + a))/b^3, -1/48*(3*(8*a*b^2*c^2 - 4*a^2*b*c*d + a^3*d^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*b^3*d^2*x^5 + 2*(12*b^3*c*d + a*b^2*d^2)*x^3 + 3*(8*b^3*c^2 + 4*a*b^2*c*d - a^2*b*d^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
47,1,158,0,1.156490," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, a b c - a^{2} d\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(2 \, b^{2} d x^{3} + {\left(4 \, b^{2} c + a b d\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, b^{2}}, -\frac{{\left(4 \, a b c - a^{2} d\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, b^{2} d x^{3} + {\left(4 \, b^{2} c + a b d\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, b^{2}}\right]"," ",0,"[-1/16*((4*a*b*c - a^2*d)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(2*b^2*d*x^3 + (4*b^2*c + a*b*d)*x)*sqrt(b*x^2 + a))/b^2, -1/8*((4*a*b*c - a^2*d)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*b^2*d*x^3 + (4*b^2*c + a*b*d)*x)*sqrt(b*x^2 + a))/b^2]","A",0
48,1,94,0,0.752506," ","integrate((b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{2} + a} b x + a \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{4 \, b}, \frac{\sqrt{b x^{2} + a} b x - a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{2 \, b}\right]"," ",0,"[1/4*(2*sqrt(b*x^2 + a)*b*x + a*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/b, 1/2*(sqrt(b*x^2 + a)*b*x - a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)))/b]","A",0
49,1,596,0,1.117975," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{4 \, d}, -\frac{4 \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{4 \, d}, \frac{\sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) + \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{2 \, d}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right)}{2 \, d}\right]"," ",0,"[1/4*(2*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/d, -1/4*(4*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/d, 1/2*(sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) + sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/d, -1/2*(2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)))/d]","A",0
50,1,369,0,1.222837," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b c^{2} - a c d\right)} \sqrt{b x^{2} + a} x + {\left(a d x^{2} + a c\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{8 \, {\left(b c^{4} - a c^{3} d + {\left(b c^{3} d - a c^{2} d^{2}\right)} x^{2}\right)}}, \frac{2 \, {\left(b c^{2} - a c d\right)} \sqrt{b x^{2} + a} x - {\left(a d x^{2} + a c\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{4 \, {\left(b c^{4} - a c^{3} d + {\left(b c^{3} d - a c^{2} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(4*(b*c^2 - a*c*d)*sqrt(b*x^2 + a)*x + (a*d*x^2 + a*c)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/(b*c^4 - a*c^3*d + (b*c^3*d - a*c^2*d^2)*x^2), 1/4*(2*(b*c^2 - a*c*d)*sqrt(b*x^2 + a)*x - (a*d*x^2 + a*c)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(b*c^4 - a*c^3*d + (b*c^3*d - a*c^2*d^2)*x^2)]","B",0
51,1,698,0,1.198655," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a b c^{3} - 3 \, a^{2} c^{2} d + {\left(4 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + 2 \, {\left(4 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(2 \, b^{2} c^{3} d - 5 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{3} + {\left(4 \, b^{2} c^{4} - 9 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{32 \, {\left(b^{2} c^{7} - 2 \, a b c^{6} d + a^{2} c^{5} d^{2} + {\left(b^{2} c^{5} d^{2} - 2 \, a b c^{4} d^{3} + a^{2} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{6} d - 2 \, a b c^{5} d^{2} + a^{2} c^{4} d^{3}\right)} x^{2}\right)}}, -\frac{{\left(4 \, a b c^{3} - 3 \, a^{2} c^{2} d + {\left(4 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + 2 \, {\left(4 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(2 \, b^{2} c^{3} d - 5 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{3} + {\left(4 \, b^{2} c^{4} - 9 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(b^{2} c^{7} - 2 \, a b c^{6} d + a^{2} c^{5} d^{2} + {\left(b^{2} c^{5} d^{2} - 2 \, a b c^{4} d^{3} + a^{2} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{6} d - 2 \, a b c^{5} d^{2} + a^{2} c^{4} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/32*((4*a*b*c^3 - 3*a^2*c^2*d + (4*a*b*c*d^2 - 3*a^2*d^3)*x^4 + 2*(4*a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((2*b^2*c^3*d - 5*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^3 + (4*b^2*c^4 - 9*a*b*c^3*d + 5*a^2*c^2*d^2)*x)*sqrt(b*x^2 + a))/(b^2*c^7 - 2*a*b*c^6*d + a^2*c^5*d^2 + (b^2*c^5*d^2 - 2*a*b*c^4*d^3 + a^2*c^3*d^4)*x^4 + 2*(b^2*c^6*d - 2*a*b*c^5*d^2 + a^2*c^4*d^3)*x^2), -1/16*((4*a*b*c^3 - 3*a^2*c^2*d + (4*a*b*c*d^2 - 3*a^2*d^3)*x^4 + 2*(4*a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((2*b^2*c^3*d - 5*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^3 + (4*b^2*c^4 - 9*a*b*c^3*d + 5*a^2*c^2*d^2)*x)*sqrt(b*x^2 + a))/(b^2*c^7 - 2*a*b*c^6*d + a^2*c^5*d^2 + (b^2*c^5*d^2 - 2*a*b*c^4*d^3 + a^2*c^3*d^4)*x^4 + 2*(b^2*c^6*d - 2*a*b*c^5*d^2 + a^2*c^4*d^3)*x^2)]","B",0
52,1,1220,0,2.589127," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a b^{2} c^{5} - 12 \, a^{2} b c^{4} d + 5 \, a^{3} c^{3} d^{2} + {\left(8 \, a b^{2} c^{2} d^{3} - 12 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{6} + 3 \, {\left(8 \, a b^{2} c^{3} d^{2} - 12 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + 3 \, {\left(8 \, a b^{2} c^{4} d - 12 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(8 \, b^{3} c^{4} d^{2} - 34 \, a b^{2} c^{3} d^{3} + 41 \, a^{2} b c^{2} d^{4} - 15 \, a^{3} c d^{5}\right)} x^{5} + 2 \, {\left(12 \, b^{3} c^{5} d - 47 \, a b^{2} c^{4} d^{2} + 55 \, a^{2} b c^{3} d^{3} - 20 \, a^{3} c^{2} d^{4}\right)} x^{3} + 3 \, {\left(8 \, b^{3} c^{6} - 28 \, a b^{2} c^{5} d + 31 \, a^{2} b c^{4} d^{2} - 11 \, a^{3} c^{3} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{192 \, {\left(b^{3} c^{10} - 3 \, a b^{2} c^{9} d + 3 \, a^{2} b c^{8} d^{2} - a^{3} c^{7} d^{3} + {\left(b^{3} c^{7} d^{3} - 3 \, a b^{2} c^{6} d^{4} + 3 \, a^{2} b c^{5} d^{5} - a^{3} c^{4} d^{6}\right)} x^{6} + 3 \, {\left(b^{3} c^{8} d^{2} - 3 \, a b^{2} c^{7} d^{3} + 3 \, a^{2} b c^{6} d^{4} - a^{3} c^{5} d^{5}\right)} x^{4} + 3 \, {\left(b^{3} c^{9} d - 3 \, a b^{2} c^{8} d^{2} + 3 \, a^{2} b c^{7} d^{3} - a^{3} c^{6} d^{4}\right)} x^{2}\right)}}, -\frac{3 \, {\left(8 \, a b^{2} c^{5} - 12 \, a^{2} b c^{4} d + 5 \, a^{3} c^{3} d^{2} + {\left(8 \, a b^{2} c^{2} d^{3} - 12 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{6} + 3 \, {\left(8 \, a b^{2} c^{3} d^{2} - 12 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + 3 \, {\left(8 \, a b^{2} c^{4} d - 12 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(8 \, b^{3} c^{4} d^{2} - 34 \, a b^{2} c^{3} d^{3} + 41 \, a^{2} b c^{2} d^{4} - 15 \, a^{3} c d^{5}\right)} x^{5} + 2 \, {\left(12 \, b^{3} c^{5} d - 47 \, a b^{2} c^{4} d^{2} + 55 \, a^{2} b c^{3} d^{3} - 20 \, a^{3} c^{2} d^{4}\right)} x^{3} + 3 \, {\left(8 \, b^{3} c^{6} - 28 \, a b^{2} c^{5} d + 31 \, a^{2} b c^{4} d^{2} - 11 \, a^{3} c^{3} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, {\left(b^{3} c^{10} - 3 \, a b^{2} c^{9} d + 3 \, a^{2} b c^{8} d^{2} - a^{3} c^{7} d^{3} + {\left(b^{3} c^{7} d^{3} - 3 \, a b^{2} c^{6} d^{4} + 3 \, a^{2} b c^{5} d^{5} - a^{3} c^{4} d^{6}\right)} x^{6} + 3 \, {\left(b^{3} c^{8} d^{2} - 3 \, a b^{2} c^{7} d^{3} + 3 \, a^{2} b c^{6} d^{4} - a^{3} c^{5} d^{5}\right)} x^{4} + 3 \, {\left(b^{3} c^{9} d - 3 \, a b^{2} c^{8} d^{2} + 3 \, a^{2} b c^{7} d^{3} - a^{3} c^{6} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/192*(3*(8*a*b^2*c^5 - 12*a^2*b*c^4*d + 5*a^3*c^3*d^2 + (8*a*b^2*c^2*d^3 - 12*a^2*b*c*d^4 + 5*a^3*d^5)*x^6 + 3*(8*a*b^2*c^3*d^2 - 12*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + 3*(8*a*b^2*c^4*d - 12*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((8*b^3*c^4*d^2 - 34*a*b^2*c^3*d^3 + 41*a^2*b*c^2*d^4 - 15*a^3*c*d^5)*x^5 + 2*(12*b^3*c^5*d - 47*a*b^2*c^4*d^2 + 55*a^2*b*c^3*d^3 - 20*a^3*c^2*d^4)*x^3 + 3*(8*b^3*c^6 - 28*a*b^2*c^5*d + 31*a^2*b*c^4*d^2 - 11*a^3*c^3*d^3)*x)*sqrt(b*x^2 + a))/(b^3*c^10 - 3*a*b^2*c^9*d + 3*a^2*b*c^8*d^2 - a^3*c^7*d^3 + (b^3*c^7*d^3 - 3*a*b^2*c^6*d^4 + 3*a^2*b*c^5*d^5 - a^3*c^4*d^6)*x^6 + 3*(b^3*c^8*d^2 - 3*a*b^2*c^7*d^3 + 3*a^2*b*c^6*d^4 - a^3*c^5*d^5)*x^4 + 3*(b^3*c^9*d - 3*a*b^2*c^8*d^2 + 3*a^2*b*c^7*d^3 - a^3*c^6*d^4)*x^2), -1/96*(3*(8*a*b^2*c^5 - 12*a^2*b*c^4*d + 5*a^3*c^3*d^2 + (8*a*b^2*c^2*d^3 - 12*a^2*b*c*d^4 + 5*a^3*d^5)*x^6 + 3*(8*a*b^2*c^3*d^2 - 12*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + 3*(8*a*b^2*c^4*d - 12*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((8*b^3*c^4*d^2 - 34*a*b^2*c^3*d^3 + 41*a^2*b*c^2*d^4 - 15*a^3*c*d^5)*x^5 + 2*(12*b^3*c^5*d - 47*a*b^2*c^4*d^2 + 55*a^2*b*c^3*d^3 - 20*a^3*c^2*d^4)*x^3 + 3*(8*b^3*c^6 - 28*a*b^2*c^5*d + 31*a^2*b*c^4*d^2 - 11*a^3*c^3*d^3)*x)*sqrt(b*x^2 + a))/(b^3*c^10 - 3*a*b^2*c^9*d + 3*a^2*b*c^8*d^2 - a^3*c^7*d^3 + (b^3*c^7*d^3 - 3*a*b^2*c^6*d^4 + 3*a^2*b*c^5*d^5 - a^3*c^4*d^6)*x^6 + 3*(b^3*c^8*d^2 - 3*a*b^2*c^7*d^3 + 3*a^2*b*c^6*d^4 - a^3*c^5*d^5)*x^4 + 3*(b^3*c^9*d - 3*a*b^2*c^8*d^2 + 3*a^2*b*c^7*d^3 - a^3*c^6*d^4)*x^2)]","B",0
53,1,502,0,1.354736," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b^{2} c^{2} d + 6 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(128 \, b^{5} d^{3} x^{9} + 16 \, {\left(30 \, b^{5} c d^{2} + 11 \, a b^{4} d^{3}\right)} x^{7} + 8 \, {\left(80 \, b^{5} c^{2} d + 90 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{5} + 10 \, {\left(32 \, b^{5} c^{3} + 112 \, a b^{4} c^{2} d + 6 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{3} + 5 \, {\left(160 \, a b^{4} c^{3} + 48 \, a^{2} b^{3} c^{2} d - 18 \, a^{3} b^{2} c d^{2} + 3 \, a^{4} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{2560 \, b^{4}}, -\frac{15 \, {\left(32 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b^{2} c^{2} d + 6 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(128 \, b^{5} d^{3} x^{9} + 16 \, {\left(30 \, b^{5} c d^{2} + 11 \, a b^{4} d^{3}\right)} x^{7} + 8 \, {\left(80 \, b^{5} c^{2} d + 90 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{5} + 10 \, {\left(32 \, b^{5} c^{3} + 112 \, a b^{4} c^{2} d + 6 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{3} + 5 \, {\left(160 \, a b^{4} c^{3} + 48 \, a^{2} b^{3} c^{2} d - 18 \, a^{3} b^{2} c d^{2} + 3 \, a^{4} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{1280 \, b^{4}}\right]"," ",0,"[-1/2560*(15*(32*a^2*b^3*c^3 - 16*a^3*b^2*c^2*d + 6*a^4*b*c*d^2 - a^5*d^3)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(128*b^5*d^3*x^9 + 16*(30*b^5*c*d^2 + 11*a*b^4*d^3)*x^7 + 8*(80*b^5*c^2*d + 90*a*b^4*c*d^2 + a^2*b^3*d^3)*x^5 + 10*(32*b^5*c^3 + 112*a*b^4*c^2*d + 6*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^3 + 5*(160*a*b^4*c^3 + 48*a^2*b^3*c^2*d - 18*a^3*b^2*c*d^2 + 3*a^4*b*d^3)*x)*sqrt(b*x^2 + a))/b^4, -1/1280*(15*(32*a^2*b^3*c^3 - 16*a^3*b^2*c^2*d + 6*a^4*b*c*d^2 - a^5*d^3)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (128*b^5*d^3*x^9 + 16*(30*b^5*c*d^2 + 11*a*b^4*d^3)*x^7 + 8*(80*b^5*c^2*d + 90*a*b^4*c*d^2 + a^2*b^3*d^3)*x^5 + 10*(32*b^5*c^3 + 112*a*b^4*c^2*d + 6*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^3 + 5*(160*a*b^4*c^3 + 48*a^2*b^3*c^2*d - 18*a^3*b^2*c*d^2 + 3*a^4*b*d^3)*x)*sqrt(b*x^2 + a))/b^4]","A",0
54,1,344,0,1.306870," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(48 \, a^{2} b^{2} c^{2} - 16 \, a^{3} b c d + 3 \, a^{4} d^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(48 \, b^{4} d^{2} x^{7} + 8 \, {\left(16 \, b^{4} c d + 9 \, a b^{3} d^{2}\right)} x^{5} + 2 \, {\left(48 \, b^{4} c^{2} + 112 \, a b^{3} c d + 3 \, a^{2} b^{2} d^{2}\right)} x^{3} + 3 \, {\left(80 \, a b^{3} c^{2} + 16 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, b^{3}}, -\frac{3 \, {\left(48 \, a^{2} b^{2} c^{2} - 16 \, a^{3} b c d + 3 \, a^{4} d^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(48 \, b^{4} d^{2} x^{7} + 8 \, {\left(16 \, b^{4} c d + 9 \, a b^{3} d^{2}\right)} x^{5} + 2 \, {\left(48 \, b^{4} c^{2} + 112 \, a b^{3} c d + 3 \, a^{2} b^{2} d^{2}\right)} x^{3} + 3 \, {\left(80 \, a b^{3} c^{2} + 16 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{384 \, b^{3}}\right]"," ",0,"[1/768*(3*(48*a^2*b^2*c^2 - 16*a^3*b*c*d + 3*a^4*d^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(48*b^4*d^2*x^7 + 8*(16*b^4*c*d + 9*a*b^3*d^2)*x^5 + 2*(48*b^4*c^2 + 112*a*b^3*c*d + 3*a^2*b^2*d^2)*x^3 + 3*(80*a*b^3*c^2 + 16*a^2*b^2*c*d - 3*a^3*b*d^2)*x)*sqrt(b*x^2 + a))/b^3, -1/384*(3*(48*a^2*b^2*c^2 - 16*a^3*b*c*d + 3*a^4*d^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (48*b^4*d^2*x^7 + 8*(16*b^4*c*d + 9*a*b^3*d^2)*x^5 + 2*(48*b^4*c^2 + 112*a*b^3*c*d + 3*a^2*b^2*d^2)*x^3 + 3*(80*a*b^3*c^2 + 16*a^2*b^2*c*d - 3*a^3*b*d^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
55,1,210,0,0.932966," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, a^{2} b c - a^{3} d\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, b^{3} d x^{5} + 2 \, {\left(6 \, b^{3} c + 7 \, a b^{2} d\right)} x^{3} + 3 \, {\left(10 \, a b^{2} c + a^{2} b d\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, b^{2}}, -\frac{3 \, {\left(6 \, a^{2} b c - a^{3} d\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, b^{3} d x^{5} + 2 \, {\left(6 \, b^{3} c + 7 \, a b^{2} d\right)} x^{3} + 3 \, {\left(10 \, a b^{2} c + a^{2} b d\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, b^{2}}\right]"," ",0,"[-1/96*(3*(6*a^2*b*c - a^3*d)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*b^3*d*x^5 + 2*(6*b^3*c + 7*a*b^2*d)*x^3 + 3*(10*a*b^2*c + a^2*b*d)*x)*sqrt(b*x^2 + a))/b^2, -1/48*(3*(6*a^2*b*c - a^3*d)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*b^3*d*x^5 + 2*(6*b^3*c + 7*a*b^2*d)*x^3 + 3*(10*a*b^2*c + a^2*b*d)*x)*sqrt(b*x^2 + a))/b^2]","A",0
56,1,124,0,0.703445," ","integrate((b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, b^{2} x^{3} + 5 \, a b x\right)} \sqrt{b x^{2} + a}}{16 \, b}, -\frac{3 \, a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, b^{2} x^{3} + 5 \, a b x\right)} \sqrt{b x^{2} + a}}{8 \, b}\right]"," ",0,"[1/16*(3*a^2*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*b^2*x^3 + 5*a*b*x)*sqrt(b*x^2 + a))/b, -1/8*(3*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*b^2*x^3 + 5*a*b*x)*sqrt(b*x^2 + a))/b]","A",0
57,1,721,0,1.445198," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{2} + a} b d x - {\left(2 \, b c - 3 \, a d\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{4 \, d^{2}}, \frac{2 \, \sqrt{b x^{2} + a} b d x + 2 \, {\left(2 \, b c - 3 \, a d\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{4 \, d^{2}}, \frac{2 \, \sqrt{b x^{2} + a} b d x - 2 \, {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) - {\left(2 \, b c - 3 \, a d\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{4 \, d^{2}}, \frac{\sqrt{b x^{2} + a} b d x + {\left(2 \, b c - 3 \, a d\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right)}{2 \, d^{2}}\right]"," ",0,"[1/4*(2*sqrt(b*x^2 + a)*b*d*x - (2*b*c - 3*a*d)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - (b*c - a*d)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/d^2, 1/4*(2*sqrt(b*x^2 + a)*b*d*x + 2*(2*b*c - 3*a*d)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (b*c - a*d)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/d^2, 1/4*(2*sqrt(b*x^2 + a)*b*d*x - 2*(b*c - a*d)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) - (2*b*c - 3*a*d)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/d^2, 1/2*(sqrt(b*x^2 + a)*b*d*x + (2*b*c - 3*a*d)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (b*c - a*d)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)))/d^2]","A",0
58,1,907,0,1.363550," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(b c d - a d^{2}\right)} \sqrt{b x^{2} + a} x - 4 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - {\left(2 \, b c^{2} + a c d + {\left(2 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{8 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}}, -\frac{4 \, {\left(b c d - a d^{2}\right)} \sqrt{b x^{2} + a} x + 8 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, b c^{2} + a c d + {\left(2 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{8 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}}, -\frac{2 \, {\left(b c d - a d^{2}\right)} \sqrt{b x^{2} + a} x - {\left(2 \, b c^{2} + a c d + {\left(2 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) - 2 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{4 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}}, -\frac{2 \, {\left(b c d - a d^{2}\right)} \sqrt{b x^{2} + a} x + 4 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, b c^{2} + a c d + {\left(2 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right)}{4 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}}\right]"," ",0,"[-1/8*(4*(b*c*d - a*d^2)*sqrt(b*x^2 + a)*x - 4*(b*c*d*x^2 + b*c^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - (2*b*c^2 + a*c*d + (2*b*c*d + a*d^2)*x^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/(c*d^3*x^2 + c^2*d^2), -1/8*(4*(b*c*d - a*d^2)*sqrt(b*x^2 + a)*x + 8*(b*c*d*x^2 + b*c^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*b*c^2 + a*c*d + (2*b*c*d + a*d^2)*x^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/(c*d^3*x^2 + c^2*d^2), -1/4*(2*(b*c*d - a*d^2)*sqrt(b*x^2 + a)*x - (2*b*c^2 + a*c*d + (2*b*c*d + a*d^2)*x^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) - 2*(b*c*d*x^2 + b*c^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/(c*d^3*x^2 + c^2*d^2), -1/4*(2*(b*c*d - a*d^2)*sqrt(b*x^2 + a)*x + 4*(b*c*d*x^2 + b*c^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*b*c^2 + a*c*d + (2*b*c*d + a*d^2)*x^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)))/(c*d^3*x^2 + c^2*d^2)]","A",0
59,1,526,0,1.205490," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} d^{2} x^{4} + 2 \, a^{2} c d x^{2} + a^{2} c^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3} + 5 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x\right)} \sqrt{b x^{2} + a}}{32 \, {\left(b c^{6} - a c^{5} d + {\left(b c^{4} d^{2} - a c^{3} d^{3}\right)} x^{4} + 2 \, {\left(b c^{5} d - a c^{4} d^{2}\right)} x^{2}\right)}}, -\frac{3 \, {\left(a^{2} d^{2} x^{4} + 2 \, a^{2} c d x^{2} + a^{2} c^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3} + 5 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(b c^{6} - a c^{5} d + {\left(b c^{4} d^{2} - a c^{3} d^{3}\right)} x^{4} + 2 \, {\left(b c^{5} d - a c^{4} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/32*(3*(a^2*d^2*x^4 + 2*a^2*c*d*x^2 + a^2*c^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^3 + 5*(a*b*c^3 - a^2*c^2*d)*x)*sqrt(b*x^2 + a))/(b*c^6 - a*c^5*d + (b*c^4*d^2 - a*c^3*d^3)*x^4 + 2*(b*c^5*d - a*c^4*d^2)*x^2), -1/16*(3*(a^2*d^2*x^4 + 2*a^2*c*d*x^2 + a^2*c^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^3 + 5*(a*b*c^3 - a^2*c^2*d)*x)*sqrt(b*x^2 + a))/(b*c^6 - a*c^5*d + (b*c^4*d^2 - a*c^3*d^3)*x^4 + 2*(b*c^5*d - a*c^4*d^2)*x^2)]","B",0
60,1,972,0,1.892843," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, a^{2} b c^{4} - 5 \, a^{3} c^{3} d + {\left(6 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{6} + 3 \, {\left(6 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{4} + 3 \, {\left(6 \, a^{2} b c^{3} d - 5 \, a^{3} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(4 \, b^{3} c^{4} d + 4 \, a b^{2} c^{3} d^{2} - 23 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{5} + 2 \, {\left(6 \, b^{3} c^{5} + 5 \, a b^{2} c^{4} d - 31 \, a^{2} b c^{3} d^{2} + 20 \, a^{3} c^{2} d^{3}\right)} x^{3} + 3 \, {\left(10 \, a b^{2} c^{5} - 21 \, a^{2} b c^{4} d + 11 \, a^{3} c^{3} d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{192 \, {\left(b^{2} c^{9} - 2 \, a b c^{8} d + a^{2} c^{7} d^{2} + {\left(b^{2} c^{6} d^{3} - 2 \, a b c^{5} d^{4} + a^{2} c^{4} d^{5}\right)} x^{6} + 3 \, {\left(b^{2} c^{7} d^{2} - 2 \, a b c^{6} d^{3} + a^{2} c^{5} d^{4}\right)} x^{4} + 3 \, {\left(b^{2} c^{8} d - 2 \, a b c^{7} d^{2} + a^{2} c^{6} d^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(6 \, a^{2} b c^{4} - 5 \, a^{3} c^{3} d + {\left(6 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{6} + 3 \, {\left(6 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{4} + 3 \, {\left(6 \, a^{2} b c^{3} d - 5 \, a^{3} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(4 \, b^{3} c^{4} d + 4 \, a b^{2} c^{3} d^{2} - 23 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{5} + 2 \, {\left(6 \, b^{3} c^{5} + 5 \, a b^{2} c^{4} d - 31 \, a^{2} b c^{3} d^{2} + 20 \, a^{3} c^{2} d^{3}\right)} x^{3} + 3 \, {\left(10 \, a b^{2} c^{5} - 21 \, a^{2} b c^{4} d + 11 \, a^{3} c^{3} d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, {\left(b^{2} c^{9} - 2 \, a b c^{8} d + a^{2} c^{7} d^{2} + {\left(b^{2} c^{6} d^{3} - 2 \, a b c^{5} d^{4} + a^{2} c^{4} d^{5}\right)} x^{6} + 3 \, {\left(b^{2} c^{7} d^{2} - 2 \, a b c^{6} d^{3} + a^{2} c^{5} d^{4}\right)} x^{4} + 3 \, {\left(b^{2} c^{8} d - 2 \, a b c^{7} d^{2} + a^{2} c^{6} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/192*(3*(6*a^2*b*c^4 - 5*a^3*c^3*d + (6*a^2*b*c*d^3 - 5*a^3*d^4)*x^6 + 3*(6*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^4 + 3*(6*a^2*b*c^3*d - 5*a^3*c^2*d^2)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((4*b^3*c^4*d + 4*a*b^2*c^3*d^2 - 23*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^5 + 2*(6*b^3*c^5 + 5*a*b^2*c^4*d - 31*a^2*b*c^3*d^2 + 20*a^3*c^2*d^3)*x^3 + 3*(10*a*b^2*c^5 - 21*a^2*b*c^4*d + 11*a^3*c^3*d^2)*x)*sqrt(b*x^2 + a))/(b^2*c^9 - 2*a*b*c^8*d + a^2*c^7*d^2 + (b^2*c^6*d^3 - 2*a*b*c^5*d^4 + a^2*c^4*d^5)*x^6 + 3*(b^2*c^7*d^2 - 2*a*b*c^6*d^3 + a^2*c^5*d^4)*x^4 + 3*(b^2*c^8*d - 2*a*b*c^7*d^2 + a^2*c^6*d^3)*x^2), -1/96*(3*(6*a^2*b*c^4 - 5*a^3*c^3*d + (6*a^2*b*c*d^3 - 5*a^3*d^4)*x^6 + 3*(6*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^4 + 3*(6*a^2*b*c^3*d - 5*a^3*c^2*d^2)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((4*b^3*c^4*d + 4*a*b^2*c^3*d^2 - 23*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^5 + 2*(6*b^3*c^5 + 5*a*b^2*c^4*d - 31*a^2*b*c^3*d^2 + 20*a^3*c^2*d^3)*x^3 + 3*(10*a*b^2*c^5 - 21*a^2*b*c^4*d + 11*a^3*c^3*d^2)*x)*sqrt(b*x^2 + a))/(b^2*c^9 - 2*a*b*c^8*d + a^2*c^7*d^2 + (b^2*c^6*d^3 - 2*a*b*c^5*d^4 + a^2*c^4*d^5)*x^6 + 3*(b^2*c^7*d^2 - 2*a*b*c^6*d^3 + a^2*c^5*d^4)*x^4 + 3*(b^2*c^8*d - 2*a*b*c^7*d^2 + a^2*c^6*d^3)*x^2)]","B",0
61,1,1604,0,5.357986," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(48 \, a^{2} b^{2} c^{6} - 80 \, a^{3} b c^{5} d + 35 \, a^{4} c^{4} d^{2} + {\left(48 \, a^{2} b^{2} c^{2} d^{4} - 80 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{8} + 4 \, {\left(48 \, a^{2} b^{2} c^{3} d^{3} - 80 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{6} + 6 \, {\left(48 \, a^{2} b^{2} c^{4} d^{2} - 80 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{4} + 4 \, {\left(48 \, a^{2} b^{2} c^{5} d - 80 \, a^{3} b c^{4} d^{2} + 35 \, a^{4} c^{3} d^{3}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(16 \, b^{4} c^{5} d^{2} + 24 \, a b^{3} c^{4} d^{3} - 210 \, a^{2} b^{2} c^{3} d^{4} + 275 \, a^{3} b c^{2} d^{5} - 105 \, a^{4} c d^{6}\right)} x^{7} + {\left(64 \, b^{4} c^{6} d + 88 \, a b^{3} c^{5} d^{2} - 780 \, a^{2} b^{2} c^{4} d^{3} + 1013 \, a^{3} b c^{3} d^{4} - 385 \, a^{4} c^{2} d^{5}\right)} x^{5} + {\left(96 \, b^{4} c^{7} + 112 \, a b^{3} c^{6} d - 1050 \, a^{2} b^{2} c^{5} d^{2} + 1353 \, a^{3} b c^{4} d^{3} - 511 \, a^{4} c^{3} d^{4}\right)} x^{3} + 3 \, {\left(80 \, a b^{3} c^{7} - 256 \, a^{2} b^{2} c^{6} d + 269 \, a^{3} b c^{5} d^{2} - 93 \, a^{4} c^{4} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{1536 \, {\left(b^{3} c^{12} - 3 \, a b^{2} c^{11} d + 3 \, a^{2} b c^{10} d^{2} - a^{3} c^{9} d^{3} + {\left(b^{3} c^{8} d^{4} - 3 \, a b^{2} c^{7} d^{5} + 3 \, a^{2} b c^{6} d^{6} - a^{3} c^{5} d^{7}\right)} x^{8} + 4 \, {\left(b^{3} c^{9} d^{3} - 3 \, a b^{2} c^{8} d^{4} + 3 \, a^{2} b c^{7} d^{5} - a^{3} c^{6} d^{6}\right)} x^{6} + 6 \, {\left(b^{3} c^{10} d^{2} - 3 \, a b^{2} c^{9} d^{3} + 3 \, a^{2} b c^{8} d^{4} - a^{3} c^{7} d^{5}\right)} x^{4} + 4 \, {\left(b^{3} c^{11} d - 3 \, a b^{2} c^{10} d^{2} + 3 \, a^{2} b c^{9} d^{3} - a^{3} c^{8} d^{4}\right)} x^{2}\right)}}, -\frac{3 \, {\left(48 \, a^{2} b^{2} c^{6} - 80 \, a^{3} b c^{5} d + 35 \, a^{4} c^{4} d^{2} + {\left(48 \, a^{2} b^{2} c^{2} d^{4} - 80 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{8} + 4 \, {\left(48 \, a^{2} b^{2} c^{3} d^{3} - 80 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{6} + 6 \, {\left(48 \, a^{2} b^{2} c^{4} d^{2} - 80 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{4} + 4 \, {\left(48 \, a^{2} b^{2} c^{5} d - 80 \, a^{3} b c^{4} d^{2} + 35 \, a^{4} c^{3} d^{3}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(16 \, b^{4} c^{5} d^{2} + 24 \, a b^{3} c^{4} d^{3} - 210 \, a^{2} b^{2} c^{3} d^{4} + 275 \, a^{3} b c^{2} d^{5} - 105 \, a^{4} c d^{6}\right)} x^{7} + {\left(64 \, b^{4} c^{6} d + 88 \, a b^{3} c^{5} d^{2} - 780 \, a^{2} b^{2} c^{4} d^{3} + 1013 \, a^{3} b c^{3} d^{4} - 385 \, a^{4} c^{2} d^{5}\right)} x^{5} + {\left(96 \, b^{4} c^{7} + 112 \, a b^{3} c^{6} d - 1050 \, a^{2} b^{2} c^{5} d^{2} + 1353 \, a^{3} b c^{4} d^{3} - 511 \, a^{4} c^{3} d^{4}\right)} x^{3} + 3 \, {\left(80 \, a b^{3} c^{7} - 256 \, a^{2} b^{2} c^{6} d + 269 \, a^{3} b c^{5} d^{2} - 93 \, a^{4} c^{4} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, {\left(b^{3} c^{12} - 3 \, a b^{2} c^{11} d + 3 \, a^{2} b c^{10} d^{2} - a^{3} c^{9} d^{3} + {\left(b^{3} c^{8} d^{4} - 3 \, a b^{2} c^{7} d^{5} + 3 \, a^{2} b c^{6} d^{6} - a^{3} c^{5} d^{7}\right)} x^{8} + 4 \, {\left(b^{3} c^{9} d^{3} - 3 \, a b^{2} c^{8} d^{4} + 3 \, a^{2} b c^{7} d^{5} - a^{3} c^{6} d^{6}\right)} x^{6} + 6 \, {\left(b^{3} c^{10} d^{2} - 3 \, a b^{2} c^{9} d^{3} + 3 \, a^{2} b c^{8} d^{4} - a^{3} c^{7} d^{5}\right)} x^{4} + 4 \, {\left(b^{3} c^{11} d - 3 \, a b^{2} c^{10} d^{2} + 3 \, a^{2} b c^{9} d^{3} - a^{3} c^{8} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/1536*(3*(48*a^2*b^2*c^6 - 80*a^3*b*c^5*d + 35*a^4*c^4*d^2 + (48*a^2*b^2*c^2*d^4 - 80*a^3*b*c*d^5 + 35*a^4*d^6)*x^8 + 4*(48*a^2*b^2*c^3*d^3 - 80*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^6 + 6*(48*a^2*b^2*c^4*d^2 - 80*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^4 + 4*(48*a^2*b^2*c^5*d - 80*a^3*b*c^4*d^2 + 35*a^4*c^3*d^3)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((16*b^4*c^5*d^2 + 24*a*b^3*c^4*d^3 - 210*a^2*b^2*c^3*d^4 + 275*a^3*b*c^2*d^5 - 105*a^4*c*d^6)*x^7 + (64*b^4*c^6*d + 88*a*b^3*c^5*d^2 - 780*a^2*b^2*c^4*d^3 + 1013*a^3*b*c^3*d^4 - 385*a^4*c^2*d^5)*x^5 + (96*b^4*c^7 + 112*a*b^3*c^6*d - 1050*a^2*b^2*c^5*d^2 + 1353*a^3*b*c^4*d^3 - 511*a^4*c^3*d^4)*x^3 + 3*(80*a*b^3*c^7 - 256*a^2*b^2*c^6*d + 269*a^3*b*c^5*d^2 - 93*a^4*c^4*d^3)*x)*sqrt(b*x^2 + a))/(b^3*c^12 - 3*a*b^2*c^11*d + 3*a^2*b*c^10*d^2 - a^3*c^9*d^3 + (b^3*c^8*d^4 - 3*a*b^2*c^7*d^5 + 3*a^2*b*c^6*d^6 - a^3*c^5*d^7)*x^8 + 4*(b^3*c^9*d^3 - 3*a*b^2*c^8*d^4 + 3*a^2*b*c^7*d^5 - a^3*c^6*d^6)*x^6 + 6*(b^3*c^10*d^2 - 3*a*b^2*c^9*d^3 + 3*a^2*b*c^8*d^4 - a^3*c^7*d^5)*x^4 + 4*(b^3*c^11*d - 3*a*b^2*c^10*d^2 + 3*a^2*b*c^9*d^3 - a^3*c^8*d^4)*x^2), -1/768*(3*(48*a^2*b^2*c^6 - 80*a^3*b*c^5*d + 35*a^4*c^4*d^2 + (48*a^2*b^2*c^2*d^4 - 80*a^3*b*c*d^5 + 35*a^4*d^6)*x^8 + 4*(48*a^2*b^2*c^3*d^3 - 80*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^6 + 6*(48*a^2*b^2*c^4*d^2 - 80*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^4 + 4*(48*a^2*b^2*c^5*d - 80*a^3*b*c^4*d^2 + 35*a^4*c^3*d^3)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((16*b^4*c^5*d^2 + 24*a*b^3*c^4*d^3 - 210*a^2*b^2*c^3*d^4 + 275*a^3*b*c^2*d^5 - 105*a^4*c*d^6)*x^7 + (64*b^4*c^6*d + 88*a*b^3*c^5*d^2 - 780*a^2*b^2*c^4*d^3 + 1013*a^3*b*c^3*d^4 - 385*a^4*c^2*d^5)*x^5 + (96*b^4*c^7 + 112*a*b^3*c^6*d - 1050*a^2*b^2*c^5*d^2 + 1353*a^3*b*c^4*d^3 - 511*a^4*c^3*d^4)*x^3 + 3*(80*a*b^3*c^7 - 256*a^2*b^2*c^6*d + 269*a^3*b*c^5*d^2 - 93*a^4*c^4*d^3)*x)*sqrt(b*x^2 + a))/(b^3*c^12 - 3*a*b^2*c^11*d + 3*a^2*b*c^10*d^2 - a^3*c^9*d^3 + (b^3*c^8*d^4 - 3*a*b^2*c^7*d^5 + 3*a^2*b*c^6*d^6 - a^3*c^5*d^7)*x^8 + 4*(b^3*c^9*d^3 - 3*a*b^2*c^8*d^4 + 3*a^2*b*c^7*d^5 - a^3*c^6*d^6)*x^6 + 6*(b^3*c^10*d^2 - 3*a*b^2*c^9*d^3 + 3*a^2*b*c^8*d^4 - a^3*c^7*d^5)*x^4 + 4*(b^3*c^11*d - 3*a*b^2*c^10*d^2 + 3*a^2*b*c^9*d^3 - a^3*c^8*d^4)*x^2)]","B",0
62,1,608,0,2.029702," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(320 \, a^{3} b^{3} c^{3} - 120 \, a^{4} b^{2} c^{2} d + 36 \, a^{5} b c d^{2} - 5 \, a^{6} d^{3}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(1280 \, b^{6} d^{3} x^{11} + 128 \, {\left(36 \, b^{6} c d^{2} + 25 \, a b^{5} d^{3}\right)} x^{9} + 144 \, {\left(40 \, b^{6} c^{2} d + 84 \, a b^{5} c d^{2} + 15 \, a^{2} b^{4} d^{3}\right)} x^{7} + 8 \, {\left(320 \, b^{6} c^{3} + 2040 \, a b^{5} c^{2} d + 1116 \, a^{2} b^{4} c d^{2} + 5 \, a^{3} b^{3} d^{3}\right)} x^{5} + 10 \, {\left(832 \, a b^{5} c^{3} + 1416 \, a^{2} b^{4} c^{2} d + 36 \, a^{3} b^{3} c d^{2} - 5 \, a^{4} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(704 \, a^{2} b^{4} c^{3} + 120 \, a^{3} b^{3} c^{2} d - 36 \, a^{4} b^{2} c d^{2} + 5 \, a^{5} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{30720 \, b^{4}}, -\frac{15 \, {\left(320 \, a^{3} b^{3} c^{3} - 120 \, a^{4} b^{2} c^{2} d + 36 \, a^{5} b c d^{2} - 5 \, a^{6} d^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(1280 \, b^{6} d^{3} x^{11} + 128 \, {\left(36 \, b^{6} c d^{2} + 25 \, a b^{5} d^{3}\right)} x^{9} + 144 \, {\left(40 \, b^{6} c^{2} d + 84 \, a b^{5} c d^{2} + 15 \, a^{2} b^{4} d^{3}\right)} x^{7} + 8 \, {\left(320 \, b^{6} c^{3} + 2040 \, a b^{5} c^{2} d + 1116 \, a^{2} b^{4} c d^{2} + 5 \, a^{3} b^{3} d^{3}\right)} x^{5} + 10 \, {\left(832 \, a b^{5} c^{3} + 1416 \, a^{2} b^{4} c^{2} d + 36 \, a^{3} b^{3} c d^{2} - 5 \, a^{4} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(704 \, a^{2} b^{4} c^{3} + 120 \, a^{3} b^{3} c^{2} d - 36 \, a^{4} b^{2} c d^{2} + 5 \, a^{5} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{15360 \, b^{4}}\right]"," ",0,"[-1/30720*(15*(320*a^3*b^3*c^3 - 120*a^4*b^2*c^2*d + 36*a^5*b*c*d^2 - 5*a^6*d^3)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(1280*b^6*d^3*x^11 + 128*(36*b^6*c*d^2 + 25*a*b^5*d^3)*x^9 + 144*(40*b^6*c^2*d + 84*a*b^5*c*d^2 + 15*a^2*b^4*d^3)*x^7 + 8*(320*b^6*c^3 + 2040*a*b^5*c^2*d + 1116*a^2*b^4*c*d^2 + 5*a^3*b^3*d^3)*x^5 + 10*(832*a*b^5*c^3 + 1416*a^2*b^4*c^2*d + 36*a^3*b^3*c*d^2 - 5*a^4*b^2*d^3)*x^3 + 15*(704*a^2*b^4*c^3 + 120*a^3*b^3*c^2*d - 36*a^4*b^2*c*d^2 + 5*a^5*b*d^3)*x)*sqrt(b*x^2 + a))/b^4, -1/15360*(15*(320*a^3*b^3*c^3 - 120*a^4*b^2*c^2*d + 36*a^5*b*c*d^2 - 5*a^6*d^3)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (1280*b^6*d^3*x^11 + 128*(36*b^6*c*d^2 + 25*a*b^5*d^3)*x^9 + 144*(40*b^6*c^2*d + 84*a*b^5*c*d^2 + 15*a^2*b^4*d^3)*x^7 + 8*(320*b^6*c^3 + 2040*a*b^5*c^2*d + 1116*a^2*b^4*c*d^2 + 5*a^3*b^3*d^3)*x^5 + 10*(832*a*b^5*c^3 + 1416*a^2*b^4*c^2*d + 36*a^3*b^3*c*d^2 - 5*a^4*b^2*d^3)*x^3 + 15*(704*a^2*b^4*c^3 + 120*a^3*b^3*c^2*d - 36*a^4*b^2*c*d^2 + 5*a^5*b*d^3)*x)*sqrt(b*x^2 + a))/b^4]","A",0
63,1,420,0,1.794213," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(80 \, a^{3} b^{2} c^{2} - 20 \, a^{4} b c d + 3 \, a^{5} d^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(384 \, b^{5} d^{2} x^{9} + 48 \, {\left(20 \, b^{5} c d + 21 \, a b^{4} d^{2}\right)} x^{7} + 8 \, {\left(80 \, b^{5} c^{2} + 340 \, a b^{4} c d + 93 \, a^{2} b^{3} d^{2}\right)} x^{5} + 10 \, {\left(208 \, a b^{4} c^{2} + 236 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} x^{3} + 15 \, {\left(176 \, a^{2} b^{3} c^{2} + 20 \, a^{3} b^{2} c d - 3 \, a^{4} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{7680 \, b^{3}}, -\frac{15 \, {\left(80 \, a^{3} b^{2} c^{2} - 20 \, a^{4} b c d + 3 \, a^{5} d^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(384 \, b^{5} d^{2} x^{9} + 48 \, {\left(20 \, b^{5} c d + 21 \, a b^{4} d^{2}\right)} x^{7} + 8 \, {\left(80 \, b^{5} c^{2} + 340 \, a b^{4} c d + 93 \, a^{2} b^{3} d^{2}\right)} x^{5} + 10 \, {\left(208 \, a b^{4} c^{2} + 236 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} x^{3} + 15 \, {\left(176 \, a^{2} b^{3} c^{2} + 20 \, a^{3} b^{2} c d - 3 \, a^{4} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{3840 \, b^{3}}\right]"," ",0,"[1/7680*(15*(80*a^3*b^2*c^2 - 20*a^4*b*c*d + 3*a^5*d^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(384*b^5*d^2*x^9 + 48*(20*b^5*c*d + 21*a*b^4*d^2)*x^7 + 8*(80*b^5*c^2 + 340*a*b^4*c*d + 93*a^2*b^3*d^2)*x^5 + 10*(208*a*b^4*c^2 + 236*a^2*b^3*c*d + 3*a^3*b^2*d^2)*x^3 + 15*(176*a^2*b^3*c^2 + 20*a^3*b^2*c*d - 3*a^4*b*d^2)*x)*sqrt(b*x^2 + a))/b^3, -1/3840*(15*(80*a^3*b^2*c^2 - 20*a^4*b*c*d + 3*a^5*d^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (384*b^5*d^2*x^9 + 48*(20*b^5*c*d + 21*a*b^4*d^2)*x^7 + 8*(80*b^5*c^2 + 340*a*b^4*c*d + 93*a^2*b^3*d^2)*x^5 + 10*(208*a*b^4*c^2 + 236*a^2*b^3*c*d + 3*a^3*b^2*d^2)*x^3 + 15*(176*a^2*b^3*c^2 + 20*a^3*b^2*c*d - 3*a^4*b*d^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
64,1,260,0,1.931428," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, a^{3} b c - a^{4} d\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(48 \, b^{4} d x^{7} + 8 \, {\left(8 \, b^{4} c + 17 \, a b^{3} d\right)} x^{5} + 2 \, {\left(104 \, a b^{3} c + 59 \, a^{2} b^{2} d\right)} x^{3} + 3 \, {\left(88 \, a^{2} b^{2} c + 5 \, a^{3} b d\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, b^{2}}, -\frac{15 \, {\left(8 \, a^{3} b c - a^{4} d\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(48 \, b^{4} d x^{7} + 8 \, {\left(8 \, b^{4} c + 17 \, a b^{3} d\right)} x^{5} + 2 \, {\left(104 \, a b^{3} c + 59 \, a^{2} b^{2} d\right)} x^{3} + 3 \, {\left(88 \, a^{2} b^{2} c + 5 \, a^{3} b d\right)} x\right)} \sqrt{b x^{2} + a}}{384 \, b^{2}}\right]"," ",0,"[-1/768*(15*(8*a^3*b*c - a^4*d)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(48*b^4*d*x^7 + 8*(8*b^4*c + 17*a*b^3*d)*x^5 + 2*(104*a*b^3*c + 59*a^2*b^2*d)*x^3 + 3*(88*a^2*b^2*c + 5*a^3*b*d)*x)*sqrt(b*x^2 + a))/b^2, -1/384*(15*(8*a^3*b*c - a^4*d)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (48*b^4*d*x^7 + 8*(8*b^4*c + 17*a*b^3*d)*x^5 + 2*(104*a*b^3*c + 59*a^2*b^2*d)*x^3 + 3*(88*a^2*b^2*c + 5*a^3*b*d)*x)*sqrt(b*x^2 + a))/b^2]","A",0
65,1,146,0,1.714290," ","integrate((b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(8 \, b^{3} x^{5} + 26 \, a b^{2} x^{3} + 33 \, a^{2} b x\right)} \sqrt{b x^{2} + a}}{96 \, b}, -\frac{15 \, a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, b^{3} x^{5} + 26 \, a b^{2} x^{3} + 33 \, a^{2} b x\right)} \sqrt{b x^{2} + a}}{48 \, b}\right]"," ",0,"[1/96*(15*a^3*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(8*b^3*x^5 + 26*a*b^2*x^3 + 33*a^2*b*x)*sqrt(b*x^2 + a))/b, -1/48*(15*a^3*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*b^3*x^5 + 26*a*b^2*x^3 + 33*a^2*b*x)*sqrt(b*x^2 + a))/b]","A",0
66,1,935,0,3.399439," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} - {\left(4 \, b^{2} c d - 9 \, a b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, d^{3}}, -\frac{{\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - {\left(2 \, b^{2} d^{2} x^{3} - {\left(4 \, b^{2} c d - 9 \, a b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, d^{3}}, \frac{8 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) + {\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} - {\left(4 \, b^{2} c d - 9 \, a b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, d^{3}}, -\frac{{\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) - {\left(2 \, b^{2} d^{2} x^{3} - {\left(4 \, b^{2} c d - 9 \, a b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, d^{3}}\right]"," ",0,"[1/16*((8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 2*(2*b^2*d^2*x^3 - (4*b^2*c*d - 9*a*b*d^2)*x)*sqrt(b*x^2 + a))/d^3, -1/8*((8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - (2*b^2*d^2*x^3 - (4*b^2*c*d - 9*a*b*d^2)*x)*sqrt(b*x^2 + a))/d^3, 1/16*(8*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) + (8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*b^2*d^2*x^3 - (4*b^2*c*d - 9*a*b*d^2)*x)*sqrt(b*x^2 + a))/d^3, -1/8*((8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) - (2*b^2*d^2*x^3 - (4*b^2*c*d - 9*a*b*d^2)*x)*sqrt(b*x^2 + a))/d^3]","A",0
67,1,1236,0,2.679524," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(4 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(4 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + {\left(4 \, b^{2} c^{3} - 3 \, a b c^{2} d - a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - 3 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 4 \, {\left(b^{2} c d^{2} x^{3} + {\left(2 \, b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, {\left(c d^{4} x^{2} + c^{2} d^{3}\right)}}, \frac{4 \, {\left(4 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(4 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(4 \, b^{2} c^{3} - 3 \, a b c^{2} d - a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - 3 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left(b^{2} c d^{2} x^{3} + {\left(2 \, b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, {\left(c d^{4} x^{2} + c^{2} d^{3}\right)}}, -\frac{{\left(4 \, b^{2} c^{3} - 3 \, a b c^{2} d - a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - 3 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) + {\left(4 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(4 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(b^{2} c d^{2} x^{3} + {\left(2 \, b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{4 \, {\left(c d^{4} x^{2} + c^{2} d^{3}\right)}}, \frac{2 \, {\left(4 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(4 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(4 \, b^{2} c^{3} - 3 \, a b c^{2} d - a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - 3 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) + 2 \, {\left(b^{2} c d^{2} x^{3} + {\left(2 \, b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{4 \, {\left(c d^{4} x^{2} + c^{2} d^{3}\right)}}\right]"," ",0,"[-1/8*(2*(4*b^2*c^3 - 5*a*b*c^2*d + (4*b^2*c^2*d - 5*a*b*c*d^2)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + (4*b^2*c^3 - 3*a*b*c^2*d - a^2*c*d^2 + (4*b^2*c^2*d - 3*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 4*(b^2*c*d^2*x^3 + (2*b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*sqrt(b*x^2 + a))/(c*d^4*x^2 + c^2*d^3), 1/8*(4*(4*b^2*c^3 - 5*a*b*c^2*d + (4*b^2*c^2*d - 5*a*b*c*d^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (4*b^2*c^3 - 3*a*b*c^2*d - a^2*c*d^2 + (4*b^2*c^2*d - 3*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*(b^2*c*d^2*x^3 + (2*b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*sqrt(b*x^2 + a))/(c*d^4*x^2 + c^2*d^3), -1/4*((4*b^2*c^3 - 3*a*b*c^2*d - a^2*c*d^2 + (4*b^2*c^2*d - 3*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) + (4*b^2*c^3 - 5*a*b*c^2*d + (4*b^2*c^2*d - 5*a*b*c*d^2)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(b^2*c*d^2*x^3 + (2*b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*sqrt(b*x^2 + a))/(c*d^4*x^2 + c^2*d^3), 1/4*(2*(4*b^2*c^3 - 5*a*b*c^2*d + (4*b^2*c^2*d - 5*a*b*c*d^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (4*b^2*c^3 - 3*a*b*c^2*d - a^2*c*d^2 + (4*b^2*c^2*d - 3*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) + 2*(b^2*c*d^2*x^3 + (2*b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*sqrt(b*x^2 + a))/(c*d^4*x^2 + c^2*d^3)]","A",0
68,1,1517,0,3.101172," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + {\left(8 \, b^{2} c^{4} + 4 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(8 \, b^{2} c^{2} d^{2} + 4 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(8 \, b^{2} c^{3} d + 4 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 4 \, {\left(3 \, {\left(2 \, b^{2} c^{2} d^{2} - a b c d^{3} - a^{2} d^{4}\right)} x^{3} + {\left(4 \, b^{2} c^{3} d + a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{32 \, {\left(c^{2} d^{5} x^{4} + 2 \, c^{3} d^{4} x^{2} + c^{4} d^{3}\right)}}, -\frac{32 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, b^{2} c^{4} + 4 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(8 \, b^{2} c^{2} d^{2} + 4 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(8 \, b^{2} c^{3} d + 4 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{c}} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a c^{2} x + {\left(2 \, b c^{2} - a c d\right)} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b c - a d}{c}}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left(3 \, {\left(2 \, b^{2} c^{2} d^{2} - a b c d^{3} - a^{2} d^{4}\right)} x^{3} + {\left(4 \, b^{2} c^{3} d + a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{32 \, {\left(c^{2} d^{5} x^{4} + 2 \, c^{3} d^{4} x^{2} + c^{4} d^{3}\right)}}, \frac{{\left(8 \, b^{2} c^{4} + 4 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(8 \, b^{2} c^{2} d^{2} + 4 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(8 \, b^{2} c^{3} d + 4 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) + 8 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(3 \, {\left(2 \, b^{2} c^{2} d^{2} - a b c d^{3} - a^{2} d^{4}\right)} x^{3} + {\left(4 \, b^{2} c^{3} d + a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(c^{2} d^{5} x^{4} + 2 \, c^{3} d^{4} x^{2} + c^{4} d^{3}\right)}}, -\frac{16 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, b^{2} c^{4} + 4 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(8 \, b^{2} c^{2} d^{2} + 4 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(8 \, b^{2} c^{3} d + 4 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{c}} \arctan\left(\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b c - a d}{c}}}{2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + {\left(a b c - a^{2} d\right)} x\right)}}\right) + 2 \, {\left(3 \, {\left(2 \, b^{2} c^{2} d^{2} - a b c d^{3} - a^{2} d^{4}\right)} x^{3} + {\left(4 \, b^{2} c^{3} d + a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(c^{2} d^{5} x^{4} + 2 \, c^{3} d^{4} x^{2} + c^{4} d^{3}\right)}}\right]"," ",0,"[1/32*(16*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + (8*b^2*c^4 + 4*a*b*c^3*d + 3*a^2*c^2*d^2 + (8*b^2*c^2*d^2 + 4*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(8*b^2*c^3*d + 4*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 4*(3*(2*b^2*c^2*d^2 - a*b*c*d^3 - a^2*d^4)*x^3 + (4*b^2*c^3*d + a*b*c^2*d^2 - 5*a^2*c*d^3)*x)*sqrt(b*x^2 + a))/(c^2*d^5*x^4 + 2*c^3*d^4*x^2 + c^4*d^3), -1/32*(32*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*b^2*c^4 + 4*a*b*c^3*d + 3*a^2*c^2*d^2 + (8*b^2*c^2*d^2 + 4*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(8*b^2*c^3*d + 4*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt((b*c - a*d)/c)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 - 4*(a*c^2*x + (2*b*c^2 - a*c*d)*x^3)*sqrt(b*x^2 + a)*sqrt((b*c - a*d)/c))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*(3*(2*b^2*c^2*d^2 - a*b*c*d^3 - a^2*d^4)*x^3 + (4*b^2*c^3*d + a*b*c^2*d^2 - 5*a^2*c*d^3)*x)*sqrt(b*x^2 + a))/(c^2*d^5*x^4 + 2*c^3*d^4*x^2 + c^4*d^3), 1/16*((8*b^2*c^4 + 4*a*b*c^3*d + 3*a^2*c^2*d^2 + (8*b^2*c^2*d^2 + 4*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(8*b^2*c^3*d + 4*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) + 8*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(3*(2*b^2*c^2*d^2 - a*b*c*d^3 - a^2*d^4)*x^3 + (4*b^2*c^3*d + a*b*c^2*d^2 - 5*a^2*c*d^3)*x)*sqrt(b*x^2 + a))/(c^2*d^5*x^4 + 2*c^3*d^4*x^2 + c^4*d^3), -1/16*(16*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*b^2*c^4 + 4*a*b*c^3*d + 3*a^2*c^2*d^2 + (8*b^2*c^2*d^2 + 4*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(8*b^2*c^3*d + 4*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-(b*c - a*d)/c)*arctan(1/2*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(-(b*c - a*d)/c)/((b^2*c - a*b*d)*x^3 + (a*b*c - a^2*d)*x)) + 2*(3*(2*b^2*c^2*d^2 - a*b*c*d^3 - a^2*d^4)*x^3 + (4*b^2*c^3*d + a*b*c^2*d^2 - 5*a^2*c*d^3)*x)*sqrt(b*x^2 + a))/(c^2*d^5*x^4 + 2*c^3*d^4*x^2 + c^4*d^3)]","B",0
69,1,706,0,1.513062," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} d^{3} x^{6} + 3 \, a^{3} c d^{2} x^{4} + 3 \, a^{3} c^{2} d x^{2} + a^{3} c^{3}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(8 \, b^{3} c^{4} + 2 \, a b^{2} c^{3} d + 5 \, a^{2} b c^{2} d^{2} - 15 \, a^{3} c d^{3}\right)} x^{5} + 2 \, {\left(13 \, a b^{2} c^{4} + 7 \, a^{2} b c^{3} d - 20 \, a^{3} c^{2} d^{2}\right)} x^{3} + 33 \, {\left(a^{2} b c^{4} - a^{3} c^{3} d\right)} x\right)} \sqrt{b x^{2} + a}}{192 \, {\left(b c^{8} - a c^{7} d + {\left(b c^{5} d^{3} - a c^{4} d^{4}\right)} x^{6} + 3 \, {\left(b c^{6} d^{2} - a c^{5} d^{3}\right)} x^{4} + 3 \, {\left(b c^{7} d - a c^{6} d^{2}\right)} x^{2}\right)}}, -\frac{15 \, {\left(a^{3} d^{3} x^{6} + 3 \, a^{3} c d^{2} x^{4} + 3 \, a^{3} c^{2} d x^{2} + a^{3} c^{3}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(8 \, b^{3} c^{4} + 2 \, a b^{2} c^{3} d + 5 \, a^{2} b c^{2} d^{2} - 15 \, a^{3} c d^{3}\right)} x^{5} + 2 \, {\left(13 \, a b^{2} c^{4} + 7 \, a^{2} b c^{3} d - 20 \, a^{3} c^{2} d^{2}\right)} x^{3} + 33 \, {\left(a^{2} b c^{4} - a^{3} c^{3} d\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, {\left(b c^{8} - a c^{7} d + {\left(b c^{5} d^{3} - a c^{4} d^{4}\right)} x^{6} + 3 \, {\left(b c^{6} d^{2} - a c^{5} d^{3}\right)} x^{4} + 3 \, {\left(b c^{7} d - a c^{6} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/192*(15*(a^3*d^3*x^6 + 3*a^3*c*d^2*x^4 + 3*a^3*c^2*d*x^2 + a^3*c^3)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((8*b^3*c^4 + 2*a*b^2*c^3*d + 5*a^2*b*c^2*d^2 - 15*a^3*c*d^3)*x^5 + 2*(13*a*b^2*c^4 + 7*a^2*b*c^3*d - 20*a^3*c^2*d^2)*x^3 + 33*(a^2*b*c^4 - a^3*c^3*d)*x)*sqrt(b*x^2 + a))/(b*c^8 - a*c^7*d + (b*c^5*d^3 - a*c^4*d^4)*x^6 + 3*(b*c^6*d^2 - a*c^5*d^3)*x^4 + 3*(b*c^7*d - a*c^6*d^2)*x^2), -1/96*(15*(a^3*d^3*x^6 + 3*a^3*c*d^2*x^4 + 3*a^3*c^2*d*x^2 + a^3*c^3)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((8*b^3*c^4 + 2*a*b^2*c^3*d + 5*a^2*b*c^2*d^2 - 15*a^3*c*d^3)*x^5 + 2*(13*a*b^2*c^4 + 7*a^2*b*c^3*d - 20*a^3*c^2*d^2)*x^3 + 33*(a^2*b*c^4 - a^3*c^3*d)*x)*sqrt(b*x^2 + a))/(b*c^8 - a*c^7*d + (b*c^5*d^3 - a*c^4*d^4)*x^6 + 3*(b*c^6*d^2 - a*c^5*d^3)*x^4 + 3*(b*c^7*d - a*c^6*d^2)*x^2)]","B",0
70,1,1258,0,2.682171," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(8 \, a^{3} b c^{5} - 7 \, a^{4} c^{4} d + {\left(8 \, a^{3} b c d^{4} - 7 \, a^{4} d^{5}\right)} x^{8} + 4 \, {\left(8 \, a^{3} b c^{2} d^{3} - 7 \, a^{4} c d^{4}\right)} x^{6} + 6 \, {\left(8 \, a^{3} b c^{3} d^{2} - 7 \, a^{4} c^{2} d^{3}\right)} x^{4} + 4 \, {\left(8 \, a^{3} b c^{4} d - 7 \, a^{4} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(16 \, b^{4} c^{5} d + 8 \, a b^{3} c^{4} d^{2} + 26 \, a^{2} b^{2} c^{3} d^{3} - 155 \, a^{3} b c^{2} d^{4} + 105 \, a^{4} c d^{5}\right)} x^{7} + {\left(64 \, b^{4} c^{6} + 24 \, a b^{3} c^{5} d + 100 \, a^{2} b^{2} c^{4} d^{2} - 573 \, a^{3} b c^{3} d^{3} + 385 \, a^{4} c^{2} d^{4}\right)} x^{5} + {\left(208 \, a b^{3} c^{6} + 50 \, a^{2} b^{2} c^{5} d - 769 \, a^{3} b c^{4} d^{2} + 511 \, a^{4} c^{3} d^{3}\right)} x^{3} + 3 \, {\left(88 \, a^{2} b^{2} c^{6} - 181 \, a^{3} b c^{5} d + 93 \, a^{4} c^{4} d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{1536 \, {\left(b^{2} c^{11} - 2 \, a b c^{10} d + a^{2} c^{9} d^{2} + {\left(b^{2} c^{7} d^{4} - 2 \, a b c^{6} d^{5} + a^{2} c^{5} d^{6}\right)} x^{8} + 4 \, {\left(b^{2} c^{8} d^{3} - 2 \, a b c^{7} d^{4} + a^{2} c^{6} d^{5}\right)} x^{6} + 6 \, {\left(b^{2} c^{9} d^{2} - 2 \, a b c^{8} d^{3} + a^{2} c^{7} d^{4}\right)} x^{4} + 4 \, {\left(b^{2} c^{10} d - 2 \, a b c^{9} d^{2} + a^{2} c^{8} d^{3}\right)} x^{2}\right)}}, -\frac{15 \, {\left(8 \, a^{3} b c^{5} - 7 \, a^{4} c^{4} d + {\left(8 \, a^{3} b c d^{4} - 7 \, a^{4} d^{5}\right)} x^{8} + 4 \, {\left(8 \, a^{3} b c^{2} d^{3} - 7 \, a^{4} c d^{4}\right)} x^{6} + 6 \, {\left(8 \, a^{3} b c^{3} d^{2} - 7 \, a^{4} c^{2} d^{3}\right)} x^{4} + 4 \, {\left(8 \, a^{3} b c^{4} d - 7 \, a^{4} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(16 \, b^{4} c^{5} d + 8 \, a b^{3} c^{4} d^{2} + 26 \, a^{2} b^{2} c^{3} d^{3} - 155 \, a^{3} b c^{2} d^{4} + 105 \, a^{4} c d^{5}\right)} x^{7} + {\left(64 \, b^{4} c^{6} + 24 \, a b^{3} c^{5} d + 100 \, a^{2} b^{2} c^{4} d^{2} - 573 \, a^{3} b c^{3} d^{3} + 385 \, a^{4} c^{2} d^{4}\right)} x^{5} + {\left(208 \, a b^{3} c^{6} + 50 \, a^{2} b^{2} c^{5} d - 769 \, a^{3} b c^{4} d^{2} + 511 \, a^{4} c^{3} d^{3}\right)} x^{3} + 3 \, {\left(88 \, a^{2} b^{2} c^{6} - 181 \, a^{3} b c^{5} d + 93 \, a^{4} c^{4} d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, {\left(b^{2} c^{11} - 2 \, a b c^{10} d + a^{2} c^{9} d^{2} + {\left(b^{2} c^{7} d^{4} - 2 \, a b c^{6} d^{5} + a^{2} c^{5} d^{6}\right)} x^{8} + 4 \, {\left(b^{2} c^{8} d^{3} - 2 \, a b c^{7} d^{4} + a^{2} c^{6} d^{5}\right)} x^{6} + 6 \, {\left(b^{2} c^{9} d^{2} - 2 \, a b c^{8} d^{3} + a^{2} c^{7} d^{4}\right)} x^{4} + 4 \, {\left(b^{2} c^{10} d - 2 \, a b c^{9} d^{2} + a^{2} c^{8} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/1536*(15*(8*a^3*b*c^5 - 7*a^4*c^4*d + (8*a^3*b*c*d^4 - 7*a^4*d^5)*x^8 + 4*(8*a^3*b*c^2*d^3 - 7*a^4*c*d^4)*x^6 + 6*(8*a^3*b*c^3*d^2 - 7*a^4*c^2*d^3)*x^4 + 4*(8*a^3*b*c^4*d - 7*a^4*c^3*d^2)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((16*b^4*c^5*d + 8*a*b^3*c^4*d^2 + 26*a^2*b^2*c^3*d^3 - 155*a^3*b*c^2*d^4 + 105*a^4*c*d^5)*x^7 + (64*b^4*c^6 + 24*a*b^3*c^5*d + 100*a^2*b^2*c^4*d^2 - 573*a^3*b*c^3*d^3 + 385*a^4*c^2*d^4)*x^5 + (208*a*b^3*c^6 + 50*a^2*b^2*c^5*d - 769*a^3*b*c^4*d^2 + 511*a^4*c^3*d^3)*x^3 + 3*(88*a^2*b^2*c^6 - 181*a^3*b*c^5*d + 93*a^4*c^4*d^2)*x)*sqrt(b*x^2 + a))/(b^2*c^11 - 2*a*b*c^10*d + a^2*c^9*d^2 + (b^2*c^7*d^4 - 2*a*b*c^6*d^5 + a^2*c^5*d^6)*x^8 + 4*(b^2*c^8*d^3 - 2*a*b*c^7*d^4 + a^2*c^6*d^5)*x^6 + 6*(b^2*c^9*d^2 - 2*a*b*c^8*d^3 + a^2*c^7*d^4)*x^4 + 4*(b^2*c^10*d - 2*a*b*c^9*d^2 + a^2*c^8*d^3)*x^2), -1/768*(15*(8*a^3*b*c^5 - 7*a^4*c^4*d + (8*a^3*b*c*d^4 - 7*a^4*d^5)*x^8 + 4*(8*a^3*b*c^2*d^3 - 7*a^4*c*d^4)*x^6 + 6*(8*a^3*b*c^3*d^2 - 7*a^4*c^2*d^3)*x^4 + 4*(8*a^3*b*c^4*d - 7*a^4*c^3*d^2)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((16*b^4*c^5*d + 8*a*b^3*c^4*d^2 + 26*a^2*b^2*c^3*d^3 - 155*a^3*b*c^2*d^4 + 105*a^4*c*d^5)*x^7 + (64*b^4*c^6 + 24*a*b^3*c^5*d + 100*a^2*b^2*c^4*d^2 - 573*a^3*b*c^3*d^3 + 385*a^4*c^2*d^4)*x^5 + (208*a*b^3*c^6 + 50*a^2*b^2*c^5*d - 769*a^3*b*c^4*d^2 + 511*a^4*c^3*d^3)*x^3 + 3*(88*a^2*b^2*c^6 - 181*a^3*b*c^5*d + 93*a^4*c^4*d^2)*x)*sqrt(b*x^2 + a))/(b^2*c^11 - 2*a*b*c^10*d + a^2*c^9*d^2 + (b^2*c^7*d^4 - 2*a*b*c^6*d^5 + a^2*c^5*d^6)*x^8 + 4*(b^2*c^8*d^3 - 2*a*b*c^7*d^4 + a^2*c^6*d^5)*x^6 + 6*(b^2*c^9*d^2 - 2*a*b*c^8*d^3 + a^2*c^7*d^4)*x^4 + 4*(b^2*c^10*d - 2*a*b*c^9*d^2 + a^2*c^8*d^3)*x^2)]","B",0
71,1,42,0,0.850161," ","integrate((-x^2+1)^(1/2)/(x^2+1),x, algorithm=""fricas"")","-\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-x^{2} + 1}}{2 \, x}\right) + 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-x^2 + 1)/x) + 2*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
72,1,67,0,0.638627," ","integrate((x^2+1)^(1/2)/(x^2-1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{9 \, x^{2} - 2 \, \sqrt{2} {\left(3 \, x^{2} + 1\right)} - 2 \, \sqrt{x^{2} + 1} {\left(3 \, \sqrt{2} x - 4 \, x\right)} + 3}{x^{2} - 1}\right) - \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"1/2*sqrt(2)*log((9*x^2 - 2*sqrt(2)*(3*x^2 + 1) - 2*sqrt(x^2 + 1)*(3*sqrt(2)*x - 4*x) + 3)/(x^2 - 1)) - log(-x + sqrt(x^2 + 1))","B",0
73,1,74,0,1.129073," ","integrate((-x^2+1)^(1/2)/(2*x^2-1),x, algorithm=""fricas"")","\arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + \frac{1}{4} \, \log\left(-\frac{x^{2} + \sqrt{-x^{2} + 1} {\left(x + 1\right)} - x - 1}{x^{2}}\right) - \frac{1}{4} \, \log\left(-\frac{x^{2} - \sqrt{-x^{2} + 1} {\left(x - 1\right)} + x - 1}{x^{2}}\right)"," ",0,"arctan((sqrt(-x^2 + 1) - 1)/x) + 1/4*log(-(x^2 + sqrt(-x^2 + 1)*(x + 1) - x - 1)/x^2) - 1/4*log(-(x^2 - sqrt(-x^2 + 1)*(x - 1) + x - 1)/x^2)","B",0
74,1,300,0,1.179975," ","integrate((d*x^2+c)^3/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(16 \, b^{3} c^{3} - 24 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(18 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(24 \, b^{3} c^{2} d - 18 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, b^{4}}, -\frac{3 \, {\left(16 \, b^{3} c^{3} - 24 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(18 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(24 \, b^{3} c^{2} d - 18 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, b^{4}}\right]"," ",0,"[-1/96*(3*(16*b^3*c^3 - 24*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*b^3*d^3*x^5 + 2*(18*b^3*c*d^2 - 5*a*b^2*d^3)*x^3 + 3*(24*b^3*c^2*d - 18*a*b^2*c*d^2 + 5*a^2*b*d^3)*x)*sqrt(b*x^2 + a))/b^4, -1/48*(3*(16*b^3*c^3 - 24*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*b^3*d^3*x^5 + 2*(18*b^3*c*d^2 - 5*a*b^2*d^3)*x^3 + 3*(24*b^3*c^2*d - 18*a*b^2*c*d^2 + 5*a^2*b*d^3)*x)*sqrt(b*x^2 + a))/b^4]","A",0
75,1,192,0,1.311066," ","integrate((d*x^2+c)^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} + {\left(8 \, b^{2} c d - 3 \, a b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, b^{3}}, -\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, b^{2} d^{2} x^{3} + {\left(8 \, b^{2} c d - 3 \, a b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, b^{3}}\right]"," ",0,"[1/16*((8*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*b^2*d^2*x^3 + (8*b^2*c*d - 3*a*b*d^2)*x)*sqrt(b*x^2 + a))/b^3, -1/8*((8*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*b^2*d^2*x^3 + (8*b^2*c*d - 3*a*b*d^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
76,1,113,0,0.673891," ","integrate((d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{2} + a} b d x - {\left(2 \, b c - a d\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{4 \, b^{2}}, \frac{\sqrt{b x^{2} + a} b d x - {\left(2 \, b c - a d\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{2 \, b^{2}}\right]"," ",0,"[1/4*(2*sqrt(b*x^2 + a)*b*d*x - (2*b*c - a*d)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/b^2, 1/2*(sqrt(b*x^2 + a)*b*d*x - (2*b*c - a*d)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)))/b^2]","A",0
77,1,59,0,1.248390," ","integrate(1/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{2 \, \sqrt{b}}, -\frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{b}\right]"," ",0,"[1/2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a)/sqrt(b), -sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a))/b]","A",0
78,1,241,0,1.451578," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{4 \, \sqrt{b c^{2} - a c d}}, -\frac{\sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{2 \, {\left(b c^{2} - a c d\right)}}\right]"," ",0,"[1/4*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2))/sqrt(b*c^2 - a*c*d), -1/2*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x))/(b*c^2 - a*c*d)]","B",0
79,1,463,0,1.624864," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(b c^{2} d - a c d^{2}\right)} \sqrt{b x^{2} + a} x - {\left(2 \, b c^{2} - a c d + {\left(2 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{8 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x^{2}\right)}}, -\frac{2 \, {\left(b c^{2} d - a c d^{2}\right)} \sqrt{b x^{2} + a} x + {\left(2 \, b c^{2} - a c d + {\left(2 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{4 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(4*(b*c^2*d - a*c*d^2)*sqrt(b*x^2 + a)*x - (2*b*c^2 - a*c*d + (2*b*c*d - a*d^2)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x^2), -1/4*(2*(b*c^2*d - a*c*d^2)*sqrt(b*x^2 + a)*x + (2*b*c^2 - a*c*d + (2*b*c*d - a*d^2)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x^2)]","B",0
80,1,864,0,1.969411," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{{\left(8 \, b^{2} c^{4} - 8 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(8 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(8 \, b^{2} c^{3} d - 8 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 4 \, {\left(3 \, {\left(2 \, b^{2} c^{3} d^{2} - 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{3} + {\left(8 \, b^{2} c^{4} d - 13 \, a b c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{32 \, {\left(b^{3} c^{8} - 3 \, a b^{2} c^{7} d + 3 \, a^{2} b c^{6} d^{2} - a^{3} c^{5} d^{3} + {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4}\right)} x^{2}\right)}}, -\frac{{\left(8 \, b^{2} c^{4} - 8 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(8 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(8 \, b^{2} c^{3} d - 8 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(3 \, {\left(2 \, b^{2} c^{3} d^{2} - 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{3} + {\left(8 \, b^{2} c^{4} d - 13 \, a b c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(b^{3} c^{8} - 3 \, a b^{2} c^{7} d + 3 \, a^{2} b c^{6} d^{2} - a^{3} c^{5} d^{3} + {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/32*((8*b^2*c^4 - 8*a*b*c^3*d + 3*a^2*c^2*d^2 + (8*b^2*c^2*d^2 - 8*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(8*b^2*c^3*d - 8*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 4*(3*(2*b^2*c^3*d^2 - 3*a*b*c^2*d^3 + a^2*c*d^4)*x^3 + (8*b^2*c^4*d - 13*a*b*c^3*d^2 + 5*a^2*c^2*d^3)*x)*sqrt(b*x^2 + a))/(b^3*c^8 - 3*a*b^2*c^7*d + 3*a^2*b*c^6*d^2 - a^3*c^5*d^3 + (b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*x^4 + 2*(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4)*x^2), -1/16*((8*b^2*c^4 - 8*a*b*c^3*d + 3*a^2*c^2*d^2 + (8*b^2*c^2*d^2 - 8*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(8*b^2*c^3*d - 8*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(3*(2*b^2*c^3*d^2 - 3*a*b*c^2*d^3 + a^2*c*d^4)*x^3 + (8*b^2*c^4*d - 13*a*b*c^3*d^2 + 5*a^2*c^2*d^3)*x)*sqrt(b*x^2 + a))/(b^3*c^8 - 3*a*b^2*c^7*d + 3*a^2*b*c^6*d^2 - a^3*c^5*d^3 + (b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*x^4 + 2*(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4)*x^2)]","B",0
81,1,584,0,1.385539," ","integrate((d*x^2+c)^4/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, a^{2} b^{3} c^{3} d - 144 \, a^{3} b^{2} c^{2} d^{2} + 120 \, a^{4} b c d^{3} - 35 \, a^{5} d^{4} + {\left(64 \, a b^{4} c^{3} d - 144 \, a^{2} b^{3} c^{2} d^{2} + 120 \, a^{3} b^{2} c d^{3} - 35 \, a^{4} b d^{4}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, a b^{4} d^{4} x^{7} + 2 \, {\left(24 \, a b^{4} c d^{3} - 7 \, a^{2} b^{3} d^{4}\right)} x^{5} + {\left(144 \, a b^{4} c^{2} d^{2} - 120 \, a^{2} b^{3} c d^{3} + 35 \, a^{3} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(16 \, b^{5} c^{4} - 64 \, a b^{4} c^{3} d + 144 \, a^{2} b^{3} c^{2} d^{2} - 120 \, a^{3} b^{2} c d^{3} + 35 \, a^{4} b d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, {\left(a b^{6} x^{2} + a^{2} b^{5}\right)}}, -\frac{3 \, {\left(64 \, a^{2} b^{3} c^{3} d - 144 \, a^{3} b^{2} c^{2} d^{2} + 120 \, a^{4} b c d^{3} - 35 \, a^{5} d^{4} + {\left(64 \, a b^{4} c^{3} d - 144 \, a^{2} b^{3} c^{2} d^{2} + 120 \, a^{3} b^{2} c d^{3} - 35 \, a^{4} b d^{4}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, a b^{4} d^{4} x^{7} + 2 \, {\left(24 \, a b^{4} c d^{3} - 7 \, a^{2} b^{3} d^{4}\right)} x^{5} + {\left(144 \, a b^{4} c^{2} d^{2} - 120 \, a^{2} b^{3} c d^{3} + 35 \, a^{3} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(16 \, b^{5} c^{4} - 64 \, a b^{4} c^{3} d + 144 \, a^{2} b^{3} c^{2} d^{2} - 120 \, a^{3} b^{2} c d^{3} + 35 \, a^{4} b d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, {\left(a b^{6} x^{2} + a^{2} b^{5}\right)}}\right]"," ",0,"[-1/96*(3*(64*a^2*b^3*c^3*d - 144*a^3*b^2*c^2*d^2 + 120*a^4*b*c*d^3 - 35*a^5*d^4 + (64*a*b^4*c^3*d - 144*a^2*b^3*c^2*d^2 + 120*a^3*b^2*c*d^3 - 35*a^4*b*d^4)*x^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*a*b^4*d^4*x^7 + 2*(24*a*b^4*c*d^3 - 7*a^2*b^3*d^4)*x^5 + (144*a*b^4*c^2*d^2 - 120*a^2*b^3*c*d^3 + 35*a^3*b^2*d^4)*x^3 + 3*(16*b^5*c^4 - 64*a*b^4*c^3*d + 144*a^2*b^3*c^2*d^2 - 120*a^3*b^2*c*d^3 + 35*a^4*b*d^4)*x)*sqrt(b*x^2 + a))/(a*b^6*x^2 + a^2*b^5), -1/48*(3*(64*a^2*b^3*c^3*d - 144*a^3*b^2*c^2*d^2 + 120*a^4*b*c*d^3 - 35*a^5*d^4 + (64*a*b^4*c^3*d - 144*a^2*b^3*c^2*d^2 + 120*a^3*b^2*c*d^3 - 35*a^4*b*d^4)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*a*b^4*d^4*x^7 + 2*(24*a*b^4*c*d^3 - 7*a^2*b^3*d^4)*x^5 + (144*a*b^4*c^2*d^2 - 120*a^2*b^3*c*d^3 + 35*a^3*b^2*d^4)*x^3 + 3*(16*b^5*c^4 - 64*a*b^4*c^3*d + 144*a^2*b^3*c^2*d^2 - 120*a^3*b^2*c*d^3 + 35*a^4*b*d^4)*x)*sqrt(b*x^2 + a))/(a*b^6*x^2 + a^2*b^5)]","A",0
82,1,416,0,0.888261," ","integrate((d*x^2+c)^3/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a^{2} b^{2} c^{2} d - 12 \, a^{3} b c d^{2} + 5 \, a^{4} d^{3} + {\left(8 \, a b^{3} c^{2} d - 12 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, a b^{3} d^{3} x^{5} + {\left(12 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{3} + {\left(8 \, b^{4} c^{3} - 24 \, a b^{3} c^{2} d + 36 \, a^{2} b^{2} c d^{2} - 15 \, a^{3} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(a b^{5} x^{2} + a^{2} b^{4}\right)}}, -\frac{3 \, {\left(8 \, a^{2} b^{2} c^{2} d - 12 \, a^{3} b c d^{2} + 5 \, a^{4} d^{3} + {\left(8 \, a b^{3} c^{2} d - 12 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, a b^{3} d^{3} x^{5} + {\left(12 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{3} + {\left(8 \, b^{4} c^{3} - 24 \, a b^{3} c^{2} d + 36 \, a^{2} b^{2} c d^{2} - 15 \, a^{3} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, {\left(a b^{5} x^{2} + a^{2} b^{4}\right)}}\right]"," ",0,"[1/16*(3*(8*a^2*b^2*c^2*d - 12*a^3*b*c*d^2 + 5*a^4*d^3 + (8*a*b^3*c^2*d - 12*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*a*b^3*d^3*x^5 + (12*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^3 + (8*b^4*c^3 - 24*a*b^3*c^2*d + 36*a^2*b^2*c*d^2 - 15*a^3*b*d^3)*x)*sqrt(b*x^2 + a))/(a*b^5*x^2 + a^2*b^4), -1/8*(3*(8*a^2*b^2*c^2*d - 12*a^3*b*c*d^2 + 5*a^4*d^3 + (8*a*b^3*c^2*d - 12*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*a*b^3*d^3*x^5 + (12*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^3 + (8*b^4*c^3 - 24*a*b^3*c^2*d + 36*a^2*b^2*c*d^2 - 15*a^3*b*d^3)*x)*sqrt(b*x^2 + a))/(a*b^5*x^2 + a^2*b^4)]","A",0
83,1,276,0,0.942411," ","integrate((d*x^2+c)^2/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(a b^{2} d^{2} x^{3} + {\left(2 \, b^{3} c^{2} - 4 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{4 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, -\frac{{\left(4 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(a b^{2} d^{2} x^{3} + {\left(2 \, b^{3} c^{2} - 4 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}\right]"," ",0,"[-1/4*((4*a^2*b*c*d - 3*a^3*d^2 + (4*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(a*b^2*d^2*x^3 + (2*b^3*c^2 - 4*a*b^2*c*d + 3*a^2*b*d^2)*x)*sqrt(b*x^2 + a))/(a*b^4*x^2 + a^2*b^3), -1/2*((4*a^2*b*c*d - 3*a^3*d^2 + (4*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (a*b^2*d^2*x^3 + (2*b^3*c^2 - 4*a*b^2*c*d + 3*a^2*b*d^2)*x)*sqrt(b*x^2 + a))/(a*b^4*x^2 + a^2*b^3)]","A",0
84,1,167,0,0.889022," ","integrate((d*x^2+c)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - a b d\right)} \sqrt{b x^{2} + a} x + {\left(a b d x^{2} + a^{2} d\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}, \frac{{\left(b^{2} c - a b d\right)} \sqrt{b x^{2} + a} x - {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{a b^{3} x^{2} + a^{2} b^{2}}\right]"," ",0,"[1/2*(2*(b^2*c - a*b*d)*sqrt(b*x^2 + a)*x + (a*b*d*x^2 + a^2*d)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/(a*b^3*x^2 + a^2*b^2), ((b^2*c - a*b*d)*sqrt(b*x^2 + a)*x - (a*b*d*x^2 + a^2*d)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)))/(a*b^3*x^2 + a^2*b^2)]","A",0
85,1,23,0,0.956930," ","integrate(1/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2} + a} x}{a b x^{2} + a^{2}}"," ",0,"sqrt(b*x^2 + a)*x/(a*b*x^2 + a^2)","A",0
86,1,441,0,1.221401," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{2} c^{2} - a b c d\right)} \sqrt{b x^{2} + a} x - {\left(a b d x^{2} + a^{2} d\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{4 \, {\left(a^{2} b^{2} c^{3} - 2 \, a^{3} b c^{2} d + a^{4} c d^{2} + {\left(a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d + a^{3} b c d^{2}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{2} c^{2} - a b c d\right)} \sqrt{b x^{2} + a} x + {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{2 \, {\left(a^{2} b^{2} c^{3} - 2 \, a^{3} b c^{2} d + a^{4} c d^{2} + {\left(a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d + a^{3} b c d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(4*(b^2*c^2 - a*b*c*d)*sqrt(b*x^2 + a)*x - (a*b*d*x^2 + a^2*d)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)))/(a^2*b^2*c^3 - 2*a^3*b*c^2*d + a^4*c*d^2 + (a*b^3*c^3 - 2*a^2*b^2*c^2*d + a^3*b*c*d^2)*x^2), 1/2*(2*(b^2*c^2 - a*b*c*d)*sqrt(b*x^2 + a)*x + (a*b*d*x^2 + a^2*d)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(a^2*b^2*c^3 - 2*a^3*b*c^2*d + a^4*c*d^2 + (a*b^3*c^3 - 2*a^2*b^2*c^2*d + a^3*b*c*d^2)*x^2)]","B",0
87,1,864,0,2.222547," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(4 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 4 \, {\left({\left(2 \, b^{3} c^{3} d - a b^{2} c^{2} d^{2} - a^{2} b c d^{3}\right)} x^{3} + {\left(2 \, b^{3} c^{4} - 2 \, a b^{2} c^{3} d + a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, {\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} + {\left(a b^{4} c^{5} d - 3 \, a^{2} b^{3} c^{4} d^{2} + 3 \, a^{3} b^{2} c^{3} d^{3} - a^{4} b c^{2} d^{4}\right)} x^{4} + {\left(a b^{4} c^{6} - 2 \, a^{2} b^{3} c^{5} d + 2 \, a^{4} b c^{3} d^{3} - a^{5} c^{2} d^{4}\right)} x^{2}\right)}}, \frac{{\left(4 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(4 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left({\left(2 \, b^{3} c^{3} d - a b^{2} c^{2} d^{2} - a^{2} b c d^{3}\right)} x^{3} + {\left(2 \, b^{3} c^{4} - 2 \, a b^{2} c^{3} d + a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{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} + {\left(a b^{4} c^{5} d - 3 \, a^{2} b^{3} c^{4} d^{2} + 3 \, a^{3} b^{2} c^{3} d^{3} - a^{4} b c^{2} d^{4}\right)} x^{4} + {\left(a b^{4} c^{6} - 2 \, a^{2} b^{3} c^{5} d + 2 \, a^{4} b c^{3} d^{3} - a^{5} c^{2} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*((4*a^2*b*c^2*d - a^3*c*d^2 + (4*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (4*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 4*((2*b^3*c^3*d - a*b^2*c^2*d^2 - a^2*b*c*d^3)*x^3 + (2*b^3*c^4 - 2*a*b^2*c^3*d + a^2*b*c^2*d^2 - a^3*c*d^3)*x)*sqrt(b*x^2 + a))/(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 + (a*b^4*c^5*d - 3*a^2*b^3*c^4*d^2 + 3*a^3*b^2*c^3*d^3 - a^4*b*c^2*d^4)*x^4 + (a*b^4*c^6 - 2*a^2*b^3*c^5*d + 2*a^4*b*c^3*d^3 - a^5*c^2*d^4)*x^2), 1/4*((4*a^2*b*c^2*d - a^3*c*d^2 + (4*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (4*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*((2*b^3*c^3*d - a*b^2*c^2*d^2 - a^2*b*c*d^3)*x^3 + (2*b^3*c^4 - 2*a*b^2*c^3*d + a^2*b*c^2*d^2 - a^3*c*d^3)*x)*sqrt(b*x^2 + a))/(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 + (a*b^4*c^5*d - 3*a^2*b^3*c^4*d^2 + 3*a^3*b^2*c^3*d^3 - a^4*b*c^2*d^4)*x^4 + (a*b^4*c^6 - 2*a^2*b^3*c^5*d + 2*a^4*b*c^3*d^3 - a^5*c^2*d^4)*x^2)]","B",0
88,1,1482,0,3.781732," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, a^{2} b^{2} c^{4} d - 4 \, a^{3} b c^{3} d^{2} + a^{4} c^{2} d^{3} + {\left(8 \, a b^{3} c^{2} d^{3} - 4 \, a^{2} b^{2} c d^{4} + a^{3} b d^{5}\right)} x^{6} + {\left(16 \, a b^{3} c^{3} d^{2} - 2 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} x^{4} + {\left(8 \, a b^{3} c^{4} d + 12 \, a^{2} b^{2} c^{3} d^{2} - 7 \, a^{3} b c^{2} d^{3} + 2 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 4 \, {\left({\left(8 \, b^{4} c^{4} d^{2} + 2 \, a b^{3} c^{3} d^{3} - 13 \, a^{2} b^{2} c^{2} d^{4} + 3 \, a^{3} b c d^{5}\right)} x^{5} + {\left(16 \, b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} - 7 \, a^{2} b^{2} c^{3} d^{3} - 8 \, a^{3} b c^{2} d^{4} + 3 \, a^{4} c d^{5}\right)} x^{3} + {\left(8 \, b^{4} c^{6} - 8 \, a b^{3} c^{5} d + 12 \, a^{2} b^{2} c^{4} d^{2} - 17 \, a^{3} b c^{3} d^{3} + 5 \, a^{4} c^{2} d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{32 \, {\left(a^{2} b^{4} c^{9} - 4 \, a^{3} b^{3} c^{8} d + 6 \, a^{4} b^{2} c^{7} d^{2} - 4 \, a^{5} b c^{6} d^{3} + a^{6} c^{5} d^{4} + {\left(a b^{5} c^{7} d^{2} - 4 \, a^{2} b^{4} c^{6} d^{3} + 6 \, a^{3} b^{3} c^{5} d^{4} - 4 \, a^{4} b^{2} c^{4} d^{5} + a^{5} b c^{3} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{8} d - 7 \, a^{2} b^{4} c^{7} d^{2} + 8 \, a^{3} b^{3} c^{6} d^{3} - 2 \, a^{4} b^{2} c^{5} d^{4} - 2 \, a^{5} b c^{4} d^{5} + a^{6} c^{3} d^{6}\right)} x^{4} + {\left(a b^{5} c^{9} - 2 \, a^{2} b^{4} c^{8} d - 2 \, a^{3} b^{3} c^{7} d^{2} + 8 \, a^{4} b^{2} c^{6} d^{3} - 7 \, a^{5} b c^{5} d^{4} + 2 \, a^{6} c^{4} d^{5}\right)} x^{2}\right)}}, \frac{3 \, {\left(8 \, a^{2} b^{2} c^{4} d - 4 \, a^{3} b c^{3} d^{2} + a^{4} c^{2} d^{3} + {\left(8 \, a b^{3} c^{2} d^{3} - 4 \, a^{2} b^{2} c d^{4} + a^{3} b d^{5}\right)} x^{6} + {\left(16 \, a b^{3} c^{3} d^{2} - 2 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} x^{4} + {\left(8 \, a b^{3} c^{4} d + 12 \, a^{2} b^{2} c^{3} d^{2} - 7 \, a^{3} b c^{2} d^{3} + 2 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left({\left(8 \, b^{4} c^{4} d^{2} + 2 \, a b^{3} c^{3} d^{3} - 13 \, a^{2} b^{2} c^{2} d^{4} + 3 \, a^{3} b c d^{5}\right)} x^{5} + {\left(16 \, b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} - 7 \, a^{2} b^{2} c^{3} d^{3} - 8 \, a^{3} b c^{2} d^{4} + 3 \, a^{4} c d^{5}\right)} x^{3} + {\left(8 \, b^{4} c^{6} - 8 \, a b^{3} c^{5} d + 12 \, a^{2} b^{2} c^{4} d^{2} - 17 \, a^{3} b c^{3} d^{3} + 5 \, a^{4} c^{2} d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(a^{2} b^{4} c^{9} - 4 \, a^{3} b^{3} c^{8} d + 6 \, a^{4} b^{2} c^{7} d^{2} - 4 \, a^{5} b c^{6} d^{3} + a^{6} c^{5} d^{4} + {\left(a b^{5} c^{7} d^{2} - 4 \, a^{2} b^{4} c^{6} d^{3} + 6 \, a^{3} b^{3} c^{5} d^{4} - 4 \, a^{4} b^{2} c^{4} d^{5} + a^{5} b c^{3} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{8} d - 7 \, a^{2} b^{4} c^{7} d^{2} + 8 \, a^{3} b^{3} c^{6} d^{3} - 2 \, a^{4} b^{2} c^{5} d^{4} - 2 \, a^{5} b c^{4} d^{5} + a^{6} c^{3} d^{6}\right)} x^{4} + {\left(a b^{5} c^{9} - 2 \, a^{2} b^{4} c^{8} d - 2 \, a^{3} b^{3} c^{7} d^{2} + 8 \, a^{4} b^{2} c^{6} d^{3} - 7 \, a^{5} b c^{5} d^{4} + 2 \, a^{6} c^{4} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/32*(3*(8*a^2*b^2*c^4*d - 4*a^3*b*c^3*d^2 + a^4*c^2*d^3 + (8*a*b^3*c^2*d^3 - 4*a^2*b^2*c*d^4 + a^3*b*d^5)*x^6 + (16*a*b^3*c^3*d^2 - 2*a^3*b*c*d^4 + a^4*d^5)*x^4 + (8*a*b^3*c^4*d + 12*a^2*b^2*c^3*d^2 - 7*a^3*b*c^2*d^3 + 2*a^4*c*d^4)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 4*((8*b^4*c^4*d^2 + 2*a*b^3*c^3*d^3 - 13*a^2*b^2*c^2*d^4 + 3*a^3*b*c*d^5)*x^5 + (16*b^4*c^5*d - 4*a*b^3*c^4*d^2 - 7*a^2*b^2*c^3*d^3 - 8*a^3*b*c^2*d^4 + 3*a^4*c*d^5)*x^3 + (8*b^4*c^6 - 8*a*b^3*c^5*d + 12*a^2*b^2*c^4*d^2 - 17*a^3*b*c^3*d^3 + 5*a^4*c^2*d^4)*x)*sqrt(b*x^2 + a))/(a^2*b^4*c^9 - 4*a^3*b^3*c^8*d + 6*a^4*b^2*c^7*d^2 - 4*a^5*b*c^6*d^3 + a^6*c^5*d^4 + (a*b^5*c^7*d^2 - 4*a^2*b^4*c^6*d^3 + 6*a^3*b^3*c^5*d^4 - 4*a^4*b^2*c^4*d^5 + a^5*b*c^3*d^6)*x^6 + (2*a*b^5*c^8*d - 7*a^2*b^4*c^7*d^2 + 8*a^3*b^3*c^6*d^3 - 2*a^4*b^2*c^5*d^4 - 2*a^5*b*c^4*d^5 + a^6*c^3*d^6)*x^4 + (a*b^5*c^9 - 2*a^2*b^4*c^8*d - 2*a^3*b^3*c^7*d^2 + 8*a^4*b^2*c^6*d^3 - 7*a^5*b*c^5*d^4 + 2*a^6*c^4*d^5)*x^2), 1/16*(3*(8*a^2*b^2*c^4*d - 4*a^3*b*c^3*d^2 + a^4*c^2*d^3 + (8*a*b^3*c^2*d^3 - 4*a^2*b^2*c*d^4 + a^3*b*d^5)*x^6 + (16*a*b^3*c^3*d^2 - 2*a^3*b*c*d^4 + a^4*d^5)*x^4 + (8*a*b^3*c^4*d + 12*a^2*b^2*c^3*d^2 - 7*a^3*b*c^2*d^3 + 2*a^4*c*d^4)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*((8*b^4*c^4*d^2 + 2*a*b^3*c^3*d^3 - 13*a^2*b^2*c^2*d^4 + 3*a^3*b*c*d^5)*x^5 + (16*b^4*c^5*d - 4*a*b^3*c^4*d^2 - 7*a^2*b^2*c^3*d^3 - 8*a^3*b*c^2*d^4 + 3*a^4*c*d^5)*x^3 + (8*b^4*c^6 - 8*a*b^3*c^5*d + 12*a^2*b^2*c^4*d^2 - 17*a^3*b*c^3*d^3 + 5*a^4*c^2*d^4)*x)*sqrt(b*x^2 + a))/(a^2*b^4*c^9 - 4*a^3*b^3*c^8*d + 6*a^4*b^2*c^7*d^2 - 4*a^5*b*c^6*d^3 + a^6*c^5*d^4 + (a*b^5*c^7*d^2 - 4*a^2*b^4*c^6*d^3 + 6*a^3*b^3*c^5*d^4 - 4*a^4*b^2*c^4*d^5 + a^5*b*c^3*d^6)*x^6 + (2*a*b^5*c^8*d - 7*a^2*b^4*c^7*d^2 + 8*a^3*b^3*c^6*d^3 - 2*a^4*b^2*c^5*d^4 - 2*a^5*b*c^4*d^5 + a^6*c^3*d^6)*x^4 + (a*b^5*c^9 - 2*a^2*b^4*c^8*d - 2*a^3*b^3*c^7*d^2 + 8*a^4*b^2*c^6*d^3 - 7*a^5*b*c^5*d^4 + 2*a^6*c^4*d^5)*x^2)]","B",0
89,1,684,0,1.307770," ","integrate((d*x^2+c)^4/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(48 \, a^{4} b^{2} c^{2} d^{2} - 80 \, a^{5} b c d^{3} + 35 \, a^{6} d^{4} + {\left(48 \, a^{2} b^{4} c^{2} d^{2} - 80 \, a^{3} b^{3} c d^{3} + 35 \, a^{4} b^{2} d^{4}\right)} x^{4} + 2 \, {\left(48 \, a^{3} b^{3} c^{2} d^{2} - 80 \, a^{4} b^{2} c d^{3} + 35 \, a^{5} b d^{4}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(6 \, a^{2} b^{4} d^{4} x^{7} + 3 \, {\left(16 \, a^{2} b^{4} c d^{3} - 7 \, a^{3} b^{3} d^{4}\right)} x^{5} + 4 \, {\left(4 \, b^{6} c^{4} + 8 \, a b^{5} c^{3} d - 48 \, a^{2} b^{4} c^{2} d^{2} + 80 \, a^{3} b^{3} c d^{3} - 35 \, a^{4} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(8 \, a b^{5} c^{4} - 48 \, a^{3} b^{3} c^{2} d^{2} + 80 \, a^{4} b^{2} c d^{3} - 35 \, a^{5} b d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, {\left(a^{2} b^{7} x^{4} + 2 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}, -\frac{3 \, {\left(48 \, a^{4} b^{2} c^{2} d^{2} - 80 \, a^{5} b c d^{3} + 35 \, a^{6} d^{4} + {\left(48 \, a^{2} b^{4} c^{2} d^{2} - 80 \, a^{3} b^{3} c d^{3} + 35 \, a^{4} b^{2} d^{4}\right)} x^{4} + 2 \, {\left(48 \, a^{3} b^{3} c^{2} d^{2} - 80 \, a^{4} b^{2} c d^{3} + 35 \, a^{5} b d^{4}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(6 \, a^{2} b^{4} d^{4} x^{7} + 3 \, {\left(16 \, a^{2} b^{4} c d^{3} - 7 \, a^{3} b^{3} d^{4}\right)} x^{5} + 4 \, {\left(4 \, b^{6} c^{4} + 8 \, a b^{5} c^{3} d - 48 \, a^{2} b^{4} c^{2} d^{2} + 80 \, a^{3} b^{3} c d^{3} - 35 \, a^{4} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(8 \, a b^{5} c^{4} - 48 \, a^{3} b^{3} c^{2} d^{2} + 80 \, a^{4} b^{2} c d^{3} - 35 \, a^{5} b d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{24 \, {\left(a^{2} b^{7} x^{4} + 2 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}\right]"," ",0,"[1/48*(3*(48*a^4*b^2*c^2*d^2 - 80*a^5*b*c*d^3 + 35*a^6*d^4 + (48*a^2*b^4*c^2*d^2 - 80*a^3*b^3*c*d^3 + 35*a^4*b^2*d^4)*x^4 + 2*(48*a^3*b^3*c^2*d^2 - 80*a^4*b^2*c*d^3 + 35*a^5*b*d^4)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(6*a^2*b^4*d^4*x^7 + 3*(16*a^2*b^4*c*d^3 - 7*a^3*b^3*d^4)*x^5 + 4*(4*b^6*c^4 + 8*a*b^5*c^3*d - 48*a^2*b^4*c^2*d^2 + 80*a^3*b^3*c*d^3 - 35*a^4*b^2*d^4)*x^3 + 3*(8*a*b^5*c^4 - 48*a^3*b^3*c^2*d^2 + 80*a^4*b^2*c*d^3 - 35*a^5*b*d^4)*x)*sqrt(b*x^2 + a))/(a^2*b^7*x^4 + 2*a^3*b^6*x^2 + a^4*b^5), -1/24*(3*(48*a^4*b^2*c^2*d^2 - 80*a^5*b*c*d^3 + 35*a^6*d^4 + (48*a^2*b^4*c^2*d^2 - 80*a^3*b^3*c*d^3 + 35*a^4*b^2*d^4)*x^4 + 2*(48*a^3*b^3*c^2*d^2 - 80*a^4*b^2*c*d^3 + 35*a^5*b*d^4)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (6*a^2*b^4*d^4*x^7 + 3*(16*a^2*b^4*c*d^3 - 7*a^3*b^3*d^4)*x^5 + 4*(4*b^6*c^4 + 8*a*b^5*c^3*d - 48*a^2*b^4*c^2*d^2 + 80*a^3*b^3*c*d^3 - 35*a^4*b^2*d^4)*x^3 + 3*(8*a*b^5*c^4 - 48*a^3*b^3*c^2*d^2 + 80*a^4*b^2*c*d^3 - 35*a^5*b*d^4)*x)*sqrt(b*x^2 + a))/(a^2*b^7*x^4 + 2*a^3*b^6*x^2 + a^4*b^5)]","A",0
90,1,486,0,1.213087," ","integrate((d*x^2+c)^3/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, a^{4} b c d^{2} - 5 \, a^{5} d^{3} + {\left(6 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(6 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(3 \, a^{2} b^{3} d^{3} x^{5} + 2 \, {\left(2 \, b^{5} c^{3} + 3 \, a b^{4} c^{2} d - 12 \, a^{2} b^{3} c d^{2} + 10 \, a^{3} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(2 \, a b^{4} c^{3} - 6 \, a^{3} b^{2} c d^{2} + 5 \, a^{4} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{12 \, {\left(a^{2} b^{6} x^{4} + 2 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}, -\frac{3 \, {\left(6 \, a^{4} b c d^{2} - 5 \, a^{5} d^{3} + {\left(6 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{4} + 2 \, {\left(6 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(3 \, a^{2} b^{3} d^{3} x^{5} + 2 \, {\left(2 \, b^{5} c^{3} + 3 \, a b^{4} c^{2} d - 12 \, a^{2} b^{3} c d^{2} + 10 \, a^{3} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(2 \, a b^{4} c^{3} - 6 \, a^{3} b^{2} c d^{2} + 5 \, a^{4} b d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{2} b^{6} x^{4} + 2 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}\right]"," ",0,"[-1/12*(3*(6*a^4*b*c*d^2 - 5*a^5*d^3 + (6*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^4 + 2*(6*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(3*a^2*b^3*d^3*x^5 + 2*(2*b^5*c^3 + 3*a*b^4*c^2*d - 12*a^2*b^3*c*d^2 + 10*a^3*b^2*d^3)*x^3 + 3*(2*a*b^4*c^3 - 6*a^3*b^2*c*d^2 + 5*a^4*b*d^3)*x)*sqrt(b*x^2 + a))/(a^2*b^6*x^4 + 2*a^3*b^5*x^2 + a^4*b^4), -1/6*(3*(6*a^4*b*c*d^2 - 5*a^5*d^3 + (6*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^4 + 2*(6*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (3*a^2*b^3*d^3*x^5 + 2*(2*b^5*c^3 + 3*a*b^4*c^2*d - 12*a^2*b^3*c*d^2 + 10*a^3*b^2*d^3)*x^3 + 3*(2*a*b^4*c^3 - 6*a^3*b^2*c*d^2 + 5*a^4*b*d^3)*x)*sqrt(b*x^2 + a))/(a^2*b^6*x^4 + 2*a^3*b^5*x^2 + a^4*b^4)]","A",0
91,1,318,0,1.125741," ","integrate((d*x^2+c)^2/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, {\left(b^{4} c^{2} + a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{3} + 3 \, {\left(a b^{3} c^{2} - a^{3} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}, -\frac{3 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, {\left(b^{4} c^{2} + a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{3} + 3 \, {\left(a b^{3} c^{2} - a^{3} b d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}\right]"," ",0,"[1/6*(3*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*(b^4*c^2 + a*b^3*c*d - 2*a^2*b^2*d^2)*x^3 + 3*(a*b^3*c^2 - a^3*b*d^2)*x)*sqrt(b*x^2 + a))/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3), -1/3*(3*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*(b^4*c^2 + a*b^3*c*d - 2*a^2*b^2*d^2)*x^3 + 3*(a*b^3*c^2 - a^3*b*d^2)*x)*sqrt(b*x^2 + a))/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3)]","A",0
92,1,54,0,0.953518," ","integrate((d*x^2+c)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b c + a d\right)} x^{3} + 3 \, a c x\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}}"," ",0,"1/3*((2*b*c + a*d)*x^3 + 3*a*c*x)*sqrt(b*x^2 + a)/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)","A",0
93,1,47,0,0.579740," ","integrate(1/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b x^{3} + 3 \, a x\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}}"," ",0,"1/3*(2*b*x^3 + 3*a*x)*sqrt(b*x^2 + a)/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)","A",0
94,1,764,0,1.740607," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(2 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d + 5 \, a^{2} b^{2} c d^{2}\right)} x^{3} + 3 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 2 \, a^{3} b c d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{12 \, {\left(a^{4} b^{3} c^{4} - 3 \, a^{5} b^{2} c^{3} d + 3 \, a^{6} b c^{2} d^{2} - a^{7} c d^{3} + {\left(a^{2} b^{5} c^{4} - 3 \, a^{3} b^{4} c^{3} d + 3 \, a^{4} b^{3} c^{2} d^{2} - a^{5} b^{2} c d^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{4} c^{4} - 3 \, a^{4} b^{3} c^{3} d + 3 \, a^{5} b^{2} c^{2} d^{2} - a^{6} b c d^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(a^{2} b^{2} d^{2} x^{4} + 2 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(2 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d + 5 \, a^{2} b^{2} c d^{2}\right)} x^{3} + 3 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 2 \, a^{3} b c d^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{4} b^{3} c^{4} - 3 \, a^{5} b^{2} c^{3} d + 3 \, a^{6} b c^{2} d^{2} - a^{7} c d^{3} + {\left(a^{2} b^{5} c^{4} - 3 \, a^{3} b^{4} c^{3} d + 3 \, a^{4} b^{3} c^{2} d^{2} - a^{5} b^{2} c d^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{4} c^{4} - 3 \, a^{4} b^{3} c^{3} d + 3 \, a^{5} b^{2} c^{2} d^{2} - a^{6} b c d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((2*b^4*c^3 - 7*a*b^3*c^2*d + 5*a^2*b^2*c*d^2)*x^3 + 3*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 2*a^3*b*c*d^2)*x)*sqrt(b*x^2 + a))/(a^4*b^3*c^4 - 3*a^5*b^2*c^3*d + 3*a^6*b*c^2*d^2 - a^7*c*d^3 + (a^2*b^5*c^4 - 3*a^3*b^4*c^3*d + 3*a^4*b^3*c^2*d^2 - a^5*b^2*c*d^3)*x^4 + 2*(a^3*b^4*c^4 - 3*a^4*b^3*c^3*d + 3*a^5*b^2*c^2*d^2 - a^6*b*c*d^3)*x^2), -1/6*(3*(a^2*b^2*d^2*x^4 + 2*a^3*b*d^2*x^2 + a^4*d^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((2*b^4*c^3 - 7*a*b^3*c^2*d + 5*a^2*b^2*c*d^2)*x^3 + 3*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 2*a^3*b*c*d^2)*x)*sqrt(b*x^2 + a))/(a^4*b^3*c^4 - 3*a^5*b^2*c^3*d + 3*a^6*b*c^2*d^2 - a^7*c*d^3 + (a^2*b^5*c^4 - 3*a^3*b^4*c^3*d + 3*a^4*b^3*c^2*d^2 - a^5*b^2*c*d^3)*x^4 + 2*(a^3*b^4*c^4 - 3*a^4*b^3*c^3*d + 3*a^5*b^2*c^2*d^2 - a^6*b*c*d^3)*x^2)]","B",0
95,1,1440,0,3.590392," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(6 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(6 \, a^{2} b^{3} c^{2} d^{2} + 11 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} x^{4} + {\left(12 \, a^{3} b^{2} c^{2} d^{2} + 4 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(4 \, b^{5} c^{4} d - 20 \, a b^{4} c^{3} d^{2} + 13 \, a^{2} b^{3} c^{2} d^{3} + 3 \, a^{3} b^{2} c d^{4}\right)} x^{5} + 2 \, {\left(2 \, b^{5} c^{5} - 7 \, a b^{4} c^{4} d - 4 \, a^{2} b^{3} c^{3} d^{2} + 6 \, a^{3} b^{2} c^{2} d^{3} + 3 \, a^{4} b c d^{4}\right)} x^{3} + 3 \, {\left(2 \, a b^{4} c^{5} - 8 \, a^{2} b^{3} c^{4} d + 6 \, a^{3} b^{2} c^{3} d^{2} - a^{4} b c^{2} d^{3} + a^{5} c d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{24 \, {\left(a^{4} b^{4} c^{7} - 4 \, a^{5} b^{3} c^{6} d + 6 \, a^{6} b^{2} c^{5} d^{2} - 4 \, a^{7} b c^{4} d^{3} + a^{8} c^{3} d^{4} + {\left(a^{2} b^{6} c^{6} d - 4 \, a^{3} b^{5} c^{5} d^{2} + 6 \, a^{4} b^{4} c^{4} d^{3} - 4 \, a^{5} b^{3} c^{3} d^{4} + a^{6} b^{2} c^{2} d^{5}\right)} x^{6} + {\left(a^{2} b^{6} c^{7} - 2 \, a^{3} b^{5} c^{6} d - 2 \, a^{4} b^{4} c^{5} d^{2} + 8 \, a^{5} b^{3} c^{4} d^{3} - 7 \, a^{6} b^{2} c^{3} d^{4} + 2 \, a^{7} b c^{2} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{5} c^{7} - 7 \, a^{4} b^{4} c^{6} d + 8 \, a^{5} b^{3} c^{5} d^{2} - 2 \, a^{6} b^{2} c^{4} d^{3} - 2 \, a^{7} b c^{3} d^{4} + a^{8} c^{2} d^{5}\right)} x^{2}\right)}}, -\frac{3 \, {\left(6 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(6 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(6 \, a^{2} b^{3} c^{2} d^{2} + 11 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} x^{4} + {\left(12 \, a^{3} b^{2} c^{2} d^{2} + 4 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(4 \, b^{5} c^{4} d - 20 \, a b^{4} c^{3} d^{2} + 13 \, a^{2} b^{3} c^{2} d^{3} + 3 \, a^{3} b^{2} c d^{4}\right)} x^{5} + 2 \, {\left(2 \, b^{5} c^{5} - 7 \, a b^{4} c^{4} d - 4 \, a^{2} b^{3} c^{3} d^{2} + 6 \, a^{3} b^{2} c^{2} d^{3} + 3 \, a^{4} b c d^{4}\right)} x^{3} + 3 \, {\left(2 \, a b^{4} c^{5} - 8 \, a^{2} b^{3} c^{4} d + 6 \, a^{3} b^{2} c^{3} d^{2} - a^{4} b c^{2} d^{3} + a^{5} c d^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{12 \, {\left(a^{4} b^{4} c^{7} - 4 \, a^{5} b^{3} c^{6} d + 6 \, a^{6} b^{2} c^{5} d^{2} - 4 \, a^{7} b c^{4} d^{3} + a^{8} c^{3} d^{4} + {\left(a^{2} b^{6} c^{6} d - 4 \, a^{3} b^{5} c^{5} d^{2} + 6 \, a^{4} b^{4} c^{4} d^{3} - 4 \, a^{5} b^{3} c^{3} d^{4} + a^{6} b^{2} c^{2} d^{5}\right)} x^{6} + {\left(a^{2} b^{6} c^{7} - 2 \, a^{3} b^{5} c^{6} d - 2 \, a^{4} b^{4} c^{5} d^{2} + 8 \, a^{5} b^{3} c^{4} d^{3} - 7 \, a^{6} b^{2} c^{3} d^{4} + 2 \, a^{7} b c^{2} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{5} c^{7} - 7 \, a^{4} b^{4} c^{6} d + 8 \, a^{5} b^{3} c^{5} d^{2} - 2 \, a^{6} b^{2} c^{4} d^{3} - 2 \, a^{7} b c^{3} d^{4} + a^{8} c^{2} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/24*(3*(6*a^4*b*c^2*d^2 - a^5*c*d^3 + (6*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (6*a^2*b^3*c^2*d^2 + 11*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*x^4 + (12*a^3*b^2*c^2*d^2 + 4*a^4*b*c*d^3 - a^5*d^4)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((4*b^5*c^4*d - 20*a*b^4*c^3*d^2 + 13*a^2*b^3*c^2*d^3 + 3*a^3*b^2*c*d^4)*x^5 + 2*(2*b^5*c^5 - 7*a*b^4*c^4*d - 4*a^2*b^3*c^3*d^2 + 6*a^3*b^2*c^2*d^3 + 3*a^4*b*c*d^4)*x^3 + 3*(2*a*b^4*c^5 - 8*a^2*b^3*c^4*d + 6*a^3*b^2*c^3*d^2 - a^4*b*c^2*d^3 + a^5*c*d^4)*x)*sqrt(b*x^2 + a))/(a^4*b^4*c^7 - 4*a^5*b^3*c^6*d + 6*a^6*b^2*c^5*d^2 - 4*a^7*b*c^4*d^3 + a^8*c^3*d^4 + (a^2*b^6*c^6*d - 4*a^3*b^5*c^5*d^2 + 6*a^4*b^4*c^4*d^3 - 4*a^5*b^3*c^3*d^4 + a^6*b^2*c^2*d^5)*x^6 + (a^2*b^6*c^7 - 2*a^3*b^5*c^6*d - 2*a^4*b^4*c^5*d^2 + 8*a^5*b^3*c^4*d^3 - 7*a^6*b^2*c^3*d^4 + 2*a^7*b*c^2*d^5)*x^4 + (2*a^3*b^5*c^7 - 7*a^4*b^4*c^6*d + 8*a^5*b^3*c^5*d^2 - 2*a^6*b^2*c^4*d^3 - 2*a^7*b*c^3*d^4 + a^8*c^2*d^5)*x^2), -1/12*(3*(6*a^4*b*c^2*d^2 - a^5*c*d^3 + (6*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (6*a^2*b^3*c^2*d^2 + 11*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*x^4 + (12*a^3*b^2*c^2*d^2 + 4*a^4*b*c*d^3 - a^5*d^4)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((4*b^5*c^4*d - 20*a*b^4*c^3*d^2 + 13*a^2*b^3*c^2*d^3 + 3*a^3*b^2*c*d^4)*x^5 + 2*(2*b^5*c^5 - 7*a*b^4*c^4*d - 4*a^2*b^3*c^3*d^2 + 6*a^3*b^2*c^2*d^3 + 3*a^4*b*c*d^4)*x^3 + 3*(2*a*b^4*c^5 - 8*a^2*b^3*c^4*d + 6*a^3*b^2*c^3*d^2 - a^4*b*c^2*d^3 + a^5*c*d^4)*x)*sqrt(b*x^2 + a))/(a^4*b^4*c^7 - 4*a^5*b^3*c^6*d + 6*a^6*b^2*c^5*d^2 - 4*a^7*b*c^4*d^3 + a^8*c^3*d^4 + (a^2*b^6*c^6*d - 4*a^3*b^5*c^5*d^2 + 6*a^4*b^4*c^4*d^3 - 4*a^5*b^3*c^3*d^4 + a^6*b^2*c^2*d^5)*x^6 + (a^2*b^6*c^7 - 2*a^3*b^5*c^6*d - 2*a^4*b^4*c^5*d^2 + 8*a^5*b^3*c^4*d^3 - 7*a^6*b^2*c^3*d^4 + 2*a^7*b*c^2*d^5)*x^4 + (2*a^3*b^5*c^7 - 7*a^4*b^4*c^6*d + 8*a^5*b^3*c^5*d^2 - 2*a^6*b^2*c^4*d^3 - 2*a^7*b*c^3*d^4 + a^8*c^2*d^5)*x^2)]","B",0
96,1,2250,0,12.490661," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(48 \, a^{4} b^{2} c^{4} d^{2} - 16 \, a^{5} b c^{3} d^{3} + 3 \, a^{6} c^{2} d^{4} + {\left(48 \, a^{2} b^{4} c^{2} d^{4} - 16 \, a^{3} b^{3} c d^{5} + 3 \, a^{4} b^{2} d^{6}\right)} x^{8} + 2 \, {\left(48 \, a^{2} b^{4} c^{3} d^{3} + 32 \, a^{3} b^{3} c^{2} d^{4} - 13 \, a^{4} b^{2} c d^{5} + 3 \, a^{5} b d^{6}\right)} x^{6} + {\left(48 \, a^{2} b^{4} c^{4} d^{2} + 176 \, a^{3} b^{3} c^{3} d^{3} - 13 \, a^{4} b^{2} c^{2} d^{4} - 4 \, a^{5} b c d^{5} + 3 \, a^{6} d^{6}\right)} x^{4} + 2 \, {\left(48 \, a^{3} b^{3} c^{4} d^{2} + 32 \, a^{4} b^{2} c^{3} d^{3} - 13 \, a^{5} b c^{2} d^{4} + 3 \, a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{b c^{2} - a c d} \log\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(2 \, b c - a d\right)} x^{3} + a c x\right)} \sqrt{b c^{2} - a c d} \sqrt{b x^{2} + a}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 4 \, {\left({\left(16 \, b^{6} c^{5} d^{2} - 104 \, a b^{5} c^{4} d^{3} + 46 \, a^{2} b^{4} c^{3} d^{4} + 51 \, a^{3} b^{3} c^{2} d^{5} - 9 \, a^{4} b^{2} c d^{6}\right)} x^{7} + {\left(32 \, b^{6} c^{6} d - 184 \, a b^{5} c^{5} d^{2} + 8 \, a^{2} b^{4} c^{4} d^{3} + 75 \, a^{3} b^{3} c^{3} d^{4} + 87 \, a^{4} b^{2} c^{2} d^{5} - 18 \, a^{5} b c d^{6}\right)} x^{5} + {\left(16 \, b^{6} c^{7} - 56 \, a b^{5} c^{6} d - 152 \, a^{2} b^{4} c^{5} d^{2} + 96 \, a^{3} b^{3} c^{4} d^{3} + 84 \, a^{4} b^{2} c^{3} d^{4} + 21 \, a^{5} b c^{2} d^{5} - 9 \, a^{6} c d^{6}\right)} x^{3} + 3 \, {\left(8 \, a b^{5} c^{7} - 40 \, a^{2} b^{4} c^{6} d + 32 \, a^{3} b^{3} c^{5} d^{2} - 16 \, a^{4} b^{2} c^{4} d^{3} + 21 \, a^{5} b c^{3} d^{4} - 5 \, a^{6} c^{2} d^{5}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, {\left(a^{4} b^{5} c^{10} - 5 \, a^{5} b^{4} c^{9} d + 10 \, a^{6} b^{3} c^{8} d^{2} - 10 \, a^{7} b^{2} c^{7} d^{3} + 5 \, a^{8} b c^{6} d^{4} - a^{9} c^{5} d^{5} + {\left(a^{2} b^{7} c^{8} d^{2} - 5 \, a^{3} b^{6} c^{7} d^{3} + 10 \, a^{4} b^{5} c^{6} d^{4} - 10 \, a^{5} b^{4} c^{5} d^{5} + 5 \, a^{6} b^{3} c^{4} d^{6} - a^{7} b^{2} c^{3} d^{7}\right)} x^{8} + 2 \, {\left(a^{2} b^{7} c^{9} d - 4 \, a^{3} b^{6} c^{8} d^{2} + 5 \, a^{4} b^{5} c^{7} d^{3} - 5 \, a^{6} b^{3} c^{5} d^{5} + 4 \, a^{7} b^{2} c^{4} d^{6} - a^{8} b c^{3} d^{7}\right)} x^{6} + {\left(a^{2} b^{7} c^{10} - a^{3} b^{6} c^{9} d - 9 \, a^{4} b^{5} c^{8} d^{2} + 25 \, a^{5} b^{4} c^{7} d^{3} - 25 \, a^{6} b^{3} c^{6} d^{4} + 9 \, a^{7} b^{2} c^{5} d^{5} + a^{8} b c^{4} d^{6} - a^{9} c^{3} d^{7}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{10} - 4 \, a^{4} b^{5} c^{9} d + 5 \, a^{5} b^{4} c^{8} d^{2} - 5 \, a^{7} b^{2} c^{6} d^{4} + 4 \, a^{8} b c^{5} d^{5} - a^{9} c^{4} d^{6}\right)} x^{2}\right)}}, -\frac{3 \, {\left(48 \, a^{4} b^{2} c^{4} d^{2} - 16 \, a^{5} b c^{3} d^{3} + 3 \, a^{6} c^{2} d^{4} + {\left(48 \, a^{2} b^{4} c^{2} d^{4} - 16 \, a^{3} b^{3} c d^{5} + 3 \, a^{4} b^{2} d^{6}\right)} x^{8} + 2 \, {\left(48 \, a^{2} b^{4} c^{3} d^{3} + 32 \, a^{3} b^{3} c^{2} d^{4} - 13 \, a^{4} b^{2} c d^{5} + 3 \, a^{5} b d^{6}\right)} x^{6} + {\left(48 \, a^{2} b^{4} c^{4} d^{2} + 176 \, a^{3} b^{3} c^{3} d^{3} - 13 \, a^{4} b^{2} c^{2} d^{4} - 4 \, a^{5} b c d^{5} + 3 \, a^{6} d^{6}\right)} x^{4} + 2 \, {\left(48 \, a^{3} b^{3} c^{4} d^{2} + 32 \, a^{4} b^{2} c^{3} d^{3} - 13 \, a^{5} b c^{2} d^{4} + 3 \, a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{-b c^{2} + a c d} \arctan\left(\frac{\sqrt{-b c^{2} + a c d} {\left({\left(2 \, b c - a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a}}{2 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(16 \, b^{6} c^{5} d^{2} - 104 \, a b^{5} c^{4} d^{3} + 46 \, a^{2} b^{4} c^{3} d^{4} + 51 \, a^{3} b^{3} c^{2} d^{5} - 9 \, a^{4} b^{2} c d^{6}\right)} x^{7} + {\left(32 \, b^{6} c^{6} d - 184 \, a b^{5} c^{5} d^{2} + 8 \, a^{2} b^{4} c^{4} d^{3} + 75 \, a^{3} b^{3} c^{3} d^{4} + 87 \, a^{4} b^{2} c^{2} d^{5} - 18 \, a^{5} b c d^{6}\right)} x^{5} + {\left(16 \, b^{6} c^{7} - 56 \, a b^{5} c^{6} d - 152 \, a^{2} b^{4} c^{5} d^{2} + 96 \, a^{3} b^{3} c^{4} d^{3} + 84 \, a^{4} b^{2} c^{3} d^{4} + 21 \, a^{5} b c^{2} d^{5} - 9 \, a^{6} c d^{6}\right)} x^{3} + 3 \, {\left(8 \, a b^{5} c^{7} - 40 \, a^{2} b^{4} c^{6} d + 32 \, a^{3} b^{3} c^{5} d^{2} - 16 \, a^{4} b^{2} c^{4} d^{3} + 21 \, a^{5} b c^{3} d^{4} - 5 \, a^{6} c^{2} d^{5}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, {\left(a^{4} b^{5} c^{10} - 5 \, a^{5} b^{4} c^{9} d + 10 \, a^{6} b^{3} c^{8} d^{2} - 10 \, a^{7} b^{2} c^{7} d^{3} + 5 \, a^{8} b c^{6} d^{4} - a^{9} c^{5} d^{5} + {\left(a^{2} b^{7} c^{8} d^{2} - 5 \, a^{3} b^{6} c^{7} d^{3} + 10 \, a^{4} b^{5} c^{6} d^{4} - 10 \, a^{5} b^{4} c^{5} d^{5} + 5 \, a^{6} b^{3} c^{4} d^{6} - a^{7} b^{2} c^{3} d^{7}\right)} x^{8} + 2 \, {\left(a^{2} b^{7} c^{9} d - 4 \, a^{3} b^{6} c^{8} d^{2} + 5 \, a^{4} b^{5} c^{7} d^{3} - 5 \, a^{6} b^{3} c^{5} d^{5} + 4 \, a^{7} b^{2} c^{4} d^{6} - a^{8} b c^{3} d^{7}\right)} x^{6} + {\left(a^{2} b^{7} c^{10} - a^{3} b^{6} c^{9} d - 9 \, a^{4} b^{5} c^{8} d^{2} + 25 \, a^{5} b^{4} c^{7} d^{3} - 25 \, a^{6} b^{3} c^{6} d^{4} + 9 \, a^{7} b^{2} c^{5} d^{5} + a^{8} b c^{4} d^{6} - a^{9} c^{3} d^{7}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{10} - 4 \, a^{4} b^{5} c^{9} d + 5 \, a^{5} b^{4} c^{8} d^{2} - 5 \, a^{7} b^{2} c^{6} d^{4} + 4 \, a^{8} b c^{5} d^{5} - a^{9} c^{4} d^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/96*(3*(48*a^4*b^2*c^4*d^2 - 16*a^5*b*c^3*d^3 + 3*a^6*c^2*d^4 + (48*a^2*b^4*c^2*d^4 - 16*a^3*b^3*c*d^5 + 3*a^4*b^2*d^6)*x^8 + 2*(48*a^2*b^4*c^3*d^3 + 32*a^3*b^3*c^2*d^4 - 13*a^4*b^2*c*d^5 + 3*a^5*b*d^6)*x^6 + (48*a^2*b^4*c^4*d^2 + 176*a^3*b^3*c^3*d^3 - 13*a^4*b^2*c^2*d^4 - 4*a^5*b*c*d^5 + 3*a^6*d^6)*x^4 + 2*(48*a^3*b^3*c^4*d^2 + 32*a^4*b^2*c^3*d^3 - 13*a^5*b*c^2*d^4 + 3*a^6*c*d^5)*x^2)*sqrt(b*c^2 - a*c*d)*log(((8*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(4*a*b*c^2 - 3*a^2*c*d)*x^2 + 4*((2*b*c - a*d)*x^3 + a*c*x)*sqrt(b*c^2 - a*c*d)*sqrt(b*x^2 + a))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 4*((16*b^6*c^5*d^2 - 104*a*b^5*c^4*d^3 + 46*a^2*b^4*c^3*d^4 + 51*a^3*b^3*c^2*d^5 - 9*a^4*b^2*c*d^6)*x^7 + (32*b^6*c^6*d - 184*a*b^5*c^5*d^2 + 8*a^2*b^4*c^4*d^3 + 75*a^3*b^3*c^3*d^4 + 87*a^4*b^2*c^2*d^5 - 18*a^5*b*c*d^6)*x^5 + (16*b^6*c^7 - 56*a*b^5*c^6*d - 152*a^2*b^4*c^5*d^2 + 96*a^3*b^3*c^4*d^3 + 84*a^4*b^2*c^3*d^4 + 21*a^5*b*c^2*d^5 - 9*a^6*c*d^6)*x^3 + 3*(8*a*b^5*c^7 - 40*a^2*b^4*c^6*d + 32*a^3*b^3*c^5*d^2 - 16*a^4*b^2*c^4*d^3 + 21*a^5*b*c^3*d^4 - 5*a^6*c^2*d^5)*x)*sqrt(b*x^2 + a))/(a^4*b^5*c^10 - 5*a^5*b^4*c^9*d + 10*a^6*b^3*c^8*d^2 - 10*a^7*b^2*c^7*d^3 + 5*a^8*b*c^6*d^4 - a^9*c^5*d^5 + (a^2*b^7*c^8*d^2 - 5*a^3*b^6*c^7*d^3 + 10*a^4*b^5*c^6*d^4 - 10*a^5*b^4*c^5*d^5 + 5*a^6*b^3*c^4*d^6 - a^7*b^2*c^3*d^7)*x^8 + 2*(a^2*b^7*c^9*d - 4*a^3*b^6*c^8*d^2 + 5*a^4*b^5*c^7*d^3 - 5*a^6*b^3*c^5*d^5 + 4*a^7*b^2*c^4*d^6 - a^8*b*c^3*d^7)*x^6 + (a^2*b^7*c^10 - a^3*b^6*c^9*d - 9*a^4*b^5*c^8*d^2 + 25*a^5*b^4*c^7*d^3 - 25*a^6*b^3*c^6*d^4 + 9*a^7*b^2*c^5*d^5 + a^8*b*c^4*d^6 - a^9*c^3*d^7)*x^4 + 2*(a^3*b^6*c^10 - 4*a^4*b^5*c^9*d + 5*a^5*b^4*c^8*d^2 - 5*a^7*b^2*c^6*d^4 + 4*a^8*b*c^5*d^5 - a^9*c^4*d^6)*x^2), -1/48*(3*(48*a^4*b^2*c^4*d^2 - 16*a^5*b*c^3*d^3 + 3*a^6*c^2*d^4 + (48*a^2*b^4*c^2*d^4 - 16*a^3*b^3*c*d^5 + 3*a^4*b^2*d^6)*x^8 + 2*(48*a^2*b^4*c^3*d^3 + 32*a^3*b^3*c^2*d^4 - 13*a^4*b^2*c*d^5 + 3*a^5*b*d^6)*x^6 + (48*a^2*b^4*c^4*d^2 + 176*a^3*b^3*c^3*d^3 - 13*a^4*b^2*c^2*d^4 - 4*a^5*b*c*d^5 + 3*a^6*d^6)*x^4 + 2*(48*a^3*b^3*c^4*d^2 + 32*a^4*b^2*c^3*d^3 - 13*a^5*b*c^2*d^4 + 3*a^6*c*d^5)*x^2)*sqrt(-b*c^2 + a*c*d)*arctan(1/2*sqrt(-b*c^2 + a*c*d)*((2*b*c - a*d)*x^2 + a*c)*sqrt(b*x^2 + a)/((b^2*c^2 - a*b*c*d)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((16*b^6*c^5*d^2 - 104*a*b^5*c^4*d^3 + 46*a^2*b^4*c^3*d^4 + 51*a^3*b^3*c^2*d^5 - 9*a^4*b^2*c*d^6)*x^7 + (32*b^6*c^6*d - 184*a*b^5*c^5*d^2 + 8*a^2*b^4*c^4*d^3 + 75*a^3*b^3*c^3*d^4 + 87*a^4*b^2*c^2*d^5 - 18*a^5*b*c*d^6)*x^5 + (16*b^6*c^7 - 56*a*b^5*c^6*d - 152*a^2*b^4*c^5*d^2 + 96*a^3*b^3*c^4*d^3 + 84*a^4*b^2*c^3*d^4 + 21*a^5*b*c^2*d^5 - 9*a^6*c*d^6)*x^3 + 3*(8*a*b^5*c^7 - 40*a^2*b^4*c^6*d + 32*a^3*b^3*c^5*d^2 - 16*a^4*b^2*c^4*d^3 + 21*a^5*b*c^3*d^4 - 5*a^6*c^2*d^5)*x)*sqrt(b*x^2 + a))/(a^4*b^5*c^10 - 5*a^5*b^4*c^9*d + 10*a^6*b^3*c^8*d^2 - 10*a^7*b^2*c^7*d^3 + 5*a^8*b*c^6*d^4 - a^9*c^5*d^5 + (a^2*b^7*c^8*d^2 - 5*a^3*b^6*c^7*d^3 + 10*a^4*b^5*c^6*d^4 - 10*a^5*b^4*c^5*d^5 + 5*a^6*b^3*c^4*d^6 - a^7*b^2*c^3*d^7)*x^8 + 2*(a^2*b^7*c^9*d - 4*a^3*b^6*c^8*d^2 + 5*a^4*b^5*c^7*d^3 - 5*a^6*b^3*c^5*d^5 + 4*a^7*b^2*c^4*d^6 - a^8*b*c^3*d^7)*x^6 + (a^2*b^7*c^10 - a^3*b^6*c^9*d - 9*a^4*b^5*c^8*d^2 + 25*a^5*b^4*c^7*d^3 - 25*a^6*b^3*c^6*d^4 + 9*a^7*b^2*c^5*d^5 + a^8*b*c^4*d^6 - a^9*c^3*d^7)*x^4 + 2*(a^3*b^6*c^10 - 4*a^4*b^5*c^9*d + 5*a^5*b^4*c^8*d^2 - 5*a^7*b^2*c^6*d^4 + 4*a^8*b*c^5*d^5 - a^9*c^4*d^6)*x^2)]","B",0
97,1,229,0,1.615410," ","integrate((b*x^2+a)^3/(d*x^2+c)^(11/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(5 \, b^{3} c^{3} d + 12 \, a b^{2} c^{2} d^{2} + 24 \, a^{2} b c d^{3} + 64 \, a^{3} d^{4}\right)} x^{9} + 315 \, a^{3} c^{4} x + 9 \, {\left(5 \, b^{3} c^{4} + 12 \, a b^{2} c^{3} d + 24 \, a^{2} b c^{2} d^{2} + 64 \, a^{3} c d^{3}\right)} x^{7} + 63 \, {\left(3 \, a b^{2} c^{4} + 6 \, a^{2} b c^{3} d + 16 \, a^{3} c^{2} d^{2}\right)} x^{5} + 105 \, {\left(3 \, a^{2} b c^{4} + 8 \, a^{3} c^{3} d\right)} x^{3}\right)} \sqrt{d x^{2} + c}}{315 \, {\left(c^{5} d^{5} x^{10} + 5 \, c^{6} d^{4} x^{8} + 10 \, c^{7} d^{3} x^{6} + 10 \, c^{8} d^{2} x^{4} + 5 \, c^{9} d x^{2} + c^{10}\right)}}"," ",0,"1/315*(2*(5*b^3*c^3*d + 12*a*b^2*c^2*d^2 + 24*a^2*b*c*d^3 + 64*a^3*d^4)*x^9 + 315*a^3*c^4*x + 9*(5*b^3*c^4 + 12*a*b^2*c^3*d + 24*a^2*b*c^2*d^2 + 64*a^3*c*d^3)*x^7 + 63*(3*a*b^2*c^4 + 6*a^2*b*c^3*d + 16*a^3*c^2*d^2)*x^5 + 105*(3*a^2*b*c^4 + 8*a^3*c^3*d)*x^3)*sqrt(d*x^2 + c)/(c^5*d^5*x^10 + 5*c^6*d^4*x^8 + 10*c^7*d^3*x^6 + 10*c^8*d^2*x^4 + 5*c^9*d*x^2 + c^10)","A",0
98,1,151,0,0.967767," ","integrate((b*x^2+a)^2/(d*x^2+c)^(9/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(3 \, b^{2} c^{2} d + 8 \, a b c d^{2} + 24 \, a^{2} d^{3}\right)} x^{7} + 105 \, a^{2} c^{3} x + 7 \, {\left(3 \, b^{2} c^{3} + 8 \, a b c^{2} d + 24 \, a^{2} c d^{2}\right)} x^{5} + 70 \, {\left(a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c}}{105 \, {\left(c^{4} d^{4} x^{8} + 4 \, c^{5} d^{3} x^{6} + 6 \, c^{6} d^{2} x^{4} + 4 \, c^{7} d x^{2} + c^{8}\right)}}"," ",0,"1/105*(2*(3*b^2*c^2*d + 8*a*b*c*d^2 + 24*a^2*d^3)*x^7 + 105*a^2*c^3*x + 7*(3*b^2*c^3 + 8*a*b*c^2*d + 24*a^2*c*d^2)*x^5 + 70*(a*b*c^3 + 3*a^2*c^2*d)*x^3)*sqrt(d*x^2 + c)/(c^4*d^4*x^8 + 4*c^5*d^3*x^6 + 6*c^6*d^2*x^4 + 4*c^7*d*x^2 + c^8)","A",0
99,1,87,0,0.748616," ","integrate((b*x^2+a)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(b c d + 4 \, a d^{2}\right)} x^{5} + 15 \, a c^{2} x + 5 \, {\left(b c^{2} + 4 \, a c d\right)} x^{3}\right)} \sqrt{d x^{2} + c}}{15 \, {\left(c^{3} d^{3} x^{6} + 3 \, c^{4} d^{2} x^{4} + 3 \, c^{5} d x^{2} + c^{6}\right)}}"," ",0,"1/15*(2*(b*c*d + 4*a*d^2)*x^5 + 15*a*c^2*x + 5*(b*c^2 + 4*a*c*d)*x^3)*sqrt(d*x^2 + c)/(c^3*d^3*x^6 + 3*c^4*d^2*x^4 + 3*c^5*d*x^2 + c^6)","A",0
100,1,47,0,0.871878," ","integrate(1/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, d x^{3} + 3 \, c x\right)} \sqrt{d x^{2} + c}}{3 \, {\left(c^{2} d^{2} x^{4} + 2 \, c^{3} d x^{2} + c^{4}\right)}}"," ",0,"1/3*(2*d*x^3 + 3*c*x)*sqrt(d*x^2 + c)/(c^2*d^2*x^4 + 2*c^3*d*x^2 + c^4)","A",0
101,1,442,0,1.406890," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{d x^{2} + c} x - {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, {\left(a b^{2} c^{4} - 2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(a b^{2} c^{3} d - 2 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x^{2}\right)}}, -\frac{2 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{d x^{2} + c} x - {\left(b c d x^{2} + b c^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{2 \, {\left(a b^{2} c^{4} - 2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(a b^{2} c^{3} d - 2 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(4*(a*b*c*d - a^2*d^2)*sqrt(d*x^2 + c)*x - (b*c*d*x^2 + b*c^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b^2*c^4 - 2*a^2*b*c^3*d + a^3*c^2*d^2 + (a*b^2*c^3*d - 2*a^2*b*c^2*d^2 + a^3*c*d^3)*x^2), -1/2*(2*(a*b*c*d - a^2*d^2)*sqrt(d*x^2 + c)*x - (b*c*d*x^2 + b*c^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(a*b^2*c^4 - 2*a^2*b*c^3*d + a^3*c^2*d^2 + (a*b^2*c^3*d - 2*a^2*b*c^2*d^2 + a^3*c*d^3)*x^2)]","B",0
102,1,459,0,1.350394," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x - {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{2}\right)}}, \frac{2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x + \sqrt{a b c - a^{2} d} {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{4 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(4*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x - (a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^2), 1/4*(2*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x + sqrt(a*b*c - a^2*d)*(a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^2)]","B",0
103,1,698,0,1.560348," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, a^{2} b c^{2} - 4 \, a^{3} c d + {\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{3} + {\left(5 \, a^{2} b^{2} c^{2} - 9 \, a^{3} b c d + 4 \, a^{4} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{32 \, {\left(a^{5} b^{2} c^{2} - 2 \, a^{6} b c d + a^{7} d^{2} + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(a^{4} b^{3} c^{2} - 2 \, a^{5} b^{2} c d + a^{6} b d^{2}\right)} x^{2}\right)}}, \frac{{\left(3 \, a^{2} b c^{2} - 4 \, a^{3} c d + {\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left({\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{3} + {\left(5 \, a^{2} b^{2} c^{2} - 9 \, a^{3} b c d + 4 \, a^{4} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, {\left(a^{5} b^{2} c^{2} - 2 \, a^{6} b c d + a^{7} d^{2} + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(a^{4} b^{3} c^{2} - 2 \, a^{5} b^{2} c d + a^{6} b d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/32*((3*a^2*b*c^2 - 4*a^3*c*d + (3*b^3*c^2 - 4*a*b^2*c*d)*x^4 + 2*(3*a*b^2*c^2 - 4*a^2*b*c*d)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^3 + (5*a^2*b^2*c^2 - 9*a^3*b*c*d + 4*a^4*d^2)*x)*sqrt(d*x^2 + c))/(a^5*b^2*c^2 - 2*a^6*b*c*d + a^7*d^2 + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*x^4 + 2*(a^4*b^3*c^2 - 2*a^5*b^2*c*d + a^6*b*d^2)*x^2), 1/16*((3*a^2*b*c^2 - 4*a^3*c*d + (3*b^3*c^2 - 4*a*b^2*c*d)*x^4 + 2*(3*a*b^2*c^2 - 4*a^2*b*c*d)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*((3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^3 + (5*a^2*b^2*c^2 - 9*a^3*b*c*d + 4*a^4*d^2)*x)*sqrt(d*x^2 + c))/(a^5*b^2*c^2 - 2*a^6*b*c*d + a^7*d^2 + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*x^4 + 2*(a^4*b^3*c^2 - 2*a^5*b^2*c*d + a^6*b*d^2)*x^2)]","B",0
104,1,972,0,2.227721," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, a^{3} b c^{3} - 6 \, a^{4} c^{2} d + {\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{6} + 3 \, {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{4} + 3 \, {\left(5 \, a^{2} b^{2} c^{3} - 6 \, a^{3} b c^{2} d\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{5} + 2 \, {\left(20 \, a^{2} b^{3} c^{3} - 31 \, a^{3} b^{2} c^{2} d + 5 \, a^{4} b c d^{2} + 6 \, a^{5} d^{3}\right)} x^{3} + 3 \, {\left(11 \, a^{3} b^{2} c^{3} - 21 \, a^{4} b c^{2} d + 10 \, a^{5} c d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{192 \, {\left(a^{7} b^{2} c^{2} - 2 \, a^{8} b c d + a^{9} d^{2} + {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} x^{6} + 3 \, {\left(a^{5} b^{4} c^{2} - 2 \, a^{6} b^{3} c d + a^{7} b^{2} d^{2}\right)} x^{4} + 3 \, {\left(a^{6} b^{3} c^{2} - 2 \, a^{7} b^{2} c d + a^{8} b d^{2}\right)} x^{2}\right)}}, \frac{3 \, {\left(5 \, a^{3} b c^{3} - 6 \, a^{4} c^{2} d + {\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{6} + 3 \, {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{4} + 3 \, {\left(5 \, a^{2} b^{2} c^{3} - 6 \, a^{3} b c^{2} d\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{5} + 2 \, {\left(20 \, a^{2} b^{3} c^{3} - 31 \, a^{3} b^{2} c^{2} d + 5 \, a^{4} b c d^{2} + 6 \, a^{5} d^{3}\right)} x^{3} + 3 \, {\left(11 \, a^{3} b^{2} c^{3} - 21 \, a^{4} b c^{2} d + 10 \, a^{5} c d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, {\left(a^{7} b^{2} c^{2} - 2 \, a^{8} b c d + a^{9} d^{2} + {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} x^{6} + 3 \, {\left(a^{5} b^{4} c^{2} - 2 \, a^{6} b^{3} c d + a^{7} b^{2} d^{2}\right)} x^{4} + 3 \, {\left(a^{6} b^{3} c^{2} - 2 \, a^{7} b^{2} c d + a^{8} b d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/192*(3*(5*a^3*b*c^3 - 6*a^4*c^2*d + (5*b^4*c^3 - 6*a*b^3*c^2*d)*x^6 + 3*(5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^4 + 3*(5*a^2*b^2*c^3 - 6*a^3*b*c^2*d)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^5 + 2*(20*a^2*b^3*c^3 - 31*a^3*b^2*c^2*d + 5*a^4*b*c*d^2 + 6*a^5*d^3)*x^3 + 3*(11*a^3*b^2*c^3 - 21*a^4*b*c^2*d + 10*a^5*c*d^2)*x)*sqrt(d*x^2 + c))/(a^7*b^2*c^2 - 2*a^8*b*c*d + a^9*d^2 + (a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*x^6 + 3*(a^5*b^4*c^2 - 2*a^6*b^3*c*d + a^7*b^2*d^2)*x^4 + 3*(a^6*b^3*c^2 - 2*a^7*b^2*c*d + a^8*b*d^2)*x^2), 1/96*(3*(5*a^3*b*c^3 - 6*a^4*c^2*d + (5*b^4*c^3 - 6*a*b^3*c^2*d)*x^6 + 3*(5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^4 + 3*(5*a^2*b^2*c^3 - 6*a^3*b*c^2*d)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^5 + 2*(20*a^2*b^3*c^3 - 31*a^3*b^2*c^2*d + 5*a^4*b*c*d^2 + 6*a^5*d^3)*x^3 + 3*(11*a^3*b^2*c^3 - 21*a^4*b*c^2*d + 10*a^5*c*d^2)*x)*sqrt(d*x^2 + c))/(a^7*b^2*c^2 - 2*a^8*b*c*d + a^9*d^2 + (a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*x^6 + 3*(a^5*b^4*c^2 - 2*a^6*b^3*c*d + a^7*b^2*d^2)*x^4 + 3*(a^6*b^3*c^2 - 2*a^7*b^2*c*d + a^8*b*d^2)*x^2)]","B",0
105,1,27,0,0.867501," ","integrate(1/(b*c/d+b*x^2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{d x^{2} + c} d x}{b c d x^{2} + b c^{2}}"," ",0,"sqrt(d*x^2 + c)*d*x/(b*c*d*x^2 + b*c^2)","A",0
106,1,23,0,0.627246," ","integrate(1/(x^2+1)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-x^{2} + 1}}{2 \, x}\right)"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-x^2 + 1)/x)","A",0
107,1,241,0,1.197344," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, {\left(a b c - a^{2} d\right)}}, \frac{\arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{2 \, \sqrt{a b c - a^{2} d}}\right]"," ",0,"[-1/4*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2))/(a*b*c - a^2*d), 1/2*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x))/sqrt(a*b*c - a^2*d)]","B",0
108,1,44,0,1.210514," ","integrate((x^2-1)/(x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, x^{2} + {\left(x^{2} + 1\right)} \log\left(-x + \sqrt{x^{2} + 1}\right) + 2 \, \sqrt{x^{2} + 1} x + 2}{x^{2} + 1}"," ",0,"-(2*x^2 + (x^2 + 1)*log(-x + sqrt(x^2 + 1)) + 2*sqrt(x^2 + 1)*x + 2)/(x^2 + 1)","B",0
109,0,0,0,0.685650," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} b x^{2} + 27 \, a^{3}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*b*x^2 + 27*a^3)*(-b*x^2 + a)^(2/3), x)","F",0
110,0,0,0,0.862805," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{4} + 6 \, a b x^{2} + 9 \, a^{2}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b^2*x^4 + 6*a*b*x^2 + 9*a^2)*(-b*x^2 + a)^(2/3), x)","F",0
111,0,0,0,0.917332," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b*x^2 + 3*a)*(-b*x^2 + a)^(2/3), x)","F",0
112,-1,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,0,0,0,1.093854," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{2} x^{4} + 6 \, a b x^{2} + 9 \, a^{2}}, x\right)"," ",0,"integral((-b*x^2 + a)^(2/3)/(b^2*x^4 + 6*a*b*x^2 + 9*a^2), x)","F",0
114,-1,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,0,0,0,0.827058," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{4} x^{8} + 8 \, a b^{3} x^{6} + 18 \, a^{2} b^{2} x^{4} - 27 \, a^{4}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral(-(b^4*x^8 + 8*a*b^3*x^6 + 18*a^2*b^2*x^4 - 27*a^4)*(-b*x^2 + a)^(2/3), x)","F",0
117,0,0,0,1.684684," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{3} x^{6} + 5 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} - 9 \, a^{3}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral(-(b^3*x^6 + 5*a*b^2*x^4 + 3*a^2*b*x^2 - 9*a^3)*(-b*x^2 + a)^(2/3), x)","F",0
118,0,0,0,1.275779," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} x^{4} + 2 \, a b x^{2} - 3 \, a^{2}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral(-(b^2*x^4 + 2*a*b*x^2 - 3*a^2)*(-b*x^2 + a)^(2/3), x)","F",0
119,-1,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,0,0,0,1.292659," ","integrate((b*x^2+3*a)^4/(-b*x^2+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{4} x^{8} + 12 \, a b^{3} x^{6} + 54 \, a^{2} b^{2} x^{4} + 108 \, a^{3} b x^{2} + 81 \, a^{4}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b x^{2} - a}, x\right)"," ",0,"integral(-(b^4*x^8 + 12*a*b^3*x^6 + 54*a^2*b^2*x^4 + 108*a^3*b*x^2 + 81*a^4)*(-b*x^2 + a)^(2/3)/(b*x^2 - a), x)","F",0
123,0,0,0,1.326902," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} b x^{2} + 27 \, a^{3}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b x^{2} - a}, x\right)"," ",0,"integral(-(b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*b*x^2 + 27*a^3)*(-b*x^2 + a)^(2/3)/(b*x^2 - a), x)","F",0
124,0,0,0,1.322711," ","integrate((b*x^2+3*a)^2/(-b*x^2+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{4} + 6 \, a b x^{2} + 9 \, a^{2}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b x^{2} - a}, x\right)"," ",0,"integral(-(b^2*x^4 + 6*a*b*x^2 + 9*a^2)*(-b*x^2 + a)^(2/3)/(b*x^2 - a), x)","F",0
125,0,0,0,0.703097," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b x^{2} - a}, x\right)"," ",0,"integral(-(b*x^2 + 3*a)*(-b*x^2 + a)^(2/3)/(b*x^2 - a), x)","F",0
126,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,0,0,0,1.041605," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} b x^{2} + 27 \, a^{3}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*b*x^2 + 27*a^3)*(-b*x^2 + a)^(2/3)/(b^2*x^4 - 2*a*b*x^2 + a^2), x)","F",0
130,0,0,0,1.553973," ","integrate((b*x^2+3*a)^2/(-b*x^2+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 6 \, a b x^{2} + 9 \, a^{2}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 6*a*b*x^2 + 9*a^2)*(-b*x^2 + a)^(2/3)/(b^2*x^4 - 2*a*b*x^2 + a^2), x)","F",0
131,0,0,0,1.319991," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((b*x^2 + 3*a)*(-b*x^2 + a)^(2/3)/(b^2*x^4 - 2*a*b*x^2 + a^2), x)","F",0
132,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,0,0,0,1.153625," ","integrate((b*x^2+3*a)^4/(-b*x^2+a)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{4} x^{8} + 12 \, a b^{3} x^{6} + 54 \, a^{2} b^{2} x^{4} + 108 \, a^{3} b x^{2} + 81 \, a^{4}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{3} x^{6} - 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} - a^{3}}, x\right)"," ",0,"integral(-(b^4*x^8 + 12*a*b^3*x^6 + 54*a^2*b^2*x^4 + 108*a^3*b*x^2 + 81*a^4)*(-b*x^2 + a)^(2/3)/(b^3*x^6 - 3*a*b^2*x^4 + 3*a^2*b*x^2 - a^3), x)","F",0
136,0,0,0,1.522878," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{3} x^{6} + 9 \, a b^{2} x^{4} + 27 \, a^{2} b x^{2} + 27 \, a^{3}\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{3} x^{6} - 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} - a^{3}}, x\right)"," ",0,"integral(-(b^3*x^6 + 9*a*b^2*x^4 + 27*a^2*b*x^2 + 27*a^3)*(-b*x^2 + a)^(2/3)/(b^3*x^6 - 3*a*b^2*x^4 + 3*a^2*b*x^2 - a^3), x)","F",0
137,1,42,0,1.374636," ","integrate((b*x^2+3*a)^2/(-b*x^2+a)^(7/3),x, algorithm=""fricas"")","-\frac{3 \, {\left(b x^{3} - 3 \, a x\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}}"," ",0,"-3*(b*x^3 - 3*a*x)*(-b*x^2 + a)^(2/3)/(b^2*x^4 - 2*a*b*x^2 + a^2)","A",0
138,0,0,0,1.253424," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b^{3} x^{6} - 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} - a^{3}}, x\right)"," ",0,"integral(-(b*x^2 + 3*a)*(-b*x^2 + a)^(2/3)/(b^3*x^6 - 3*a*b^2*x^4 + 3*a^2*b*x^2 - a^3), x)","F",0
139,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(1/(-b*x^2-3*a)/(b*x^2-a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate(1/(-b*x^2+3*a)/(b*x^2+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate(1/(-d*x^2+c)/(3*d*x^2+c)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate(1/(-3*d*x^2+c)^(1/3)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,1,1943,0,4.454118," ","integrate(1/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{10368 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} + 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} + 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, {\left(x^{5} + 18 \, x^{4} + 24 \, x^{3} - 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) - \frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{2592 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} + 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} + 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, {\left(x^{5} + 18 \, x^{4} + 24 \, x^{3} - 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) + \frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{10368 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} - 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} - {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} - 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 72 \, {\left(x^{5} - 18 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) + \frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{2592 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} - 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} - {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} - 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 72 \, {\left(x^{5} - 18 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) - \frac{1}{1296} \cdot 432^{\frac{5}{6}} \arctan\left(\frac{432^{\frac{5}{6}} {\left(x^{5} - 18 \, x^{3} + 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \sqrt{3} 2^{\frac{1}{3}} {\left(432^{\frac{5}{6}} {\left(x^{4} + 9 \, x^{2}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 288 \, \sqrt{3} {\left(2 \, x^{4} - 3 \, x^{2}\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 6 \cdot 432^{\frac{1}{6}} {\left(x^{6} + 141 \, x^{4} - 153 \, x^{2} + 27\right)}\right)} - 648 \cdot 432^{\frac{1}{6}} {\left(3 \, x^{3} - x\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, \sqrt{3} {\left(7 \, x^{5} + 6 \, x^{3} - 9 \, x\right)}}{36 \, {\left(x^{6} - 225 \, x^{4} + 243 \, x^{2} - 27\right)}}\right) - \frac{1}{2592} \cdot 432^{\frac{5}{6}} \arctan\left(-\frac{\sqrt{2} {\left(18 \, \sqrt{3} 2^{\frac{2}{3}} {\left(29 \, x^{11} + 879 \, x^{9} - 12078 \, x^{7} + 10638 \, x^{5} - 3807 \, x^{3} + 243 \, x\right)} - 2 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{10} + 153 \, x^{8} - 1701 \, x^{6} + 459 \, x^{4}\right)} - 216 \, \sqrt{3} 2^{\frac{1}{3}} {\left(31 \, x^{9} - 297 \, x^{7} - 27 \, x^{5} - 27 \, x^{3}\right)}\right)} - 36 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(\sqrt{3} {\left(x^{11} + 1167 \, x^{9} - 13158 \, x^{7} + 17550 \, x^{5} - 4779 \, x^{3} + 243 \, x\right)} - 8 \, \sqrt{3} {\left(13 \, x^{10} - 6 \, x^{8} - 1404 \, x^{6} + 1350 \, x^{4} - 81 \, x^{2}\right)}\right)} - 3 \cdot 432^{\frac{1}{6}} {\left(x^{12} + 7620 \, x^{10} - 92115 \, x^{8} + 169776 \, x^{6} - 109269 \, x^{4} + 16524 \, x^{2} - 729\right)}\right)} \sqrt{\frac{6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} + 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} + 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, {\left(x^{5} + 18 \, x^{4} + 24 \, x^{3} - 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}} - 216 \, {\left(\sqrt{3} 2^{\frac{2}{3}} {\left(x^{10} + 144 \, x^{8} - 918 \, x^{6} + 2808 \, x^{4} - 243 \, x^{2}\right)} - 3 \cdot 432^{\frac{1}{6}} {\left(31 \, x^{9} - 568 \, x^{7} + 1710 \, x^{5} - 432 \, x^{3} + 27 \, x\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 18 \, \sqrt{3} {\left(x^{12} - 366 \, x^{10} + 14535 \, x^{8} - 42660 \, x^{6} + 58239 \, x^{4} - 14094 \, x^{2} + 729\right)} + 144 \, \sqrt{3} {\left(11 \, x^{11} - 807 \, x^{9} + 4518 \, x^{7} - 5238 \, x^{5} + 3807 \, x^{3} - 243 \, x\right)} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(432^{\frac{5}{6}} {\left(x^{11} - 1215 \, x^{9} + 11754 \, x^{7} - 21006 \, x^{5} + 5589 \, x^{3} - 243 \, x\right)} - 432 \, \sqrt{3} 2^{\frac{1}{3}} {\left(13 \, x^{10} - 120 \, x^{8} + 1242 \, x^{6} - 1728 \, x^{4} + 81 \, x^{2}\right)}\right)}}{18 \, {\left(x^{12} - 8334 \, x^{10} + 110727 \, x^{8} - 301860 \, x^{6} + 187839 \, x^{4} - 21870 \, x^{2} + 729\right)}}\right) - \frac{1}{2592} \cdot 432^{\frac{5}{6}} \arctan\left(\frac{\sqrt{2} {\left(18 \, \sqrt{3} 2^{\frac{2}{3}} {\left(29 \, x^{11} + 879 \, x^{9} - 12078 \, x^{7} + 10638 \, x^{5} - 3807 \, x^{3} + 243 \, x\right)} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{10} + 153 \, x^{8} - 1701 \, x^{6} + 459 \, x^{4}\right)} + 216 \, \sqrt{3} 2^{\frac{1}{3}} {\left(31 \, x^{9} - 297 \, x^{7} - 27 \, x^{5} - 27 \, x^{3}\right)}\right)} - 36 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(\sqrt{3} {\left(x^{11} + 1167 \, x^{9} - 13158 \, x^{7} + 17550 \, x^{5} - 4779 \, x^{3} + 243 \, x\right)} + 8 \, \sqrt{3} {\left(13 \, x^{10} - 6 \, x^{8} - 1404 \, x^{6} + 1350 \, x^{4} - 81 \, x^{2}\right)}\right)} + 3 \cdot 432^{\frac{1}{6}} {\left(x^{12} + 7620 \, x^{10} - 92115 \, x^{8} + 169776 \, x^{6} - 109269 \, x^{4} + 16524 \, x^{2} - 729\right)}\right)} \sqrt{\frac{6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} - 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} - {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} - 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 72 \, {\left(x^{5} - 18 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}} - 216 \, {\left(\sqrt{3} 2^{\frac{2}{3}} {\left(x^{10} + 144 \, x^{8} - 918 \, x^{6} + 2808 \, x^{4} - 243 \, x^{2}\right)} + 3 \cdot 432^{\frac{1}{6}} {\left(31 \, x^{9} - 568 \, x^{7} + 1710 \, x^{5} - 432 \, x^{3} + 27 \, x\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 18 \, \sqrt{3} {\left(x^{12} - 366 \, x^{10} + 14535 \, x^{8} - 42660 \, x^{6} + 58239 \, x^{4} - 14094 \, x^{2} + 729\right)} - 144 \, \sqrt{3} {\left(11 \, x^{11} - 807 \, x^{9} + 4518 \, x^{7} - 5238 \, x^{5} + 3807 \, x^{3} - 243 \, x\right)} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(432^{\frac{5}{6}} {\left(x^{11} - 1215 \, x^{9} + 11754 \, x^{7} - 21006 \, x^{5} + 5589 \, x^{3} - 243 \, x\right)} + 432 \, \sqrt{3} 2^{\frac{1}{3}} {\left(13 \, x^{10} - 120 \, x^{8} + 1242 \, x^{6} - 1728 \, x^{4} + 81 \, x^{2}\right)}\right)}}{18 \, {\left(x^{12} - 8334 \, x^{10} + 110727 \, x^{8} - 301860 \, x^{6} + 187839 \, x^{4} - 21870 \, x^{2} + 729\right)}}\right)"," ",0,"-1/20736*432^(5/6)*sqrt(3)*log(10368*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) + 144*432^(1/6)*sqrt(3)*(x^5 - x^3) + (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) + 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) - 72*(x^5 + 18*x^4 + 24*x^3 - 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 1/20736*432^(5/6)*sqrt(3)*log(2592*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) + 144*432^(1/6)*sqrt(3)*(x^5 - x^3) + (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) + 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) - 72*(x^5 + 18*x^4 + 24*x^3 - 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) + 1/20736*432^(5/6)*sqrt(3)*log(10368*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) - 144*432^(1/6)*sqrt(3)*(x^5 - x^3) - (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) - 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) + 72*(x^5 - 18*x^4 + 24*x^3 + 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) + 1/20736*432^(5/6)*sqrt(3)*log(2592*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) - 144*432^(1/6)*sqrt(3)*(x^5 - x^3) - (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) - 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) + 72*(x^5 - 18*x^4 + 24*x^3 + 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 1/1296*432^(5/6)*arctan(1/36*(432^(5/6)*(x^5 - 18*x^3 + 9*x)*(-x^2 + 1)^(1/3) + sqrt(3)*2^(1/3)*(432^(5/6)*(x^4 + 9*x^2)*(-x^2 + 1)^(2/3) - 288*sqrt(3)*(2*x^4 - 3*x^2)*(-x^2 + 1)^(1/3) + 6*432^(1/6)*(x^6 + 141*x^4 - 153*x^2 + 27)) - 648*432^(1/6)*(3*x^3 - x)*(-x^2 + 1)^(2/3) - 72*sqrt(3)*(7*x^5 + 6*x^3 - 9*x))/(x^6 - 225*x^4 + 243*x^2 - 27)) - 1/2592*432^(5/6)*arctan(-1/18*(sqrt(2)*(18*sqrt(3)*2^(2/3)*(29*x^11 + 879*x^9 - 12078*x^7 + 10638*x^5 - 3807*x^3 + 243*x) - 2*(-x^2 + 1)^(2/3)*(432^(5/6)*(x^10 + 153*x^8 - 1701*x^6 + 459*x^4) - 216*sqrt(3)*2^(1/3)*(31*x^9 - 297*x^7 - 27*x^5 - 27*x^3)) - 36*(-x^2 + 1)^(1/3)*(sqrt(3)*(x^11 + 1167*x^9 - 13158*x^7 + 17550*x^5 - 4779*x^3 + 243*x) - 8*sqrt(3)*(13*x^10 - 6*x^8 - 1404*x^6 + 1350*x^4 - 81*x^2)) - 3*432^(1/6)*(x^12 + 7620*x^10 - 92115*x^8 + 169776*x^6 - 109269*x^4 + 16524*x^2 - 729))*sqrt((6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) + 144*432^(1/6)*sqrt(3)*(x^5 - x^3) + (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) + 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) - 72*(x^5 + 18*x^4 + 24*x^3 - 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 216*(sqrt(3)*2^(2/3)*(x^10 + 144*x^8 - 918*x^6 + 2808*x^4 - 243*x^2) - 3*432^(1/6)*(31*x^9 - 568*x^7 + 1710*x^5 - 432*x^3 + 27*x))*(-x^2 + 1)^(2/3) - 18*sqrt(3)*(x^12 - 366*x^10 + 14535*x^8 - 42660*x^6 + 58239*x^4 - 14094*x^2 + 729) + 144*sqrt(3)*(11*x^11 - 807*x^9 + 4518*x^7 - 5238*x^5 + 3807*x^3 - 243*x) - (-x^2 + 1)^(1/3)*(432^(5/6)*(x^11 - 1215*x^9 + 11754*x^7 - 21006*x^5 + 5589*x^3 - 243*x) - 432*sqrt(3)*2^(1/3)*(13*x^10 - 120*x^8 + 1242*x^6 - 1728*x^4 + 81*x^2)))/(x^12 - 8334*x^10 + 110727*x^8 - 301860*x^6 + 187839*x^4 - 21870*x^2 + 729)) - 1/2592*432^(5/6)*arctan(1/18*(sqrt(2)*(18*sqrt(3)*2^(2/3)*(29*x^11 + 879*x^9 - 12078*x^7 + 10638*x^5 - 3807*x^3 + 243*x) + 2*(-x^2 + 1)^(2/3)*(432^(5/6)*(x^10 + 153*x^8 - 1701*x^6 + 459*x^4) + 216*sqrt(3)*2^(1/3)*(31*x^9 - 297*x^7 - 27*x^5 - 27*x^3)) - 36*(-x^2 + 1)^(1/3)*(sqrt(3)*(x^11 + 1167*x^9 - 13158*x^7 + 17550*x^5 - 4779*x^3 + 243*x) + 8*sqrt(3)*(13*x^10 - 6*x^8 - 1404*x^6 + 1350*x^4 - 81*x^2)) + 3*432^(1/6)*(x^12 + 7620*x^10 - 92115*x^8 + 169776*x^6 - 109269*x^4 + 16524*x^2 - 729))*sqrt((6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) - 144*432^(1/6)*sqrt(3)*(x^5 - x^3) - (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) - 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) + 72*(x^5 - 18*x^4 + 24*x^3 + 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 216*(sqrt(3)*2^(2/3)*(x^10 + 144*x^8 - 918*x^6 + 2808*x^4 - 243*x^2) + 3*432^(1/6)*(31*x^9 - 568*x^7 + 1710*x^5 - 432*x^3 + 27*x))*(-x^2 + 1)^(2/3) - 18*sqrt(3)*(x^12 - 366*x^10 + 14535*x^8 - 42660*x^6 + 58239*x^4 - 14094*x^2 + 729) - 144*sqrt(3)*(11*x^11 - 807*x^9 + 4518*x^7 - 5238*x^5 + 3807*x^3 - 243*x) + (-x^2 + 1)^(1/3)*(432^(5/6)*(x^11 - 1215*x^9 + 11754*x^7 - 21006*x^5 + 5589*x^3 - 243*x) + 432*sqrt(3)*2^(1/3)*(13*x^10 - 120*x^8 + 1242*x^6 - 1728*x^4 + 81*x^2)))/(x^12 - 8334*x^10 + 110727*x^8 - 301860*x^6 + 187839*x^4 - 21870*x^2 + 729))","B",0
147,1,1685,0,4.160191," ","integrate(1/(-x^2+3)/(x^2+1)^(1/3),x, algorithm=""fricas"")","\frac{1}{2592} \cdot 432^{\frac{5}{6}} \sqrt{3} \arctan\left(-\frac{2592 \, x^{11} - 393984 \, x^{9} - 699840 \, x^{7} - 373248 \, x^{5} - 69984 \, x^{3} - \sqrt{6} {\left(18 \, \sqrt{3} 2^{\frac{2}{3}} {\left(19 \, x^{11} + 111 \, x^{9} + 6030 \, x^{7} + 7182 \, x^{5} + 2511 \, x^{3} + 243 \, x\right)} + 3 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{12} + 924 \, x^{10} - 33363 \, x^{8} - 60912 \, x^{6} - 36693 \, x^{4} - 8748 \, x^{2} - 729\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(x^{10} - 78 \, x^{8} - 720 \, x^{6} - 594 \, x^{4} - 81 \, x^{2}\right)} + 432 \, \sqrt{3} 2^{\frac{1}{3}} {\left(13 \, x^{9} - 177 \, x^{7} - 153 \, x^{5} - 27 \, x^{3}\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 36 \, {\left(96 \, x^{10} - 4032 \, x^{8} - 2592 \, x^{6} + \sqrt{3} {\left(x^{11} + 369 \, x^{9} - 3654 \, x^{7} - 5454 \, x^{5} - 2187 \, x^{3} - 243 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{2 \cdot 2^{\frac{2}{3}} {\left(x^{6} - 57 \, x^{4} - 117 \, x^{2} - 27\right)} + {\left(x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{3} + x\right)} + 24 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 9 \, x^{2}\right)}\right)} - 8 \, {\left(6 \, x^{4} - 18 \, x^{2} + \sqrt{3} {\left(x^{5} - 9 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 8 \cdot 432^{\frac{1}{6}} {\left(x^{5} + 18 \, x^{3} + 9 \, x\right)}}{x^{6} - 9 \, x^{4} + 27 \, x^{2} - 27}} + 216 \, {\left(\sqrt{3} 2^{\frac{2}{3}} {\left(x^{10} + 276 \, x^{8} + 1206 \, x^{6} + 756 \, x^{4} + 81 \, x^{2}\right)} + 432^{\frac{1}{6}} \sqrt{3} {\left(31 \, x^{9} - 1620 \, x^{7} - 2070 \, x^{5} - 756 \, x^{3} - 81 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 18 \, \sqrt{3} {\left(x^{12} + 1422 \, x^{10} + 21447 \, x^{8} + 27108 \, x^{6} + 16767 \, x^{4} + 6318 \, x^{2} + 729\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(x^{11} - 681 \, x^{9} + 4338 \, x^{7} + 6102 \, x^{5} + 2349 \, x^{3} + 243 \, x\right)} + 3888 \, \sqrt{3} 2^{\frac{1}{3}} {\left(x^{10} + 44 \, x^{8} + 94 \, x^{6} + 60 \, x^{4} + 9 \, x^{2}\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}{54 \, {\left(x^{12} - 2178 \, x^{10} + 46791 \, x^{8} + 83268 \, x^{6} + 47871 \, x^{4} + 10206 \, x^{2} + 729\right)}}\right) + \frac{1}{2592} \cdot 432^{\frac{5}{6}} \sqrt{3} \arctan\left(-\frac{2592 \, x^{11} - 393984 \, x^{9} - 699840 \, x^{7} - 373248 \, x^{5} - 69984 \, x^{3} + \sqrt{6} {\left(18 \, \sqrt{3} 2^{\frac{2}{3}} {\left(19 \, x^{11} + 111 \, x^{9} + 6030 \, x^{7} + 7182 \, x^{5} + 2511 \, x^{3} + 243 \, x\right)} - 3 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{12} + 924 \, x^{10} - 33363 \, x^{8} - 60912 \, x^{6} - 36693 \, x^{4} - 8748 \, x^{2} - 729\right)} - {\left(432^{\frac{5}{6}} \sqrt{3} {\left(x^{10} - 78 \, x^{8} - 720 \, x^{6} - 594 \, x^{4} - 81 \, x^{2}\right)} - 432 \, \sqrt{3} 2^{\frac{1}{3}} {\left(13 \, x^{9} - 177 \, x^{7} - 153 \, x^{5} - 27 \, x^{3}\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - 36 \, {\left(96 \, x^{10} - 4032 \, x^{8} - 2592 \, x^{6} - \sqrt{3} {\left(x^{11} + 369 \, x^{9} - 3654 \, x^{7} - 5454 \, x^{5} - 2187 \, x^{3} - 243 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{2 \cdot 2^{\frac{2}{3}} {\left(x^{6} - 57 \, x^{4} - 117 \, x^{2} - 27\right)} - {\left(x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{3} + x\right)} - 24 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 9 \, x^{2}\right)}\right)} - 8 \, {\left(6 \, x^{4} - 18 \, x^{2} - \sqrt{3} {\left(x^{5} - 9 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 8 \cdot 432^{\frac{1}{6}} {\left(x^{5} + 18 \, x^{3} + 9 \, x\right)}}{x^{6} - 9 \, x^{4} + 27 \, x^{2} - 27}} - 216 \, {\left(\sqrt{3} 2^{\frac{2}{3}} {\left(x^{10} + 276 \, x^{8} + 1206 \, x^{6} + 756 \, x^{4} + 81 \, x^{2}\right)} - 432^{\frac{1}{6}} \sqrt{3} {\left(31 \, x^{9} - 1620 \, x^{7} - 2070 \, x^{5} - 756 \, x^{3} - 81 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - 18 \, \sqrt{3} {\left(x^{12} + 1422 \, x^{10} + 21447 \, x^{8} + 27108 \, x^{6} + 16767 \, x^{4} + 6318 \, x^{2} + 729\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(x^{11} - 681 \, x^{9} + 4338 \, x^{7} + 6102 \, x^{5} + 2349 \, x^{3} + 243 \, x\right)} - 3888 \, \sqrt{3} 2^{\frac{1}{3}} {\left(x^{10} + 44 \, x^{8} + 94 \, x^{6} + 60 \, x^{4} + 9 \, x^{2}\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}{54 \, {\left(x^{12} - 2178 \, x^{10} + 46791 \, x^{8} + 83268 \, x^{6} + 47871 \, x^{4} + 10206 \, x^{2} + 729\right)}}\right) + \frac{1}{5184} \cdot 432^{\frac{5}{6}} \log\left(-\frac{432^{\frac{5}{6}} {\left(x^{6} + 69 \, x^{4} + 63 \, x^{2} + 27\right)} + 864 \, {\left(9 \, x^{3} + \sqrt{3} {\left(x^{4} + 9 \, x^{2}\right)} + 9 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 432 \cdot 2^{\frac{1}{3}} {\left(5 \, x^{5} + 30 \, x^{3} + 9 \, x\right)} + 432 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(2^{\frac{2}{3}} {\left(x^{5} + 18 \, x^{3} + 9 \, x\right)} + 4 \cdot 432^{\frac{1}{6}} {\left(x^{4} + 3 \, x^{2}\right)}\right)}}{x^{6} - 9 \, x^{4} + 27 \, x^{2} - 27}\right) - \frac{1}{5184} \cdot 432^{\frac{5}{6}} \log\left(\frac{432^{\frac{5}{6}} {\left(x^{6} + 69 \, x^{4} + 63 \, x^{2} + 27\right)} - 864 \, {\left(9 \, x^{3} - \sqrt{3} {\left(x^{4} + 9 \, x^{2}\right)} + 9 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - 432 \cdot 2^{\frac{1}{3}} {\left(5 \, x^{5} + 30 \, x^{3} + 9 \, x\right)} - 432 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(2^{\frac{2}{3}} {\left(x^{5} + 18 \, x^{3} + 9 \, x\right)} - 4 \cdot 432^{\frac{1}{6}} {\left(x^{4} + 3 \, x^{2}\right)}\right)}}{x^{6} - 9 \, x^{4} + 27 \, x^{2} - 27}\right) - \frac{1}{10368} \cdot 432^{\frac{5}{6}} \log\left(\frac{31104 \, {\left(2 \cdot 2^{\frac{2}{3}} {\left(x^{6} - 57 \, x^{4} - 117 \, x^{2} - 27\right)} + {\left(x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{3} + x\right)} + 24 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 9 \, x^{2}\right)}\right)} - 8 \, {\left(6 \, x^{4} - 18 \, x^{2} + \sqrt{3} {\left(x^{5} - 9 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 8 \cdot 432^{\frac{1}{6}} {\left(x^{5} + 18 \, x^{3} + 9 \, x\right)}\right)}}{x^{6} - 9 \, x^{4} + 27 \, x^{2} - 27}\right) + \frac{1}{10368} \cdot 432^{\frac{5}{6}} \log\left(\frac{31104 \, {\left(2 \cdot 2^{\frac{2}{3}} {\left(x^{6} - 57 \, x^{4} - 117 \, x^{2} - 27\right)} - {\left(x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{3} + x\right)} - 24 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 9 \, x^{2}\right)}\right)} - 8 \, {\left(6 \, x^{4} - 18 \, x^{2} - \sqrt{3} {\left(x^{5} - 9 \, x\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 8 \cdot 432^{\frac{1}{6}} {\left(x^{5} + 18 \, x^{3} + 9 \, x\right)}\right)}}{x^{6} - 9 \, x^{4} + 27 \, x^{2} - 27}\right)"," ",0,"1/2592*432^(5/6)*sqrt(3)*arctan(-1/54*(2592*x^11 - 393984*x^9 - 699840*x^7 - 373248*x^5 - 69984*x^3 - sqrt(6)*(18*sqrt(3)*2^(2/3)*(19*x^11 + 111*x^9 + 6030*x^7 + 7182*x^5 + 2511*x^3 + 243*x) + 3*432^(1/6)*sqrt(3)*(x^12 + 924*x^10 - 33363*x^8 - 60912*x^6 - 36693*x^4 - 8748*x^2 - 729) + (432^(5/6)*sqrt(3)*(x^10 - 78*x^8 - 720*x^6 - 594*x^4 - 81*x^2) + 432*sqrt(3)*2^(1/3)*(13*x^9 - 177*x^7 - 153*x^5 - 27*x^3))*(x^2 + 1)^(2/3) + 36*(96*x^10 - 4032*x^8 - 2592*x^6 + sqrt(3)*(x^11 + 369*x^9 - 3654*x^7 - 5454*x^5 - 2187*x^3 - 243*x))*(x^2 + 1)^(1/3))*sqrt((2*2^(2/3)*(x^6 - 57*x^4 - 117*x^2 - 27) + (x^2 + 1)^(2/3)*(432^(5/6)*(x^3 + x) + 24*2^(1/3)*(x^4 + 9*x^2)) - 8*(6*x^4 - 18*x^2 + sqrt(3)*(x^5 - 9*x))*(x^2 + 1)^(1/3) - 8*432^(1/6)*(x^5 + 18*x^3 + 9*x))/(x^6 - 9*x^4 + 27*x^2 - 27)) + 216*(sqrt(3)*2^(2/3)*(x^10 + 276*x^8 + 1206*x^6 + 756*x^4 + 81*x^2) + 432^(1/6)*sqrt(3)*(31*x^9 - 1620*x^7 - 2070*x^5 - 756*x^3 - 81*x))*(x^2 + 1)^(2/3) + 18*sqrt(3)*(x^12 + 1422*x^10 + 21447*x^8 + 27108*x^6 + 16767*x^4 + 6318*x^2 + 729) + (432^(5/6)*sqrt(3)*(x^11 - 681*x^9 + 4338*x^7 + 6102*x^5 + 2349*x^3 + 243*x) + 3888*sqrt(3)*2^(1/3)*(x^10 + 44*x^8 + 94*x^6 + 60*x^4 + 9*x^2))*(x^2 + 1)^(1/3))/(x^12 - 2178*x^10 + 46791*x^8 + 83268*x^6 + 47871*x^4 + 10206*x^2 + 729)) + 1/2592*432^(5/6)*sqrt(3)*arctan(-1/54*(2592*x^11 - 393984*x^9 - 699840*x^7 - 373248*x^5 - 69984*x^3 + sqrt(6)*(18*sqrt(3)*2^(2/3)*(19*x^11 + 111*x^9 + 6030*x^7 + 7182*x^5 + 2511*x^3 + 243*x) - 3*432^(1/6)*sqrt(3)*(x^12 + 924*x^10 - 33363*x^8 - 60912*x^6 - 36693*x^4 - 8748*x^2 - 729) - (432^(5/6)*sqrt(3)*(x^10 - 78*x^8 - 720*x^6 - 594*x^4 - 81*x^2) - 432*sqrt(3)*2^(1/3)*(13*x^9 - 177*x^7 - 153*x^5 - 27*x^3))*(x^2 + 1)^(2/3) - 36*(96*x^10 - 4032*x^8 - 2592*x^6 - sqrt(3)*(x^11 + 369*x^9 - 3654*x^7 - 5454*x^5 - 2187*x^3 - 243*x))*(x^2 + 1)^(1/3))*sqrt((2*2^(2/3)*(x^6 - 57*x^4 - 117*x^2 - 27) - (x^2 + 1)^(2/3)*(432^(5/6)*(x^3 + x) - 24*2^(1/3)*(x^4 + 9*x^2)) - 8*(6*x^4 - 18*x^2 - sqrt(3)*(x^5 - 9*x))*(x^2 + 1)^(1/3) + 8*432^(1/6)*(x^5 + 18*x^3 + 9*x))/(x^6 - 9*x^4 + 27*x^2 - 27)) - 216*(sqrt(3)*2^(2/3)*(x^10 + 276*x^8 + 1206*x^6 + 756*x^4 + 81*x^2) - 432^(1/6)*sqrt(3)*(31*x^9 - 1620*x^7 - 2070*x^5 - 756*x^3 - 81*x))*(x^2 + 1)^(2/3) - 18*sqrt(3)*(x^12 + 1422*x^10 + 21447*x^8 + 27108*x^6 + 16767*x^4 + 6318*x^2 + 729) + (432^(5/6)*sqrt(3)*(x^11 - 681*x^9 + 4338*x^7 + 6102*x^5 + 2349*x^3 + 243*x) - 3888*sqrt(3)*2^(1/3)*(x^10 + 44*x^8 + 94*x^6 + 60*x^4 + 9*x^2))*(x^2 + 1)^(1/3))/(x^12 - 2178*x^10 + 46791*x^8 + 83268*x^6 + 47871*x^4 + 10206*x^2 + 729)) + 1/5184*432^(5/6)*log(-(432^(5/6)*(x^6 + 69*x^4 + 63*x^2 + 27) + 864*(9*x^3 + sqrt(3)*(x^4 + 9*x^2) + 9*x)*(x^2 + 1)^(2/3) + 432*2^(1/3)*(5*x^5 + 30*x^3 + 9*x) + 432*(x^2 + 1)^(1/3)*(2^(2/3)*(x^5 + 18*x^3 + 9*x) + 4*432^(1/6)*(x^4 + 3*x^2)))/(x^6 - 9*x^4 + 27*x^2 - 27)) - 1/5184*432^(5/6)*log((432^(5/6)*(x^6 + 69*x^4 + 63*x^2 + 27) - 864*(9*x^3 - sqrt(3)*(x^4 + 9*x^2) + 9*x)*(x^2 + 1)^(2/3) - 432*2^(1/3)*(5*x^5 + 30*x^3 + 9*x) - 432*(x^2 + 1)^(1/3)*(2^(2/3)*(x^5 + 18*x^3 + 9*x) - 4*432^(1/6)*(x^4 + 3*x^2)))/(x^6 - 9*x^4 + 27*x^2 - 27)) - 1/10368*432^(5/6)*log(31104*(2*2^(2/3)*(x^6 - 57*x^4 - 117*x^2 - 27) + (x^2 + 1)^(2/3)*(432^(5/6)*(x^3 + x) + 24*2^(1/3)*(x^4 + 9*x^2)) - 8*(6*x^4 - 18*x^2 + sqrt(3)*(x^5 - 9*x))*(x^2 + 1)^(1/3) - 8*432^(1/6)*(x^5 + 18*x^3 + 9*x))/(x^6 - 9*x^4 + 27*x^2 - 27)) + 1/10368*432^(5/6)*log(31104*(2*2^(2/3)*(x^6 - 57*x^4 - 117*x^2 - 27) - (x^2 + 1)^(2/3)*(432^(5/6)*(x^3 + x) - 24*2^(1/3)*(x^4 + 9*x^2)) - 8*(6*x^4 - 18*x^2 - sqrt(3)*(x^5 - 9*x))*(x^2 + 1)^(1/3) + 8*432^(1/6)*(x^5 + 18*x^3 + 9*x))/(x^6 - 9*x^4 + 27*x^2 - 27))","B",0
148,1,285,0,16.352586," ","integrate((3-x)/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{4^{\frac{1}{6}} \sqrt{3} {\left(12 \cdot 4^{\frac{2}{3}} {\left(x^{4} + 3 \, x^{3} + 3 \, x^{2} + 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(x^{6} - 18 \, x^{5} - 117 \, x^{4} - 36 \, x^{3} + 207 \, x^{2} + 54 \, x - 27\right)} + 12 \, {\left(x^{5} + 19 \, x^{4} + 42 \, x^{3} + 6 \, x^{2} - 27 \, x - 9\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, {\left(x^{6} + 54 \, x^{5} + 171 \, x^{4} + 108 \, x^{3} - 81 \, x^{2} - 162 \, x - 27\right)}}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \log\left(\frac{6 \cdot 4^{\frac{2}{3}} {\left(x^{2} + 3 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(x^{4} + 18 \, x^{3} + 24 \, x^{2} - 18 \, x - 9\right)} - 6 \, {\left(x^{3} + 7 \, x^{2} + 3 \, x - 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}{x^{4} + 6 \, x^{2} + 9}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \log\left(\frac{4^{\frac{2}{3}} {\left(x^{2} + 3\right)} + 6 \cdot 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)} + 12 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{x^{2} + 3}\right)"," ",0,"-1/6*4^(1/6)*sqrt(3)*arctan(1/6*4^(1/6)*sqrt(3)*(12*4^(2/3)*(x^4 + 3*x^3 + 3*x^2 + 9*x)*(-x^2 + 1)^(2/3) + 4^(1/3)*(x^6 - 18*x^5 - 117*x^4 - 36*x^3 + 207*x^2 + 54*x - 27) + 12*(x^5 + 19*x^4 + 42*x^3 + 6*x^2 - 27*x - 9)*(-x^2 + 1)^(1/3))/(x^6 + 54*x^5 + 171*x^4 + 108*x^3 - 81*x^2 - 162*x - 27)) - 1/24*4^(2/3)*log((6*4^(2/3)*(x^2 + 3*x)*(-x^2 + 1)^(2/3) + 4^(1/3)*(x^4 + 18*x^3 + 24*x^2 - 18*x - 9) - 6*(x^3 + 7*x^2 + 3*x - 3)*(-x^2 + 1)^(1/3))/(x^4 + 6*x^2 + 9)) + 1/12*4^(2/3)*log((4^(2/3)*(x^2 + 3) + 6*4^(1/3)*(-x^2 + 1)^(1/3)*(x + 1) + 12*(-x^2 + 1)^(2/3))/(x^2 + 3))","B",0
149,1,315,0,15.632497," ","integrate((3+x)/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{4^{\frac{1}{6}} \sqrt{3} {\left(12 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{4} - 3 \, x^{3} + 3 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 12 \, \left(-1\right)^{\frac{1}{3}} {\left(x^{5} - 19 \, x^{4} + 42 \, x^{3} - 6 \, x^{2} - 27 \, x + 9\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} {\left(x^{6} + 18 \, x^{5} - 117 \, x^{4} + 36 \, x^{3} + 207 \, x^{2} - 54 \, x - 27\right)}\right)}}{6 \, {\left(x^{6} - 54 \, x^{5} + 171 \, x^{4} - 108 \, x^{3} - 81 \, x^{2} + 162 \, x - 27\right)}}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{6 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} - 3 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{4} - 18 \, x^{3} + 24 \, x^{2} + 18 \, x - 9\right)} - 6 \, {\left(x^{3} - 7 \, x^{2} + 3 \, x + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}{x^{4} + 6 \, x^{2} + 9}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{6 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x - 1\right)} + 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)} - 12 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{x^{2} + 3}\right)"," ",0,"-1/6*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*sqrt(3)*(12*4^(2/3)*(-1)^(2/3)*(x^4 - 3*x^3 + 3*x^2 - 9*x)*(-x^2 + 1)^(2/3) + 12*(-1)^(1/3)*(x^5 - 19*x^4 + 42*x^3 - 6*x^2 - 27*x + 9)*(-x^2 + 1)^(1/3) + 4^(1/3)*(x^6 + 18*x^5 - 117*x^4 + 36*x^3 + 207*x^2 - 54*x - 27))/(x^6 - 54*x^5 + 171*x^4 - 108*x^3 - 81*x^2 + 162*x - 27)) - 1/24*4^(2/3)*(-1)^(1/3)*log(-(6*4^(2/3)*(-1)^(1/3)*(x^2 - 3*x)*(-x^2 + 1)^(2/3) - 4^(1/3)*(-1)^(2/3)*(x^4 - 18*x^3 + 24*x^2 + 18*x - 9) - 6*(x^3 - 7*x^2 + 3*x + 3)*(-x^2 + 1)^(1/3))/(x^4 + 6*x^2 + 9)) + 1/12*4^(2/3)*(-1)^(1/3)*log(-(6*4^(1/3)*(-1)^(2/3)*(-x^2 + 1)^(1/3)*(x - 1) + 4^(2/3)*(-1)^(1/3)*(x^2 + 3) - 12*(-x^2 + 1)^(2/3))/(x^2 + 3))","B",0
150,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/3)/(9*a*d/b+d*x^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(-9*a*d/b+d*x^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(1/(b*x^2-a)^(1/3)/(-9*a*d/b+d*x^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate(1/(-b*x^2-a)^(1/3)/(9*a*d/b+d*x^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate(1/(b*x^2+2)^(1/3)/(18*d/b+d*x^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate(1/(b*x^2-2)^(1/3)/(-18*d/b+d*x^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate(1/(3*x^2+2)^(1/3)/(d*x^2+6*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/3)/(d*x^2-6*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(1/(3*x^2-2)^(1/3)/(d*x^2-6*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate(1/(-3*x^2-2)^(1/3)/(d*x^2+6*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,1,1395,0,8.020216," ","integrate(1/(x^2+1)^(1/3)/(x^2+9),x, algorithm=""fricas"")","\frac{1}{144} \, \sqrt{3} \log\left(\frac{4 \, {\left(x^{6} + 1647 \, x^{4} + 891 \, x^{2} + 18 \, {\left(3 \, x^{4} + 32 \, \sqrt{3} x^{3} + 126 \, x^{2} + 27\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 108 \, \sqrt{3} {\left(x^{5} + 10 \, x^{3} + 9 \, x\right)} + 6 \, {\left(81 \, x^{4} + 162 \, x^{2} + \sqrt{3} {\left(x^{5} + 210 \, x^{3} + 81 \, x\right)} + 81\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 243\right)}}{x^{6} + 27 \, x^{4} + 243 \, x^{2} + 729}\right) - \frac{1}{144} \, \sqrt{3} \log\left(\frac{4 \, {\left(x^{6} + 1647 \, x^{4} + 891 \, x^{2} + 18 \, {\left(3 \, x^{4} - 32 \, \sqrt{3} x^{3} + 126 \, x^{2} + 27\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - 108 \, \sqrt{3} {\left(x^{5} + 10 \, x^{3} + 9 \, x\right)} + 6 \, {\left(81 \, x^{4} + 162 \, x^{2} - \sqrt{3} {\left(x^{5} + 210 \, x^{3} + 81 \, x\right)} + 81\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 243\right)}}{x^{6} + 27 \, x^{4} + 243 \, x^{2} + 729}\right) - \frac{1}{36} \, \arctan\left(\frac{384 \, x^{11} - 130320 \, x^{9} + 2379456 \, x^{7} - 629856 \, x^{5} - 1259712 \, x^{3} + 36 \, {\left(388 \, x^{9} - 27864 \, x^{7} + 303264 \, x^{5} + 17496 \, x^{3} + \sqrt{3} {\left(x^{10} + 549 \, x^{8} - 8046 \, x^{6} + 129762 \, x^{4} - 19683 \, x^{2} + 59049\right)} - 236196 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + \sqrt{3} {\left(x^{12} - 234 \, x^{10} + 229311 \, x^{8} - 1214028 \, x^{6} + 6816879 \, x^{4} + 6022998 \, x^{2} + 531441\right)} + 2 \, {\left(x^{12} + 50616 \, x^{10} - 1869399 \, x^{8} - 3773304 \, x^{6} - 6908733 \, x^{4} + 72 \, {\left(x^{10} + 1620 \, x^{8} - 63666 \, x^{6} - 43740 \, x^{4} + 59049 \, x^{2} + 12 \, \sqrt{3} {\left(11 \, x^{9} - 261 \, x^{7} - 6075 \, x^{5} - 2187 \, x^{3}\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 6 \, \sqrt{3} {\left(43 \, x^{11} + 14055 \, x^{9} - 563922 \, x^{7} - 1307826 \, x^{5} - 898857 \, x^{3} + 177147 \, x\right)} + 6 \, {\left(453 \, x^{10} + 21141 \, x^{8} - 1483758 \, x^{6} - 1404054 \, x^{4} - 885735 \, x^{2} + \sqrt{3} {\left(x^{11} + 8985 \, x^{9} - 349110 \, x^{7} + 118098 \, x^{5} + 32805 \, x^{3} - 177147 \, x\right)} + 531441\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1594323\right)} \sqrt{\frac{x^{6} + 1647 \, x^{4} + 891 \, x^{2} + 18 \, {\left(3 \, x^{4} - 32 \, \sqrt{3} x^{3} + 126 \, x^{2} + 27\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - 108 \, \sqrt{3} {\left(x^{5} + 10 \, x^{3} + 9 \, x\right)} + 6 \, {\left(81 \, x^{4} + 162 \, x^{2} - \sqrt{3} {\left(x^{5} + 210 \, x^{3} + 81 \, x\right)} + 81\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 243}{x^{6} + 27 \, x^{4} + 243 \, x^{2} + 729}} + 12 \, {\left(x^{11} - 6423 \, x^{9} + 225018 \, x^{7} - 1106622 \, x^{5} - 1541835 \, x^{3} + 3 \, \sqrt{3} {\left(37 \, x^{10} - 675 \, x^{8} + 34722 \, x^{6} - 97686 \, x^{4} + 59049 \, x^{2} + 59049\right)} - 177147 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 8503056 \, x}{x^{12} - 48978 \, x^{10} + 2332071 \, x^{8} - 16419996 \, x^{6} - 24151041 \, x^{4} - 9565938 \, x^{2} + 4782969}\right) + \frac{1}{36} \, \arctan\left(-\frac{384 \, x^{11} - 130320 \, x^{9} + 2379456 \, x^{7} - 629856 \, x^{5} - 1259712 \, x^{3} + 36 \, {\left(388 \, x^{9} - 27864 \, x^{7} + 303264 \, x^{5} + 17496 \, x^{3} - \sqrt{3} {\left(x^{10} + 549 \, x^{8} - 8046 \, x^{6} + 129762 \, x^{4} - 19683 \, x^{2} + 59049\right)} - 236196 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - \sqrt{3} {\left(x^{12} - 234 \, x^{10} + 229311 \, x^{8} - 1214028 \, x^{6} + 6816879 \, x^{4} + 6022998 \, x^{2} + 531441\right)} + 2 \, {\left(x^{12} + 50616 \, x^{10} - 1869399 \, x^{8} - 3773304 \, x^{6} - 6908733 \, x^{4} + 72 \, {\left(x^{10} + 1620 \, x^{8} - 63666 \, x^{6} - 43740 \, x^{4} + 59049 \, x^{2} - 12 \, \sqrt{3} {\left(11 \, x^{9} - 261 \, x^{7} - 6075 \, x^{5} - 2187 \, x^{3}\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - 6 \, \sqrt{3} {\left(43 \, x^{11} + 14055 \, x^{9} - 563922 \, x^{7} - 1307826 \, x^{5} - 898857 \, x^{3} + 177147 \, x\right)} + 6 \, {\left(453 \, x^{10} + 21141 \, x^{8} - 1483758 \, x^{6} - 1404054 \, x^{4} - 885735 \, x^{2} - \sqrt{3} {\left(x^{11} + 8985 \, x^{9} - 349110 \, x^{7} + 118098 \, x^{5} + 32805 \, x^{3} - 177147 \, x\right)} + 531441\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1594323\right)} \sqrt{\frac{x^{6} + 1647 \, x^{4} + 891 \, x^{2} + 18 \, {\left(3 \, x^{4} + 32 \, \sqrt{3} x^{3} + 126 \, x^{2} + 27\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 108 \, \sqrt{3} {\left(x^{5} + 10 \, x^{3} + 9 \, x\right)} + 6 \, {\left(81 \, x^{4} + 162 \, x^{2} + \sqrt{3} {\left(x^{5} + 210 \, x^{3} + 81 \, x\right)} + 81\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 243}{x^{6} + 27 \, x^{4} + 243 \, x^{2} + 729}} + 12 \, {\left(x^{11} - 6423 \, x^{9} + 225018 \, x^{7} - 1106622 \, x^{5} - 1541835 \, x^{3} - 3 \, \sqrt{3} {\left(37 \, x^{10} - 675 \, x^{8} + 34722 \, x^{6} - 97686 \, x^{4} + 59049 \, x^{2} + 59049\right)} - 177147 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 8503056 \, x}{x^{12} - 48978 \, x^{10} + 2332071 \, x^{8} - 16419996 \, x^{6} - 24151041 \, x^{4} - 9565938 \, x^{2} + 4782969}\right) - \frac{1}{36} \, \arctan\left(\frac{6 \, {\left(11 \, x^{5} + 30 \, x^{3} + 6 \, {\left(23 \, x^{3} + 27 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + {\left(x^{5} - 240 \, x^{3} - 81 \, x\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}} - 81 \, x\right)}}{x^{6} - 1971 \, x^{4} - 1701 \, x^{2} - 729}\right)"," ",0,"1/144*sqrt(3)*log(4*(x^6 + 1647*x^4 + 891*x^2 + 18*(3*x^4 + 32*sqrt(3)*x^3 + 126*x^2 + 27)*(x^2 + 1)^(2/3) + 108*sqrt(3)*(x^5 + 10*x^3 + 9*x) + 6*(81*x^4 + 162*x^2 + sqrt(3)*(x^5 + 210*x^3 + 81*x) + 81)*(x^2 + 1)^(1/3) - 243)/(x^6 + 27*x^4 + 243*x^2 + 729)) - 1/144*sqrt(3)*log(4*(x^6 + 1647*x^4 + 891*x^2 + 18*(3*x^4 - 32*sqrt(3)*x^3 + 126*x^2 + 27)*(x^2 + 1)^(2/3) - 108*sqrt(3)*(x^5 + 10*x^3 + 9*x) + 6*(81*x^4 + 162*x^2 - sqrt(3)*(x^5 + 210*x^3 + 81*x) + 81)*(x^2 + 1)^(1/3) - 243)/(x^6 + 27*x^4 + 243*x^2 + 729)) - 1/36*arctan((384*x^11 - 130320*x^9 + 2379456*x^7 - 629856*x^5 - 1259712*x^3 + 36*(388*x^9 - 27864*x^7 + 303264*x^5 + 17496*x^3 + sqrt(3)*(x^10 + 549*x^8 - 8046*x^6 + 129762*x^4 - 19683*x^2 + 59049) - 236196*x)*(x^2 + 1)^(2/3) + sqrt(3)*(x^12 - 234*x^10 + 229311*x^8 - 1214028*x^6 + 6816879*x^4 + 6022998*x^2 + 531441) + 2*(x^12 + 50616*x^10 - 1869399*x^8 - 3773304*x^6 - 6908733*x^4 + 72*(x^10 + 1620*x^8 - 63666*x^6 - 43740*x^4 + 59049*x^2 + 12*sqrt(3)*(11*x^9 - 261*x^7 - 6075*x^5 - 2187*x^3))*(x^2 + 1)^(2/3) + 6*sqrt(3)*(43*x^11 + 14055*x^9 - 563922*x^7 - 1307826*x^5 - 898857*x^3 + 177147*x) + 6*(453*x^10 + 21141*x^8 - 1483758*x^6 - 1404054*x^4 - 885735*x^2 + sqrt(3)*(x^11 + 8985*x^9 - 349110*x^7 + 118098*x^5 + 32805*x^3 - 177147*x) + 531441)*(x^2 + 1)^(1/3) + 1594323)*sqrt((x^6 + 1647*x^4 + 891*x^2 + 18*(3*x^4 - 32*sqrt(3)*x^3 + 126*x^2 + 27)*(x^2 + 1)^(2/3) - 108*sqrt(3)*(x^5 + 10*x^3 + 9*x) + 6*(81*x^4 + 162*x^2 - sqrt(3)*(x^5 + 210*x^3 + 81*x) + 81)*(x^2 + 1)^(1/3) - 243)/(x^6 + 27*x^4 + 243*x^2 + 729)) + 12*(x^11 - 6423*x^9 + 225018*x^7 - 1106622*x^5 - 1541835*x^3 + 3*sqrt(3)*(37*x^10 - 675*x^8 + 34722*x^6 - 97686*x^4 + 59049*x^2 + 59049) - 177147*x)*(x^2 + 1)^(1/3) - 8503056*x)/(x^12 - 48978*x^10 + 2332071*x^8 - 16419996*x^6 - 24151041*x^4 - 9565938*x^2 + 4782969)) + 1/36*arctan(-(384*x^11 - 130320*x^9 + 2379456*x^7 - 629856*x^5 - 1259712*x^3 + 36*(388*x^9 - 27864*x^7 + 303264*x^5 + 17496*x^3 - sqrt(3)*(x^10 + 549*x^8 - 8046*x^6 + 129762*x^4 - 19683*x^2 + 59049) - 236196*x)*(x^2 + 1)^(2/3) - sqrt(3)*(x^12 - 234*x^10 + 229311*x^8 - 1214028*x^6 + 6816879*x^4 + 6022998*x^2 + 531441) + 2*(x^12 + 50616*x^10 - 1869399*x^8 - 3773304*x^6 - 6908733*x^4 + 72*(x^10 + 1620*x^8 - 63666*x^6 - 43740*x^4 + 59049*x^2 - 12*sqrt(3)*(11*x^9 - 261*x^7 - 6075*x^5 - 2187*x^3))*(x^2 + 1)^(2/3) - 6*sqrt(3)*(43*x^11 + 14055*x^9 - 563922*x^7 - 1307826*x^5 - 898857*x^3 + 177147*x) + 6*(453*x^10 + 21141*x^8 - 1483758*x^6 - 1404054*x^4 - 885735*x^2 - sqrt(3)*(x^11 + 8985*x^9 - 349110*x^7 + 118098*x^5 + 32805*x^3 - 177147*x) + 531441)*(x^2 + 1)^(1/3) + 1594323)*sqrt((x^6 + 1647*x^4 + 891*x^2 + 18*(3*x^4 + 32*sqrt(3)*x^3 + 126*x^2 + 27)*(x^2 + 1)^(2/3) + 108*sqrt(3)*(x^5 + 10*x^3 + 9*x) + 6*(81*x^4 + 162*x^2 + sqrt(3)*(x^5 + 210*x^3 + 81*x) + 81)*(x^2 + 1)^(1/3) - 243)/(x^6 + 27*x^4 + 243*x^2 + 729)) + 12*(x^11 - 6423*x^9 + 225018*x^7 - 1106622*x^5 - 1541835*x^3 - 3*sqrt(3)*(37*x^10 - 675*x^8 + 34722*x^6 - 97686*x^4 + 59049*x^2 + 59049) - 177147*x)*(x^2 + 1)^(1/3) - 8503056*x)/(x^12 - 48978*x^10 + 2332071*x^8 - 16419996*x^6 - 24151041*x^4 - 9565938*x^2 + 4782969)) - 1/36*arctan(6*(11*x^5 + 30*x^3 + 6*(23*x^3 + 27*x)*(x^2 + 1)^(2/3) + (x^5 - 240*x^3 - 81*x)*(x^2 + 1)^(1/3) - 81*x)/(x^6 - 1971*x^4 - 1701*x^2 - 729))","B",0
161,-1,0,0,0.000000," ","integrate(1/(b*x^2+1)^(1/3)/(b*x^2+9),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,1,269,0,3.720969," ","integrate(1/(-x^2+1)^(1/3)/(-x^2+9),x, algorithm=""fricas"")","-\frac{1}{36} \, \sqrt{3} \arctan\left(\frac{36 \, \sqrt{3} {\left(x^{4} - 32 \, x^{3} - 42 \, x^{2} + 9\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 12 \, \sqrt{3} {\left(x^{5} + 27 \, x^{4} - 210 \, x^{3} - 54 \, x^{2} + 81 \, x + 27\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \sqrt{3} {\left(x^{6} - 108 \, x^{5} - 567 \, x^{4} + 1080 \, x^{3} + 459 \, x^{2} - 972 \, x - 405\right)}}{3 \, {\left(x^{6} + 108 \, x^{5} - 1647 \, x^{4} - 1080 \, x^{3} + 891 \, x^{2} + 972 \, x + 243\right)}}\right) - \frac{1}{72} \, \log\left(\frac{x^{3} + 33 \, x^{2} + 18 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} {\left(x + 1\right)} - 6 \, {\left(x^{2} + 6 \, x - 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 9 \, x - 9}{x^{3} + 9 \, x^{2} + 27 \, x + 27}\right) + \frac{1}{36} \, \log\left(-\frac{x^{3} - 33 \, x^{2} + 18 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} {\left(x - 1\right)} + 6 \, {\left(x^{2} - 6 \, x - 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 9 \, x + 9}{x^{3} + 9 \, x^{2} + 27 \, x + 27}\right)"," ",0,"-1/36*sqrt(3)*arctan(1/3*(36*sqrt(3)*(x^4 - 32*x^3 - 42*x^2 + 9)*(-x^2 + 1)^(2/3) + 12*sqrt(3)*(x^5 + 27*x^4 - 210*x^3 - 54*x^2 + 81*x + 27)*(-x^2 + 1)^(1/3) + sqrt(3)*(x^6 - 108*x^5 - 567*x^4 + 1080*x^3 + 459*x^2 - 972*x - 405))/(x^6 + 108*x^5 - 1647*x^4 - 1080*x^3 + 891*x^2 + 972*x + 243)) - 1/72*log((x^3 + 33*x^2 + 18*(-x^2 + 1)^(2/3)*(x + 1) - 6*(x^2 + 6*x - 3)*(-x^2 + 1)^(1/3) - 9*x - 9)/(x^3 + 9*x^2 + 27*x + 27)) + 1/36*log(-(x^3 - 33*x^2 + 18*(-x^2 + 1)^(2/3)*(x - 1) + 6*(x^2 - 6*x - 3)*(-x^2 + 1)^(1/3) - 9*x + 9)/(x^3 + 9*x^2 + 27*x + 27))","B",0
163,1,315,0,2.248292," ","integrate((c^2*x^2-1)^(1/2)/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} - 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} \sqrt{-d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right)}{8 \, {\left(c^{5} d^{3} x^{4} - 2 \, c^{3} d^{3} x^{2} + c d^{3}\right)}}, \frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c \sqrt{d} x}{c^{4} d x^{4} - d}\right)}{4 \, {\left(c^{5} d^{3} x^{4} - 2 \, c^{3} d^{3} x^{2} + c d^{3}\right)}}\right]"," ",0,"[1/8*(4*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 - 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*sqrt(-d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)))/(c^5*d^3*x^4 - 2*c^3*d^3*x^2 + c*d^3), 1/4*(2*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*sqrt(d)*x/(c^4*d*x^4 - d)))/(c^5*d^3*x^4 - 2*c^3*d^3*x^2 + c*d^3)]","A",0
164,1,303,0,1.605332," ","integrate(1/(c^2*x^2-1)^(3/2)/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} - 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} \sqrt{-d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right)}{8 \, {\left(c^{5} d x^{4} - 2 \, c^{3} d x^{2} + c d\right)}}, \frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c \sqrt{d} x}{c^{4} d x^{4} - d}\right)}{4 \, {\left(c^{5} d x^{4} - 2 \, c^{3} d x^{2} + c d\right)}}\right]"," ",0,"[1/8*(4*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 - 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*sqrt(-d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)))/(c^5*d*x^4 - 2*c^3*d*x^2 + c*d), 1/4*(2*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*sqrt(d)*x/(c^4*d*x^4 - d)))/(c^5*d*x^4 - 2*c^3*d*x^2 + c*d)]","A",0
165,1,314,0,1.764860," ","integrate(1/(c^2*x^2-1)^(1/2)/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c x + {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} + 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} \sqrt{-d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right)}{8 \, {\left(c^{5} d^{2} x^{4} - 2 \, c^{3} d^{2} x^{2} + c d^{2}\right)}}, -\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{c^{2} x^{2} - 1} c \sqrt{d} x}{c^{4} d x^{4} - d}\right)}{4 \, {\left(c^{5} d^{2} x^{4} - 2 \, c^{3} d^{2} x^{2} + c d^{2}\right)}}\right]"," ",0,"[-1/8*(4*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*x + (c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 + 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*sqrt(-d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)))/(c^5*d^2*x^4 - 2*c^3*d^2*x^2 + c*d^2), -1/4*(2*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(c^2*x^2 - 1)*c*sqrt(d)*x/(c^4*d*x^4 - d)))/(c^5*d^2*x^4 - 2*c^3*d^2*x^2 + c*d^2)]","A",0
166,0,0,0,1.434930," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x^{2} + c}, x\right)"," ",0,"integral((b*x^2 + a)^(3/2)*sqrt(d*x^2 + c), x)","F",0
167,0,0,0,0.966921," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c), x)","F",0
168,0,0,0,1.531929," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral(sqrt(d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
169,0,0,0,1.268565," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
170,0,0,0,1.344247," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
171,0,0,0,1.205170," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4), x)","F",0
172,0,0,0,1.116340," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d x^{4} + {\left(b c + a d\right)} x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}, x\right)"," ",0,"integral((b*d*x^4 + (b*c + a*d)*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c), x)","F",0
173,0,0,0,1.286820," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*(d*x^2 + c)^(3/2), x)","F",0
174,0,0,0,0.837023," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral((d*x^2 + c)^(3/2)/sqrt(b*x^2 + a), x)","F",0
175,0,0,0,1.361393," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*(d*x^2 + c)^(3/2)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
176,0,0,0,1.144678," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*(d*x^2 + c)^(3/2)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
177,0,0,0,0.978669," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}{b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*(d*x^2 + c)^(3/2)/(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4), x)","F",0
178,0,0,0,0.887501," ","integrate((b*x^2+2)^(1/2)*(d*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}, x\right)"," ",0,"integral(sqrt(b*x^2 + 2)*sqrt(d*x^2 + 3), x)","F",0
179,0,0,0,1.320145," ","integrate((-6*x^2+3)^(1/2)*(4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, x^{2} + 2} \sqrt{-6 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(4*x^2 + 2)*sqrt(-6*x^2 + 3), x)","F",0
180,1,38,0,0.911069," ","integrate((4*x^2+2)^(1/2)*(6*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, x^{3} + 3 \, x\right)} \sqrt{6 \, x^{2} + 3} \sqrt{4 \, x^{2} + 2}}{3 \, {\left(2 \, x^{2} + 1\right)}}"," ",0,"1/3*(2*x^3 + 3*x)*sqrt(6*x^2 + 3)*sqrt(4*x^2 + 2)/(2*x^2 + 1)","B",0
181,0,0,0,1.256862," ","integrate((b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}, x\right)"," ",0,"integral(sqrt(b*x^2 + 2)/sqrt(d*x^2 + 3), x)","F",0
182,0,0,0,1.390766," ","integrate((-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 4}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(-x^2 + 4)/sqrt(d*x^2 + c), x)","F",0
183,0,0,0,1.310563," ","integrate((x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 4}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(x^2 + 4)/sqrt(d*x^2 + c), x)","F",0
184,0,0,0,1.216153," ","integrate((-x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-x^2 + 1)*sqrt(-3*x^2 + 2)/(3*x^2 - 2), x)","F",0
185,0,0,0,1.222857," ","integrate((-x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + 4} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-x^2 + 4)*sqrt(-3*x^2 + 2)/(3*x^2 - 2), x)","F",0
186,0,0,0,1.307710," ","integrate((-4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{2} + 2} \sqrt{-4 \, x^{2} + 1}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^2 + 2)*sqrt(-4*x^2 + 1)/(3*x^2 - 2), x)","F",0
187,0,0,0,1.328732," ","integrate((x^2+1)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-x^{2} + 1}}{x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(x^2 + 1)*sqrt(-x^2 + 1)/(x^2 - 1), x)","F",0
188,0,0,0,1.396276," ","integrate((x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 1)*sqrt(-3*x^2 + 2)/(3*x^2 - 2), x)","F",0
189,0,0,0,1.039470," ","integrate((x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 4} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 4)*sqrt(-3*x^2 + 2)/(3*x^2 - 2), x)","F",0
190,0,0,0,1.299690," ","integrate((4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(4*x^2 + 1)*sqrt(-3*x^2 + 2)/(3*x^2 - 2), x)","F",0
191,0,0,0,1.217318," ","integrate((-x^2+1)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 1}}{\sqrt{x^{2} + 1}}, x\right)"," ",0,"integral(sqrt(-x^2 + 1)/sqrt(x^2 + 1), x)","F",0
192,0,0,0,1.382220," ","integrate((-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}, x\right)"," ",0,"integral(sqrt(-x^2 + 1)/sqrt(3*x^2 + 2), x)","F",0
193,0,0,0,1.205391," ","integrate((-x^2+4)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 4}}{\sqrt{3 \, x^{2} + 2}}, x\right)"," ",0,"integral(sqrt(-x^2 + 4)/sqrt(3*x^2 + 2), x)","F",0
194,0,0,0,1.265561," ","integrate((-4*x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-4 \, x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}, x\right)"," ",0,"integral(sqrt(-4*x^2 + 1)/sqrt(3*x^2 + 2), x)","F",0
195,0,0,0,1.319468," ","integrate((x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}, x\right)"," ",0,"integral(sqrt(x^2 + 1)/sqrt(3*x^2 + 2), x)","F",0
196,0,0,0,1.250533," ","integrate((x^2+4)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 4}}{\sqrt{3 \, x^{2} + 2}}, x\right)"," ",0,"integral(sqrt(x^2 + 4)/sqrt(3*x^2 + 2), x)","F",0
197,0,0,0,1.281170," ","integrate((4*x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}, x\right)"," ",0,"integral(sqrt(4*x^2 + 1)/sqrt(3*x^2 + 2), x)","F",0
198,0,0,0,0.692466," ","integrate((-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 1}}{\sqrt{2 \, x^{2} - 1}}, x\right)"," ",0,"integral(sqrt(-x^2 + 1)/sqrt(2*x^2 - 1), x)","F",0
199,0,0,0,1.292369," ","integrate((b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
200,0,0,0,1.390466," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
201,0,0,0,1.309492," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/2)/sqrt(d*x^2 + c), x)","F",0
202,0,0,0,1.232619," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
203,0,0,0,1.265738," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b d x^{4} + {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b*d*x^4 + (b*c + a*d)*x^2 + a*c), x)","F",0
204,0,0,0,1.256596," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2), x)","F",0
205,0,0,0,1.053736," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{3} d x^{8} + {\left(b^{3} c + 3 \, a b^{2} d\right)} x^{6} + 3 \, {\left(a b^{2} c + a^{2} b d\right)} x^{4} + a^{3} c + {\left(3 \, a^{2} b c + a^{3} d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^3*d*x^8 + (b^3*c + 3*a*b^2*d)*x^6 + 3*(a*b^2*c + a^2*b*d)*x^4 + a^3*c + (3*a^2*b*c + a^3*d)*x^2), x)","F",0
206,0,0,0,0.702847," ","integrate(1/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{4} d x^{10} + {\left(b^{4} c + 4 \, a b^{3} d\right)} x^{8} + 2 \, {\left(2 \, a b^{3} c + 3 \, a^{2} b^{2} d\right)} x^{6} + a^{4} c + 2 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} b d\right)} x^{4} + {\left(4 \, a^{3} b c + a^{4} d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^4*d*x^10 + (b^4*c + 4*a*b^3*d)*x^8 + 2*(2*a*b^3*c + 3*a^2*b^2*d)*x^6 + a^4*c + 2*(3*a^2*b^2*c + 2*a^3*b*d)*x^4 + (4*a^3*b*c + a^4*d)*x^2), x)","F",0
207,0,0,0,1.338413," ","integrate((b*x^2+a)^(7/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
208,0,0,0,1.276553," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
209,0,0,0,1.062084," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x^{2} + c}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/2)*sqrt(d*x^2 + c)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
210,0,0,0,1.288199," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
211,0,0,0,1.269401," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b d^{2} x^{6} + {\left(2 \, b c d + a d^{2}\right)} x^{4} + a c^{2} + {\left(b c^{2} + 2 \, a c d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b*d^2*x^6 + (2*b*c*d + a*d^2)*x^4 + a*c^2 + (b*c^2 + 2*a*c*d)*x^2), x)","F",0
212,0,0,0,1.393545," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{2} d^{2} x^{8} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^2*d^2*x^8 + 2*(b^2*c*d + a*b*d^2)*x^6 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(a*b*c^2 + a^2*c*d)*x^2), x)","F",0
213,0,0,0,0.710571," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b^{3} d^{2} x^{10} + {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} x^{8} + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x^{6} + a^{3} c^{2} + {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{4} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b^3*d^2*x^10 + (2*b^3*c*d + 3*a*b^2*d^2)*x^8 + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*x^6 + a^3*c^2 + (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*x^4 + (3*a^2*b*c^2 + 2*a^3*c*d)*x^2), x)","F",0
214,0,0,0,1.028855," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b d x^{4} + {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b*d*x^4 + (b*c + a*d)*x^2 + a*c), x)","F",0
215,0,0,0,1.159268," ","integrate(1/(-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{d x^{2} + c}}{b d x^{4} + {\left(b c - a d\right)} x^{2} - a c}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(d*x^2 + c)/(b*d*x^4 + (b*c - a*d)*x^2 - a*c), x)","F",0
216,0,0,0,0.732182," ","integrate(1/(b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x^{2} + a} \sqrt{-d x^{2} + c}}{b d x^{4} - {\left(b c - a d\right)} x^{2} - a c}, x\right)"," ",0,"integral(-sqrt(b*x^2 + a)*sqrt(-d*x^2 + c)/(b*d*x^4 - (b*c - a*d)*x^2 - a*c), x)","F",0
217,0,0,0,1.273150," ","integrate(1/(-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-b x^{2} + a} \sqrt{-d x^{2} + c}}{b d x^{4} - {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral(sqrt(-b*x^2 + a)*sqrt(-d*x^2 + c)/(b*d*x^4 - (b*c + a*d)*x^2 + a*c), x)","F",0
218,0,0,0,1.180695," ","integrate(1/(-x^2+1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x^{2} + 2} \sqrt{-x^{2} + 1}}{5 \, x^{4} - 3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(5*x^2 + 2)*sqrt(-x^2 + 1)/(5*x^4 - 3*x^2 - 2), x)","F",0
219,0,0,0,1.323856," ","integrate(1/(-x^2+1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x^{2} + 2} \sqrt{-x^{2} + 1}}{2 \, {\left(2 \, x^{4} - x^{2} - 1\right)}}, x\right)"," ",0,"integral(-1/2*sqrt(4*x^2 + 2)*sqrt(-x^2 + 1)/(2*x^4 - x^2 - 1), x)","F",0
220,0,0,0,1.289731," ","integrate(1/(-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 1}}{3 \, x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 2)*sqrt(-x^2 + 1)/(3*x^4 - x^2 - 2), x)","F",0
221,0,0,0,1.250478," ","integrate(1/(-x^2+1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{2 \, x^{2} + 2} \sqrt{-x^{2} + 1}}{2 \, {\left(x^{4} - 1\right)}}, x\right)"," ",0,"integral(-1/2*sqrt(2*x^2 + 2)*sqrt(-x^2 + 1)/(x^4 - 1), x)","F",0
222,0,0,0,1.371448," ","integrate(1/(-x^2+1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 2} \sqrt{-x^{2} + 1}}{x^{4} + x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 2)*sqrt(-x^2 + 1)/(x^4 + x^2 - 2), x)","F",0
223,0,0,0,1.189574," ","integrate(1/(-x^2+1)^(1/2)/(-x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 2} \sqrt{-x^{2} + 1}}{x^{4} - 3 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(-x^2 + 2)*sqrt(-x^2 + 1)/(x^4 - 3*x^2 + 2), x)","F",0
224,1,68,0,1.298471," ","integrate(1/(-2*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(-\frac{x^{6} + 5 \, x^{4} - 2 \, \sqrt{2} {\left(x^{3} + x\right)} \sqrt{-x^{2} + 1} \sqrt{-2 \, x^{2} + 2} - 5 \, x^{2} - 1}{x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1}\right)"," ",0,"1/8*sqrt(2)*log(-(x^6 + 5*x^4 - 2*sqrt(2)*(x^3 + x)*sqrt(-x^2 + 1)*sqrt(-2*x^2 + 2) - 5*x^2 - 1)/(x^6 - 3*x^4 + 3*x^2 - 1))","B",0
225,0,0,0,1.274206," ","integrate(1/(-3*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{4} - 5 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(-x^2 + 1)*sqrt(-3*x^2 + 2)/(3*x^4 - 5*x^2 + 2), x)","F",0
226,0,0,0,1.274030," ","integrate(1/(-4*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 1} \sqrt{-4 \, x^{2} + 2}}{2 \, {\left(2 \, x^{4} - 3 \, x^{2} + 1\right)}}, x\right)"," ",0,"integral(1/2*sqrt(-x^2 + 1)*sqrt(-4*x^2 + 2)/(2*x^4 - 3*x^2 + 1), x)","F",0
227,0,0,0,1.381157," ","integrate(1/(-5*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 1} \sqrt{-5 \, x^{2} + 2}}{5 \, x^{4} - 7 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(-x^2 + 1)*sqrt(-5*x^2 + 2)/(5*x^4 - 7*x^2 + 2), x)","F",0
228,0,0,0,1.226518," ","integrate(1/(x^2+1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x^{2} + 2} \sqrt{x^{2} + 1}}{5 \, x^{4} + 7 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(5*x^2 + 2)*sqrt(x^2 + 1)/(5*x^4 + 7*x^2 + 2), x)","F",0
229,0,0,0,1.148010," ","integrate(1/(x^2+1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x^{2} + 2} \sqrt{x^{2} + 1}}{2 \, {\left(2 \, x^{4} + 3 \, x^{2} + 1\right)}}, x\right)"," ",0,"integral(1/2*sqrt(4*x^2 + 2)*sqrt(x^2 + 1)/(2*x^4 + 3*x^2 + 1), x)","F",0
230,0,0,0,1.256948," ","integrate(1/(x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} + 1}}{3 \, x^{4} + 5 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(3*x^2 + 2)*sqrt(x^2 + 1)/(3*x^4 + 5*x^2 + 2), x)","F",0
231,1,34,0,1.293264," ","integrate(1/(x^2+1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{2 \, x^{2} + 2} \sqrt{x^{2} + 1} x}{x^{4} - 1}\right)"," ",0,"-1/4*sqrt(2)*arctan(sqrt(2)*sqrt(2*x^2 + 2)*sqrt(x^2 + 1)*x/(x^4 - 1))","B",0
232,0,0,0,0.982487," ","integrate(1/(x^2+1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 2} \sqrt{x^{2} + 1}}{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(x^2 + 2)*sqrt(x^2 + 1)/(x^4 + 3*x^2 + 2), x)","F",0
233,0,0,0,1.191015," ","integrate(1/(-x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-x^{2} + 2}}{x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 1)*sqrt(-x^2 + 2)/(x^4 - x^2 - 2), x)","F",0
234,0,0,0,1.491183," ","integrate(1/(-2*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-2 \, x^{2} + 2}}{2 \, {\left(x^{4} - 1\right)}}, x\right)"," ",0,"integral(-1/2*sqrt(x^2 + 1)*sqrt(-2*x^2 + 2)/(x^4 - 1), x)","F",0
235,0,0,0,1.628282," ","integrate(1/(-3*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{4} + x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 1)*sqrt(-3*x^2 + 2)/(3*x^4 + x^2 - 2), x)","F",0
236,0,0,0,1.019602," ","integrate(1/(-4*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-4 \, x^{2} + 2}}{2 \, {\left(2 \, x^{4} + x^{2} - 1\right)}}, x\right)"," ",0,"integral(-1/2*sqrt(x^2 + 1)*sqrt(-4*x^2 + 2)/(2*x^4 + x^2 - 1), x)","F",0
237,0,0,0,1.408570," ","integrate(1/(-5*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-5 \, x^{2} + 2}}{5 \, x^{4} + 3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 1)*sqrt(-5*x^2 + 2)/(5*x^4 + 3*x^2 - 2), x)","F",0
238,0,0,0,1.472656," ","integrate(1/(x^2-1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x^{2} + 2} \sqrt{x^{2} - 1}}{5 \, x^{4} - 3 \, x^{2} - 2}, x\right)"," ",0,"integral(sqrt(5*x^2 + 2)*sqrt(x^2 - 1)/(5*x^4 - 3*x^2 - 2), x)","F",0
239,0,0,0,1.229165," ","integrate(1/(x^2-1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x^{2} + 2} \sqrt{x^{2} - 1}}{2 \, {\left(2 \, x^{4} - x^{2} - 1\right)}}, x\right)"," ",0,"integral(1/2*sqrt(4*x^2 + 2)*sqrt(x^2 - 1)/(2*x^4 - x^2 - 1), x)","F",0
240,0,0,0,0.863853," ","integrate(1/(x^2-1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} - 1}}{3 \, x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(sqrt(3*x^2 + 2)*sqrt(x^2 - 1)/(3*x^4 - x^2 - 2), x)","F",0
241,0,0,0,0.961567," ","integrate(1/(x^2-1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{2} + 2} \sqrt{x^{2} - 1}}{2 \, {\left(x^{4} - 1\right)}}, x\right)"," ",0,"integral(1/2*sqrt(2*x^2 + 2)*sqrt(x^2 - 1)/(x^4 - 1), x)","F",0
242,0,0,0,1.225127," ","integrate(1/(x^2-1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 2} \sqrt{x^{2} - 1}}{x^{4} + x^{2} - 2}, x\right)"," ",0,"integral(sqrt(x^2 + 2)*sqrt(x^2 - 1)/(x^4 + x^2 - 2), x)","F",0
243,0,0,0,1.241624," ","integrate(1/(-x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} - 1} \sqrt{-x^{2} + 2}}{x^{4} - 3 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(x^2 - 1)*sqrt(-x^2 + 2)/(x^4 - 3*x^2 + 2), x)","F",0
244,1,34,0,1.168117," ","integrate(1/(-2*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{x^{2} - 1} \sqrt{-2 \, x^{2} + 2} x}{x^{4} - 1}\right)"," ",0,"1/4*sqrt(2)*arctan(sqrt(2)*sqrt(x^2 - 1)*sqrt(-2*x^2 + 2)*x/(x^4 - 1))","A",0
245,0,0,0,1.187524," ","integrate(1/(-3*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} - 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{4} - 5 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(x^2 - 1)*sqrt(-3*x^2 + 2)/(3*x^4 - 5*x^2 + 2), x)","F",0
246,0,0,0,1.073268," ","integrate(1/(-4*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} - 1} \sqrt{-4 \, x^{2} + 2}}{2 \, {\left(2 \, x^{4} - 3 \, x^{2} + 1\right)}}, x\right)"," ",0,"integral(-1/2*sqrt(x^2 - 1)*sqrt(-4*x^2 + 2)/(2*x^4 - 3*x^2 + 1), x)","F",0
247,0,0,0,1.194054," ","integrate(1/(-5*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} - 1} \sqrt{-5 \, x^{2} + 2}}{5 \, x^{4} - 7 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(x^2 - 1)*sqrt(-5*x^2 + 2)/(5*x^4 - 7*x^2 + 2), x)","F",0
248,0,0,0,1.205912," ","integrate(1/(-x^2-1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x^{2} + 2} \sqrt{-x^{2} - 1}}{5 \, x^{4} + 7 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(5*x^2 + 2)*sqrt(-x^2 - 1)/(5*x^4 + 7*x^2 + 2), x)","F",0
249,0,0,0,1.025746," ","integrate(1/(-x^2-1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x^{2} + 2} \sqrt{-x^{2} - 1}}{2 \, {\left(2 \, x^{4} + 3 \, x^{2} + 1\right)}}, x\right)"," ",0,"integral(-1/2*sqrt(4*x^2 + 2)*sqrt(-x^2 - 1)/(2*x^4 + 3*x^2 + 1), x)","F",0
250,0,0,0,1.113828," ","integrate(1/(-x^2-1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} - 1}}{3 \, x^{4} + 5 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 2)*sqrt(-x^2 - 1)/(3*x^4 + 5*x^2 + 2), x)","F",0
251,1,104,0,1.153151," ","integrate(1/(-x^2-1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{2 \, {\left(2 \, \sqrt{2 \, x^{2} + 2} \sqrt{-x^{2} - 1} x + \sqrt{2} {\left(x^{4} - 1\right)}\right)}}{x^{4} + 2 \, x^{2} + 1}\right) - \frac{1}{8} \, \sqrt{2} \log\left(\frac{2 \, {\left(2 \, \sqrt{2 \, x^{2} + 2} \sqrt{-x^{2} - 1} x - \sqrt{2} {\left(x^{4} - 1\right)}\right)}}{x^{4} + 2 \, x^{2} + 1}\right)"," ",0,"1/8*sqrt(2)*log(2*(2*sqrt(2*x^2 + 2)*sqrt(-x^2 - 1)*x + sqrt(2)*(x^4 - 1))/(x^4 + 2*x^2 + 1)) - 1/8*sqrt(2)*log(2*(2*sqrt(2*x^2 + 2)*sqrt(-x^2 - 1)*x - sqrt(2)*(x^4 - 1))/(x^4 + 2*x^2 + 1))","B",0
252,0,0,0,1.094636," ","integrate(1/(-x^2-1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 2} \sqrt{-x^{2} - 1}}{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 2)*sqrt(-x^2 - 1)/(x^4 + 3*x^2 + 2), x)","F",0
253,0,0,0,1.099834," ","integrate(1/(-x^2-1)^(1/2)/(-x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 2} \sqrt{-x^{2} - 1}}{x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(sqrt(-x^2 + 2)*sqrt(-x^2 - 1)/(x^4 - x^2 - 2), x)","F",0
254,0,0,0,1.176977," ","integrate(1/(-2*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} - 1} \sqrt{-2 \, x^{2} + 2}}{2 \, {\left(x^{4} - 1\right)}}, x\right)"," ",0,"integral(1/2*sqrt(-x^2 - 1)*sqrt(-2*x^2 + 2)/(x^4 - 1), x)","F",0
255,0,0,0,1.126442," ","integrate(1/(-3*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} - 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{4} + x^{2} - 2}, x\right)"," ",0,"integral(sqrt(-x^2 - 1)*sqrt(-3*x^2 + 2)/(3*x^4 + x^2 - 2), x)","F",0
256,0,0,0,1.267118," ","integrate(1/(-4*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} - 1} \sqrt{-4 \, x^{2} + 2}}{2 \, {\left(2 \, x^{4} + x^{2} - 1\right)}}, x\right)"," ",0,"integral(1/2*sqrt(-x^2 - 1)*sqrt(-4*x^2 + 2)/(2*x^4 + x^2 - 1), x)","F",0
257,0,0,0,1.226563," ","integrate(1/(-5*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} - 1} \sqrt{-5 \, x^{2} + 2}}{5 \, x^{4} + 3 \, x^{2} - 2}, x\right)"," ",0,"integral(sqrt(-x^2 - 1)*sqrt(-5*x^2 + 2)/(5*x^4 + 3*x^2 - 2), x)","F",0
258,0,0,0,1.089242," ","integrate((b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x^{2} + a} \sqrt{-d x^{2} + c}}{d x^{2} - c}, x\right)"," ",0,"integral(-sqrt(b*x^2 + a)*sqrt(-d*x^2 + c)/(d*x^2 - c), x)","F",0
259,0,0,0,1.280643," ","integrate((-b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} - a} \sqrt{-d x^{2} + c}}{d x^{2} - c}, x\right)"," ",0,"integral(-sqrt(-b*x^2 - a)*sqrt(-d*x^2 + c)/(d*x^2 - c), x)","F",0
260,0,0,0,1.272389," ","integrate((b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} - c}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)/sqrt(d*x^2 - c), x)","F",0
261,0,0,0,1.318217," ","integrate((-b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-b x^{2} - a}}{\sqrt{d x^{2} - c}}, x\right)"," ",0,"integral(sqrt(-b*x^2 - a)/sqrt(d*x^2 - c), x)","F",0
262,0,0,0,1.200524," ","integrate((-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{-d x^{2} + c}}{d x^{2} - c}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(-d*x^2 + c)/(d*x^2 - c), x)","F",0
263,0,0,0,0.762490," ","integrate((b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x^{2} - a} \sqrt{-d x^{2} + c}}{d x^{2} - c}, x\right)"," ",0,"integral(-sqrt(b*x^2 - a)*sqrt(-d*x^2 + c)/(d*x^2 - c), x)","F",0
264,0,0,0,1.130810," ","integrate((-b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-b x^{2} + a}}{\sqrt{d x^{2} - c}}, x\right)"," ",0,"integral(sqrt(-b*x^2 + a)/sqrt(d*x^2 - c), x)","F",0
265,0,0,0,0.889124," ","integrate((b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} - a}}{\sqrt{d x^{2} - c}}, x\right)"," ",0,"integral(sqrt(b*x^2 - a)/sqrt(d*x^2 - c), x)","F",0
266,0,0,0,1.129441," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
267,0,0,0,0.740420," ","integrate((-b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-b x^{2} - a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(-b*x^2 - a)/sqrt(d*x^2 + c), x)","F",0
268,0,0,0,1.274448," ","integrate((b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x^{2} + a} \sqrt{-d x^{2} - c}}{d x^{2} + c}, x\right)"," ",0,"integral(-sqrt(b*x^2 + a)*sqrt(-d*x^2 - c)/(d*x^2 + c), x)","F",0
269,0,0,0,0.770944," ","integrate((-b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} - a} \sqrt{-d x^{2} - c}}{d x^{2} + c}, x\right)"," ",0,"integral(-sqrt(-b*x^2 - a)*sqrt(-d*x^2 - c)/(d*x^2 + c), x)","F",0
270,0,0,0,1.168818," ","integrate((-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(-b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
271,0,0,0,1.161833," ","integrate((b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} - a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(b*x^2 - a)/sqrt(d*x^2 + c), x)","F",0
272,0,0,0,1.321498," ","integrate((-b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{-d x^{2} - c}}{d x^{2} + c}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(-d*x^2 - c)/(d*x^2 + c), x)","F",0
273,0,0,0,1.217144," ","integrate((b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x^{2} - a} \sqrt{-d x^{2} - c}}{d x^{2} + c}, x\right)"," ",0,"integral(-sqrt(b*x^2 - a)*sqrt(-d*x^2 - c)/(d*x^2 + c), x)","F",0
274,0,0,0,1.296124," ","integrate((d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{d x^{2} + c}}{b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(d*x^2 + c)/(b*x^2 - a), x)","F",0
275,0,0,0,1.204368," ","integrate((-d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{-d x^{2} - c}}{b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(-d*x^2 - c)/(b*x^2 - a), x)","F",0
276,0,0,0,1.309294," ","integrate((d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} - a}}, x\right)"," ",0,"integral(sqrt(d*x^2 + c)/sqrt(b*x^2 - a), x)","F",0
277,0,0,0,1.204058," ","integrate((-d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-d x^{2} - c}}{\sqrt{b x^{2} - a}}, x\right)"," ",0,"integral(sqrt(-d*x^2 - c)/sqrt(b*x^2 - a), x)","F",0
278,0,0,0,1.231000," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{-d x^{2} + c}}{b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(-d*x^2 + c)/(b*x^2 - a), x)","F",0
279,0,0,0,1.123540," ","integrate((d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{d x^{2} - c}}{b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(d*x^2 - c)/(b*x^2 - a), x)","F",0
280,0,0,0,1.101105," ","integrate((-d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-d x^{2} + c}}{\sqrt{b x^{2} - a}}, x\right)"," ",0,"integral(sqrt(-d*x^2 + c)/sqrt(b*x^2 - a), x)","F",0
281,0,0,0,1.291919," ","integrate((d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{2} - c}}{\sqrt{b x^{2} - a}}, x\right)"," ",0,"integral(sqrt(d*x^2 - c)/sqrt(b*x^2 - a), x)","F",0
282,0,0,0,0.832026," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral(sqrt(d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
283,0,0,0,1.439681," ","integrate((-d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-d x^{2} - c}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral(sqrt(-d*x^2 - c)/sqrt(b*x^2 + a), x)","F",0
284,0,0,0,1.170872," ","integrate((d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} - a} \sqrt{d x^{2} + c}}{b x^{2} + a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 - a)*sqrt(d*x^2 + c)/(b*x^2 + a), x)","F",0
285,0,0,0,1.110651," ","integrate((-d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} - a} \sqrt{-d x^{2} - c}}{b x^{2} + a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 - a)*sqrt(-d*x^2 - c)/(b*x^2 + a), x)","F",0
286,0,0,0,0.911954," ","integrate((-d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-d x^{2} + c}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral(sqrt(-d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
287,0,0,0,1.086971," ","integrate((d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{2} - c}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral(sqrt(d*x^2 - c)/sqrt(b*x^2 + a), x)","F",0
288,0,0,0,0.889748," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} - a} \sqrt{-d x^{2} + c}}{b x^{2} + a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 - a)*sqrt(-d*x^2 + c)/(b*x^2 + a), x)","F",0
289,0,0,0,1.394016," ","integrate((d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} - a} \sqrt{d x^{2} - c}}{b x^{2} + a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 - a)*sqrt(d*x^2 - c)/(b*x^2 + a), x)","F",0
290,0,0,0,1.276830," ","integrate(1/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}}{b d x^{4} + {\left(3 \, b + 2 \, d\right)} x^{2} + 6}, x\right)"," ",0,"integral(sqrt(b*x^2 + 2)*sqrt(d*x^2 + 3)/(b*d*x^4 + (3*b + 2*d)*x^2 + 6), x)","F",0
291,0,0,0,1.245105," ","integrate(1/(-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{2} + c} \sqrt{-x^{2} + 4}}{d x^{4} + {\left(c - 4 \, d\right)} x^{2} - 4 \, c}, x\right)"," ",0,"integral(-sqrt(d*x^2 + c)*sqrt(-x^2 + 4)/(d*x^4 + (c - 4*d)*x^2 - 4*c), x)","F",0
292,0,0,0,1.244913," ","integrate(1/(x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{2} + c} \sqrt{x^{2} + 4}}{d x^{4} + {\left(c + 4 \, d\right)} x^{2} + 4 \, c}, x\right)"," ",0,"integral(sqrt(d*x^2 + c)*sqrt(x^2 + 4)/(d*x^4 + (c + 4*d)*x^2 + 4*c), x)","F",0
293,0,0,0,1.256778," ","integrate(1/(-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{2 \, x^{2} - 1} \sqrt{-x^{2} + 1}}{2 \, x^{4} - 3 \, x^{2} + 1}, x\right)"," ",0,"integral(-sqrt(2*x^2 - 1)*sqrt(-x^2 + 1)/(2*x^4 - 3*x^2 + 1), x)","F",0
294,0,0,0,1.210450," ","integrate((-c^2*x^2+1)^(1/2)/(c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{\sqrt{c^{2} x^{2} + 1}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/sqrt(c^2*x^2 + 1), x)","F",0
295,0,0,0,0.872846," ","integrate((b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}, x\right)"," ",0,"integral(sqrt(b*x^2 + 2)/sqrt(d*x^2 + 3), x)","F",0
296,0,0,0,1.252771," ","integrate((3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} - 1} \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(3*x^2 - 1)*sqrt(-3*x^2 + 2)/(3*x^2 - 2), x)","F",0
297,0,0,0,1.456223," ","integrate((1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1-2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a\right)} \sqrt{\frac{b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a}{a}} \sqrt{-\frac{b x^{2} - \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a}{a}}}{4 \, {\left(c x^{4} - b x^{2} + a\right)}}, x\right)"," ",0,"integral(-1/4*(b*x^2 + sqrt(b^2 - 4*a*c)*x^2 - 2*a)*sqrt((b*x^2 + sqrt(b^2 - 4*a*c)*x^2 + 2*a)/a)*sqrt(-(b*x^2 - sqrt(b^2 - 4*a*c)*x^2 - 2*a)/a)/(c*x^4 - b*x^2 + a), x)","F",0
298,0,0,0,1.517075," ","integrate((1-2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1-2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a\right)} \sqrt{-\frac{b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a}{a}} \sqrt{-\frac{b x^{2} - \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a}{a}}}{4 \, {\left(c x^{4} - b x^{2} + a\right)}}, x\right)"," ",0,"integral(-1/4*(b*x^2 + sqrt(b^2 - 4*a*c)*x^2 - 2*a)*sqrt(-(b*x^2 + sqrt(b^2 - 4*a*c)*x^2 - 2*a)/a)*sqrt(-(b*x^2 - sqrt(b^2 - 4*a*c)*x^2 - 2*a)/a)/(c*x^4 - b*x^2 + a), x)","F",0
299,0,0,0,1.102347," ","integrate((1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a\right)} \sqrt{\frac{b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a}{a}} \sqrt{\frac{b x^{2} - \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a}{a}}}{4 \, {\left(c x^{4} + b x^{2} + a\right)}}, x\right)"," ",0,"integral(1/4*(b*x^2 + sqrt(b^2 - 4*a*c)*x^2 + 2*a)*sqrt((b*x^2 + sqrt(b^2 - 4*a*c)*x^2 + 2*a)/a)*sqrt((b*x^2 - sqrt(b^2 - 4*a*c)*x^2 + 2*a)/a)/(c*x^4 + b*x^2 + a), x)","F",0
300,0,0,0,1.311324," ","integrate((1-2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a\right)} \sqrt{-\frac{b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a}{a}} \sqrt{\frac{b x^{2} - \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a}{a}}}{4 \, {\left(c x^{4} + b x^{2} + a\right)}}, x\right)"," ",0,"integral(1/4*(b*x^2 + sqrt(b^2 - 4*a*c)*x^2 + 2*a)*sqrt(-(b*x^2 + sqrt(b^2 - 4*a*c)*x^2 - 2*a)/a)*sqrt((b*x^2 - sqrt(b^2 - 4*a*c)*x^2 + 2*a)/a)/(c*x^4 + b*x^2 + a), x)","F",0
301,0,0,0,1.198677," ","integrate((-2*x^2+1)^m/(-x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + 1} {\left(-2 \, x^{2} + 1\right)}^{m}}{x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-x^2 + 1)*(-2*x^2 + 1)^m/(x^2 - 1), x)","F",0
302,0,0,0,0.969572," ","integrate(1/(x^2-1)^(1/2)/(7+x^2-4*3^(1/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{2} + 4 \, \sqrt{3} + 7\right)} \sqrt{x^{2} - 4 \, \sqrt{3} + 7} \sqrt{x^{2} - 1}}{x^{6} + 13 \, x^{4} - 13 \, x^{2} - 1}, x\right)"," ",0,"integral((x^2 + 4*sqrt(3) + 7)*sqrt(x^2 - 4*sqrt(3) + 7)*sqrt(x^2 - 1)/(x^6 + 13*x^4 - 13*x^2 - 1), x)","F",0
303,0,0,0,1.099089," ","integrate(1/(3+x^2*(-3+3^(1/2)))^(1/2)/(3-3*3^(1/2)+2*3^(1/2)*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{\sqrt{3} x^{2} - 3 \, x^{2} + 3} \sqrt{\sqrt{3} {\left(2 \, x^{2} - 3\right)} + 3} {\left(\sqrt{3} + 1\right)}}{6 \, {\left(2 \, x^{4} - 6 \, x^{2} + 3\right)}}, x\right)"," ",0,"integral(-1/6*sqrt(sqrt(3)*x^2 - 3*x^2 + 3)*sqrt(sqrt(3)*(2*x^2 - 3) + 3)*(sqrt(3) + 1)/(2*x^4 - 6*x^2 + 3), x)","F",0
304,1,553,0,9.143234," ","integrate(1/(3*x^2+2)^(1/4)/(3*x^2+4),x, algorithm=""fricas"")","\frac{1}{72} \cdot 18^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{6 \cdot 18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{3} + 54 \, x^{4} + 24 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{3}{4}} x + 12 \, \sqrt{2} {\left(3 \, x^{2} + 4\right)} \sqrt{3 \, x^{2} + 2} + 72 \, x^{2} - {\left(18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{3} - 4 \, x\right)} \sqrt{3 \, x^{2} + 2} + 72 \, {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{2} + 6 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{3} + 4 \, x\right)} + 48 \, \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{3}{4}}\right)} \sqrt{\frac{3 \, \sqrt{2} x^{2} + 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{3 \, x^{2} + 2}}{3 \, x^{2} + 4}}}{6 \, {\left(9 \, x^{4} - 24 \, x^{2} - 16\right)}}\right) - \frac{1}{72} \cdot 18^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{6 \cdot 18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{3} - 54 \, x^{4} + 24 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{3}{4}} x - 12 \, \sqrt{2} {\left(3 \, x^{2} + 4\right)} \sqrt{3 \, x^{2} + 2} - 72 \, x^{2} - {\left(18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{3} - 4 \, x\right)} \sqrt{3 \, x^{2} + 2} - 72 \, {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{2} + 6 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{3} + 4 \, x\right)} - 48 \, \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{3}{4}}\right)} \sqrt{\frac{3 \, \sqrt{2} x^{2} - 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{3 \, x^{2} + 2}}{3 \, x^{2} + 4}}}{6 \, {\left(9 \, x^{4} - 24 \, x^{2} - 16\right)}}\right) + \frac{1}{288} \cdot 18^{\frac{3}{4}} \sqrt{2} \log\left(\frac{36 \, {\left(3 \, \sqrt{2} x^{2} + 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{3 \, x^{2} + 2}\right)}}{3 \, x^{2} + 4}\right) - \frac{1}{288} \cdot 18^{\frac{3}{4}} \sqrt{2} \log\left(\frac{36 \, {\left(3 \, \sqrt{2} x^{2} - 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{3 \, x^{2} + 2}\right)}}{3 \, x^{2} + 4}\right)"," ",0,"1/72*18^(3/4)*sqrt(2)*arctan(-1/6*(6*18^(3/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x^3 + 54*x^4 + 24*18^(1/4)*sqrt(2)*(3*x^2 + 2)^(3/4)*x + 12*sqrt(2)*(3*x^2 + 4)*sqrt(3*x^2 + 2) + 72*x^2 - (18^(3/4)*sqrt(2)*(3*x^3 - 4*x)*sqrt(3*x^2 + 2) + 72*(3*x^2 + 2)^(1/4)*x^2 + 6*18^(1/4)*sqrt(2)*(3*x^3 + 4*x) + 48*sqrt(2)*(3*x^2 + 2)^(3/4))*sqrt((3*sqrt(2)*x^2 + 2*18^(1/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x + 4*sqrt(3*x^2 + 2))/(3*x^2 + 4)))/(9*x^4 - 24*x^2 - 16)) - 1/72*18^(3/4)*sqrt(2)*arctan(1/6*(6*18^(3/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x^3 - 54*x^4 + 24*18^(1/4)*sqrt(2)*(3*x^2 + 2)^(3/4)*x - 12*sqrt(2)*(3*x^2 + 4)*sqrt(3*x^2 + 2) - 72*x^2 - (18^(3/4)*sqrt(2)*(3*x^3 - 4*x)*sqrt(3*x^2 + 2) - 72*(3*x^2 + 2)^(1/4)*x^2 + 6*18^(1/4)*sqrt(2)*(3*x^3 + 4*x) - 48*sqrt(2)*(3*x^2 + 2)^(3/4))*sqrt((3*sqrt(2)*x^2 - 2*18^(1/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x + 4*sqrt(3*x^2 + 2))/(3*x^2 + 4)))/(9*x^4 - 24*x^2 - 16)) + 1/288*18^(3/4)*sqrt(2)*log(36*(3*sqrt(2)*x^2 + 2*18^(1/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x + 4*sqrt(3*x^2 + 2))/(3*x^2 + 4)) - 1/288*18^(3/4)*sqrt(2)*log(36*(3*sqrt(2)*x^2 - 2*18^(1/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x + 4*sqrt(3*x^2 + 2))/(3*x^2 + 4))","B",0
305,1,553,0,9.051169," ","integrate(1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{1}{72} \cdot 18^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{6 \cdot 18^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{3} + 54 \, x^{4} + 24 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x + 12 \, \sqrt{2} {\left(3 \, x^{2} - 4\right)} \sqrt{-3 \, x^{2} + 2} - 72 \, x^{2} + {\left(18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{3} + 4 \, x\right)} \sqrt{-3 \, x^{2} + 2} - 72 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{2} - 6 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{3} - 4 \, x\right)} - 48 \, \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}\right)} \sqrt{-\frac{3 \, \sqrt{2} x^{2} + 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 4}}}{6 \, {\left(9 \, x^{4} + 24 \, x^{2} - 16\right)}}\right) - \frac{1}{72} \cdot 18^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{6 \cdot 18^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{3} - 54 \, x^{4} + 24 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x - 12 \, \sqrt{2} {\left(3 \, x^{2} - 4\right)} \sqrt{-3 \, x^{2} + 2} + 72 \, x^{2} + {\left(18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{3} + 4 \, x\right)} \sqrt{-3 \, x^{2} + 2} + 72 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{2} - 6 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{3} - 4 \, x\right)} + 48 \, \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}\right)} \sqrt{-\frac{3 \, \sqrt{2} x^{2} - 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 4}}}{6 \, {\left(9 \, x^{4} + 24 \, x^{2} - 16\right)}}\right) + \frac{1}{288} \cdot 18^{\frac{3}{4}} \sqrt{2} \log\left(-\frac{36 \, {\left(3 \, \sqrt{2} x^{2} + 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}\right)}}{3 \, x^{2} - 4}\right) - \frac{1}{288} \cdot 18^{\frac{3}{4}} \sqrt{2} \log\left(-\frac{36 \, {\left(3 \, \sqrt{2} x^{2} - 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}\right)}}{3 \, x^{2} - 4}\right)"," ",0,"1/72*18^(3/4)*sqrt(2)*arctan(-1/6*(6*18^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x^3 + 54*x^4 + 24*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(3/4)*x + 12*sqrt(2)*(3*x^2 - 4)*sqrt(-3*x^2 + 2) - 72*x^2 + (18^(3/4)*sqrt(2)*(3*x^3 + 4*x)*sqrt(-3*x^2 + 2) - 72*(-3*x^2 + 2)^(1/4)*x^2 - 6*18^(1/4)*sqrt(2)*(3*x^3 - 4*x) - 48*sqrt(2)*(-3*x^2 + 2)^(3/4))*sqrt(-(3*sqrt(2)*x^2 + 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4)))/(9*x^4 + 24*x^2 - 16)) - 1/72*18^(3/4)*sqrt(2)*arctan(1/6*(6*18^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x^3 - 54*x^4 + 24*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(3/4)*x - 12*sqrt(2)*(3*x^2 - 4)*sqrt(-3*x^2 + 2) + 72*x^2 + (18^(3/4)*sqrt(2)*(3*x^3 + 4*x)*sqrt(-3*x^2 + 2) + 72*(-3*x^2 + 2)^(1/4)*x^2 - 6*18^(1/4)*sqrt(2)*(3*x^3 - 4*x) + 48*sqrt(2)*(-3*x^2 + 2)^(3/4))*sqrt(-(3*sqrt(2)*x^2 - 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4)))/(9*x^4 + 24*x^2 - 16)) + 1/288*18^(3/4)*sqrt(2)*log(-36*(3*sqrt(2)*x^2 + 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4)) - 1/288*18^(3/4)*sqrt(2)*log(-36*(3*sqrt(2)*x^2 - 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4))","B",0
306,1,755,0,28.018116," ","integrate(1/(b*x^2+2)^(1/4)/(b*x^2+4),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \arctan\left(-\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{1}{4}} x^{3} + b^{2} x^{4} + 8 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{3}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x + 4 \, b x^{2} + 4 \, \sqrt{\frac{1}{2}} {\left(b^{2} x^{2} + 4 \, b\right)} \sqrt{b x^{2} + 2} \sqrt{\frac{1}{b^{2}}} - 2 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b x^{2} + 2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b^{3} x^{3} + 4 \, b^{2} x\right)} \frac{1}{b^{2}}^{\frac{3}{4}} + 16 \, \sqrt{\frac{1}{2}} {\left(b x^{2} + 2\right)}^{\frac{3}{4}} b \sqrt{\frac{1}{b^{2}}} + \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(b^{2} x^{3} - 4 \, b x\right)} \sqrt{b x^{2} + 2} \frac{1}{b^{2}}^{\frac{1}{4}}\right)} \sqrt{\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x + \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} + 2 \, \sqrt{b x^{2} + 2}}{b x^{2} + 4}}}{b^{2} x^{4} - 8 \, b x^{2} - 16}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \arctan\left(\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{1}{4}} x^{3} - b^{2} x^{4} + 8 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{3}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x - 4 \, b x^{2} - 4 \, \sqrt{\frac{1}{2}} {\left(b^{2} x^{2} + 4 \, b\right)} \sqrt{b x^{2} + 2} \sqrt{\frac{1}{b^{2}}} + 2 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b x^{2} - 2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b^{3} x^{3} + 4 \, b^{2} x\right)} \frac{1}{b^{2}}^{\frac{3}{4}} + 16 \, \sqrt{\frac{1}{2}} {\left(b x^{2} + 2\right)}^{\frac{3}{4}} b \sqrt{\frac{1}{b^{2}}} - \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(b^{2} x^{3} - 4 \, b x\right)} \sqrt{b x^{2} + 2} \frac{1}{b^{2}}^{\frac{1}{4}}\right)} \sqrt{-\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x - \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} - 2 \, \sqrt{b x^{2} + 2}}{b x^{2} + 4}}}{b^{2} x^{4} - 8 \, b x^{2} - 16}\right) + \frac{1}{16} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x + \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} + 2 \, \sqrt{b x^{2} + 2}}{2 \, {\left(b x^{2} + 4\right)}}\right) - \frac{1}{16} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \log\left(-\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x - \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} - 2 \, \sqrt{b x^{2} + 2}}{2 \, {\left(b x^{2} + 4\right)}}\right)"," ",0,"1/4*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*arctan(-(2*sqrt(2)*(1/2)^(1/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(1/4)*x^3 + b^2*x^4 + 8*sqrt(2)*(1/2)^(3/4)*(b*x^2 + 2)^(3/4)*b^2*(b^(-2))^(3/4)*x + 4*b*x^2 + 4*sqrt(1/2)*(b^2*x^2 + 4*b)*sqrt(b*x^2 + 2)*sqrt(b^(-2)) - 2*sqrt(1/2)*(4*(b*x^2 + 2)^(1/4)*b*x^2 + 2*sqrt(2)*(1/2)^(3/4)*(b^3*x^3 + 4*b^2*x)*(b^(-2))^(3/4) + 16*sqrt(1/2)*(b*x^2 + 2)^(3/4)*b*sqrt(b^(-2)) + sqrt(2)*(1/2)^(1/4)*(b^2*x^3 - 4*b*x)*sqrt(b*x^2 + 2)*(b^(-2))^(1/4))*sqrt((2*sqrt(2)*(1/2)^(3/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x + sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 + 2*sqrt(b*x^2 + 2))/(b*x^2 + 4)))/(b^2*x^4 - 8*b*x^2 - 16)) - 1/4*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*arctan((2*sqrt(2)*(1/2)^(1/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(1/4)*x^3 - b^2*x^4 + 8*sqrt(2)*(1/2)^(3/4)*(b*x^2 + 2)^(3/4)*b^2*(b^(-2))^(3/4)*x - 4*b*x^2 - 4*sqrt(1/2)*(b^2*x^2 + 4*b)*sqrt(b*x^2 + 2)*sqrt(b^(-2)) + 2*sqrt(1/2)*(4*(b*x^2 + 2)^(1/4)*b*x^2 - 2*sqrt(2)*(1/2)^(3/4)*(b^3*x^3 + 4*b^2*x)*(b^(-2))^(3/4) + 16*sqrt(1/2)*(b*x^2 + 2)^(3/4)*b*sqrt(b^(-2)) - sqrt(2)*(1/2)^(1/4)*(b^2*x^3 - 4*b*x)*sqrt(b*x^2 + 2)*(b^(-2))^(1/4))*sqrt(-(2*sqrt(2)*(1/2)^(3/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x - sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 - 2*sqrt(b*x^2 + 2))/(b*x^2 + 4)))/(b^2*x^4 - 8*b*x^2 - 16)) + 1/16*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*log(1/2*(2*sqrt(2)*(1/2)^(3/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x + sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 + 2*sqrt(b*x^2 + 2))/(b*x^2 + 4)) - 1/16*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*log(-1/2*(2*sqrt(2)*(1/2)^(3/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x - sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 - 2*sqrt(b*x^2 + 2))/(b*x^2 + 4))","B",0
307,1,776,0,27.758545," ","integrate(1/(-b*x^2+2)^(1/4)/(-b*x^2+4),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \arctan\left(-\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{1}{4}} x^{3} + b^{2} x^{4} + 8 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{3}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x - 4 \, b x^{2} + 4 \, \sqrt{\frac{1}{2}} {\left(b^{2} x^{2} - 4 \, b\right)} \sqrt{-b x^{2} + 2} \sqrt{\frac{1}{b^{2}}} - 2 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b x^{2} + 2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b^{3} x^{3} - 4 \, b^{2} x\right)} \frac{1}{b^{2}}^{\frac{3}{4}} + 16 \, \sqrt{\frac{1}{2}} {\left(-b x^{2} + 2\right)}^{\frac{3}{4}} b \sqrt{\frac{1}{b^{2}}} - \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(b^{2} x^{3} + 4 \, b x\right)} \sqrt{-b x^{2} + 2} \frac{1}{b^{2}}^{\frac{1}{4}}\right)} \sqrt{-\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x + \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} + 2 \, \sqrt{-b x^{2} + 2}}{b x^{2} - 4}}}{b^{2} x^{4} + 8 \, b x^{2} - 16}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \arctan\left(-\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{1}{4}} x^{3} - b^{2} x^{4} + 8 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{3}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x + 4 \, b x^{2} - 4 \, \sqrt{\frac{1}{2}} {\left(b^{2} x^{2} - 4 \, b\right)} \sqrt{-b x^{2} + 2} \sqrt{\frac{1}{b^{2}}} + 2 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b x^{2} - 2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(b^{3} x^{3} - 4 \, b^{2} x\right)} \frac{1}{b^{2}}^{\frac{3}{4}} + 16 \, \sqrt{\frac{1}{2}} {\left(-b x^{2} + 2\right)}^{\frac{3}{4}} b \sqrt{\frac{1}{b^{2}}} + \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(b^{2} x^{3} + 4 \, b x\right)} \sqrt{-b x^{2} + 2} \frac{1}{b^{2}}^{\frac{1}{4}}\right)} \sqrt{\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x - \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} - 2 \, \sqrt{-b x^{2} + 2}}{b x^{2} - 4}}}{b^{2} x^{4} + 8 \, b x^{2} - 16}\right) + \frac{1}{16} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \log\left(-\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x + \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} + 2 \, \sqrt{-b x^{2} + 2}}{2 \, {\left(b x^{2} - 4\right)}}\right) - \frac{1}{16} \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{1}{4}} \frac{1}{b^{2}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{2}}^{\frac{3}{4}} x - \sqrt{\frac{1}{2}} b^{2} \sqrt{\frac{1}{b^{2}}} x^{2} - 2 \, \sqrt{-b x^{2} + 2}}{2 \, {\left(b x^{2} - 4\right)}}\right)"," ",0,"1/4*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*arctan(-(2*sqrt(2)*(1/2)^(1/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(1/4)*x^3 + b^2*x^4 + 8*sqrt(2)*(1/2)^(3/4)*(-b*x^2 + 2)^(3/4)*b^2*(b^(-2))^(3/4)*x - 4*b*x^2 + 4*sqrt(1/2)*(b^2*x^2 - 4*b)*sqrt(-b*x^2 + 2)*sqrt(b^(-2)) - 2*sqrt(1/2)*(4*(-b*x^2 + 2)^(1/4)*b*x^2 + 2*sqrt(2)*(1/2)^(3/4)*(b^3*x^3 - 4*b^2*x)*(b^(-2))^(3/4) + 16*sqrt(1/2)*(-b*x^2 + 2)^(3/4)*b*sqrt(b^(-2)) - sqrt(2)*(1/2)^(1/4)*(b^2*x^3 + 4*b*x)*sqrt(-b*x^2 + 2)*(b^(-2))^(1/4))*sqrt(-(2*sqrt(2)*(1/2)^(3/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x + sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 + 2*sqrt(-b*x^2 + 2))/(b*x^2 - 4)))/(b^2*x^4 + 8*b*x^2 - 16)) + 1/4*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*arctan(-(2*sqrt(2)*(1/2)^(1/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(1/4)*x^3 - b^2*x^4 + 8*sqrt(2)*(1/2)^(3/4)*(-b*x^2 + 2)^(3/4)*b^2*(b^(-2))^(3/4)*x + 4*b*x^2 - 4*sqrt(1/2)*(b^2*x^2 - 4*b)*sqrt(-b*x^2 + 2)*sqrt(b^(-2)) + 2*sqrt(1/2)*(4*(-b*x^2 + 2)^(1/4)*b*x^2 - 2*sqrt(2)*(1/2)^(3/4)*(b^3*x^3 - 4*b^2*x)*(b^(-2))^(3/4) + 16*sqrt(1/2)*(-b*x^2 + 2)^(3/4)*b*sqrt(b^(-2)) + sqrt(2)*(1/2)^(1/4)*(b^2*x^3 + 4*b*x)*sqrt(-b*x^2 + 2)*(b^(-2))^(1/4))*sqrt((2*sqrt(2)*(1/2)^(3/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x - sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 - 2*sqrt(-b*x^2 + 2))/(b*x^2 - 4)))/(b^2*x^4 + 8*b*x^2 - 16)) + 1/16*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*log(-1/2*(2*sqrt(2)*(1/2)^(3/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x + sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 + 2*sqrt(-b*x^2 + 2))/(b*x^2 - 4)) - 1/16*sqrt(2)*(1/2)^(1/4)*(b^(-2))^(1/4)*log(1/2*(2*sqrt(2)*(1/2)^(3/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-2))^(3/4)*x - sqrt(1/2)*b^2*sqrt(b^(-2))*x^2 - 2*sqrt(-b*x^2 + 2))/(b*x^2 - 4))","B",0
308,1,286,0,24.629511," ","integrate(1/(3*x^2+a)^(1/4)/(3*x^2+2*a),x, algorithm=""fricas"")","\left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(6 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} a^{3} \left(-\frac{1}{a^{3}}\right)^{\frac{3}{4}} + \left(\frac{1}{36}\right)^{\frac{1}{4}} \sqrt{3 \, x^{2} + a} a \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}}\right)} \sqrt{-a \sqrt{-\frac{1}{a^{3}}}} - \left(\frac{1}{36}\right)^{\frac{1}{4}} {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}} a \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}}\right)}}{x}\right) - \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} \log\left(\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{3 \, x^{2} + a} a^{2} x \left(-\frac{1}{a^{3}}\right)^{\frac{3}{4}} + {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}} a^{2} \sqrt{-\frac{1}{a^{3}}} - 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a x \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} + {\left(3 \, x^{2} + a\right)}^{\frac{3}{4}}}{3 \, x^{2} + 2 \, a}\right) + \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} \log\left(-\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{3 \, x^{2} + a} a^{2} x \left(-\frac{1}{a^{3}}\right)^{\frac{3}{4}} - {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}} a^{2} \sqrt{-\frac{1}{a^{3}}} - 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a x \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} - {\left(3 \, x^{2} + a\right)}^{\frac{3}{4}}}{3 \, x^{2} + 2 \, a}\right)"," ",0,"(1/36)^(1/4)*(-1/a^3)^(1/4)*arctan(2*(sqrt(1/2)*(6*(1/36)^(3/4)*a^3*(-1/a^3)^(3/4) + (1/36)^(1/4)*sqrt(3*x^2 + a)*a*(-1/a^3)^(1/4))*sqrt(-a*sqrt(-1/a^3)) - (1/36)^(1/4)*(3*x^2 + a)^(1/4)*a*(-1/a^3)^(1/4))/x) - 1/4*(1/36)^(1/4)*(-1/a^3)^(1/4)*log((18*(1/36)^(3/4)*sqrt(3*x^2 + a)*a^2*x*(-1/a^3)^(3/4) + (3*x^2 + a)^(1/4)*a^2*sqrt(-1/a^3) - 3*(1/36)^(1/4)*a*x*(-1/a^3)^(1/4) + (3*x^2 + a)^(3/4))/(3*x^2 + 2*a)) + 1/4*(1/36)^(1/4)*(-1/a^3)^(1/4)*log(-(18*(1/36)^(3/4)*sqrt(3*x^2 + a)*a^2*x*(-1/a^3)^(3/4) - (3*x^2 + a)^(1/4)*a^2*sqrt(-1/a^3) - 3*(1/36)^(1/4)*a*x*(-1/a^3)^(1/4) - (3*x^2 + a)^(3/4))/(3*x^2 + 2*a))","B",0
309,1,286,0,23.721656," ","integrate(1/(-3*x^2+a)^(1/4)/(-3*x^2+2*a),x, algorithm=""fricas"")","\left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(6 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} a^{3} \left(-\frac{1}{a^{3}}\right)^{\frac{3}{4}} - \left(\frac{1}{36}\right)^{\frac{1}{4}} \sqrt{-3 \, x^{2} + a} a \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}}\right)} \sqrt{a \sqrt{-\frac{1}{a^{3}}}} - \left(\frac{1}{36}\right)^{\frac{1}{4}} {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}} a \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}}\right)}}{x}\right) + \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} \log\left(-\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{-3 \, x^{2} + a} a^{2} x \left(-\frac{1}{a^{3}}\right)^{\frac{3}{4}} + {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}} a^{2} \sqrt{-\frac{1}{a^{3}}} + 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a x \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} - {\left(-3 \, x^{2} + a\right)}^{\frac{3}{4}}}{3 \, x^{2} - 2 \, a}\right) - \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} \log\left(\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{-3 \, x^{2} + a} a^{2} x \left(-\frac{1}{a^{3}}\right)^{\frac{3}{4}} - {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}} a^{2} \sqrt{-\frac{1}{a^{3}}} + 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a x \left(-\frac{1}{a^{3}}\right)^{\frac{1}{4}} + {\left(-3 \, x^{2} + a\right)}^{\frac{3}{4}}}{3 \, x^{2} - 2 \, a}\right)"," ",0,"(1/36)^(1/4)*(-1/a^3)^(1/4)*arctan(2*(sqrt(1/2)*(6*(1/36)^(3/4)*a^3*(-1/a^3)^(3/4) - (1/36)^(1/4)*sqrt(-3*x^2 + a)*a*(-1/a^3)^(1/4))*sqrt(a*sqrt(-1/a^3)) - (1/36)^(1/4)*(-3*x^2 + a)^(1/4)*a*(-1/a^3)^(1/4))/x) + 1/4*(1/36)^(1/4)*(-1/a^3)^(1/4)*log(-(18*(1/36)^(3/4)*sqrt(-3*x^2 + a)*a^2*x*(-1/a^3)^(3/4) + (-3*x^2 + a)^(1/4)*a^2*sqrt(-1/a^3) + 3*(1/36)^(1/4)*a*x*(-1/a^3)^(1/4) - (-3*x^2 + a)^(3/4))/(3*x^2 - 2*a)) - 1/4*(1/36)^(1/4)*(-1/a^3)^(1/4)*log((18*(1/36)^(3/4)*sqrt(-3*x^2 + a)*a^2*x*(-1/a^3)^(3/4) - (-3*x^2 + a)^(1/4)*a^2*sqrt(-1/a^3) + 3*(1/36)^(1/4)*a*x*(-1/a^3)^(1/4) + (-3*x^2 + a)^(3/4))/(3*x^2 - 2*a))","B",0
310,1,337,0,137.832054," ","integrate(1/(b*x^2+a)^(1/4)/(b*x^2+2*a),x, algorithm=""fricas"")","\left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a^{3} b \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} \sqrt{b x^{2} + a} a \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)} \sqrt{-a b \sqrt{-\frac{1}{a^{3} b^{2}}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} {\left(b x^{2} + a\right)}^{\frac{1}{4}} a \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)}}{x}\right) - \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{b x^{2} + a} a^{2} b^{2} x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} + {\left(b x^{2} + a\right)}^{\frac{1}{4}} a^{2} b \sqrt{-\frac{1}{a^{3} b^{2}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} + {\left(b x^{2} + a\right)}^{\frac{3}{4}}}{b x^{2} + 2 \, a}\right) + \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(-\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{b x^{2} + a} a^{2} b^{2} x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} - {\left(b x^{2} + a\right)}^{\frac{1}{4}} a^{2} b \sqrt{-\frac{1}{a^{3} b^{2}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} - {\left(b x^{2} + a\right)}^{\frac{3}{4}}}{b x^{2} + 2 \, a}\right)"," ",0,"(1/4)^(1/4)*(-1/(a^3*b^2))^(1/4)*arctan(2*(sqrt(1/2)*(2*(1/4)^(3/4)*a^3*b*(-1/(a^3*b^2))^(3/4) + (1/4)^(1/4)*sqrt(b*x^2 + a)*a*(-1/(a^3*b^2))^(1/4))*sqrt(-a*b*sqrt(-1/(a^3*b^2))) - (1/4)^(1/4)*(b*x^2 + a)^(1/4)*a*(-1/(a^3*b^2))^(1/4))/x) - 1/4*(1/4)^(1/4)*(-1/(a^3*b^2))^(1/4)*log((2*(1/4)^(3/4)*sqrt(b*x^2 + a)*a^2*b^2*x*(-1/(a^3*b^2))^(3/4) + (b*x^2 + a)^(1/4)*a^2*b*sqrt(-1/(a^3*b^2)) - (1/4)^(1/4)*a*b*x*(-1/(a^3*b^2))^(1/4) + (b*x^2 + a)^(3/4))/(b*x^2 + 2*a)) + 1/4*(1/4)^(1/4)*(-1/(a^3*b^2))^(1/4)*log(-(2*(1/4)^(3/4)*sqrt(b*x^2 + a)*a^2*b^2*x*(-1/(a^3*b^2))^(3/4) - (b*x^2 + a)^(1/4)*a^2*b*sqrt(-1/(a^3*b^2)) - (1/4)^(1/4)*a*b*x*(-1/(a^3*b^2))^(1/4) - (b*x^2 + a)^(3/4))/(b*x^2 + 2*a))","B",0
311,1,343,0,129.691428," ","integrate(1/(-b*x^2+a)^(1/4)/(-b*x^2+2*a),x, algorithm=""fricas"")","\left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a^{3} b \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} \sqrt{-b x^{2} + a} a \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)} \sqrt{a b \sqrt{-\frac{1}{a^{3} b^{2}}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} {\left(-b x^{2} + a\right)}^{\frac{1}{4}} a \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)}}{x}\right) + \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(-\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{-b x^{2} + a} a^{2} b^{2} x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} + {\left(-b x^{2} + a\right)}^{\frac{1}{4}} a^{2} b \sqrt{-\frac{1}{a^{3} b^{2}}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} - {\left(-b x^{2} + a\right)}^{\frac{3}{4}}}{b x^{2} - 2 \, a}\right) - \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{-b x^{2} + a} a^{2} b^{2} x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} - {\left(-b x^{2} + a\right)}^{\frac{1}{4}} a^{2} b \sqrt{-\frac{1}{a^{3} b^{2}}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(-\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} + {\left(-b x^{2} + a\right)}^{\frac{3}{4}}}{b x^{2} - 2 \, a}\right)"," ",0,"(1/4)^(1/4)*(-1/(a^3*b^2))^(1/4)*arctan(2*(sqrt(1/2)*(2*(1/4)^(3/4)*a^3*b*(-1/(a^3*b^2))^(3/4) - (1/4)^(1/4)*sqrt(-b*x^2 + a)*a*(-1/(a^3*b^2))^(1/4))*sqrt(a*b*sqrt(-1/(a^3*b^2))) - (1/4)^(1/4)*(-b*x^2 + a)^(1/4)*a*(-1/(a^3*b^2))^(1/4))/x) + 1/4*(1/4)^(1/4)*(-1/(a^3*b^2))^(1/4)*log(-(2*(1/4)^(3/4)*sqrt(-b*x^2 + a)*a^2*b^2*x*(-1/(a^3*b^2))^(3/4) + (-b*x^2 + a)^(1/4)*a^2*b*sqrt(-1/(a^3*b^2)) + (1/4)^(1/4)*a*b*x*(-1/(a^3*b^2))^(1/4) - (-b*x^2 + a)^(3/4))/(b*x^2 - 2*a)) - 1/4*(1/4)^(1/4)*(-1/(a^3*b^2))^(1/4)*log((2*(1/4)^(3/4)*sqrt(-b*x^2 + a)*a^2*b^2*x*(-1/(a^3*b^2))^(3/4) - (-b*x^2 + a)^(1/4)*a^2*b*sqrt(-1/(a^3*b^2)) + (1/4)^(1/4)*a*b*x*(-1/(a^3*b^2))^(1/4) + (-b*x^2 + a)^(3/4))/(b*x^2 - 2*a))","B",0
312,1,104,0,9.421192," ","integrate(1/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{6} \arctan\left(\frac{\sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, x}\right) + \frac{1}{24} \, \sqrt{6} \log\left(-\frac{9 \, x^{4} - 6 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} x^{3} + 12 \, \sqrt{3 \, x^{2} - 1} x^{2} - 4 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} x + 12 \, x^{2} - 4}{9 \, x^{4} - 12 \, x^{2} + 4}\right)"," ",0,"1/12*sqrt(6)*arctan(1/3*sqrt(6)*(3*x^2 - 1)^(1/4)/x) + 1/24*sqrt(6)*log(-(9*x^4 - 6*sqrt(6)*(3*x^2 - 1)^(1/4)*x^3 + 12*sqrt(3*x^2 - 1)*x^2 - 4*sqrt(6)*(3*x^2 - 1)^(3/4)*x + 12*x^2 - 4)/(9*x^4 - 12*x^2 + 4))","B",0
313,1,243,0,9.292725," ","integrate(1/(-3*x^2-2)/(-3*x^2-1)^(1/4),x, algorithm=""fricas"")","-\frac{1}{24} \, \sqrt{6} \log\left(\frac{\sqrt{6} \sqrt{-3 \, x^{2} - 1} x - \sqrt{6} x + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, {\left(3 \, x^{2} + 2\right)}}\right) + \frac{1}{24} \, \sqrt{6} \log\left(-\frac{\sqrt{6} \sqrt{-3 \, x^{2} - 1} x - \sqrt{6} x - 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, {\left(3 \, x^{2} + 2\right)}}\right) + \frac{1}{24} i \, \sqrt{6} \log\left(\frac{i \, \sqrt{6} \sqrt{-3 \, x^{2} - 1} x + i \, \sqrt{6} x + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, {\left(3 \, x^{2} + 2\right)}}\right) - \frac{1}{24} i \, \sqrt{6} \log\left(\frac{-i \, \sqrt{6} \sqrt{-3 \, x^{2} - 1} x - i \, \sqrt{6} x + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, {\left(3 \, x^{2} + 2\right)}}\right)"," ",0,"-1/24*sqrt(6)*log(1/3*(sqrt(6)*sqrt(-3*x^2 - 1)*x - sqrt(6)*x + 2*(-3*x^2 - 1)^(3/4) - 2*(-3*x^2 - 1)^(1/4))/(3*x^2 + 2)) + 1/24*sqrt(6)*log(-1/3*(sqrt(6)*sqrt(-3*x^2 - 1)*x - sqrt(6)*x - 2*(-3*x^2 - 1)^(3/4) + 2*(-3*x^2 - 1)^(1/4))/(3*x^2 + 2)) + 1/24*I*sqrt(6)*log(1/3*(I*sqrt(6)*sqrt(-3*x^2 - 1)*x + I*sqrt(6)*x + 2*(-3*x^2 - 1)^(3/4) + 2*(-3*x^2 - 1)^(1/4))/(3*x^2 + 2)) - 1/24*I*sqrt(6)*log(1/3*(-I*sqrt(6)*sqrt(-3*x^2 - 1)*x - I*sqrt(6)*x + 2*(-3*x^2 - 1)^(3/4) + 2*(-3*x^2 - 1)^(1/4))/(3*x^2 + 2))","C",0
314,1,274,0,29.664430," ","integrate(1/(b*x^2-2)/(b*x^2-1)^(1/4),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}}}{\sqrt{b} x}\right) + \sqrt{2} \sqrt{b} \log\left(-\frac{b^{2} x^{4} - 2 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}} b^{\frac{3}{2}} x^{3} + 4 \, \sqrt{b x^{2} - 1} b x^{2} + 4 \, b x^{2} - 4 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{3}{4}} \sqrt{b} x - 4}{b^{2} x^{4} - 4 \, b x^{2} + 4}\right)}{8 \, b}, \frac{2 \, \sqrt{2} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}} \sqrt{-b}}{b x}\right) - \sqrt{2} \sqrt{-b} \log\left(-\frac{b^{2} x^{4} + 2 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}} \sqrt{-b} b x^{3} - 4 \, \sqrt{b x^{2} - 1} b x^{2} + 4 \, b x^{2} - 4 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{3}{4}} \sqrt{-b} x - 4}{b^{2} x^{4} - 4 \, b x^{2} + 4}\right)}{8 \, b}\right]"," ",0,"[1/8*(2*sqrt(2)*sqrt(b)*arctan(sqrt(2)*(b*x^2 - 1)^(1/4)/(sqrt(b)*x)) + sqrt(2)*sqrt(b)*log(-(b^2*x^4 - 2*sqrt(2)*(b*x^2 - 1)^(1/4)*b^(3/2)*x^3 + 4*sqrt(b*x^2 - 1)*b*x^2 + 4*b*x^2 - 4*sqrt(2)*(b*x^2 - 1)^(3/4)*sqrt(b)*x - 4)/(b^2*x^4 - 4*b*x^2 + 4)))/b, 1/8*(2*sqrt(2)*sqrt(-b)*arctan(sqrt(2)*(b*x^2 - 1)^(1/4)*sqrt(-b)/(b*x)) - sqrt(2)*sqrt(-b)*log(-(b^2*x^4 + 2*sqrt(2)*(b*x^2 - 1)^(1/4)*sqrt(-b)*b*x^3 - 4*sqrt(b*x^2 - 1)*b*x^2 + 4*b*x^2 - 4*sqrt(2)*(b*x^2 - 1)^(3/4)*sqrt(-b)*x - 4)/(b^2*x^4 - 4*b*x^2 + 4)))/b]","B",0
315,1,273,0,29.243520," ","integrate(1/(-b*x^2-2)/(-b*x^2-1)^(1/4),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(-b x^{2} - 1\right)}^{\frac{1}{4}}}{\sqrt{b} x}\right) + \sqrt{2} \sqrt{b} \log\left(-\frac{b^{2} x^{4} + 4 \, \sqrt{-b x^{2} - 1} b x^{2} - 4 \, b x^{2} - 2 \, \sqrt{2} {\left({\left(-b x^{2} - 1\right)}^{\frac{1}{4}} b x^{3} + 2 \, {\left(-b x^{2} - 1\right)}^{\frac{3}{4}} x\right)} \sqrt{b} - 4}{b^{2} x^{4} + 4 \, b x^{2} + 4}\right)}{8 \, b}, \frac{2 \, \sqrt{2} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(-b x^{2} - 1\right)}^{\frac{1}{4}} \sqrt{-b}}{b x}\right) - \sqrt{2} \sqrt{-b} \log\left(-\frac{b^{2} x^{4} - 4 \, \sqrt{-b x^{2} - 1} b x^{2} - 4 \, b x^{2} + 2 \, \sqrt{2} {\left({\left(-b x^{2} - 1\right)}^{\frac{1}{4}} b x^{3} - 2 \, {\left(-b x^{2} - 1\right)}^{\frac{3}{4}} x\right)} \sqrt{-b} - 4}{b^{2} x^{4} + 4 \, b x^{2} + 4}\right)}{8 \, b}\right]"," ",0,"[1/8*(2*sqrt(2)*sqrt(b)*arctan(sqrt(2)*(-b*x^2 - 1)^(1/4)/(sqrt(b)*x)) + sqrt(2)*sqrt(b)*log(-(b^2*x^4 + 4*sqrt(-b*x^2 - 1)*b*x^2 - 4*b*x^2 - 2*sqrt(2)*((-b*x^2 - 1)^(1/4)*b*x^3 + 2*(-b*x^2 - 1)^(3/4)*x)*sqrt(b) - 4)/(b^2*x^4 + 4*b*x^2 + 4)))/b, 1/8*(2*sqrt(2)*sqrt(-b)*arctan(sqrt(2)*(-b*x^2 - 1)^(1/4)*sqrt(-b)/(b*x)) - sqrt(2)*sqrt(-b)*log(-(b^2*x^4 - 4*sqrt(-b*x^2 - 1)*b*x^2 - 4*b*x^2 + 2*sqrt(2)*((-b*x^2 - 1)^(1/4)*b*x^3 - 2*(-b*x^2 - 1)^(3/4)*x)*sqrt(-b) - 4)/(b^2*x^4 + 4*b*x^2 + 4)))/b]","B",0
316,1,276,0,20.454582," ","integrate(1/(3*x^2-2*a)/(3*x^2-a)^(1/4),x, algorithm=""fricas"")","-\left(\frac{1}{36}\right)^{\frac{1}{4}} \frac{1}{a^{3}}^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(6 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} a^{3} \frac{1}{a^{3}}^{\frac{3}{4}} + \left(\frac{1}{36}\right)^{\frac{1}{4}} \sqrt{3 \, x^{2} - a} a \frac{1}{a^{3}}^{\frac{1}{4}}\right)} \sqrt{a \sqrt{\frac{1}{a^{3}}}} - \left(\frac{1}{36}\right)^{\frac{1}{4}} {\left(3 \, x^{2} - a\right)}^{\frac{1}{4}} a \frac{1}{a^{3}}^{\frac{1}{4}}\right)}}{x}\right) - \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{3 \, x^{2} - a} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}} x + {\left(3 \, x^{2} - a\right)}^{\frac{1}{4}} a^{2} \sqrt{\frac{1}{a^{3}}} + 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a \frac{1}{a^{3}}^{\frac{1}{4}} x + {\left(3 \, x^{2} - a\right)}^{\frac{3}{4}}}{3 \, x^{2} - 2 \, a}\right) + \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(-\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{3 \, x^{2} - a} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}} x - {\left(3 \, x^{2} - a\right)}^{\frac{1}{4}} a^{2} \sqrt{\frac{1}{a^{3}}} + 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a \frac{1}{a^{3}}^{\frac{1}{4}} x - {\left(3 \, x^{2} - a\right)}^{\frac{3}{4}}}{3 \, x^{2} - 2 \, a}\right)"," ",0,"-(1/36)^(1/4)*(a^(-3))^(1/4)*arctan(2*(sqrt(1/2)*(6*(1/36)^(3/4)*a^3*(a^(-3))^(3/4) + (1/36)^(1/4)*sqrt(3*x^2 - a)*a*(a^(-3))^(1/4))*sqrt(a*sqrt(a^(-3))) - (1/36)^(1/4)*(3*x^2 - a)^(1/4)*a*(a^(-3))^(1/4))/x) - 1/4*(1/36)^(1/4)*(a^(-3))^(1/4)*log((18*(1/36)^(3/4)*sqrt(3*x^2 - a)*a^2*(a^(-3))^(3/4)*x + (3*x^2 - a)^(1/4)*a^2*sqrt(a^(-3)) + 3*(1/36)^(1/4)*a*(a^(-3))^(1/4)*x + (3*x^2 - a)^(3/4))/(3*x^2 - 2*a)) + 1/4*(1/36)^(1/4)*(a^(-3))^(1/4)*log(-(18*(1/36)^(3/4)*sqrt(3*x^2 - a)*a^2*(a^(-3))^(3/4)*x - (3*x^2 - a)^(1/4)*a^2*sqrt(a^(-3)) + 3*(1/36)^(1/4)*a*(a^(-3))^(1/4)*x - (3*x^2 - a)^(3/4))/(3*x^2 - 2*a))","B",0
317,1,278,0,20.761661," ","integrate(1/(-3*x^2-2*a)/(-3*x^2-a)^(1/4),x, algorithm=""fricas"")","-\left(\frac{1}{36}\right)^{\frac{1}{4}} \frac{1}{a^{3}}^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(6 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} a^{3} \frac{1}{a^{3}}^{\frac{3}{4}} - \left(\frac{1}{36}\right)^{\frac{1}{4}} \sqrt{-3 \, x^{2} - a} a \frac{1}{a^{3}}^{\frac{1}{4}}\right)} \sqrt{-a \sqrt{\frac{1}{a^{3}}}} - \left(\frac{1}{36}\right)^{\frac{1}{4}} {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}} a \frac{1}{a^{3}}^{\frac{1}{4}}\right)}}{x}\right) + \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(-\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{-3 \, x^{2} - a} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}} x + {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}} a^{2} \sqrt{\frac{1}{a^{3}}} - 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a \frac{1}{a^{3}}^{\frac{1}{4}} x - {\left(-3 \, x^{2} - a\right)}^{\frac{3}{4}}}{3 \, x^{2} + 2 \, a}\right) - \frac{1}{4} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(\frac{18 \, \left(\frac{1}{36}\right)^{\frac{3}{4}} \sqrt{-3 \, x^{2} - a} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}} x - {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}} a^{2} \sqrt{\frac{1}{a^{3}}} - 3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} a \frac{1}{a^{3}}^{\frac{1}{4}} x + {\left(-3 \, x^{2} - a\right)}^{\frac{3}{4}}}{3 \, x^{2} + 2 \, a}\right)"," ",0,"-(1/36)^(1/4)*(a^(-3))^(1/4)*arctan(2*(sqrt(1/2)*(6*(1/36)^(3/4)*a^3*(a^(-3))^(3/4) - (1/36)^(1/4)*sqrt(-3*x^2 - a)*a*(a^(-3))^(1/4))*sqrt(-a*sqrt(a^(-3))) - (1/36)^(1/4)*(-3*x^2 - a)^(1/4)*a*(a^(-3))^(1/4))/x) + 1/4*(1/36)^(1/4)*(a^(-3))^(1/4)*log(-(18*(1/36)^(3/4)*sqrt(-3*x^2 - a)*a^2*(a^(-3))^(3/4)*x + (-3*x^2 - a)^(1/4)*a^2*sqrt(a^(-3)) - 3*(1/36)^(1/4)*a*(a^(-3))^(1/4)*x - (-3*x^2 - a)^(3/4))/(3*x^2 + 2*a)) - 1/4*(1/36)^(1/4)*(a^(-3))^(1/4)*log((18*(1/36)^(3/4)*sqrt(-3*x^2 - a)*a^2*(a^(-3))^(3/4)*x - (-3*x^2 - a)^(1/4)*a^2*sqrt(a^(-3)) - 3*(1/36)^(1/4)*a*(a^(-3))^(1/4)*x + (-3*x^2 - a)^(3/4))/(3*x^2 + 2*a))","B",0
318,1,338,0,111.056453," ","integrate(1/(b*x^2-2*a)/(b*x^2-a)^(1/4),x, algorithm=""fricas"")","-\left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a^{3} b \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} \sqrt{b x^{2} - a} a \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)} \sqrt{a b \sqrt{\frac{1}{a^{3} b^{2}}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} {\left(b x^{2} - a\right)}^{\frac{1}{4}} a \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)}}{x}\right) - \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{b x^{2} - a} a^{2} b^{2} x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} + {\left(b x^{2} - a\right)}^{\frac{1}{4}} a^{2} b \sqrt{\frac{1}{a^{3} b^{2}}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} + {\left(b x^{2} - a\right)}^{\frac{3}{4}}}{b x^{2} - 2 \, a}\right) + \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(-\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{b x^{2} - a} a^{2} b^{2} x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} - {\left(b x^{2} - a\right)}^{\frac{1}{4}} a^{2} b \sqrt{\frac{1}{a^{3} b^{2}}} + \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} - {\left(b x^{2} - a\right)}^{\frac{3}{4}}}{b x^{2} - 2 \, a}\right)"," ",0,"-(1/4)^(1/4)*(1/(a^3*b^2))^(1/4)*arctan(2*(sqrt(1/2)*(2*(1/4)^(3/4)*a^3*b*(1/(a^3*b^2))^(3/4) + (1/4)^(1/4)*sqrt(b*x^2 - a)*a*(1/(a^3*b^2))^(1/4))*sqrt(a*b*sqrt(1/(a^3*b^2))) - (1/4)^(1/4)*(b*x^2 - a)^(1/4)*a*(1/(a^3*b^2))^(1/4))/x) - 1/4*(1/4)^(1/4)*(1/(a^3*b^2))^(1/4)*log((2*(1/4)^(3/4)*sqrt(b*x^2 - a)*a^2*b^2*x*(1/(a^3*b^2))^(3/4) + (b*x^2 - a)^(1/4)*a^2*b*sqrt(1/(a^3*b^2)) + (1/4)^(1/4)*a*b*x*(1/(a^3*b^2))^(1/4) + (b*x^2 - a)^(3/4))/(b*x^2 - 2*a)) + 1/4*(1/4)^(1/4)*(1/(a^3*b^2))^(1/4)*log(-(2*(1/4)^(3/4)*sqrt(b*x^2 - a)*a^2*b^2*x*(1/(a^3*b^2))^(3/4) - (b*x^2 - a)^(1/4)*a^2*b*sqrt(1/(a^3*b^2)) + (1/4)^(1/4)*a*b*x*(1/(a^3*b^2))^(1/4) - (b*x^2 - a)^(3/4))/(b*x^2 - 2*a))","B",0
319,1,350,0,110.161472," ","integrate(1/(-b*x^2-2*a)/(-b*x^2-a)^(1/4),x, algorithm=""fricas"")","-\left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, {\left(\sqrt{\frac{1}{2}} {\left(2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} a^{3} b \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} \sqrt{-b x^{2} - a} a \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)} \sqrt{-a b \sqrt{\frac{1}{a^{3} b^{2}}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} {\left(-b x^{2} - a\right)}^{\frac{1}{4}} a \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}}\right)}}{x}\right) + \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(-\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{-b x^{2} - a} a^{2} b^{2} x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} + {\left(-b x^{2} - a\right)}^{\frac{1}{4}} a^{2} b \sqrt{\frac{1}{a^{3} b^{2}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} - {\left(-b x^{2} - a\right)}^{\frac{3}{4}}}{b x^{2} + 2 \, a}\right) - \frac{1}{4} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} \log\left(\frac{2 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} \sqrt{-b x^{2} - a} a^{2} b^{2} x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{3}{4}} - {\left(-b x^{2} - a\right)}^{\frac{1}{4}} a^{2} b \sqrt{\frac{1}{a^{3} b^{2}}} - \left(\frac{1}{4}\right)^{\frac{1}{4}} a b x \left(\frac{1}{a^{3} b^{2}}\right)^{\frac{1}{4}} + {\left(-b x^{2} - a\right)}^{\frac{3}{4}}}{b x^{2} + 2 \, a}\right)"," ",0,"-(1/4)^(1/4)*(1/(a^3*b^2))^(1/4)*arctan(2*(sqrt(1/2)*(2*(1/4)^(3/4)*a^3*b*(1/(a^3*b^2))^(3/4) - (1/4)^(1/4)*sqrt(-b*x^2 - a)*a*(1/(a^3*b^2))^(1/4))*sqrt(-a*b*sqrt(1/(a^3*b^2))) - (1/4)^(1/4)*(-b*x^2 - a)^(1/4)*a*(1/(a^3*b^2))^(1/4))/x) + 1/4*(1/4)^(1/4)*(1/(a^3*b^2))^(1/4)*log(-(2*(1/4)^(3/4)*sqrt(-b*x^2 - a)*a^2*b^2*x*(1/(a^3*b^2))^(3/4) + (-b*x^2 - a)^(1/4)*a^2*b*sqrt(1/(a^3*b^2)) - (1/4)^(1/4)*a*b*x*(1/(a^3*b^2))^(1/4) - (-b*x^2 - a)^(3/4))/(b*x^2 + 2*a)) - 1/4*(1/4)^(1/4)*(1/(a^3*b^2))^(1/4)*log((2*(1/4)^(3/4)*sqrt(-b*x^2 - a)*a^2*b^2*x*(1/(a^3*b^2))^(3/4) - (-b*x^2 - a)^(1/4)*a^2*b*sqrt(1/(a^3*b^2)) - (1/4)^(1/4)*a*b*x*(1/(a^3*b^2))^(1/4) + (-b*x^2 - a)^(3/4))/(b*x^2 + 2*a))","B",0
320,1,91,0,8.366078," ","integrate(1/(-x^2+2)/(x^2-1)^(1/4),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x^{2} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{8} \, \sqrt{2} \log\left(-\frac{x^{4} + 2 \, \sqrt{2} {\left(x^{2} - 1\right)}^{\frac{1}{4}} x^{3} + 4 \, \sqrt{x^{2} - 1} x^{2} + 4 \, \sqrt{2} {\left(x^{2} - 1\right)}^{\frac{3}{4}} x + 4 \, x^{2} - 4}{x^{4} - 4 \, x^{2} + 4}\right)"," ",0,"-1/4*sqrt(2)*arctan(sqrt(2)*(x^2 - 1)^(1/4)/x) + 1/8*sqrt(2)*log(-(x^4 + 2*sqrt(2)*(x^2 - 1)^(1/4)*x^3 + 4*sqrt(x^2 - 1)*x^2 + 4*sqrt(2)*(x^2 - 1)^(3/4)*x + 4*x^2 - 4)/(x^4 - 4*x^2 + 4))","B",0
321,-1,0,0,0.000000," ","integrate((b*x^2+a)^(7/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate((b*x^2+a)^(5/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((b*x^2+a)^(3/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((b*x^2+a)^(1/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(7/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(9/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(11/4)/(d*x^2+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate((b*x^2+a)^(7/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate((b*x^2+a)^(5/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate((b*x^2+a)^(3/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate((b*x^2+a)^(1/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(7/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(9/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^(11/4)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,0,0,0,1.487275," ","integrate((b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
342,0,0,0,1.547934," ","integrate((b*x^2+a)^p*(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3)*(b*x^2 + a)^p, x)","F",0
343,0,0,0,1.543839," ","integrate((b*x^2+a)^p*(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*(b*x^2 + a)^p, x)","F",0
344,0,0,0,1.421713," ","integrate((b*x^2+a)^p*(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x^{2} + c\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((d*x^2 + c)*(b*x^2 + a)^p, x)","F",0
345,0,0,0,1.139668," ","integrate((b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((b*x^2 + a)^p, x)","F",0
346,0,0,0,1.294516," ","integrate((b*x^2+a)^p/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{d x^{2} + c}, x\right)"," ",0,"integral((b*x^2 + a)^p/(d*x^2 + c), x)","F",0
347,0,0,0,1.328131," ","integrate((b*x^2+a)^p/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
348,0,0,0,1.383633," ","integrate((b*x^2+a)^p/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
349,1,91,0,0.997058," ","integrate((b*x^2+a)^(-1-b*c/(-2*a*d+2*b*c))*(d*x^2+c)^(-1+a*d/(-2*a*d+2*b*c)),x, algorithm=""fricas"")","\frac{b d x^{5} + {\left(b c + a d\right)} x^{3} + a c x}{{\left(b x^{2} + a\right)}^{\frac{3 \, b c - 2 \, a d}{2 \, {\left(b c - a d\right)}}} {\left(d x^{2} + c\right)}^{\frac{2 \, b c - 3 \, a d}{2 \, {\left(b c - a d\right)}}} a c}"," ",0,"(b*d*x^5 + (b*c + a*d)*x^3 + a*c*x)/((b*x^2 + a)^(1/2*(3*b*c - 2*a*d)/(b*c - a*d))*(d*x^2 + c)^(1/2*(2*b*c - 3*a*d)/(b*c - a*d))*a*c)","A",0
