1,1,96,0,0.474570," ","integrate((b*x^3+a)*(d*x^3+c)^4,x, algorithm=""maxima"")","\frac{1}{16} \, b d^{4} x^{16} + \frac{1}{13} \, {\left(4 \, b c d^{3} + a d^{4}\right)} x^{13} + \frac{1}{5} \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} x^{10} + \frac{2}{7} \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} x^{7} + a c^{4} x + \frac{1}{4} \, {\left(b c^{4} + 4 \, a c^{3} d\right)} x^{4}"," ",0,"1/16*b*d^4*x^16 + 1/13*(4*b*c*d^3 + a*d^4)*x^13 + 1/5*(3*b*c^2*d^2 + 2*a*c*d^3)*x^10 + 2/7*(2*b*c^3*d + 3*a*c^2*d^2)*x^7 + a*c^4*x + 1/4*(b*c^4 + 4*a*c^3*d)*x^4","A",0
2,1,70,0,0.561654," ","integrate((b*x^3+a)*(d*x^3+c)^3,x, algorithm=""maxima"")","\frac{1}{13} \, b d^{3} x^{13} + \frac{1}{10} \, {\left(3 \, b c d^{2} + a d^{3}\right)} x^{10} + \frac{3}{7} \, {\left(b c^{2} d + a c d^{2}\right)} x^{7} + a c^{3} x + \frac{1}{4} \, {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{4}"," ",0,"1/13*b*d^3*x^13 + 1/10*(3*b*c*d^2 + a*d^3)*x^10 + 3/7*(b*c^2*d + a*c*d^2)*x^7 + a*c^3*x + 1/4*(b*c^3 + 3*a*c^2*d)*x^4","A",0
3,1,48,0,0.480712," ","integrate((b*x^3+a)*(d*x^3+c)^2,x, algorithm=""maxima"")","\frac{1}{10} \, b d^{2} x^{10} + \frac{1}{7} \, {\left(2 \, b c d + a d^{2}\right)} x^{7} + \frac{1}{4} \, {\left(b c^{2} + 2 \, a c d\right)} x^{4} + a c^{2} x"," ",0,"1/10*b*d^2*x^10 + 1/7*(2*b*c*d + a*d^2)*x^7 + 1/4*(b*c^2 + 2*a*c*d)*x^4 + a*c^2*x","A",0
4,1,24,0,0.535626," ","integrate((b*x^3+a)*(d*x^3+c),x, algorithm=""maxima"")","\frac{1}{7} \, b d x^{7} + \frac{1}{4} \, {\left(b c + a d\right)} x^{4} + a c x"," ",0,"1/7*b*d*x^7 + 1/4*(b*c + a*d)*x^4 + a*c*x","A",0
5,1,128,0,1.276565," ","integrate((b*x^3+a)/(d*x^3+c),x, algorithm=""maxima"")","\frac{b x}{d} - \frac{\sqrt{3} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left(b c - a d\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} - \frac{{\left(b c - a d\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \, d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"b*x/d - 1/3*sqrt(3)*(b*c - a*d)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(d^2*(c/d)^(2/3)) + 1/6*(b*c - a*d)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(d^2*(c/d)^(2/3)) - 1/3*(b*c - a*d)*log(x + (c/d)^(1/3))/(d^2*(c/d)^(2/3))","A",0
6,1,158,0,1.157079," ","integrate((b*x^3+a)/(d*x^3+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b c - a d\right)} x}{3 \, {\left(c d^{2} x^{3} + c^{2} d\right)}} + \frac{\sqrt{3} {\left(b c + 2 \, a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{9 \, c d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} - \frac{{\left(b c + 2 \, a d\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{18 \, c d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left(b c + 2 \, a d\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \, c d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"-1/3*(b*c - a*d)*x/(c*d^2*x^3 + c^2*d) + 1/9*sqrt(3)*(b*c + 2*a*d)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(c*d^2*(c/d)^(2/3)) - 1/18*(b*c + 2*a*d)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(c*d^2*(c/d)^(2/3)) + 1/9*(b*c + 2*a*d)*log(x + (c/d)^(1/3))/(c*d^2*(c/d)^(2/3))","A",0
7,1,192,0,1.434408," ","integrate((b*x^3+a)/(d*x^3+c)^3,x, algorithm=""maxima"")","\frac{{\left(b c d + 5 \, a d^{2}\right)} x^{4} - 2 \, {\left(b c^{2} - 4 \, a c d\right)} x}{18 \, {\left(c^{2} d^{3} x^{6} + 2 \, c^{3} d^{2} x^{3} + c^{4} d\right)}} + \frac{\sqrt{3} {\left(b c + 5 \, a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{27 \, c^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} - \frac{{\left(b c + 5 \, a d\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{54 \, c^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left(b c + 5 \, a d\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{27 \, c^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"1/18*((b*c*d + 5*a*d^2)*x^4 - 2*(b*c^2 - 4*a*c*d)*x)/(c^2*d^3*x^6 + 2*c^3*d^2*x^3 + c^4*d) + 1/27*sqrt(3)*(b*c + 5*a*d)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(c^2*d^2*(c/d)^(2/3)) - 1/54*(b*c + 5*a*d)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(c^2*d^2*(c/d)^(2/3)) + 1/27*(b*c + 5*a*d)*log(x + (c/d)^(1/3))/(c^2*d^2*(c/d)^(2/3))","A",0
8,1,124,0,0.546806," ","integrate((b*x^3+a)^2*(d*x^3+c)^3,x, algorithm=""maxima"")","\frac{1}{16} \, b^{2} d^{3} x^{16} + \frac{1}{13} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{13} + \frac{1}{10} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{10} + \frac{1}{7} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{7} + a^{2} c^{3} x + \frac{1}{4} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{4}"," ",0,"1/16*b^2*d^3*x^16 + 1/13*(3*b^2*c*d^2 + 2*a*b*d^3)*x^13 + 1/10*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^10 + 1/7*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^7 + a^2*c^3*x + 1/4*(2*a*b*c^3 + 3*a^2*c^2*d)*x^4","A",0
9,1,82,0,0.707258," ","integrate((b*x^3+a)^2*(d*x^3+c)^2,x, algorithm=""maxima"")","\frac{1}{13} \, b^{2} d^{2} x^{13} + \frac{1}{5} \, {\left(b^{2} c d + a b d^{2}\right)} x^{10} + \frac{1}{7} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{7} + a^{2} c^{2} x + \frac{1}{2} \, {\left(a b c^{2} + a^{2} c d\right)} x^{4}"," ",0,"1/13*b^2*d^2*x^13 + 1/5*(b^2*c*d + a*b*d^2)*x^10 + 1/7*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^7 + a^2*c^2*x + 1/2*(a*b*c^2 + a^2*c*d)*x^4","A",0
10,1,48,0,0.574393," ","integrate((b*x^3+a)^2*(d*x^3+c),x, algorithm=""maxima"")","\frac{1}{10} \, b^{2} d x^{10} + \frac{1}{7} \, {\left(b^{2} c + 2 \, a b d\right)} x^{7} + \frac{1}{4} \, {\left(2 \, a b c + a^{2} d\right)} x^{4} + a^{2} c x"," ",0,"1/10*b^2*d*x^10 + 1/7*(b^2*c + 2*a*b*d)*x^7 + 1/4*(2*a*b*c + a^2*d)*x^4 + a^2*c*x","A",0
11,1,189,0,1.230007," ","integrate((b*x^3+a)^2/(d*x^3+c),x, algorithm=""maxima"")","\frac{b^{2} d x^{4} - 4 \, {\left(b^{2} c - 2 \, a b d\right)} x}{4 \, d^{2}} + \frac{\sqrt{3} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \, d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"1/4*(b^2*d*x^4 - 4*(b^2*c - 2*a*b*d)*x)/d^2 + 1/3*sqrt(3)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(d^3*(c/d)^(2/3)) - 1/6*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(d^3*(c/d)^(2/3)) + 1/3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x + (c/d)^(1/3))/(d^3*(c/d)^(2/3))","A",0
12,1,226,0,1.281955," ","integrate((b*x^3+a)^2/(d*x^3+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{3 \, {\left(c d^{3} x^{3} + c^{2} d^{2}\right)}} + \frac{b^{2} x}{d^{2}} - \frac{2 \, \sqrt{3} {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{9 \, c d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \, c d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}} - \frac{2 \, {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \, c d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(c*d^3*x^3 + c^2*d^2) + b^2*x/d^2 - 2/9*sqrt(3)*(2*b^2*c^2 - a*b*c*d - a^2*d^2)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(c*d^3*(c/d)^(2/3)) + 1/9*(2*b^2*c^2 - a*b*c*d - a^2*d^2)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(c*d^3*(c/d)^(2/3)) - 2/9*(2*b^2*c^2 - a*b*c*d - a^2*d^2)*log(x + (c/d)^(1/3))/(c*d^3*(c/d)^(2/3))","A",0
13,1,267,0,1.321126," ","integrate((b*x^3+a)^2/(d*x^3+c)^3,x, algorithm=""maxima"")","-\frac{{\left(7 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 5 \, a^{2} d^{3}\right)} x^{4} + 4 \, {\left(b^{2} c^{3} + a b c^{2} d - 2 \, a^{2} c d^{2}\right)} x}{18 \, {\left(c^{2} d^{4} x^{6} + 2 \, c^{3} d^{3} x^{3} + c^{4} d^{2}\right)}} + \frac{\sqrt{3} {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{27 \, c^{2} d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{54 \, c^{2} d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{27 \, c^{2} d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"-1/18*((7*b^2*c^2*d - 2*a*b*c*d^2 - 5*a^2*d^3)*x^4 + 4*(b^2*c^3 + a*b*c^2*d - 2*a^2*c*d^2)*x)/(c^2*d^4*x^6 + 2*c^3*d^3*x^3 + c^4*d^2) + 1/27*sqrt(3)*(2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(c^2*d^3*(c/d)^(2/3)) - 1/54*(2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(c^2*d^3*(c/d)^(2/3)) + 1/27*(2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*log(x + (c/d)^(1/3))/(c^2*d^3*(c/d)^(2/3))","A",0
14,1,364,0,1.188768," ","integrate((d*x^3+c)^4/(b*x^3+a),x, algorithm=""maxima"")","\frac{14 \, b^{3} d^{4} x^{10} + 20 \, {\left(4 \, b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{7} + 35 \, {\left(6 \, b^{3} c^{2} d^{2} - 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{4} + 140 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x}{140 \, b^{4}} + \frac{\sqrt{3} {\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)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\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)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\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)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/140*(14*b^3*d^4*x^10 + 20*(4*b^3*c*d^3 - a*b^2*d^4)*x^7 + 35*(6*b^3*c^2*d^2 - 4*a*b^2*c*d^3 + a^2*b*d^4)*x^4 + 140*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*x)/b^4 + 1/3*sqrt(3)*(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)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^5*(a/b)^(2/3)) - 1/6*(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)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^5*(a/b)^(2/3)) + 1/3*(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)*log(x + (a/b)^(1/3))/(b^5*(a/b)^(2/3))","A",0
15,1,273,0,1.318934," ","integrate((d*x^3+c)^3/(b*x^3+a),x, algorithm=""maxima"")","\frac{4 \, b^{2} d^{3} x^{7} + 7 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{4} + 28 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} x}{28 \, b^{3}} + \frac{\sqrt{3} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/28*(4*b^2*d^3*x^7 + 7*(3*b^2*c*d^2 - a*b*d^3)*x^4 + 28*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*x)/b^3 + 1/3*sqrt(3)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^4*(a/b)^(2/3)) - 1/6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^4*(a/b)^(2/3)) + 1/3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(x + (a/b)^(1/3))/(b^4*(a/b)^(2/3))","A",0
16,1,190,0,1.321037," ","integrate((d*x^3+c)^2/(b*x^3+a),x, algorithm=""maxima"")","\frac{b d^{2} x^{4} + 4 \, {\left(2 \, b c d - a d^{2}\right)} x}{4 \, b^{2}} + \frac{\sqrt{3} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/4*(b*d^2*x^4 + 4*(2*b*c*d - a*d^2)*x)/b^2 + 1/3*sqrt(3)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^3*(a/b)^(2/3)) - 1/6*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) + 1/3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3))","A",0
17,1,128,0,1.075385," ","integrate((d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{d x}{b} + \frac{\sqrt{3} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b c - a d\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b c - a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"d*x/b + 1/3*sqrt(3)*(b*c - a*d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^2*(a/b)^(2/3)) - 1/6*(b*c - a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) + 1/3*(b*c - a*d)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))","A",0
18,1,293,0,1.235328," ","integrate(1/(b*x^3+a)/(d*x^3+c),x, algorithm=""maxima"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(b c \left(\frac{c}{d}\right)^{\frac{1}{3}} - a d \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)} \left(\frac{c}{d}\right)^{\frac{1}{3}}} - \frac{\log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a d \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} + \frac{\log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b c \left(\frac{c}{d}\right)^{\frac{2}{3}} - a d \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}} + \frac{\log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, {\left(b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a d \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} - \frac{\log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \, {\left(b c \left(\frac{c}{d}\right)^{\frac{2}{3}} - a d \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}}"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/((b*c*(a/b)^(1/3) - a*d*(a/b)^(1/3))*(a/b)^(1/3)) - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/((b*c*(c/d)^(1/3) - a*d*(c/d)^(1/3))*(c/d)^(1/3)) - 1/6*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*c*(a/b)^(2/3) - a*d*(a/b)^(2/3)) + 1/6*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(b*c*(c/d)^(2/3) - a*d*(c/d)^(2/3)) + 1/3*log(x + (a/b)^(1/3))/(b*c*(a/b)^(2/3) - a*d*(a/b)^(2/3)) - 1/3*log(x + (c/d)^(1/3))/(b*c*(c/d)^(2/3) - a*d*(c/d)^(2/3))","A",0
19,1,489,0,1.298131," ","integrate(1/(b*x^3+a)/(d*x^3+c)^2,x, algorithm=""maxima"")","\frac{\sqrt{3} b \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(b^{2} c^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b c d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} d^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{\sqrt{3} {\left(5 \, b c - 2 \, a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{9 \, {\left(b^{2} c^{3} \left(\frac{c}{d}\right)^{\frac{1}{3}} - 2 \, a b c^{2} d \left(\frac{c}{d}\right)^{\frac{1}{3}} + a^{2} c d^{2} \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)} \left(\frac{c}{d}\right)^{\frac{1}{3}}} - \frac{d x}{3 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{3}\right)}} - \frac{b \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b^{2} c^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b c d \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{2} d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} + \frac{{\left(5 \, b c - 2 \, a d\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{18 \, {\left(b^{2} c^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 2 \, a b c^{2} d \left(\frac{c}{d}\right)^{\frac{2}{3}} + a^{2} c d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}} + \frac{b \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, {\left(b^{2} c^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b c d \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{2} d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} - \frac{{\left(5 \, b c - 2 \, a d\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \, {\left(b^{2} c^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 2 \, a b c^{2} d \left(\frac{c}{d}\right)^{\frac{2}{3}} + a^{2} c d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}}"," ",0,"1/3*sqrt(3)*b*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/((b^2*c^2*(a/b)^(1/3) - 2*a*b*c*d*(a/b)^(1/3) + a^2*d^2*(a/b)^(1/3))*(a/b)^(1/3)) - 1/9*sqrt(3)*(5*b*c - 2*a*d)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/((b^2*c^3*(c/d)^(1/3) - 2*a*b*c^2*d*(c/d)^(1/3) + a^2*c*d^2*(c/d)^(1/3))*(c/d)^(1/3)) - 1/3*d*x/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^3) - 1/6*b*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*c^2*(a/b)^(2/3) - 2*a*b*c*d*(a/b)^(2/3) + a^2*d^2*(a/b)^(2/3)) + 1/18*(5*b*c - 2*a*d)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(b^2*c^3*(c/d)^(2/3) - 2*a*b*c^2*d*(c/d)^(2/3) + a^2*c*d^2*(c/d)^(2/3)) + 1/3*b*log(x + (a/b)^(1/3))/(b^2*c^2*(a/b)^(2/3) - 2*a*b*c*d*(a/b)^(2/3) + a^2*d^2*(a/b)^(2/3)) - 1/9*(5*b*c - 2*a*d)*log(x + (c/d)^(1/3))/(b^2*c^3*(c/d)^(2/3) - 2*a*b*c^2*d*(c/d)^(2/3) + a^2*c*d^2*(c/d)^(2/3))","A",0
20,1,509,0,1.346018," ","integrate((d*x^3+c)^5/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} x}{3 \, {\left(a b^{6} x^{3} + a^{2} b^{5}\right)}} + \frac{14 \, b^{3} d^{5} x^{10} + 20 \, {\left(5 \, b^{3} c d^{4} - 2 \, a b^{2} d^{5}\right)} x^{7} + 35 \, {\left(10 \, b^{3} c^{2} d^{3} - 10 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} x^{4} + 140 \, {\left(10 \, b^{3} c^{3} d^{2} - 20 \, a b^{2} c^{2} d^{3} + 15 \, a^{2} b c d^{4} - 4 \, a^{3} d^{5}\right)} x}{140 \, b^{5}} + \frac{\sqrt{3} {\left(2 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 40 \, a^{2} b^{3} c^{3} d^{2} + 70 \, a^{3} b^{2} c^{2} d^{3} - 50 \, a^{4} b c d^{4} + 13 \, a^{5} d^{5}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 40 \, a^{2} b^{3} c^{3} d^{2} + 70 \, a^{3} b^{2} c^{2} d^{3} - 50 \, a^{4} b c d^{4} + 13 \, a^{5} d^{5}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 40 \, a^{2} b^{3} c^{3} d^{2} + 70 \, a^{3} b^{2} c^{2} d^{3} - 50 \, a^{4} b c d^{4} + 13 \, a^{5} d^{5}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*x/(a*b^6*x^3 + a^2*b^5) + 1/140*(14*b^3*d^5*x^10 + 20*(5*b^3*c*d^4 - 2*a*b^2*d^5)*x^7 + 35*(10*b^3*c^2*d^3 - 10*a*b^2*c*d^4 + 3*a^2*b*d^5)*x^4 + 140*(10*b^3*c^3*d^2 - 20*a*b^2*c^2*d^3 + 15*a^2*b*c*d^4 - 4*a^3*d^5)*x)/b^5 + 1/9*sqrt(3)*(2*b^5*c^5 + 5*a*b^4*c^4*d - 40*a^2*b^3*c^3*d^2 + 70*a^3*b^2*c^2*d^3 - 50*a^4*b*c*d^4 + 13*a^5*d^5)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^6*(a/b)^(2/3)) - 1/18*(2*b^5*c^5 + 5*a*b^4*c^4*d - 40*a^2*b^3*c^3*d^2 + 70*a^3*b^2*c^2*d^3 - 50*a^4*b*c*d^4 + 13*a^5*d^5)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^6*(a/b)^(2/3)) + 1/9*(2*b^5*c^5 + 5*a*b^4*c^4*d - 40*a^2*b^3*c^3*d^2 + 70*a^3*b^2*c^2*d^3 - 50*a^4*b*c*d^4 + 13*a^5*d^5)*log(x + (a/b)^(1/3))/(a*b^6*(a/b)^(2/3))","A",0
21,1,397,0,1.156016," ","integrate((d*x^3+c)^4/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x}{3 \, {\left(a b^{5} x^{3} + a^{2} b^{4}\right)}} + \frac{2 \, b^{2} d^{4} x^{7} + 7 \, {\left(2 \, b^{2} c d^{3} - a b d^{4}\right)} x^{4} + 14 \, {\left(6 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x}{14 \, b^{4}} + \frac{2 \, \sqrt{3} {\left(b^{4} c^{4} + 2 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{4} c^{4} + 2 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, {\left(b^{4} c^{4} + 2 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x/(a*b^5*x^3 + a^2*b^4) + 1/14*(2*b^2*d^4*x^7 + 7*(2*b^2*c*d^3 - a*b*d^4)*x^4 + 14*(6*b^2*c^2*d^2 - 8*a*b*c*d^3 + 3*a^2*d^4)*x)/b^4 + 2/9*sqrt(3)*(b^4*c^4 + 2*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 5*a^4*d^4)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^5*(a/b)^(2/3)) - 1/9*(b^4*c^4 + 2*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 5*a^4*d^4)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^5*(a/b)^(2/3)) + 2/9*(b^4*c^4 + 2*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 5*a^4*d^4)*log(x + (a/b)^(1/3))/(a*b^5*(a/b)^(2/3))","A",0
22,1,306,0,1.219005," ","integrate((d*x^3+c)^3/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{3 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}} + \frac{b d^{3} x^{4} + 4 \, {\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} x}{4 \, b^{3}} + \frac{\sqrt{3} {\left(2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 12 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 12 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 12 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x/(a*b^4*x^3 + a^2*b^3) + 1/4*(b*d^3*x^4 + 4*(3*b*c*d^2 - 2*a*d^3)*x)/b^3 + 1/9*sqrt(3)*(2*b^3*c^3 + 3*a*b^2*c^2*d - 12*a^2*b*c*d^2 + 7*a^3*d^3)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^4*(a/b)^(2/3)) - 1/18*(2*b^3*c^3 + 3*a*b^2*c^2*d - 12*a^2*b*c*d^2 + 7*a^3*d^3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^4*(a/b)^(2/3)) + 1/9*(2*b^3*c^3 + 3*a*b^2*c^2*d - 12*a^2*b*c*d^2 + 7*a^3*d^3)*log(x + (a/b)^(1/3))/(a*b^4*(a/b)^(2/3))","A",0
23,1,220,0,1.394819," ","integrate((d*x^3+c)^2/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{3 \, {\left(a b^{3} x^{3} + a^{2} b^{2}\right)}} + \frac{d^{2} x}{b^{2}} + \frac{2 \, \sqrt{3} {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(a*b^3*x^3 + a^2*b^2) + d^2*x/b^2 + 2/9*sqrt(3)*(b^2*c^2 + a*b*c*d - 2*a^2*d^2)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3*(a/b)^(2/3)) - 1/9*(b^2*c^2 + a*b*c*d - 2*a^2*d^2)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3*(a/b)^(2/3)) + 2/9*(b^2*c^2 + a*b*c*d - 2*a^2*d^2)*log(x + (a/b)^(1/3))/(a*b^3*(a/b)^(2/3))","A",0
24,1,158,0,1.438891," ","integrate((d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c - a d\right)} x}{3 \, {\left(a b^{2} x^{3} + a^{2} b\right)}} + \frac{\sqrt{3} {\left(2 \, b c + a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, b c + a d\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b c + a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b*c - a*d)*x/(a*b^2*x^3 + a^2*b) + 1/9*sqrt(3)*(2*b*c + a*d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2*(a/b)^(2/3)) - 1/18*(2*b*c + a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2*(a/b)^(2/3)) + 1/9*(2*b*c + a*d)*log(x + (a/b)^(1/3))/(a*b^2*(a/b)^(2/3))","A",0
25,1,489,0,1.290194," ","integrate(1/(b*x^3+a)^2/(d*x^3+c),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(2 \, b c - 5 \, a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, {\left(a b^{2} c^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{2} b c d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{3} d^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{\sqrt{3} d \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(b^{2} c^{2} \left(\frac{c}{d}\right)^{\frac{1}{3}} - 2 \, a b c d \left(\frac{c}{d}\right)^{\frac{1}{3}} + a^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)} \left(\frac{c}{d}\right)^{\frac{1}{3}}} + \frac{b x}{3 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{3}\right)}} - \frac{{\left(2 \, b c - 5 \, a d\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, {\left(a b^{2} c^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} b c d \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{3} d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} - \frac{d \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b^{2} c^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 2 \, a b c d \left(\frac{c}{d}\right)^{\frac{2}{3}} + a^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}} + \frac{{\left(2 \, b c - 5 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{2} c^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} b c d \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{3} d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} + \frac{d \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \, {\left(b^{2} c^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 2 \, a b c d \left(\frac{c}{d}\right)^{\frac{2}{3}} + a^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}}"," ",0,"1/9*sqrt(3)*(2*b*c - 5*a*d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/((a*b^2*c^2*(a/b)^(1/3) - 2*a^2*b*c*d*(a/b)^(1/3) + a^3*d^2*(a/b)^(1/3))*(a/b)^(1/3)) + 1/3*sqrt(3)*d*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/((b^2*c^2*(c/d)^(1/3) - 2*a*b*c*d*(c/d)^(1/3) + a^2*d^2*(c/d)^(1/3))*(c/d)^(1/3)) + 1/3*b*x/(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^3) - 1/18*(2*b*c - 5*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2*c^2*(a/b)^(2/3) - 2*a^2*b*c*d*(a/b)^(2/3) + a^3*d^2*(a/b)^(2/3)) - 1/6*d*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(b^2*c^2*(c/d)^(2/3) - 2*a*b*c*d*(c/d)^(2/3) + a^2*d^2*(c/d)^(2/3)) + 1/9*(2*b*c - 5*a*d)*log(x + (a/b)^(1/3))/(a*b^2*c^2*(a/b)^(2/3) - 2*a^2*b*c*d*(a/b)^(2/3) + a^3*d^2*(a/b)^(2/3)) + 1/3*d*log(x + (c/d)^(1/3))/(b^2*c^2*(c/d)^(2/3) - 2*a*b*c*d*(c/d)^(2/3) + a^2*d^2*(c/d)^(2/3))","A",0
26,1,784,0,1.257288," ","integrate(1/(b*x^3+a)^2/(d*x^3+c)^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} {\left(b^{2} c - 4 \, a b d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, {\left(a b^{3} c^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}} - 3 \, a^{2} b^{2} c^{2} d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 3 \, a^{3} b c d^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{4} d^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{2 \, \sqrt{3} {\left(4 \, b c d - a d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{9 \, {\left(b^{3} c^{4} \left(\frac{c}{d}\right)^{\frac{1}{3}} - 3 \, a b^{2} c^{3} d \left(\frac{c}{d}\right)^{\frac{1}{3}} + 3 \, a^{2} b c^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{1}{3}} - a^{3} c d^{3} \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)} \left(\frac{c}{d}\right)^{\frac{1}{3}}} - \frac{{\left(b^{2} c - 4 \, a b d\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, {\left(a b^{3} c^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a^{2} b^{2} c^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, a^{3} b c d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{4} d^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} - \frac{{\left(4 \, b c d - a d^{2}\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \, {\left(b^{3} c^{4} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 3 \, a b^{2} c^{3} d \left(\frac{c}{d}\right)^{\frac{2}{3}} + 3 \, a^{2} b c^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} - a^{3} c d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}} + \frac{2 \, {\left(b^{2} c - 4 \, a b d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{3} c^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a^{2} b^{2} c^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, a^{3} b c d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{4} d^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}} + \frac{2 \, {\left(4 \, b c d - a d^{2}\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \, {\left(b^{3} c^{4} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 3 \, a b^{2} c^{3} d \left(\frac{c}{d}\right)^{\frac{2}{3}} + 3 \, a^{2} b c^{2} d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} - a^{3} c d^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}} + \frac{{\left(b^{2} c d + a b d^{2}\right)} x^{4} + {\left(b^{2} c^{2} + a^{2} d^{2}\right)} x}{3 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x^{6} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{3}\right)}}"," ",0,"2/9*sqrt(3)*(b^2*c - 4*a*b*d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/((a*b^3*c^3*(a/b)^(1/3) - 3*a^2*b^2*c^2*d*(a/b)^(1/3) + 3*a^3*b*c*d^2*(a/b)^(1/3) - a^4*d^3*(a/b)^(1/3))*(a/b)^(1/3)) + 2/9*sqrt(3)*(4*b*c*d - a*d^2)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/((b^3*c^4*(c/d)^(1/3) - 3*a*b^2*c^3*d*(c/d)^(1/3) + 3*a^2*b*c^2*d^2*(c/d)^(1/3) - a^3*c*d^3*(c/d)^(1/3))*(c/d)^(1/3)) - 1/9*(b^2*c - 4*a*b*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3*c^3*(a/b)^(2/3) - 3*a^2*b^2*c^2*d*(a/b)^(2/3) + 3*a^3*b*c*d^2*(a/b)^(2/3) - a^4*d^3*(a/b)^(2/3)) - 1/9*(4*b*c*d - a*d^2)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(b^3*c^4*(c/d)^(2/3) - 3*a*b^2*c^3*d*(c/d)^(2/3) + 3*a^2*b*c^2*d^2*(c/d)^(2/3) - a^3*c*d^3*(c/d)^(2/3)) + 2/9*(b^2*c - 4*a*b*d)*log(x + (a/b)^(1/3))/(a*b^3*c^3*(a/b)^(2/3) - 3*a^2*b^2*c^2*d*(a/b)^(2/3) + 3*a^3*b*c*d^2*(a/b)^(2/3) - a^4*d^3*(a/b)^(2/3)) + 2/9*(4*b*c*d - a*d^2)*log(x + (c/d)^(1/3))/(b^3*c^4*(c/d)^(2/3) - 3*a*b^2*c^3*d*(c/d)^(2/3) + 3*a^2*b*c^2*d^2*(c/d)^(2/3) - a^3*c*d^3*(c/d)^(2/3)) + 1/3*((b^2*c*d + a*b*d^2)*x^4 + (b^2*c^2 + a^2*d^2)*x)/(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x^6 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^3)","B",0
27,1,322,0,1.218772," ","integrate((-b*x^3+a)*(b*x^3+a)^(2/3),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}} + \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b - \frac{b x^{3} + a}{x^{3}}\right)} x^{2}}\right)} a - \frac{1}{54} \, {\left(\frac{2 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} + \frac{3 \, {\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{3} - \frac{2 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2} b}{x^{6}}}\right)} b"," ",0,"-1/9*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3) + 3*(b*x^3 + a)^(2/3)*a/((b - (b*x^3 + a)/x^3)*x^2))*a - 1/54*(2*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) + 3*((b*x^3 + a)^(2/3)*a^2*b/x^2 + 2*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^3 - 2*(b*x^3 + a)*b^2/x^3 + (b*x^3 + a)^2*b/x^6))*b","B",0
28,1,244,0,1.216275," ","integrate((-b*x^3+a)/(b*x^3+a)^(1/3),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}}\right)} a - \frac{1}{18} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} - \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b^{2} - \frac{{\left(b x^{3} + a\right)} b}{x^{3}}\right)} x^{2}}\right)} b"," ",0,"-1/6*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3))*a - 1/18*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) - 6*(b*x^3 + a)^(2/3)*a/((b^2 - (b*x^3 + a)*b/x^3)*x^2))*b","B",0
29,1,130,0,1.253815," ","integrate((-b*x^3+a)/(b*x^3+a)^(4/3),x, algorithm=""maxima"")","\frac{1}{6} \, b {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} + \frac{6 \, x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}}\right)} + \frac{x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}"," ",0,"1/6*b*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) + 6*x/((b*x^3 + a)^(1/3)*b) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3)) + x/(b*x^3 + a)^(1/3)","A",0
30,1,50,0,0.523075," ","integrate((-b*x^3+a)/(b*x^3+a)^(7/3),x, algorithm=""maxima"")","-\frac{{\left(b - \frac{4 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} x^{4}}{4 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a} - \frac{b x^{4}}{4 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a}"," ",0,"-1/4*(b - 4*(b*x^3 + a)/x^3)*x^4/((b*x^3 + a)^(4/3)*a) - 1/4*b*x^4/((b*x^3 + a)^(4/3)*a)","A",0
31,1,85,0,0.624045," ","integrate((-b*x^3+a)/(b*x^3+a)^(10/3),x, algorithm=""maxima"")","\frac{{\left(4 \, b - \frac{7 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} b x^{7}}{28 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a^{2}} + \frac{{\left(2 \, b^{2} - \frac{7 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{14 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} x^{7}}{14 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a^{2}}"," ",0,"1/28*(4*b - 7*(b*x^3 + a)/x^3)*b*x^7/((b*x^3 + a)^(7/3)*a^2) + 1/14*(2*b^2 - 7*(b*x^3 + a)*b/x^3 + 14*(b*x^3 + a)^2/x^6)*x^7/((b*x^3 + a)^(7/3)*a^2)","A",0
32,1,119,0,0.583874," ","integrate((-b*x^3+a)/(b*x^3+a)^(13/3),x, algorithm=""maxima"")","-\frac{{\left(14 \, b^{2} - \frac{40 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{35 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} b x^{10}}{140 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{3}} - \frac{{\left(14 \, b^{3} - \frac{60 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{105 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{140 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} x^{10}}{140 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{3}}"," ",0,"-1/140*(14*b^2 - 40*(b*x^3 + a)*b/x^3 + 35*(b*x^3 + a)^2/x^6)*b*x^10/((b*x^3 + a)^(10/3)*a^3) - 1/140*(14*b^3 - 60*(b*x^3 + a)*b^2/x^3 + 105*(b*x^3 + a)^2*b/x^6 - 140*(b*x^3 + a)^3/x^9)*x^10/((b*x^3 + a)^(10/3)*a^3)","B",0
33,1,153,0,0.538078," ","integrate((-b*x^3+a)/(b*x^3+a)^(16/3),x, algorithm=""maxima"")","\frac{{\left(140 \, b^{3} - \frac{546 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{780 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} b x^{13}}{1820 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{4}} + \frac{{\left(35 \, b^{4} - \frac{182 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{390 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3} b}{x^{9}} + \frac{455 \, {\left(b x^{3} + a\right)}^{4}}{x^{12}}\right)} x^{13}}{455 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{4}}"," ",0,"1/1820*(140*b^3 - 546*(b*x^3 + a)*b^2/x^3 + 780*(b*x^3 + a)^2*b/x^6 - 455*(b*x^3 + a)^3/x^9)*b*x^13/((b*x^3 + a)^(13/3)*a^4) + 1/455*(35*b^4 - 182*(b*x^3 + a)*b^3/x^3 + 390*(b*x^3 + a)^2*b^2/x^6 - 455*(b*x^3 + a)^3*b/x^9 + 455*(b*x^3 + a)^4/x^12)*x^13/((b*x^3 + a)^(13/3)*a^4)","B",0
34,0,0,0,0.000000," ","integrate((b*x^3+a)^(7/3)/(-b*x^3+a),x, algorithm=""maxima"")","-\int \frac{{\left(b x^{3} + a\right)}^{\frac{7}{3}}}{b x^{3} - a}\,{d x}"," ",0,"-integrate((b*x^3 + a)^(7/3)/(b*x^3 - a), x)","F",0
35,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(-b*x^3+a),x, algorithm=""maxima"")","-\int \frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{b x^{3} - a}\,{d x}"," ",0,"-integrate((b*x^3 + a)^(4/3)/(b*x^3 - a), x)","F",0
36,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(-b*x^3+a),x, algorithm=""maxima"")","-\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b x^{3} - a}\,{d x}"," ",0,"-integrate((b*x^3 + a)^(1/3)/(b*x^3 - a), x)","F",0
37,0,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(2/3),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b x^{3} - a\right)}}\,{d x}"," ",0,"-integrate(1/((b*x^3 + a)^(2/3)*(b*x^3 - a)), x)","F",0
38,0,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(5/3),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{5}{3}} {\left(b x^{3} - a\right)}}\,{d x}"," ",0,"-integrate(1/((b*x^3 + a)^(5/3)*(b*x^3 - a)), x)","F",0
39,0,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(8/3),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{8}{3}} {\left(b x^{3} - a\right)}}\,{d x}"," ",0,"-integrate(1/((b*x^3 + a)^(8/3)*(b*x^3 - a)), x)","F",0
40,1,552,0,1.526865," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(2/3),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}} + \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b - \frac{b x^{3} + a}{x^{3}}\right)} x^{2}}\right)} a^{2} - \frac{1}{27} \, {\left(\frac{2 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} + \frac{3 \, {\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{3} - \frac{2 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2} b}{x^{6}}}\right)} a b - \frac{1}{243} \, {\left(\frac{4 \, \sqrt{3} a^{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} - \frac{2 \, a^{3} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, a^{3} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}} + \frac{3 \, {\left(\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{3} b^{2}}{x^{2}} + \frac{11 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{3} b}{x^{5}} - \frac{4 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a^{3}}{x^{8}}\right)}}{b^{5} - \frac{3 \, {\left(b x^{3} + a\right)} b^{4}}{x^{3}} + \frac{3 \, {\left(b x^{3} + a\right)}^{2} b^{3}}{x^{6}} - \frac{{\left(b x^{3} + a\right)}^{3} b^{2}}{x^{9}}}\right)} b^{2}"," ",0,"-1/9*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3) + 3*(b*x^3 + a)^(2/3)*a/((b - (b*x^3 + a)/x^3)*x^2))*a^2 - 1/27*(2*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) + 3*((b*x^3 + a)^(2/3)*a^2*b/x^2 + 2*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^3 - 2*(b*x^3 + a)*b^2/x^3 + (b*x^3 + a)^2*b/x^6))*a*b - 1/243*(4*sqrt(3)*a^3*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) - 2*a^3*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*a^3*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3) + 3*(2*(b*x^3 + a)^(2/3)*a^3*b^2/x^2 + 11*(b*x^3 + a)^(5/3)*a^3*b/x^5 - 4*(b*x^3 + a)^(8/3)*a^3/x^8)/(b^5 - 3*(b*x^3 + a)*b^4/x^3 + 3*(b*x^3 + a)^2*b^3/x^6 - (b*x^3 + a)^3*b^2/x^9))*b^2","B",0
41,1,436,0,1.396183," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(1/3),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}}\right)} a^{2} - \frac{1}{9} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} - \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b^{2} - \frac{{\left(b x^{3} + a\right)} b}{x^{3}}\right)} x^{2}}\right)} a b - \frac{1}{54} \, {\left(\frac{4 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} - \frac{2 \, a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}} - \frac{3 \, {\left(\frac{7 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} - \frac{4 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{4} - \frac{2 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}}}\right)} b^{2}"," ",0,"-1/6*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3))*a^2 - 1/9*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) - 6*(b*x^3 + a)^(2/3)*a/((b^2 - (b*x^3 + a)*b/x^3)*x^2))*a*b - 1/54*(4*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) - 2*a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3) - 3*(7*(b*x^3 + a)^(2/3)*a^2*b/x^2 - 4*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^4 - 2*(b*x^3 + a)*b^3/x^3 + (b*x^3 + a)^2*b^2/x^6))*b^2","B",0
42,1,296,0,1.373023," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(4/3),x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} {\left(\frac{4 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} + \frac{3 \, {\left(3 \, a b - \frac{4 \, {\left(b x^{3} + a\right)} a}{x^{3}}\right)}}{\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{3}}{x} - \frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}} b^{2}}{x^{4}}} - \frac{2 \, a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}}\right)} + \frac{1}{3} \, a b {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} + \frac{6 \, x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}}\right)} + \frac{a x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}"," ",0,"1/9*b^2*(4*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) + 3*(3*a*b - 4*(b*x^3 + a)*a/x^3)/((b*x^3 + a)^(1/3)*b^3/x - (b*x^3 + a)^(4/3)*b^2/x^4) - 2*a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3)) + 1/3*a*b*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) + 6*x/((b*x^3 + a)^(1/3)*b) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3)) + a*x/(b*x^3 + a)^(1/3)","B",0
43,1,180,0,1.354383," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(7/3),x, algorithm=""maxima"")","-\frac{{\left(b - \frac{4 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} x^{4}}{4 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}}} - \frac{b x^{4}}{2 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}}} - \frac{1}{12} \, {\left(\frac{3 \, {\left(b + \frac{4 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} x^{4}}{{\left(b x^{3} + a\right)}^{\frac{4}{3}} b^{2}} + \frac{4 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} - \frac{2 \, \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}}\right)} b^{2}"," ",0,"-1/4*(b - 4*(b*x^3 + a)/x^3)*x^4/(b*x^3 + a)^(4/3) - 1/2*b*x^4/(b*x^3 + a)^(4/3) - 1/12*(3*(b + 4*(b*x^3 + a)/x^3)*x^4/((b*x^3 + a)^(4/3)*b^2) + 4*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) - 2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3))*b^2","B",0
44,1,105,0,0.498065," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(10/3),x, algorithm=""maxima"")","\frac{{\left(4 \, b - \frac{7 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} b x^{7}}{14 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a} + \frac{b^{2} x^{7}}{7 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a} + \frac{{\left(2 \, b^{2} - \frac{7 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{14 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} x^{7}}{14 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a}"," ",0,"1/14*(4*b - 7*(b*x^3 + a)/x^3)*b*x^7/((b*x^3 + a)^(7/3)*a) + 1/7*b^2*x^7/((b*x^3 + a)^(7/3)*a) + 1/14*(2*b^2 - 7*(b*x^3 + a)*b/x^3 + 14*(b*x^3 + a)^2/x^6)*x^7/((b*x^3 + a)^(7/3)*a)","A",0
45,1,155,0,0.585377," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(13/3),x, algorithm=""maxima"")","-\frac{{\left(7 \, b - \frac{10 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} b^{2} x^{10}}{70 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{2}} - \frac{{\left(14 \, b^{2} - \frac{40 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{35 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} b x^{10}}{70 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{2}} - \frac{{\left(14 \, b^{3} - \frac{60 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{105 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{140 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} x^{10}}{140 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{2}}"," ",0,"-1/70*(7*b - 10*(b*x^3 + a)/x^3)*b^2*x^10/((b*x^3 + a)^(10/3)*a^2) - 1/70*(14*b^2 - 40*(b*x^3 + a)*b/x^3 + 35*(b*x^3 + a)^2/x^6)*b*x^10/((b*x^3 + a)^(10/3)*a^2) - 1/140*(14*b^3 - 60*(b*x^3 + a)*b^2/x^3 + 105*(b*x^3 + a)^2*b/x^6 - 140*(b*x^3 + a)^3/x^9)*x^10/((b*x^3 + a)^(10/3)*a^2)","A",0
46,1,206,0,0.573677," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(16/3),x, algorithm=""maxima"")","\frac{{\left(35 \, b^{2} - \frac{91 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{65 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} b^{2} x^{13}}{455 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{3}} + \frac{{\left(140 \, b^{3} - \frac{546 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{780 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} b x^{13}}{910 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{3}} + \frac{{\left(35 \, b^{4} - \frac{182 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{390 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3} b}{x^{9}} + \frac{455 \, {\left(b x^{3} + a\right)}^{4}}{x^{12}}\right)} x^{13}}{455 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{3}}"," ",0,"1/455*(35*b^2 - 91*(b*x^3 + a)*b/x^3 + 65*(b*x^3 + a)^2/x^6)*b^2*x^13/((b*x^3 + a)^(13/3)*a^3) + 1/910*(140*b^3 - 546*(b*x^3 + a)*b^2/x^3 + 780*(b*x^3 + a)^2*b/x^6 - 455*(b*x^3 + a)^3/x^9)*b*x^13/((b*x^3 + a)^(13/3)*a^3) + 1/455*(35*b^4 - 182*(b*x^3 + a)*b^3/x^3 + 390*(b*x^3 + a)^2*b^2/x^6 - 455*(b*x^3 + a)^3*b/x^9 + 455*(b*x^3 + a)^4/x^12)*x^13/((b*x^3 + a)^(13/3)*a^3)","B",0
47,1,257,0,0.510208," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(19/3),x, algorithm=""maxima"")","-\frac{{\left(455 \, b^{3} - \frac{1680 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{2184 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{1040 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} b^{2} x^{16}}{7280 \, {\left(b x^{3} + a\right)}^{\frac{16}{3}} a^{4}} - \frac{{\left(455 \, b^{4} - \frac{2240 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{4368 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{4160 \, {\left(b x^{3} + a\right)}^{3} b}{x^{9}} + \frac{1820 \, {\left(b x^{3} + a\right)}^{4}}{x^{12}}\right)} b x^{16}}{3640 \, {\left(b x^{3} + a\right)}^{\frac{16}{3}} a^{4}} - \frac{{\left(91 \, b^{5} - \frac{560 \, {\left(b x^{3} + a\right)} b^{4}}{x^{3}} + \frac{1456 \, {\left(b x^{3} + a\right)}^{2} b^{3}}{x^{6}} - \frac{2080 \, {\left(b x^{3} + a\right)}^{3} b^{2}}{x^{9}} + \frac{1820 \, {\left(b x^{3} + a\right)}^{4} b}{x^{12}} - \frac{1456 \, {\left(b x^{3} + a\right)}^{5}}{x^{15}}\right)} x^{16}}{1456 \, {\left(b x^{3} + a\right)}^{\frac{16}{3}} a^{4}}"," ",0,"-1/7280*(455*b^3 - 1680*(b*x^3 + a)*b^2/x^3 + 2184*(b*x^3 + a)^2*b/x^6 - 1040*(b*x^3 + a)^3/x^9)*b^2*x^16/((b*x^3 + a)^(16/3)*a^4) - 1/3640*(455*b^4 - 2240*(b*x^3 + a)*b^3/x^3 + 4368*(b*x^3 + a)^2*b^2/x^6 - 4160*(b*x^3 + a)^3*b/x^9 + 1820*(b*x^3 + a)^4/x^12)*b*x^16/((b*x^3 + a)^(16/3)*a^4) - 1/1456*(91*b^5 - 560*(b*x^3 + a)*b^4/x^3 + 1456*(b*x^3 + a)^2*b^3/x^6 - 2080*(b*x^3 + a)^3*b^2/x^9 + 1820*(b*x^3 + a)^4*b/x^12 - 1456*(b*x^3 + a)^5/x^15)*x^16/((b*x^3 + a)^(16/3)*a^4)","B",0
48,0,0,0,0.000000," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(4/3),x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(b x^{3} - a\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)*(b*x^3 - a)^2, x)","F",0
49,0,0,0,0.000000," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(1/3),x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b x^{3} - a\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(b*x^3 - a)^2, x)","F",0
50,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(2/3), x)","F",0
51,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(5/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(5/3), x)","F",0
52,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(8/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(8/3), x)","F",0
53,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(11/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{11}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(11/3), x)","F",0
54,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(14/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{14}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(14/3), x)","F",0
55,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(17/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{17}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(17/3), x)","F",0
56,1,406,0,1.678182," ","integrate((b*x^3+a)^(5/3)*(d*x^3+c),x, algorithm=""maxima"")","-\frac{1}{54} \, {\left(\frac{10 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{5 \, a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{10 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}} + \frac{3 \, {\left(\frac{5 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} - \frac{8 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{2} - \frac{2 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2}}{x^{6}}}\right)} c + \frac{1}{486} \, {\left(\frac{10 \, \sqrt{3} a^{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{5 \, a^{3} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{10 \, a^{3} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} + \frac{3 \, {\left(\frac{5 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{3} b^{2}}{x^{2}} - \frac{13 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{3} b}{x^{5}} - \frac{10 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a^{3}}{x^{8}}\right)}}{b^{4} - \frac{3 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{3 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{{\left(b x^{3} + a\right)}^{3} b}{x^{9}}}\right)} d"," ",0,"-1/54*(10*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - 5*a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 10*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3) + 3*(5*(b*x^3 + a)^(2/3)*a^2*b/x^2 - 8*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^2 - 2*(b*x^3 + a)*b/x^3 + (b*x^3 + a)^2/x^6))*c + 1/486*(10*sqrt(3)*a^3*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - 5*a^3*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 10*a^3*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) + 3*(5*(b*x^3 + a)^(2/3)*a^3*b^2/x^2 - 13*(b*x^3 + a)^(5/3)*a^3*b/x^5 - 10*(b*x^3 + a)^(8/3)*a^3/x^8)/(b^4 - 3*(b*x^3 + a)*b^3/x^3 + 3*(b*x^3 + a)^2*b^2/x^6 - (b*x^3 + a)^3*b/x^9))*d","B",0
57,1,322,0,1.436599," ","integrate((b*x^3+a)^(2/3)*(d*x^3+c),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}} + \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b - \frac{b x^{3} + a}{x^{3}}\right)} x^{2}}\right)} c + \frac{1}{54} \, {\left(\frac{2 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} + \frac{3 \, {\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{3} - \frac{2 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2} b}{x^{6}}}\right)} d"," ",0,"-1/9*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3) + 3*(b*x^3 + a)^(2/3)*a/((b - (b*x^3 + a)/x^3)*x^2))*c + 1/54*(2*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) + 3*((b*x^3 + a)^(2/3)*a^2*b/x^2 + 2*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^3 - 2*(b*x^3 + a)*b^2/x^3 + (b*x^3 + a)^2*b/x^6))*d","B",0
58,1,244,0,1.197503," ","integrate((d*x^3+c)/(b*x^3+a)^(1/3),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}}\right)} c + \frac{1}{18} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} - \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b^{2} - \frac{{\left(b x^{3} + a\right)} b}{x^{3}}\right)} x^{2}}\right)} d"," ",0,"-1/6*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3))*c + 1/18*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) - 6*(b*x^3 + a)^(2/3)*a/((b^2 - (b*x^3 + a)*b/x^3)*x^2))*d","B",0
59,1,134,0,1.223502," ","integrate((d*x^3+c)/(b*x^3+a)^(4/3),x, algorithm=""maxima"")","-\frac{1}{6} \, d {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} + \frac{6 \, x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}}\right)} + \frac{c x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} a}"," ",0,"-1/6*d*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) + 6*x/((b*x^3 + a)^(1/3)*b) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3)) + c*x/((b*x^3 + a)^(1/3)*a)","A",0
60,1,51,0,0.469777," ","integrate((d*x^3+c)/(b*x^3+a)^(7/3),x, algorithm=""maxima"")","-\frac{{\left(b - \frac{4 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} c x^{4}}{4 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a^{2}} + \frac{d x^{4}}{4 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a}"," ",0,"-1/4*(b - 4*(b*x^3 + a)/x^3)*c*x^4/((b*x^3 + a)^(4/3)*a^2) + 1/4*d*x^4/((b*x^3 + a)^(4/3)*a)","A",0
61,1,86,0,0.607903," ","integrate((d*x^3+c)/(b*x^3+a)^(10/3),x, algorithm=""maxima"")","-\frac{{\left(4 \, b - \frac{7 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} d x^{7}}{28 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a^{2}} + \frac{{\left(2 \, b^{2} - \frac{7 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{14 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} c x^{7}}{14 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a^{3}}"," ",0,"-1/28*(4*b - 7*(b*x^3 + a)/x^3)*d*x^7/((b*x^3 + a)^(7/3)*a^2) + 1/14*(2*b^2 - 7*(b*x^3 + a)*b/x^3 + 14*(b*x^3 + a)^2/x^6)*c*x^7/((b*x^3 + a)^(7/3)*a^3)","A",0
62,1,120,0,0.499254," ","integrate((d*x^3+c)/(b*x^3+a)^(13/3),x, algorithm=""maxima"")","\frac{{\left(14 \, b^{2} - \frac{40 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{35 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} d x^{10}}{140 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{3}} - \frac{{\left(14 \, b^{3} - \frac{60 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{105 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{140 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} c x^{10}}{140 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{4}}"," ",0,"1/140*(14*b^2 - 40*(b*x^3 + a)*b/x^3 + 35*(b*x^3 + a)^2/x^6)*d*x^10/((b*x^3 + a)^(10/3)*a^3) - 1/140*(14*b^3 - 60*(b*x^3 + a)*b^2/x^3 + 105*(b*x^3 + a)^2*b/x^6 - 140*(b*x^3 + a)^3/x^9)*c*x^10/((b*x^3 + a)^(10/3)*a^4)","A",0
63,1,154,0,0.656790," ","integrate((d*x^3+c)/(b*x^3+a)^(16/3),x, algorithm=""maxima"")","-\frac{{\left(140 \, b^{3} - \frac{546 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{780 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} d x^{13}}{1820 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{4}} + \frac{{\left(35 \, b^{4} - \frac{182 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{390 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3} b}{x^{9}} + \frac{455 \, {\left(b x^{3} + a\right)}^{4}}{x^{12}}\right)} c x^{13}}{455 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{5}}"," ",0,"-1/1820*(140*b^3 - 546*(b*x^3 + a)*b^2/x^3 + 780*(b*x^3 + a)^2*b/x^6 - 455*(b*x^3 + a)^3/x^9)*d*x^13/((b*x^3 + a)^(13/3)*a^4) + 1/455*(35*b^4 - 182*(b*x^3 + a)*b^3/x^3 + 390*(b*x^3 + a)^2*b^2/x^6 - 455*(b*x^3 + a)^3*b/x^9 + 455*(b*x^3 + a)^4/x^12)*c*x^13/((b*x^3 + a)^(13/3)*a^5)","A",0
64,0,0,0,0.000000," ","integrate((b*x^3+a)^(7/3)*(d*x^3+c),x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{7}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(7/3)*(d*x^3 + c), x)","F",0
65,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)*(d*x^3+c),x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)*(d*x^3 + c), x)","F",0
66,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)*(d*x^3+c),x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x^3 + c), x)","F",0
67,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(2/3),x, algorithm=""maxima"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(2/3), x)","F",0
68,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(5/3),x, algorithm=""maxima"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(5/3), x)","F",0
69,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(8/3),x, algorithm=""maxima"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(8/3), x)","F",0
70,1,672,0,1.294196," ","integrate((b*x^3+a)^(5/3)*(d*x^3+c)^2,x, algorithm=""maxima"")","-\frac{1}{54} \, {\left(\frac{10 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{5 \, a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{10 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}} + \frac{3 \, {\left(\frac{5 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} - \frac{8 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{2} - \frac{2 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2}}{x^{6}}}\right)} c^{2} + \frac{1}{243} \, {\left(\frac{10 \, \sqrt{3} a^{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{5 \, a^{3} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{10 \, a^{3} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} + \frac{3 \, {\left(\frac{5 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{3} b^{2}}{x^{2}} - \frac{13 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{3} b}{x^{5}} - \frac{10 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a^{3}}{x^{8}}\right)}}{b^{4} - \frac{3 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{3 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{{\left(b x^{3} + a\right)}^{3} b}{x^{9}}}\right)} c d - \frac{1}{2916} \, {\left(\frac{20 \, \sqrt{3} a^{4} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} - \frac{10 \, a^{4} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{20 \, a^{4} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}} + \frac{3 \, {\left(\frac{10 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{4} b^{3}}{x^{2}} - \frac{36 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{4} b^{2}}{x^{5}} - \frac{75 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a^{4} b}{x^{8}} + \frac{20 \, {\left(b x^{3} + a\right)}^{\frac{11}{3}} a^{4}}{x^{11}}\right)}}{b^{6} - \frac{4 \, {\left(b x^{3} + a\right)} b^{5}}{x^{3}} + \frac{6 \, {\left(b x^{3} + a\right)}^{2} b^{4}}{x^{6}} - \frac{4 \, {\left(b x^{3} + a\right)}^{3} b^{3}}{x^{9}} + \frac{{\left(b x^{3} + a\right)}^{4} b^{2}}{x^{12}}}\right)} d^{2}"," ",0,"-1/54*(10*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - 5*a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 10*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3) + 3*(5*(b*x^3 + a)^(2/3)*a^2*b/x^2 - 8*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^2 - 2*(b*x^3 + a)*b/x^3 + (b*x^3 + a)^2/x^6))*c^2 + 1/243*(10*sqrt(3)*a^3*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - 5*a^3*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 10*a^3*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) + 3*(5*(b*x^3 + a)^(2/3)*a^3*b^2/x^2 - 13*(b*x^3 + a)^(5/3)*a^3*b/x^5 - 10*(b*x^3 + a)^(8/3)*a^3/x^8)/(b^4 - 3*(b*x^3 + a)*b^3/x^3 + 3*(b*x^3 + a)^2*b^2/x^6 - (b*x^3 + a)^3*b/x^9))*c*d - 1/2916*(20*sqrt(3)*a^4*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) - 10*a^4*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 20*a^4*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3) + 3*(10*(b*x^3 + a)^(2/3)*a^4*b^3/x^2 - 36*(b*x^3 + a)^(5/3)*a^4*b^2/x^5 - 75*(b*x^3 + a)^(8/3)*a^4*b/x^8 + 20*(b*x^3 + a)^(11/3)*a^4/x^11)/(b^6 - 4*(b*x^3 + a)*b^5/x^3 + 6*(b*x^3 + a)^2*b^4/x^6 - 4*(b*x^3 + a)^3*b^3/x^9 + (b*x^3 + a)^4*b^2/x^12))*d^2","B",0
71,1,552,0,1.479166," ","integrate((b*x^3+a)^(2/3)*(d*x^3+c)^2,x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}} + \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b - \frac{b x^{3} + a}{x^{3}}\right)} x^{2}}\right)} c^{2} + \frac{1}{27} \, {\left(\frac{2 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} + \frac{3 \, {\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{3} - \frac{2 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2} b}{x^{6}}}\right)} c d - \frac{1}{243} \, {\left(\frac{4 \, \sqrt{3} a^{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} - \frac{2 \, a^{3} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, a^{3} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}} + \frac{3 \, {\left(\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{3} b^{2}}{x^{2}} + \frac{11 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{3} b}{x^{5}} - \frac{4 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a^{3}}{x^{8}}\right)}}{b^{5} - \frac{3 \, {\left(b x^{3} + a\right)} b^{4}}{x^{3}} + \frac{3 \, {\left(b x^{3} + a\right)}^{2} b^{3}}{x^{6}} - \frac{{\left(b x^{3} + a\right)}^{3} b^{2}}{x^{9}}}\right)} d^{2}"," ",0,"-1/9*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3) + 3*(b*x^3 + a)^(2/3)*a/((b - (b*x^3 + a)/x^3)*x^2))*c^2 + 1/27*(2*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) + 3*((b*x^3 + a)^(2/3)*a^2*b/x^2 + 2*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^3 - 2*(b*x^3 + a)*b^2/x^3 + (b*x^3 + a)^2*b/x^6))*c*d - 1/243*(4*sqrt(3)*a^3*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) - 2*a^3*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*a^3*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3) + 3*(2*(b*x^3 + a)^(2/3)*a^3*b^2/x^2 + 11*(b*x^3 + a)^(5/3)*a^3*b/x^5 - 4*(b*x^3 + a)^(8/3)*a^3/x^8)/(b^5 - 3*(b*x^3 + a)*b^4/x^3 + 3*(b*x^3 + a)^2*b^3/x^6 - (b*x^3 + a)^3*b^2/x^9))*d^2","B",0
72,1,436,0,1.275282," ","integrate((d*x^3+c)^2/(b*x^3+a)^(1/3),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{1}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{1}{3}}}\right)} c^{2} + \frac{1}{9} \, {\left(\frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} - \frac{a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}} - \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{{\left(b^{2} - \frac{{\left(b x^{3} + a\right)} b}{x^{3}}\right)} x^{2}}\right)} c d - \frac{1}{54} \, {\left(\frac{4 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} - \frac{2 \, a^{2} \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, a^{2} \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}} - \frac{3 \, {\left(\frac{7 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2} b}{x^{2}} - \frac{4 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{x^{5}}\right)}}{b^{4} - \frac{2 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{{\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}}}\right)} d^{2}"," ",0,"-1/6*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(1/3) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(1/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(1/3))*c^2 + 1/9*(2*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) - a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3) - 6*(b*x^3 + a)^(2/3)*a/((b^2 - (b*x^3 + a)*b/x^3)*x^2))*c*d - 1/54*(4*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) - 2*a^2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*a^2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3) - 3*(7*(b*x^3 + a)^(2/3)*a^2*b/x^2 - 4*(b*x^3 + a)^(5/3)*a^2/x^5)/(b^4 - 2*(b*x^3 + a)*b^3/x^3 + (b*x^3 + a)^2*b^2/x^6))*d^2","B",0
73,1,301,0,1.136578," ","integrate((d*x^3+c)^2/(b*x^3+a)^(4/3),x, algorithm=""maxima"")","\frac{1}{9} \, d^{2} {\left(\frac{4 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} + \frac{3 \, {\left(3 \, a b - \frac{4 \, {\left(b x^{3} + a\right)} a}{x^{3}}\right)}}{\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{3}}{x} - \frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}} b^{2}}{x^{4}}} - \frac{2 \, a \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, a \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}}\right)} - \frac{1}{3} \, c d {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{4}{3}}} + \frac{6 \, x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b} - \frac{\log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{4}{3}}} + \frac{2 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{4}{3}}}\right)} + \frac{c^{2} x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} a}"," ",0,"1/9*d^2*(4*sqrt(3)*a*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) + 3*(3*a*b - 4*(b*x^3 + a)*a/x^3)/((b*x^3 + a)^(1/3)*b^3/x - (b*x^3 + a)^(4/3)*b^2/x^4) - 2*a*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*a*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3)) - 1/3*c*d*(2*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(4/3) + 6*x/((b*x^3 + a)^(1/3)*b) - log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(4/3) + 2*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(4/3)) + c^2*x/((b*x^3 + a)^(1/3)*a)","B",0
74,1,190,0,1.193263," ","integrate((d*x^3+c)^2/(b*x^3+a)^(7/3),x, algorithm=""maxima"")","-\frac{{\left(b - \frac{4 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} c^{2} x^{4}}{4 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a^{2}} + \frac{c d x^{4}}{2 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a} - \frac{1}{12} \, {\left(\frac{3 \, {\left(b + \frac{4 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} x^{4}}{{\left(b x^{3} + a\right)}^{\frac{4}{3}} b^{2}} + \frac{4 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{7}{3}}} - \frac{2 \, \log\left(b^{\frac{2}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}}}{x} + \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{b^{\frac{7}{3}}} + \frac{4 \, \log\left(-b^{\frac{1}{3}} + \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right)}{b^{\frac{7}{3}}}\right)} d^{2}"," ",0,"-1/4*(b - 4*(b*x^3 + a)/x^3)*c^2*x^4/((b*x^3 + a)^(4/3)*a^2) + 1/2*c*d*x^4/((b*x^3 + a)^(4/3)*a) - 1/12*(3*(b + 4*(b*x^3 + a)/x^3)*x^4/((b*x^3 + a)^(4/3)*b^2) + 4*sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(b*x^3 + a)^(1/3)/x)/b^(1/3))/b^(7/3) - 2*log(b^(2/3) + (b*x^3 + a)^(1/3)*b^(1/3)/x + (b*x^3 + a)^(2/3)/x^2)/b^(7/3) + 4*log(-b^(1/3) + (b*x^3 + a)^(1/3)/x)/b^(7/3))*d^2","A",0
75,1,109,0,0.507987," ","integrate((d*x^3+c)^2/(b*x^3+a)^(10/3),x, algorithm=""maxima"")","-\frac{{\left(4 \, b - \frac{7 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} c d x^{7}}{14 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a^{2}} + \frac{d^{2} x^{7}}{7 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a} + \frac{{\left(2 \, b^{2} - \frac{7 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{14 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} c^{2} x^{7}}{14 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a^{3}}"," ",0,"-1/14*(4*b - 7*(b*x^3 + a)/x^3)*c*d*x^7/((b*x^3 + a)^(7/3)*a^2) + 1/7*d^2*x^7/((b*x^3 + a)^(7/3)*a) + 1/14*(2*b^2 - 7*(b*x^3 + a)*b/x^3 + 14*(b*x^3 + a)^2/x^6)*c^2*x^7/((b*x^3 + a)^(7/3)*a^3)","A",0
76,1,159,0,0.712177," ","integrate((d*x^3+c)^2/(b*x^3+a)^(13/3),x, algorithm=""maxima"")","-\frac{{\left(7 \, b - \frac{10 \, {\left(b x^{3} + a\right)}}{x^{3}}\right)} d^{2} x^{10}}{70 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{2}} + \frac{{\left(14 \, b^{2} - \frac{40 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{35 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} c d x^{10}}{70 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{3}} - \frac{{\left(14 \, b^{3} - \frac{60 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{105 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{140 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} c^{2} x^{10}}{140 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a^{4}}"," ",0,"-1/70*(7*b - 10*(b*x^3 + a)/x^3)*d^2*x^10/((b*x^3 + a)^(10/3)*a^2) + 1/70*(14*b^2 - 40*(b*x^3 + a)*b/x^3 + 35*(b*x^3 + a)^2/x^6)*c*d*x^10/((b*x^3 + a)^(10/3)*a^3) - 1/140*(14*b^3 - 60*(b*x^3 + a)*b^2/x^3 + 105*(b*x^3 + a)^2*b/x^6 - 140*(b*x^3 + a)^3/x^9)*c^2*x^10/((b*x^3 + a)^(10/3)*a^4)","A",0
77,1,210,0,0.502958," ","integrate((d*x^3+c)^2/(b*x^3+a)^(16/3),x, algorithm=""maxima"")","\frac{{\left(35 \, b^{2} - \frac{91 \, {\left(b x^{3} + a\right)} b}{x^{3}} + \frac{65 \, {\left(b x^{3} + a\right)}^{2}}{x^{6}}\right)} d^{2} x^{13}}{455 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{3}} - \frac{{\left(140 \, b^{3} - \frac{546 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{780 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} c d x^{13}}{910 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{4}} + \frac{{\left(35 \, b^{4} - \frac{182 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{390 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{455 \, {\left(b x^{3} + a\right)}^{3} b}{x^{9}} + \frac{455 \, {\left(b x^{3} + a\right)}^{4}}{x^{12}}\right)} c^{2} x^{13}}{455 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} a^{5}}"," ",0,"1/455*(35*b^2 - 91*(b*x^3 + a)*b/x^3 + 65*(b*x^3 + a)^2/x^6)*d^2*x^13/((b*x^3 + a)^(13/3)*a^3) - 1/910*(140*b^3 - 546*(b*x^3 + a)*b^2/x^3 + 780*(b*x^3 + a)^2*b/x^6 - 455*(b*x^3 + a)^3/x^9)*c*d*x^13/((b*x^3 + a)^(13/3)*a^4) + 1/455*(35*b^4 - 182*(b*x^3 + a)*b^3/x^3 + 390*(b*x^3 + a)^2*b^2/x^6 - 455*(b*x^3 + a)^3*b/x^9 + 455*(b*x^3 + a)^4/x^12)*c^2*x^13/((b*x^3 + a)^(13/3)*a^5)","A",0
78,1,261,0,0.643184," ","integrate((d*x^3+c)^2/(b*x^3+a)^(19/3),x, algorithm=""maxima"")","-\frac{{\left(455 \, b^{3} - \frac{1680 \, {\left(b x^{3} + a\right)} b^{2}}{x^{3}} + \frac{2184 \, {\left(b x^{3} + a\right)}^{2} b}{x^{6}} - \frac{1040 \, {\left(b x^{3} + a\right)}^{3}}{x^{9}}\right)} d^{2} x^{16}}{7280 \, {\left(b x^{3} + a\right)}^{\frac{16}{3}} a^{4}} + \frac{{\left(455 \, b^{4} - \frac{2240 \, {\left(b x^{3} + a\right)} b^{3}}{x^{3}} + \frac{4368 \, {\left(b x^{3} + a\right)}^{2} b^{2}}{x^{6}} - \frac{4160 \, {\left(b x^{3} + a\right)}^{3} b}{x^{9}} + \frac{1820 \, {\left(b x^{3} + a\right)}^{4}}{x^{12}}\right)} c d x^{16}}{3640 \, {\left(b x^{3} + a\right)}^{\frac{16}{3}} a^{5}} - \frac{{\left(91 \, b^{5} - \frac{560 \, {\left(b x^{3} + a\right)} b^{4}}{x^{3}} + \frac{1456 \, {\left(b x^{3} + a\right)}^{2} b^{3}}{x^{6}} - \frac{2080 \, {\left(b x^{3} + a\right)}^{3} b^{2}}{x^{9}} + \frac{1820 \, {\left(b x^{3} + a\right)}^{4} b}{x^{12}} - \frac{1456 \, {\left(b x^{3} + a\right)}^{5}}{x^{15}}\right)} c^{2} x^{16}}{1456 \, {\left(b x^{3} + a\right)}^{\frac{16}{3}} a^{6}}"," ",0,"-1/7280*(455*b^3 - 1680*(b*x^3 + a)*b^2/x^3 + 2184*(b*x^3 + a)^2*b/x^6 - 1040*(b*x^3 + a)^3/x^9)*d^2*x^16/((b*x^3 + a)^(16/3)*a^4) + 1/3640*(455*b^4 - 2240*(b*x^3 + a)*b^3/x^3 + 4368*(b*x^3 + a)^2*b^2/x^6 - 4160*(b*x^3 + a)^3*b/x^9 + 1820*(b*x^3 + a)^4/x^12)*c*d*x^16/((b*x^3 + a)^(16/3)*a^5) - 1/1456*(91*b^5 - 560*(b*x^3 + a)*b^4/x^3 + 1456*(b*x^3 + a)^2*b^3/x^6 - 2080*(b*x^3 + a)^3*b^2/x^9 + 1820*(b*x^3 + a)^4*b/x^12 - 1456*(b*x^3 + a)^5/x^15)*c^2*x^16/((b*x^3 + a)^(16/3)*a^6)","A",0
79,0,0,0,0.000000," ","integrate((b*x^3+a)^(7/3)*(d*x^3+c)^2,x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{7}{3}} {\left(d x^{3} + c\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(7/3)*(d*x^3 + c)^2, x)","F",0
80,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)*(d*x^3+c)^2,x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(d x^{3} + c\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)*(d*x^3 + c)^2, x)","F",0
81,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)*(d*x^3+c)^2,x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x^3 + c)^2, x)","F",0
82,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(2/3), x)","F",0
83,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(5/3),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(5/3), x)","F",0
84,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(8/3),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(8/3), x)","F",0
85,1,182,0,0.626165," ","integrate((b*x^3+a)^3/(d*x^3+c)^(13/3),x, algorithm=""maxima"")","\frac{b^{3} x^{10}}{10 \, {\left(d x^{3} + c\right)}^{\frac{10}{3}} c} - \frac{3 \, a b^{2} {\left(7 \, d - \frac{10 \, {\left(d x^{3} + c\right)}}{x^{3}}\right)} x^{10}}{70 \, {\left(d x^{3} + c\right)}^{\frac{10}{3}} c^{2}} + \frac{3 \, {\left(14 \, d^{2} - \frac{40 \, {\left(d x^{3} + c\right)} d}{x^{3}} + \frac{35 \, {\left(d x^{3} + c\right)}^{2}}{x^{6}}\right)} a^{2} b x^{10}}{140 \, {\left(d x^{3} + c\right)}^{\frac{10}{3}} c^{3}} - \frac{{\left(14 \, d^{3} - \frac{60 \, {\left(d x^{3} + c\right)} d^{2}}{x^{3}} + \frac{105 \, {\left(d x^{3} + c\right)}^{2} d}{x^{6}} - \frac{140 \, {\left(d x^{3} + c\right)}^{3}}{x^{9}}\right)} a^{3} x^{10}}{140 \, {\left(d x^{3} + c\right)}^{\frac{10}{3}} c^{4}}"," ",0,"1/10*b^3*x^10/((d*x^3 + c)^(10/3)*c) - 3/70*a*b^2*(7*d - 10*(d*x^3 + c)/x^3)*x^10/((d*x^3 + c)^(10/3)*c^2) + 3/140*(14*d^2 - 40*(d*x^3 + c)*d/x^3 + 35*(d*x^3 + c)^2/x^6)*a^2*b*x^10/((d*x^3 + c)^(10/3)*c^3) - 1/140*(14*d^3 - 60*(d*x^3 + c)*d^2/x^3 + 105*(d*x^3 + c)^2*d/x^6 - 140*(d*x^3 + c)^3/x^9)*a^3*x^10/((d*x^3 + c)^(10/3)*c^4)","A",0
86,0,0,0,0.000000," ","integrate((b*x^3+a)^(8/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}{d x^{3} + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^(8/3)/(d*x^3 + c), x)","F",0
87,0,0,0,0.000000," ","integrate((b*x^3+a)^(5/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}{d x^{3} + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^(5/3)/(d*x^3 + c), x)","F",0
88,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{d x^{3} + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/(d*x^3 + c), x)","F",0
89,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*(d*x^3 + c)), x)","F",0
90,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(d x^{3} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(4/3)*(d*x^3 + c)), x)","F",0
91,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{7}{3}} {\left(d x^{3} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(7/3)*(d*x^3 + c)), x)","F",0
92,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(10/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{10}{3}} {\left(d x^{3} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(10/3)*(d*x^3 + c)), x)","F",0
93,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{d x^{3} + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)/(d*x^3 + c), x)","F",0
94,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/(d*x^3 + c), x)","F",0
95,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(d x^{3} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*(d*x^3 + c)), x)","F",0
96,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{5}{3}} {\left(d x^{3} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(5/3)*(d*x^3 + c)), x)","F",0
97,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(8/3)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{8}{3}} {\left(d x^{3} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(8/3)*(d*x^3 + c)), x)","F",0
98,0,0,0,0.000000," ","integrate((b*x^3+a)^(8/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}{{\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(8/3)/(d*x^3 + c)^2, x)","F",0
99,0,0,0,0.000000," ","integrate((b*x^3+a)^(5/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}{{\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(5/3)/(d*x^3 + c)^2, x)","F",0
100,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{{\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/(d*x^3 + c)^2, x)","F",0
101,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*(d*x^3 + c)^2), x)","F",0
102,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(4/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(4/3)*(d*x^3 + c)^2), x)","F",0
103,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{7}{3}} {\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(7/3)*(d*x^3 + c)^2), x)","F",0
104,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{{\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)/(d*x^3 + c)^2, x)","F",0
105,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{{\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/(d*x^3 + c)^2, x)","F",0
106,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*(d*x^3 + c)^2), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{5}{3}} {\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(5/3)*(d*x^3 + c)^2), x)","F",0
108,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(8/3)/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{8}{3}} {\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(8/3)*(d*x^3 + c)^2), x)","F",0
109,0,0,0,0.000000," ","integrate((b*x^3+a)^(14/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{14}{3}}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(14/3)/(d*x^3 + c)^3, x)","F",0
110,0,0,0,0.000000," ","integrate((b*x^3+a)^(11/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{11}{3}}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(11/3)/(d*x^3 + c)^3, x)","F",0
111,0,0,0,0.000000," ","integrate((b*x^3+a)^(8/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(8/3)/(d*x^3 + c)^3, x)","F",0
112,0,0,0,0.000000," ","integrate((b*x^3+a)^(5/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(5/3)/(d*x^3 + c)^3, x)","F",0
113,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/(d*x^3 + c)^3, x)","F",0
114,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*(d*x^3 + c)^3), x)","F",0
115,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(4/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(4/3)*(d*x^3 + c)^3), x)","F",0
116,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{7}{3}} {\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(7/3)*(d*x^3 + c)^3), x)","F",0
117,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)/(d*x^3 + c)^3, x)","F",0
118,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/(d*x^3 + c)^3, x)","F",0
119,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*(d*x^3 + c)^3), x)","F",0
120,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{5}{3}} {\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(5/3)*(d*x^3 + c)^3), x)","F",0
121,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(8/3)/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{8}{3}} {\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(8/3)*(d*x^3 + c)^3), x)","F",0
122,0,0,0,0.000000," ","integrate((b*x^3+a)^(7/4)/(d*x^3+c)^(37/12),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{7}{4}}}{{\left(d x^{3} + c\right)}^{\frac{37}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(7/4)/(d*x^3 + c)^(37/12), x)","F",0
123,0,0,0,0.000000," ","integrate((b*x^3+a)^(5/4)/(d*x^3+c)^(31/12),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{5}{4}}}{{\left(d x^{3} + c\right)}^{\frac{31}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(5/4)/(d*x^3 + c)^(31/12), x)","F",0
124,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/4)/(d*x^3+c)^(25/12),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{3}{4}}}{{\left(d x^{3} + c\right)}^{\frac{25}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/4)/(d*x^3 + c)^(25/12), x)","F",0
125,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/4)/(d*x^3+c)^(19/12),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{4}}}{{\left(d x^{3} + c\right)}^{\frac{19}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/4)/(d*x^3 + c)^(19/12), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/4)/(d*x^3+c)^(13/12),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{4}} {\left(d x^{3} + c\right)}^{\frac{13}{12}}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/4)*(d*x^3 + c)^(13/12)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(3/4)/(d*x^3+c)^(7/12),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{3}{4}} {\left(d x^{3} + c\right)}^{\frac{7}{12}}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(3/4)*(d*x^3 + c)^(7/12)), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/4)/(d*x^3+c)^(1/12),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{5}{4}} {\left(d x^{3} + c\right)}^{\frac{1}{12}}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(5/4)*(d*x^3 + c)^(1/12)), x)","F",0
129,0,0,0,0.000000," ","integrate((d*x^3+c)^(5/12)/(b*x^3+a)^(7/4),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{5}{12}}}{{\left(b x^{3} + a\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(5/12)/(b*x^3 + a)^(7/4), x)","F",0
130,0,0,0,0.000000," ","integrate((d*x^3+c)^(11/12)/(b*x^3+a)^(9/4),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{11}{12}}}{{\left(b x^{3} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(11/12)/(b*x^3 + a)^(9/4), x)","F",0
131,0,0,0,0.000000," ","integrate((d*x^3+c)^(17/12)/(b*x^3+a)^(11/4),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{17}{12}}}{{\left(b x^{3} + a\right)}^{\frac{11}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(17/12)/(b*x^3 + a)^(11/4), x)","F",0
132,0,0,0,0.000000," ","integrate((d*x^3+c)^(23/12)/(b*x^3+a)^(13/4),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{23}{12}}}{{\left(b x^{3} + a\right)}^{\frac{13}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(23/12)/(b*x^3 + a)^(13/4), x)","F",0
133,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c)^p,x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{m} {\left(d x^{3} + c\right)}^{p}\,{d x}"," ",0,"integrate((b*x^3 + a)^m*(d*x^3 + c)^p, x)","F",0
134,0,0,0,0.000000," ","integrate((b*x^3+a)^2*(d*x^3+c)^q,x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{2} {\left(d x^{3} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^3 + a)^2*(d*x^3 + c)^q, x)","F",0
135,0,0,0,0.000000," ","integrate((b*x^3+a)*(d*x^3+c)^q,x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)} {\left(d x^{3} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^3 + a)*(d*x^3 + c)^q, x)","F",0
136,0,0,0,0.000000," ","integrate((d*x^3+c)^q/(b*x^3+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{q}}{b x^{3} + a}\,{d x}"," ",0,"integrate((d*x^3 + c)^q/(b*x^3 + a), x)","F",0
137,0,0,0,0.000000," ","integrate((d*x^3+c)^q/(b*x^3+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{3} + c\right)}^{q}}{{\left(b x^{3} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^3 + c)^q/(b*x^3 + a)^2, x)","F",0
138,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c)^3,x, algorithm=""maxima"")","\int {\left(d x^{3} + c\right)}^{3} {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((d*x^3 + c)^3*(b*x^3 + a)^m, x)","F",0
139,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c)^2,x, algorithm=""maxima"")","\int {\left(d x^{3} + c\right)}^{2} {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((d*x^3 + c)^2*(b*x^3 + a)^m, x)","F",0
140,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c),x, algorithm=""maxima"")","\int {\left(d x^{3} + c\right)} {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((d*x^3 + c)*(b*x^3 + a)^m, x)","F",0
141,0,0,0,0.000000," ","integrate((b*x^3+a)^m,x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((b*x^3 + a)^m, x)","F",0
142,0,0,0,0.000000," ","integrate((b*x^3+a)^m/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{m}}{d x^{3} + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^m/(d*x^3 + c), x)","F",0
143,0,0,0,0.000000," ","integrate((b*x^3+a)^m/(d*x^3+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{m}}{{\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^m/(d*x^3 + c)^2, x)","F",0
144,0,0,0,0.000000," ","integrate((b*x^3+a)^m/(d*x^3+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{3} + a\right)}^{m}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^m/(d*x^3 + c)^3, x)","F",0
145,0,0,0,0.000000," ","integrate((b*x^3+a)^(-1-b*c/(-3*a*d+3*b*c))*(d*x^3+c)^(-1+a*d/(-3*a*d+3*b*c)),x, algorithm=""maxima"")","\int {\left(b x^{3} + a\right)}^{-\frac{b c}{3 \, {\left(b c - a d\right)}} - 1} {\left(d x^{3} + c\right)}^{\frac{a d}{3 \, {\left(b c - a d\right)}} - 1}\,{d x}"," ",0,"integrate((b*x^3 + a)^(-1/3*b*c/(b*c - a*d) - 1)*(d*x^3 + c)^(1/3*a*d/(b*c - a*d) - 1), x)","F",0
146,1,96,0,0.651056," ","integrate((b*x^4+a)*(d*x^4+c)^4,x, algorithm=""maxima"")","\frac{1}{21} \, b d^{4} x^{21} + \frac{1}{17} \, {\left(4 \, b c d^{3} + a d^{4}\right)} x^{17} + \frac{2}{13} \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} x^{13} + \frac{2}{9} \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} x^{9} + a c^{4} x + \frac{1}{5} \, {\left(b c^{4} + 4 \, a c^{3} d\right)} x^{5}"," ",0,"1/21*b*d^4*x^21 + 1/17*(4*b*c*d^3 + a*d^4)*x^17 + 2/13*(3*b*c^2*d^2 + 2*a*c*d^3)*x^13 + 2/9*(2*b*c^3*d + 3*a*c^2*d^2)*x^9 + a*c^4*x + 1/5*(b*c^4 + 4*a*c^3*d)*x^5","A",0
147,1,70,0,0.647006," ","integrate((b*x^4+a)*(d*x^4+c)^3,x, algorithm=""maxima"")","\frac{1}{17} \, b d^{3} x^{17} + \frac{1}{13} \, {\left(3 \, b c d^{2} + a d^{3}\right)} x^{13} + \frac{1}{3} \, {\left(b c^{2} d + a c d^{2}\right)} x^{9} + \frac{1}{5} \, {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{5} + a c^{3} x"," ",0,"1/17*b*d^3*x^17 + 1/13*(3*b*c*d^2 + a*d^3)*x^13 + 1/3*(b*c^2*d + a*c*d^2)*x^9 + 1/5*(b*c^3 + 3*a*c^2*d)*x^5 + a*c^3*x","A",0
148,1,48,0,0.604936," ","integrate((b*x^4+a)*(d*x^4+c)^2,x, algorithm=""maxima"")","\frac{1}{13} \, b d^{2} x^{13} + \frac{1}{9} \, {\left(2 \, b c d + a d^{2}\right)} x^{9} + \frac{1}{5} \, {\left(b c^{2} + 2 \, a c d\right)} x^{5} + a c^{2} x"," ",0,"1/13*b*d^2*x^13 + 1/9*(2*b*c*d + a*d^2)*x^9 + 1/5*(b*c^2 + 2*a*c*d)*x^5 + a*c^2*x","A",0
149,1,24,0,0.492962," ","integrate((b*x^4+a)*(d*x^4+c),x, algorithm=""maxima"")","\frac{1}{9} \, b d x^{9} + \frac{1}{5} \, {\left(b c + a d\right)} x^{5} + a c x"," ",0,"1/9*b*d*x^9 + 1/5*(b*c + a*d)*x^5 + a*c*x","A",0
150,1,212,0,1.277863," ","integrate((b*x^4+a)/(d*x^4+c),x, algorithm=""maxima"")","\frac{b x}{d} - \frac{\frac{2 \, \sqrt{2} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b c - a d\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c - a d\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{8 \, d}"," ",0,"b*x/d - 1/8*(2*sqrt(2)*(b*c - a*d)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b*c - a*d)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b*c - a*d)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b*c - a*d)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/d","A",0
151,1,236,0,1.157552," ","integrate((b*x^4+a)/(d*x^4+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b c - a d\right)} x}{4 \, {\left(c d^{2} x^{4} + c^{2} d\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(b c + 3 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b c + 3 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b c + 3 \, a d\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c + 3 \, a d\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{32 \, c d}"," ",0,"-1/4*(b*c - a*d)*x/(c*d^2*x^4 + c^2*d) + 1/32*(2*sqrt(2)*(b*c + 3*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b*c + 3*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b*c + 3*a*d)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b*c + 3*a*d)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c*d)","A",0
152,1,271,0,1.211214," ","integrate((b*x^4+a)/(d*x^4+c)^3,x, algorithm=""maxima"")","\frac{{\left(b c d + 7 \, a d^{2}\right)} x^{5} - {\left(3 \, b c^{2} - 11 \, a c d\right)} x}{32 \, {\left(c^{2} d^{3} x^{8} + 2 \, c^{3} d^{2} x^{4} + c^{4} d\right)}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(b c + 7 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b c + 7 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b c + 7 \, a d\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c + 7 \, a d\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)}}{256 \, c^{2} d}"," ",0,"1/32*((b*c*d + 7*a*d^2)*x^5 - (3*b*c^2 - 11*a*c*d)*x)/(c^2*d^3*x^8 + 2*c^3*d^2*x^4 + c^4*d) + 3/256*(2*sqrt(2)*(b*c + 7*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b*c + 7*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b*c + 7*a*d)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b*c + 7*a*d)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c^2*d)","A",0
153,1,158,0,0.546500," ","integrate((b*x^4+a)^2*(d*x^4+c)^4,x, algorithm=""maxima"")","\frac{1}{25} \, b^{2} d^{4} x^{25} + \frac{2}{21} \, {\left(2 \, b^{2} c d^{3} + a b d^{4}\right)} x^{21} + \frac{1}{17} \, {\left(6 \, b^{2} c^{2} d^{2} + 8 \, a b c d^{3} + a^{2} d^{4}\right)} x^{17} + \frac{4}{13} \, {\left(b^{2} c^{3} d + 3 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{13} + \frac{1}{9} \, {\left(b^{2} c^{4} + 8 \, a b c^{3} d + 6 \, a^{2} c^{2} d^{2}\right)} x^{9} + a^{2} c^{4} x + \frac{2}{5} \, {\left(a b c^{4} + 2 \, a^{2} c^{3} d\right)} x^{5}"," ",0,"1/25*b^2*d^4*x^25 + 2/21*(2*b^2*c*d^3 + a*b*d^4)*x^21 + 1/17*(6*b^2*c^2*d^2 + 8*a*b*c*d^3 + a^2*d^4)*x^17 + 4/13*(b^2*c^3*d + 3*a*b*c^2*d^2 + a^2*c*d^3)*x^13 + 1/9*(b^2*c^4 + 8*a*b*c^3*d + 6*a^2*c^2*d^2)*x^9 + a^2*c^4*x + 2/5*(a*b*c^4 + 2*a^2*c^3*d)*x^5","A",0
154,1,124,0,0.543767," ","integrate((b*x^4+a)^2*(d*x^4+c)^3,x, algorithm=""maxima"")","\frac{1}{21} \, b^{2} d^{3} x^{21} + \frac{1}{17} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{17} + \frac{1}{13} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{13} + \frac{1}{9} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{9} + a^{2} c^{3} x + \frac{1}{5} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{5}"," ",0,"1/21*b^2*d^3*x^21 + 1/17*(3*b^2*c*d^2 + 2*a*b*d^3)*x^17 + 1/13*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^13 + 1/9*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^9 + a^2*c^3*x + 1/5*(2*a*b*c^3 + 3*a^2*c^2*d)*x^5","A",0
155,1,82,0,0.694952," ","integrate((b*x^4+a)^2*(d*x^4+c)^2,x, algorithm=""maxima"")","\frac{1}{17} \, b^{2} d^{2} x^{17} + \frac{2}{13} \, {\left(b^{2} c d + a b d^{2}\right)} x^{13} + \frac{1}{9} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{9} + \frac{2}{5} \, {\left(a b c^{2} + a^{2} c d\right)} x^{5} + a^{2} c^{2} x"," ",0,"1/17*b^2*d^2*x^17 + 2/13*(b^2*c*d + a*b*d^2)*x^13 + 1/9*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^9 + 2/5*(a*b*c^2 + a^2*c*d)*x^5 + a^2*c^2*x","A",0
156,1,48,0,0.477886," ","integrate((b*x^4+a)^2*(d*x^4+c),x, algorithm=""maxima"")","\frac{1}{13} \, b^{2} d x^{13} + \frac{1}{9} \, {\left(b^{2} c + 2 \, a b d\right)} x^{9} + \frac{1}{5} \, {\left(2 \, a b c + a^{2} d\right)} x^{5} + a^{2} c x"," ",0,"1/13*b^2*d*x^13 + 1/9*(b^2*c + 2*a*b*d)*x^9 + 1/5*(2*a*b*c + a^2*d)*x^5 + a^2*c*x","A",0
157,1,286,0,1.285154," ","integrate((b*x^4+a)^2/(d*x^4+c),x, algorithm=""maxima"")","\frac{b^{2} d x^{5} - 5 \, {\left(b^{2} c - 2 \, a b d\right)} x}{5 \, d^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{8 \, d^{2}}"," ",0,"1/5*(b^2*d*x^5 - 5*(b^2*c - 2*a*b*d)*x)/d^2 + 1/8*(2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/d^2","A",0
158,1,319,0,1.103702," ","integrate((b*x^4+a)^2/(d*x^4+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{4 \, {\left(c d^{3} x^{4} + c^{2} d^{2}\right)}} + \frac{b^{2} x}{d^{2}} - \frac{\frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{32 \, c d^{2}}"," ",0,"1/4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(c*d^3*x^4 + c^2*d^2) + b^2*x/d^2 - 1/32*(2*sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c*d^2)","A",0
159,1,361,0,1.220443," ","integrate((b*x^4+a)^2/(d*x^4+c)^3,x, algorithm=""maxima"")","-\frac{{\left(9 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 7 \, a^{2} d^{3}\right)} x^{5} + {\left(5 \, b^{2} c^{3} + 6 \, a b c^{2} d - 11 \, a^{2} c d^{2}\right)} x}{32 \, {\left(c^{2} d^{4} x^{8} + 2 \, c^{3} d^{3} x^{4} + c^{4} d^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{256 \, c^{2} d^{2}}"," ",0,"-1/32*((9*b^2*c^2*d - 2*a*b*c*d^2 - 7*a^2*d^3)*x^5 + (5*b^2*c^3 + 6*a*b*c^2*d - 11*a^2*c*d^2)*x)/(c^2*d^4*x^8 + 2*c^3*d^3*x^4 + c^4*d^2) + 1/256*(2*sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c^2*d^2)","A",0
160,1,489,0,1.437223," ","integrate((d*x^4+c)^4/(b*x^4+a),x, algorithm=""maxima"")","\frac{45 \, b^{3} d^{4} x^{13} + 65 \, {\left(4 \, b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{9} + 117 \, {\left(6 \, b^{3} c^{2} d^{2} - 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{5} + 585 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x}{585 \, b^{4}} + \frac{\frac{2 \, \sqrt{2} {\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)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\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)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\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)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\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)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{8 \, b^{4}}"," ",0,"1/585*(45*b^3*d^4*x^13 + 65*(4*b^3*c*d^3 - a*b^2*d^4)*x^9 + 117*(6*b^3*c^2*d^2 - 4*a*b^2*c*d^3 + a^2*b*d^4)*x^5 + 585*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*x)/b^4 + 1/8*(2*sqrt(2)*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^4","A",0
161,1,385,0,1.209999," ","integrate((d*x^4+c)^3/(b*x^4+a),x, algorithm=""maxima"")","\frac{5 \, b^{2} d^{3} x^{9} + 9 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{5} + 45 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} x}{45 \, b^{3}} + \frac{\frac{2 \, \sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{8 \, b^{3}}"," ",0,"1/45*(5*b^2*d^3*x^9 + 9*(3*b^2*c*d^2 - a*b*d^3)*x^5 + 45*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*x)/b^3 + 1/8*(2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^3","A",0
162,1,287,0,1.092938," ","integrate((d*x^4+c)^2/(b*x^4+a),x, algorithm=""maxima"")","\frac{b d^{2} x^{5} + 5 \, {\left(2 \, b c d - a d^{2}\right)} x}{5 \, b^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{8 \, b^{2}}"," ",0,"1/5*(b*d^2*x^5 + 5*(2*b*c*d - a*d^2)*x)/b^2 + 1/8*(2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^2","A",0
163,1,212,0,1.126330," ","integrate((d*x^4+c)/(b*x^4+a),x, algorithm=""maxima"")","\frac{d x}{b} + \frac{\frac{2 \, \sqrt{2} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b c - a d\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c - a d\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{8 \, b}"," ",0,"d*x/b + 1/8*(2*sqrt(2)*(b*c - a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b*c - a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b*c - a*d)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b*c - a*d)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b","A",0
164,1,365,0,1.433630," ","integrate(1/(b*x^4+a)/(d*x^4+c),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{8 \, {\left(b c - a d\right)}} - \frac{\frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} d^{\frac{3}{4}} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}}} - \frac{\sqrt{2} d^{\frac{3}{4}} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}}}}{8 \, {\left(b c - a d\right)}}"," ",0,"1/8*(2*sqrt(2)*b*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(3/4)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(3/4)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/a^(3/4))/(b*c - a*d) - 1/8*(2*sqrt(2)*d*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*d*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*d^(3/4)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/c^(3/4) - sqrt(2)*d^(3/4)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/c^(3/4))/(b*c - a*d)","A",0
165,1,481,0,1.566422," ","integrate(1/(b*x^4+a)/(d*x^4+c)^2,x, algorithm=""maxima"")","-\frac{d x}{4 \, {\left({\left(b c^{2} d - a c d^{2}\right)} x^{4} + b c^{3} - a c^{2} d\right)}} + \frac{\frac{2 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{8 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{32 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}}"," ",0,"-1/4*d*x/((b*c^2*d - a*c*d^2)*x^4 + b*c^3 - a*c^2*d) + 1/8*(2*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(7/4)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(7/4)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/a^(3/4))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/32*(2*sqrt(2)*(7*b*c*d - 3*a*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(7*b*c*d - 3*a*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(7*b*c*d - 3*a*d^2)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(7*b*c*d - 3*a*d^2)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)","A",0
166,1,644,0,1.445910," ","integrate((d*x^4+c)^5/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} x}{4 \, {\left(a b^{6} x^{4} + a^{2} b^{5}\right)}} + \frac{45 \, b^{3} d^{5} x^{13} + 65 \, {\left(5 \, b^{3} c d^{4} - 2 \, a b^{2} d^{5}\right)} x^{9} + 117 \, {\left(10 \, b^{3} c^{2} d^{3} - 10 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} x^{5} + 585 \, {\left(10 \, b^{3} c^{3} d^{2} - 20 \, a b^{2} c^{2} d^{3} + 15 \, a^{2} b c d^{4} - 4 \, a^{3} d^{5}\right)} x}{585 \, b^{5}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 50 \, a^{2} b^{3} c^{3} d^{2} + 90 \, a^{3} b^{2} c^{2} d^{3} - 65 \, a^{4} b c d^{4} + 17 \, a^{5} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 50 \, a^{2} b^{3} c^{3} d^{2} + 90 \, a^{3} b^{2} c^{2} d^{3} - 65 \, a^{4} b c d^{4} + 17 \, a^{5} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 50 \, a^{2} b^{3} c^{3} d^{2} + 90 \, a^{3} b^{2} c^{2} d^{3} - 65 \, a^{4} b c d^{4} + 17 \, a^{5} d^{5}\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 50 \, a^{2} b^{3} c^{3} d^{2} + 90 \, a^{3} b^{2} c^{2} d^{3} - 65 \, a^{4} b c d^{4} + 17 \, a^{5} d^{5}\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{32 \, a b^{5}}"," ",0,"1/4*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*x/(a*b^6*x^4 + a^2*b^5) + 1/585*(45*b^3*d^5*x^13 + 65*(5*b^3*c*d^4 - 2*a*b^2*d^5)*x^9 + 117*(10*b^3*c^2*d^3 - 10*a*b^2*c*d^4 + 3*a^2*b*d^5)*x^5 + 585*(10*b^3*c^3*d^2 - 20*a*b^2*c^2*d^3 + 15*a^2*b*c*d^4 - 4*a^3*d^5)*x)/b^5 + 1/32*(2*sqrt(2)*(3*b^5*c^5 + 5*a*b^4*c^4*d - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 65*a^4*b*c*d^4 + 17*a^5*d^5)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*b^5*c^5 + 5*a*b^4*c^4*d - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 65*a^4*b*c*d^4 + 17*a^5*d^5)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*b^5*c^5 + 5*a*b^4*c^4*d - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 65*a^4*b*c*d^4 + 17*a^5*d^5)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*b^5*c^5 + 5*a*b^4*c^4*d - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 65*a^4*b*c*d^4 + 17*a^5*d^5)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^5)","A",0
167,1,521,0,1.453937," ","integrate((d*x^4+c)^4/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x}{4 \, {\left(a b^{5} x^{4} + a^{2} b^{4}\right)}} + \frac{5 \, b^{2} d^{4} x^{9} + 18 \, {\left(2 \, b^{2} c d^{3} - a b d^{4}\right)} x^{5} + 45 \, {\left(6 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x}{45 \, b^{4}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 13 \, a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 13 \, a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 13 \, a^{4} d^{4}\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 13 \, a^{4} d^{4}\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{32 \, a b^{4}}"," ",0,"1/4*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x/(a*b^5*x^4 + a^2*b^4) + 1/45*(5*b^2*d^4*x^9 + 18*(2*b^2*c*d^3 - a*b*d^4)*x^5 + 45*(6*b^2*c^2*d^2 - 8*a*b*c*d^3 + 3*a^2*d^4)*x)/b^4 + 1/32*(2*sqrt(2)*(3*b^4*c^4 + 4*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 13*a^4*d^4)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*b^4*c^4 + 4*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 13*a^4*d^4)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*b^4*c^4 + 4*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 13*a^4*d^4)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*b^4*c^4 + 4*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 13*a^4*d^4)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^4)","A",0
168,1,405,0,1.309350," ","integrate((d*x^4+c)^3/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{4 \, {\left(a b^{4} x^{4} + a^{2} b^{3}\right)}} + \frac{b d^{3} x^{5} + 5 \, {\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} x}{5 \, b^{3}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{32 \, a b^{3}}"," ",0,"1/4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x/(a*b^4*x^4 + a^2*b^3) + 1/5*(b*d^3*x^5 + 5*(3*b*c*d^2 - 2*a*d^3)*x)/b^3 + 3/32*(2*sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^3)","A",0
169,1,319,0,1.260594," ","integrate((d*x^4+c)^2/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{4 \, {\left(a b^{3} x^{4} + a^{2} b^{2}\right)}} + \frac{d^{2} x}{b^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{32 \, a b^{2}}"," ",0,"1/4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(a*b^3*x^4 + a^2*b^2) + d^2*x/b^2 + 1/32*(2*sqrt(2)*(3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^2)","A",0
170,1,236,0,1.348131," ","integrate((d*x^4+c)/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c - a d\right)} x}{4 \, {\left(a b^{2} x^{4} + a^{2} b\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, b c + a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, b c + a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, b c + a d\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b c + a d\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{32 \, a b}"," ",0,"1/4*(b*c - a*d)*x/(a*b^2*x^4 + a^2*b) + 1/32*(2*sqrt(2)*(3*b*c + a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*b*c + a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*b*c + a*d)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*b*c + a*d)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b)","A",0
171,1,470,0,1.456915," ","integrate(1/(b*x^4+a)^2/(d*x^4+c),x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(3 \, b c - 7 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, b c - 7 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, b c - 7 \, a d\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b c - 7 \, a d\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b}{32 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}} + \frac{b x}{4 \, {\left({\left(a b^{2} c - a^{2} b d\right)} x^{4} + a^{2} b c - a^{3} d\right)}} + \frac{\frac{2 \, \sqrt{2} d^{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} d^{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} d^{\frac{7}{4}} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}}} - \frac{\sqrt{2} d^{\frac{7}{4}} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}}}}{8 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"1/32*(2*sqrt(2)*(3*b*c - 7*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*b*c - 7*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*b*c - 7*a*d)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*b*c - 7*a*d)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2) + 1/4*b*x/((a*b^2*c - a^2*b*d)*x^4 + a^2*b*c - a^3*d) + 1/8*(2*sqrt(2)*d^2*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*d^2*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*d^(7/4)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/c^(3/4) - sqrt(2)*d^(7/4)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/c^(3/4))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2)","A",0
172,1,670,0,1.292470," ","integrate(1/(b*x^4+a)^2/(d*x^4+c)^2,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b^{2}}{32 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)}} + \frac{{\left(b^{2} c d + a b d^{2}\right)} x^{5} + {\left(b^{2} c^{2} + a^{2} d^{2}\right)} x}{4 \, {\left({\left(a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x^{8} + a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{4}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{d} x - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \log\left(\sqrt{d} x^{2} + \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \log\left(\sqrt{d} x^{2} - \sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{32 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)}}"," ",0,"1/32*(2*sqrt(2)*(3*b*c - 11*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*b*c - 11*a*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*b*c - 11*a*d)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*b*c - 11*a*d)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^2/(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3) + 1/4*((b^2*c*d + a*b*d^2)*x^5 + (b^2*c^2 + a^2*d^2)*x)/((a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x^8 + a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^4) + 1/32*(2*sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x + sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*arctan(1/2*sqrt(2)*(2*sqrt(d)*x - sqrt(2)*c^(1/4)*d^(1/4))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*log(sqrt(d)*x^2 + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*log(sqrt(d)*x^2 - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)","A",0
173,0,0,0,0.000000," ","integrate((-b*x^4+a)^(5/2)/(-d*x^4+c),x, algorithm=""maxima"")","-\int \frac{{\left(-b x^{4} + a\right)}^{\frac{5}{2}}}{d x^{4} - c}\,{d x}"," ",0,"-integrate((-b*x^4 + a)^(5/2)/(d*x^4 - c), x)","F",0
174,0,0,0,0.000000," ","integrate((-b*x^4+a)^(3/2)/(-d*x^4+c),x, algorithm=""maxima"")","-\int \frac{{\left(-b x^{4} + a\right)}^{\frac{3}{2}}}{d x^{4} - c}\,{d x}"," ",0,"-integrate((-b*x^4 + a)^(3/2)/(d*x^4 - c), x)","F",0
175,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(-d*x^4+c),x, algorithm=""maxima"")","-\int \frac{\sqrt{-b x^{4} + a}}{d x^{4} - c}\,{d x}"," ",0,"-integrate(sqrt(-b*x^4 + a)/(d*x^4 - c), x)","F",0
176,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/2)/(-d*x^4+c),x, algorithm=""maxima"")","-\int \frac{1}{\sqrt{-b x^{4} + a} {\left(d x^{4} - c\right)}}\,{d x}"," ",0,"-integrate(1/(sqrt(-b*x^4 + a)*(d*x^4 - c)), x)","F",0
177,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(3/2)/(-d*x^4+c),x, algorithm=""maxima"")","-\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{2}} {\left(d x^{4} - c\right)}}\,{d x}"," ",0,"-integrate(1/((-b*x^4 + a)^(3/2)*(d*x^4 - c)), x)","F",0
178,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(5/2)/(-d*x^4+c),x, algorithm=""maxima"")","-\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{5}{2}} {\left(d x^{4} - c\right)}}\,{d x}"," ",0,"-integrate(1/((-b*x^4 + a)^(5/2)*(d*x^4 - c)), x)","F",0
179,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/2)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)/(d*x^4 + c), x)","F",0
180,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/2)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{4} + a}}{d x^{4} + c}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)/(d*x^4 + c), x)","F",0
181,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/2)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b x^{4} + a} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^4 + a)*(d*x^4 + c)), x)","F",0
182,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/2)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/2)*(d*x^4 + c)), x)","F",0
183,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/2)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{2}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/2)*(d*x^4 + c)), x)","F",0
184,0,0,0,0.000000," ","integrate((-b*x^4+a)^(7/2)/(-d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{7}{2}}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(7/2)/(d*x^4 - c)^2, x)","F",0
185,0,0,0,0.000000," ","integrate((-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{5}{2}}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(5/2)/(d*x^4 - c)^2, x)","F",0
186,0,0,0,0.000000," ","integrate((-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{3}{2}}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(3/2)/(d*x^4 - c)^2, x)","F",0
187,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{4} + a}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-b*x^4 + a)/(d*x^4 - c)^2, x)","F",0
188,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-b x^{4} + a} {\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^4 + a)*(d*x^4 - c)^2), x)","F",0
189,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{2}} {\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/2)*(d*x^4 - c)^2), x)","F",0
190,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{5}{2}} {\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(5/2)*(d*x^4 - c)^2), x)","F",0
191,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/2)/(-b*c*x^4+a*c),x, algorithm=""maxima"")","-\int \frac{\sqrt{b x^{4} + a}}{b c x^{4} - a c}\,{d x}"," ",0,"-integrate(sqrt(b*x^4 + a)/(b*c*x^4 - a*c), x)","F",0
192,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(b*c*x^4+a*c),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{4} + a}}{b c x^{4} + a c}\,{d x}"," ",0,"integrate(sqrt(-b*x^4 + a)/(b*c*x^4 + a*c), x)","F",0
193,0,0,0,0.000000," ","integrate((b*x^4+a)^(7/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(7/4)/(d*x^4 + c), x)","F",0
194,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/(d*x^4 + c), x)","F",0
195,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*(d*x^4 + c)), x)","F",0
196,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*(d*x^4 + c)), x)","F",0
197,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(9/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{9}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(9/4)*(d*x^4 + c)), x)","F",0
198,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(13/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{13}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(13/4)*(d*x^4 + c)), x)","F",0
199,0,0,0,0.000000," ","integrate((b*x^4+a)^(9/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{9}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(9/4)/(d*x^4 + c), x)","F",0
200,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/(d*x^4 + c), x)","F",0
201,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/(d*x^4 + c), x)","F",0
202,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*(d*x^4 + c)), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(7/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{7}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(7/4)*(d*x^4 + c)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(11/4)/(d*x^4+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{11}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(11/4)*(d*x^4 + c)), x)","F",0
205,0,0,0,0.000000," ","integrate((b*x^4+a)^(11/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{11}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(11/4)/(d*x^4 + c)^2, x)","F",0
206,0,0,0,0.000000," ","integrate((b*x^4+a)^(7/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(7/4)/(d*x^4 + c)^2, x)","F",0
207,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/(d*x^4 + c)^2, x)","F",0
208,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*(d*x^4 + c)^2), x)","F",0
209,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*(d*x^4 + c)^2), x)","F",0
210,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(9/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{9}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(9/4)*(d*x^4 + c)^2), x)","F",0
211,0,0,0,0.000000," ","integrate((b*x^4+a)^(9/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{9}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(9/4)/(d*x^4 + c)^2, x)","F",0
212,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/(d*x^4 + c)^2, x)","F",0
213,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/(d*x^4 + c)^2, x)","F",0
214,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*(d*x^4 + c)^2), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(7/4)/(d*x^4+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{7}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(7/4)*(d*x^4 + c)^2), x)","F",0
216,0,0,0,0.000000," ","integrate(1/(x^4+1)^(1/4)/(x^4+2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{4} + 2\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^4 + 2)*(x^4 + 1)^(1/4)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(a-(a-b)*x^4)/(b*x^4+a)^(1/4),x, algorithm=""maxima"")","-\int \frac{1}{{\left({\left(a - b\right)} x^{4} - a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/(((a - b)*x^4 - a)*(b*x^4 + a)^(1/4)), x)","F",0
218,0,0,0,0.000000," ","integrate((b*x^4+a)^p*(d*x^4+c)^q,x, algorithm=""maxima"")","\int {\left(b x^{4} + a\right)}^{p} {\left(d x^{4} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + a)^p*(d*x^4 + c)^q, x)","F",0
219,0,0,0,0.000000," ","integrate((b*x^4+a)^2*(d*x^4+c)^q,x, algorithm=""maxima"")","\int {\left(b x^{4} + a\right)}^{2} {\left(d x^{4} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + a)^2*(d*x^4 + c)^q, x)","F",0
220,0,0,0,0.000000," ","integrate((b*x^4+a)*(d*x^4+c)^q,x, algorithm=""maxima"")","\int {\left(b x^{4} + a\right)} {\left(d x^{4} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + a)*(d*x^4 + c)^q, x)","F",0
221,0,0,0,0.000000," ","integrate((d*x^4+c)^q/(b*x^4+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{4} + c\right)}^{q}}{b x^{4} + a}\,{d x}"," ",0,"integrate((d*x^4 + c)^q/(b*x^4 + a), x)","F",0
222,0,0,0,0.000000," ","integrate((d*x^4+c)^q/(b*x^4+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{4} + c\right)}^{q}}{{\left(b x^{4} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^4 + c)^q/(b*x^4 + a)^2, x)","F",0
223,0,0,0,0.000000," ","integrate(1/(b*x^5+a)^(1/5)/(d*x^5+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{5} + a\right)}^{\frac{1}{5}} {\left(d x^{5} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^5 + a)^(1/5)*(d*x^5 + c)), x)","F",0
224,1,164,0,1.452799," ","integrate((c+d/x)^3*(a+b/x)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, \sqrt{a + \frac{b}{x}} x - \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{\sqrt{a}}\right)} c^{3} - 3 \, {\left(\sqrt{a} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 2 \, \sqrt{a + \frac{b}{x}}\right)} c^{2} d - \frac{2}{15} \, d^{3} {\left(\frac{3 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{2}}}{b^{2}} - \frac{5 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a}{b^{2}}\right)} - \frac{2 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} c d^{2}}{b}"," ",0,"1/2*(2*sqrt(a + b/x)*x - b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/sqrt(a))*c^3 - 3*(sqrt(a)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 2*sqrt(a + b/x))*c^2*d - 2/15*d^3*(3*(a + b/x)^(5/2)/b^2 - 5*(a + b/x)^(3/2)*a/b^2) - 2*(a + b/x)^(3/2)*c*d^2/b","A",0
225,1,126,0,1.191246," ","integrate((c+d/x)^2*(a+b/x)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, \sqrt{a + \frac{b}{x}} x - \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{\sqrt{a}}\right)} c^{2} - 2 \, {\left(\sqrt{a} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 2 \, \sqrt{a + \frac{b}{x}}\right)} c d - \frac{2 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} d^{2}}{3 \, b}"," ",0,"1/2*(2*sqrt(a + b/x)*x - b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/sqrt(a))*c^2 - 2*(sqrt(a)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 2*sqrt(a + b/x))*c*d - 2/3*(a + b/x)^(3/2)*d^2/b","A",0
226,1,106,0,1.371072," ","integrate((c+d/x)*(a+b/x)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, \sqrt{a + \frac{b}{x}} x - \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{\sqrt{a}}\right)} c - {\left(\sqrt{a} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 2 \, \sqrt{a + \frac{b}{x}}\right)} d"," ",0,"1/2*(2*sqrt(a + b/x)*x - b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/sqrt(a))*c - (sqrt(a)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 2*sqrt(a + b/x))*d","A",0
227,1,50,0,1.200980," ","integrate((a+b/x)^(1/2),x, algorithm=""maxima"")","\sqrt{a + \frac{b}{x}} x - \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{2 \, \sqrt{a}}"," ",0,"sqrt(a + b/x)*x - 1/2*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/sqrt(a)","A",0
228,0,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x),x, algorithm=""maxima"")","\int \frac{\sqrt{a + \frac{b}{x}}}{c + \frac{d}{x}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)/(c + d/x), x)","F",0
229,0,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a + \frac{b}{x}}}{{\left(c + \frac{d}{x}\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)/(c + d/x)^2, x)","F",0
230,0,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a + \frac{b}{x}}}{{\left(c + \frac{d}{x}\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)/(c + d/x)^3, x)","F",0
231,1,190,0,1.487790," ","integrate((a+b/x)^(3/2)*(c+d/x)^3,x, algorithm=""maxima"")","-\frac{6 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} c d^{2}}{5 \, b} + \frac{1}{2} \, {\left(2 \, \sqrt{a + \frac{b}{x}} a x - 3 \, \sqrt{a} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - 4 \, \sqrt{a + \frac{b}{x}} b\right)} c^{3} - {\left(3 \, a^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} + 6 \, \sqrt{a + \frac{b}{x}} a\right)} c^{2} d - \frac{2}{35} \, {\left(\frac{5 \, {\left(a + \frac{b}{x}\right)}^{\frac{7}{2}}}{b^{2}} - \frac{7 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} a}{b^{2}}\right)} d^{3}"," ",0,"-6/5*(a + b/x)^(5/2)*c*d^2/b + 1/2*(2*sqrt(a + b/x)*a*x - 3*sqrt(a)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 4*sqrt(a + b/x)*b)*c^3 - (3*a^(3/2)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 2*(a + b/x)^(3/2) + 6*sqrt(a + b/x)*a)*c^2*d - 2/35*(5*(a + b/x)^(7/2)/b^2 - 7*(a + b/x)^(5/2)*a/b^2)*d^3","A",0
232,1,152,0,1.160219," ","integrate((a+b/x)^(3/2)*(c+d/x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} d^{2}}{5 \, b} + \frac{1}{2} \, {\left(2 \, \sqrt{a + \frac{b}{x}} a x - 3 \, \sqrt{a} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - 4 \, \sqrt{a + \frac{b}{x}} b\right)} c^{2} - \frac{2}{3} \, {\left(3 \, a^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} + 6 \, \sqrt{a + \frac{b}{x}} a\right)} c d"," ",0,"-2/5*(a + b/x)^(5/2)*d^2/b + 1/2*(2*sqrt(a + b/x)*a*x - 3*sqrt(a)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 4*sqrt(a + b/x)*b)*c^2 - 2/3*(3*a^(3/2)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 2*(a + b/x)^(3/2) + 6*sqrt(a + b/x)*a)*c*d","A",0
233,1,132,0,1.325572," ","integrate((a+b/x)^(3/2)*(c+d/x),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, \sqrt{a + \frac{b}{x}} a x - 3 \, \sqrt{a} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - 4 \, \sqrt{a + \frac{b}{x}} b\right)} c - \frac{1}{3} \, {\left(3 \, a^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} + 6 \, \sqrt{a + \frac{b}{x}} a\right)} d"," ",0,"1/2*(2*sqrt(a + b/x)*a*x - 3*sqrt(a)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 4*sqrt(a + b/x)*b)*c - 1/3*(3*a^(3/2)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 2*(a + b/x)^(3/2) + 6*sqrt(a + b/x)*a)*d","A",0
234,1,63,0,1.201555," ","integrate((a+b/x)^(3/2),x, algorithm=""maxima"")","\sqrt{a + \frac{b}{x}} a x - \frac{3}{2} \, \sqrt{a} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - 2 \, \sqrt{a + \frac{b}{x}} b"," ",0,"sqrt(a + b/x)*a*x - 3/2*sqrt(a)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 2*sqrt(a + b/x)*b","A",0
235,0,0,0,0.000000," ","integrate((a+b/x)^(3/2)/(c+d/x),x, algorithm=""maxima"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}}}{c + \frac{d}{x}}\,{d x}"," ",0,"integrate((a + b/x)^(3/2)/(c + d/x), x)","F",0
236,0,0,0,0.000000," ","integrate((a+b/x)^(3/2)/(c+d/x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}}}{{\left(c + \frac{d}{x}\right)}^{2}}\,{d x}"," ",0,"integrate((a + b/x)^(3/2)/(c + d/x)^2, x)","F",0
237,0,0,0,0.000000," ","integrate((a+b/x)^(3/2)/(c+d/x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}}}{{\left(c + \frac{d}{x}\right)}^{3}}\,{d x}"," ",0,"integrate((a + b/x)^(3/2)/(c + d/x)^3, x)","F",0
238,1,219,0,1.206921," ","integrate((a+b/x)^(5/2)*(c+d/x)^3,x, algorithm=""maxima"")","-\frac{6 \, {\left(a + \frac{b}{x}\right)}^{\frac{7}{2}} c d^{2}}{7 \, b} + \frac{1}{6} \, {\left(6 \, \sqrt{a + \frac{b}{x}} a^{2} x - 15 \, a^{\frac{3}{2}} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - 4 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} b - 24 \, \sqrt{a + \frac{b}{x}} a b\right)} c^{3} - \frac{1}{5} \, {\left(15 \, a^{\frac{5}{2}} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 6 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} + 10 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a + 30 \, \sqrt{a + \frac{b}{x}} a^{2}\right)} c^{2} d - \frac{2}{63} \, {\left(\frac{7 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{2}}}{b^{2}} - \frac{9 \, {\left(a + \frac{b}{x}\right)}^{\frac{7}{2}} a}{b^{2}}\right)} d^{3}"," ",0,"-6/7*(a + b/x)^(7/2)*c*d^2/b + 1/6*(6*sqrt(a + b/x)*a^2*x - 15*a^(3/2)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 4*(a + b/x)^(3/2)*b - 24*sqrt(a + b/x)*a*b)*c^3 - 1/5*(15*a^(5/2)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 6*(a + b/x)^(5/2) + 10*(a + b/x)^(3/2)*a + 30*sqrt(a + b/x)*a^2)*c^2*d - 2/63*(7*(a + b/x)^(9/2)/b^2 - 9*(a + b/x)^(7/2)*a/b^2)*d^3","A",0
239,1,181,0,1.250752," ","integrate((a+b/x)^(5/2)*(c+d/x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a + \frac{b}{x}\right)}^{\frac{7}{2}} d^{2}}{7 \, b} + \frac{1}{6} \, {\left(6 \, \sqrt{a + \frac{b}{x}} a^{2} x - 15 \, a^{\frac{3}{2}} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - 4 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} b - 24 \, \sqrt{a + \frac{b}{x}} a b\right)} c^{2} - \frac{2}{15} \, {\left(15 \, a^{\frac{5}{2}} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 6 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} + 10 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a + 30 \, \sqrt{a + \frac{b}{x}} a^{2}\right)} c d"," ",0,"-2/7*(a + b/x)^(7/2)*d^2/b + 1/6*(6*sqrt(a + b/x)*a^2*x - 15*a^(3/2)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 4*(a + b/x)^(3/2)*b - 24*sqrt(a + b/x)*a*b)*c^2 - 2/15*(15*a^(5/2)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 6*(a + b/x)^(5/2) + 10*(a + b/x)^(3/2)*a + 30*sqrt(a + b/x)*a^2)*c*d","A",0
240,1,161,0,1.505408," ","integrate((a+b/x)^(5/2)*(c+d/x),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(6 \, \sqrt{a + \frac{b}{x}} a^{2} x - 15 \, a^{\frac{3}{2}} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - 4 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} b - 24 \, \sqrt{a + \frac{b}{x}} a b\right)} c - \frac{1}{15} \, {\left(15 \, a^{\frac{5}{2}} \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) + 6 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} + 10 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a + 30 \, \sqrt{a + \frac{b}{x}} a^{2}\right)} d"," ",0,"1/6*(6*sqrt(a + b/x)*a^2*x - 15*a^(3/2)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 4*(a + b/x)^(3/2)*b - 24*sqrt(a + b/x)*a*b)*c - 1/15*(15*a^(5/2)*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) + 6*(a + b/x)^(5/2) + 10*(a + b/x)^(3/2)*a + 30*sqrt(a + b/x)*a^2)*d","A",0
241,1,78,0,1.249001," ","integrate((a+b/x)^(5/2),x, algorithm=""maxima"")","\sqrt{a + \frac{b}{x}} a^{2} x - \frac{5}{2} \, a^{\frac{3}{2}} b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right) - \frac{2}{3} \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} b - 4 \, \sqrt{a + \frac{b}{x}} a b"," ",0,"sqrt(a + b/x)*a^2*x - 5/2*a^(3/2)*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a))) - 2/3*(a + b/x)^(3/2)*b - 4*sqrt(a + b/x)*a*b","A",0
242,0,0,0,0.000000," ","integrate((a+b/x)^(5/2)/(c+d/x),x, algorithm=""maxima"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}}}{c + \frac{d}{x}}\,{d x}"," ",0,"integrate((a + b/x)^(5/2)/(c + d/x), x)","F",0
243,0,0,0,0.000000," ","integrate((a+b/x)^(5/2)/(c+d/x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}}}{{\left(c + \frac{d}{x}\right)}^{2}}\,{d x}"," ",0,"integrate((a + b/x)^(5/2)/(c + d/x)^2, x)","F",0
244,0,0,0,0.000000," ","integrate((a+b/x)^(5/2)/(c+d/x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}}}{{\left(c + \frac{d}{x}\right)}^{3}}\,{d x}"," ",0,"integrate((a + b/x)^(5/2)/(c + d/x)^3, x)","F",0
245,1,166,0,1.326812," ","integrate((c+d/x)^3/(a+b/x)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, c^{3} {\left(\frac{2 \, \sqrt{a + \frac{b}{x}} b}{{\left(a + \frac{b}{x}\right)} a - a^{2}} + \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}}\right)} - \frac{2}{3} \, d^{3} {\left(\frac{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}}}{b^{2}} - \frac{3 \, \sqrt{a + \frac{b}{x}} a}{b^{2}}\right)} - \frac{3 \, c^{2} d \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{6 \, \sqrt{a + \frac{b}{x}} c d^{2}}{b}"," ",0,"1/2*c^3*(2*sqrt(a + b/x)*b/((a + b/x)*a - a^2) + b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(3/2)) - 2/3*d^3*((a + b/x)^(3/2)/b^2 - 3*sqrt(a + b/x)*a/b^2) - 3*c^2*d*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/sqrt(a) - 6*sqrt(a + b/x)*c*d^2/b","A",0
246,1,129,0,1.243720," ","integrate((c+d/x)^2/(a+b/x)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, c^{2} {\left(\frac{2 \, \sqrt{a + \frac{b}{x}} b}{{\left(a + \frac{b}{x}\right)} a - a^{2}} + \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}}\right)} - \frac{2 \, c d \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{2 \, \sqrt{a + \frac{b}{x}} d^{2}}{b}"," ",0,"1/2*c^2*(2*sqrt(a + b/x)*b/((a + b/x)*a - a^2) + b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(3/2)) - 2*c*d*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/sqrt(a) - 2*sqrt(a + b/x)*d^2/b","B",0
247,1,109,0,1.297922," ","integrate((c+d/x)/(a+b/x)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, c {\left(\frac{2 \, \sqrt{a + \frac{b}{x}} b}{{\left(a + \frac{b}{x}\right)} a - a^{2}} + \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}}\right)} - \frac{d \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{\sqrt{a}}"," ",0,"1/2*c*(2*sqrt(a + b/x)*b/((a + b/x)*a - a^2) + b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(3/2)) - d*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/sqrt(a)","B",0
248,1,67,0,1.207942," ","integrate(1/(a+b/x)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a + \frac{b}{x}} b}{{\left(a + \frac{b}{x}\right)} a - a^{2}} + \frac{b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{2 \, a^{\frac{3}{2}}}"," ",0,"sqrt(a + b/x)*b/((a + b/x)*a - a^2) + 1/2*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(3/2)","A",0
249,0,0,0,0.000000," ","integrate(1/(c+d/x)/(a+b/x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a + \frac{b}{x}} {\left(c + \frac{d}{x}\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x)*(c + d/x)), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(c+d/x)^2/(a+b/x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a + \frac{b}{x}} {\left(c + \frac{d}{x}\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x)*(c + d/x)^2), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(c+d/x)^3/(a+b/x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a + \frac{b}{x}} {\left(c + \frac{d}{x}\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x)*(c + d/x)^3), x)","F",0
252,1,200,0,1.258635," ","integrate((c+d/x)^3/(a+b/x)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, c^{3} {\left(\frac{2 \, {\left(3 \, {\left(a + \frac{b}{x}\right)} b - 2 \, a b\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{2} - \sqrt{a + \frac{b}{x}} a^{3}} + \frac{3 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}}\right)} - 3 \, c^{2} d {\left(\frac{\log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2}{\sqrt{a + \frac{b}{x}} a}\right)} - 2 \, d^{3} {\left(\frac{\sqrt{a + \frac{b}{x}}}{b^{2}} + \frac{a}{\sqrt{a + \frac{b}{x}} b^{2}}\right)} + \frac{6 \, c d^{2}}{\sqrt{a + \frac{b}{x}} b}"," ",0,"1/2*c^3*(2*(3*(a + b/x)*b - 2*a*b)/((a + b/x)^(3/2)*a^2 - sqrt(a + b/x)*a^3) + 3*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(5/2)) - 3*c^2*d*(log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(3/2) + 2/(sqrt(a + b/x)*a)) - 2*d^3*(sqrt(a + b/x)/b^2 + a/(sqrt(a + b/x)*b^2)) + 6*c*d^2/(sqrt(a + b/x)*b)","A",0
253,1,164,0,1.157219," ","integrate((c+d/x)^2/(a+b/x)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, c^{2} {\left(\frac{2 \, {\left(3 \, {\left(a + \frac{b}{x}\right)} b - 2 \, a b\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{2} - \sqrt{a + \frac{b}{x}} a^{3}} + \frac{3 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}}\right)} - 2 \, c d {\left(\frac{\log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2}{\sqrt{a + \frac{b}{x}} a}\right)} + \frac{2 \, d^{2}}{\sqrt{a + \frac{b}{x}} b}"," ",0,"1/2*c^2*(2*(3*(a + b/x)*b - 2*a*b)/((a + b/x)^(3/2)*a^2 - sqrt(a + b/x)*a^3) + 3*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(5/2)) - 2*c*d*(log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(3/2) + 2/(sqrt(a + b/x)*a)) + 2*d^2/(sqrt(a + b/x)*b)","A",0
254,1,144,0,1.373565," ","integrate((c+d/x)/(a+b/x)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, c {\left(\frac{2 \, {\left(3 \, {\left(a + \frac{b}{x}\right)} b - 2 \, a b\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{2} - \sqrt{a + \frac{b}{x}} a^{3}} + \frac{3 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}}\right)} - d {\left(\frac{\log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2}{\sqrt{a + \frac{b}{x}} a}\right)}"," ",0,"1/2*c*(2*(3*(a + b/x)*b - 2*a*b)/((a + b/x)^(3/2)*a^2 - sqrt(a + b/x)*a^3) + 3*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(5/2)) - d*(log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(3/2) + 2/(sqrt(a + b/x)*a))","B",0
255,1,85,0,1.182761," ","integrate(1/(a+b/x)^(3/2),x, algorithm=""maxima"")","\frac{3 \, {\left(a + \frac{b}{x}\right)} b - 2 \, a b}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{2} - \sqrt{a + \frac{b}{x}} a^{3}} + \frac{3 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{2 \, a^{\frac{5}{2}}}"," ",0,"(3*(a + b/x)*b - 2*a*b)/((a + b/x)^(3/2)*a^2 - sqrt(a + b/x)*a^3) + 3/2*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(5/2)","A",0
256,0,0,0,0.000000," ","integrate(1/(a+b/x)^(3/2)/(c+d/x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} {\left(c + \frac{d}{x}\right)}}\,{d x}"," ",0,"integrate(1/((a + b/x)^(3/2)*(c + d/x)), x)","F",0
257,0,0,0,0.000000," ","integrate(1/(a+b/x)^(3/2)/(c+d/x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} {\left(c + \frac{d}{x}\right)}^{2}}\,{d x}"," ",0,"integrate(1/((a + b/x)^(3/2)*(c + d/x)^2), x)","F",0
258,0,0,0,0.000000," ","integrate(1/(a+b/x)^(3/2)/(c+d/x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} {\left(c + \frac{d}{x}\right)}^{3}}\,{d x}"," ",0,"integrate(1/((a + b/x)^(3/2)*(c + d/x)^3), x)","F",0
259,1,228,0,1.340692," ","integrate((c+d/x)^3/(a+b/x)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, c^{3} {\left(\frac{2 \, {\left(15 \, {\left(a + \frac{b}{x}\right)}^{2} b - 10 \, {\left(a + \frac{b}{x}\right)} a b - 2 \, a^{2} b\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} a^{3} - {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{4}} + \frac{15 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{7}{2}}}\right)} - c^{2} d {\left(\frac{3 \, \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}} + \frac{2 \, {\left(4 \, a + \frac{3 \, b}{x}\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{2}}\right)} + \frac{2}{3} \, d^{3} {\left(\frac{3}{\sqrt{a + \frac{b}{x}} b^{2}} - \frac{a}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} b^{2}}\right)} + \frac{2 \, c d^{2}}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} b}"," ",0,"1/6*c^3*(2*(15*(a + b/x)^2*b - 10*(a + b/x)*a*b - 2*a^2*b)/((a + b/x)^(5/2)*a^3 - (a + b/x)^(3/2)*a^4) + 15*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(7/2)) - c^2*d*(3*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(5/2) + 2*(4*a + 3*b/x)/((a + b/x)^(3/2)*a^2)) + 2/3*d^3*(3/(sqrt(a + b/x)*b^2) - a/((a + b/x)^(3/2)*b^2)) + 2*c*d^2/((a + b/x)^(3/2)*b)","A",0
260,1,190,0,1.307945," ","integrate((c+d/x)^2/(a+b/x)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, c^{2} {\left(\frac{2 \, {\left(15 \, {\left(a + \frac{b}{x}\right)}^{2} b - 10 \, {\left(a + \frac{b}{x}\right)} a b - 2 \, a^{2} b\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} a^{3} - {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{4}} + \frac{15 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{7}{2}}}\right)} - \frac{2}{3} \, c d {\left(\frac{3 \, \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}} + \frac{2 \, {\left(4 \, a + \frac{3 \, b}{x}\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{2}}\right)} + \frac{2 \, d^{2}}{3 \, {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} b}"," ",0,"1/6*c^2*(2*(15*(a + b/x)^2*b - 10*(a + b/x)*a*b - 2*a^2*b)/((a + b/x)^(5/2)*a^3 - (a + b/x)^(3/2)*a^4) + 15*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(7/2)) - 2/3*c*d*(3*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(5/2) + 2*(4*a + 3*b/x)/((a + b/x)^(3/2)*a^2)) + 2/3*d^2/((a + b/x)^(3/2)*b)","A",0
261,1,170,0,1.251263," ","integrate((c+d/x)/(a+b/x)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, c {\left(\frac{2 \, {\left(15 \, {\left(a + \frac{b}{x}\right)}^{2} b - 10 \, {\left(a + \frac{b}{x}\right)} a b - 2 \, a^{2} b\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} a^{3} - {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{4}} + \frac{15 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{7}{2}}}\right)} - \frac{1}{3} \, d {\left(\frac{3 \, \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}} + \frac{2 \, {\left(4 \, a + \frac{3 \, b}{x}\right)}}{{\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{2}}\right)}"," ",0,"1/6*c*(2*(15*(a + b/x)^2*b - 10*(a + b/x)*a*b - 2*a^2*b)/((a + b/x)^(5/2)*a^3 - (a + b/x)^(3/2)*a^4) + 15*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(7/2)) - 1/3*d*(3*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(5/2) + 2*(4*a + 3*b/x)/((a + b/x)^(3/2)*a^2))","A",0
262,1,101,0,1.290902," ","integrate(1/(a+b/x)^(5/2),x, algorithm=""maxima"")","\frac{15 \, {\left(a + \frac{b}{x}\right)}^{2} b - 10 \, {\left(a + \frac{b}{x}\right)} a b - 2 \, a^{2} b}{3 \, {\left({\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} a^{3} - {\left(a + \frac{b}{x}\right)}^{\frac{3}{2}} a^{4}\right)}} + \frac{5 \, b \log\left(\frac{\sqrt{a + \frac{b}{x}} - \sqrt{a}}{\sqrt{a + \frac{b}{x}} + \sqrt{a}}\right)}{2 \, a^{\frac{7}{2}}}"," ",0,"1/3*(15*(a + b/x)^2*b - 10*(a + b/x)*a*b - 2*a^2*b)/((a + b/x)^(5/2)*a^3 - (a + b/x)^(3/2)*a^4) + 5/2*b*log((sqrt(a + b/x) - sqrt(a))/(sqrt(a + b/x) + sqrt(a)))/a^(7/2)","A",0
263,0,0,0,0.000000," ","integrate(1/(a+b/x)^(5/2)/(c+d/x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} {\left(c + \frac{d}{x}\right)}}\,{d x}"," ",0,"integrate(1/((a + b/x)^(5/2)*(c + d/x)), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(a+b/x)^(5/2)/(c+d/x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} {\left(c + \frac{d}{x}\right)}^{2}}\,{d x}"," ",0,"integrate(1/((a + b/x)^(5/2)*(c + d/x)^2), x)","F",0
265,0,0,0,0.000000," ","integrate(1/(a+b/x)^(5/2)/(c+d/x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a + \frac{b}{x}\right)}^{\frac{5}{2}} {\left(c + \frac{d}{x}\right)}^{3}}\,{d x}"," ",0,"integrate(1/((a + b/x)^(5/2)*(c + d/x)^3), x)","F",0
266,0,0,0,0.000000," ","integrate((c+d/x)^(1/2)*(a+b/x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a + \frac{b}{x}} \sqrt{c + \frac{d}{x}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)*sqrt(c + d/x), x)","F",0
267,0,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a + \frac{b}{x}}}{\sqrt{c + \frac{d}{x}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)/sqrt(c + d/x), x)","F",0
268,0,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a + \frac{b}{x}}}{{\left(c + \frac{d}{x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)/(c + d/x)^(3/2), x)","F",0
269,0,0,0,0.000000," ","integrate((a+b/x)^p*(c+d/x)^q,x, algorithm=""maxima"")","\int {\left(a + \frac{b}{x}\right)}^{p} {\left(c + \frac{d}{x}\right)}^{q}\,{d x}"," ",0,"integrate((a + b/x)^p*(c + d/x)^q, x)","F",0
270,1,33,0,1.304710," ","integrate((a+b/x^2)/(c+d/x^2),x, algorithm=""maxima"")","\frac{a x}{c} + \frac{{\left(b c - a d\right)} \arctan\left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d} c}"," ",0,"a*x/c + (b*c - a*d)*arctan(c*x/sqrt(c*d))/(sqrt(c*d)*c)","A",0
271,0,0,0,0.000000," ","integrate((c+d/x^2)^(1/2)*(a+b/x^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a + \frac{b}{x^{2}}} \sqrt{c + \frac{d}{x^{2}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^2)*sqrt(c + d/x^2), x)","F",0
272,0,0,0,0.000000," ","integrate((a+b/x^2)^(1/2)/(c+d/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a + \frac{b}{x^{2}}}}{\sqrt{c + \frac{d}{x^{2}}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^2)/sqrt(c + d/x^2), x)","F",0
273,0,0,0,0.000000," ","integrate((a+b/x^2)^(1/2)/(c+d/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a + \frac{b}{x^{2}}}}{{\left(c + \frac{d}{x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^2)/(c + d/x^2)^(3/2), x)","F",0
274,0,0,0,0.000000," ","integrate((a+b/x^2)^p*(c+d/x^2)^q,x, algorithm=""maxima"")","\int {\left(a + \frac{b}{x^{2}}\right)}^{p} {\left(c + \frac{d}{x^{2}}\right)}^{q}\,{d x}"," ",0,"integrate((a + b/x^2)^p*(c + d/x^2)^q, x)","F",0
275,1,128,0,1.294335," ","integrate((a+b/x^3)/(c+d/x^3),x, algorithm=""maxima"")","\frac{a x}{c} + \frac{\sqrt{3} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{d}{c}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{c}\right)^{\frac{1}{3}}}\right)}{3 \, c^{2} \left(\frac{d}{c}\right)^{\frac{2}{3}}} - \frac{{\left(b c - a d\right)} \log\left(x^{2} - x \left(\frac{d}{c}\right)^{\frac{1}{3}} + \left(\frac{d}{c}\right)^{\frac{2}{3}}\right)}{6 \, c^{2} \left(\frac{d}{c}\right)^{\frac{2}{3}}} + \frac{{\left(b c - a d\right)} \log\left(x + \left(\frac{d}{c}\right)^{\frac{1}{3}}\right)}{3 \, c^{2} \left(\frac{d}{c}\right)^{\frac{2}{3}}}"," ",0,"a*x/c + 1/3*sqrt(3)*(b*c - a*d)*arctan(1/3*sqrt(3)*(2*x - (d/c)^(1/3))/(d/c)^(1/3))/(c^2*(d/c)^(2/3)) - 1/6*(b*c - a*d)*log(x^2 - x*(d/c)^(1/3) + (d/c)^(2/3))/(c^2*(d/c)^(2/3)) + 1/3*(b*c - a*d)*log(x + (d/c)^(1/3))/(c^2*(d/c)^(2/3))","A",0
276,1,47,0,0.638405," ","integrate((a+b*x^(1/2))/(c+d*x^(1/2)),x, algorithm=""maxima"")","\frac{b d x - 2 \, {\left(b c - a d\right)} \sqrt{x}}{d^{2}} + \frac{2 \, {\left(b c^{2} - a c d\right)} \log\left(d \sqrt{x} + c\right)}{d^{3}}"," ",0,"(b*d*x - 2*(b*c - a*d)*sqrt(x))/d^2 + 2*(b*c^2 - a*c*d)*log(d*sqrt(x) + c)/d^3","A",0
277,1,20,0,0.550243," ","integrate((-1+x^(1/3))/(1+x^(1/3)),x, algorithm=""maxima"")","x - 3 \, x^{\frac{2}{3}} + 6 \, x^{\frac{1}{3}} - 6 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"x - 3*x^(2/3) + 6*x^(1/3) - 6*log(x^(1/3) + 1)","A",0
278,1,23,0,0.564292," ","integrate((1+x^(2/3))/(-1+x^(2/3)),x, algorithm=""maxima"")","x + 6 \, x^{\frac{1}{3}} - 3 \, \log\left(x^{\frac{1}{3}} + 1\right) + 3 \, \log\left(x^{\frac{1}{3}} - 1\right)"," ",0,"x + 6*x^(1/3) - 3*log(x^(1/3) + 1) + 3*log(x^(1/3) - 1)","A",0
279,1,71,0,1.134810," ","integrate((-16+x^(3/4))/(16+x^(3/4)),x, algorithm=""maxima"")","\frac{256}{3} \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(-\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} - x^{\frac{1}{4}}\right)}\right) - \frac{128}{3} \cdot 2^{\frac{1}{3}} \log\left(4 \cdot 2^{\frac{2}{3}} - 2 \cdot 2^{\frac{1}{3}} x^{\frac{1}{4}} + \sqrt{x}\right) + \frac{256}{3} \cdot 2^{\frac{1}{3}} \log\left(2 \cdot 2^{\frac{1}{3}} + x^{\frac{1}{4}}\right) + x - 128 \, x^{\frac{1}{4}}"," ",0,"256/3*sqrt(3)*2^(1/3)*arctan(-1/6*sqrt(3)*2^(2/3)*(2^(1/3) - x^(1/4))) - 128/3*2^(1/3)*log(4*2^(2/3) - 2*2^(1/3)*x^(1/4) + sqrt(x)) + 256/3*2^(1/3)*log(2*2^(1/3) + x^(1/4)) + x - 128*x^(1/4)","A",0
280,1,22,0,0.558382," ","integrate((1+1/x^(1/3))/(-1+1/x^(1/3)),x, algorithm=""maxima"")","-x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log\left(x^{\frac{1}{3}} - 1\right)"," ",0,"-x - 3*x^(2/3) - 6*x^(1/3) - 6*log(x^(1/3) - 1)","A",0
281,0,0,0,0.000000," ","integrate((a-b*x^n)^(3/2)*(a+b*x^n)^(3/2),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{\frac{3}{2}} {\left(-b x^{n} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2)*(-b*x^n + a)^(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate((a-b*x^n)^(1/2)*(a+b*x^n)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b x^{n} + a} \sqrt{-b x^{n} + a}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*sqrt(-b*x^n + a), x)","F",0
283,0,0,0,0.000000," ","integrate((a-b*x^n)^p*(a+b*x^n)^p,x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
284,1,186,0,0.614390," ","integrate((a+b*x^n)*(c+d*x^n)^4,x, algorithm=""maxima"")","a c^{4} x + \frac{b d^{4} x^{5 \, n + 1}}{5 \, n + 1} + \frac{4 \, b c d^{3} x^{4 \, n + 1}}{4 \, n + 1} + \frac{a d^{4} x^{4 \, n + 1}}{4 \, n + 1} + \frac{6 \, b c^{2} d^{2} x^{3 \, n + 1}}{3 \, n + 1} + \frac{4 \, a c d^{3} x^{3 \, n + 1}}{3 \, n + 1} + \frac{4 \, b c^{3} d x^{2 \, n + 1}}{2 \, n + 1} + \frac{6 \, a c^{2} d^{2} x^{2 \, n + 1}}{2 \, n + 1} + \frac{b c^{4} x^{n + 1}}{n + 1} + \frac{4 \, a c^{3} d x^{n + 1}}{n + 1}"," ",0,"a*c^4*x + b*d^4*x^(5*n + 1)/(5*n + 1) + 4*b*c*d^3*x^(4*n + 1)/(4*n + 1) + a*d^4*x^(4*n + 1)/(4*n + 1) + 6*b*c^2*d^2*x^(3*n + 1)/(3*n + 1) + 4*a*c*d^3*x^(3*n + 1)/(3*n + 1) + 4*b*c^3*d*x^(2*n + 1)/(2*n + 1) + 6*a*c^2*d^2*x^(2*n + 1)/(2*n + 1) + b*c^4*x^(n + 1)/(n + 1) + 4*a*c^3*d*x^(n + 1)/(n + 1)","A",0
285,1,140,0,0.502596," ","integrate((a+b*x^n)*(c+d*x^n)^3,x, algorithm=""maxima"")","a c^{3} x + \frac{b d^{3} x^{4 \, n + 1}}{4 \, n + 1} + \frac{3 \, b c d^{2} x^{3 \, n + 1}}{3 \, n + 1} + \frac{a d^{3} x^{3 \, n + 1}}{3 \, n + 1} + \frac{3 \, b c^{2} d x^{2 \, n + 1}}{2 \, n + 1} + \frac{3 \, a c d^{2} x^{2 \, n + 1}}{2 \, n + 1} + \frac{b c^{3} x^{n + 1}}{n + 1} + \frac{3 \, a c^{2} d x^{n + 1}}{n + 1}"," ",0,"a*c^3*x + b*d^3*x^(4*n + 1)/(4*n + 1) + 3*b*c*d^2*x^(3*n + 1)/(3*n + 1) + a*d^3*x^(3*n + 1)/(3*n + 1) + 3*b*c^2*d*x^(2*n + 1)/(2*n + 1) + 3*a*c*d^2*x^(2*n + 1)/(2*n + 1) + b*c^3*x^(n + 1)/(n + 1) + 3*a*c^2*d*x^(n + 1)/(n + 1)","A",0
286,1,94,0,0.439651," ","integrate((a+b*x^n)*(c+d*x^n)^2,x, algorithm=""maxima"")","a c^{2} x + \frac{b d^{2} x^{3 \, n + 1}}{3 \, n + 1} + \frac{2 \, b c d x^{2 \, n + 1}}{2 \, n + 1} + \frac{a d^{2} x^{2 \, n + 1}}{2 \, n + 1} + \frac{b c^{2} x^{n + 1}}{n + 1} + \frac{2 \, a c d x^{n + 1}}{n + 1}"," ",0,"a*c^2*x + b*d^2*x^(3*n + 1)/(3*n + 1) + 2*b*c*d*x^(2*n + 1)/(2*n + 1) + a*d^2*x^(2*n + 1)/(2*n + 1) + b*c^2*x^(n + 1)/(n + 1) + 2*a*c*d*x^(n + 1)/(n + 1)","A",0
287,1,48,0,0.510448," ","integrate((a+b*x^n)*(c+d*x^n),x, algorithm=""maxima"")","a c x + \frac{b d x^{2 \, n + 1}}{2 \, n + 1} + \frac{b c x^{n + 1}}{n + 1} + \frac{a d x^{n + 1}}{n + 1}"," ",0,"a*c*x + b*d*x^(2*n + 1)/(2*n + 1) + b*c*x^(n + 1)/(n + 1) + a*d*x^(n + 1)/(n + 1)","A",0
288,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n),x, algorithm=""maxima"")","-{\left(b c - a d\right)} \int \frac{1}{d^{2} x^{n} + c d}\,{d x} + \frac{b x}{d}"," ",0,"-(b*c - a*d)*integrate(1/(d^2*x^n + c*d), x) + b*x/d","F",0
289,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","{\left(a d {\left(n - 1\right)} + b c\right)} \int \frac{1}{c d^{2} n x^{n} + c^{2} d n}\,{d x} - \frac{{\left(b c - a d\right)} x}{c d^{2} n x^{n} + c^{2} d n}"," ",0,"(a*d*(n - 1) + b*c)*integrate(1/(c*d^2*n*x^n + c^2*d*n), x) - (b*c - a*d)*x/(c*d^2*n*x^n + c^2*d*n)","F",0
290,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n)^3,x, algorithm=""maxima"")","{\left({\left(2 \, n^{2} - 3 \, n + 1\right)} a d + b c {\left(n - 1\right)}\right)} \int \frac{1}{2 \, {\left(c^{2} d^{2} n^{2} x^{n} + c^{3} d n^{2}\right)}}\,{d x} + \frac{{\left(a d^{2} {\left(2 \, n - 1\right)} + b c d\right)} x x^{n} + {\left(a c d {\left(3 \, n - 1\right)} - b c^{2} {\left(n - 1\right)}\right)} x}{2 \, {\left(c^{2} d^{3} n^{2} x^{2 \, n} + 2 \, c^{3} d^{2} n^{2} x^{n} + c^{4} d n^{2}\right)}}"," ",0,"((2*n^2 - 3*n + 1)*a*d + b*c*(n - 1))*integrate(1/2/(c^2*d^2*n^2*x^n + c^3*d*n^2), x) + 1/2*((a*d^2*(2*n - 1) + b*c*d)*x*x^n + (a*c*d*(3*n - 1) - b*c^2*(n - 1))*x)/(c^2*d^3*n^2*x^(2*n) + 2*c^3*d^2*n^2*x^n + c^4*d*n^2)","F",0
291,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n)^4,x, algorithm=""maxima"")","{\left({\left(2 \, n^{2} - 3 \, n + 1\right)} b c + {\left(6 \, n^{3} - 11 \, n^{2} + 6 \, n - 1\right)} a d\right)} \int \frac{1}{6 \, {\left(c^{3} d^{2} n^{3} x^{n} + c^{4} d n^{3}\right)}}\,{d x} + \frac{{\left({\left(6 \, n^{2} - 5 \, n + 1\right)} a d^{3} + b c d^{2} {\left(2 \, n - 1\right)}\right)} x x^{2 \, n} + {\left({\left(15 \, n^{2} - 11 \, n + 2\right)} a c d^{2} + b c^{2} d {\left(5 \, n - 2\right)}\right)} x x^{n} - {\left({\left(2 \, n^{2} - 3 \, n + 1\right)} b c^{3} - {\left(11 \, n^{2} - 6 \, n + 1\right)} a c^{2} d\right)} x}{6 \, {\left(c^{3} d^{4} n^{3} x^{3 \, n} + 3 \, c^{4} d^{3} n^{3} x^{2 \, n} + 3 \, c^{5} d^{2} n^{3} x^{n} + c^{6} d n^{3}\right)}}"," ",0,"((2*n^2 - 3*n + 1)*b*c + (6*n^3 - 11*n^2 + 6*n - 1)*a*d)*integrate(1/6/(c^3*d^2*n^3*x^n + c^4*d*n^3), x) + 1/6*(((6*n^2 - 5*n + 1)*a*d^3 + b*c*d^2*(2*n - 1))*x*x^(2*n) + ((15*n^2 - 11*n + 2)*a*c*d^2 + b*c^2*d*(5*n - 2))*x*x^n - ((2*n^2 - 3*n + 1)*b*c^3 - (11*n^2 - 6*n + 1)*a*c^2*d)*x)/(c^3*d^4*n^3*x^(3*n) + 3*c^4*d^3*n^3*x^(2*n) + 3*c^5*d^2*n^3*x^n + c^6*d*n^3)","F",0
292,1,242,0,0.622418," ","integrate((a+b*x^n)^2*(d+e*x^n)^3,x, algorithm=""maxima"")","a^{2} d^{3} x + \frac{b^{2} e^{3} x^{5 \, n + 1}}{5 \, n + 1} + \frac{3 \, b^{2} d e^{2} x^{4 \, n + 1}}{4 \, n + 1} + \frac{2 \, a b e^{3} x^{4 \, n + 1}}{4 \, n + 1} + \frac{3 \, b^{2} d^{2} e x^{3 \, n + 1}}{3 \, n + 1} + \frac{6 \, a b d e^{2} x^{3 \, n + 1}}{3 \, n + 1} + \frac{a^{2} e^{3} x^{3 \, n + 1}}{3 \, n + 1} + \frac{b^{2} d^{3} x^{2 \, n + 1}}{2 \, n + 1} + \frac{6 \, a b d^{2} e x^{2 \, n + 1}}{2 \, n + 1} + \frac{3 \, a^{2} d e^{2} x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a b d^{3} x^{n + 1}}{n + 1} + \frac{3 \, a^{2} d^{2} e x^{n + 1}}{n + 1}"," ",0,"a^2*d^3*x + b^2*e^3*x^(5*n + 1)/(5*n + 1) + 3*b^2*d*e^2*x^(4*n + 1)/(4*n + 1) + 2*a*b*e^3*x^(4*n + 1)/(4*n + 1) + 3*b^2*d^2*e*x^(3*n + 1)/(3*n + 1) + 6*a*b*d*e^2*x^(3*n + 1)/(3*n + 1) + a^2*e^3*x^(3*n + 1)/(3*n + 1) + b^2*d^3*x^(2*n + 1)/(2*n + 1) + 6*a*b*d^2*e*x^(2*n + 1)/(2*n + 1) + 3*a^2*d*e^2*x^(2*n + 1)/(2*n + 1) + 2*a*b*d^3*x^(n + 1)/(n + 1) + 3*a^2*d^2*e*x^(n + 1)/(n + 1)","A",0
293,1,168,0,0.604440," ","integrate((a+b*x^n)^2*(d+e*x^n)^2,x, algorithm=""maxima"")","a^{2} d^{2} x + \frac{b^{2} e^{2} x^{4 \, n + 1}}{4 \, n + 1} + \frac{2 \, b^{2} d e x^{3 \, n + 1}}{3 \, n + 1} + \frac{2 \, a b e^{2} x^{3 \, n + 1}}{3 \, n + 1} + \frac{b^{2} d^{2} x^{2 \, n + 1}}{2 \, n + 1} + \frac{4 \, a b d e x^{2 \, n + 1}}{2 \, n + 1} + \frac{a^{2} e^{2} x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a b d^{2} x^{n + 1}}{n + 1} + \frac{2 \, a^{2} d e x^{n + 1}}{n + 1}"," ",0,"a^2*d^2*x + b^2*e^2*x^(4*n + 1)/(4*n + 1) + 2*b^2*d*e*x^(3*n + 1)/(3*n + 1) + 2*a*b*e^2*x^(3*n + 1)/(3*n + 1) + b^2*d^2*x^(2*n + 1)/(2*n + 1) + 4*a*b*d*e*x^(2*n + 1)/(2*n + 1) + a^2*e^2*x^(2*n + 1)/(2*n + 1) + 2*a*b*d^2*x^(n + 1)/(n + 1) + 2*a^2*d*e*x^(n + 1)/(n + 1)","A",0
294,1,94,0,0.632637," ","integrate((a+b*x^n)^2*(c+d*x^n),x, algorithm=""maxima"")","a^{2} c x + \frac{b^{2} d x^{3 \, n + 1}}{3 \, n + 1} + \frac{b^{2} c x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a b d x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a b c x^{n + 1}}{n + 1} + \frac{a^{2} d x^{n + 1}}{n + 1}"," ",0,"a^2*c*x + b^2*d*x^(3*n + 1)/(3*n + 1) + b^2*c*x^(2*n + 1)/(2*n + 1) + 2*a*b*d*x^(2*n + 1)/(2*n + 1) + 2*a*b*c*x^(n + 1)/(n + 1) + a^2*d*x^(n + 1)/(n + 1)","A",0
295,0,0,0,0.000000," ","integrate((a+b*x^n)^2/(c+d*x^n),x, algorithm=""maxima"")","{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \int \frac{1}{d^{3} x^{n} + c d^{2}}\,{d x} + \frac{b^{2} d x x^{n} - {\left(b^{2} c {\left(n + 1\right)} - 2 \, a b d {\left(n + 1\right)}\right)} x}{d^{2} {\left(n + 1\right)}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*integrate(1/(d^3*x^n + c*d^2), x) + (b^2*d*x*x^n - (b^2*c*(n + 1) - 2*a*b*d*(n + 1))*x)/(d^2*(n + 1))","F",0
296,0,0,0,0.000000," ","integrate((a+b*x^n)^2/(c+d*x^n)^2,x, algorithm=""maxima"")","-{\left(b^{2} c^{2} {\left(n + 1\right)} - a^{2} d^{2} {\left(n - 1\right)} - 2 \, a b c d\right)} \int \frac{1}{c d^{3} n x^{n} + c^{2} d^{2} n}\,{d x} + \frac{b^{2} c d n x x^{n} + {\left(b^{2} c^{2} {\left(n + 1\right)} - 2 \, a b c d + a^{2} d^{2}\right)} x}{c d^{3} n x^{n} + c^{2} d^{2} n}"," ",0,"-(b^2*c^2*(n + 1) - a^2*d^2*(n - 1) - 2*a*b*c*d)*integrate(1/(c*d^3*n*x^n + c^2*d^2*n), x) + (b^2*c*d*n*x*x^n + (b^2*c^2*(n + 1) - 2*a*b*c*d + a^2*d^2)*x)/(c*d^3*n*x^n + c^2*d^2*n)","F",0
297,0,0,0,0.000000," ","integrate((a+b*x^n)^2/(c+d*x^n)^3,x, algorithm=""maxima"")","{\left({\left(2 \, n^{2} - 3 \, n + 1\right)} a^{2} d^{2} + b^{2} c^{2} {\left(n + 1\right)} + 2 \, a b c d {\left(n - 1\right)}\right)} \int \frac{1}{2 \, {\left(c^{2} d^{3} n^{2} x^{n} + c^{3} d^{2} n^{2}\right)}}\,{d x} - \frac{{\left(b^{2} c^{2} d {\left(2 \, n + 1\right)} - a^{2} d^{3} {\left(2 \, n - 1\right)} - 2 \, a b c d^{2}\right)} x x^{n} - {\left(a^{2} c d^{2} {\left(3 \, n - 1\right)} - b^{2} c^{3} {\left(n + 1\right)} - 2 \, a b c^{2} d {\left(n - 1\right)}\right)} x}{2 \, {\left(c^{2} d^{4} n^{2} x^{2 \, n} + 2 \, c^{3} d^{3} n^{2} x^{n} + c^{4} d^{2} n^{2}\right)}}"," ",0,"((2*n^2 - 3*n + 1)*a^2*d^2 + b^2*c^2*(n + 1) + 2*a*b*c*d*(n - 1))*integrate(1/2/(c^2*d^3*n^2*x^n + c^3*d^2*n^2), x) - 1/2*((b^2*c^2*d*(2*n + 1) - a^2*d^3*(2*n - 1) - 2*a*b*c*d^2)*x*x^n - (a^2*c*d^2*(3*n - 1) - b^2*c^3*(n + 1) - 2*a*b*c^2*d*(n - 1))*x)/(c^2*d^4*n^2*x^(2*n) + 2*c^3*d^3*n^2*x^n + c^4*d^2*n^2)","F",0
298,0,0,0,0.000000," ","integrate((c+d*x^n)^4/(a+b*x^n),x, algorithm=""maxima"")","{\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)} \int \frac{1}{b^{5} x^{n} + a b^{4}}\,{d x} + \frac{{\left(2 \, n^{2} + 3 \, n + 1\right)} b^{3} d^{4} x x^{3 \, n} + {\left(4 \, {\left(3 \, n^{2} + 4 \, n + 1\right)} b^{3} c d^{3} - {\left(3 \, n^{2} + 4 \, n + 1\right)} a b^{2} d^{4}\right)} x x^{2 \, n} + {\left(6 \, {\left(6 \, n^{2} + 5 \, n + 1\right)} b^{3} c^{2} d^{2} - 4 \, {\left(6 \, n^{2} + 5 \, n + 1\right)} a b^{2} c d^{3} + {\left(6 \, n^{2} + 5 \, n + 1\right)} a^{2} b d^{4}\right)} x x^{n} + {\left(4 \, {\left(6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1\right)} b^{3} c^{3} d - 6 \, {\left(6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1\right)} a b^{2} c^{2} d^{2} + 4 \, {\left(6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1\right)} a^{2} b c d^{3} - {\left(6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1\right)} a^{3} d^{4}\right)} x}{{\left(6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1\right)} b^{4}}"," ",0,"(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)*integrate(1/(b^5*x^n + a*b^4), x) + ((2*n^2 + 3*n + 1)*b^3*d^4*x*x^(3*n) + (4*(3*n^2 + 4*n + 1)*b^3*c*d^3 - (3*n^2 + 4*n + 1)*a*b^2*d^4)*x*x^(2*n) + (6*(6*n^2 + 5*n + 1)*b^3*c^2*d^2 - 4*(6*n^2 + 5*n + 1)*a*b^2*c*d^3 + (6*n^2 + 5*n + 1)*a^2*b*d^4)*x*x^n + (4*(6*n^3 + 11*n^2 + 6*n + 1)*b^3*c^3*d - 6*(6*n^3 + 11*n^2 + 6*n + 1)*a*b^2*c^2*d^2 + 4*(6*n^3 + 11*n^2 + 6*n + 1)*a^2*b*c*d^3 - (6*n^3 + 11*n^2 + 6*n + 1)*a^3*d^4)*x)/((6*n^3 + 11*n^2 + 6*n + 1)*b^4)","F",0
299,0,0,0,0.000000," ","integrate((c+d*x^n)^3/(a+b*x^n),x, algorithm=""maxima"")","{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \int \frac{1}{b^{4} x^{n} + a b^{3}}\,{d x} + \frac{b^{2} d^{3} {\left(n + 1\right)} x x^{2 \, n} + {\left(3 \, b^{2} c d^{2} {\left(2 \, n + 1\right)} - a b d^{3} {\left(2 \, n + 1\right)}\right)} x x^{n} + {\left(3 \, {\left(2 \, n^{2} + 3 \, n + 1\right)} b^{2} c^{2} d - 3 \, {\left(2 \, n^{2} + 3 \, n + 1\right)} a b c d^{2} + {\left(2 \, n^{2} + 3 \, n + 1\right)} a^{2} d^{3}\right)} x}{{\left(2 \, n^{2} + 3 \, n + 1\right)} b^{3}}"," ",0,"(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*integrate(1/(b^4*x^n + a*b^3), x) + (b^2*d^3*(n + 1)*x*x^(2*n) + (3*b^2*c*d^2*(2*n + 1) - a*b*d^3*(2*n + 1))*x*x^n + (3*(2*n^2 + 3*n + 1)*b^2*c^2*d - 3*(2*n^2 + 3*n + 1)*a*b*c*d^2 + (2*n^2 + 3*n + 1)*a^2*d^3)*x)/((2*n^2 + 3*n + 1)*b^3)","F",0
300,0,0,0,0.000000," ","integrate((c+d*x^n)^2/(a+b*x^n),x, algorithm=""maxima"")","{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \int \frac{1}{b^{3} x^{n} + a b^{2}}\,{d x} + \frac{b d^{2} x x^{n} + {\left(2 \, b c d {\left(n + 1\right)} - a d^{2} {\left(n + 1\right)}\right)} x}{b^{2} {\left(n + 1\right)}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*integrate(1/(b^3*x^n + a*b^2), x) + (b*d^2*x*x^n + (2*b*c*d*(n + 1) - a*d^2*(n + 1))*x)/(b^2*(n + 1))","F",0
301,0,0,0,0.000000," ","integrate((c+d*x^n)/(a+b*x^n),x, algorithm=""maxima"")","{\left(b c - a d\right)} \int \frac{1}{b^{2} x^{n} + a b}\,{d x} + \frac{d x}{b}"," ",0,"(b*c - a*d)*integrate(1/(b^2*x^n + a*b), x) + d*x/b","F",0
302,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/(c+d*x^n),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*(d*x^n + c)), x)","F",0
303,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/(c+d*x^n)^2,x, algorithm=""maxima"")","b^{2} \int \frac{1}{a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{n}}\,{d x} - {\left(b c d {\left(2 \, n - 1\right)} - a d^{2} {\left(n - 1\right)}\right)} \int \frac{1}{b^{2} c^{4} n - 2 \, a b c^{3} d n + a^{2} c^{2} d^{2} n + {\left(b^{2} c^{3} d n - 2 \, a b c^{2} d^{2} n + a^{2} c d^{3} n\right)} x^{n}}\,{d x} - \frac{d x}{b c^{3} n - a c^{2} d n + {\left(b c^{2} d n - a c d^{2} n\right)} x^{n}}"," ",0,"b^2*integrate(1/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^n), x) - (b*c*d*(2*n - 1) - a*d^2*(n - 1))*integrate(1/(b^2*c^4*n - 2*a*b*c^3*d*n + a^2*c^2*d^2*n + (b^2*c^3*d*n - 2*a*b*c^2*d^2*n + a^2*c*d^3*n)*x^n), x) - d*x/(b*c^3*n - a*c^2*d*n + (b*c^2*d*n - a*c*d^2*n)*x^n)","F",0
304,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/(c+d*x^n)^3,x, algorithm=""maxima"")","-b^{3} \int -\frac{1}{a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{n}}\,{d x} + {\left({\left(6 \, n^{2} - 5 \, n + 1\right)} b^{2} c^{2} d - 2 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} a b c d^{2} + {\left(2 \, n^{2} - 3 \, n + 1\right)} a^{2} d^{3}\right)} \int -\frac{1}{2 \, {\left(b^{3} c^{6} n^{2} - 3 \, a b^{2} c^{5} d n^{2} + 3 \, a^{2} b c^{4} d^{2} n^{2} - a^{3} c^{3} d^{3} n^{2} + {\left(b^{3} c^{5} d n^{2} - 3 \, a b^{2} c^{4} d^{2} n^{2} + 3 \, a^{2} b c^{3} d^{3} n^{2} - a^{3} c^{2} d^{4} n^{2}\right)} x^{n}\right)}}\,{d x} - \frac{{\left(b c d^{2} {\left(4 \, n - 1\right)} - a d^{3} {\left(2 \, n - 1\right)}\right)} x x^{n} + {\left(b c^{2} d {\left(5 \, n - 1\right)} - a c d^{2} {\left(3 \, n - 1\right)}\right)} x}{2 \, {\left(b^{2} c^{6} n^{2} - 2 \, a b c^{5} d n^{2} + a^{2} c^{4} d^{2} n^{2} + {\left(b^{2} c^{4} d^{2} n^{2} - 2 \, a b c^{3} d^{3} n^{2} + a^{2} c^{2} d^{4} n^{2}\right)} x^{2 \, n} + 2 \, {\left(b^{2} c^{5} d n^{2} - 2 \, a b c^{4} d^{2} n^{2} + a^{2} c^{3} d^{3} n^{2}\right)} x^{n}\right)}}"," ",0,"-b^3*integrate(-1/(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3 + (b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^n), x) + ((6*n^2 - 5*n + 1)*b^2*c^2*d - 2*(3*n^2 - 4*n + 1)*a*b*c*d^2 + (2*n^2 - 3*n + 1)*a^2*d^3)*integrate(-1/2/(b^3*c^6*n^2 - 3*a*b^2*c^5*d*n^2 + 3*a^2*b*c^4*d^2*n^2 - a^3*c^3*d^3*n^2 + (b^3*c^5*d*n^2 - 3*a*b^2*c^4*d^2*n^2 + 3*a^2*b*c^3*d^3*n^2 - a^3*c^2*d^4*n^2)*x^n), x) - 1/2*((b*c*d^2*(4*n - 1) - a*d^3*(2*n - 1))*x*x^n + (b*c^2*d*(5*n - 1) - a*c*d^2*(3*n - 1))*x)/(b^2*c^6*n^2 - 2*a*b*c^5*d*n^2 + a^2*c^4*d^2*n^2 + (b^2*c^4*d^2*n^2 - 2*a*b*c^3*d^3*n^2 + a^2*c^2*d^4*n^2)*x^(2*n) + 2*(b^2*c^5*d*n^2 - 2*a*b*c^4*d^2*n^2 + a^2*c^3*d^3*n^2)*x^n)","F",0
305,0,0,0,0.000000," ","integrate((c+d*x^n)^4/(a+b*x^n)^2,x, algorithm=""maxima"")","-{\left(a^{4} d^{4} {\left(3 \, n + 1\right)} - 4 \, a^{3} b c d^{3} {\left(2 \, n + 1\right)} + 6 \, a^{2} b^{2} c^{2} d^{2} {\left(n + 1\right)} - b^{4} c^{4} {\left(n - 1\right)} - 4 \, a b^{3} c^{3} d\right)} \int \frac{1}{a b^{5} n x^{n} + a^{2} b^{4} n}\,{d x} + \frac{{\left(n^{2} + n\right)} a b^{3} d^{4} x x^{3 \, n} + {\left(4 \, {\left(2 \, n^{2} + n\right)} a b^{3} c d^{3} - {\left(3 \, n^{2} + n\right)} a^{2} b^{2} d^{4}\right)} x x^{2 \, n} + {\left(6 \, {\left(2 \, n^{3} + 3 \, n^{2} + n\right)} a b^{3} c^{2} d^{2} - 4 \, {\left(4 \, n^{3} + 4 \, n^{2} + n\right)} a^{2} b^{2} c d^{3} + {\left(6 \, n^{3} + 5 \, n^{2} + n\right)} a^{3} b d^{4}\right)} x x^{n} + {\left({\left(2 \, n^{2} + 3 \, n + 1\right)} b^{4} c^{4} - 4 \, {\left(2 \, n^{2} + 3 \, n + 1\right)} a b^{3} c^{3} d + 6 \, {\left(2 \, n^{3} + 5 \, n^{2} + 4 \, n + 1\right)} a^{2} b^{2} c^{2} d^{2} - 4 \, {\left(4 \, n^{3} + 8 \, n^{2} + 5 \, n + 1\right)} a^{3} b c d^{3} + {\left(6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1\right)} a^{4} d^{4}\right)} x}{{\left(2 \, n^{3} + 3 \, n^{2} + n\right)} a b^{5} x^{n} + {\left(2 \, n^{3} + 3 \, n^{2} + n\right)} a^{2} b^{4}}"," ",0,"-(a^4*d^4*(3*n + 1) - 4*a^3*b*c*d^3*(2*n + 1) + 6*a^2*b^2*c^2*d^2*(n + 1) - b^4*c^4*(n - 1) - 4*a*b^3*c^3*d)*integrate(1/(a*b^5*n*x^n + a^2*b^4*n), x) + ((n^2 + n)*a*b^3*d^4*x*x^(3*n) + (4*(2*n^2 + n)*a*b^3*c*d^3 - (3*n^2 + n)*a^2*b^2*d^4)*x*x^(2*n) + (6*(2*n^3 + 3*n^2 + n)*a*b^3*c^2*d^2 - 4*(4*n^3 + 4*n^2 + n)*a^2*b^2*c*d^3 + (6*n^3 + 5*n^2 + n)*a^3*b*d^4)*x*x^n + ((2*n^2 + 3*n + 1)*b^4*c^4 - 4*(2*n^2 + 3*n + 1)*a*b^3*c^3*d + 6*(2*n^3 + 5*n^2 + 4*n + 1)*a^2*b^2*c^2*d^2 - 4*(4*n^3 + 8*n^2 + 5*n + 1)*a^3*b*c*d^3 + (6*n^3 + 11*n^2 + 6*n + 1)*a^4*d^4)*x)/((2*n^3 + 3*n^2 + n)*a*b^5*x^n + (2*n^3 + 3*n^2 + n)*a^2*b^4)","F",0
306,0,0,0,0.000000," ","integrate((c+d*x^n)^3/(a+b*x^n)^2,x, algorithm=""maxima"")","{\left(a^{3} d^{3} {\left(2 \, n + 1\right)} - 3 \, a^{2} b c d^{2} {\left(n + 1\right)} + b^{3} c^{3} {\left(n - 1\right)} + 3 \, a b^{2} c^{2} d\right)} \int \frac{1}{a b^{4} n x^{n} + a^{2} b^{3} n}\,{d x} + \frac{a b^{2} d^{3} n x x^{2 \, n} + {\left(3 \, {\left(n^{2} + n\right)} a b^{2} c d^{2} - {\left(2 \, n^{2} + n\right)} a^{2} b d^{3}\right)} x x^{n} + {\left(3 \, {\left(n^{2} + 2 \, n + 1\right)} a^{2} b c d^{2} - {\left(2 \, n^{2} + 3 \, n + 1\right)} a^{3} d^{3} + b^{3} c^{3} {\left(n + 1\right)} - 3 \, a b^{2} c^{2} d {\left(n + 1\right)}\right)} x}{{\left(n^{2} + n\right)} a b^{4} x^{n} + {\left(n^{2} + n\right)} a^{2} b^{3}}"," ",0,"(a^3*d^3*(2*n + 1) - 3*a^2*b*c*d^2*(n + 1) + b^3*c^3*(n - 1) + 3*a*b^2*c^2*d)*integrate(1/(a*b^4*n*x^n + a^2*b^3*n), x) + (a*b^2*d^3*n*x*x^(2*n) + (3*(n^2 + n)*a*b^2*c*d^2 - (2*n^2 + n)*a^2*b*d^3)*x*x^n + (3*(n^2 + 2*n + 1)*a^2*b*c*d^2 - (2*n^2 + 3*n + 1)*a^3*d^3 + b^3*c^3*(n + 1) - 3*a*b^2*c^2*d*(n + 1))*x)/((n^2 + n)*a*b^4*x^n + (n^2 + n)*a^2*b^3)","F",0
307,0,0,0,0.000000," ","integrate((c+d*x^n)^2/(a+b*x^n)^2,x, algorithm=""maxima"")","-{\left(a^{2} d^{2} {\left(n + 1\right)} - b^{2} c^{2} {\left(n - 1\right)} - 2 \, a b c d\right)} \int \frac{1}{a b^{3} n x^{n} + a^{2} b^{2} n}\,{d x} + \frac{a b d^{2} n x x^{n} + {\left(a^{2} d^{2} {\left(n + 1\right)} + b^{2} c^{2} - 2 \, a b c d\right)} x}{a b^{3} n x^{n} + a^{2} b^{2} n}"," ",0,"-(a^2*d^2*(n + 1) - b^2*c^2*(n - 1) - 2*a*b*c*d)*integrate(1/(a*b^3*n*x^n + a^2*b^2*n), x) + (a*b*d^2*n*x*x^n + (a^2*d^2*(n + 1) + b^2*c^2 - 2*a*b*c*d)*x)/(a*b^3*n*x^n + a^2*b^2*n)","F",0
308,0,0,0,0.000000," ","integrate((c+d*x^n)/(a+b*x^n)^2,x, algorithm=""maxima"")","{\left(b c {\left(n - 1\right)} + a d\right)} \int \frac{1}{a b^{2} n x^{n} + a^{2} b n}\,{d x} + \frac{{\left(b c - a d\right)} x}{a b^{2} n x^{n} + a^{2} b n}"," ",0,"(b*c*(n - 1) + a*d)*integrate(1/(a*b^2*n*x^n + a^2*b*n), x) + (b*c - a*d)*x/(a*b^2*n*x^n + a^2*b*n)","F",0
309,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""maxima"")","d^{2} \int \frac{1}{b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{n}}\,{d x} - {\left(a b d {\left(2 \, n - 1\right)} - b^{2} c {\left(n - 1\right)}\right)} \int \frac{1}{a^{2} b^{2} c^{2} n - 2 \, a^{3} b c d n + a^{4} d^{2} n + {\left(a b^{3} c^{2} n - 2 \, a^{2} b^{2} c d n + a^{3} b d^{2} n\right)} x^{n}}\,{d x} + \frac{b x}{a^{2} b c n - a^{3} d n + {\left(a b^{2} c n - a^{2} b d n\right)} x^{n}}"," ",0,"d^2*integrate(1/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^n), x) - (a*b*d*(2*n - 1) - b^2*c*(n - 1))*integrate(1/(a^2*b^2*c^2*n - 2*a^3*b*c*d*n + a^4*d^2*n + (a*b^3*c^2*n - 2*a^2*b^2*c*d*n + a^3*b*d^2*n)*x^n), x) + b*x/(a^2*b*c*n - a^3*d*n + (a*b^2*c*n - a^2*b*d*n)*x^n)","F",0
310,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/(c+d*x^n)^2,x, algorithm=""maxima"")","{\left(a b^{2} d {\left(3 \, n - 1\right)} - b^{3} c {\left(n - 1\right)}\right)} \int -\frac{1}{a^{2} b^{3} c^{3} n - 3 \, a^{3} b^{2} c^{2} d n + 3 \, a^{4} b c d^{2} n - a^{5} d^{3} n + {\left(a b^{4} c^{3} n - 3 \, a^{2} b^{3} c^{2} d n + 3 \, a^{3} b^{2} c d^{2} n - a^{4} b d^{3} n\right)} x^{n}}\,{d x} - {\left(b c d^{2} {\left(3 \, n - 1\right)} - a d^{3} {\left(n - 1\right)}\right)} \int -\frac{1}{b^{3} c^{5} n - 3 \, a b^{2} c^{4} d n + 3 \, a^{2} b c^{3} d^{2} n - a^{3} c^{2} d^{3} n + {\left(b^{3} c^{4} d n - 3 \, a b^{2} c^{3} d^{2} n + 3 \, a^{2} b c^{2} d^{3} n - a^{3} c d^{4} n\right)} x^{n}}\,{d x} + \frac{{\left(b^{2} c d + a b d^{2}\right)} x x^{n} + {\left(b^{2} c^{2} + a^{2} d^{2}\right)} x}{a^{2} b^{2} c^{4} n - 2 \, a^{3} b c^{3} d n + a^{4} c^{2} d^{2} n + {\left(a b^{3} c^{3} d n - 2 \, a^{2} b^{2} c^{2} d^{2} n + a^{3} b c d^{3} n\right)} x^{2 \, n} + {\left(a b^{3} c^{4} n - a^{2} b^{2} c^{3} d n - a^{3} b c^{2} d^{2} n + a^{4} c d^{3} n\right)} x^{n}}"," ",0,"(a*b^2*d*(3*n - 1) - b^3*c*(n - 1))*integrate(-1/(a^2*b^3*c^3*n - 3*a^3*b^2*c^2*d*n + 3*a^4*b*c*d^2*n - a^5*d^3*n + (a*b^4*c^3*n - 3*a^2*b^3*c^2*d*n + 3*a^3*b^2*c*d^2*n - a^4*b*d^3*n)*x^n), x) - (b*c*d^2*(3*n - 1) - a*d^3*(n - 1))*integrate(-1/(b^3*c^5*n - 3*a*b^2*c^4*d*n + 3*a^2*b*c^3*d^2*n - a^3*c^2*d^3*n + (b^3*c^4*d*n - 3*a*b^2*c^3*d^2*n + 3*a^2*b*c^2*d^3*n - a^3*c*d^4*n)*x^n), x) + ((b^2*c*d + a*b*d^2)*x*x^n + (b^2*c^2 + a^2*d^2)*x)/(a^2*b^2*c^4*n - 2*a^3*b*c^3*d*n + a^4*c^2*d^2*n + (a*b^3*c^3*d*n - 2*a^2*b^2*c^2*d^2*n + a^3*b*c*d^3*n)*x^(2*n) + (a*b^3*c^4*n - a^2*b^2*c^3*d*n - a^3*b*c^2*d^2*n + a^4*c*d^3*n)*x^n)","F",0
311,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/(c+d*x^n)^3,x, algorithm=""maxima"")","{\left({\left(12 \, n^{2} - 7 \, n + 1\right)} b^{2} c^{2} d^{2} - 2 \, {\left(4 \, n^{2} - 5 \, n + 1\right)} a b c d^{3} + {\left(2 \, n^{2} - 3 \, n + 1\right)} a^{2} d^{4}\right)} \int \frac{1}{2 \, {\left(b^{4} c^{7} n^{2} - 4 \, a b^{3} c^{6} d n^{2} + 6 \, a^{2} b^{2} c^{5} d^{2} n^{2} - 4 \, a^{3} b c^{4} d^{3} n^{2} + a^{4} c^{3} d^{4} n^{2} + {\left(b^{4} c^{6} d n^{2} - 4 \, a b^{3} c^{5} d^{2} n^{2} + 6 \, a^{2} b^{2} c^{4} d^{3} n^{2} - 4 \, a^{3} b c^{3} d^{4} n^{2} + a^{4} c^{2} d^{5} n^{2}\right)} x^{n}\right)}}\,{d x} - {\left(a b^{3} d {\left(4 \, n - 1\right)} - b^{4} c {\left(n - 1\right)}\right)} \int \frac{1}{a^{2} b^{4} c^{4} n - 4 \, a^{3} b^{3} c^{3} d n + 6 \, a^{4} b^{2} c^{2} d^{2} n - 4 \, a^{5} b c d^{3} n + a^{6} d^{4} n + {\left(a b^{5} c^{4} n - 4 \, a^{2} b^{4} c^{3} d n + 6 \, a^{3} b^{3} c^{2} d^{2} n - 4 \, a^{4} b^{2} c d^{3} n + a^{5} b d^{4} n\right)} x^{n}}\,{d x} + \frac{{\left(a b^{2} c d^{3} {\left(6 \, n - 1\right)} - a^{2} b d^{4} {\left(2 \, n - 1\right)} + 2 \, b^{3} c^{2} d^{2} n\right)} x x^{2 \, n} + {\left(a b^{2} c^{2} d^{2} {\left(7 \, n - 1\right)} - a^{3} d^{4} {\left(2 \, n - 1\right)} + 4 \, b^{3} c^{3} d n + 3 \, a^{2} b c d^{3} n\right)} x x^{n} + {\left(a^{2} b c^{2} d^{2} {\left(7 \, n - 1\right)} - a^{3} c d^{3} {\left(3 \, n - 1\right)} + 2 \, b^{3} c^{4} n\right)} x}{2 \, {\left(a^{2} b^{3} c^{7} n^{2} - 3 \, a^{3} b^{2} c^{6} d n^{2} + 3 \, a^{4} b c^{5} d^{2} n^{2} - a^{5} c^{4} d^{3} n^{2} + {\left(a b^{4} c^{5} d^{2} n^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} n^{2} + 3 \, a^{3} b^{2} c^{3} d^{4} n^{2} - a^{4} b c^{2} d^{5} n^{2}\right)} x^{3 \, n} + {\left(2 \, a b^{4} c^{6} d n^{2} - 5 \, a^{2} b^{3} c^{5} d^{2} n^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} n^{2} + a^{4} b c^{3} d^{4} n^{2} - a^{5} c^{2} d^{5} n^{2}\right)} x^{2 \, n} + {\left(a b^{4} c^{7} n^{2} - a^{2} b^{3} c^{6} d n^{2} - 3 \, a^{3} b^{2} c^{5} d^{2} n^{2} + 5 \, a^{4} b c^{4} d^{3} n^{2} - 2 \, a^{5} c^{3} d^{4} n^{2}\right)} x^{n}\right)}}"," ",0,"((12*n^2 - 7*n + 1)*b^2*c^2*d^2 - 2*(4*n^2 - 5*n + 1)*a*b*c*d^3 + (2*n^2 - 3*n + 1)*a^2*d^4)*integrate(1/2/(b^4*c^7*n^2 - 4*a*b^3*c^6*d*n^2 + 6*a^2*b^2*c^5*d^2*n^2 - 4*a^3*b*c^4*d^3*n^2 + a^4*c^3*d^4*n^2 + (b^4*c^6*d*n^2 - 4*a*b^3*c^5*d^2*n^2 + 6*a^2*b^2*c^4*d^3*n^2 - 4*a^3*b*c^3*d^4*n^2 + a^4*c^2*d^5*n^2)*x^n), x) - (a*b^3*d*(4*n - 1) - b^4*c*(n - 1))*integrate(1/(a^2*b^4*c^4*n - 4*a^3*b^3*c^3*d*n + 6*a^4*b^2*c^2*d^2*n - 4*a^5*b*c*d^3*n + a^6*d^4*n + (a*b^5*c^4*n - 4*a^2*b^4*c^3*d*n + 6*a^3*b^3*c^2*d^2*n - 4*a^4*b^2*c*d^3*n + a^5*b*d^4*n)*x^n), x) + 1/2*((a*b^2*c*d^3*(6*n - 1) - a^2*b*d^4*(2*n - 1) + 2*b^3*c^2*d^2*n)*x*x^(2*n) + (a*b^2*c^2*d^2*(7*n - 1) - a^3*d^4*(2*n - 1) + 4*b^3*c^3*d*n + 3*a^2*b*c*d^3*n)*x*x^n + (a^2*b*c^2*d^2*(7*n - 1) - a^3*c*d^3*(3*n - 1) + 2*b^3*c^4*n)*x)/(a^2*b^3*c^7*n^2 - 3*a^3*b^2*c^6*d*n^2 + 3*a^4*b*c^5*d^2*n^2 - a^5*c^4*d^3*n^2 + (a*b^4*c^5*d^2*n^2 - 3*a^2*b^3*c^4*d^3*n^2 + 3*a^3*b^2*c^3*d^4*n^2 - a^4*b*c^2*d^5*n^2)*x^(3*n) + (2*a*b^4*c^6*d*n^2 - 5*a^2*b^3*c^5*d^2*n^2 + 3*a^3*b^2*c^4*d^3*n^2 + a^4*b*c^3*d^4*n^2 - a^5*c^2*d^5*n^2)*x^(2*n) + (a*b^4*c^7*n^2 - a^2*b^3*c^6*d*n^2 - 3*a^3*b^2*c^5*d^2*n^2 + 5*a^4*b*c^4*d^3*n^2 - 2*a^5*c^3*d^4*n^2)*x^n)","F",0
312,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^q,x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(d*x^n + c)^q, x)","F",0
313,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^3,x, algorithm=""maxima"")","\int {\left(d x^{n} + c\right)}^{3} {\left(b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^n + c)^3*(b*x^n + a)^p, x)","F",0
314,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^2,x, algorithm=""maxima"")","\int {\left(d x^{n} + c\right)}^{2} {\left(b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^n + c)^2*(b*x^n + a)^p, x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n),x, algorithm=""maxima"")","\int {\left(d x^{n} + c\right)} {\left(b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^n + c)*(b*x^n + a)^p, x)","F",0
316,0,0,0,0.000000," ","integrate((a+b*x^n)^p,x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^n + a)^p, x)","F",0
317,0,0,0,0.000000," ","integrate((a+b*x^n)^p/(c+d*x^n),x, algorithm=""maxima"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{d x^{n} + c}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(d*x^n + c), x)","F",0
318,0,0,0,0.000000," ","integrate((a+b*x^n)^p/(c+d*x^n)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{{\left(d x^{n} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(d*x^n + c)^2, x)","F",0
319,0,0,0,0.000000," ","integrate((a+b*x^n)^p/(c+d*x^n)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{{\left(d x^{n} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(d*x^n + c)^3, x)","F",0
320,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^(-1-1/n-p),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{-p - \frac{1}{n} - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(d*x^n + c)^(-p - 1/n - 1), x)","F",0
321,0,0,0,0.000000," ","integrate((a+b*x^n)^3*(c+d*x^n)^(-4-1/n),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{3} {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 4}\,{d x}"," ",0,"integrate((b*x^n + a)^3*(d*x^n + c)^(-1/n - 4), x)","F",0
322,0,0,0,0.000000," ","integrate((a+b*x^n)^2*(c+d*x^n)^(-3-1/n),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{2} {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 3}\,{d x}"," ",0,"integrate((b*x^n + a)^2*(d*x^n + c)^(-1/n - 3), x)","F",0
323,0,0,0,0.000000," ","integrate((a+b*x^n)*(c+d*x^n)^(-2-1/n),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 2}\,{d x}"," ",0,"integrate((b*x^n + a)*(d*x^n + c)^(-1/n - 2), x)","F",0
324,0,0,0,0.000000," ","integrate((c+d*x^n)^(-1-1/n),x, algorithm=""maxima"")","\int {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 1}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n - 1), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/((c+d*x^n)^(1/n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{\left(\frac{1}{n}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*(d*x^n + c)^(1/n)), x)","F",0
326,0,0,0,0.000000," ","integrate((c+d*x^n)^(1-1/n)/(a+b*x^n)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 1)/(b*x^n + a)^2, x)","F",0
327,0,0,0,0.000000," ","integrate((c+d*x^n)^(2-1/n)/(a+b*x^n)^3,x, algorithm=""maxima"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 2}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 2)/(b*x^n + a)^3, x)","F",0
328,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^(-2-1/n-p),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{-p - \frac{1}{n} - 2}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(d*x^n + c)^(-p - 1/n - 2), x)","F",0
329,0,0,0,0.000000," ","integrate((a+b*x^n)^((a*d*n-b*c*(1+n))/(-a*d+b*c)/n)*(c+d*x^n)^((a*d*n-b*c*n+a*d)/(-a*d*n+b*c*n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{b c {\left(n + 1\right)} - a d n}{{\left(b c - a d\right)} n}} {\left(d x^{n} + c\right)}^{\frac{b c n - a d n - a d}{b c n - a d n}}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^((b*c*(n + 1) - a*d*n)/((b*c - a*d)*n))*(d*x^n + c)^((b*c*n - a*d*n - a*d)/(b*c*n - a*d*n))), x)","F",0
330,0,0,0,0.000000," ","integrate((a+b*x^n)^2*(c+d*x^n)^(-4-1/n),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)}^{2} {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 4}\,{d x}"," ",0,"integrate((b*x^n + a)^2*(d*x^n + c)^(-1/n - 4), x)","F",0
331,0,0,0,0.000000," ","integrate((a+b*x^n)*(c+d*x^n)^(-3-1/n),x, algorithm=""maxima"")","\int {\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 3}\,{d x}"," ",0,"integrate((b*x^n + a)*(d*x^n + c)^(-1/n - 3), x)","F",0
332,0,0,0,0.000000," ","integrate((c+d*x^n)^(-2-1/n),x, algorithm=""maxima"")","\int {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 2}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n - 2), x)","F",0
333,0,0,0,0.000000," ","integrate((c+d*x^n)^(-1-1/n)/(a+b*x^n),x, algorithm=""maxima"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n - 1)/(b*x^n + a), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/((c+d*x^n)^(1/n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} {\left(d x^{n} + c\right)}^{\left(\frac{1}{n}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*(d*x^n + c)^(1/n)), x)","F",0
335,0,0,0,0.000000," ","integrate((c+d*x^n)^(1-1/n)/(a+b*x^n)^3,x, algorithm=""maxima"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 1}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 1)/(b*x^n + a)^3, x)","F",0
336,0,0,0,0.000000," ","integrate((c+d*x^n)^(2-1/n)/(a+b*x^n)^4,x, algorithm=""maxima"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 2}}{{\left(b x^{n} + a\right)}^{4}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 2)/(b*x^n + a)^4, x)","F",0
337,1,178,0,0.500131," ","integrate(x^5*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b x^{6}}{9 \, d^{2}} + \frac{2 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{2} x^{4}}{21 \, d^{4}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a x^{4}}{7 \, d^{2}} + \frac{8 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{4} x^{2}}{105 \, d^{6}} + \frac{4 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a c^{2} x^{2}}{35 \, d^{4}} + \frac{16 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{6}}{315 \, d^{8}} + \frac{8 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a c^{4}}{105 \, d^{6}}"," ",0,"1/9*(d^2*x^2 - c^2)^(3/2)*b*x^6/d^2 + 2/21*(d^2*x^2 - c^2)^(3/2)*b*c^2*x^4/d^4 + 1/7*(d^2*x^2 - c^2)^(3/2)*a*x^4/d^2 + 8/105*(d^2*x^2 - c^2)^(3/2)*b*c^4*x^2/d^6 + 4/35*(d^2*x^2 - c^2)^(3/2)*a*c^2*x^2/d^4 + 16/315*(d^2*x^2 - c^2)^(3/2)*b*c^6/d^8 + 8/105*(d^2*x^2 - c^2)^(3/2)*a*c^4/d^6","A",0
338,1,124,0,0.497710," ","integrate(x^3*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b x^{4}}{7 \, d^{2}} + \frac{4 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{2} x^{2}}{35 \, d^{4}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a x^{2}}{5 \, d^{2}} + \frac{8 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{4}}{105 \, d^{6}} + \frac{2 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a c^{2}}{15 \, d^{4}}"," ",0,"1/7*(d^2*x^2 - c^2)^(3/2)*b*x^4/d^2 + 4/35*(d^2*x^2 - c^2)^(3/2)*b*c^2*x^2/d^4 + 1/5*(d^2*x^2 - c^2)^(3/2)*a*x^2/d^2 + 8/105*(d^2*x^2 - c^2)^(3/2)*b*c^4/d^6 + 2/15*(d^2*x^2 - c^2)^(3/2)*a*c^2/d^4","A",0
339,1,70,0,0.619312," ","integrate(x*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b x^{2}}{5 \, d^{2}} + \frac{2 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{2}}{15 \, d^{4}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a}{3 \, d^{2}}"," ",0,"1/5*(d^2*x^2 - c^2)^(3/2)*b*x^2/d^2 + 2/15*(d^2*x^2 - c^2)^(3/2)*b*c^2/d^4 + 1/3*(d^2*x^2 - c^2)^(3/2)*a/d^2","A",0
340,1,52,0,1.299958," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x,x, algorithm=""maxima"")","a c \arcsin\left(\frac{c}{d {\left| x \right|}}\right) + \sqrt{d^{2} x^{2} - c^{2}} a + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b}{3 \, d^{2}}"," ",0,"a*c*arcsin(c/(d*abs(x))) + sqrt(d^2*x^2 - c^2)*a + 1/3*(d^2*x^2 - c^2)^(3/2)*b/d^2","A",0
341,1,98,0,1.462424," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^3,x, algorithm=""maxima"")","b c \arcsin\left(\frac{c}{d {\left| x \right|}}\right) - \frac{a d^{2} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{2 \, c} + \sqrt{d^{2} x^{2} - c^{2}} b - \frac{\sqrt{d^{2} x^{2} - c^{2}} a d^{2}}{2 \, c^{2}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a}{2 \, c^{2} x^{2}}"," ",0,"b*c*arcsin(c/(d*abs(x))) - 1/2*a*d^2*arcsin(c/(d*abs(x)))/c + sqrt(d^2*x^2 - c^2)*b - 1/2*sqrt(d^2*x^2 - c^2)*a*d^2/c^2 + 1/2*(d^2*x^2 - c^2)^(3/2)*a/(c^2*x^2)","A",0
342,1,162,0,1.352653," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{b d^{2} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{2 \, c} - \frac{a d^{4} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{8 \, c^{3}} - \frac{\sqrt{d^{2} x^{2} - c^{2}} b d^{2}}{2 \, c^{2}} - \frac{\sqrt{d^{2} x^{2} - c^{2}} a d^{4}}{8 \, c^{4}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b}{2 \, c^{2} x^{2}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a d^{2}}{8 \, c^{4} x^{2}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a}{4 \, c^{2} x^{4}}"," ",0,"-1/2*b*d^2*arcsin(c/(d*abs(x)))/c - 1/8*a*d^4*arcsin(c/(d*abs(x)))/c^3 - 1/2*sqrt(d^2*x^2 - c^2)*b*d^2/c^2 - 1/8*sqrt(d^2*x^2 - c^2)*a*d^4/c^4 + 1/2*(d^2*x^2 - c^2)^(3/2)*b/(c^2*x^2) + 1/8*(d^2*x^2 - c^2)^(3/2)*a*d^2/(c^4*x^2) + 1/4*(d^2*x^2 - c^2)^(3/2)*a/(c^2*x^4)","A",0
343,1,246,0,0.548437," ","integrate(x^4*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b x^{5}}{8 \, d^{2}} + \frac{5 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{2} x^{3}}{48 \, d^{4}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a x^{3}}{6 \, d^{2}} - \frac{5 \, b c^{8} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{128 \, d^{7}} - \frac{a c^{6} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{16 \, d^{5}} + \frac{5 \, \sqrt{d^{2} x^{2} - c^{2}} b c^{6} x}{128 \, d^{6}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a c^{4} x}{16 \, d^{4}} + \frac{5 \, {\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{4} x}{64 \, d^{6}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a c^{2} x}{8 \, d^{4}}"," ",0,"1/8*(d^2*x^2 - c^2)^(3/2)*b*x^5/d^2 + 5/48*(d^2*x^2 - c^2)^(3/2)*b*c^2*x^3/d^4 + 1/6*(d^2*x^2 - c^2)^(3/2)*a*x^3/d^2 - 5/128*b*c^8*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^7 - 1/16*a*c^6*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^5 + 5/128*sqrt(d^2*x^2 - c^2)*b*c^6*x/d^6 + 1/16*sqrt(d^2*x^2 - c^2)*a*c^4*x/d^4 + 5/64*(d^2*x^2 - c^2)^(3/2)*b*c^4*x/d^6 + 1/8*(d^2*x^2 - c^2)^(3/2)*a*c^2*x/d^4","A",0
344,1,192,0,0.666076," ","integrate(x^2*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b x^{3}}{6 \, d^{2}} - \frac{b c^{6} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{16 \, d^{5}} - \frac{a c^{4} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{8 \, d^{3}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} b c^{4} x}{16 \, d^{4}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a c^{2} x}{8 \, d^{2}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b c^{2} x}{8 \, d^{4}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a x}{4 \, d^{2}}"," ",0,"1/6*(d^2*x^2 - c^2)^(3/2)*b*x^3/d^2 - 1/16*b*c^6*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^5 - 1/8*a*c^4*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^3 + 1/16*sqrt(d^2*x^2 - c^2)*b*c^4*x/d^4 + 1/8*sqrt(d^2*x^2 - c^2)*a*c^2*x/d^2 + 1/8*(d^2*x^2 - c^2)^(3/2)*b*c^2*x/d^4 + 1/4*(d^2*x^2 - c^2)^(3/2)*a*x/d^2","A",0
345,1,137,0,0.542691," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{b c^{4} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{8 \, d^{3}} - \frac{a c^{2} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{2 \, d} + \frac{1}{2} \, \sqrt{d^{2} x^{2} - c^{2}} a x + \frac{\sqrt{d^{2} x^{2} - c^{2}} b c^{2} x}{8 \, d^{2}} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} b x}{4 \, d^{2}}"," ",0,"-1/8*b*c^4*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^3 - 1/2*a*c^2*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d + 1/2*sqrt(d^2*x^2 - c^2)*a*x + 1/8*sqrt(d^2*x^2 - c^2)*b*c^2*x/d^2 + 1/4*(d^2*x^2 - c^2)^(3/2)*b*x/d^2","A",0
346,1,105,0,1.499758," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^2,x, algorithm=""maxima"")","-\frac{b c^{2} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{2 \, d} + a d \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right) + \frac{1}{2} \, \sqrt{d^{2} x^{2} - c^{2}} b x - \frac{\sqrt{d^{2} x^{2} - c^{2}} a}{x}"," ",0,"-1/2*b*c^2*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d + a*d*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d) + 1/2*sqrt(d^2*x^2 - c^2)*b*x - sqrt(d^2*x^2 - c^2)*a/x","A",0
347,1,75,0,1.471922," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^4,x, algorithm=""maxima"")","b d \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right) - \frac{\sqrt{d^{2} x^{2} - c^{2}} b}{x} + \frac{{\left(d^{2} x^{2} - c^{2}\right)}^{\frac{3}{2}} a}{3 \, c^{2} x^{3}}"," ",0,"b*d*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d) - sqrt(d^2*x^2 - c^2)*b/x + 1/3*(d^2*x^2 - c^2)^(3/2)*a/(c^2*x^3)","A",0
348,1,153,0,0.554428," ","integrate(x^4*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c^{2} x^{2} - 1} b x^{5}}{6 \, c^{2}} + \frac{\sqrt{c^{2} x^{2} - 1} a x^{3}}{4 \, c^{2}} + \frac{5 \, \sqrt{c^{2} x^{2} - 1} b x^{3}}{24 \, c^{4}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} a x}{8 \, c^{4}} + \frac{3 \, a \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{8 \, c^{5}} + \frac{5 \, \sqrt{c^{2} x^{2} - 1} b x}{16 \, c^{6}} + \frac{5 \, b \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{16 \, c^{7}}"," ",0,"1/6*sqrt(c^2*x^2 - 1)*b*x^5/c^2 + 1/4*sqrt(c^2*x^2 - 1)*a*x^3/c^2 + 5/24*sqrt(c^2*x^2 - 1)*b*x^3/c^4 + 3/8*sqrt(c^2*x^2 - 1)*a*x/c^4 + 3/8*a*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5 + 5/16*sqrt(c^2*x^2 - 1)*b*x/c^6 + 5/16*b*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7","A",0
349,1,95,0,0.633086," ","integrate(x^3*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c^{2} x^{2} - 1} b x^{4}}{5 \, c^{2}} + \frac{\sqrt{c^{2} x^{2} - 1} a x^{2}}{3 \, c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} b x^{2}}{15 \, c^{4}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1} a}{3 \, c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} b}{15 \, c^{6}}"," ",0,"1/5*sqrt(c^2*x^2 - 1)*b*x^4/c^2 + 1/3*sqrt(c^2*x^2 - 1)*a*x^2/c^2 + 4/15*sqrt(c^2*x^2 - 1)*b*x^2/c^4 + 2/3*sqrt(c^2*x^2 - 1)*a/c^4 + 8/15*sqrt(c^2*x^2 - 1)*b/c^6","A",0
350,1,113,0,0.537487," ","integrate(x^2*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c^{2} x^{2} - 1} b x^{3}}{4 \, c^{2}} + \frac{\sqrt{c^{2} x^{2} - 1} a x}{2 \, c^{2}} + \frac{a \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{2 \, c^{3}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} b x}{8 \, c^{4}} + \frac{3 \, b \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{8 \, c^{5}}"," ",0,"1/4*sqrt(c^2*x^2 - 1)*b*x^3/c^2 + 1/2*sqrt(c^2*x^2 - 1)*a*x/c^2 + 1/2*a*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3 + 3/8*sqrt(c^2*x^2 - 1)*b*x/c^4 + 3/8*b*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5","A",0
351,1,54,0,0.469472," ","integrate(x*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c^{2} x^{2} - 1} b x^{2}}{3 \, c^{2}} + \frac{\sqrt{c^{2} x^{2} - 1} a}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1} b}{3 \, c^{4}}"," ",0,"1/3*sqrt(c^2*x^2 - 1)*b*x^2/c^2 + sqrt(c^2*x^2 - 1)*a/c^2 + 2/3*sqrt(c^2*x^2 - 1)*b/c^4","A",0
352,1,74,0,0.496748," ","integrate((b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\frac{a \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c} + \frac{\sqrt{c^{2} x^{2} - 1} b x}{2 \, c^{2}} + \frac{b \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{2 \, c^{3}}"," ",0,"a*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c + 1/2*sqrt(c^2*x^2 - 1)*b*x/c^2 + 1/2*b*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3","A",0
353,1,29,0,1.152275," ","integrate((b*x^2+a)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","-a \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\sqrt{c^{2} x^{2} - 1} b}{c^{2}}"," ",0,"-a*arcsin(1/(c*abs(x))) + sqrt(c^2*x^2 - 1)*b/c^2","A",0
354,1,44,0,1.176771," ","integrate((b*x^2+a)/x^2/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\frac{b \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c} + \frac{\sqrt{c^{2} x^{2} - 1} a}{x}"," ",0,"b*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c + sqrt(c^2*x^2 - 1)*a/x","A",0
355,1,45,0,1.225704," ","integrate((b*x^2+a)/x^3/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - b \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\sqrt{c^{2} x^{2} - 1} a}{2 \, x^{2}}"," ",0,"-1/2*a*c^2*arcsin(1/(c*abs(x))) - b*arcsin(1/(c*abs(x))) + 1/2*sqrt(c^2*x^2 - 1)*a/x^2","A",0
356,1,54,0,1.232527," ","integrate((b*x^2+a)/x^4/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{c^{2} x^{2} - 1} a c^{2}}{3 \, x} + \frac{\sqrt{c^{2} x^{2} - 1} b}{x} + \frac{\sqrt{c^{2} x^{2} - 1} a}{3 \, x^{3}}"," ",0,"2/3*sqrt(c^2*x^2 - 1)*a*c^2/x + sqrt(c^2*x^2 - 1)*b/x + 1/3*sqrt(c^2*x^2 - 1)*a/x^3","A",0
357,1,85,0,1.106825," ","integrate((b*x^2+a)/x^5/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","-\frac{3}{8} \, a c^{4} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{1}{2} \, b c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{3 \, \sqrt{c^{2} x^{2} - 1} a c^{2}}{8 \, x^{2}} + \frac{\sqrt{c^{2} x^{2} - 1} b}{2 \, x^{2}} + \frac{\sqrt{c^{2} x^{2} - 1} a}{4 \, x^{4}}"," ",0,"-3/8*a*c^4*arcsin(1/(c*abs(x))) - 1/2*b*c^2*arcsin(1/(c*abs(x))) + 3/8*sqrt(c^2*x^2 - 1)*a*c^2/x^2 + 1/2*sqrt(c^2*x^2 - 1)*b/x^2 + 1/4*sqrt(c^2*x^2 - 1)*a/x^4","A",0
358,1,196,0,0.568304," ","integrate(x^4*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d^{2} x^{2} - c^{2}} b x^{5}}{6 \, d^{2}} + \frac{5 \, \sqrt{d^{2} x^{2} - c^{2}} b c^{2} x^{3}}{24 \, d^{4}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a x^{3}}{4 \, d^{2}} + \frac{5 \, b c^{6} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{16 \, d^{7}} + \frac{3 \, a c^{4} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{8 \, d^{5}} + \frac{5 \, \sqrt{d^{2} x^{2} - c^{2}} b c^{4} x}{16 \, d^{6}} + \frac{3 \, \sqrt{d^{2} x^{2} - c^{2}} a c^{2} x}{8 \, d^{4}}"," ",0,"1/6*sqrt(d^2*x^2 - c^2)*b*x^5/d^2 + 5/24*sqrt(d^2*x^2 - c^2)*b*c^2*x^3/d^4 + 1/4*sqrt(d^2*x^2 - c^2)*a*x^3/d^2 + 5/16*b*c^6*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^7 + 3/8*a*c^4*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^5 + 5/16*sqrt(d^2*x^2 - c^2)*b*c^4*x/d^6 + 3/8*sqrt(d^2*x^2 - c^2)*a*c^2*x/d^4","A",0
359,1,124,0,0.551210," ","integrate(x^3*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d^{2} x^{2} - c^{2}} b x^{4}}{5 \, d^{2}} + \frac{4 \, \sqrt{d^{2} x^{2} - c^{2}} b c^{2} x^{2}}{15 \, d^{4}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a x^{2}}{3 \, d^{2}} + \frac{8 \, \sqrt{d^{2} x^{2} - c^{2}} b c^{4}}{15 \, d^{6}} + \frac{2 \, \sqrt{d^{2} x^{2} - c^{2}} a c^{2}}{3 \, d^{4}}"," ",0,"1/5*sqrt(d^2*x^2 - c^2)*b*x^4/d^2 + 4/15*sqrt(d^2*x^2 - c^2)*b*c^2*x^2/d^4 + 1/3*sqrt(d^2*x^2 - c^2)*a*x^2/d^2 + 8/15*sqrt(d^2*x^2 - c^2)*b*c^4/d^6 + 2/3*sqrt(d^2*x^2 - c^2)*a*c^2/d^4","A",0
360,1,142,0,0.638651," ","integrate(x^2*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d^{2} x^{2} - c^{2}} b x^{3}}{4 \, d^{2}} + \frac{3 \, b c^{4} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{8 \, d^{5}} + \frac{a c^{2} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{2 \, d^{3}} + \frac{3 \, \sqrt{d^{2} x^{2} - c^{2}} b c^{2} x}{8 \, d^{4}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a x}{2 \, d^{2}}"," ",0,"1/4*sqrt(d^2*x^2 - c^2)*b*x^3/d^2 + 3/8*b*c^4*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^5 + 1/2*a*c^2*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^3 + 3/8*sqrt(d^2*x^2 - c^2)*b*c^2*x/d^4 + 1/2*sqrt(d^2*x^2 - c^2)*a*x/d^2","A",0
361,1,69,0,0.644512," ","integrate(x*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d^{2} x^{2} - c^{2}} b x^{2}}{3 \, d^{2}} + \frac{2 \, \sqrt{d^{2} x^{2} - c^{2}} b c^{2}}{3 \, d^{4}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a}{d^{2}}"," ",0,"1/3*sqrt(d^2*x^2 - c^2)*b*x^2/d^2 + 2/3*sqrt(d^2*x^2 - c^2)*b*c^2/d^4 + sqrt(d^2*x^2 - c^2)*a/d^2","A",0
362,1,89,0,0.458984," ","integrate((b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{b c^{2} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{2 \, d^{3}} + \frac{a \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{d} + \frac{\sqrt{d^{2} x^{2} - c^{2}} b x}{2 \, d^{2}}"," ",0,"1/2*b*c^2*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^3 + a*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d + 1/2*sqrt(d^2*x^2 - c^2)*b*x/d^2","A",0
363,1,37,0,1.341980," ","integrate((b*x^2+a)/x/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{a \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{c} + \frac{\sqrt{d^{2} x^{2} - c^{2}} b}{d^{2}}"," ",0,"-a*arcsin(c/(d*abs(x)))/c + sqrt(d^2*x^2 - c^2)*b/d^2","A",0
364,1,55,0,1.256618," ","integrate((b*x^2+a)/x^2/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{b \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{d} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a}{c^{2} x}"," ",0,"b*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d + sqrt(d^2*x^2 - c^2)*a/(c^2*x)","A",0
365,1,60,0,1.292252," ","integrate((b*x^2+a)/x^3/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{b \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{c} - \frac{a d^{2} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{2 \, c^{3}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a}{2 \, c^{2} x^{2}}"," ",0,"-b*arcsin(c/(d*abs(x)))/c - 1/2*a*d^2*arcsin(c/(d*abs(x)))/c^3 + 1/2*sqrt(d^2*x^2 - c^2)*a/(c^2*x^2)","A",0
366,1,75,0,1.319074," ","integrate((b*x^2+a)/x^4/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d^{2} x^{2} - c^{2}} b}{c^{2} x} + \frac{2 \, \sqrt{d^{2} x^{2} - c^{2}} a d^{2}}{3 \, c^{4} x} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a}{3 \, c^{2} x^{3}}"," ",0,"sqrt(d^2*x^2 - c^2)*b/(c^2*x) + 2/3*sqrt(d^2*x^2 - c^2)*a*d^2/(c^4*x) + 1/3*sqrt(d^2*x^2 - c^2)*a/(c^2*x^3)","A",0
367,1,114,0,1.207655," ","integrate((b*x^2+a)/x^5/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{b d^{2} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{2 \, c^{3}} - \frac{3 \, a d^{4} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{8 \, c^{5}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} b}{2 \, c^{2} x^{2}} + \frac{3 \, \sqrt{d^{2} x^{2} - c^{2}} a d^{2}}{8 \, c^{4} x^{2}} + \frac{\sqrt{d^{2} x^{2} - c^{2}} a}{4 \, c^{2} x^{4}}"," ",0,"-1/2*b*d^2*arcsin(c/(d*abs(x)))/c^3 - 3/8*a*d^4*arcsin(c/(d*abs(x)))/c^5 + 1/2*sqrt(d^2*x^2 - c^2)*b/(c^2*x^2) + 3/8*sqrt(d^2*x^2 - c^2)*a*d^2/(c^4*x^2) + 1/4*sqrt(d^2*x^2 - c^2)*a/(c^2*x^4)","A",0
368,1,196,0,0.492474," ","integrate(x^4*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{b x^{5}}{4 \, \sqrt{d^{2} x^{2} - c^{2}} d^{2}} + \frac{5 \, b c^{2} x^{3}}{8 \, \sqrt{d^{2} x^{2} - c^{2}} d^{4}} + \frac{a x^{3}}{2 \, \sqrt{d^{2} x^{2} - c^{2}} d^{2}} - \frac{15 \, b c^{4} x}{8 \, \sqrt{d^{2} x^{2} - c^{2}} d^{6}} - \frac{3 \, a c^{2} x}{2 \, \sqrt{d^{2} x^{2} - c^{2}} d^{4}} + \frac{15 \, b c^{4} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{8 \, d^{7}} + \frac{3 \, a c^{2} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{2 \, d^{5}}"," ",0,"1/4*b*x^5/(sqrt(d^2*x^2 - c^2)*d^2) + 5/8*b*c^2*x^3/(sqrt(d^2*x^2 - c^2)*d^4) + 1/2*a*x^3/(sqrt(d^2*x^2 - c^2)*d^2) - 15/8*b*c^4*x/(sqrt(d^2*x^2 - c^2)*d^6) - 3/2*a*c^2*x/(sqrt(d^2*x^2 - c^2)*d^4) + 15/8*b*c^4*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^7 + 3/2*a*c^2*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^5","A",0
369,1,123,0,0.463932," ","integrate(x^3*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{b x^{4}}{3 \, \sqrt{d^{2} x^{2} - c^{2}} d^{2}} + \frac{4 \, b c^{2} x^{2}}{3 \, \sqrt{d^{2} x^{2} - c^{2}} d^{4}} + \frac{a x^{2}}{\sqrt{d^{2} x^{2} - c^{2}} d^{2}} - \frac{8 \, b c^{4}}{3 \, \sqrt{d^{2} x^{2} - c^{2}} d^{6}} - \frac{2 \, a c^{2}}{\sqrt{d^{2} x^{2} - c^{2}} d^{4}}"," ",0,"1/3*b*x^4/(sqrt(d^2*x^2 - c^2)*d^2) + 4/3*b*c^2*x^2/(sqrt(d^2*x^2 - c^2)*d^4) + a*x^2/(sqrt(d^2*x^2 - c^2)*d^2) - 8/3*b*c^4/(sqrt(d^2*x^2 - c^2)*d^6) - 2*a*c^2/(sqrt(d^2*x^2 - c^2)*d^4)","A",0
370,1,138,0,0.499660," ","integrate(x^2*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{b x^{3}}{2 \, \sqrt{d^{2} x^{2} - c^{2}} d^{2}} - \frac{3 \, b c^{2} x}{2 \, \sqrt{d^{2} x^{2} - c^{2}} d^{4}} - \frac{a x}{\sqrt{d^{2} x^{2} - c^{2}} d^{2}} + \frac{3 \, b c^{2} \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{2 \, d^{5}} + \frac{a \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{d^{3}}"," ",0,"1/2*b*x^3/(sqrt(d^2*x^2 - c^2)*d^2) - 3/2*b*c^2*x/(sqrt(d^2*x^2 - c^2)*d^4) - a*x/(sqrt(d^2*x^2 - c^2)*d^2) + 3/2*b*c^2*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^5 + a*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^3","A",0
371,1,69,0,0.576476," ","integrate(x*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{b x^{2}}{\sqrt{d^{2} x^{2} - c^{2}} d^{2}} - \frac{2 \, b c^{2}}{\sqrt{d^{2} x^{2} - c^{2}} d^{4}} - \frac{a}{\sqrt{d^{2} x^{2} - c^{2}} d^{2}}"," ",0,"b*x^2/(sqrt(d^2*x^2 - c^2)*d^2) - 2*b*c^2/(sqrt(d^2*x^2 - c^2)*d^4) - a/(sqrt(d^2*x^2 - c^2)*d^2)","A",0
372,1,76,0,0.547918," ","integrate((b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{a x}{\sqrt{d^{2} x^{2} - c^{2}} c^{2}} - \frac{b x}{\sqrt{d^{2} x^{2} - c^{2}} d^{2}} + \frac{b \log\left(2 \, d^{2} x + 2 \, \sqrt{d^{2} x^{2} - c^{2}} d\right)}{d^{3}}"," ",0,"-a*x/(sqrt(d^2*x^2 - c^2)*c^2) - b*x/(sqrt(d^2*x^2 - c^2)*d^2) + b*log(2*d^2*x + 2*sqrt(d^2*x^2 - c^2)*d)/d^3","A",0
373,1,58,0,1.462861," ","integrate((b*x^2+a)/x/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{a \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{c^{3}} - \frac{a}{\sqrt{d^{2} x^{2} - c^{2}} c^{2}} - \frac{b}{\sqrt{d^{2} x^{2} - c^{2}} d^{2}}"," ",0,"a*arcsin(c/(d*abs(x)))/c^3 - a/(sqrt(d^2*x^2 - c^2)*c^2) - b/(sqrt(d^2*x^2 - c^2)*d^2)","A",0
374,1,71,0,1.364974," ","integrate((b*x^2+a)/x^2/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{b x}{\sqrt{d^{2} x^{2} - c^{2}} c^{2}} - \frac{2 \, a d^{2} x}{\sqrt{d^{2} x^{2} - c^{2}} c^{4}} + \frac{a}{\sqrt{d^{2} x^{2} - c^{2}} c^{2} x}"," ",0,"-b*x/(sqrt(d^2*x^2 - c^2)*c^2) - 2*a*d^2*x/(sqrt(d^2*x^2 - c^2)*c^4) + a/(sqrt(d^2*x^2 - c^2)*c^2*x)","A",0
375,1,104,0,1.264890," ","integrate((b*x^2+a)/x^3/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{b \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{c^{3}} + \frac{3 \, a d^{2} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{2 \, c^{5}} - \frac{b}{\sqrt{d^{2} x^{2} - c^{2}} c^{2}} - \frac{3 \, a d^{2}}{2 \, \sqrt{d^{2} x^{2} - c^{2}} c^{4}} + \frac{a}{2 \, \sqrt{d^{2} x^{2} - c^{2}} c^{2} x^{2}}"," ",0,"b*arcsin(c/(d*abs(x)))/c^3 + 3/2*a*d^2*arcsin(c/(d*abs(x)))/c^5 - b/(sqrt(d^2*x^2 - c^2)*c^2) - 3/2*a*d^2/(sqrt(d^2*x^2 - c^2)*c^4) + 1/2*a/(sqrt(d^2*x^2 - c^2)*c^2*x^2)","A",0
376,1,125,0,1.341806," ","integrate((b*x^2+a)/x^4/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, b d^{2} x}{\sqrt{d^{2} x^{2} - c^{2}} c^{4}} - \frac{8 \, a d^{4} x}{3 \, \sqrt{d^{2} x^{2} - c^{2}} c^{6}} + \frac{b}{\sqrt{d^{2} x^{2} - c^{2}} c^{2} x} + \frac{4 \, a d^{2}}{3 \, \sqrt{d^{2} x^{2} - c^{2}} c^{4} x} + \frac{a}{3 \, \sqrt{d^{2} x^{2} - c^{2}} c^{2} x^{3}}"," ",0,"-2*b*d^2*x/(sqrt(d^2*x^2 - c^2)*c^4) - 8/3*a*d^4*x/(sqrt(d^2*x^2 - c^2)*c^6) + b/(sqrt(d^2*x^2 - c^2)*c^2*x) + 4/3*a*d^2/(sqrt(d^2*x^2 - c^2)*c^4*x) + 1/3*a/(sqrt(d^2*x^2 - c^2)*c^2*x^3)","A",0
377,1,162,0,1.480276," ","integrate((b*x^2+a)/x^5/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{3 \, b d^{2} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{2 \, c^{5}} + \frac{15 \, a d^{4} \arcsin\left(\frac{c}{d {\left| x \right|}}\right)}{8 \, c^{7}} - \frac{3 \, b d^{2}}{2 \, \sqrt{d^{2} x^{2} - c^{2}} c^{4}} - \frac{15 \, a d^{4}}{8 \, \sqrt{d^{2} x^{2} - c^{2}} c^{6}} + \frac{b}{2 \, \sqrt{d^{2} x^{2} - c^{2}} c^{2} x^{2}} + \frac{5 \, a d^{2}}{8 \, \sqrt{d^{2} x^{2} - c^{2}} c^{4} x^{2}} + \frac{a}{4 \, \sqrt{d^{2} x^{2} - c^{2}} c^{2} x^{4}}"," ",0,"3/2*b*d^2*arcsin(c/(d*abs(x)))/c^5 + 15/8*a*d^4*arcsin(c/(d*abs(x)))/c^7 - 3/2*b*d^2/(sqrt(d^2*x^2 - c^2)*c^4) - 15/8*a*d^4/(sqrt(d^2*x^2 - c^2)*c^6) + 1/2*b/(sqrt(d^2*x^2 - c^2)*c^2*x^2) + 5/8*a*d^2/(sqrt(d^2*x^2 - c^2)*c^4*x^2) + 1/4*a/(sqrt(d^2*x^2 - c^2)*c^2*x^4)","A",0
378,1,23,0,1.350818," ","integrate((c^2*x^2+1)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\sqrt{c^{2} x^{2} - 1} - \arcsin\left(\frac{1}{c {\left| x \right|}}\right)"," ",0,"sqrt(c^2*x^2 - 1) - arcsin(1/(c*abs(x)))","A",0
379,1,79,0,1.244274," ","integrate((d*x^2+c)/(x^((a^2*d+2*b^2*c)/(a^2*d+b^2*c)))/(b*x-a)^(1/2)/(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b^{2} c + a^{2} d\right)} \sqrt{b x + a} \sqrt{b x - a} x e^{\left(-\frac{2 \, b^{2} c \log\left(x\right)}{b^{2} c + a^{2} d} - \frac{a^{2} d \log\left(x\right)}{b^{2} c + a^{2} d}\right)}}{a^{2} b^{2}}"," ",0,"(b^2*c + a^2*d)*sqrt(b*x + a)*sqrt(b*x - a)*x*e^(-2*b^2*c*log(x)/(b^2*c + a^2*d) - a^2*d*log(x)/(b^2*c + a^2*d))/(a^2*b^2)","A",0
380,0,0,0,0.000000," ","integrate(1/(1+x)^(1/2)/(-1-x^(1/2))^(1/2)/(-1+x^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{x + 1} \sqrt{\sqrt{x} - 1} \sqrt{-\sqrt{x} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x + 1)*sqrt(sqrt(x) - 1)*sqrt(-sqrt(x) - 1)), x)","F",0
381,0,0,0,0.000000," ","integrate(1/(b^2*x+a^2)^(1/2)/(a-b*x^(1/2))^(1/2)/(a+b*x^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b^{2} x + a^{2}} \sqrt{b \sqrt{x} + a} \sqrt{-b \sqrt{x} + a}}\,{d x}"," ",0,"integrate(1/(sqrt(b^2*x + a^2)*sqrt(b*sqrt(x) + a)*sqrt(-b*sqrt(x) + a)), x)","F",0
382,0,0,0,0.000000," ","integrate((a-b*x^n)^p*(a+b*x^n)^p*(c+d*x^(2*n))^q,x, algorithm=""maxima"")","\int {\left(d x^{2 \, n} + c\right)}^{q} {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^(2*n) + c)^q*(b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
383,0,0,0,0.000000," ","integrate((a-b*x^n)^p*(a+b*x^n)^p*(a^2+b^2*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(b^{2} x^{2 \, n} + a^{2}\right)}^{p} {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + a^2)^p*(b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
384,0,0,0,0.000000," ","integrate((c+d*x^(2*n))^p/(a-b*x^n)/(a+b*x^n),x, algorithm=""maxima"")","-\int \frac{{\left(d x^{2 \, n} + c\right)}^{p}}{{\left(b x^{n} + a\right)} {\left(b x^{n} - a\right)}}\,{d x}"," ",0,"-integrate((d*x^(2*n) + c)^p/((b*x^n + a)*(b*x^n - a)), x)","F",0
385,0,0,0,0.000000," ","integrate((a-b*x^(1/2*n))^p*(a+b*x^(1/2*n))^p*(a^2*d*(1+p)/b^2/(1+(-n*p-2*n-1)/n)+d*x^n)^((-n*p-2*n-1)/n),x, algorithm=""maxima"")","\int \frac{{\left(b x^{\frac{1}{2} \, n} + a\right)}^{p} {\left(-b x^{\frac{1}{2} \, n} + a\right)}^{p}}{{\left(d x^{n} - \frac{a^{2} d {\left(p + 1\right)}}{b^{2} {\left(\frac{n p + 2 \, n + 1}{n} - 1\right)}}\right)}^{\frac{n p + 2 \, n + 1}{n}}}\,{d x}"," ",0,"integrate((b*x^(1/2*n) + a)^p*(-b*x^(1/2*n) + a)^p/(d*x^n - a^2*d*(p + 1)/(b^2*((n*p + 2*n + 1)/n - 1)))^((n*p + 2*n + 1)/n), x)","F",0
